%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO543^1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/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 1.32s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 51 ( 15 unt; 0 typ; 3 def)
% Number of atoms : 473 ( 242 equ; 0 cnn)
% Maximal formula atoms : 4 ( 9 avg)
% Number of connectives : 445 ( 104 ~; 124 |; 135 &; 78 @)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 92 ( 92 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 6 con; 0-4 aty)
% Number of variables : 102 ( 66 ^; 32 !; 4 ?; 102 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
epsii: ( ( $i > $i ) > $o ) > $i > $i ).
thf(func_def_2,type,
if: $o > ( $i > $i ) > ( $i > $i ) > $i > $i ).
thf(func_def_3,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_15,type,
sK0: $i > $i ).
thf(func_def_18,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f204,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f86,f195,f201,f203]) ).
thf(f203,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[status(thm)],[f202]) ).
thf(f202,plain,
( $false
| ~ spl2_1 ),
inference(equality_resolution,[status(thm)],[f70]) ).
thf(f70,plain,
( ! [X1: $i > $i] : ( sK0 != X1 )
| ~ spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f69]) ).
thf(f69,definition,
( spl2_1
<=> ! [X1: $i > $i] : ( sK0 != X1 ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f201,plain,
( spl2_1
| spl2_3
| ~ spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f200,f72,f76,f69]) ).
thf(f76,definition,
( spl2_3
<=> ( ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK1
& ( sK0 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) ) )
= sK0 ) ),
introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition]) ).
thf(f72,definition,
( spl2_2
<=> ( $false = sK1 ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f200,plain,
( ! [X1: $i > $i] :
( ( ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK1
& ( sK0 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) ) )
= sK0 )
| ( sK0 != X1 ) )
| ~ spl2_2 ),
inference(trivial_inequality_removal,[status(thm)],[f199]) ).
thf(f199,plain,
( ! [X1: $i > $i] :
( ( ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK1
& ( sK0 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) ) )
= sK0 )
| ( sK0 != X1 )
| ( $false = $true ) )
| ~ spl2_2 ),
inference(forward_demodulation,[status(thm)],[f172,f74]) ).
thf(f74,plain,
( ( $false = sK1 )
| ~ spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f72]) ).
thf(f172,plain,
! [X1: $i > $i] :
( ( sK1 = $true )
| ( ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK1
& ( sK0 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) ) )
= sK0 )
| ( sK0 != X1 ) ),
inference(duplicate_literal_removal,[status(thm)],[f168]) ).
thf(f168,plain,
! [X1: $i > $i] :
( ( sK1 = $true )
| ( sK1 = $true )
| ( sK0 != X1 )
| ( ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK1
& ( sK0 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) ) )
= sK0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f167]) ).
thf(f167,plain,
! [X1: $i > $i] :
( ( sK0 != X1 )
| ( ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK1
& ( sK0 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) ) )
= sK0 )
| ( $true
= ( ( sK0
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK1
& ( sK0 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) ) ) )
& sK1 ) )
| ( sK1 = $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f166]) ).
thf(f166,plain,
! [X1: $i > $i] :
( ( $false
= ( sK0 = X1 ) )
| ( sK1 = $true )
| ( ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK1
& ( sK0 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) ) )
= sK0 )
| ( $true
= ( ( sK0
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK1
& ( sK0 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) ) ) )
& sK1 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f157]) ).
thf(f157,plain,
! [X1: $i > $i] :
( ( $true
= ( sK0
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK1
& ( sK0 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) ) ) ) )
| ( sK1 = $true )
| ( $false
= ( sK0 = X1 ) )
| ( $true
= ( ( sK0
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK1
& ( sK0 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) ) ) )
& sK1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f156]) ).
thf(f156,plain,
! [X1: $i > $i] :
( ( $true
= ( ~ sK1
& ( sK0
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK1
& ( sK0 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) ) ) ) ) )
| ( $false
= ( sK0 = X1 ) )
| ( sK1 = $true )
| ( $true
= ( ( sK0
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK1
& ( sK0 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) ) ) )
& sK1 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f155]) ).
thf(f155,plain,
! [X1: $i > $i] :
( ( $false = ( ~ sK1 ) )
| ( $true
= ( ( sK0
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK1
& ( sK0 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) ) ) )
& sK1 ) )
| ( $false
= ( sK0 = X1 ) )
| ( $true
= ( ~ sK1
& ( sK0
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK1
& ( sK0 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f154]) ).
