%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU683^2 : 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 09:36:22 AM UTC 2026
% Result : Theorem 1.60s 1.35s
% Output : Refutation 1.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 12
% Syntax : Number of formulae : 85 ( 46 unt; 0 typ; 4 def)
% Number of atoms : 623 ( 176 equ; 0 cnn)
% Maximal formula atoms : 12 ( 7 avg)
% Number of connectives : 658 ( 30 ~; 33 |; 54 &; 434 @)
% ( 4 <=>; 72 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 18 usr; 15 con; 0-2 aty)
% ( 26 !!; 5 ??; 0 @@+; 0 @@-)
% Number of variables : 156 ( 75 ^; 61 !; 20 ?; 156 :)
% 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_7,type,
singleton: $i > $o ).
thf(func_def_8,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_20,type,
sK0: $i > $o ).
thf(func_def_27,type,
ph6:
!>[X0: $tType] : X0 ).
thf(f124,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f97,f98,f107,f116,f123]) ).
thf(f123,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[status(thm)],[f122]) ).
thf(f122,plain,
( $false
| ~ spl4_1 ),
inference(trivial_inequality_removal,[status(thm)],[f118]) ).
thf(f118,plain,
( ( $true = $false )
| ~ spl4_1 ),
inference(superposition,[status(thm)],[f82,f30]) ).
thf(f30,plain,
( ( sK0 @ sK3 )
= $true ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ( uniqinunit = $true )
& ( dsetconstrI = $true )
& ( ( ex1 @ sK1
@ ^ [Y0: $i] : ( sK0 @ Y0 ) )
= $true )
& ( $true
= ( in @ sK2 @ sK1 ) )
& ( $true
= ( in @ sK3 @ sK1 ) )
& ( ( sK0 @ sK3 )
= $true )
& ( sK3 != sK2 )
& ( ( sK0 @ sK2 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f19,f22,f21,f20]) ).
thf(f20,plain,
( ? [X0: $i > $o,X1: $i] :
( ( ( ex1 @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $true )
& ? [X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
& ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ( $true
= ( X0 @ X3 ) )
& ( X2 != X3 )
& ( $true
= ( X0 @ X2 ) ) ) ) )
=> ( ( ( ex1 @ sK1
@ ^ [Y0: $i] : ( sK0 @ Y0 ) )
= $true )
& ? [X2: $i] :
( ( $true
= ( in @ X2 @ sK1 ) )
& ? [X3: $i] :
( ( ( in @ X3 @ sK1 )
= $true )
& ( $true
= ( sK0 @ X3 ) )
& ( X2 != X3 )
& ( $true
= ( sK0 @ X2 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ sK1 ) )
& ? [X3: $i] :
( ( ( in @ X3 @ sK1 )
= $true )
& ( $true
= ( sK0 @ X3 ) )
& ( X2 != X3 )
& ( $true
= ( sK0 @ X2 ) ) ) )
=> ( ( $true
= ( in @ sK2 @ sK1 ) )
& ? [X3: $i] :
( ( ( in @ X3 @ sK1 )
= $true )
& ( $true
= ( sK0 @ X3 ) )
& ( sK2 != X3 )
& ( ( sK0 @ sK2 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f22,plain,
( ? [X3: $i] :
( ( ( in @ X3 @ sK1 )
= $true )
& ( $true
= ( sK0 @ X3 ) )
& ( sK2 != X3 )
& ( ( sK0 @ sK2 )
= $true ) )
=> ( ( $true
= ( in @ sK3 @ sK1 ) )
& ( ( sK0 @ sK3 )
= $true )
& ( sK3 != sK2 )
& ( ( sK0 @ sK2 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
( ( uniqinunit = $true )
& ( dsetconstrI = $true )
& ? [X0: $i > $o,X1: $i] :
( ( ( ex1 @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $true )
& ? [X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
& ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ( $true
= ( X0 @ X3 ) )
& ( X2 != X3 )
& ( $true
= ( X0 @ X2 ) ) ) ) ) ),
inference(flattening,[status(thm)],[f18]) ).
thf(f18,plain,
( ? [X0: $i > $o,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( X2 != X3 )
& ( $true
= ( X0 @ X3 ) )
& ( $true
= ( X0 @ X2 ) )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( $true
= ( in @ X2 @ X1 ) ) )
& ( ( ex1 @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $true ) )
& ( uniqinunit = $true )
& ( dsetconstrI = $true ) ),
inference(ennf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
~ ( ( dsetconstrI = $true )
=> ( ( uniqinunit = $true )
=> ! [X0: $i > $o,X1: $i] :
( ( ( ex1 @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $true )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( $true
= ( X0 @ X2 ) )
=> ( ( $true
= ( X0 @ X3 ) )
=> ( X2 = X3 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( ( dsetconstrI = $true )
=> ( ( uniqinunit = $true )
=> ! [X0: $i > $o,X1: $i] :
( ( ( ex1 @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ! [X4: $i] :
( ( ( in @ X4 @ X1 )
= $true )
=> ( ( $true
= ( X0 @ X3 ) )
=> ( ( $true
= ( X0 @ X4 ) )
=> ( X3 = X4 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( dsetconstrI
=> ( uniqinunit
=> ! [X0: $i > $o,X1: $i] :
( ( ex1 @ X1
@ ^ [X2: $i] : ( X0 @ X2 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( X0 @ X3 )
=> ( ( X0 @ X4 )
=> ( X3 = X4 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( dsetconstrI
=> ( uniqinunit
=> ! [X1: $i > $o,X0: $i] :
( ( ex1 @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( dsetconstrI
=> ( uniqinunit
=> ! [X1: $i > $o,X0: $i] :
( ( ex1 @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.oSlHkk0Jmm/DTF2THF_22247.p',ex1E2) ).
thf(f82,plain,
( ( ( sK0 @ sK3 )
= $false )
| ~ spl4_1 ),
inference(avatar_component_clause,[status(thm)],[f80]) ).
thf(f80,definition,
( spl4_1
<=> ( ( sK0 @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition]) ).
thf(f116,plain,
( ~ spl4_2
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f115]) ).
thf(f115,plain,
( $false
| ~ spl4_2
| ~ spl4_4 ),
inference(subsumption_resolution,[status(thm)],[f108,f29]) ).
