%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO540^1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:54:30 AM UTC 2026
% Result : Theorem 1.63s 1.34s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 50 ( 15 unt; 0 typ; 3 def)
% Number of atoms : 566 ( 212 equ; 0 cnn)
% Maximal formula atoms : 4 ( 11 avg)
% Number of connectives : 399 ( 97 ~; 105 |; 121 &; 72 @)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 7 con; 0-3 aty)
% Number of variables : 95 ( 60 ^; 31 !; 4 ?; 95 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
eps: ( $i > $o ) > $i ).
thf(func_def_2,type,
if: $o > $i > $i > $i ).
thf(func_def_3,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_18,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f147,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f93,f95,f99,f146]) ).
thf(f146,plain,
( spl2_2
| spl2_4
| ~ spl2_1 ),
inference(avatar_split_clause,[status(thm)],[f145,f72,f84,f76]) ).
thf(f76,definition,
( spl2_2
<=> ! [X1: $i] : ( sK1 != X1 ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f84,definition,
( spl2_4
<=> ( ( eps
@ ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& sK0 )
| ( ( sK1 = Y0 )
& ~ sK0 ) ) )
= sK1 ) ),
introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition]) ).
thf(f72,definition,
( spl2_1
<=> ( sK0 = $false ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f145,plain,
( ! [X1: $i] :
( ( ( eps
@ ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& sK0 )
| ( ( sK1 = Y0 )
& ~ sK0 ) ) )
= sK1 )
| ( sK1 != X1 ) )
| ~ spl2_1 ),
inference(trivial_inequality_removal,[status(thm)],[f144]) ).
thf(f144,plain,
( ! [X1: $i] :
( ( $false = $true )
| ( ( eps
@ ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& sK0 )
| ( ( sK1 = Y0 )
& ~ sK0 ) ) )
= sK1 )
| ( sK1 != X1 ) )
| ~ spl2_1 ),
inference(forward_demodulation,[status(thm)],[f136,f74]) ).
thf(f74,plain,
( ( sK0 = $false )
| ~ spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f72]) ).
thf(f136,plain,
! [X1: $i] :
( ( sK0 = $true )
| ( ( eps
@ ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& sK0 )
| ( ( sK1 = Y0 )
& ~ sK0 ) ) )
= sK1 )
| ( sK1 != X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f135]) ).
thf(f135,plain,
! [X1: $i] :
( ( ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& sK0 )
| ( ( sK1 = Y0 )
& ~ sK0 ) ) ) )
= $true )
| ( sK0 = $true )
| ( sK1 != X1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f133]) ).
thf(f133,plain,
! [X1: $i] :
( ( sK0 = $true )
| ( sK1 != X1 )
| ( ( ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& sK0 )
| ( ( sK1 = Y0 )
& ~ sK0 ) ) ) )
& ~ sK0 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f132]) ).
thf(f132,plain,
! [X1: $i] :
( ( sK1 != X1 )
| ( sK0 = $true )
| ( sK0 = $true )
| ( ( ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& sK0 )
| ( ( sK1 = Y0 )
& ~ sK0 ) ) ) )
& ~ sK0 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f123]) ).
thf(f123,plain,
! [X1: $i] :
( ( sK0 = $true )
| ( sK1 != X1 )
| ( $false = ( ~ sK0 ) )
| ( ( ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& sK0 )
| ( ( sK1 = Y0 )
& ~ sK0 ) ) ) )
& ~ sK0 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f122]) ).
thf(f122,plain,
! [X1: $i] :
( ( sK1 != X1 )
| ( ( ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& sK0 )
| ( ( sK1 = Y0 )
& ~ sK0 ) ) ) )
& sK0 )
= $true )
| ( $false = ( ~ sK0 ) )
| ( ( ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& sK0 )
| ( ( sK1 = Y0 )
& ~ sK0 ) ) ) )
& ~ sK0 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f121]) ).
thf(f121,plain,
! [X1: $i] :
( ( sK1 != X1 )
| ( ( ( ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& sK0 )
| ( ( sK1 = Y0 )
& ~ sK0 ) ) ) )
& sK0 )
| ( ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& sK0 )
| ( ( sK1 = Y0 )
& ~ sK0 ) ) ) )
& ~ sK0 ) )
= $true )
| ( $false = ( ~ sK0 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f120]) ).
thf(f120,plain,
! [X1: $i] :
( ( $false
= ( sK1 = X1 ) )
| ( ( ( ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& sK0 )
| ( ( sK1 = Y0 )
& ~ sK0 ) ) ) )
& sK0 )
| ( ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& sK0 )
| ( ( sK1 = Y0 )
& ~ sK0 ) ) ) )
& ~ sK0 ) )
= $true )
| ( $false = ( ~ sK0 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f101]) ).
thf(f101,plain,
! [X1: $i] :
( ( ( ( sK1 = X1 )
& ~ sK0 )
= $false )
| ( ( ( ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& sK0 )
| ( ( sK1 = Y0 )
& ~ sK0 ) ) ) )
& sK0 )
| ( ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& sK0 )
| ( ( sK1 = Y0 )
& ~ sK0 ) ) ) )
& ~ sK0 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f100]) ).