thf(f154,plain,
! [X1: $i > $i] :
( ( $true
= ( ( ~ sK1
& ( sK0
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK1
& ( sK0 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) ) ) ) )
| ( ( sK0
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK1
& ( sK0 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) ) ) )
& sK1 ) ) )
| ( $false
= ( sK0 = X1 ) )
| ( $false = ( ~ sK1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f153]) ).
thf(f153,plain,
! [X1: $i > $i] :
( ( $false
= ( ~ sK1
& ( sK0 = X1 ) ) )
| ( $true
= ( ( ~ sK1
& ( sK0
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK1
& ( sK0 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) ) ) ) )
| ( ( sK0
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK1
& ( sK0 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) ) ) )
& sK1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f151]) ).
thf(f151,plain,
! [X1: $i > $i] :
( ( $false
= ( ( ~ sK1
& ( sK0 = X1 ) )
| ( ( sK0 = X1 )
& sK1 ) ) )
| ( $true
= ( ( ~ sK1
& ( sK0
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK1
& ( sK0 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) ) ) ) )
| ( ( sK0
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK1
& ( sK0 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) ) ) )
& sK1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f148]) ).
thf(f148,plain,
! [X1: $i > $i] :
( ( $true
= ( ^ [Y0: $i > $i] :
( ( ~ sK1
& ( sK0 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) )
@ ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK1
& ( sK0 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) ) ) ) )
| ( $false
= ( ^ [Y0: $i > $i] :
( ( ~ sK1
& ( sK0 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) )
@ X1 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f195,plain,
~ spl2_3,
inference(avatar_contradiction_clause,[status(thm)],[f194]) ).
thf(f194,plain,
( $false
| ~ spl2_3 ),
inference(trivial_inequality_removal,[status(thm)],[f150]) ).
thf(f150,plain,
( ( sK0 != sK0 )
| ~ spl2_3 ),
inference(superposition,[status(thm)],[f19,f78]) ).
thf(f78,plain,
( ( ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK1
& ( sK0 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) ) )
= sK0 )
| ~ spl2_3 ),
inference(avatar_component_clause,[status(thm)],[f76]) ).
thf(f19,plain,
( ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK1
& ( sK0 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) ) )
!= sK0 ),
inference(beta_eta_normalization,[status(thm)],[f18]) ).
thf(f18,plain,
( sK0
!= ( ^ [Y0: $o,Y1: $i > $i,Y2: $i > $i] :
( epsii
@ ^ [Y3: $i > $i] :
( ( ~ Y0
& ( Y2 = Y3 ) )
| ( ( Y1 = Y3 )
& Y0 ) ) )
@ sK1
@ sK0
@ sK0 ) ),
inference(definition_unfolding,[status(thm)],[f15,f16]) ).
thf(f16,plain,
( if
= ( ^ [Y0: $o,Y1: $i > $i,Y2: $i > $i] :
( epsii
@ ^ [Y3: $i > $i] :
( ( ~ Y0
& ( Y2 = Y3 ) )
| ( ( Y1 = Y3 )
& Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( if
= ( ^ [Y0: $o,Y1: $i > $i,Y2: $i > $i] :
( epsii
@ ^ [Y3: $i > $i] :
( ( ~ Y0
& ( Y2 = Y3 ) )
| ( ( Y1 = Y3 )
& Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
( if
= ( ^ [X0: $o,X1: $i > $i,X2: $i > $i] :
( epsii
@ ^ [X3: $i > $i] :
( ( X0
& ( X1 = X3 ) )
| ( ( X2 = X3 )
& ~ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( if
= ( ^ [X2: $o,X1: $i > $i,X3: $i > $i] :
( epsii
@ ^ [X4: $i > $i] :
( ( X2
& ( X1 = X4 ) )
| ( ( X3 = X4 )
& ~ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.rg1nfRGPID/DTF2THF_19592.p',ifd) ).
thf(f15,plain,
( ( if @ sK1 @ sK0 @ sK0 )
!= sK0 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( if @ sK1 @ sK0 @ sK0 )
!= sK0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f11,f13]) ).
