%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU707^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n001.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 09:36:33 AM UTC 2026
% Result : Theorem 1.57s 1.28s
% Output : Refutation 1.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 15
% Syntax : Number of formulae : 109 ( 27 unt; 0 typ; 2 def)
% Number of atoms : 1276 ( 476 equ; 13 cnn)
% Maximal formula atoms : 10 ( 11 avg)
% Number of connectives : 1295 ( 232 ~; 204 |; 196 &; 601 @)
% ( 9 <=>; 53 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 26 usr; 22 con; 0-4 aty)
% Number of variables : 293 ( 77 ^; 166 !; 50 ?; 293 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
setunion: $i > $i ).
thf(func_def_2,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_3,type,
singleton: $i > $o ).
thf(func_def_7,type,
if: $i > $o > $i > $i > $i ).
thf(func_def_35,type,
ph15:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
sK16: $o > $i ).
thf(f345,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f121,f136,f344]) ).
thf(f344,plain,
~ spl14_4,
inference(avatar_contradiction_clause,[status(thm)],[f343]) ).
thf(f343,plain,
( $false
| ~ spl14_4 ),
inference(trivial_inequality_removal,[status(thm)],[f317]) ).
thf(f317,plain,
( ( $true = $false )
| ~ spl14_4 ),
inference(backward_demodulation,[status(thm)],[f56,f302]) ).
thf(f302,plain,
( ! [X0: $o] : ( $false = X0 )
| ~ spl14_4 ),
inference(subsumption_resolution,[status(thm)],[f261,f275]) ).
thf(f275,plain,
( ! [X0: $o] :
( ( sK16 @ X0 )
= sK7 )
| ~ spl14_4 ),
inference(duplicate_literal_removal,[status(thm)],[f274]) ).
thf(f274,plain,
( ! [X0: $o] :
( ( ( sK16 @ X0 )
= sK7 )
| ( ( sK16 @ X0 )
= sK7 ) )
| ~ spl14_4 ),
inference(equality_proxy_clausification,[status(thm)],[f271]) ).
thf(f271,plain,
( ! [X0: $o] :
( ( ( sK16 @ X0 )
= sK7 )
| ( ( sK7
= ( sK16 @ X0 ) )
= $true ) )
| ~ spl14_4 ),
inference(binary_proxy_clausification,[status(thm)],[f270]) ).
thf(f270,plain,
( ! [X0: $o] :
( ( $true
= ( ~ X0
& ( sK7
= ( sK16 @ X0 ) ) ) )
| ( ( sK16 @ X0 )
= sK7 ) )
| ~ spl14_4 ),
inference(equality_proxy_clausification,[status(thm)],[f269]) ).
thf(f269,plain,
( ! [X0: $o] :
( ( ( sK7
= ( sK16 @ X0 ) )
= $true )
| ( $true
= ( ~ X0
& ( sK7
= ( sK16 @ X0 ) ) ) ) )
| ~ spl14_4 ),
inference(duplicate_literal_removal,[status(thm)],[f268]) ).
thf(f268,plain,
( ! [X0: $o] :
( ( $true
= ( ~ X0
& ( sK7
= ( sK16 @ X0 ) ) ) )
| ( ( sK7
= ( sK16 @ X0 ) )
= $true )
| ( ( sK7
= ( sK16 @ X0 ) )
= $true ) )
| ~ spl14_4 ),
inference(binary_proxy_clausification,[status(thm)],[f266]) ).
thf(f266,plain,
( ! [X0: $o] :
( ( $true
= ( ( sK7
= ( sK16 @ X0 ) )
& X0 ) )
| ( $true
= ( ~ X0
& ( sK7
= ( sK16 @ X0 ) ) ) )
| ( ( sK7
= ( sK16 @ X0 ) )
= $true ) )
| ~ spl14_4 ),
inference(binary_proxy_clausification,[status(thm)],[f254]) ).
thf(f254,plain,
( ! [X0: $o] :
( ( $true
= ( ( ( sK7
= ( sK16 @ X0 ) )
& X0 )
| ( ~ X0
& ( sK7
= ( sK16 @ X0 ) ) ) ) )
| ( ( sK7
= ( sK16 @ X0 ) )
= $true ) )
| ~ spl14_4 ),
inference(binary_proxy_clausification,[status(thm)],[f253]) ).
thf(f253,plain,
( ! [X0: $o] :
( ( sK7
= ( sK16 @ X0 ) )
!= ( ( ( sK7
= ( sK16 @ X0 ) )
& X0 )
| ( ~ X0
& ( sK7
= ( sK16 @ X0 ) ) ) ) )
| ~ spl14_4 ),
inference(beta_eta_normalization,[status(thm)],[f252]) ).
thf(f252,plain,
( ! [X0: $o] :
( ( sK7
= ( sK16 @ X0 ) )
!= ( ^ [Y0: $i] :
( ( ( sK7 = Y0 )
& X0 )
| ( ~ X0
& ( sK7 = Y0 ) ) )
@ ( sK16 @ X0 ) ) )
| ~ spl14_4 ),
inference(negative_extensionality,[status(thm)],[f250]) ).
thf(f250,plain,
( ! [X0: $o] :
( ( ^ [Y0: $i] :
( ( ( sK7 = Y0 )
& X0 )
| ( ~ X0
& ( sK7 = Y0 ) ) ) )
!= ( (=) @ sK7 ) )
| ~ spl14_4 ),
inference(trivial_inequality_removal,[status(thm)],[f249]) ).
thf(f249,plain,
( ! [X0: $o] :
( ( $true != $true )
| ( ( ^ [Y0: $i] :
( ( ( sK7 = Y0 )
& X0 )
| ( ~ X0
& ( sK7 = Y0 ) ) ) )
!= ( (=) @ sK7 ) ) )
| ~ spl14_4 ),
inference(constrained_superposition,[status(thm)],[f151,f177]) ).
thf(f177,plain,
! [X0: $o] :
( $true
= ( singleton
@ ( dsetconstr @ sK8
@ ^ [Y0: $i] :
( ( ( sK7 = Y0 )
& X0 )
| ( ~ X0
& ( sK7 = Y0 ) ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f176]) ).
thf(f176,plain,
! [X0: $o] :
( ( $true
= ( singleton
@ ( dsetconstr @ sK8
@ ^ [Y0: $i] :
( ( ( sK7 = Y0 )
& X0 )
| ( ~ X0
& ( sK7 = Y0 ) ) ) ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f129,f56]) ).
thf(f129,plain,
! [X0: $i,X1: $o] :
( ( $true
!= ( in @ X0 @ sK8 ) )
| ( ( singleton
@ ( dsetconstr @ sK8
@ ^ [Y0: $i] :
( ( ( X0 = Y0 )
& X1 )
| ( ~ X1
& ( sK7 = Y0 ) ) ) ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f128]) ).
thf(f128,plain,
! [X0: $i,X1: $o] :
( ( $true != $true )
| ( ( singleton
@ ( dsetconstr @ sK8
@ ^ [Y0: $i] :
( ( ( X0 = Y0 )
& X1 )
| ( ~ X1
& ( sK7 = Y0 ) ) ) ) )
= $true )
| ( $true
!= ( in @ X0 @ sK8 ) ) ),
inference(superposition,[status(thm)],[f78,f56]) ).
thf(f78,plain,
! [X6: $i,X7: $i,X4: $o,X5: $i] :
( ( $true
!= ( in @ X7 @ X6 ) )
| ( ( singleton
@ ( dsetconstr @ X6
@ ^ [Y0: $i] :
( ( ( X5 = Y0 )
& X4 )
| ( ~ X4
& ( X7 = Y0 ) ) ) ) )
= $true )
| ( ( in @ X5 @ X6 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f76]) ).
thf(f76,plain,
! [X6: $i,X7: $i,X4: $o,X5: $i] :
( ( $true
!= ( in @ X7 @ X6 ) )
| ( ( in @ X5 @ X6 )
!= $true )
| ( ( singleton
@ ( dsetconstr @ X6
@ ^ [Y0: $i] :
( ( ( X5 = Y0 )
& X4 )
| ( ~ X4
& ( X7 = Y0 ) ) ) ) )
= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f58,f52]) ).
thf(f52,plain,
ifSingleton = $true,
inference(cnf_transformation,[status(thm)],[f36]) ).
thf(f36,plain,
( ( theeq = $true )
& ( ( in @ sK7 @ sK8 )
= $true )
& ( $true = sK6 )
& ( sK7
!= ( if @ sK8 @ sK6 @ sK7 @ sK9 ) )
& ( ( in @ sK9 @ sK8 )
= $true )
& ( ifSingleton = $true )
& ( iftrueProp1 = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9])],[f20,f35,f34]) ).
thf(f34,plain,
( ? [X0: $o,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
& ? [X3: $i] :
( ( $true = X0 )
& ( ( if @ X2 @ X0 @ X1 @ X3 )
!= X1 )
& ( ( in @ X3 @ X2 )
= $true ) ) )
=> ( ( ( in @ sK7 @ sK8 )
= $true )
& ? [X3: $i] :
( ( $true = sK6 )
& ( sK7
!= ( if @ sK8 @ sK6 @ sK7 @ X3 ) )
& ( $true
= ( in @ X3 @ sK8 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f35,plain,
( ? [X3: $i] :
( ( $true = sK6 )
& ( sK7
!= ( if @ sK8 @ sK6 @ sK7 @ X3 ) )
& ( $true
= ( in @ X3 @ sK8 ) ) )
=> ( ( $true = sK6 )
& ( sK7
!= ( if @ sK8 @ sK6 @ sK7 @ sK9 ) )
& ( ( in @ sK9 @ sK8 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f20,plain,
( ( theeq = $true )
& ? [X0: $o,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
& ? [X3: $i] :
( ( $true = X0 )
& ( ( if @ X2 @ X0 @ X1 @ X3 )
!= X1 )
& ( ( in @ X3 @ X2 )
= $true ) ) )
& ( ifSingleton = $true )
& ( iftrueProp1 = $true ) ),
inference(flattening,[status(thm)],[f19]) ).
thf(f19,plain,
( ? [X0: $o,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( ( if @ X2 @ X0 @ X1 @ X3 )
!= X1 )
& ( $true = X0 )
& ( ( in @ X3 @ X2 )
= $true ) )
& ( $true
= ( in @ X1 @ X2 ) ) )
& ( theeq = $true )
& ( ifSingleton = $true )
& ( iftrueProp1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
~ ( ( iftrueProp1 = $true )
=> ( ( ifSingleton = $true )
=> ( ( theeq = $true )
=> ! [X0: $o,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
=> ( ( $true = X0 )
=> ( ( if @ X2 @ X0 @ X1 @ X3 )
= X1 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
~ ( iftrueProp1
=> ( ifSingleton
=> ( theeq
=> ! [X0: $o,X1: $i,X2: $i] :
( ( in @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( X0
=> ( ( if @ X2 @ X0 @ X1 @ X3 )
= X1 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( iftrueProp1
=> ( ifSingleton
=> ( theeq
=> ! [X1: $o,X2: $i,X0: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( X1
=> ( ( if @ X0 @ X1 @ X2 @ X3 )
= X2 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( iftrueProp1
=> ( ifSingleton
=> ( theeq
=> ! [X1: $o,X2: $i,X0: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( X1
=> ( ( if @ X0 @ X1 @ X2 @ X3 )
= X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.jN8ZtNNWQF/DTF2THF_4433.p',iftrue) ).
thf(f58,plain,
! [X6: $i,X7: $i,X4: $o,X5: $i] :
( ( ( singleton
@ ( dsetconstr @ X6
@ ^ [Y0: $i] :
( ( ( X5 = Y0 )
& X4 )
| ( ~ X4
& ( X7 = Y0 ) ) ) ) )
= $true )
| ( $true
!= ( in @ X7 @ X6 ) )
| ( ( in @ X5 @ X6 )
!= $true )
| ( ifSingleton != $true ) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
thf(f41,plain,
( ( ( ifSingleton = $true )
| ( ( $true
!= ( singleton
@ ( dsetconstr @ sK12
@ ^ [Y0: $i] :
( ( ( sK11 = Y0 )
& sK10 )
| ( ~ sK10
& ( sK13 = Y0 ) ) ) ) ) )
& ( ( in @ sK13 @ sK12 )
= $true )
& ( $true
= ( in @ sK11 @ sK12 ) ) ) )
& ( ! [X4: $o,X5: $i,X6: $i] :
( ! [X7: $i] :
( ( ( singleton
@ ( dsetconstr @ X6
@ ^ [Y0: $i] :
( ( ( X5 = Y0 )
& X4 )
| ( ~ X4
& ( X7 = Y0 ) ) ) ) )
= $true )
| ( $true
!= ( in @ X7 @ X6 ) ) )
| ( ( in @ X5 @ X6 )
!= $true ) )
| ( ifSingleton != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13])],[f38,f40,f39]) ).