thf(f100,plain,
! [X1: $i] :
( ( $false
= ( ( ( sK1 = X1 )
& sK0 )
| ( ( sK1 = X1 )
& ~ sK0 ) ) )
| ( ( ( ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& sK0 )
| ( ( sK1 = Y0 )
& ~ sK0 ) ) ) )
& sK0 )
| ( ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& sK0 )
| ( ( sK1 = Y0 )
& ~ sK0 ) ) ) )
& ~ sK0 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f96]) ).
thf(f96,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& sK0 )
| ( ( sK1 = Y0 )
& ~ sK0 ) )
@ X1 ) )
| ( ( ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& sK0 )
| ( ( sK1 = Y0 )
& ~ sK0 ) )
@ ( eps
@ ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& sK0 )
| ( ( sK1 = Y0 )
& ~ sK0 ) ) ) )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f99,plain,
~ spl2_4,
inference(avatar_contradiction_clause,[status(thm)],[f98]) ).
thf(f98,plain,
( $false
| ~ spl2_4 ),
inference(trivial_inequality_removal,[status(thm)],[f97]) ).
thf(f97,plain,
( ( sK1 != sK1 )
| ~ spl2_4 ),
inference(superposition,[status(thm)],[f19,f86]) ).
thf(f86,plain,
( ( ( eps
@ ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& sK0 )
| ( ( sK1 = Y0 )
& ~ sK0 ) ) )
= sK1 )
| ~ spl2_4 ),
inference(avatar_component_clause,[status(thm)],[f84]) ).
thf(f19,plain,
( ( eps
@ ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& sK0 )
| ( ( sK1 = Y0 )
& ~ sK0 ) ) )
!= sK1 ),
inference(beta_eta_normalization,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ^ [Y0: $o,Y1: $i,Y2: $i] :
( eps
@ ^ [Y3: $i] :
( ( ( Y1 = Y3 )
& Y0 )
| ( ( Y2 = Y3 )
& ~ Y0 ) ) )
@ sK0
@ sK1
@ sK1 )
!= sK1 ),
inference(definition_unfolding,[status(thm)],[f15,f16]) ).
thf(f16,plain,
( if
= ( ^ [Y0: $o,Y1: $i,Y2: $i] :
( eps
@ ^ [Y3: $i] :
( ( ( Y1 = Y3 )
& Y0 )
| ( ( Y2 = Y3 )
& ~ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( if
= ( ^ [Y0: $o,Y1: $i,Y2: $i] :
( eps
@ ^ [Y3: $i] :
( ( ( Y1 = Y3 )
& Y0 )
| ( ( Y2 = Y3 )
& ~ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ^ [X0: $o,X1: $i,X2: $i] :
( eps
@ ^ [X3: $i] :
( ( ~ X0
& ( X2 = X3 ) )
| ( X0
& ( X1 = X3 ) ) ) ) )
= if ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( ( ^ [X2: $o,X1: $i,X3: $i] :
( eps
@ ^ [X4: $i] :
( ( ~ X2
& ( X3 = X4 ) )
| ( X2
& ( X1 = X4 ) ) ) ) )
= if ),
file('/export/starexec/sandbox/tmp/tmp.O0PMKi6bfH/DTF2THF_19544.p',ifd) ).
thf(f15,plain,
( ( if @ sK0 @ sK1 @ sK1 )
!= sK1 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( if @ sK0 @ sK1 @ sK1 )
!= sK1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f11,f13]) ).
thf(f13,plain,
( ? [X0: $o,X1: $i] :
( ( if @ X0 @ X1 @ X1 )
!= X1 )
=> ( ( if @ sK0 @ sK1 @ sK1 )
!= sK1 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
? [X0: $o,X1: $i] :
( ( if @ X0 @ X1 @ X1 )
!= X1 ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
~ ! [X0: $o,X1: $i] :
( ( if @ X0 @ X1 @ X1 )
= X1 ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X2: $o,X1: $i] :
( ( if @ X2 @ X1 @ X1 )
= X1 ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
! [X2: $o,X1: $i] :
( ( if @ X2 @ X1 @ X1 )
= X1 ),
file('/export/starexec/sandbox/tmp/tmp.O0PMKi6bfH/DTF2THF_19544.p',conj) ).
thf(f95,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[status(thm)],[f94]) ).
thf(f94,plain,
( $false
| ~ spl2_2 ),
inference(equality_resolution,[status(thm)],[f77]) ).
thf(f77,plain,
( ! [X1: $i] : ( sK1 != X1 )
| ~ spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f76]) ).
thf(f93,plain,
( spl2_1
| spl2_4
| spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f32,f76,f84,f72]) ).
thf(f32,plain,
! [X1: $i] :
( ( sK0 = $false )
| ( ( eps
@ ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& sK0 )
| ( ( sK1 = Y0 )
& ~ sK0 ) ) )
= sK1 )
| ( sK1 != X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
! [X1: $i] :
( ( sK0 = $false )
| ( $false
= ( sK1 = X1 ) )
| ( ( eps
@ ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& sK0 )
| ( ( sK1 = Y0 )
& ~ sK0 ) ) )
= sK1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
! [X1: $i] :
( ( ( eps
@ ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& sK0 )
| ( ( sK1 = Y0 )
& ~ sK0 ) ) )
= sK1 )
| ( ( ( sK1 = X1 )
& sK0 )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
! [X1: $i] :
( ( ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& sK0 )
| ( ( sK1 = Y0 )
& ~ sK0 ) ) ) )
= $true )
| ( ( ( sK1 = X1 )
& sK0 )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f28]) ).