thf(f13,plain,
( ? [X0: $i > $i,X1: $o] :
( ( if @ X1 @ X0 @ X0 )
!= X0 )
=> ( ( if @ sK1 @ sK0 @ sK0 )
!= sK0 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
? [X0: $i > $i,X1: $o] :
( ( if @ X1 @ X0 @ X0 )
!= X0 ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
~ ! [X0: $i > $i,X1: $o] :
( ( if @ X1 @ X0 @ X0 )
= X0 ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X1: $i > $i,X2: $o] :
( ( if @ X2 @ X1 @ X1 )
= X1 ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
! [X1: $i > $i,X2: $o] :
( ( if @ X2 @ X1 @ X1 )
= X1 ),
file('/export/starexec/sandbox2/tmp/tmp.rg1nfRGPID/DTF2THF_19592.p',conj) ).
thf(f86,plain,
( spl2_1
| spl2_2
| spl2_3 ),
inference(avatar_split_clause,[status(thm)],[f60,f76,f72,f69]) ).
thf(f60,plain,
! [X1: $i > $i] :
( ( sK0 != X1 )
| ( ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK1
& ( sK0 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) ) )
= sK0 )
| ( $false = sK1 ) ),
inference(duplicate_literal_removal,[status(thm)],[f59]) ).
thf(f59,plain,
! [X1: $i > $i] :
( ( ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK1
& ( sK0 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) ) )
= sK0 )
| ( $false = sK1 )
| ( $false = sK1 )
| ( sK0 != X1 ) ),
inference(not_proxy_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
! [X1: $i > $i] :
( ( sK0 != X1 )
| ( $false = sK1 )
| ( $true = ( ~ sK1 ) )
| ( ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK1
& ( sK0 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) ) )
= sK0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
! [X1: $i > $i] :
( ( $false = sK1 )
| ( ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK1
& ( sK0 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) ) )
= sK0 )
| ( sK0 != X1 )
| ( $true
= ( ~ sK1
& ( sK0
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK1
& ( sK0 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) ) ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
! [X1: $i > $i] :
( ( $true
= ( sK0
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK1
& ( sK0 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) ) ) ) )
| ( $false = sK1 )
| ( $true
= ( ~ sK1
& ( sK0
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK1
& ( sK0 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) ) ) ) ) )
| ( sK0 != X1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
! [X1: $i > $i] :
( ( $true
= ( ( sK0
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK1
& ( sK0 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) ) ) )
& sK1 ) )
| ( $false = sK1 )
| ( $true
= ( ~ sK1
& ( sK0
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK1
& ( sK0 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) ) ) ) ) )
| ( sK0 != X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
! [X1: $i > $i] :
( ( $false
= ( sK0 = X1 ) )
| ( $true
= ( ( sK0
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK1
& ( sK0 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) ) ) )
& sK1 ) )
| ( $false = sK1 )
| ( $true
= ( ~ sK1
& ( sK0
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK1
& ( sK0 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
! [X1: $i > $i] :
( ( $false
= ( ( sK0 = X1 )
& sK1 ) )
| ( $true
= ( ~ sK1
& ( sK0
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK1
& ( sK0 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) ) ) ) ) )
| ( $true
= ( ( sK0
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK1
& ( sK0 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) ) ) )
& sK1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
! [X1: $i > $i] :
( ( $false
= ( ( ~ sK1
& ( sK0 = X1 ) )
| ( ( sK0 = X1 )
& sK1 ) ) )
| ( $true
= ( ( sK0
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK1
& ( sK0 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) ) ) )
& sK1 ) )
| ( $true
= ( ~ sK1
& ( sK0
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK1
& ( sK0 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
! [X1: $i > $i] :
( ( $true
= ( ( ~ sK1
& ( sK0
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK1
& ( sK0 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) ) ) ) )
| ( ( sK0
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK1
& ( sK0 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) ) ) )
& sK1 ) ) )
| ( $false
= ( ( ~ sK1
& ( sK0 = X1 ) )
| ( ( sK0 = X1 )
& sK1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
! [X1: $i > $i] :
( ( $true
= ( ^ [Y0: $i > $i] :
( ( ~ sK1
& ( sK0 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) )
@ ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK1
& ( sK0 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) ) ) ) )
| ( $false
= ( ^ [Y0: $i > $i] :
( ( ~ sK1
& ( sK0 = Y0 ) )
| ( ( sK0 = Y0 )
& sK1 ) )
@ X1 ) ) ),
introduced(definition,[],[choice_axiom]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO543^1 : TPTP v9.2.1. Released v5.2.0.
% 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.33 % Computer : n017.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue Feb 24 14:32:11 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : SYO543^1 : TPTP v9.2.1. Released v5.2.0.