thf(f39,plain,
( ? [X0: $o,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( ( singleton
@ ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( ( X1 = Y0 )
& X0 )
| ( ~ X0
& ( X3 = Y0 ) ) ) ) )
!= $true )
& ( ( in @ X3 @ X2 )
= $true ) )
& ( $true
= ( in @ X1 @ X2 ) ) )
=> ( ? [X3: $i] :
( ( ( singleton
@ ( dsetconstr @ sK12
@ ^ [Y0: $i] :
( ( ( sK11 = Y0 )
& sK10 )
| ( ~ sK10
& ( X3 = Y0 ) ) ) ) )
!= $true )
& ( ( in @ X3 @ sK12 )
= $true ) )
& ( $true
= ( in @ sK11 @ sK12 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f40,plain,
( ? [X3: $i] :
( ( ( singleton
@ ( dsetconstr @ sK12
@ ^ [Y0: $i] :
( ( ( sK11 = Y0 )
& sK10 )
| ( ~ sK10
& ( X3 = Y0 ) ) ) ) )
!= $true )
& ( ( in @ X3 @ sK12 )
= $true ) )
=> ( ( $true
!= ( singleton
@ ( dsetconstr @ sK12
@ ^ [Y0: $i] :
( ( ( sK11 = Y0 )
& sK10 )
| ( ~ sK10
& ( sK13 = Y0 ) ) ) ) ) )
& ( ( in @ sK13 @ sK12 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f38,plain,
( ( ( ifSingleton = $true )
| ? [X0: $o,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( ( singleton
@ ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( ( X1 = Y0 )
& X0 )
| ( ~ X0
& ( X3 = Y0 ) ) ) ) )
!= $true )
& ( ( in @ X3 @ X2 )
= $true ) )
& ( $true
= ( in @ X1 @ X2 ) ) ) )
& ( ! [X4: $o,X5: $i,X6: $i] :
( ! [X7: $i] :
( ( ( singleton
@ ( dsetconstr @ X6
@ ^ [Y0: $i] :
( ( ( X5 = Y0 )
& X4 )
| ( ~ X4
& ( X7 = Y0 ) ) ) ) )
= $true )
| ( $true
!= ( in @ X7 @ X6 ) ) )
| ( ( in @ X5 @ X6 )
!= $true ) )
| ( ifSingleton != $true ) ) ),
inference(rectify,[status(thm)],[f37]) ).
thf(f37,plain,
( ( ( ifSingleton = $true )
| ? [X0: $o,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( ( singleton
@ ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( ( X1 = Y0 )
& X0 )
| ( ~ X0
& ( X3 = Y0 ) ) ) ) )
!= $true )
& ( ( in @ X3 @ X2 )
= $true ) )
& ( $true
= ( in @ X1 @ X2 ) ) ) )
& ( ! [X0: $o,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( ( singleton
@ ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( ( X1 = Y0 )
& X0 )
| ( ~ X0
& ( X3 = Y0 ) ) ) ) )
= $true )
| ( ( in @ X3 @ X2 )
!= $true ) )
| ( $true
!= ( in @ X1 @ X2 ) ) )
| ( ifSingleton != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ifSingleton = $true )
<=> ! [X0: $o,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( ( singleton
@ ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( ( X1 = Y0 )
& X0 )
| ( ~ X0
& ( X3 = Y0 ) ) ) ) )
= $true )
| ( ( in @ X3 @ X2 )
!= $true ) )
| ( $true
!= ( in @ X1 @ X2 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ifSingleton = $true )
<=> ! [X0: $o,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
=> ( ( singleton
@ ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( ( X1 = Y0 )
& X0 )
| ( ~ X0
& ( X3 = Y0 ) ) ) ) )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $o,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( singleton
@ ( dsetconstr @ X2
@ ^ [X4: $i] :
( ( ( X3 = X4 )
& ~ X0 )
| ( X0
& ( X1 = X4 ) ) ) ) ) ) )
= ifSingleton ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X1: $o,X2: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( singleton
@ ( dsetconstr @ X0
@ ^ [X4: $i] :
( ( ( X3 = X4 )
& ~ X1 )
| ( X1
& ( X2 = X4 ) ) ) ) ) ) )
= ifSingleton ),
file('/export/starexec/sandbox2/tmp/tmp.jN8ZtNNWQF/DTF2THF_4433.p',ifSingleton) ).
thf(f151,plain,
( ( $true
!= ( singleton @ ( dsetconstr @ sK8 @ ( (=) @ sK7 ) ) ) )
| ~ spl14_4 ),
inference(subsumption_resolution,[status(thm)],[f141,f84]) ).
thf(f84,plain,
( sK7
!= ( setunion @ ( dsetconstr @ sK8 @ ( (=) @ sK7 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f83]) ).
thf(f83,plain,
( sK7
!= ( setunion
@ ( dsetconstr @ sK8
@ ^ [Y0: $i] : ( sK7 = Y0 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f82]) ).
thf(f82,plain,
( sK7
!= ( setunion
@ ( dsetconstr @ sK8
@ ^ [Y0: $i] :
( $false
| ( sK7 = Y0 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f81]) ).
thf(f81,plain,
( sK7
!= ( setunion
@ ( dsetconstr @ sK8
@ ^ [Y0: $i] :
( ( ( sK9 = Y0 )
& $false )
| ( sK7 = Y0 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f80]) ).
thf(f80,plain,
( sK7
!= ( setunion
@ ( dsetconstr @ sK8
@ ^ [Y0: $i] :
( ( ( sK9 = Y0 )
& ~ $true )
| ( sK7 = Y0 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f79]) ).
thf(f79,plain,
( sK7
!= ( setunion
@ ( dsetconstr @ sK8
@ ^ [Y0: $i] :
( ( ( sK9 = Y0 )
& ~ $true )
| ( $true
& ( sK7 = Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f72]) ).
thf(f72,plain,
( sK7
!= ( ^ [Y0: $i,Y1: $o,Y2: $i,Y3: $i] :
( setunion
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y3 = Y4 )
& ~ Y1 )
| ( Y1
& ( Y2 = Y4 ) ) ) ) )
@ sK8
@ $true
@ sK7
@ sK9 ) ),
inference(definition_unfolding,[status(thm)],[f54,f62,f55]) ).
thf(f55,plain,
$true = sK6,
inference(cnf_transformation,[status(thm)],[f36]) ).
thf(f62,plain,
( if
= ( ^ [Y0: $i,Y1: $o,Y2: $i,Y3: $i] :
( setunion
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y3 = Y4 )
& ~ Y1 )
| ( Y1
& ( Y2 = Y4 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( if
= ( ^ [Y0: $i,Y1: $o,Y2: $i,Y3: $i] :
( setunion
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y3 = Y4 )
& ~ Y1 )
| ( Y1
& ( Y2 = Y4 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [X0: $i,X1: $o,X2: $i,X3: $i] :
( setunion
@ ( dsetconstr @ X0
@ ^ [X4: $i] :
( ( ( X2 = X4 )
& X1 )
| ( ~ X1
& ( X3 = X4 ) ) ) ) ) )
= if ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( ( ^ [X0: $i,X1: $o,X2: $i,X3: $i] :
( setunion
@ ( dsetconstr @ X0
@ ^ [X4: $i] :
( ( ( X2 = X4 )
& X1 )
| ( ~ X1
& ( X3 = X4 ) ) ) ) ) )
= if ),
file('/export/starexec/sandbox2/tmp/tmp.jN8ZtNNWQF/DTF2THF_4433.p',if) ).
thf(f54,plain,
( sK7
!= ( if @ sK8 @ sK6 @ sK7 @ sK9 ) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
thf(f141,plain,
( ( $true
!= ( singleton @ ( dsetconstr @ sK8 @ ( (=) @ sK7 ) ) ) )
| ( sK7
= ( setunion @ ( dsetconstr @ sK8 @ ( (=) @ sK7 ) ) ) )
| ~ spl14_4 ),
inference(trivial_inequality_removal,[status(thm)],[f139]) ).
thf(f139,plain,
( ( $true != $true )
| ( sK7
= ( setunion @ ( dsetconstr @ sK8 @ ( (=) @ sK7 ) ) ) )
| ( $true
!= ( singleton @ ( dsetconstr @ sK8 @ ( (=) @ sK7 ) ) ) )
| ~ spl14_4 ),
inference(superposition,[status(thm)],[f91,f117]) ).
thf(f117,plain,
( ( $true
= ( in @ sK7 @ ( dsetconstr @ sK8 @ ( (=) @ sK7 ) ) ) )
| ~ spl14_4 ),
inference(avatar_component_clause,[status(thm)],[f115]) ).
thf(f115,definition,
( spl14_4
<=> ( $true
= ( in @ sK7 @ ( dsetconstr @ sK8 @ ( (=) @ sK7 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl14_4])],[avatar_definition]) ).
thf(f91,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( ( setunion @ X0 )
= X1 )
| ( $true
!= ( singleton @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f68]) ).
thf(f68,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( ( setunion @ X0 )
= X1 )
| ( $true != $true )
| ( $true
!= ( singleton @ X0 ) ) ),
inference(definition_unfolding,[status(thm)],[f50,f57]) ).
thf(f57,plain,
theeq = $true,
inference(cnf_transformation,[status(thm)],[f36]) ).
thf(f50,plain,
! [X0: $i,X1: $i] :
( ( ( setunion @ X0 )
= X1 )
| ( ( in @ X1 @ X0 )
!= $true )
| ( $true
!= ( singleton @ X0 ) )
| ( theeq != $true ) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ! [X0: $i] :
( ! [X1: $i] :
( ( ( setunion @ X0 )
= X1 )
| ( ( in @ X1 @ X0 )
!= $true ) )
| ( $true
!= ( singleton @ X0 ) ) )
| ( theeq != $true ) )
& ( ( theeq = $true )
| ( ( ( setunion @ sK4 )
!= sK5 )
& ( ( in @ sK5 @ sK4 )
= $true )
& ( $true
= ( singleton @ sK4 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f30,f32,f31]) ).
thf(f31,plain,
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( setunion @ X2 )
!= X3 )
& ( ( in @ X3 @ X2 )
= $true ) )
& ( ( singleton @ X2 )
= $true ) )
=> ( ? [X3: $i] :
( ( ( setunion @ sK4 )
!= X3 )
& ( $true
= ( in @ X3 @ sK4 ) ) )
& ( $true
= ( singleton @ sK4 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f32,plain,
( ? [X3: $i] :
( ( ( setunion @ sK4 )
!= X3 )
& ( $true
= ( in @ X3 @ sK4 ) ) )
=> ( ( ( setunion @ sK4 )
!= sK5 )
& ( ( in @ sK5 @ sK4 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f30,plain,
( ( ! [X0: $i] :
( ! [X1: $i] :
( ( ( setunion @ X0 )
= X1 )
| ( ( in @ X1 @ X0 )
!= $true ) )
| ( $true
!= ( singleton @ X0 ) ) )
| ( theeq != $true ) )
& ( ( theeq = $true )
| ? [X2: $i] :
( ? [X3: $i] :
( ( ( setunion @ X2 )
!= X3 )
& ( ( in @ X3 @ X2 )
= $true ) )
& ( ( singleton @ X2 )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ! [X0: $i] :
( ! [X1: $i] :
( ( ( setunion @ X0 )
= X1 )
| ( ( in @ X1 @ X0 )
!= $true ) )
| ( $true
!= ( singleton @ X0 ) ) )
| ( theeq != $true ) )
& ( ( theeq = $true )
| ? [X0: $i] :
( ? [X1: $i] :
( ( ( setunion @ X0 )
!= X1 )
& ( ( in @ X1 @ X0 )
= $true ) )
& ( $true
= ( singleton @ X0 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ! [X0: $i] :
( ! [X1: $i] :
( ( ( setunion @ X0 )
= X1 )
| ( ( in @ X1 @ X0 )
!= $true ) )
| ( $true
!= ( singleton @ X0 ) ) )
<=> ( theeq = $true ) ),
inference(ennf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( theeq = $true )
<=> ! [X0: $i] :
( ( $true
= ( singleton @ X0 ) )
=> ! [X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( ( setunion @ X0 )
= X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: $i] :
( ( ( singleton @ X0 )
=> ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( ( setunion @ X0 )
= X1 ) ) )
= theeq ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X5: $i] :
( ( ( singleton @ X5 )
=> ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( ( setunion @ X5 )
= X2 ) ) )
= theeq ),
file('/export/starexec/sandbox2/tmp/tmp.jN8ZtNNWQF/DTF2THF_4433.p',theeq) ).
thf(f261,plain,
( ! [X0: $o] :
( ( $false = X0 )
| ( ( sK16 @ X0 )
!= sK7 ) )
| ~ spl14_4 ),
inference(duplicate_literal_removal,[status(thm)],[f260]) ).
thf(f260,plain,
( ! [X0: $o] :
( ( ( sK16 @ X0 )
!= sK7 )
| ( ( sK16 @ X0 )
!= sK7 )
| ( $false = X0 ) )
| ~ spl14_4 ),
inference(equality_proxy_clausification,[status(thm)],[f259]) ).
thf(f259,plain,
( ! [X0: $o] :
( ( ( sK16 @ X0 )
!= sK7 )
| ( ( sK7
= ( sK16 @ X0 ) )
= $false )
| ( $false = X0 ) )
| ~ spl14_4 ),
inference(binary_proxy_clausification,[status(thm)],[f258]) ).
thf(f258,plain,
( ! [X0: $o] :
( ( ( sK16 @ X0 )
!= sK7 )
| ( ( ( sK7
= ( sK16 @ X0 ) )
& X0 )
= $false ) )
| ~ spl14_4 ),
inference(binary_proxy_clausification,[status(thm)],[f256]) ).
thf(f256,plain,
( ! [X0: $o] :
( ( ( ( ( sK7
= ( sK16 @ X0 ) )
& X0 )
| ( ~ X0
& ( sK7
= ( sK16 @ X0 ) ) ) )
= $false )
| ( ( sK16 @ X0 )
!= sK7 ) )
| ~ spl14_4 ),
inference(equality_proxy_clausification,[status(thm)],[f255]) ).
thf(f255,plain,
( ! [X0: $o] :
( ( ( sK7
= ( sK16 @ X0 ) )
= $false )
| ( ( ( ( sK7
= ( sK16 @ X0 ) )
& X0 )
| ( ~ X0
& ( sK7
= ( sK16 @ X0 ) ) ) )
= $false ) )
| ~ spl14_4 ),
inference(binary_proxy_clausification,[status(thm)],[f253]) ).