thf(f28,plain,
! [X1: $i] :
( ( ( ( sK1 = X1 )
& sK0 )
= $false )
| ( ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& sK0 )
| ( ( sK1 = Y0 )
& ~ sK0 ) ) ) )
= $true )
| ( ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& sK0 )
| ( ( sK1 = Y0 )
& ~ sK0 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
! [X1: $i] :
( ( ( ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& sK0 )
| ( ( sK1 = Y0 )
& ~ sK0 ) ) ) )
& ~ sK0 )
= $true )
| ( ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& sK0 )
| ( ( sK1 = Y0 )
& ~ sK0 ) ) ) )
= $true )
| ( ( ( sK1 = X1 )
& sK0 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
! [X1: $i] :
( ( ( ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& sK0 )
| ( ( sK1 = Y0 )
& ~ sK0 ) ) ) )
& sK0 )
= $true )
| ( ( ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& sK0 )
| ( ( sK1 = Y0 )
& ~ sK0 ) ) ) )
& ~ sK0 )
= $true )
| ( ( ( sK1 = X1 )
& sK0 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
! [X1: $i] :
( ( ( ( ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& sK0 )
| ( ( sK1 = Y0 )
& ~ sK0 ) ) ) )
& sK0 )
| ( ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& sK0 )
| ( ( sK1 = Y0 )
& ~ sK0 ) ) ) )
& ~ sK0 ) )
= $true )
| ( ( ( sK1 = X1 )
& sK0 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
! [X1: $i] :
( ( $false
= ( ( ( sK1 = X1 )
& sK0 )
| ( ( sK1 = X1 )
& ~ sK0 ) ) )
| ( ( ( ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& sK0 )
| ( ( sK1 = Y0 )
& ~ sK0 ) ) ) )
& sK0 )
| ( ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& sK0 )
| ( ( sK1 = Y0 )
& ~ sK0 ) ) ) )
& ~ sK0 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& sK0 )
| ( ( sK1 = Y0 )
& ~ sK0 ) )
@ ( eps
@ ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& sK0 )
| ( ( sK1 = Y0 )
& ~ sK0 ) ) ) )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& sK0 )
| ( ( sK1 = Y0 )
& ~ sK0 ) )
@ X1 ) ) ),
introduced(definition,[],[choice_axiom]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO540^1 : TPTP v9.2.1. Released v5.2.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n017.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 14:32:11 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.46 ---- Original DTF file ---
% 0.19/0.46 thf(spec,logic,$$dhol).
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % File : SYO540^1 : TPTP v9.2.1. Released v5.2.0.
% 0.19/0.46 % Domain : Syntactic
% 0.19/0.46 % Problem : Property of if-then-else on $i defined from choice on $i
% 0.19/0.46 % Version : Especial.
% 0.19/0.46 % English : A choice operator on $i is used to define an if-then-else operator
% 0.19/0.46 % at $i. Check that if the then-part and the else-part are both X,
% 0.19/0.46 % it returns X.
% 0.19/0.46
% 0.19/0.46 % Refs : [Bro11] Brown E. (2011), Email to Geoff Sutcliffe
% 0.19/0.46 % Source : [Bro11]
% 0.19/0.46 % Names : CHOICE15c [Bro11]
% 0.19/0.46
% 0.19/0.46 % Status : Theorem
% 0.19/0.46 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.38 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.22 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, 0.43 v6.1.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.2.0
% 0.19/0.46 % Syntax : Number of formulae : 5 ( 2 unt; 2 typ; 1 def)
% 0.19/0.46 % Number of atoms : 4 ( 4 equ; 0 cnn)
% 0.19/0.46 % Maximal formula atoms : 1 ( 1 avg)
% 0.19/0.46 % Number of connectives : 12 ( 1 ~; 1 |; 2 &; 7 @)
% 0.19/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.19/0.46 % Maximal formula depth : 5 ( 3 avg)
% 0.19/0.46 % Number of types : 2 ( 0 usr)
% 0.19/0.46 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.19/0.46 % Number of symbols : 3 ( 2 usr; 0 con; 1-3 aty)
% 0.19/0.46 % Number of variables : 8 ( 4 ^; 3 !; 1 ?; 8 :)
% 0.19/0.46 % SPC : TH0_THM_EQU_NAR
% 0.19/0.46
% 0.19/0.46 % Comments :
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 thf(eps,type,
% 0.19/0.46 eps: ( $i > $o ) > $i ).
% 0.19/0.46
% 0.19/0.46 thf(choiceax,axiom,
% 0.19/0.46 ! [P: $i > $o] :
% 0.19/0.46 ( ? [X: $i] : ( P @ X )
% 0.19/0.46 => ( P @ ( eps @ P ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(if,type,
% 0.19/0.46 if: $o > $i > $i > $i ).