thf(f29,plain,
sK3 != sK2,
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f108,plain,
( ( sK3 = sK2 )
| ~ spl4_2
| ~ spl4_4 ),
inference(superposition,[status(thm)],[f95,f86]) ).
thf(f86,plain,
( ( sK3 = sK5 )
| ~ spl4_2 ),
inference(avatar_component_clause,[status(thm)],[f84]) ).
thf(f84,definition,
( spl4_2
<=> ( sK3 = sK5 ) ),
introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition]) ).
thf(f95,plain,
( ( sK5 = sK2 )
| ~ spl4_4 ),
inference(avatar_component_clause,[status(thm)],[f93]) ).
thf(f93,definition,
( spl4_4
<=> ( sK5 = sK2 ) ),
introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition]) ).
thf(f107,plain,
~ spl4_3,
inference(avatar_contradiction_clause,[status(thm)],[f106]) ).
thf(f106,plain,
( $false
| ~ spl4_3 ),
inference(trivial_inequality_removal,[status(thm)],[f103]) ).
thf(f103,plain,
( ( $true = $false )
| ~ spl4_3 ),
inference(superposition,[status(thm)],[f28,f91]) ).
thf(f91,plain,
( ( ( sK0 @ sK2 )
= $false )
| ~ spl4_3 ),
inference(avatar_component_clause,[status(thm)],[f89]) ).
thf(f89,definition,
( spl4_3
<=> ( ( sK0 @ sK2 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition]) ).
thf(f28,plain,
( ( sK0 @ sK2 )
= $true ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f98,plain,
( spl4_2
| spl4_1 ),
inference(avatar_split_clause,[status(thm)],[f75,f80,f84]) ).
thf(f75,plain,
( ( ( sK0 @ sK3 )
= $false )
| ( sK3 = sK5 ) ),
inference(trivial_inequality_removal,[status(thm)],[f73]) ).
thf(f73,plain,
( ( ( sK0 @ sK3 )
= $false )
| ( sK3 = sK5 )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f31,f70]) ).
thf(f70,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK1 )
= $false )
| ( ( sK0 @ X0 )
= $false )
| ( sK5 = X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f68]) ).
thf(f68,plain,
! [X0: $i] :
( ( sK5 = X0 )
| ( $true = $false )
| ( ( in @ X0 @ sK1 )
= $false )
| ( ( sK0 @ X0 )
= $false ) ),
inference(superposition,[status(thm)],[f60,f64]) ).
thf(f64,plain,
! [X0: $i] :
( ( ( in @ X0 @ ( setadjoin @ sK5 @ emptyset ) )
= $true )
| ( ( in @ X0 @ sK1 )
= $false )
| ( ( sK0 @ X0 )
= $false ) ),
inference(superposition,[status(thm)],[f54,f45]) ).
thf(f45,plain,
( ( dsetconstr @ sK1 @ sK0 )
= ( setadjoin @ sK5 @ emptyset ) ),
inference(equality_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
( ( ( setadjoin @ sK5 @ emptyset )
= ( dsetconstr @ sK1 @ sK0 ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
( $true
= ( ( ( setadjoin @ sK5 @ emptyset )
= ( dsetconstr @ sK1 @ sK0 ) )
& ( in @ sK5 @ ( dsetconstr @ sK1 @ sK0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f41]) ).
thf(f41,plain,
( ( ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK1 @ sK0 ) )
& ( in @ Y0 @ ( dsetconstr @ sK1 @ sK0 ) ) )
@ sK5 )
= $true ),
inference(sigma_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK1 @ sK0 ) )
& ( in @ Y0 @ ( dsetconstr @ sK1 @ sK0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
( $true
= ( ^ [Y0: $i,Y1: $i > $o] :
( ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= Y2 )
& ( in @ Y3 @ Y2 ) ) )
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) )
@ sK1
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) ),
inference(definition_unfolding,[status(thm)],[f33,f36]) ).
thf(f36,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= Y2 )
& ( in @ Y3 @ Y2 ) ) )
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f25,f26]) ).
thf(f26,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
( singleton
= ( ^ [X0: $i] :
? [X1: $i] :
( ( in @ X1 @ X0 )
& ( ( setadjoin @ X1 @ emptyset )
= X0 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( singleton
= ( ^ [X0: $i] :
? [X2: $i] :
( ( in @ X2 @ X0 )
& ( ( setadjoin @ X2 @ emptyset )
= X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.oSlHkk0Jmm/DTF2THF_22247.p',singleton) ).
thf(f25,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,axiom,
( ex1
= ( ^ [X0: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.oSlHkk0Jmm/DTF2THF_22247.p',ex1) ).
thf(f33,plain,
( ( ex1 @ sK1
@ ^ [Y0: $i] : ( sK0 @ Y0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f54,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ( in @ X2 @ ( dsetconstr @ X1 @ X3 ) )
= $true )
| ( ( in @ X2 @ X1 )
= $false )
| ( ( X3 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ( in @ X2 @ X1 )
= $false )
| ( $true
= ( ( X3 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ X1 @ X3 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ( in @ X2 @ X1 )
=> ( ( X3 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ X1 @ X3 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f51]) ).
thf(f51,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ^ [Y0: $i > $o] :
( ( in @ X2 @ X1 )
=> ( ( Y0 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ X1 @ Y0 ) ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f50]) ).
thf(f50,plain,
! [X2: $i,X1: $i] :
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( in @ X2 @ X1 )
=> ( ( Y0 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ X1 @ Y0 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f49]) ).
thf(f49,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ Y0 @ X1 )
=> ( ( Y1 @ Y0 )
=> ( in @ Y0 @ ( dsetconstr @ X1 @ Y1 ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ Y0 @ X1 )
=> ( ( Y1 @ Y0 )
=> ( in @ Y0 @ ( dsetconstr @ X1 @ Y1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f47]) ).
thf(f47,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( in @ Y1 @ ( dsetconstr @ Y0 @ Y2 ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( in @ Y1 @ ( dsetconstr @ Y0 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f38]) ).
thf(f38,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f34,f24]) ).
thf(f24,plain,
( dsetconstrI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( dsetconstrI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
=> ( ( X0 @ X1 )
=> ( in @ X1
@ ( dsetconstr @ X2
@ ^ [X3: $i] : ( X0 @ X3 ) ) ) ) )
= dsetconstrI ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: $i > $o,X2: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) )
= dsetconstrI ),
file('/export/starexec/sandbox/tmp/tmp.oSlHkk0Jmm/DTF2THF_22247.p',dsetconstrI) ).