thf(f56,plain,
( ( in @ sK7 @ sK8 )
= $true ),
inference(cnf_transformation,[status(thm)],[f36]) ).
thf(f136,plain,
~ spl14_5,
inference(avatar_contradiction_clause,[status(thm)],[f135]) ).
thf(f135,plain,
( $false
| ~ spl14_5 ),
inference(trivial_inequality_removal,[status(thm)],[f132]) ).
thf(f132,plain,
( ( $true != $true )
| ~ spl14_5 ),
inference(superposition,[status(thm)],[f120,f56]) ).
thf(f120,plain,
( ! [X0: $i] :
( $true
!= ( in @ X0 @ sK8 ) )
| ~ spl14_5 ),
inference(avatar_component_clause,[status(thm)],[f119]) ).
thf(f119,definition,
( spl14_5
<=> ! [X0: $i] :
( $true
!= ( in @ X0 @ sK8 ) ) ),
introduced(definition,[new_symbols(naming,[spl14_5])],[avatar_definition]) ).
thf(f121,plain,
( spl14_4
| spl14_5 ),
inference(avatar_split_clause,[status(thm)],[f113,f119,f115]) ).
thf(f113,plain,
! [X0: $i] :
( ( $true
= ( in @ sK7 @ ( dsetconstr @ sK8 @ ( (=) @ sK7 ) ) ) )
| ( $true
!= ( in @ X0 @ sK8 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f111]) ).
thf(f111,plain,
! [X0: $i] :
( ( $true != $true )
| ( $true
= ( in @ sK7 @ ( dsetconstr @ sK8 @ ( (=) @ sK7 ) ) ) )
| ( $true
!= ( in @ X0 @ sK8 ) ) ),
inference(superposition,[status(thm)],[f90,f56]) ).
thf(f90,plain,
! [X2: $i,X3: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
| ( ( in @ X0 @ ( dsetconstr @ X2 @ ( (=) @ X0 ) ) )
= $true )
| ( ( in @ X3 @ X2 )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f89]) ).
thf(f89,plain,
! [X2: $i,X3: $i,X0: $i] :
( ( $true
= ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 = Y0 ) ) ) )
| ( $true
!= ( in @ X0 @ X2 ) )
| ( ( in @ X3 @ X2 )
!= $true ) ),
inference(boolean_simplification,[status(thm)],[f88]) ).
thf(f88,plain,
! [X2: $i,X3: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
| ( $true
= ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] :
( $false
| ( X0 = Y0 ) ) ) ) )
| ( ( in @ X3 @ X2 )
!= $true ) ),
inference(boolean_simplification,[status(thm)],[f87]) ).
thf(f87,plain,
! [X2: $i,X3: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
| ( ( in @ X3 @ X2 )
!= $true )
| ( $true
= ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( $false
& ( X3 = Y0 ) )
| ( X0 = Y0 ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f86]) ).
thf(f86,plain,
! [X2: $i,X3: $i,X0: $i] :
( ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( ~ $true
& ( X3 = Y0 ) )
| ( X0 = Y0 ) ) ) )
= $true )
| ( ( in @ X3 @ X2 )
!= $true )
| ( $true
!= ( in @ X0 @ X2 ) ) ),
inference(boolean_simplification,[status(thm)],[f85]) ).
thf(f85,plain,
! [X2: $i,X3: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
| ( ( in @ X3 @ X2 )
!= $true )
| ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( ~ $true
& ( X3 = Y0 ) )
| ( ( X0 = Y0 )
& $true ) ) ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f77]) ).
thf(f77,plain,
! [X2: $i,X3: $i,X0: $i] :
( ( $true != $true )
| ( ( in @ X3 @ X2 )
!= $true )
| ( $true
!= ( in @ X0 @ X2 ) )
| ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( ~ $true
& ( X3 = Y0 ) )
| ( ( X0 = Y0 )
& $true ) ) ) )
= $true ) ),
inference(equality_resolution,[status(thm)],[f63]) ).
thf(f63,plain,
! [X2: $i,X3: $i,X0: $i,X1: $o] :
( ( $true != X1 )
| ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( ~ X1
& ( X3 = Y0 ) )
| ( ( X0 = Y0 )
& X1 ) ) ) )
= $true )
| ( ( in @ X3 @ X2 )
!= $true )
| ( $true
!= ( in @ X0 @ X2 ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f46,f51]) ).
thf(f51,plain,
iftrueProp1 = $true,
inference(cnf_transformation,[status(thm)],[f36]) ).
thf(f46,plain,
! [X2: $i,X3: $i,X0: $i,X1: $o] :
( ( $true != X1 )
| ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( ~ X1
& ( X3 = Y0 ) )
| ( ( X0 = Y0 )
& X1 ) ) ) )
= $true )
| ( ( in @ X3 @ X2 )
!= $true )
| ( $true
!= ( in @ X0 @ X2 ) )
| ( iftrueProp1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ! [X0: $i,X1: $o,X2: $i] :
( ! [X3: $i] :
( ( $true != X1 )
| ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( ~ X1
& ( X3 = Y0 ) )
| ( ( X0 = Y0 )
& X1 ) ) ) )
= $true )
| ( ( in @ X3 @ X2 )
!= $true ) )
| ( $true
!= ( in @ X0 @ X2 ) ) )
| ( iftrueProp1 != $true ) )
& ( ( iftrueProp1 = $true )
| ( ( sK1 = $true )
& ( ( in @ sK0
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] :
( ( ~ sK1
& ( sK3 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) ) ) )
!= $true )
& ( $true
= ( in @ sK3 @ sK2 ) )
& ( ( in @ sK0 @ sK2 )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f25,f27,f26]) ).
thf(f26,plain,
( ? [X4: $i,X5: $o,X6: $i] :
( ? [X7: $i] :
( ( $true = X5 )
& ( $true
!= ( in @ X4
@ ( dsetconstr @ X6
@ ^ [Y0: $i] :
( ( ~ X5
& ( X7 = Y0 ) )
| ( ( X4 = Y0 )
& X5 ) ) ) ) )
& ( $true
= ( in @ X7 @ X6 ) ) )
& ( ( in @ X4 @ X6 )
= $true ) )
=> ( ? [X7: $i] :
( ( sK1 = $true )
& ( $true
!= ( in @ sK0
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] :
( ( ~ sK1
& ( X7 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) ) ) ) )
& ( $true
= ( in @ X7 @ sK2 ) ) )
& ( ( in @ sK0 @ sK2 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f27,plain,
( ? [X7: $i] :
( ( sK1 = $true )
& ( $true
!= ( in @ sK0
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] :
( ( ~ sK1
& ( X7 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) ) ) ) )
& ( $true
= ( in @ X7 @ sK2 ) ) )
=> ( ( sK1 = $true )
& ( ( in @ sK0
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] :
( ( ~ sK1
& ( sK3 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) ) ) )
!= $true )
& ( $true
= ( in @ sK3 @ sK2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f25,plain,
( ( ! [X0: $i,X1: $o,X2: $i] :
( ! [X3: $i] :
( ( $true != X1 )
| ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( ~ X1
& ( X3 = Y0 ) )
| ( ( X0 = Y0 )
& X1 ) ) ) )
= $true )
| ( ( in @ X3 @ X2 )
!= $true ) )
| ( $true
!= ( in @ X0 @ X2 ) ) )
| ( iftrueProp1 != $true ) )
& ( ( iftrueProp1 = $true )
| ? [X4: $i,X5: $o,X6: $i] :
( ? [X7: $i] :
( ( $true = X5 )
& ( $true
!= ( in @ X4
@ ( dsetconstr @ X6
@ ^ [Y0: $i] :
( ( ~ X5
& ( X7 = Y0 ) )
| ( ( X4 = Y0 )
& X5 ) ) ) ) )
& ( $true
= ( in @ X7 @ X6 ) ) )
& ( ( in @ X4 @ X6 )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ! [X0: $i,X1: $o,X2: $i] :
( ! [X3: $i] :
( ( $true != X1 )
| ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( ~ X1
& ( X3 = Y0 ) )
| ( ( X0 = Y0 )
& X1 ) ) ) )
= $true )
| ( ( in @ X3 @ X2 )
!= $true ) )
| ( $true
!= ( in @ X0 @ X2 ) ) )
| ( iftrueProp1 != $true ) )
& ( ( iftrueProp1 = $true )
| ? [X0: $i,X1: $o,X2: $i] :
( ? [X3: $i] :
( ( $true = X1 )
& ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( ~ X1
& ( X3 = Y0 ) )
| ( ( X0 = Y0 )
& X1 ) ) ) )
!= $true )
& ( ( in @ X3 @ X2 )
= $true ) )
& ( $true
= ( in @ X0 @ X2 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( ! [X0: $i,X1: $o,X2: $i] :
( ! [X3: $i] :
( ( $true != X1 )
| ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( ~ X1
& ( X3 = Y0 ) )
| ( ( X0 = Y0 )
& X1 ) ) ) )
= $true )
| ( ( in @ X3 @ X2 )
!= $true ) )
| ( $true
!= ( in @ X0 @ X2 ) ) )
<=> ( iftrueProp1 = $true ) ),
inference(flattening,[status(thm)],[f21]) ).
thf(f21,plain,
( ! [X0: $i,X1: $o,X2: $i] :
( ! [X3: $i] :
( ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( ~ X1
& ( X3 = Y0 ) )
| ( ( X0 = Y0 )
& X1 ) ) ) )
= $true )
| ( $true != X1 )
| ( ( in @ X3 @ X2 )
!= $true ) )
| ( $true
!= ( in @ X0 @ X2 ) ) )
<=> ( iftrueProp1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ! [X0: $i,X1: $o,X2: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
=> ( ( $true = X1 )
=> ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] :
( ( ~ X1
& ( X3 = Y0 ) )
| ( ( X0 = Y0 )
& X1 ) ) ) )
= $true ) ) ) )
<=> ( iftrueProp1 = $true ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
( iftrueProp1
= ( ! [X0: $i,X1: $o,X2: $i] :
( ( in @ X0 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( X1
=> ( in @ X0
@ ( dsetconstr @ X2
@ ^ [X4: $i] :
( ( X1
& ( X0 = X4 ) )
| ( ( X3 = X4 )
& ~ X1 ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( iftrueProp1
= ( ! [X2: $i,X1: $o,X0: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( X1
=> ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X4: $i] :
( ( X1
& ( X2 = X4 ) )
| ( ( X3 = X4 )
& ~ X1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.jN8ZtNNWQF/DTF2THF_4433.p',iftrueProp1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU707^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.14/0.32 % Computer : n001.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue Feb 24 12:32:20 EST 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.44 ---- Original DTF file ---
% 0.18/0.44 thf(spec,logic,$$dhol).
% 0.18/0.44 %------------------------------------------------------------------------------
% 0.18/0.44 % File : SEU707^2 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.44 % Domain : Set Theory
% 0.18/0.44 % Problem : Conditionals
% 0.18/0.44 % Version : Especial > Reduced > Especial.
% 0.18/0.44 % English : (! A:i.! phi:o.! x:i.in x A -> (! y:i.in y A -> phi ->
% 0.18/0.44 % if A phi x y = x))
% 0.18/0.44
% 0.18/0.44 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.18/0.44 % Source : [Bro08]
% 0.18/0.44 % Names : ZFC209l [Bro08]
% 0.18/0.44
% 0.18/0.44 % Status : Theorem
% 0.18/0.44 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0, 0.29 v7.4.0, 0.11 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v6.1.0, 0.14 v6.0.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.3.0, 0.60 v5.2.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v3.7.0
% 0.18/0.44 % Syntax : Number of formulae : 13 ( 4 unt; 8 typ; 4 def)
% 0.18/0.44 % Number of atoms : 28 ( 12 equ; 0 cnn)
% 0.18/0.44 % Maximal formula atoms : 6 ( 5 avg)
% 0.18/0.44 % Number of connectives : 55 ( 3 ~; 3 |; 6 &; 30 @)
% 0.18/0.44 % ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% 0.18/0.44 % Maximal formula depth : 12 ( 3 avg)
% 0.18/0.44 % Number of types : 2 ( 0 usr)
% 0.18/0.44 % Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% 0.18/0.44 % Number of symbols : 9 ( 8 usr; 3 con; 0-4 aty)
% 0.18/0.44 % Number of variables : 21 ( 7 ^; 14 !; 0 ?; 21 :)
% 0.18/0.44 % SPC : TH0_THM_EQU_NAR
% 0.18/0.44
% 0.18/0.44 % Comments : http://mathgate.info/detsetitem.php?id=263
% 0.18/0.44 %------------------------------------------------------------------------------
% 0.18/0.44 thf(in_type,type,
% 0.18/0.44 in: $i > $i > $o ).
% 0.18/0.44
% 0.18/0.44 thf(setunion_type,type,
% 0.18/0.44 setunion: $i > $i ).
% 0.18/0.44
% 0.18/0.44 thf(dsetconstr_type,type,
% 0.18/0.44 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.18/0.44
% 0.18/0.44 thf(singleton_type,type,
% 0.18/0.44 singleton: $i > $o ).
% 0.18/0.44
% 0.18/0.44 thf(iftrueProp1_type,type,
% 0.18/0.44 iftrueProp1: $o ).
% 0.18/0.44
% 0.18/0.44 thf(iftrueProp1,definition,
% 0.18/0.44 ( iftrueProp1
% 0.18/0.44 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.18/0.44 ( ( in @ Xx @ A )
% 0.18/0.44 => ! [Xy: $i] :
% 0.18/0.44 ( ( in @ Xy @ A )
% 0.18/0.44 => ( Xphi
% 0.18/0.44 => ( in @ Xx
% 0.18/0.44 @ ( dsetconstr @ A
% 0.18/0.44 @ ^ [Xz: $i] :
% 0.18/0.44 ( ( Xphi
% 0.18/0.44 & ( Xz = Xx ) )
% 0.18/0.44 | ( ~ Xphi
% 0.18/0.44 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 thf(ifSingleton_type,type,
% 0.18/0.44 ifSingleton: $o ).