% 0.19/0.46
% 0.19/0.46 thf(ifd,definition,
% 0.19/0.46 ( if
% 0.19/0.46 = ( ^ [B: $o,X: $i,Y: $i] :
% 0.19/0.46 ( eps
% 0.19/0.46 @ ^ [Z: $i] :
% 0.19/0.46 ( ( B
% 0.19/0.46 & ( Z = X ) )
% 0.19/0.46 | ( ~ B
% 0.19/0.46 & ( Z = Y ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(conj,conjecture,
% 0.19/0.46 ! [B: $o,X: $i] :
% 0.19/0.46 ( ( if @ B @ X @ X )
% 0.19/0.46 = X ) ).
% 0.19/0.46
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 ------------------------
% 1.63/1.30 ---- Embedded in THF ---
% 1.63/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.63/1.30 %%% Generated on Tue Feb 24 14:32:12 EST 2026
% 1.63/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 1.63/1.30 %%% Logic specification used:
% 1.63/1.30 %%% thf(spec, logic, $$dhol).
% 1.63/1.30
% 1.63/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.O0PMKi6bfH/DTF2DTF19544.p
% See solution above
% 1.63/1.30 ------------------------
% 1.63/1.31 ---- Cleaned THF ---
% 1.63/1.31 thf(eps,type,
% 1.63/1.31 eps: ( $i > $o ) > $i ).
% 1.63/1.31
% 1.63/1.31 thf(choiceax,axiom,
% 1.63/1.31 ! [P: $i > $o] :
% 1.63/1.31 ( ? [X: $i] : ( P @ X )
% 1.63/1.31 => ( P @ ( eps @ P ) ) ) ).
% 1.63/1.31
% 1.63/1.31 thf(if,type,
% 1.63/1.31 if: $o > $i > $i > $i ).
% 1.63/1.31
% 1.63/1.31 thf(ifd,definition,
% 1.63/1.31 ( if
% 1.63/1.31 = ( ^ [B: $o,X: $i,Y: $i] :
% 1.63/1.31 ( eps
% 1.63/1.31 @ ^ [Z: $i] :
% 1.63/1.31 ( ( B
% 1.63/1.31 & ( Z = X ) )
% 1.63/1.31 | ( ~ B
% 1.63/1.31 & ( Z = Y ) ) ) ) ) ) ).
% 1.63/1.31
% 1.63/1.31 thf(conj,conjecture,
% 1.63/1.31 ! [B: $o,X: $i] :
% 1.63/1.31 ( ( if @ B @ X @ X )
% 1.63/1.31 = X ) ).
% 1.63/1.31 ------------------------
% 1.63/1.33 % (19734)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_19544 for (2999ds/183Mi)
% 1.63/1.33 % (19739)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_19544 for (2999ds/275Mi)
% 1.63/1.33 % (19739)Refutation not found, incomplete strategy
% 1.63/1.33 % (19739)------------------------------
% 1.63/1.33 % (19739)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.33 % (19739)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.33
% 1.63/1.33
% 1.63/1.33 % (19739)Memory used [KB]: 5373
% 1.63/1.33 % (19739)Time elapsed: 0.002 s
% 1.63/1.33 % (19739)Instructions burned: 1 (million)
% 1.63/1.33 % (19739)------------------------------
% 1.63/1.33 % (19739)------------------------------
% 1.63/1.33 % (19735)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_19544 for (2999ds/4Mi)
% 1.63/1.33 % (19736)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_19544 for (2999ds/27Mi)
% 1.63/1.33 % (19737)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_19544 for (2999ds/2Mi)
% 1.63/1.34 % (19740)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_19544 for (2999ds/18Mi)
% 1.63/1.34 % (19738)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_19544 for (2999ds/2Mi)
% 1.63/1.34 % (19737)Instruction limit reached!
% 1.63/1.34 % (19737)------------------------------
% 1.63/1.34 % (19737)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.34 % (19737)Termination reason: Unknown
% 1.63/1.34 % (19737)Termination phase: Saturation
% 1.63/1.34 % (19738)Instruction limit reached!
% 1.63/1.34 % (19738)------------------------------
% 1.63/1.34 % (19738)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.34 % (19738)Termination reason: Unknown
% 1.63/1.34 % (19738)Termination phase: Unused predicate definition removal
% 1.63/1.34
% 1.63/1.34 % (19738)Memory used [KB]: 895
% 1.63/1.34 % (19738)Time elapsed: 0.002 s
% 1.63/1.34 % (19738)Instructions burned: 2 (million)
% 1.63/1.34 % (19738)------------------------------
% 1.63/1.34 % (19738)------------------------------
% 1.63/1.34
% 1.63/1.34 % (19737)Memory used [KB]: 895
% 1.63/1.34 % (19737)Time elapsed: 0.003 s
% 1.63/1.34 % (19737)Instructions burned: 2 (million)
% 1.63/1.34 % (19737)------------------------------
% 1.63/1.34 % (19737)------------------------------
% 1.63/1.34 % (19735)Instruction limit reached!