% 0.20/0.46 % Domain : Syntactic
% 0.20/0.46 % Problem : If-then-else on $i>$i defined from choice on $i>$i
% 0.20/0.46 % Version : Especial.
% 0.20/0.46 % English : A choice operator on ($i>$i) is used to define an if-then-else
% 0.20/0.46 % operator at ($i>$i). Check that if the then-part and else-part
% 0.20/0.46 % are both X, then it returns X.
% 0.20/0.46
% 0.20/0.46 % Refs : [Bro11] Brown E. (2011), Email to Geoff Sutcliffe
% 0.20/0.46 % Source : [Bro11]
% 0.20/0.46 % Names : CHOICE16c [Bro11]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.38 v8.1.0, 0.27 v7.5.0, 0.29 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.57 v6.1.0, 0.43 v5.5.0, 0.33 v5.4.0, 0.40 v5.2.0
% 0.20/0.46 % Syntax : Number of formulae : 5 ( 2 unt; 2 typ; 1 def)
% 0.20/0.46 % Number of atoms : 4 ( 4 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 1 ( 1 avg)
% 0.20/0.46 % Number of connectives : 12 ( 1 ~; 1 |; 2 &; 7 @)
% 0.20/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 5 ( 3 avg)
% 0.20/0.46 % Number of types : 2 ( 0 usr)
% 0.20/0.46 % Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 3 ( 2 usr; 0 con; 2-4 aty)
% 0.20/0.46 % Number of variables : 8 ( 4 ^; 3 !; 1 ?; 8 :)
% 0.20/0.46 % SPC : TH0_THM_EQU_NAR
% 0.20/0.46
% 0.20/0.46 % Comments :
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 thf(epsii,type,
% 0.20/0.46 epsii: ( ( $i > $i ) > $o ) > $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(choiceaxii,axiom,
% 0.20/0.46 ! [P: ( $i > $i ) > $o] :
% 0.20/0.46 ( ? [X: $i > $i] : ( P @ X )
% 0.20/0.46 => ( P @ ( epsii @ P ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(if,type,
% 0.20/0.46 if: $o > ( $i > $i ) > ( $i > $i ) > $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(ifd,definition,
% 0.20/0.46 ( if
% 0.20/0.46 = ( ^ [B: $o,X: $i > $i,Y: $i > $i] :
% 0.20/0.46 ( epsii
% 0.20/0.46 @ ^ [Z: $i > $i] :
% 0.20/0.46 ( ( B
% 0.20/0.46 & ( Z = X ) )
% 0.20/0.46 | ( ~ B
% 0.20/0.46 & ( Z = Y ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(conj,conjecture,
% 0.20/0.46 ! [B: $o,X: $i > $i] :
% 0.20/0.46 ( ( if @ B @ X @ X )
% 0.20/0.46 = X ) ).
% 0.20/0.46
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 ------------------------
% 1.43/1.29 ---- Embedded in THF ---
% 1.43/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.43/1.29 %%% Generated on Tue Feb 24 14:32:12 EST 2026
% 1.43/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.43/1.29 %%% Logic specification used:
% 1.43/1.29 %%% thf(spec, logic, $$dhol).
% 1.43/1.29
% 1.43/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.rg1nfRGPID/DTF2DTF19592.p
% See solution above
% 1.43/1.29 ------------------------
% 1.43/1.30 ---- Cleaned THF ---
% 1.63/1.30 thf(epsii,type,
% 1.63/1.30 epsii: ( ( $i > $i ) > $o ) > $i > $i ).
% 1.63/1.30
% 1.63/1.30 thf(choiceaxii,axiom,
% 1.63/1.30 ! [P: ( $i > $i ) > $o] :
% 1.63/1.30 ( ? [X: $i > $i] : ( P @ X )
% 1.63/1.30 => ( P @ ( epsii @ P ) ) ) ).
% 1.63/1.30
% 1.63/1.30 thf(if,type,
% 1.63/1.30 if: $o > ( $i > $i ) > ( $i > $i ) > $i > $i ).
% 1.63/1.30
% 1.63/1.30 thf(ifd,definition,
% 1.63/1.30 ( if
% 1.63/1.30 = ( ^ [B: $o,X: $i > $i,Y: $i > $i] :
% 1.63/1.30 ( epsii
% 1.63/1.30 @ ^ [Z: $i > $i] :
% 1.63/1.30 ( ( B
% 1.63/1.30 & ( Z = X ) )
% 1.63/1.30 | ( ~ B
% 1.63/1.30 & ( Z = Y ) ) ) ) ) ) ).