% 0.18/0.44
% 0.18/0.44 thf(ifSingleton,definition,
% 0.18/0.44 ( ifSingleton
% 0.18/0.44 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.18/0.44 ( ( in @ Xx @ A )
% 0.18/0.44 => ! [Xy: $i] :
% 0.18/0.44 ( ( in @ Xy @ A )
% 0.18/0.44 => ( singleton
% 0.18/0.44 @ ( dsetconstr @ A
% 0.18/0.44 @ ^ [Xz: $i] :
% 0.18/0.44 ( ( Xphi
% 0.18/0.44 & ( Xz = Xx ) )
% 0.18/0.44 | ( ~ Xphi
% 0.18/0.44 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 thf(if_type,type,
% 0.18/0.44 if: $i > $o > $i > $i > $i ).
% 0.18/0.44
% 0.18/0.44 thf(if,definition,
% 0.18/0.44 ( if
% 0.18/0.44 = ( ^ [A: $i,Xphi: $o,Xx: $i,Xy: $i] :
% 0.18/0.44 ( setunion
% 0.18/0.44 @ ( dsetconstr @ A
% 0.18/0.44 @ ^ [Xz: $i] :
% 0.18/0.44 ( ( Xphi
% 0.18/0.44 & ( Xz = Xx ) )
% 0.18/0.44 | ( ~ Xphi
% 0.18/0.44 & ( Xz = Xy ) ) ) ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 thf(theeq_type,type,
% 0.18/0.44 theeq: $o ).
% 0.18/0.44
% 0.18/0.44 thf(theeq,definition,
% 0.18/0.44 ( theeq
% 0.18/0.44 = ( ! [X: $i] :
% 0.18/0.44 ( ( singleton @ X )
% 0.18/0.44 => ! [Xx: $i] :
% 0.18/0.44 ( ( in @ Xx @ X )
% 0.18/0.44 => ( ( setunion @ X )
% 0.18/0.44 = Xx ) ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 thf(iftrue,conjecture,
% 0.18/0.44 ( iftrueProp1
% 0.18/0.44 => ( ifSingleton
% 0.18/0.44 => ( theeq
% 0.18/0.44 => ! [A: $i,Xphi: $o,Xx: $i] :
% 0.18/0.44 ( ( in @ Xx @ A )
% 0.18/0.44 => ! [Xy: $i] :
% 0.18/0.44 ( ( in @ Xy @ A )
% 0.18/0.44 => ( Xphi
% 0.18/0.44 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.18/0.44 = Xx ) ) ) ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 %------------------------------------------------------------------------------
% 0.18/0.44 ------------------------
% 1.41/1.18 ---- Embedded in THF ---
% 1.41/1.18 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.41/1.18 %%% Generated on Tue Feb 24 12:32:21 EST 2026
% 1.41/1.18 %%% using '$$dhol' embedding, version 1.3.0.
% 1.41/1.18 %%% Logic specification used:
% 1.41/1.18 %%% thf(spec, logic, $$dhol).
% 1.41/1.18
% 1.41/1.18 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.jN8ZtNNWQF/DTF2DTF4433.p
% See solution above
% 1.41/1.18 ------------------------
% 1.41/1.19 ---- Cleaned THF ---
% 1.41/1.19 thf(in_type,type,
% 1.41/1.19 in: $i > $i > $o ).
% 1.41/1.19
% 1.41/1.19 thf(setunion_type,type,
% 1.41/1.19 setunion: $i > $i ).
% 1.41/1.19
% 1.41/1.19 thf(dsetconstr_type,type,
% 1.41/1.19 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.41/1.19
% 1.41/1.19 thf(singleton_type,type,
% 1.41/1.19 singleton: $i > $o ).
% 1.41/1.19
% 1.41/1.19 thf(iftrueProp1_type,type,
% 1.41/1.19 iftrueProp1: $o ).
% 1.41/1.19
% 1.41/1.19 thf(iftrueProp1,definition,
% 1.41/1.19 ( iftrueProp1
% 1.41/1.19 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 1.41/1.19 ( ( in @ Xx @ A )
% 1.41/1.19 => ! [Xy: $i] :
% 1.41/1.19 ( ( in @ Xy @ A )
% 1.41/1.19 => ( Xphi
% 1.41/1.19 => ( in @ Xx
% 1.41/1.19 @ ( dsetconstr @ A
% 1.41/1.19 @ ^ [Xz: $i] :
% 1.41/1.19 ( ( Xphi
% 1.41/1.19 & ( Xz = Xx ) )
% 1.41/1.19 | ( ~ Xphi
% 1.41/1.19 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 1.41/1.19
% 1.41/1.19 thf(ifSingleton_type,type,
% 1.41/1.19 ifSingleton: $o ).
% 1.41/1.19
% 1.41/1.19 thf(ifSingleton,definition,
% 1.41/1.19 ( ifSingleton
% 1.41/1.19 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 1.41/1.19 ( ( in @ Xx @ A )
% 1.41/1.19 => ! [Xy: $i] :
% 1.41/1.19 ( ( in @ Xy @ A )
% 1.41/1.19 => ( singleton
% 1.41/1.19 @ ( dsetconstr @ A
% 1.41/1.19 @ ^ [Xz: $i] :
% 1.41/1.19 ( ( Xphi
% 1.41/1.19 & ( Xz = Xx ) )
% 1.41/1.19 | ( ~ Xphi
% 1.41/1.19 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 1.41/1.19
% 1.41/1.19 thf(if_type,type,
% 1.41/1.19 if: $i > $o > $i > $i > $i ).
% 1.41/1.19
% 1.41/1.19 thf(if,definition,
% 1.41/1.19 ( if
% 1.41/1.19 = ( ^ [A: $i,Xphi: $o,Xx: $i,Xy: $i] :
% 1.41/1.19 ( setunion
% 1.41/1.19 @ ( dsetconstr @ A
% 1.41/1.19 @ ^ [Xz: $i] :
% 1.41/1.19 ( ( Xphi
% 1.41/1.19 & ( Xz = Xx ) )
% 1.41/1.19 | ( ~ Xphi
% 1.41/1.19 & ( Xz = Xy ) ) ) ) ) ) ) ).
% 1.41/1.19
% 1.41/1.19 thf(theeq_type,type,
% 1.41/1.19 theeq: $o ).
% 1.41/1.19
% 1.41/1.19 thf(theeq,definition,
% 1.41/1.19 ( theeq
% 1.41/1.19 = ( ! [X: $i] :
% 1.41/1.19 ( ( singleton @ X )
% 1.41/1.19 => ! [Xx: $i] :
% 1.41/1.19 ( ( in @ Xx @ X )
% 1.41/1.19 => ( ( setunion @ X )
% 1.41/1.19 = Xx ) ) ) ) ) ).
% 1.41/1.19
% 1.41/1.19 thf(iftrue,conjecture,
% 1.41/1.19 ( iftrueProp1
% 1.41/1.19 => ( ifSingleton
% 1.41/1.19 => ( theeq
% 1.41/1.19 => ! [A: $i,Xphi: $o,Xx: $i] :
% 1.41/1.19 ( ( in @ Xx @ A )
% 1.41/1.19 => ! [Xy: $i] :
% 1.41/1.19 ( ( in @ Xy @ A )
% 1.41/1.19 => ( Xphi
% 1.41/1.19 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 1.41/1.19 = Xx ) ) ) ) ) ) ) ).
% 1.41/1.19 ------------------------
% 1.57/1.21 % (4656)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_4433 for (2999ds/18Mi)
% 1.57/1.21 % (4656)Instruction limit reached!
% 1.57/1.21 % (4656)------------------------------
% 1.57/1.21 % (4656)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.21 % (4656)Termination reason: Unknown
% 1.57/1.21 % (4656)Termination phase: Saturation
% 1.57/1.21
% 1.57/1.21 % (4656)Memory used [KB]: 5628
% 1.57/1.21 % (4656)Time elapsed: 0.007 s
% 1.57/1.21 % (4656)Instructions burned: 18 (million)
% 1.57/1.21 % (4656)------------------------------
% 1.57/1.21 % (4656)------------------------------
% 1.57/1.21 % (4650)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_4433 for (2999ds/183Mi)
% 1.57/1.21 % (4651)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_4433 for (2999ds/4Mi)
% 1.57/1.21 % (4652)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_4433 for (2999ds/27Mi)
% 1.57/1.21 % (4653)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_4433 for (2999ds/2Mi)
% 1.57/1.21 % (4654)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_4433 for (2999ds/2Mi)
% 1.57/1.21 % (4655)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_4433 for (2999ds/275Mi)
% 1.57/1.21 % (4653)Instruction limit reached!
% 1.57/1.21 % (4653)------------------------------
% 1.57/1.21 % (4653)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.21 % (4653)Termination reason: Unknown
% 1.57/1.21 % (4653)Termination phase: shuffling
% 1.57/1.21
% 1.57/1.21 % (4653)Memory used [KB]: 1023
% 1.57/1.21 % (4653)Time elapsed: 0.003 s
% 1.57/1.21 % (4653)Instructions burned: 2 (million)
% 1.57/1.21 % (4653)------------------------------
% 1.57/1.21 % (4653)------------------------------
% 1.57/1.21 % (4654)Instruction limit reached!
% 1.57/1.21 % (4654)------------------------------
% 1.57/1.21 % (4654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.21 % (4654)Termination reason: Unknown
% 1.57/1.21 % (4654)Termination phase: shuffling
% 1.57/1.21
% 1.57/1.21 % (4654)Memory used [KB]: 1023
% 1.57/1.21 % (4654)Time elapsed: 0.003 s
% 1.57/1.21 % (4654)Instructions burned: 2 (million)
% 1.57/1.21 % (4654)------------------------------
% 1.57/1.21 % (4654)------------------------------
% 1.57/1.22 % (4651)Instruction limit reached!
% 1.57/1.22 % (4651)------------------------------
% 1.57/1.22 % (4651)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.22 % (4651)Termination reason: Unknown
% 1.57/1.22 % (4651)Termination phase: Saturation
% 1.57/1.22
% 1.57/1.22 % (4651)Memory used [KB]: 5500
% 1.57/1.22 % (4651)Time elapsed: 0.005 s
% 1.57/1.22 % (4651)Instructions burned: 5 (million)
% 1.57/1.22 % (4651)------------------------------
% 1.57/1.22 % (4651)------------------------------
% 1.57/1.22 % (4655)Refutation not found, incomplete strategy
% 1.57/1.22 % (4655)------------------------------
% 1.57/1.22 % (4655)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.22 % (4655)Termination reason: Refutation not found, incomplete strategy
% 1.57/1.22
% 1.57/1.22
% 1.57/1.22 % (4655)Memory used [KB]: 5500
% 1.57/1.22 % (4655)Time elapsed: 0.007 s
% 1.57/1.22 % (4655)Instructions burned: 7 (million)
% 1.57/1.22 % (4655)------------------------------
% 1.57/1.22 % (4655)------------------------------
% 1.57/1.22 % (4657)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_4433 for (2999ds/3Mi)
% 1.57/1.22 % (4657)Instruction limit reached!
% 1.57/1.22 % (4657)------------------------------
% 1.57/1.22 % (4657)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.22 % (4657)Termination reason: Unknown
% 1.57/1.22 % (4657)Termination phase: Property scanning
% 1.57/1.22
% 1.57/1.22 % (4657)Memory used [KB]: 1023
% 1.57/1.22 % (4657)Time elapsed: 0.002 s
% 1.57/1.22 % (4657)Instructions burned: 4 (million)
% 1.57/1.22 % (4657)------------------------------
% 1.57/1.22 % (4657)------------------------------
% 1.57/1.22 % (4652)Refutation not found, incomplete strategy
% 1.57/1.22 % (4652)------------------------------
% 1.57/1.22 % (4652)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.22 % (4652)Termination reason: Refutation not found, incomplete strategy
% 1.57/1.22
% 1.57/1.22
% 1.57/1.22 % (4652)Memory used [KB]: 5628
% 1.57/1.22 % (4652)Time elapsed: 0.010 s
% 1.57/1.22 % (4652)Instructions burned: 13 (million)
% 1.57/1.22 % (4652)------------------------------
% 1.57/1.22 % (4652)------------------------------
% 1.57/1.23 % (4662)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_4433 for (2999ds/7Mi)
% 1.57/1.23 % (4658)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_4433 for (2999ds/37Mi)
% 1.57/1.23 % (4659)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_4433 for (2999ds/15Mi)
% 1.57/1.23 % (4662)Instruction limit reached!
% 1.57/1.23 % (4662)------------------------------
% 1.57/1.23 % (4662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.23 % (4662)Termination reason: Unknown
% 1.57/1.23 % (4662)Termination phase: Saturation
% 1.57/1.23
% 1.57/1.23 % (4662)Memory used [KB]: 1023
% 1.57/1.23 % (4662)Time elapsed: 0.003 s
% 1.57/1.23 % (4662)Instructions burned: 7 (million)
% 1.57/1.23 % (4662)------------------------------
% 1.57/1.23 % (4662)------------------------------
% 1.57/1.23 % (4660)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_4433 for (2999ds/3Mi)
% 1.57/1.24 % (4660)Instruction limit reached!