thf(f34,plain,
dsetconstrI = $true,
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f60,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) )
= $false )
| ( X1 = X2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
! [X2: $i,X1: $i] :
( ( ( X2 = X1 )
= $true )
| ( ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X2 = X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f57]) ).
thf(f57,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( Y0 = X1 ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( Y0 = X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f55]) ).
thf(f55,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f35,f27]) ).
thf(f27,plain,
( uniqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( uniqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
( uniqinunit
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X0 = X1 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( uniqinunit
= ( ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.oSlHkk0Jmm/DTF2THF_22247.p',uniqinunit) ).
thf(f35,plain,
uniqinunit = $true,
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f31,plain,
( $true
= ( in @ sK3 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f97,plain,
( spl4_4
| spl4_3 ),
inference(avatar_split_clause,[status(thm)],[f76,f89,f93]) ).
thf(f76,plain,
( ( ( sK0 @ sK2 )
= $false )
| ( sK5 = sK2 ) ),
inference(trivial_inequality_removal,[status(thm)],[f74]) ).
thf(f74,plain,
( ( ( sK0 @ sK2 )
= $false )
| ( $true = $false )
| ( sK5 = sK2 ) ),
inference(superposition,[status(thm)],[f32,f70]) ).
thf(f32,plain,
( $true
= ( in @ sK2 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU683^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n003.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 12:30:25 EST 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 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 : SEU683^2 : TPTP v9.2.1. Released v3.7.0.
% 0.16/0.39 % Domain : Set Theory
% 0.16/0.39 % Problem : Functions - Extensionality and Beta Reduction
% 0.16/0.39 % Version : Especial > Reduced > Especial.
% 0.16/0.39 % English : (! A:i.! phi:i>o.ex1 A (^ x:i.phi x) -> (! x:i.in x A ->
% 0.16/0.39 % (! y:i.in y A -> phi x -> phi y -> x = 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 : ZFC185l [Bro08]
% 0.16/0.39
% 0.16/0.39 % Status : Theorem
% 0.16/0.39 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.14 v6.1.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.60 v5.3.0, 0.80 v5.2.0, 0.60 v4.1.0, 0.67 v3.7.0
% 0.16/0.39 % Syntax : Number of formulae : 13 ( 4 unt; 8 typ; 4 def)
% 0.16/0.39 % Number of atoms : 21 ( 7 equ; 0 cnn)
% 0.16/0.39 % Maximal formula atoms : 6 ( 4 avg)
% 0.16/0.39 % Number of connectives : 40 ( 0 ~; 0 |; 1 &; 29 @)
% 0.16/0.39 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.16/0.39 % Maximal formula depth : 13 ( 3 avg)
% 0.16/0.39 % Number of types : 2 ( 0 usr)
% 0.16/0.39 % Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% 0.16/0.39 % Number of symbols : 9 ( 8 usr; 3 con; 0-2 aty)
% 0.16/0.39 % Number of variables : 16 ( 6 ^; 9 !; 1 ?; 16 :)
% 0.16/0.39 % SPC : TH0_THM_EQU_NAR
% 0.16/0.39
% 0.16/0.39 % Comments : http://mathgate.info/detsetitem.php?id=240
% 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(dsetconstrI_type,type,
% 0.16/0.39 dsetconstrI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(dsetconstrI,definition,
% 0.16/0.39 ( dsetconstrI
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( ( Xphi @ Xx )
% 0.16/0.39 => ( in @ Xx
% 0.16/0.39 @ ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(uniqinunit_type,type,
% 0.16/0.39 uniqinunit: $o ).
% 0.16/0.39
% 0.16/0.39 thf(uniqinunit,definition,
% 0.16/0.39 ( uniqinunit
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.16/0.39 => ( Xx = Xy ) ) ) ) ).
% 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(ex1_type,type,
% 0.16/0.39 ex1: $i > ( $i > $o ) > $o ).
% 0.16/0.39
% 0.16/0.39 thf(ex1,definition,
% 0.16/0.39 ( ex1
% 0.16/0.39 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( singleton
% 0.16/0.39 @ ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(ex1E2,conjecture,
% 0.16/0.39 ( dsetconstrI
% 0.16/0.39 => ( uniqinunit
% 0.16/0.39 => ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( ( ex1 @ A
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 => ! [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 @ Xx )
% 0.16/0.39 => ( ( Xphi @ Xy )
% 0.16/0.39 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 ------------------------
% 1.60/1.31 ---- Embedded in THF ---
% 1.60/1.31 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.60/1.31 %%% Generated on Tue Feb 24 12:30:26 EST 2026
% 1.60/1.31 %%% using '$$dhol' embedding, version 1.3.0.
% 1.60/1.31 %%% Logic specification used:
% 1.60/1.31 %%% thf(spec, logic, $$dhol).
% 1.60/1.31
% 1.60/1.31 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.oSlHkk0Jmm/DTF2DTF22247.p
% See solution above
% 1.60/1.31 ------------------------
% 1.60/1.32 ---- Cleaned THF ---
% 1.60/1.32 thf(in_type,type,
% 1.60/1.32 in: $i > $i > $o ).
% 1.60/1.32
% 1.60/1.32 thf(emptyset_type,type,
% 1.60/1.32 emptyset: $i ).
% 1.60/1.32
% 1.60/1.32 thf(setadjoin_type,type,
% 1.60/1.32 setadjoin: $i > $i > $i ).
% 1.60/1.32
% 1.60/1.32 thf(dsetconstr_type,type,
% 1.60/1.32 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.60/1.32
% 1.60/1.32 thf(dsetconstrI_type,type,
% 1.60/1.32 dsetconstrI: $o ).
% 1.60/1.32
% 1.60/1.32 thf(dsetconstrI,definition,
% 1.60/1.32 ( dsetconstrI
% 1.60/1.32 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.60/1.32 ( ( in @ Xx @ A )
% 1.60/1.32 => ( ( Xphi @ Xx )
% 1.60/1.32 => ( in @ Xx
% 1.60/1.32 @ ( dsetconstr @ A
% 1.60/1.32 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.60/1.32
% 1.60/1.32 thf(uniqinunit_type,type,
% 1.60/1.32 uniqinunit: $o ).