% 1.63/1.30
% 1.63/1.30 thf(conj,conjecture,
% 1.63/1.30 ! [B: $o,X: $i > $i] :
% 1.63/1.30 ( ( if @ B @ X @ X )
% 1.63/1.30 = X ) ).
% 1.63/1.30 ------------------------
% 1.63/1.31 % (19755)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_19592 for (3000ds/27Mi)
% 1.63/1.31 % (19756)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_19592 for (3000ds/2Mi)
% 1.63/1.31 % (19754)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_19592 for (3000ds/4Mi)
% 1.63/1.31 % (19756)Instruction limit reached!
% 1.63/1.31 % (19756)------------------------------
% 1.63/1.31 % (19756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.31 % (19756)Termination reason: Unknown
% 1.63/1.31 % (19756)Termination phase: Saturation
% 1.63/1.31
% 1.63/1.31 % (19756)Memory used [KB]: 5500
% 1.63/1.31 % (19756)Time elapsed: 0.002 s
% 1.63/1.31 % (19756)Instructions burned: 2 (million)
% 1.63/1.31 % (19756)------------------------------
% 1.63/1.31 % (19756)------------------------------
% 1.63/1.31 % (19755)First to succeed.
% 1.63/1.31 % (19754)Instruction limit reached!
% 1.63/1.31 % (19754)------------------------------
% 1.63/1.31 % (19754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.31 % (19754)Termination reason: Unknown
% 1.63/1.31 % (19754)Termination phase: Saturation
% 1.63/1.31
% 1.63/1.31 % (19754)Memory used [KB]: 5500
% 1.63/1.31 % (19754)Time elapsed: 0.005 s
% 1.63/1.31 % (19754)Instructions burned: 4 (million)
% 1.63/1.31 % (19754)------------------------------
% 1.63/1.31 % (19754)------------------------------
% 1.63/1.32 % (19755)Refutation found. Thanks to Tanya!
% 1.63/1.32 % SZS status Theorem for DTF2THF_19592
% 1.63/1.32 % SZS output start Proof for DTF2THF_19592
% 1.63/1.32 thf(func_def_0, type, epsii: (($i > $i) > $o) > $i > $i).
% 1.63/1.32 thf(func_def_2, type, if: $o > ($i > $i) > ($i > $i) > $i > $i).
% 1.63/1.32 thf(func_def_3, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.63/1.32 thf(func_def_15, type, sK0: $i > $i).
% 1.63/1.32 thf(func_def_18, type, ph3: !>[X0: $tType]:(X0)).
% 1.63/1.32 thf(f204,plain,(
% 1.63/1.32 $false),
% 1.63/1.32 inference(avatar_sat_refutation,[status(thm)],[f86,f195,f201,f203])).
% 1.63/1.32 thf(f203,plain,(
% 1.63/1.32 ~spl2_1),
% 1.63/1.32 inference(avatar_contradiction_clause,[status(thm)],[f202])).
% 1.63/1.32 thf(f202,plain,(
% 1.63/1.32 $false | ~spl2_1),
% 1.63/1.32 inference(equality_resolution,[status(thm)],[f70])).
% 1.63/1.32 thf(f70,plain,(
% 1.63/1.32 ( ! [X1 : $i > $i] : ((sK0 != X1)) ) | ~spl2_1),
% 1.63/1.32 inference(avatar_component_clause,[status(thm)],[f69])).
% 1.63/1.32 thf(f69,definition,(
% 1.63/1.32 spl2_1 <=> ! [X1 : $i > $i] : (sK0 != X1)),
% 1.63/1.32 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.63/1.32 thf(f201,plain,(
% 1.63/1.32 spl2_1 | spl2_3 | ~spl2_2),
% 1.63/1.32 inference(avatar_split_clause,[status(thm)],[f200,f72,f76,f69])).
% 1.63/1.32 thf(f76,definition,(
% 1.63/1.32 spl2_3 <=> ((epsii @ (^[Y0 : $i > $i]: (((~ sK1) & (sK0 = Y0)) | ((sK0 = Y0) & sK1)))) = sK0)),
% 1.63/1.32 introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition])).