% 1.57/1.24 % (4660)------------------------------
% 1.57/1.24 % (4660)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.24 % (4660)Termination reason: Unknown
% 1.57/1.24 % (4660)Termination phase: Saturation
% 1.57/1.24
% 1.57/1.24 % (4660)Memory used [KB]: 1023
% 1.57/1.24 % (4660)Time elapsed: 0.004 s
% 1.57/1.24 % (4660)Instructions burned: 4 (million)
% 1.57/1.24 % (4660)------------------------------
% 1.57/1.24 % (4660)------------------------------
% 1.57/1.24 % (4661)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_4433 for (2999ds/1041Mi)
% 1.57/1.24 % (4663)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_4433 for (2999ds/16Mi)
% 1.57/1.24 % (4659)Instruction limit reached!
% 1.57/1.24 % (4659)------------------------------
% 1.57/1.24 % (4659)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.24 % (4659)Termination reason: Unknown
% 1.57/1.24 % (4659)Termination phase: Saturation
% 1.57/1.24
% 1.57/1.24 % (4659)Memory used [KB]: 5628
% 1.57/1.24 % (4659)Time elapsed: 0.012 s
% 1.57/1.24 % (4659)Instructions burned: 16 (million)
% 1.57/1.24 % (4659)------------------------------
% 1.57/1.24 % (4659)------------------------------
% 1.57/1.24 % (4664)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_4433 for (2999ds/3Mi)
% 1.57/1.24 % (4664)Instruction limit reached!
% 1.57/1.24 % (4664)------------------------------
% 1.57/1.24 % (4664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.24 % (4664)Termination reason: Unknown
% 1.57/1.24 % (4664)Termination phase: Twee Goal Transformation
% 1.57/1.24
% 1.57/1.24 % (4664)Memory used [KB]: 1023
% 1.57/1.24 % (4664)Time elapsed: 0.002 s
% 1.57/1.24 % (4664)Instructions burned: 4 (million)
% 1.57/1.24 % (4664)------------------------------
% 1.57/1.24 % (4664)------------------------------
% 1.57/1.25 % (4663)Instruction limit reached!
% 1.57/1.25 % (4663)------------------------------
% 1.57/1.25 % (4663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.25 % (4663)Termination reason: Unknown
% 1.57/1.25 % (4663)Termination phase: Saturation
% 1.57/1.25
% 1.57/1.25 % (4663)Memory used [KB]: 5884
% 1.57/1.25 % (4663)Time elapsed: 0.013 s
% 1.57/1.25 % (4663)Instructions burned: 17 (million)
% 1.57/1.25 % (4663)------------------------------
% 1.57/1.25 % (4663)------------------------------
% 1.57/1.25 % (4658)Instruction limit reached!
% 1.57/1.25 % (4658)------------------------------
% 1.57/1.25 % (4658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.25 % (4658)Termination reason: Unknown
% 1.57/1.25 % (4658)Termination phase: Saturation
% 1.57/1.25
% 1.57/1.25 % (4658)Memory used [KB]: 5756
% 1.57/1.25 % (4658)Time elapsed: 0.022 s
% 1.57/1.25 % (4658)Instructions burned: 38 (million)
% 1.57/1.25 % (4658)------------------------------
% 1.57/1.25 % (4658)------------------------------
% 1.57/1.25 % (4667)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_4433 for (2999ds/3Mi)
% 1.57/1.25 % (4665)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_4433 for (2999ds/3Mi)
% 1.57/1.25 % (4667)Instruction limit reached!
% 1.57/1.25 % (4667)------------------------------
% 1.57/1.25 % (4667)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.25 % (4667)Termination reason: Unknown
% 1.57/1.25 % (4667)Termination phase: Property scanning
% 1.57/1.25
% 1.57/1.25 % (4667)Memory used [KB]: 1023
% 1.57/1.25 % (4667)Time elapsed: 0.002 s
% 1.57/1.25 % (4667)Instructions burned: 4 (million)
% 1.57/1.25 % (4667)------------------------------
% 1.57/1.25 % (4667)------------------------------
% 1.57/1.25 % (4665)Instruction limit reached!
% 1.57/1.25 % (4665)------------------------------
% 1.57/1.25 % (4665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.25 % (4665)Termination reason: Unknown
% 1.57/1.25 % (4665)Termination phase: Property scanning
% 1.57/1.25
% 1.57/1.25 % (4665)Memory used [KB]: 1023
% 1.57/1.25 % (4665)Time elapsed: 0.004 s
% 1.57/1.25 % (4665)Instructions burned: 4 (million)
% 1.57/1.25 % (4665)------------------------------
% 1.57/1.25 % (4665)------------------------------
% 1.57/1.26 % (4666)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_4433 for (2999ds/7Mi)
% 1.57/1.26 % (4666)Refutation not found, incomplete strategy
% 1.57/1.26 % (4666)------------------------------
% 1.57/1.26 % (4666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.26 % (4666)Termination reason: Refutation not found, incomplete strategy
% 1.57/1.26
% 1.57/1.26
% 1.57/1.26 % (4666)Memory used [KB]: 5500
% 1.57/1.26 % (4666)Time elapsed: 0.004 s
% 1.57/1.26 % (4666)Instructions burned: 5 (million)
% 1.57/1.26 % (4666)------------------------------
% 1.57/1.26 % (4666)------------------------------
% 1.57/1.26 % (4670)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_4433 for (2999ds/710Mi)
% 1.57/1.27 % (4669)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_4433 for (2999ds/18Mi)
% 1.57/1.27 % (4668)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_4433 for (2999ds/4Mi)
% 1.57/1.27 % (4668)Instruction limit reached!
% 1.57/1.27 % (4668)------------------------------
% 1.57/1.27 % (4668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.27 % (4668)Termination reason: Unknown
% 1.57/1.27 % (4668)Termination phase: Property scanning
% 1.57/1.27
% 1.57/1.27 % (4668)Memory used [KB]: 1023
% 1.57/1.27 % (4668)Time elapsed: 0.004 s
% 1.57/1.27 % (4668)Instructions burned: 4 (million)
% 1.57/1.27 % (4668)------------------------------
% 1.57/1.27 % (4668)------------------------------
% 1.57/1.27 % (4672)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_4433 for (2999ds/902Mi)
% 1.57/1.27 % (4672)Refutation not found, incomplete strategy
% 1.57/1.27 % (4672)------------------------------
% 1.57/1.27 % (4672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.27 % (4672)Termination reason: Refutation not found, incomplete strategy
% 1.57/1.27
% 1.57/1.27
% 1.57/1.27 % (4672)Memory used [KB]: 5500
% 1.57/1.27 % (4672)Time elapsed: 0.004 s
% 1.57/1.27 % (4672)Instructions burned: 6 (million)
% 1.57/1.27 % (4672)------------------------------
% 1.57/1.27 % (4672)------------------------------
% 1.57/1.27 % (4669)Instruction limit reached!
% 1.57/1.27 % (4669)------------------------------
% 1.57/1.27 % (4669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.27 % (4669)Termination reason: Unknown
% 1.57/1.27 % (4669)Termination phase: Saturation
% 1.57/1.27
% 1.57/1.27 % (4669)Memory used [KB]: 5628
% 1.57/1.27 % (4669)Time elapsed: 0.008 s
% 1.57/1.27 % (4669)Instructions burned: 20 (million)
% 1.57/1.27 % (4669)------------------------------
% 1.57/1.27 % (4669)------------------------------
% 1.57/1.27 % (4671)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_4433 for (2999ds/6Mi)
% 1.57/1.27 % (4670)First to succeed.
% 1.57/1.28 % (4671)Instruction limit reached!
% 1.57/1.28 % (4671)------------------------------
% 1.57/1.28 % (4671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.28 % (4671)Termination reason: Unknown
% 1.57/1.28 % (4671)Termination phase: Saturation
% 1.57/1.28
% 1.57/1.28 % (4671)Memory used [KB]: 5500
% 1.57/1.28 % (4671)Time elapsed: 0.005 s
% 1.57/1.28 % (4671)Instructions burned: 6 (million)
% 1.57/1.28 % (4671)------------------------------
% 1.57/1.28 % (4671)------------------------------
% 1.57/1.28 % (4670)Refutation found. Thanks to Tanya!
% 1.57/1.28 % SZS status Theorem for DTF2THF_4433
% 1.57/1.28 % SZS output start Proof for DTF2THF_4433
% 1.57/1.28 thf(func_def_0, type, in: $i > $i > $o).
% 1.57/1.28 thf(func_def_1, type, setunion: $i > $i).
% 1.57/1.28 thf(func_def_2, type, dsetconstr: $i > ($i > $o) > $i).
% 1.57/1.28 thf(func_def_3, type, singleton: $i > $o).
% 1.57/1.28 thf(func_def_7, type, if: $i > $o > $i > $i > $i).
% 1.57/1.28 thf(func_def_35, type, ph15: !>[X0: $tType]:(X0)).
% 1.57/1.28 thf(func_def_36, type, sK16: $o > $i).
% 1.57/1.28 thf(f345,plain,(
% 1.57/1.28 $false),
% 1.57/1.28 inference(avatar_sat_refutation,[status(thm)],[f121,f136,f344])).
% 1.57/1.28 thf(f344,plain,(
% 1.57/1.28 ~spl14_4),
% 1.57/1.28 inference(avatar_contradiction_clause,[status(thm)],[f343])).
% 1.57/1.28 thf(f343,plain,(
% 1.57/1.28 $false | ~spl14_4),
% 1.57/1.28 inference(trivial_inequality_removal,[status(thm)],[f317])).
% 1.57/1.28 thf(f317,plain,(
% 1.57/1.28 ($true = $false) | ~spl14_4),
% 1.57/1.28 inference(backward_demodulation,[status(thm)],[f56,f302])).
% 1.57/1.28 thf(f302,plain,(
% 1.57/1.28 ( ! [X0 : $o] : (($false = X0)) ) | ~spl14_4),
% 1.57/1.28 inference(subsumption_resolution,[status(thm)],[f261,f275])).
% 1.57/1.28 thf(f275,plain,(
% 1.57/1.28 ( ! [X0 : $o] : (((sK16 @ X0) = sK7)) ) | ~spl14_4),
% 1.57/1.28 inference(duplicate_literal_removal,[status(thm)],[f274])).
% 1.57/1.28 thf(f274,plain,(
% 1.57/1.28 ( ! [X0 : $o] : (((sK16 @ X0) = sK7) | ((sK16 @ X0) = sK7)) ) | ~spl14_4),
% 1.57/1.28 inference(equality_proxy_clausification,[status(thm)],[f271])).
% 1.57/1.28 thf(f271,plain,(
% 1.57/1.28 ( ! [X0 : $o] : (((sK16 @ X0) = sK7) | ((sK7 = (sK16 @ X0)) = $true)) ) | ~spl14_4),
% 1.57/1.28 inference(binary_proxy_clausification,[status(thm)],[f270])).
% 1.57/1.28 thf(f270,plain,(
% 1.57/1.28 ( ! [X0 : $o] : (($true = ((~ X0) & (sK7 = (sK16 @ X0)))) | ((sK16 @ X0) = sK7)) ) | ~spl14_4),
% 1.57/1.28 inference(equality_proxy_clausification,[status(thm)],[f269])).
% 1.57/1.28 thf(f269,plain,(
% 1.57/1.28 ( ! [X0 : $o] : (((sK7 = (sK16 @ X0)) = $true) | ($true = ((~ X0) & (sK7 = (sK16 @ X0))))) ) | ~spl14_4),
% 1.57/1.28 inference(duplicate_literal_removal,[status(thm)],[f268])).
% 1.57/1.28 thf(f268,plain,(
% 1.57/1.28 ( ! [X0 : $o] : (($true = ((~ X0) & (sK7 = (sK16 @ X0)))) | ((sK7 = (sK16 @ X0)) = $true) | ((sK7 = (sK16 @ X0)) = $true)) ) | ~spl14_4),
% 1.57/1.28 inference(binary_proxy_clausification,[status(thm)],[f266])).
% 1.57/1.28 thf(f266,plain,(
% 1.57/1.28 ( ! [X0 : $o] : (($true = ((sK7 = (sK16 @ X0)) & X0)) | ($true = ((~ X0) & (sK7 = (sK16 @ X0)))) | ((sK7 = (sK16 @ X0)) = $true)) ) | ~spl14_4),
% 1.57/1.28 inference(binary_proxy_clausification,[status(thm)],[f254])).
% 1.57/1.28 thf(f254,plain,(
% 1.57/1.28 ( ! [X0 : $o] : (($true = (((sK7 = (sK16 @ X0)) & X0) | ((~ X0) & (sK7 = (sK16 @ X0))))) | ((sK7 = (sK16 @ X0)) = $true)) ) | ~spl14_4),
% 1.57/1.28 inference(binary_proxy_clausification,[status(thm)],[f253])).
% 1.57/1.28 thf(f253,plain,(
% 1.57/1.28 ( ! [X0 : $o] : (((sK7 = (sK16 @ X0)) != (((sK7 = (sK16 @ X0)) & X0) | ((~ X0) & (sK7 = (sK16 @ X0)))))) ) | ~spl14_4),
% 1.57/1.28 inference(beta_eta_normalization,[status(thm)],[f252])).
% 1.57/1.28 thf(f252,plain,(
% 1.57/1.28 ( ! [X0 : $o] : (((sK7 = (sK16 @ X0)) != ((^[Y0 : $i]: (((sK7 = Y0) & X0) | ((~ X0) & (sK7 = Y0)))) @ (sK16 @ X0)))) ) | ~spl14_4),
% 1.57/1.28 inference(negative_extensionality,[status(thm)],[f250])).