% 1.60/1.32
% 1.60/1.32 thf(uniqinunit,definition,
% 1.60/1.32 ( uniqinunit
% 1.60/1.32 = ( ! [Xx: $i,Xy: $i] :
% 1.60/1.32 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 1.60/1.32 => ( Xx = Xy ) ) ) ) ).
% 1.60/1.32
% 1.60/1.32 thf(singleton_type,type,
% 1.60/1.32 singleton: $i > $o ).
% 1.60/1.32
% 1.60/1.32 thf(singleton,definition,
% 1.60/1.32 ( singleton
% 1.60/1.32 = ( ^ [A: $i] :
% 1.60/1.32 ? [Xx: $i] :
% 1.60/1.32 ( ( in @ Xx @ A )
% 1.60/1.32 & ( A
% 1.60/1.32 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 1.60/1.32
% 1.60/1.32 thf(ex1_type,type,
% 1.60/1.32 ex1: $i > ( $i > $o ) > $o ).
% 1.60/1.32
% 1.60/1.32 thf(ex1,definition,
% 1.60/1.32 ( ex1
% 1.60/1.32 = ( ^ [A: $i,Xphi: $i > $o] :
% 1.60/1.32 ( singleton
% 1.60/1.32 @ ( dsetconstr @ A
% 1.60/1.32 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 1.60/1.32
% 1.60/1.32 thf(ex1E2,conjecture,
% 1.60/1.32 ( dsetconstrI
% 1.60/1.32 => ( uniqinunit
% 1.60/1.32 => ! [A: $i,Xphi: $i > $o] :
% 1.60/1.32 ( ( ex1 @ A
% 1.60/1.32 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.60/1.32 => ! [Xx: $i] :
% 1.60/1.32 ( ( in @ Xx @ A )
% 1.60/1.32 => ! [Xy: $i] :
% 1.60/1.32 ( ( in @ Xy @ A )
% 1.60/1.32 => ( ( Xphi @ Xx )
% 1.60/1.32 => ( ( Xphi @ Xy )
% 1.60/1.32 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 1.60/1.32 ------------------------
% 1.60/1.34 % (22346)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_22247 for (2999ds/27Mi)
% 1.60/1.34 % (22347)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_22247 for (2999ds/2Mi)
% 1.60/1.34 % (22344)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_22247 for (2999ds/183Mi)
% 1.60/1.34 % (22350)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_22247 for (2999ds/18Mi)
% 1.60/1.34 % (22345)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_22247 for (2999ds/4Mi)
% 1.60/1.34 % (22349)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_22247 for (2999ds/275Mi)
% 1.60/1.34 % (22348)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_22247 for (2999ds/2Mi)
% 1.60/1.34 % (22347)Instruction limit reached!
% 1.60/1.34 % (22347)------------------------------
% 1.60/1.34 % (22347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.34 % (22347)Termination reason: Unknown
% 1.60/1.34 % (22347)Termination phase: Property scanning
% 1.60/1.34
% 1.60/1.34 % (22347)Memory used [KB]: 895
% 1.60/1.34 % (22347)Time elapsed: 0.002 s
% 1.60/1.34 % (22347)Instructions burned: 2 (million)
% 1.60/1.34 % (22347)------------------------------
% 1.60/1.34 % (22347)------------------------------
% 1.60/1.34 % (22348)Instruction limit reached!
% 1.60/1.34 % (22348)------------------------------
% 1.60/1.34 % (22348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.34 % (22348)Termination reason: Unknown
% 1.60/1.34 % (22348)Termination phase: Property scanning
% 1.60/1.34
% 1.60/1.34 % (22348)Memory used [KB]: 1023
% 1.60/1.34 % (22348)Time elapsed: 0.003 s
% 1.60/1.34 % (22348)Instructions burned: 3 (million)
% 1.60/1.34 % (22348)------------------------------
% 1.60/1.34 % (22348)------------------------------
% 1.60/1.34 % (22345)Instruction limit reached!
% 1.60/1.34 % (22345)------------------------------
% 1.60/1.34 % (22345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.34 % (22345)Termination reason: Unknown
% 1.60/1.34 % (22345)Termination phase: Saturation
% 1.60/1.34
% 1.60/1.34 % (22345)Memory used [KB]: 5500
% 1.60/1.34 % (22345)Time elapsed: 0.004 s
% 1.60/1.34 % (22345)Instructions burned: 4 (million)
% 1.60/1.34 % (22345)------------------------------
% 1.60/1.34 % (22345)------------------------------
% 1.60/1.34 % (22349)Refutation not found, incomplete strategy
% 1.60/1.34 % (22349)------------------------------
% 1.60/1.34 % (22349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.34 % (22349)Termination reason: Refutation not found, incomplete strategy
% 1.60/1.34
% 1.60/1.34
% 1.60/1.34 % (22349)Memory used [KB]: 5500
% 1.60/1.34 % (22349)Time elapsed: 0.004 s
% 1.60/1.34 % (22349)Instructions burned: 4 (million)
% 1.60/1.34 % (22349)------------------------------
% 1.60/1.34 % (22349)------------------------------
% 1.60/1.35 % (22344)First to succeed.
% 1.60/1.35 % (22346)Also succeeded, but the first one will report.
% 1.60/1.35 % (22344)Refutation found. Thanks to Tanya!
% 1.60/1.35 % SZS status Theorem for DTF2THF_22247
% 1.60/1.35 % SZS output start Proof for DTF2THF_22247
% 1.60/1.35 thf(func_def_0, type, in: $i > $i > $o).
% 1.60/1.35 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.60/1.35 thf(func_def_3, type, dsetconstr: $i > ($i > $o) > $i).
% 1.60/1.35 thf(func_def_7, type, singleton: $i > $o).
% 1.60/1.35 thf(func_def_8, type, ex1: $i > ($i > $o) > $o).
% 1.60/1.35 thf(func_def_20, type, sK0: $i > $o).
% 1.60/1.35 thf(func_def_27, type, ph6: !>[X0: $tType]:(X0)).
% 1.60/1.35 thf(f124,plain,(
% 1.60/1.35 $false),
% 1.60/1.35 inference(avatar_sat_refutation,[status(thm)],[f97,f98,f107,f116,f123])).