% 1.63/1.34 % (19735)------------------------------
% 1.63/1.34 % (19735)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.34 % (19735)Termination reason: Unknown
% 1.63/1.34 % (19735)Termination phase: Saturation
% 1.63/1.34
% 1.63/1.34 % (19735)Memory used [KB]: 5500
% 1.63/1.34 % (19735)Time elapsed: 0.005 s
% 1.63/1.34 % (19735)Instructions burned: 4 (million)
% 1.63/1.34 % (19735)------------------------------
% 1.63/1.34 % (19735)------------------------------
% 1.63/1.34 % (19736)First to succeed.
% 1.63/1.34 % (19741)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_19544 for (2999ds/3Mi)
% 1.63/1.34 % (19736)Refutation found. Thanks to Tanya!
% 1.63/1.34 % SZS status Theorem for DTF2THF_19544
% 1.63/1.34 % SZS output start Proof for DTF2THF_19544
% 1.63/1.34 thf(func_def_0, type, eps: ($i > $o) > $i).
% 1.63/1.34 thf(func_def_2, type, if: $o > $i > $i > $i).
% 1.63/1.34 thf(func_def_3, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.63/1.34 thf(func_def_18, type, ph3: !>[X0: $tType]:(X0)).
% 1.63/1.34 thf(f147,plain,(
% 1.63/1.34 $false),
% 1.63/1.34 inference(avatar_sat_refutation,[status(thm)],[f93,f95,f99,f146])).
% 1.63/1.34 thf(f146,plain,(
% 1.63/1.34 spl2_2 | spl2_4 | ~spl2_1),
% 1.63/1.34 inference(avatar_split_clause,[status(thm)],[f145,f72,f84,f76])).
% 1.63/1.34 thf(f76,definition,(
% 1.63/1.34 spl2_2 <=> ! [X1 : $i] : (sK1 != X1)),
% 1.63/1.34 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.63/1.34 thf(f84,definition,(
% 1.63/1.34 spl2_4 <=> ((eps @ (^[Y0 : $i]: (((sK1 = Y0) & sK0) | ((sK1 = Y0) & (~ sK0))))) = sK1)),
% 1.63/1.34 introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition])).
% 1.63/1.34 thf(f72,definition,(
% 1.63/1.34 spl2_1 <=> (sK0 = $false)),
% 1.63/1.34 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.63/1.34 thf(f145,plain,(
% 1.63/1.34 ( ! [X1 : $i] : (((eps @ (^[Y0 : $i]: (((sK1 = Y0) & sK0) | ((sK1 = Y0) & (~ sK0))))) = sK1) | (sK1 != X1)) ) | ~spl2_1),
% 1.63/1.34 inference(trivial_inequality_removal,[status(thm)],[f144])).
% 1.63/1.34 thf(f144,plain,(
% 1.63/1.34 ( ! [X1 : $i] : (($false = $true) | ((eps @ (^[Y0 : $i]: (((sK1 = Y0) & sK0) | ((sK1 = Y0) & (~ sK0))))) = sK1) | (sK1 != X1)) ) | ~spl2_1),
% 1.63/1.34 inference(forward_demodulation,[status(thm)],[f136,f74])).
% 1.63/1.34 thf(f74,plain,(
% 1.63/1.34 (sK0 = $false) | ~spl2_1),
% 1.63/1.34 inference(avatar_component_clause,[status(thm)],[f72])).
% 1.63/1.34 thf(f136,plain,(
% 1.63/1.34 ( ! [X1 : $i] : ((sK0 = $true) | ((eps @ (^[Y0 : $i]: (((sK1 = Y0) & sK0) | ((sK1 = Y0) & (~ sK0))))) = sK1) | (sK1 != X1)) )),
% 1.63/1.34 inference(equality_proxy_clausification,[status(thm)],[f135])).
% 1.63/1.34 thf(f135,plain,(
% 1.63/1.34 ( ! [X1 : $i] : (((sK1 = (eps @ (^[Y0 : $i]: (((sK1 = Y0) & sK0) | ((sK1 = Y0) & (~ sK0)))))) = $true) | (sK0 = $true) | (sK1 != X1)) )),
% 1.63/1.34 inference(binary_proxy_clausification,[status(thm)],[f133])).
% 1.63/1.34 thf(f133,plain,(
% 1.63/1.34 ( ! [X1 : $i] : ((sK0 = $true) | (sK1 != X1) | (((sK1 = (eps @ (^[Y0 : $i]: (((sK1 = Y0) & sK0) | ((sK1 = Y0) & (~ sK0)))))) & (~ sK0)) = $true)) )),
% 1.63/1.34 inference(duplicate_literal_removal,[status(thm)],[f132])).
% 1.63/1.34 thf(f132,plain,(
% 1.63/1.34 ( ! [X1 : $i] : ((sK1 != X1) | (sK0 = $true) | (sK0 = $true) | (((sK1 = (eps @ (^[Y0 : $i]: (((sK1 = Y0) & sK0) | ((sK1 = Y0) & (~ sK0)))))) & (~ sK0)) = $true)) )),
% 1.63/1.34 inference(not_proxy_clausification,[status(thm)],[f123])).
% 1.63/1.34 thf(f123,plain,(
% 1.63/1.34 ( ! [X1 : $i] : ((sK0 = $true) | (sK1 != X1) | ($false = (~ sK0)) | (((sK1 = (eps @ (^[Y0 : $i]: (((sK1 = Y0) & sK0) | ((sK1 = Y0) & (~ sK0)))))) & (~ sK0)) = $true)) )),
% 1.63/1.34 inference(binary_proxy_clausification,[status(thm)],[f122])).