% 1.57/1.28 thf(f250,plain,(
% 1.57/1.28 ( ! [X0 : $o] : (((^[Y0 : $i]: (((sK7 = Y0) & X0) | ((~ X0) & (sK7 = Y0)))) != (= @ sK7))) ) | ~spl14_4),
% 1.57/1.28 inference(trivial_inequality_removal,[status(thm)],[f249])).
% 1.57/1.28 thf(f249,plain,(
% 1.57/1.28 ( ! [X0 : $o] : (($true != $true) | ((^[Y0 : $i]: (((sK7 = Y0) & X0) | ((~ X0) & (sK7 = Y0)))) != (= @ sK7))) ) | ~spl14_4),
% 1.57/1.28 inference(constrained_superposition,[status(thm)],[f151,f177])).
% 1.57/1.28 thf(f177,plain,(
% 1.57/1.28 ( ! [X0 : $o] : (($true = (singleton @ (dsetconstr @ sK8 @ (^[Y0 : $i]: (((sK7 = Y0) & X0) | ((~ X0) & (sK7 = Y0)))))))) )),
% 1.57/1.28 inference(trivial_inequality_removal,[status(thm)],[f176])).
% 1.57/1.28 thf(f176,plain,(
% 1.57/1.28 ( ! [X0 : $o] : (($true = (singleton @ (dsetconstr @ sK8 @ (^[Y0 : $i]: (((sK7 = Y0) & X0) | ((~ X0) & (sK7 = Y0))))))) | ($true != $true)) )),
% 1.57/1.28 inference(superposition,[status(thm)],[f129,f56])).
% 1.57/1.28 thf(f129,plain,(
% 1.57/1.28 ( ! [X0 : $i,X1 : $o] : (($true != (in @ X0 @ sK8)) | ((singleton @ (dsetconstr @ sK8 @ (^[Y0 : $i]: (((X0 = Y0) & X1) | ((~ X1) & (sK7 = Y0)))))) = $true)) )),
% 1.57/1.28 inference(trivial_inequality_removal,[status(thm)],[f128])).
% 1.57/1.28 thf(f128,plain,(
% 1.57/1.28 ( ! [X0 : $i,X1 : $o] : (($true != $true) | ((singleton @ (dsetconstr @ sK8 @ (^[Y0 : $i]: (((X0 = Y0) & X1) | ((~ X1) & (sK7 = Y0)))))) = $true) | ($true != (in @ X0 @ sK8))) )),
% 1.57/1.28 inference(superposition,[status(thm)],[f78,f56])).
% 1.57/1.28 thf(f78,plain,(
% 1.57/1.28 ( ! [X6 : $i,X7 : $i,X4 : $o,X5 : $i] : (($true != (in @ X7 @ X6)) | ((singleton @ (dsetconstr @ X6 @ (^[Y0 : $i]: (((X5 = Y0) & X4) | ((~ X4) & (X7 = Y0)))))) = $true) | ((in @ X5 @ X6) != $true)) )),
% 1.57/1.28 inference(trivial_inequality_removal,[status(thm)],[f76])).
% 1.57/1.28 thf(f76,plain,(
% 1.57/1.28 ( ! [X6 : $i,X7 : $i,X4 : $o,X5 : $i] : (($true != (in @ X7 @ X6)) | ((in @ X5 @ X6) != $true) | ((singleton @ (dsetconstr @ X6 @ (^[Y0 : $i]: (((X5 = Y0) & X4) | ((~ X4) & (X7 = Y0)))))) = $true) | ($true != $true)) )),
% 1.57/1.28 inference(definition_unfolding,[status(thm)],[f58,f52])).
% 1.57/1.28 thf(f52,plain,(
% 1.57/1.28 (ifSingleton = $true)),
% 1.57/1.28 inference(cnf_transformation,[status(thm)],[f36])).
% 1.57/1.28 thf(f36,plain,(
% 1.57/1.28 (theeq = $true) & (((in @ sK7 @ sK8) = $true) & (($true = sK6) & (sK7 != (if @ sK8 @ sK6 @ sK7 @ sK9)) & ((in @ sK9 @ sK8) = $true))) & (ifSingleton = $true) & (iftrueProp1 = $true)),
% 1.57/1.28 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9])],[f20,f35,f34])).
% 1.57/1.28 thf(f34,plain,(
% 1.57/1.28 ? [X0 : $o,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X2)) & ? [X3 : $i] : (($true = X0) & ((if @ X2 @ X0 @ X1 @ X3) != X1) & ((in @ X3 @ X2) = $true))) => (((in @ sK7 @ sK8) = $true) & ? [X3 : $i] : (($true = sK6) & (sK7 != (if @ sK8 @ sK6 @ sK7 @ X3)) & ($true = (in @ X3 @ sK8))))),
% 1.57/1.28 introduced(definition,[],[choice_axiom])).
% 1.57/1.28 thf(f35,plain,(
% 1.57/1.28 ? [X3 : $i] : (($true = sK6) & (sK7 != (if @ sK8 @ sK6 @ sK7 @ X3)) & ($true = (in @ X3 @ sK8))) => (($true = sK6) & (sK7 != (if @ sK8 @ sK6 @ sK7 @ sK9)) & ((in @ sK9 @ sK8) = $true))),
% 1.57/1.28 introduced(definition,[],[choice_axiom])).
% 1.57/1.28 thf(f20,plain,(
% 1.57/1.28 (theeq = $true) & ? [X0 : $o,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X2)) & ? [X3 : $i] : (($true = X0) & ((if @ X2 @ X0 @ X1 @ X3) != X1) & ((in @ X3 @ X2) = $true))) & (ifSingleton = $true) & (iftrueProp1 = $true)),
% 1.57/1.28 inference(flattening,[status(thm)],[f19])).
% 1.57/1.28 thf(f19,plain,(
% 1.57/1.28 ((? [X0 : $o,X1 : $i,X2 : $i] : (? [X3 : $i] : ((((if @ X2 @ X0 @ X1 @ X3) != X1) & ($true = X0)) & ((in @ X3 @ X2) = $true)) & ($true = (in @ X1 @ X2))) & (theeq = $true)) & (ifSingleton = $true)) & (iftrueProp1 = $true)),
% 1.57/1.28 inference(ennf_transformation,[status(thm)],[f15])).
% 1.57/1.28 thf(f15,plain,(
% 1.57/1.28 ~((iftrueProp1 = $true) => ((ifSingleton = $true) => ((theeq = $true) => ! [X0 : $o,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X2)) => ! [X3 : $i] : (((in @ X3 @ X2) = $true) => (($true = X0) => ((if @ X2 @ X0 @ X1 @ X3) = X1)))))))),
% 1.57/1.28 inference(fool_elimination,[status(thm)],[f14])).
% 1.57/1.28 thf(f14,plain,(
% 1.57/1.28 ~(iftrueProp1 => (ifSingleton => (theeq => ! [X0 : $o,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => ! [X3 : $i] : ((in @ X3 @ X2) => (X0 => ((if @ X2 @ X0 @ X1 @ X3) = X1)))))))),
% 1.57/1.28 inference(rectify,[status(thm)],[f6])).
% 1.57/1.28 thf(f6,negated_conjecture,(
% 1.57/1.28 ~(iftrueProp1 => (ifSingleton => (theeq => ! [X1 : $o,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (X1 => ((if @ X0 @ X1 @ X2 @ X3) = X2)))))))),
% 1.57/1.28 inference(negated_conjecture,[status(cth)],[f5])).
% 1.57/1.28 thf(f5,conjecture,(
% 1.57/1.28 iftrueProp1 => (ifSingleton => (theeq => ! [X1 : $o,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (X1 => ((if @ X0 @ X1 @ X2 @ X3) = X2))))))),
% 1.57/1.28 file('/export/starexec/sandbox2/tmp/tmp.jN8ZtNNWQF/DTF2THF_4433.p',iftrue)).
% 1.57/1.28 thf(f58,plain,(
% 1.57/1.28 ( ! [X6 : $i,X7 : $i,X4 : $o,X5 : $i] : (((singleton @ (dsetconstr @ X6 @ (^[Y0 : $i]: (((X5 = Y0) & X4) | ((~ X4) & (X7 = Y0)))))) = $true) | ($true != (in @ X7 @ X6)) | ((in @ X5 @ X6) != $true) | (ifSingleton != $true)) )),
% 1.57/1.28 inference(cnf_transformation,[status(thm)],[f41])).
% 1.57/1.28 thf(f41,plain,(
% 1.57/1.28 ((ifSingleton = $true) | ((($true != (singleton @ (dsetconstr @ sK12 @ (^[Y0 : $i]: (((sK11 = Y0) & sK10) | ((~ sK10) & (sK13 = Y0))))))) & ((in @ sK13 @ sK12) = $true)) & ($true = (in @ sK11 @ sK12)))) & (! [X4 : $o,X5 : $i,X6 : $i] : (! [X7 : $i] : (((singleton @ (dsetconstr @ X6 @ (^[Y0 : $i]: (((X5 = Y0) & X4) | ((~ X4) & (X7 = Y0)))))) = $true) | ($true != (in @ X7 @ X6))) | ((in @ X5 @ X6) != $true)) | (ifSingleton != $true))),
% 1.57/1.28 inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13])],[f38,f40,f39])).
% 1.57/1.28 thf(f39,plain,(
% 1.57/1.28 ? [X0 : $o,X1 : $i,X2 : $i] : (? [X3 : $i] : (((singleton @ (dsetconstr @ X2 @ (^[Y0 : $i]: (((X1 = Y0) & X0) | ((~ X0) & (X3 = Y0)))))) != $true) & ((in @ X3 @ X2) = $true)) & ($true = (in @ X1 @ X2))) => (? [X3 : $i] : (((singleton @ (dsetconstr @ sK12 @ (^[Y0 : $i]: (((sK11 = Y0) & sK10) | ((~ sK10) & (X3 = Y0)))))) != $true) & ((in @ X3 @ sK12) = $true)) & ($true = (in @ sK11 @ sK12)))),
% 1.57/1.28 introduced(definition,[],[choice_axiom])).
% 1.57/1.28 thf(f40,plain,(
% 1.57/1.28 ? [X3 : $i] : (((singleton @ (dsetconstr @ sK12 @ (^[Y0 : $i]: (((sK11 = Y0) & sK10) | ((~ sK10) & (X3 = Y0)))))) != $true) & ((in @ X3 @ sK12) = $true)) => (($true != (singleton @ (dsetconstr @ sK12 @ (^[Y0 : $i]: (((sK11 = Y0) & sK10) | ((~ sK10) & (sK13 = Y0))))))) & ((in @ sK13 @ sK12) = $true))),
% 1.57/1.28 introduced(definition,[],[choice_axiom])).
% 1.57/1.28 thf(f38,plain,(
% 1.57/1.28 ((ifSingleton = $true) | ? [X0 : $o,X1 : $i,X2 : $i] : (? [X3 : $i] : (((singleton @ (dsetconstr @ X2 @ (^[Y0 : $i]: (((X1 = Y0) & X0) | ((~ X0) & (X3 = Y0)))))) != $true) & ((in @ X3 @ X2) = $true)) & ($true = (in @ X1 @ X2)))) & (! [X4 : $o,X5 : $i,X6 : $i] : (! [X7 : $i] : (((singleton @ (dsetconstr @ X6 @ (^[Y0 : $i]: (((X5 = Y0) & X4) | ((~ X4) & (X7 = Y0)))))) = $true) | ($true != (in @ X7 @ X6))) | ((in @ X5 @ X6) != $true)) | (ifSingleton != $true))),
% 1.57/1.28 inference(rectify,[status(thm)],[f37])).
% 1.57/1.28 thf(f37,plain,(
% 1.57/1.28 ((ifSingleton = $true) | ? [X0 : $o,X1 : $i,X2 : $i] : (? [X3 : $i] : (((singleton @ (dsetconstr @ X2 @ (^[Y0 : $i]: (((X1 = Y0) & X0) | ((~ X0) & (X3 = Y0)))))) != $true) & ((in @ X3 @ X2) = $true)) & ($true = (in @ X1 @ X2)))) & (! [X0 : $o,X1 : $i,X2 : $i] : (! [X3 : $i] : (((singleton @ (dsetconstr @ X2 @ (^[Y0 : $i]: (((X1 = Y0) & X0) | ((~ X0) & (X3 = Y0)))))) = $true) | ((in @ X3 @ X2) != $true)) | ($true != (in @ X1 @ X2))) | (ifSingleton != $true))),
% 1.57/1.28 inference(nnf_transformation,[status(thm)],[f23])).
% 1.57/1.28 thf(f23,plain,(
% 1.57/1.28 (ifSingleton = $true) <=> ! [X0 : $o,X1 : $i,X2 : $i] : (! [X3 : $i] : (((singleton @ (dsetconstr @ X2 @ (^[Y0 : $i]: (((X1 = Y0) & X0) | ((~ X0) & (X3 = Y0)))))) = $true) | ((in @ X3 @ X2) != $true)) | ($true != (in @ X1 @ X2)))),
% 1.57/1.28 inference(ennf_transformation,[status(thm)],[f9])).
% 1.57/1.28 thf(f9,plain,(
% 1.57/1.28 (ifSingleton = $true) <=> ! [X0 : $o,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X2)) => ! [X3 : $i] : (((in @ X3 @ X2) = $true) => ((singleton @ (dsetconstr @ X2 @ (^[Y0 : $i]: (((X1 = Y0) & X0) | ((~ X0) & (X3 = Y0)))))) = $true)))),
% 1.57/1.28 inference(fool_elimination,[status(thm)],[f8])).