% 1.60/1.35 thf(f123,plain,(
% 1.60/1.35 ~spl4_1),
% 1.60/1.35 inference(avatar_contradiction_clause,[status(thm)],[f122])).
% 1.60/1.35 thf(f122,plain,(
% 1.60/1.35 $false | ~spl4_1),
% 1.60/1.35 inference(trivial_inequality_removal,[status(thm)],[f118])).
% 1.60/1.35 thf(f118,plain,(
% 1.60/1.35 ($true = $false) | ~spl4_1),
% 1.60/1.35 inference(superposition,[status(thm)],[f82,f30])).
% 1.60/1.35 thf(f30,plain,(
% 1.60/1.35 ((sK0 @ sK3) = $true)),
% 1.60/1.35 inference(cnf_transformation,[status(thm)],[f23])).
% 1.60/1.35 thf(f23,plain,(
% 1.60/1.35 (uniqinunit = $true) & (dsetconstrI = $true) & (((ex1 @ sK1 @ (^[Y0 : $i]: (sK0 @ Y0))) = $true) & (($true = (in @ sK2 @ sK1)) & (($true = (in @ sK3 @ sK1)) & ((sK0 @ sK3) = $true) & (sK3 != sK2) & ((sK0 @ sK2) = $true))))),
% 1.60/1.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f19,f22,f21,f20])).
% 1.60/1.35 thf(f20,plain,(
% 1.60/1.35 ? [X0 : $i > $o,X1 : $i] : (((ex1 @ X1 @ (^[Y0 : $i]: (X0 @ Y0))) = $true) & ? [X2 : $i] : (($true = (in @ X2 @ X1)) & ? [X3 : $i] : (((in @ X3 @ X1) = $true) & ($true = (X0 @ X3)) & (X2 != X3) & ($true = (X0 @ X2))))) => (((ex1 @ sK1 @ (^[Y0 : $i]: (sK0 @ Y0))) = $true) & ? [X2 : $i] : (($true = (in @ X2 @ sK1)) & ? [X3 : $i] : (((in @ X3 @ sK1) = $true) & ($true = (sK0 @ X3)) & (X2 != X3) & ($true = (sK0 @ X2)))))),
% 1.60/1.35 introduced(definition,[],[choice_axiom])).
% 1.60/1.35 thf(f21,plain,(
% 1.60/1.35 ? [X2 : $i] : (($true = (in @ X2 @ sK1)) & ? [X3 : $i] : (((in @ X3 @ sK1) = $true) & ($true = (sK0 @ X3)) & (X2 != X3) & ($true = (sK0 @ X2)))) => (($true = (in @ sK2 @ sK1)) & ? [X3 : $i] : (((in @ X3 @ sK1) = $true) & ($true = (sK0 @ X3)) & (sK2 != X3) & ((sK0 @ sK2) = $true)))),
% 1.60/1.35 introduced(definition,[],[choice_axiom])).
% 1.60/1.35 thf(f22,plain,(
% 1.60/1.35 ? [X3 : $i] : (((in @ X3 @ sK1) = $true) & ($true = (sK0 @ X3)) & (sK2 != X3) & ((sK0 @ sK2) = $true)) => (($true = (in @ sK3 @ sK1)) & ((sK0 @ sK3) = $true) & (sK3 != sK2) & ((sK0 @ sK2) = $true))),
% 1.60/1.35 introduced(definition,[],[choice_axiom])).
% 1.60/1.35 thf(f19,plain,(
% 1.60/1.35 (uniqinunit = $true) & (dsetconstrI = $true) & ? [X0 : $i > $o,X1 : $i] : (((ex1 @ X1 @ (^[Y0 : $i]: (X0 @ Y0))) = $true) & ? [X2 : $i] : (($true = (in @ X2 @ X1)) & ? [X3 : $i] : (((in @ X3 @ X1) = $true) & ($true = (X0 @ X3)) & (X2 != X3) & ($true = (X0 @ X2)))))),
% 1.60/1.35 inference(flattening,[status(thm)],[f18])).
% 1.60/1.35 thf(f18,plain,(
% 1.60/1.35 (? [X0 : $i > $o,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : ((((X2 != X3) & ($true = (X0 @ X3))) & ($true = (X0 @ X2))) & ((in @ X3 @ X1) = $true)) & ($true = (in @ X2 @ X1))) & ((ex1 @ X1 @ (^[Y0 : $i]: (X0 @ Y0))) = $true)) & (uniqinunit = $true)) & (dsetconstrI = $true)),
% 1.60/1.35 inference(ennf_transformation,[status(thm)],[f17])).
% 1.60/1.35 thf(f17,plain,(
% 1.60/1.35 ~((dsetconstrI = $true) => ((uniqinunit = $true) => ! [X0 : $i > $o,X1 : $i] : (((ex1 @ X1 @ (^[Y0 : $i]: (X0 @ Y0))) = $true) => ! [X2 : $i] : (($true = (in @ X2 @ X1)) => ! [X3 : $i] : (((in @ X3 @ X1) = $true) => (($true = (X0 @ X2)) => (($true = (X0 @ X3)) => (X2 = X3))))))))),
% 1.60/1.35 inference(rectify,[status(thm)],[f11])).
% 1.60/1.35 thf(f11,plain,(
% 1.60/1.35 ~((dsetconstrI = $true) => ((uniqinunit = $true) => ! [X0 : $i > $o,X1 : $i] : (((ex1 @ X1 @ (^[Y0 : $i]: (X0 @ Y0))) = $true) => ! [X3 : $i] : (((in @ X3 @ X1) = $true) => ! [X4 : $i] : (((in @ X4 @ X1) = $true) => (($true = (X0 @ X3)) => (($true = (X0 @ X4)) => (X3 = X4))))))))),
% 1.60/1.35 inference(fool_elimination,[status(thm)],[f10])).
% 1.60/1.35 thf(f10,plain,(
% 1.60/1.35 ~(dsetconstrI => (uniqinunit => ! [X0 : $i > $o,X1 : $i] : ((ex1 @ X1 @ (^[X2 : $i] : (X0 @ X2))) => ! [X3 : $i] : ((in @ X3 @ X1) => ! [X4 : $i] : ((in @ X4 @ X1) => ((X0 @ X3) => ((X0 @ X4) => (X3 = X4))))))))),
% 1.60/1.35 inference(rectify,[status(thm)],[f6])).