% 1.63/1.34 thf(f122,plain,(
% 1.63/1.34 ( ! [X1 : $i] : ((sK1 != X1) | (((sK1 = (eps @ (^[Y0 : $i]: (((sK1 = Y0) & sK0) | ((sK1 = Y0) & (~ sK0)))))) & sK0) = $true) | ($false = (~ sK0)) | (((sK1 = (eps @ (^[Y0 : $i]: (((sK1 = Y0) & sK0) | ((sK1 = Y0) & (~ sK0)))))) & (~ sK0)) = $true)) )),
% 1.63/1.34 inference(binary_proxy_clausification,[status(thm)],[f121])).
% 1.63/1.34 thf(f121,plain,(
% 1.63/1.34 ( ! [X1 : $i] : ((sK1 != X1) | ((((sK1 = (eps @ (^[Y0 : $i]: (((sK1 = Y0) & sK0) | ((sK1 = Y0) & (~ sK0)))))) & sK0) | ((sK1 = (eps @ (^[Y0 : $i]: (((sK1 = Y0) & sK0) | ((sK1 = Y0) & (~ sK0)))))) & (~ sK0))) = $true) | ($false = (~ sK0))) )),
% 1.63/1.34 inference(equality_proxy_clausification,[status(thm)],[f120])).
% 1.63/1.34 thf(f120,plain,(
% 1.63/1.34 ( ! [X1 : $i] : (($false = (sK1 = X1)) | ((((sK1 = (eps @ (^[Y0 : $i]: (((sK1 = Y0) & sK0) | ((sK1 = Y0) & (~ sK0)))))) & sK0) | ((sK1 = (eps @ (^[Y0 : $i]: (((sK1 = Y0) & sK0) | ((sK1 = Y0) & (~ sK0)))))) & (~ sK0))) = $true) | ($false = (~ sK0))) )),
% 1.63/1.34 inference(binary_proxy_clausification,[status(thm)],[f101])).
% 1.63/1.34 thf(f101,plain,(
% 1.63/1.34 ( ! [X1 : $i] : ((((sK1 = X1) & (~ sK0)) = $false) | ((((sK1 = (eps @ (^[Y0 : $i]: (((sK1 = Y0) & sK0) | ((sK1 = Y0) & (~ sK0)))))) & sK0) | ((sK1 = (eps @ (^[Y0 : $i]: (((sK1 = Y0) & sK0) | ((sK1 = Y0) & (~ sK0)))))) & (~ sK0))) = $true)) )),
% 1.63/1.34 inference(binary_proxy_clausification,[status(thm)],[f100])).
% 1.63/1.34 thf(f100,plain,(
% 1.63/1.34 ( ! [X1 : $i] : (($false = (((sK1 = X1) & sK0) | ((sK1 = X1) & (~ sK0)))) | ((((sK1 = (eps @ (^[Y0 : $i]: (((sK1 = Y0) & sK0) | ((sK1 = Y0) & (~ sK0)))))) & sK0) | ((sK1 = (eps @ (^[Y0 : $i]: (((sK1 = Y0) & sK0) | ((sK1 = Y0) & (~ sK0)))))) & (~ sK0))) = $true)) )),
% 1.63/1.34 inference(beta_eta_normalization,[status(thm)],[f96])).
% 1.63/1.34 thf(f96,plain,(
% 1.63/1.34 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: (((sK1 = Y0) & sK0) | ((sK1 = Y0) & (~ sK0)))) @ X1)) | (((^[Y0 : $i]: (((sK1 = Y0) & sK0) | ((sK1 = Y0) & (~ sK0)))) @ (eps @ (^[Y0 : $i]: (((sK1 = Y0) & sK0) | ((sK1 = Y0) & (~ sK0)))))) = $true)) )),
% 1.63/1.34 introduced(definition,[],[choice_axiom])).
% 1.63/1.34 thf(f99,plain,(
% 1.63/1.34 ~spl2_4),
% 1.63/1.34 inference(avatar_contradiction_clause,[status(thm)],[f98])).
% 1.63/1.34 thf(f98,plain,(
% 1.63/1.34 $false | ~spl2_4),
% 1.63/1.34 inference(trivial_inequality_removal,[status(thm)],[f97])).
% 1.63/1.34 thf(f97,plain,(
% 1.63/1.34 (sK1 != sK1) | ~spl2_4),
% 1.63/1.34 inference(superposition,[status(thm)],[f19,f86])).
% 1.63/1.34 thf(f86,plain,(
% 1.63/1.34 ((eps @ (^[Y0 : $i]: (((sK1 = Y0) & sK0) | ((sK1 = Y0) & (~ sK0))))) = sK1) | ~spl2_4),
% 1.63/1.34 inference(avatar_component_clause,[status(thm)],[f84])).
% 1.63/1.34 thf(f19,plain,(
% 1.63/1.34 ((eps @ (^[Y0 : $i]: (((sK1 = Y0) & sK0) | ((sK1 = Y0) & (~ sK0))))) != sK1)),
% 1.63/1.34 inference(beta_eta_normalization,[status(thm)],[f18])).