% 1.57/1.28 thf(f8,plain,(
% 1.57/1.28 (! [X0 : $o,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => ! [X3 : $i] : ((in @ X3 @ X2) => (singleton @ (dsetconstr @ X2 @ (^[X4 : $i] : (((X3 = X4) & ~X0) | (X0 & (X1 = X4)))))))) = ifSingleton)),
% 1.57/1.28 inference(rectify,[status(thm)],[f2])).
% 1.57/1.28 thf(f2,axiom,(
% 1.57/1.28 (! [X1 : $o,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (singleton @ (dsetconstr @ X0 @ (^[X4 : $i] : (((X3 = X4) & ~X1) | (X1 & (X2 = X4)))))))) = ifSingleton)),
% 1.57/1.28 file('/export/starexec/sandbox2/tmp/tmp.jN8ZtNNWQF/DTF2THF_4433.p',ifSingleton)).
% 1.57/1.28 thf(f151,plain,(
% 1.57/1.28 ($true != (singleton @ (dsetconstr @ sK8 @ (= @ sK7)))) | ~spl14_4),
% 1.57/1.28 inference(subsumption_resolution,[status(thm)],[f141,f84])).
% 1.57/1.28 thf(f84,plain,(
% 1.57/1.28 (sK7 != (setunion @ (dsetconstr @ sK8 @ (= @ sK7))))),
% 1.57/1.28 inference(beta_eta_normalization,[status(thm)],[f83])).
% 1.57/1.28 thf(f83,plain,(
% 1.57/1.28 (sK7 != (setunion @ (dsetconstr @ sK8 @ (^[Y0 : $i]: (sK7 = Y0)))))),
% 1.57/1.28 inference(boolean_simplification,[status(thm)],[f82])).
% 1.57/1.28 thf(f82,plain,(
% 1.57/1.28 (sK7 != (setunion @ (dsetconstr @ sK8 @ (^[Y0 : $i]: ($false | (sK7 = Y0))))))),
% 1.57/1.28 inference(boolean_simplification,[status(thm)],[f81])).
% 1.57/1.28 thf(f81,plain,(
% 1.57/1.28 (sK7 != (setunion @ (dsetconstr @ sK8 @ (^[Y0 : $i]: (((sK9 = Y0) & $false) | (sK7 = Y0))))))),
% 1.57/1.28 inference(boolean_simplification,[status(thm)],[f80])).
% 1.57/1.28 thf(f80,plain,(
% 1.57/1.28 (sK7 != (setunion @ (dsetconstr @ sK8 @ (^[Y0 : $i]: (((sK9 = Y0) & (~ $true)) | (sK7 = Y0))))))),
% 1.57/1.28 inference(boolean_simplification,[status(thm)],[f79])).
% 1.57/1.28 thf(f79,plain,(
% 1.57/1.28 (sK7 != (setunion @ (dsetconstr @ sK8 @ (^[Y0 : $i]: (((sK9 = Y0) & (~ $true)) | ($true & (sK7 = Y0)))))))),
% 1.57/1.28 inference(beta_eta_normalization,[status(thm)],[f72])).
% 1.57/1.28 thf(f72,plain,(
% 1.57/1.28 (sK7 != ((^[Y0 : $i]: ((^[Y1 : $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: (setunion @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (((Y3 = Y4) & (~ Y1)) | (Y1 & (Y2 = Y4))))))))))))) @ sK8 @ $true @ sK7 @ sK9))),
% 1.57/1.28 inference(definition_unfolding,[status(thm)],[f54,f62,f55])).
% 1.57/1.28 thf(f55,plain,(
% 1.57/1.28 ($true = sK6)),
% 1.57/1.28 inference(cnf_transformation,[status(thm)],[f36])).
% 1.57/1.28 thf(f62,plain,(
% 1.57/1.28 (if = (^[Y0 : $i]: ((^[Y1 : $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: (setunion @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (((Y3 = Y4) & (~ Y1)) | (Y1 & (Y2 = Y4))))))))))))))),
% 1.57/1.28 inference(cnf_transformation,[status(thm)],[f11])).
% 1.57/1.28 thf(f11,plain,(
% 1.57/1.28 (if = (^[Y0 : $i]: ((^[Y1 : $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: (setunion @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (((Y3 = Y4) & (~ Y1)) | (Y1 & (Y2 = Y4))))))))))))))),
% 1.57/1.28 inference(fool_elimination,[status(thm)],[f10])).
% 1.57/1.28 thf(f10,plain,(
% 1.57/1.28 ((^[X0 : $i, X1 : $o, X2 : $i, X3 : $i] : (setunion @ (dsetconstr @ X0 @ (^[X4 : $i] : (((X2 = X4) & X1) | (~X1 & (X3 = X4))))))) = if)),
% 1.57/1.28 inference(rectify,[status(thm)],[f3])).
% 1.57/1.28 thf(f3,axiom,(
% 1.57/1.28 ((^[X0 : $i, X1 : $o, X2 : $i, X3 : $i] : (setunion @ (dsetconstr @ X0 @ (^[X4 : $i] : (((X2 = X4) & X1) | (~X1 & (X3 = X4))))))) = if)),
% 1.57/1.28 file('/export/starexec/sandbox2/tmp/tmp.jN8ZtNNWQF/DTF2THF_4433.p',if)).
% 1.57/1.28 thf(f54,plain,(
% 1.57/1.28 (sK7 != (if @ sK8 @ sK6 @ sK7 @ sK9))),
% 1.57/1.28 inference(cnf_transformation,[status(thm)],[f36])).
% 1.57/1.28 thf(f141,plain,(
% 1.57/1.28 ($true != (singleton @ (dsetconstr @ sK8 @ (= @ sK7)))) | (sK7 = (setunion @ (dsetconstr @ sK8 @ (= @ sK7)))) | ~spl14_4),
% 1.57/1.28 inference(trivial_inequality_removal,[status(thm)],[f139])).
% 1.57/1.28 thf(f139,plain,(
% 1.57/1.28 ($true != $true) | (sK7 = (setunion @ (dsetconstr @ sK8 @ (= @ sK7)))) | ($true != (singleton @ (dsetconstr @ sK8 @ (= @ sK7)))) | ~spl14_4),
% 1.57/1.28 inference(superposition,[status(thm)],[f91,f117])).
% 1.57/1.28 thf(f117,plain,(
% 1.57/1.28 ($true = (in @ sK7 @ (dsetconstr @ sK8 @ (= @ sK7)))) | ~spl14_4),
% 1.57/1.28 inference(avatar_component_clause,[status(thm)],[f115])).
% 1.57/1.28 thf(f115,definition,(
% 1.57/1.28 spl14_4 <=> ($true = (in @ sK7 @ (dsetconstr @ sK8 @ (= @ sK7))))),
% 1.57/1.28 introduced(definition,[new_symbols(naming,[spl14_4])],[avatar_definition])).
% 1.57/1.28 thf(f91,plain,(
% 1.57/1.28 ( ! [X0 : $i,X1 : $i] : (((in @ X1 @ X0) != $true) | ((setunion @ X0) = X1) | ($true != (singleton @ X0))) )),
% 1.57/1.28 inference(trivial_inequality_removal,[status(thm)],[f68])).
% 1.57/1.28 thf(f68,plain,(
% 1.57/1.28 ( ! [X0 : $i,X1 : $i] : (((in @ X1 @ X0) != $true) | ((setunion @ X0) = X1) | ($true != $true) | ($true != (singleton @ X0))) )),
% 1.57/1.28 inference(definition_unfolding,[status(thm)],[f50,f57])).
% 1.57/1.28 thf(f57,plain,(
% 1.57/1.28 (theeq = $true)),
% 1.57/1.28 inference(cnf_transformation,[status(thm)],[f36])).
% 1.57/1.28 thf(f50,plain,(
% 1.57/1.28 ( ! [X0 : $i,X1 : $i] : (((setunion @ X0) = X1) | ((in @ X1 @ X0) != $true) | ($true != (singleton @ X0)) | (theeq != $true)) )),
% 1.57/1.28 inference(cnf_transformation,[status(thm)],[f33])).
% 1.57/1.28 thf(f33,plain,(
% 1.57/1.28 (! [X0 : $i] : (! [X1 : $i] : (((setunion @ X0) = X1) | ((in @ X1 @ X0) != $true)) | ($true != (singleton @ X0))) | (theeq != $true)) & ((theeq = $true) | ((((setunion @ sK4) != sK5) & ((in @ sK5 @ sK4) = $true)) & ($true = (singleton @ sK4))))),
% 1.57/1.28 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f30,f32,f31])).
% 1.57/1.28 thf(f31,plain,(
% 1.57/1.28 ? [X2 : $i] : (? [X3 : $i] : (((setunion @ X2) != X3) & ((in @ X3 @ X2) = $true)) & ((singleton @ X2) = $true)) => (? [X3 : $i] : (((setunion @ sK4) != X3) & ($true = (in @ X3 @ sK4))) & ($true = (singleton @ sK4)))),
% 1.57/1.28 introduced(definition,[],[choice_axiom])).
% 1.57/1.28 thf(f32,plain,(
% 1.57/1.28 ? [X3 : $i] : (((setunion @ sK4) != X3) & ($true = (in @ X3 @ sK4))) => (((setunion @ sK4) != sK5) & ((in @ sK5 @ sK4) = $true))),
% 1.57/1.28 introduced(definition,[],[choice_axiom])).
% 1.57/1.28 thf(f30,plain,(
% 1.57/1.28 (! [X0 : $i] : (! [X1 : $i] : (((setunion @ X0) = X1) | ((in @ X1 @ X0) != $true)) | ($true != (singleton @ X0))) | (theeq != $true)) & ((theeq = $true) | ? [X2 : $i] : (? [X3 : $i] : (((setunion @ X2) != X3) & ((in @ X3 @ X2) = $true)) & ((singleton @ X2) = $true)))),
% 1.57/1.28 inference(rectify,[status(thm)],[f29])).
% 1.57/1.28 thf(f29,plain,(
% 1.57/1.28 (! [X0 : $i] : (! [X1 : $i] : (((setunion @ X0) = X1) | ((in @ X1 @ X0) != $true)) | ($true != (singleton @ X0))) | (theeq != $true)) & ((theeq = $true) | ? [X0 : $i] : (? [X1 : $i] : (((setunion @ X0) != X1) & ((in @ X1 @ X0) = $true)) & ($true = (singleton @ X0))))),
% 1.57/1.28 inference(nnf_transformation,[status(thm)],[f18])).
% 1.57/1.28 thf(f18,plain,(
% 1.57/1.28 ! [X0 : $i] : (! [X1 : $i] : (((setunion @ X0) = X1) | ((in @ X1 @ X0) != $true)) | ($true != (singleton @ X0))) <=> (theeq = $true)),
% 1.57/1.28 inference(ennf_transformation,[status(thm)],[f17])).
% 1.57/1.28 thf(f17,plain,(
% 1.57/1.28 (theeq = $true) <=> ! [X0 : $i] : (($true = (singleton @ X0)) => ! [X1 : $i] : (((in @ X1 @ X0) = $true) => ((setunion @ X0) = X1)))),
% 1.57/1.28 inference(fool_elimination,[status(thm)],[f16])).
% 1.57/1.28 thf(f16,plain,(
% 1.57/1.28 (! [X0 : $i] : ((singleton @ X0) => ! [X1 : $i] : ((in @ X1 @ X0) => ((setunion @ X0) = X1))) = theeq)),
% 1.57/1.28 inference(rectify,[status(thm)],[f4])).
% 1.57/1.28 thf(f4,axiom,(
% 1.57/1.28 (! [X5 : $i] : ((singleton @ X5) => ! [X2 : $i] : ((in @ X2 @ X5) => ((setunion @ X5) = X2))) = theeq)),
% 1.57/1.28 file('/export/starexec/sandbox2/tmp/tmp.jN8ZtNNWQF/DTF2THF_4433.p',theeq)).
% 1.57/1.28 thf(f261,plain,(
% 1.57/1.28 ( ! [X0 : $o] : (($false = X0) | ((sK16 @ X0) != sK7)) ) | ~spl14_4),
% 1.57/1.28 inference(duplicate_literal_removal,[status(thm)],[f260])).
% 1.57/1.28 thf(f260,plain,(
% 1.57/1.28 ( ! [X0 : $o] : (((sK16 @ X0) != sK7) | ((sK16 @ X0) != sK7) | ($false = X0)) ) | ~spl14_4),
% 1.57/1.28 inference(equality_proxy_clausification,[status(thm)],[f259])).
% 1.57/1.28 thf(f259,plain,(
% 1.57/1.28 ( ! [X0 : $o] : (((sK16 @ X0) != sK7) | ((sK7 = (sK16 @ X0)) = $false) | ($false = X0)) ) | ~spl14_4),
% 1.57/1.28 inference(binary_proxy_clausification,[status(thm)],[f258])).
% 1.57/1.28 thf(f258,plain,(
% 1.57/1.28 ( ! [X0 : $o] : (((sK16 @ X0) != sK7) | (((sK7 = (sK16 @ X0)) & X0) = $false)) ) | ~spl14_4),
% 1.57/1.28 inference(binary_proxy_clausification,[status(thm)],[f256])).
% 1.57/1.28 thf(f256,plain,(
% 1.57/1.28 ( ! [X0 : $o] : (((((sK7 = (sK16 @ X0)) & X0) | ((~ X0) & (sK7 = (sK16 @ X0)))) = $false) | ((sK16 @ X0) != sK7)) ) | ~spl14_4),
% 1.57/1.28 inference(equality_proxy_clausification,[status(thm)],[f255])).
% 1.57/1.28 thf(f255,plain,(
% 1.57/1.28 ( ! [X0 : $o] : (((sK7 = (sK16 @ X0)) = $false) | ((((sK7 = (sK16 @ X0)) & X0) | ((~ X0) & (sK7 = (sK16 @ X0)))) = $false)) ) | ~spl14_4),
% 1.57/1.28 inference(binary_proxy_clausification,[status(thm)],[f253])).