% 1.60/1.35 thf(f6,negated_conjecture,(
% 1.60/1.35 ~(dsetconstrI => (uniqinunit => ! [X1 : $i > $o,X0 : $i] : ((ex1 @ X0 @ (^[X2 : $i] : (X1 @ X2))) => ! [X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => ((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))))))),
% 1.60/1.35 inference(negated_conjecture,[status(cth)],[f5])).
% 1.60/1.35 thf(f5,conjecture,(
% 1.60/1.35 dsetconstrI => (uniqinunit => ! [X1 : $i > $o,X0 : $i] : ((ex1 @ X0 @ (^[X2 : $i] : (X1 @ X2))) => ! [X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => ((X1 @ X2) => ((X1 @ X3) => (X2 = X3)))))))),
% 1.60/1.35 file('/export/starexec/sandbox/tmp/tmp.oSlHkk0Jmm/DTF2THF_22247.p',ex1E2)).
% 1.60/1.35 thf(f82,plain,(
% 1.60/1.35 ((sK0 @ sK3) = $false) | ~spl4_1),
% 1.60/1.35 inference(avatar_component_clause,[status(thm)],[f80])).
% 1.60/1.35 thf(f80,definition,(
% 1.60/1.35 spl4_1 <=> ((sK0 @ sK3) = $false)),
% 1.60/1.35 introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition])).
% 1.60/1.35 thf(f116,plain,(
% 1.60/1.35 ~spl4_2 | ~spl4_4),
% 1.60/1.35 inference(avatar_contradiction_clause,[status(thm)],[f115])).
% 1.60/1.35 thf(f115,plain,(
% 1.60/1.35 $false | (~spl4_2 | ~spl4_4)),
% 1.60/1.35 inference(subsumption_resolution,[status(thm)],[f108,f29])).
% 1.60/1.35 thf(f29,plain,(
% 1.60/1.35 (sK3 != sK2)),
% 1.60/1.35 inference(cnf_transformation,[status(thm)],[f23])).
% 1.60/1.35 thf(f108,plain,(
% 1.60/1.35 (sK3 = sK2) | (~spl4_2 | ~spl4_4)),
% 1.60/1.35 inference(superposition,[status(thm)],[f95,f86])).
% 1.60/1.35 thf(f86,plain,(
% 1.60/1.35 (sK3 = sK5) | ~spl4_2),
% 1.60/1.35 inference(avatar_component_clause,[status(thm)],[f84])).
% 1.60/1.35 thf(f84,definition,(
% 1.60/1.35 spl4_2 <=> (sK3 = sK5)),
% 1.60/1.35 introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition])).
% 1.60/1.35 thf(f95,plain,(
% 1.60/1.35 (sK5 = sK2) | ~spl4_4),
% 1.60/1.35 inference(avatar_component_clause,[status(thm)],[f93])).
% 1.60/1.35 thf(f93,definition,(
% 1.60/1.35 spl4_4 <=> (sK5 = sK2)),
% 1.60/1.35 introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition])).
% 1.60/1.35 thf(f107,plain,(
% 1.60/1.35 ~spl4_3),
% 1.60/1.35 inference(avatar_contradiction_clause,[status(thm)],[f106])).
% 1.60/1.35 thf(f106,plain,(
% 1.60/1.35 $false | ~spl4_3),
% 1.60/1.35 inference(trivial_inequality_removal,[status(thm)],[f103])).
% 1.60/1.35 thf(f103,plain,(
% 1.60/1.35 ($true = $false) | ~spl4_3),
% 1.60/1.35 inference(superposition,[status(thm)],[f28,f91])).
% 1.60/1.35 thf(f91,plain,(
% 1.60/1.35 ((sK0 @ sK2) = $false) | ~spl4_3),
% 1.60/1.35 inference(avatar_component_clause,[status(thm)],[f89])).
% 1.60/1.35 thf(f89,definition,(
% 1.60/1.35 spl4_3 <=> ((sK0 @ sK2) = $false)),
% 1.60/1.35 introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition])).
% 1.60/1.35 thf(f28,plain,(
% 1.60/1.35 ((sK0 @ sK2) = $true)),
% 1.60/1.35 inference(cnf_transformation,[status(thm)],[f23])).
% 1.60/1.35 thf(f98,plain,(
% 1.60/1.35 spl4_2 | spl4_1),
% 1.60/1.35 inference(avatar_split_clause,[status(thm)],[f75,f80,f84])).
% 1.60/1.35 thf(f75,plain,(
% 1.60/1.35 ((sK0 @ sK3) = $false) | (sK3 = sK5)),
% 1.60/1.35 inference(trivial_inequality_removal,[status(thm)],[f73])).
% 1.60/1.35 thf(f73,plain,(
% 1.60/1.35 ((sK0 @ sK3) = $false) | (sK3 = sK5) | ($true = $false)),
% 1.60/1.35 inference(superposition,[status(thm)],[f31,f70])).
% 1.60/1.35 thf(f70,plain,(
% 1.60/1.35 ( ! [X0 : $i] : (((in @ X0 @ sK1) = $false) | ((sK0 @ X0) = $false) | (sK5 = X0)) )),
% 1.60/1.35 inference(trivial_inequality_removal,[status(thm)],[f68])).
% 1.60/1.35 thf(f68,plain,(
% 1.60/1.35 ( ! [X0 : $i] : ((sK5 = X0) | ($true = $false) | ((in @ X0 @ sK1) = $false) | ((sK0 @ X0) = $false)) )),
% 1.60/1.35 inference(superposition,[status(thm)],[f60,f64])).
% 1.60/1.35 thf(f64,plain,(
% 1.60/1.35 ( ! [X0 : $i] : (((in @ X0 @ (setadjoin @ sK5 @ emptyset)) = $true) | ((in @ X0 @ sK1) = $false) | ((sK0 @ X0) = $false)) )),
% 1.60/1.35 inference(superposition,[status(thm)],[f54,f45])).
% 1.60/1.35 thf(f45,plain,(
% 1.60/1.35 ((dsetconstr @ sK1 @ sK0) = (setadjoin @ sK5 @ emptyset))),
% 1.60/1.35 inference(equality_proxy_clausification,[status(thm)],[f44])).