% 1.63/1.32 thf(f72,definition,(
% 1.63/1.32 spl2_2 <=> ($false = sK1)),
% 1.63/1.32 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.63/1.32 thf(f200,plain,(
% 1.63/1.32 ( ! [X1 : $i > $i] : (((epsii @ (^[Y0 : $i > $i]: (((~ sK1) & (sK0 = Y0)) | ((sK0 = Y0) & sK1)))) = sK0) | (sK0 != X1)) ) | ~spl2_2),
% 1.63/1.32 inference(trivial_inequality_removal,[status(thm)],[f199])).
% 1.63/1.32 thf(f199,plain,(
% 1.63/1.32 ( ! [X1 : $i > $i] : (((epsii @ (^[Y0 : $i > $i]: (((~ sK1) & (sK0 = Y0)) | ((sK0 = Y0) & sK1)))) = sK0) | (sK0 != X1) | ($false = $true)) ) | ~spl2_2),
% 1.63/1.32 inference(forward_demodulation,[status(thm)],[f172,f74])).
% 1.63/1.32 thf(f74,plain,(
% 1.63/1.32 ($false = sK1) | ~spl2_2),
% 1.63/1.32 inference(avatar_component_clause,[status(thm)],[f72])).
% 1.63/1.32 thf(f172,plain,(
% 1.63/1.32 ( ! [X1 : $i > $i] : ((sK1 = $true) | ((epsii @ (^[Y0 : $i > $i]: (((~ sK1) & (sK0 = Y0)) | ((sK0 = Y0) & sK1)))) = sK0) | (sK0 != X1)) )),
% 1.63/1.32 inference(duplicate_literal_removal,[status(thm)],[f168])).
% 1.63/1.32 thf(f168,plain,(
% 1.63/1.32 ( ! [X1 : $i > $i] : ((sK1 = $true) | (sK1 = $true) | (sK0 != X1) | ((epsii @ (^[Y0 : $i > $i]: (((~ sK1) & (sK0 = Y0)) | ((sK0 = Y0) & sK1)))) = sK0)) )),
% 1.63/1.32 inference(binary_proxy_clausification,[status(thm)],[f167])).
% 1.63/1.32 thf(f167,plain,(
% 1.63/1.32 ( ! [X1 : $i > $i] : ((sK0 != X1) | ((epsii @ (^[Y0 : $i > $i]: (((~ sK1) & (sK0 = Y0)) | ((sK0 = Y0) & sK1)))) = sK0) | ($true = ((sK0 = (epsii @ (^[Y0 : $i > $i]: (((~ sK1) & (sK0 = Y0)) | ((sK0 = Y0) & sK1))))) & sK1)) | (sK1 = $true)) )),
% 1.63/1.32 inference(equality_proxy_clausification,[status(thm)],[f166])).
% 1.63/1.32 thf(f166,plain,(
% 1.63/1.32 ( ! [X1 : $i > $i] : (($false = (sK0 = X1)) | (sK1 = $true) | ((epsii @ (^[Y0 : $i > $i]: (((~ sK1) & (sK0 = Y0)) | ((sK0 = Y0) & sK1)))) = sK0) | ($true = ((sK0 = (epsii @ (^[Y0 : $i > $i]: (((~ sK1) & (sK0 = Y0)) | ((sK0 = Y0) & sK1))))) & sK1))) )),
% 1.63/1.32 inference(equality_proxy_clausification,[status(thm)],[f157])).
% 1.63/1.32 thf(f157,plain,(
% 1.63/1.32 ( ! [X1 : $i > $i] : (($true = (sK0 = (epsii @ (^[Y0 : $i > $i]: (((~ sK1) & (sK0 = Y0)) | ((sK0 = Y0) & sK1)))))) | (sK1 = $true) | ($false = (sK0 = X1)) | ($true = ((sK0 = (epsii @ (^[Y0 : $i > $i]: (((~ sK1) & (sK0 = Y0)) | ((sK0 = Y0) & sK1))))) & sK1))) )),
% 1.63/1.32 inference(binary_proxy_clausification,[status(thm)],[f156])).
% 1.63/1.32 thf(f156,plain,(
% 1.63/1.32 ( ! [X1 : $i > $i] : (($true = ((~ sK1) & (sK0 = (epsii @ (^[Y0 : $i > $i]: (((~ sK1) & (sK0 = Y0)) | ((sK0 = Y0) & sK1))))))) | ($false = (sK0 = X1)) | (sK1 = $true) | ($true = ((sK0 = (epsii @ (^[Y0 : $i > $i]: (((~ sK1) & (sK0 = Y0)) | ((sK0 = Y0) & sK1))))) & sK1))) )),
% 1.63/1.32 inference(not_proxy_clausification,[status(thm)],[f155])).