% 1.63/1.34 thf(f18,plain,(
% 1.63/1.34 (((^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((Y1 = Y3) & Y0) | ((Y2 = Y3) & (~ Y0)))))))))) @ sK0 @ sK1 @ sK1) != sK1)),
% 1.63/1.34 inference(definition_unfolding,[status(thm)],[f15,f16])).
% 1.63/1.34 thf(f16,plain,(
% 1.63/1.34 (if = (^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((Y1 = Y3) & Y0) | ((Y2 = Y3) & (~ Y0)))))))))))),
% 1.63/1.34 inference(cnf_transformation,[status(thm)],[f7])).
% 1.63/1.34 thf(f7,plain,(
% 1.63/1.34 (if = (^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((Y1 = Y3) & Y0) | ((Y2 = Y3) & (~ Y0)))))))))))),
% 1.63/1.34 inference(fool_elimination,[status(thm)],[f6])).
% 1.63/1.34 thf(f6,plain,(
% 1.63/1.34 ((^[X0 : $o, X1 : $i, X2 : $i] : (eps @ (^[X3 : $i] : ((~X0 & (X2 = X3)) | (X0 & (X1 = X3)))))) = if)),
% 1.63/1.34 inference(rectify,[status(thm)],[f2])).
% 1.63/1.34 thf(f2,axiom,(
% 1.63/1.34 ((^[X2 : $o, X1 : $i, X3 : $i] : (eps @ (^[X4 : $i] : ((~X2 & (X3 = X4)) | (X2 & (X1 = X4)))))) = if)),
% 1.63/1.34 file('/export/starexec/sandbox/tmp/tmp.O0PMKi6bfH/DTF2THF_19544.p',ifd)).
% 1.63/1.34 thf(f15,plain,(
% 1.63/1.34 ((if @ sK0 @ sK1 @ sK1) != sK1)),
% 1.63/1.34 inference(cnf_transformation,[status(thm)],[f14])).
% 1.63/1.34 thf(f14,plain,(
% 1.63/1.34 ((if @ sK0 @ sK1 @ sK1) != sK1)),
% 1.63/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f11,f13])).
% 1.63/1.34 thf(f13,plain,(
% 1.63/1.34 ? [X0 : $o,X1 : $i] : ((if @ X0 @ X1 @ X1) != X1) => ((if @ sK0 @ sK1 @ sK1) != sK1)),
% 1.63/1.34 introduced(definition,[],[choice_axiom])).
% 1.63/1.34 thf(f11,plain,(
% 1.63/1.34 ? [X0 : $o,X1 : $i] : ((if @ X0 @ X1 @ X1) != X1)),
% 1.63/1.34 inference(ennf_transformation,[status(thm)],[f10])).
% 1.63/1.34 thf(f10,plain,(
% 1.63/1.34 ~! [X0 : $o,X1 : $i] : ((if @ X0 @ X1 @ X1) = X1)),
% 1.63/1.34 inference(rectify,[status(thm)],[f4])).
% 1.63/1.34 thf(f4,negated_conjecture,(
% 1.63/1.34 ~! [X2 : $o,X1 : $i] : ((if @ X2 @ X1 @ X1) = X1)),
% 1.63/1.34 inference(negated_conjecture,[status(cth)],[f3])).
% 1.63/1.34 thf(f3,conjecture,(
% 1.63/1.34 ! [X2 : $o,X1 : $i] : ((if @ X2 @ X1 @ X1) = X1)),
% 1.63/1.34 file('/export/starexec/sandbox/tmp/tmp.O0PMKi6bfH/DTF2THF_19544.p',conj)).
% 1.63/1.34 thf(f95,plain,(
% 1.63/1.34 ~spl2_2),
% 1.63/1.34 inference(avatar_contradiction_clause,[status(thm)],[f94])).
% 1.63/1.34 thf(f94,plain,(
% 1.63/1.34 $false | ~spl2_2),
% 1.63/1.34 inference(equality_resolution,[status(thm)],[f77])).
% 1.63/1.34 thf(f77,plain,(
% 1.63/1.34 ( ! [X1 : $i] : ((sK1 != X1)) ) | ~spl2_2),
% 1.63/1.34 inference(avatar_component_clause,[status(thm)],[f76])).
% 1.63/1.34 thf(f93,plain,(
% 1.63/1.34 spl2_1 | spl2_4 | spl2_2),
% 1.63/1.34 inference(avatar_split_clause,[status(thm)],[f32,f76,f84,f72])).
% 1.63/1.34 thf(f32,plain,(
% 1.63/1.34 ( ! [X1 : $i] : ((sK0 = $false) | ((eps @ (^[Y0 : $i]: (((sK1 = Y0) & sK0) | ((sK1 = Y0) & (~ sK0))))) = sK1) | (sK1 != X1)) )),
% 1.63/1.34 inference(equality_proxy_clausification,[status(thm)],[f31])).