% 1.60/1.35 thf(f44,plain,(
% 1.60/1.35 (((setadjoin @ sK5 @ emptyset) = (dsetconstr @ sK1 @ sK0)) = $true)),
% 1.60/1.35 inference(binary_proxy_clausification,[status(thm)],[f42])).
% 1.60/1.35 thf(f42,plain,(
% 1.60/1.35 ($true = (((setadjoin @ sK5 @ emptyset) = (dsetconstr @ sK1 @ sK0)) & (in @ sK5 @ (dsetconstr @ sK1 @ sK0))))),
% 1.60/1.35 inference(beta_eta_normalization,[status(thm)],[f41])).
% 1.60/1.35 thf(f41,plain,(
% 1.60/1.35 (((^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK1 @ sK0)) & (in @ Y0 @ (dsetconstr @ sK1 @ sK0)))) @ sK5) = $true)),
% 1.60/1.35 inference(sigma_clausification,[status(thm)],[f40])).
% 1.60/1.35 thf(f40,plain,(
% 1.60/1.35 ((?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK1 @ sK0)) & (in @ Y0 @ (dsetconstr @ sK1 @ sK0))))) = $true)),
% 1.60/1.35 inference(beta_eta_normalization,[status(thm)],[f39])).
% 1.60/1.35 thf(f39,plain,(
% 1.60/1.35 ($true = ((^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = Y2) & (in @ Y3 @ Y2))))) @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))) @ sK1 @ (^[Y0 : $i]: (sK0 @ Y0))))),
% 1.60/1.35 inference(definition_unfolding,[status(thm)],[f33,f36])).
% 1.60/1.35 thf(f36,plain,(
% 1.60/1.35 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = Y2) & (in @ Y3 @ Y2))))) @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 1.60/1.35 inference(definition_unfolding,[status(thm)],[f25,f26])).
% 1.60/1.35 thf(f26,plain,(
% 1.60/1.35 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0))))))),
% 1.60/1.35 inference(cnf_transformation,[status(thm)],[f13])).
% 1.60/1.35 thf(f13,plain,(
% 1.60/1.35 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0))))))),
% 1.60/1.35 inference(fool_elimination,[status(thm)],[f12])).
% 1.60/1.35 thf(f12,plain,(
% 1.60/1.35 (singleton = (^[X0 : $i] : (? [X1 : $i] : ((in @ X1 @ X0) & ((setadjoin @ X1 @ emptyset) = X0)))))),
% 1.60/1.35 inference(rectify,[status(thm)],[f3])).
% 1.60/1.35 thf(f3,axiom,(
% 1.60/1.35 (singleton = (^[X0 : $i] : (? [X2 : $i] : ((in @ X2 @ X0) & ((setadjoin @ X2 @ emptyset) = X0)))))),
% 1.60/1.35 file('/export/starexec/sandbox/tmp/tmp.oSlHkk0Jmm/DTF2THF_22247.p',singleton)).
% 1.60/1.35 thf(f25,plain,(
% 1.60/1.35 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 1.60/1.35 inference(cnf_transformation,[status(thm)],[f16])).
% 1.60/1.35 thf(f16,plain,(
% 1.60/1.35 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 1.60/1.35 inference(fool_elimination,[status(thm)],[f4])).
% 1.60/1.35 thf(f4,axiom,(
% 1.60/1.35 (ex1 = (^[X0 : $i, X1 : $i > $o] : (singleton @ (dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2))))))),
% 1.60/1.35 file('/export/starexec/sandbox/tmp/tmp.oSlHkk0Jmm/DTF2THF_22247.p',ex1)).
% 1.60/1.35 thf(f33,plain,(
% 1.60/1.35 ((ex1 @ sK1 @ (^[Y0 : $i]: (sK0 @ Y0))) = $true)),
% 1.60/1.35 inference(cnf_transformation,[status(thm)],[f23])).
% 1.60/1.35 thf(f54,plain,(
% 1.60/1.35 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (((in @ X2 @ (dsetconstr @ X1 @ X3)) = $true) | ((in @ X2 @ X1) = $false) | ((X3 @ X2) = $false)) )),
% 1.60/1.35 inference(binary_proxy_clausification,[status(thm)],[f53])).
% 1.60/1.35 thf(f53,plain,(
% 1.60/1.35 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (((in @ X2 @ X1) = $false) | ($true = ((X3 @ X2) => (in @ X2 @ (dsetconstr @ X1 @ X3))))) )),
% 1.60/1.35 inference(binary_proxy_clausification,[status(thm)],[f52])).
% 1.60/1.35 thf(f52,plain,(
% 1.60/1.35 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : ((((in @ X2 @ X1) => ((X3 @ X2) => (in @ X2 @ (dsetconstr @ X1 @ X3)))) = $true)) )),
% 1.60/1.35 inference(beta_eta_normalization,[status(thm)],[f51])).
% 1.60/1.35 thf(f51,plain,(
% 1.60/1.35 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : ((((^[Y0 : $i > $o]: ((in @ X2 @ X1) => ((Y0 @ X2) => (in @ X2 @ (dsetconstr @ X1 @ Y0))))) @ X3) = $true)) )),
% 1.60/1.35 inference(pi_clausification,[status(thm)],[f50])).
% 1.60/1.35 thf(f50,plain,(
% 1.60/1.35 ( ! [X2 : $i,X1 : $i] : (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((in @ X2 @ X1) => ((Y0 @ X2) => (in @ X2 @ (dsetconstr @ X1 @ Y0)))))) = $true)) )),
% 1.60/1.35 inference(beta_eta_normalization,[status(thm)],[f49])).
% 1.60/1.35 thf(f49,plain,(
% 1.60/1.35 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ X1) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ X1 @ Y1))))))) @ X2) = $true)) )),
% 1.60/1.35 inference(pi_clausification,[status(thm)],[f48])).
% 1.60/1.35 thf(f48,plain,(
% 1.60/1.35 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ X1) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ X1 @ Y1)))))))))) )),
% 1.60/1.35 inference(beta_eta_normalization,[status(thm)],[f47])).
% 1.60/1.35 thf(f47,plain,(
% 1.60/1.35 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2))))))))) @ X1))) )),
% 1.60/1.35 inference(pi_clausification,[status(thm)],[f46])).
% 1.60/1.35 thf(f46,plain,(
% 1.60/1.35 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) = $true)),
% 1.60/1.35 inference(beta_eta_normalization,[status(thm)],[f38])).