% 1.63/1.32 thf(f155,plain,(
% 1.63/1.32 ( ! [X1 : $i > $i] : (($false = (~ sK1)) | ($true = ((sK0 = (epsii @ (^[Y0 : $i > $i]: (((~ sK1) & (sK0 = Y0)) | ((sK0 = Y0) & sK1))))) & sK1)) | ($false = (sK0 = X1)) | ($true = ((~ sK1) & (sK0 = (epsii @ (^[Y0 : $i > $i]: (((~ sK1) & (sK0 = Y0)) | ((sK0 = Y0) & sK1)))))))) )),
% 1.63/1.32 inference(binary_proxy_clausification,[status(thm)],[f154])).
% 1.63/1.32 thf(f154,plain,(
% 1.63/1.32 ( ! [X1 : $i > $i] : (($true = (((~ sK1) & (sK0 = (epsii @ (^[Y0 : $i > $i]: (((~ sK1) & (sK0 = Y0)) | ((sK0 = Y0) & sK1)))))) | ((sK0 = (epsii @ (^[Y0 : $i > $i]: (((~ sK1) & (sK0 = Y0)) | ((sK0 = Y0) & sK1))))) & sK1))) | ($false = (sK0 = X1)) | ($false = (~ sK1))) )),
% 1.63/1.32 inference(binary_proxy_clausification,[status(thm)],[f153])).
% 1.63/1.32 thf(f153,plain,(
% 1.63/1.32 ( ! [X1 : $i > $i] : (($false = ((~ sK1) & (sK0 = X1))) | ($true = (((~ sK1) & (sK0 = (epsii @ (^[Y0 : $i > $i]: (((~ sK1) & (sK0 = Y0)) | ((sK0 = Y0) & sK1)))))) | ((sK0 = (epsii @ (^[Y0 : $i > $i]: (((~ sK1) & (sK0 = Y0)) | ((sK0 = Y0) & sK1))))) & sK1)))) )),
% 1.63/1.32 inference(binary_proxy_clausification,[status(thm)],[f151])).
% 1.63/1.32 thf(f151,plain,(
% 1.63/1.32 ( ! [X1 : $i > $i] : (($false = (((~ sK1) & (sK0 = X1)) | ((sK0 = X1) & sK1))) | ($true = (((~ sK1) & (sK0 = (epsii @ (^[Y0 : $i > $i]: (((~ sK1) & (sK0 = Y0)) | ((sK0 = Y0) & sK1)))))) | ((sK0 = (epsii @ (^[Y0 : $i > $i]: (((~ sK1) & (sK0 = Y0)) | ((sK0 = Y0) & sK1))))) & sK1)))) )),
% 1.63/1.32 inference(beta_eta_normalization,[status(thm)],[f148])).
% 1.63/1.32 thf(f148,plain,(
% 1.63/1.32 ( ! [X1 : $i > $i] : (($true = ((^[Y0 : $i > $i]: (((~ sK1) & (sK0 = Y0)) | ((sK0 = Y0) & sK1))) @ (epsii @ (^[Y0 : $i > $i]: (((~ sK1) & (sK0 = Y0)) | ((sK0 = Y0) & sK1)))))) | ($false = ((^[Y0 : $i > $i]: (((~ sK1) & (sK0 = Y0)) | ((sK0 = Y0) & sK1))) @ X1))) )),
% 1.63/1.32 introduced(definition,[],[choice_axiom])).
% 1.63/1.32 thf(f195,plain,(
% 1.63/1.32 ~spl2_3),
% 1.63/1.32 inference(avatar_contradiction_clause,[status(thm)],[f194])).
% 1.63/1.32 thf(f194,plain,(
% 1.63/1.32 $false | ~spl2_3),
% 1.63/1.32 inference(trivial_inequality_removal,[status(thm)],[f150])).
% 1.63/1.32 thf(f150,plain,(
% 1.63/1.32 (sK0 != sK0) | ~spl2_3),
% 1.63/1.32 inference(superposition,[status(thm)],[f19,f78])).
% 1.63/1.32 thf(f78,plain,(
% 1.63/1.32 ((epsii @ (^[Y0 : $i > $i]: (((~ sK1) & (sK0 = Y0)) | ((sK0 = Y0) & sK1)))) = sK0) | ~spl2_3),
% 1.63/1.32 inference(avatar_component_clause,[status(thm)],[f76])).