% 1.57/1.28 thf(f56,plain,(
% 1.57/1.28 ((in @ sK7 @ sK8) = $true)),
% 1.57/1.28 inference(cnf_transformation,[status(thm)],[f36])).
% 1.57/1.28 thf(f136,plain,(
% 1.57/1.28 ~spl14_5),
% 1.57/1.28 inference(avatar_contradiction_clause,[status(thm)],[f135])).
% 1.57/1.28 thf(f135,plain,(
% 1.57/1.28 $false | ~spl14_5),
% 1.57/1.28 inference(trivial_inequality_removal,[status(thm)],[f132])).
% 1.57/1.28 thf(f132,plain,(
% 1.57/1.28 ($true != $true) | ~spl14_5),
% 1.57/1.28 inference(superposition,[status(thm)],[f120,f56])).
% 1.57/1.28 thf(f120,plain,(
% 1.57/1.28 ( ! [X0 : $i] : (($true != (in @ X0 @ sK8))) ) | ~spl14_5),
% 1.57/1.28 inference(avatar_component_clause,[status(thm)],[f119])).
% 1.57/1.28 thf(f119,definition,(
% 1.57/1.28 spl14_5 <=> ! [X0 : $i] : ($true != (in @ X0 @ sK8))),
% 1.57/1.28 introduced(definition,[new_symbols(naming,[spl14_5])],[avatar_definition])).
% 1.57/1.28 thf(f121,plain,(
% 1.57/1.28 spl14_4 | spl14_5),
% 1.57/1.28 inference(avatar_split_clause,[status(thm)],[f113,f119,f115])).
% 1.57/1.28 thf(f113,plain,(
% 1.57/1.28 ( ! [X0 : $i] : (($true = (in @ sK7 @ (dsetconstr @ sK8 @ (= @ sK7)))) | ($true != (in @ X0 @ sK8))) )),
% 1.57/1.28 inference(trivial_inequality_removal,[status(thm)],[f111])).
% 1.57/1.28 thf(f111,plain,(
% 1.57/1.28 ( ! [X0 : $i] : (($true != $true) | ($true = (in @ sK7 @ (dsetconstr @ sK8 @ (= @ sK7)))) | ($true != (in @ X0 @ sK8))) )),
% 1.57/1.28 inference(superposition,[status(thm)],[f90,f56])).
% 1.57/1.28 thf(f90,plain,(
% 1.57/1.28 ( ! [X2 : $i,X3 : $i,X0 : $i] : (($true != (in @ X0 @ X2)) | ((in @ X0 @ (dsetconstr @ X2 @ (= @ X0))) = $true) | ((in @ X3 @ X2) != $true)) )),
% 1.57/1.28 inference(beta_eta_normalization,[status(thm)],[f89])).
% 1.57/1.28 thf(f89,plain,(
% 1.57/1.28 ( ! [X2 : $i,X3 : $i,X0 : $i] : (($true = (in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 = Y0))))) | ($true != (in @ X0 @ X2)) | ((in @ X3 @ X2) != $true)) )),
% 1.57/1.28 inference(boolean_simplification,[status(thm)],[f88])).
% 1.57/1.28 thf(f88,plain,(
% 1.57/1.28 ( ! [X2 : $i,X3 : $i,X0 : $i] : (($true != (in @ X0 @ X2)) | ($true = (in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: ($false | (X0 = Y0)))))) | ((in @ X3 @ X2) != $true)) )),
% 1.57/1.28 inference(boolean_simplification,[status(thm)],[f87])).
% 1.57/1.28 thf(f87,plain,(
% 1.57/1.28 ( ! [X2 : $i,X3 : $i,X0 : $i] : (($true != (in @ X0 @ X2)) | ((in @ X3 @ X2) != $true) | ($true = (in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (($false & (X3 = Y0)) | (X0 = Y0))))))) )),
% 1.57/1.28 inference(boolean_simplification,[status(thm)],[f86])).
% 1.57/1.28 thf(f86,plain,(
% 1.57/1.28 ( ! [X2 : $i,X3 : $i,X0 : $i] : (((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (((~ $true) & (X3 = Y0)) | (X0 = Y0))))) = $true) | ((in @ X3 @ X2) != $true) | ($true != (in @ X0 @ X2))) )),
% 1.57/1.28 inference(boolean_simplification,[status(thm)],[f85])).
% 1.57/1.28 thf(f85,plain,(
% 1.57/1.28 ( ! [X2 : $i,X3 : $i,X0 : $i] : (($true != (in @ X0 @ X2)) | ((in @ X3 @ X2) != $true) | ((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (((~ $true) & (X3 = Y0)) | ((X0 = Y0) & $true))))) = $true)) )),
% 1.57/1.28 inference(trivial_inequality_removal,[status(thm)],[f77])).
% 1.57/1.28 thf(f77,plain,(
% 1.57/1.28 ( ! [X2 : $i,X3 : $i,X0 : $i] : (($true != $true) | ((in @ X3 @ X2) != $true) | ($true != (in @ X0 @ X2)) | ((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (((~ $true) & (X3 = Y0)) | ((X0 = Y0) & $true))))) = $true)) )),
% 1.57/1.28 inference(equality_resolution,[status(thm)],[f63])).
% 1.57/1.28 thf(f63,plain,(
% 1.57/1.28 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o] : (($true != X1) | ((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (((~ X1) & (X3 = Y0)) | ((X0 = Y0) & X1))))) = $true) | ((in @ X3 @ X2) != $true) | ($true != (in @ X0 @ X2)) | ($true != $true)) )),
% 1.57/1.28 inference(definition_unfolding,[status(thm)],[f46,f51])).
% 1.57/1.28 thf(f51,plain,(
% 1.57/1.28 (iftrueProp1 = $true)),
% 1.57/1.28 inference(cnf_transformation,[status(thm)],[f36])).
% 1.57/1.28 thf(f46,plain,(
% 1.57/1.28 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o] : (($true != X1) | ((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (((~ X1) & (X3 = Y0)) | ((X0 = Y0) & X1))))) = $true) | ((in @ X3 @ X2) != $true) | ($true != (in @ X0 @ X2)) | (iftrueProp1 != $true)) )),
% 1.57/1.28 inference(cnf_transformation,[status(thm)],[f28])).
% 1.57/1.28 thf(f28,plain,(
% 1.57/1.28 (! [X0 : $i,X1 : $o,X2 : $i] : (! [X3 : $i] : (($true != X1) | ((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (((~ X1) & (X3 = Y0)) | ((X0 = Y0) & X1))))) = $true) | ((in @ X3 @ X2) != $true)) | ($true != (in @ X0 @ X2))) | (iftrueProp1 != $true)) & ((iftrueProp1 = $true) | (((sK1 = $true) & ((in @ sK0 @ (dsetconstr @ sK2 @ (^[Y0 : $i]: (((~ sK1) & (sK3 = Y0)) | ((sK0 = Y0) & sK1))))) != $true) & ($true = (in @ sK3 @ sK2))) & ((in @ sK0 @ sK2) = $true)))),
% 1.57/1.28 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f25,f27,f26])).
% 1.57/1.28 thf(f26,plain,(
% 1.57/1.28 ? [X4 : $i,X5 : $o,X6 : $i] : (? [X7 : $i] : (($true = X5) & ($true != (in @ X4 @ (dsetconstr @ X6 @ (^[Y0 : $i]: (((~ X5) & (X7 = Y0)) | ((X4 = Y0) & X5)))))) & ($true = (in @ X7 @ X6))) & ((in @ X4 @ X6) = $true)) => (? [X7 : $i] : ((sK1 = $true) & ($true != (in @ sK0 @ (dsetconstr @ sK2 @ (^[Y0 : $i]: (((~ sK1) & (X7 = Y0)) | ((sK0 = Y0) & sK1)))))) & ($true = (in @ X7 @ sK2))) & ((in @ sK0 @ sK2) = $true))),
% 1.57/1.28 introduced(definition,[],[choice_axiom])).
% 1.57/1.28 thf(f27,plain,(
% 1.57/1.28 ? [X7 : $i] : ((sK1 = $true) & ($true != (in @ sK0 @ (dsetconstr @ sK2 @ (^[Y0 : $i]: (((~ sK1) & (X7 = Y0)) | ((sK0 = Y0) & sK1)))))) & ($true = (in @ X7 @ sK2))) => ((sK1 = $true) & ((in @ sK0 @ (dsetconstr @ sK2 @ (^[Y0 : $i]: (((~ sK1) & (sK3 = Y0)) | ((sK0 = Y0) & sK1))))) != $true) & ($true = (in @ sK3 @ sK2)))),
% 1.57/1.28 introduced(definition,[],[choice_axiom])).
% 1.57/1.28 thf(f25,plain,(
% 1.57/1.28 (! [X0 : $i,X1 : $o,X2 : $i] : (! [X3 : $i] : (($true != X1) | ((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (((~ X1) & (X3 = Y0)) | ((X0 = Y0) & X1))))) = $true) | ((in @ X3 @ X2) != $true)) | ($true != (in @ X0 @ X2))) | (iftrueProp1 != $true)) & ((iftrueProp1 = $true) | ? [X4 : $i,X5 : $o,X6 : $i] : (? [X7 : $i] : (($true = X5) & ($true != (in @ X4 @ (dsetconstr @ X6 @ (^[Y0 : $i]: (((~ X5) & (X7 = Y0)) | ((X4 = Y0) & X5)))))) & ($true = (in @ X7 @ X6))) & ((in @ X4 @ X6) = $true)))),
% 1.57/1.28 inference(rectify,[status(thm)],[f24])).
% 1.57/1.28 thf(f24,plain,(
% 1.57/1.28 (! [X0 : $i,X1 : $o,X2 : $i] : (! [X3 : $i] : (($true != X1) | ((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (((~ X1) & (X3 = Y0)) | ((X0 = Y0) & X1))))) = $true) | ((in @ X3 @ X2) != $true)) | ($true != (in @ X0 @ X2))) | (iftrueProp1 != $true)) & ((iftrueProp1 = $true) | ? [X0 : $i,X1 : $o,X2 : $i] : (? [X3 : $i] : (($true = X1) & ((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (((~ X1) & (X3 = Y0)) | ((X0 = Y0) & X1))))) != $true) & ((in @ X3 @ X2) = $true)) & ($true = (in @ X0 @ X2))))),
% 1.57/1.28 inference(nnf_transformation,[status(thm)],[f22])).
% 1.57/1.28 thf(f22,plain,(
% 1.57/1.28 ! [X0 : $i,X1 : $o,X2 : $i] : (! [X3 : $i] : (($true != X1) | ((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (((~ X1) & (X3 = Y0)) | ((X0 = Y0) & X1))))) = $true) | ((in @ X3 @ X2) != $true)) | ($true != (in @ X0 @ X2))) <=> (iftrueProp1 = $true)),
% 1.57/1.28 inference(flattening,[status(thm)],[f21])).
% 1.57/1.28 thf(f21,plain,(
% 1.57/1.28 ! [X0 : $i,X1 : $o,X2 : $i] : (! [X3 : $i] : ((((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (((~ X1) & (X3 = Y0)) | ((X0 = Y0) & X1))))) = $true) | ($true != X1)) | ((in @ X3 @ X2) != $true)) | ($true != (in @ X0 @ X2))) <=> (iftrueProp1 = $true)),
% 1.57/1.28 inference(ennf_transformation,[status(thm)],[f13])).
% 1.57/1.28 thf(f13,plain,(
% 1.57/1.28 ! [X0 : $i,X1 : $o,X2 : $i] : (($true = (in @ X0 @ X2)) => ! [X3 : $i] : (((in @ X3 @ X2) = $true) => (($true = X1) => ((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (((~ X1) & (X3 = Y0)) | ((X0 = Y0) & X1))))) = $true)))) <=> (iftrueProp1 = $true)),
% 1.57/1.28 inference(fool_elimination,[status(thm)],[f12])).
% 1.57/1.28 thf(f12,plain,(
% 1.57/1.28 (iftrueProp1 = ! [X0 : $i,X1 : $o,X2 : $i] : ((in @ X0 @ X2) => ! [X3 : $i] : ((in @ X3 @ X2) => (X1 => (in @ X0 @ (dsetconstr @ X2 @ (^[X4 : $i] : ((X1 & (X0 = X4)) | ((X3 = X4) & ~X1)))))))))),
% 1.57/1.28 inference(rectify,[status(thm)],[f1])).
% 1.57/1.28 thf(f1,axiom,(
% 1.57/1.28 (iftrueProp1 = ! [X2 : $i,X1 : $o,X0 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (X1 => (in @ X2 @ (dsetconstr @ X0 @ (^[X4 : $i] : ((X1 & (X2 = X4)) | ((X3 = X4) & ~X1)))))))))),
% 1.57/1.28 file('/export/starexec/sandbox2/tmp/tmp.jN8ZtNNWQF/DTF2THF_4433.p',iftrueProp1)).
% 1.57/1.28 % SZS output end Proof for DTF2THF_4433
% 1.57/1.28 % (4670)------------------------------
% 1.57/1.28 % (4670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.28 % (4670)Termination reason: Refutation
% 1.57/1.28
% 1.57/1.28 % (4670)Memory used [KB]: 5756
% 1.57/1.28 % (4670)Time elapsed: 0.013 s
% 1.57/1.28 % (4670)Instructions burned: 30 (million)
% 1.57/1.28 % (4670)------------------------------
% 1.57/1.28 % (4670)------------------------------
% 1.57/1.28 % (4649)Success in time 0.07 s
%------------------------------------------------------------------------------