% 1.60/1.35 thf(f38,plain,(
% 1.60/1.35 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))) = $true)),
% 1.60/1.35 inference(definition_unfolding,[status(thm)],[f34,f24])).
% 1.60/1.35 thf(f24,plain,(
% 1.60/1.35 (dsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))))),
% 1.60/1.35 inference(cnf_transformation,[status(thm)],[f15])).
% 1.60/1.35 thf(f15,plain,(
% 1.60/1.35 (dsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))))),
% 1.60/1.35 inference(fool_elimination,[status(thm)],[f14])).
% 1.60/1.35 thf(f14,plain,(
% 1.60/1.35 (! [X0 : $i > $o,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => ((X0 @ X1) => (in @ X1 @ (dsetconstr @ X2 @ (^[X3 : $i] : (X0 @ X3)))))) = dsetconstrI)),
% 1.60/1.35 inference(rectify,[status(thm)],[f1])).
% 1.60/1.35 thf(f1,axiom,(
% 1.60/1.35 (! [X1 : $i > $o,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))))) = dsetconstrI)),
% 1.60/1.35 file('/export/starexec/sandbox/tmp/tmp.oSlHkk0Jmm/DTF2THF_22247.p',dsetconstrI)).
% 1.60/1.35 thf(f34,plain,(
% 1.60/1.35 (dsetconstrI = $true)),
% 1.60/1.35 inference(cnf_transformation,[status(thm)],[f23])).
% 1.60/1.35 thf(f60,plain,(
% 1.60/1.35 ( ! [X2 : $i,X1 : $i] : (((in @ X2 @ (setadjoin @ X1 @ emptyset)) = $false) | (X1 = X2)) )),
% 1.60/1.35 inference(equality_proxy_clausification,[status(thm)],[f59])).
% 1.60/1.35 thf(f59,plain,(
% 1.60/1.35 ( ! [X2 : $i,X1 : $i] : (((X2 = X1) = $true) | ((in @ X2 @ (setadjoin @ X1 @ emptyset)) = $false)) )),
% 1.60/1.35 inference(binary_proxy_clausification,[status(thm)],[f58])).
% 1.60/1.35 thf(f58,plain,(
% 1.60/1.35 ( ! [X2 : $i,X1 : $i] : ((((in @ X2 @ (setadjoin @ X1 @ emptyset)) => (X2 = X1)) = $true)) )),
% 1.60/1.35 inference(beta_eta_normalization,[status(thm)],[f57])).
% 1.60/1.35 thf(f57,plain,(
% 1.60/1.35 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ X1 @ emptyset)) => (Y0 = X1))) @ X2))) )),
% 1.60/1.35 inference(pi_clausification,[status(thm)],[f56])).
% 1.60/1.35 thf(f56,plain,(
% 1.60/1.35 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ X1 @ emptyset)) => (Y0 = X1)))) = $true)) )),
% 1.60/1.35 inference(beta_eta_normalization,[status(thm)],[f55])).
% 1.60/1.35 thf(f55,plain,(
% 1.60/1.35 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0))))) @ X1))) )),
% 1.60/1.35 inference(pi_clausification,[status(thm)],[f37])).
% 1.60/1.35 thf(f37,plain,(
% 1.60/1.35 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) = $true)),
% 1.60/1.35 inference(definition_unfolding,[status(thm)],[f35,f27])).
% 1.60/1.35 thf(f27,plain,(
% 1.60/1.35 (uniqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))))),
% 1.60/1.35 inference(cnf_transformation,[status(thm)],[f9])).
% 1.60/1.35 thf(f9,plain,(
% 1.60/1.35 (uniqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))))),
% 1.60/1.35 inference(fool_elimination,[status(thm)],[f8])).
% 1.60/1.35 thf(f8,plain,(
% 1.60/1.35 (uniqinunit = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1)))),
% 1.60/1.35 inference(rectify,[status(thm)],[f2])).
% 1.60/1.35 thf(f2,axiom,(
% 1.60/1.35 (uniqinunit = ! [X2 : $i,X3 : $i] : ((in @ X2 @ (setadjoin @ X3 @ emptyset)) => (X2 = X3)))),
% 1.60/1.35 file('/export/starexec/sandbox/tmp/tmp.oSlHkk0Jmm/DTF2THF_22247.p',uniqinunit)).
% 1.60/1.35 thf(f35,plain,(
% 1.60/1.35 (uniqinunit = $true)),
% 1.60/1.35 inference(cnf_transformation,[status(thm)],[f23])).
% 1.60/1.35 thf(f31,plain,(
% 1.60/1.35 ($true = (in @ sK3 @ sK1))),
% 1.60/1.35 inference(cnf_transformation,[status(thm)],[f23])).
% 1.60/1.35 thf(f97,plain,(
% 1.60/1.35 spl4_4 | spl4_3),
% 1.60/1.35 inference(avatar_split_clause,[status(thm)],[f76,f89,f93])).
% 1.60/1.35 thf(f76,plain,(
% 1.60/1.35 ((sK0 @ sK2) = $false) | (sK5 = sK2)),
% 1.60/1.35 inference(trivial_inequality_removal,[status(thm)],[f74])).
% 1.60/1.35 thf(f74,plain,(
% 1.60/1.35 ((sK0 @ sK2) = $false) | ($true = $false) | (sK5 = sK2)),
% 1.60/1.35 inference(superposition,[status(thm)],[f32,f70])).
% 1.60/1.35 thf(f32,plain,(
% 1.60/1.35 ($true = (in @ sK2 @ sK1))),
% 1.60/1.35 inference(cnf_transformation,[status(thm)],[f23])).
% 1.60/1.35 % SZS output end Proof for DTF2THF_22247
% 1.60/1.35 % (22344)------------------------------
% 1.60/1.35 % (22344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.35 % (22344)Termination reason: Refutation
% 1.60/1.35
% 1.60/1.35 % (22344)Memory used [KB]: 5628
% 1.60/1.35 % (22344)Time elapsed: 0.009 s
% 1.60/1.35 % (22344)Instructions burned: 10 (million)
% 1.60/1.35 % (22344)------------------------------
% 1.60/1.35 % (22344)------------------------------
% 1.60/1.35 % (22343)Success in time 0.022 s
%------------------------------------------------------------------------------