% 1.63/1.34 thf(f31,plain,(
% 1.63/1.34 ( ! [X1 : $i] : ((sK0 = $false) | ($false = (sK1 = X1)) | ((eps @ (^[Y0 : $i]: (((sK1 = Y0) & sK0) | ((sK1 = Y0) & (~ sK0))))) = sK1)) )),
% 1.63/1.34 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.63/1.34 thf(f30,plain,(
% 1.63/1.34 ( ! [X1 : $i] : (((eps @ (^[Y0 : $i]: (((sK1 = Y0) & sK0) | ((sK1 = Y0) & (~ sK0))))) = sK1) | (((sK1 = X1) & sK0) = $false)) )),
% 1.63/1.34 inference(equality_proxy_clausification,[status(thm)],[f29])).
% 1.63/1.34 thf(f29,plain,(
% 1.63/1.34 ( ! [X1 : $i] : (((sK1 = (eps @ (^[Y0 : $i]: (((sK1 = Y0) & sK0) | ((sK1 = Y0) & (~ sK0)))))) = $true) | (((sK1 = X1) & sK0) = $false)) )),
% 1.63/1.34 inference(duplicate_literal_removal,[status(thm)],[f28])).
% 1.63/1.34 thf(f28,plain,(
% 1.63/1.34 ( ! [X1 : $i] : ((((sK1 = X1) & sK0) = $false) | ((sK1 = (eps @ (^[Y0 : $i]: (((sK1 = Y0) & sK0) | ((sK1 = Y0) & (~ sK0)))))) = $true) | ((sK1 = (eps @ (^[Y0 : $i]: (((sK1 = Y0) & sK0) | ((sK1 = Y0) & (~ sK0)))))) = $true)) )),
% 1.63/1.34 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 1.63/1.34 thf(f26,plain,(
% 1.63/1.34 ( ! [X1 : $i] : ((((sK1 = (eps @ (^[Y0 : $i]: (((sK1 = Y0) & sK0) | ((sK1 = Y0) & (~ sK0)))))) & (~ sK0)) = $true) | ((sK1 = (eps @ (^[Y0 : $i]: (((sK1 = Y0) & sK0) | ((sK1 = Y0) & (~ sK0)))))) = $true) | (((sK1 = X1) & sK0) = $false)) )),
% 1.63/1.34 inference(binary_proxy_clausification,[status(thm)],[f24])).
% 1.63/1.34 thf(f24,plain,(
% 1.63/1.34 ( ! [X1 : $i] : ((((sK1 = (eps @ (^[Y0 : $i]: (((sK1 = Y0) & sK0) | ((sK1 = Y0) & (~ sK0)))))) & sK0) = $true) | (((sK1 = (eps @ (^[Y0 : $i]: (((sK1 = Y0) & sK0) | ((sK1 = Y0) & (~ sK0)))))) & (~ sK0)) = $true) | (((sK1 = X1) & sK0) = $false)) )),
% 1.63/1.34 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 1.63/1.34 thf(f23,plain,(
% 1.63/1.34 ( ! [X1 : $i] : (((((sK1 = (eps @ (^[Y0 : $i]: (((sK1 = Y0) & sK0) | ((sK1 = Y0) & (~ sK0)))))) & sK0) | ((sK1 = (eps @ (^[Y0 : $i]: (((sK1 = Y0) & sK0) | ((sK1 = Y0) & (~ sK0)))))) & (~ sK0))) = $true) | (((sK1 = X1) & sK0) = $false)) )),
% 1.63/1.34 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.63/1.34 thf(f21,plain,(
% 1.63/1.34 ( ! [X1 : $i] : (($false = (((sK1 = X1) & sK0) | ((sK1 = X1) & (~ sK0)))) | ((((sK1 = (eps @ (^[Y0 : $i]: (((sK1 = Y0) & sK0) | ((sK1 = Y0) & (~ sK0)))))) & sK0) | ((sK1 = (eps @ (^[Y0 : $i]: (((sK1 = Y0) & sK0) | ((sK1 = Y0) & (~ sK0)))))) & (~ sK0))) = $true)) )),
% 1.63/1.34 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.63/1.34 thf(f20,plain,(
% 1.63/1.34 ( ! [X1 : $i] : ((((^[Y0 : $i]: (((sK1 = Y0) & sK0) | ((sK1 = Y0) & (~ sK0)))) @ (eps @ (^[Y0 : $i]: (((sK1 = Y0) & sK0) | ((sK1 = Y0) & (~ sK0)))))) = $true) | ($false = ((^[Y0 : $i]: (((sK1 = Y0) & sK0) | ((sK1 = Y0) & (~ sK0)))) @ X1))) )),
% 1.63/1.34 introduced(definition,[],[choice_axiom])).
% 1.63/1.34 % SZS output end Proof for DTF2THF_19544
% 1.63/1.34 % (19736)------------------------------
% 1.63/1.34 % (19736)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.34 % (19736)Termination reason: Refutation
% 1.63/1.34
% 1.63/1.34 % (19736)Memory used [KB]: 5500
% 1.63/1.34 % (19736)Time elapsed: 0.009 s
% 1.63/1.34 % (19736)Instructions burned: 8 (million)
% 1.63/1.34 % (19736)------------------------------
% 1.63/1.34 % (19736)------------------------------
% 1.63/1.34 % (19733)Success in time 0.024 s
%------------------------------------------------------------------------------