% 1.63/1.32 thf(f19,plain,(
% 1.63/1.32 ((epsii @ (^[Y0 : $i > $i]: (((~ sK1) & (sK0 = Y0)) | ((sK0 = Y0) & sK1)))) != sK0)),
% 1.63/1.32 inference(beta_eta_normalization,[status(thm)],[f18])).
% 1.63/1.32 thf(f18,plain,(
% 1.63/1.32 (sK0 != ((^[Y0 : $o]: ((^[Y1 : $i > $i]: ((^[Y2 : $i > $i]: (epsii @ (^[Y3 : $i > $i]: (((~ Y0) & (Y2 = Y3)) | ((Y1 = Y3) & Y0))))))))) @ sK1 @ sK0 @ sK0))),
% 1.63/1.32 inference(definition_unfolding,[status(thm)],[f15,f16])).
% 1.63/1.32 thf(f16,plain,(
% 1.63/1.32 (if = (^[Y0 : $o]: ((^[Y1 : $i > $i]: ((^[Y2 : $i > $i]: (epsii @ (^[Y3 : $i > $i]: (((~ Y0) & (Y2 = Y3)) | ((Y1 = Y3) & Y0))))))))))),
% 1.63/1.32 inference(cnf_transformation,[status(thm)],[f7])).
% 1.63/1.32 thf(f7,plain,(
% 1.63/1.32 (if = (^[Y0 : $o]: ((^[Y1 : $i > $i]: ((^[Y2 : $i > $i]: (epsii @ (^[Y3 : $i > $i]: (((~ Y0) & (Y2 = Y3)) | ((Y1 = Y3) & Y0))))))))))),
% 1.63/1.32 inference(fool_elimination,[status(thm)],[f6])).
% 1.63/1.32 thf(f6,plain,(
% 1.63/1.32 (if = (^[X0 : $o, X1 : $i > $i, X2 : $i > $i] : (epsii @ (^[X3 : $i > $i] : ((X0 & (X1 = X3)) | ((X2 = X3) & ~X0))))))),
% 1.63/1.32 inference(rectify,[status(thm)],[f2])).
% 1.63/1.32 thf(f2,axiom,(
% 1.63/1.32 (if = (^[X2 : $o, X1 : $i > $i, X3 : $i > $i] : (epsii @ (^[X4 : $i > $i] : ((X2 & (X1 = X4)) | ((X3 = X4) & ~X2))))))),
% 1.63/1.32 file('/export/starexec/sandbox2/tmp/tmp.rg1nfRGPID/DTF2THF_19592.p',ifd)).
% 1.63/1.32 thf(f15,plain,(
% 1.63/1.32 ((if @ sK1 @ sK0 @ sK0) != sK0)),
% 1.63/1.32 inference(cnf_transformation,[status(thm)],[f14])).
% 1.63/1.32 thf(f14,plain,(
% 1.63/1.32 ((if @ sK1 @ sK0 @ sK0) != sK0)),
% 1.63/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f11,f13])).
% 1.63/1.32 thf(f13,plain,(
% 1.63/1.32 ? [X0 : $i > $i,X1 : $o] : ((if @ X1 @ X0 @ X0) != X0) => ((if @ sK1 @ sK0 @ sK0) != sK0)),
% 1.63/1.32 introduced(definition,[],[choice_axiom])).
% 1.63/1.32 thf(f11,plain,(
% 1.63/1.32 ? [X0 : $i > $i,X1 : $o] : ((if @ X1 @ X0 @ X0) != X0)),
% 1.63/1.32 inference(ennf_transformation,[status(thm)],[f10])).
% 1.63/1.32 thf(f10,plain,(
% 1.63/1.32 ~! [X0 : $i > $i,X1 : $o] : ((if @ X1 @ X0 @ X0) = X0)),
% 1.63/1.32 inference(rectify,[status(thm)],[f4])).
% 1.63/1.32 thf(f4,negated_conjecture,(
% 1.63/1.32 ~! [X1 : $i > $i,X2 : $o] : ((if @ X2 @ X1 @ X1) = X1)),
% 1.63/1.32 inference(negated_conjecture,[status(cth)],[f3])).
% 1.63/1.32 thf(f3,conjecture,(
% 1.63/1.32 ! [X1 : $i > $i,X2 : $o] : ((if @ X2 @ X1 @ X1) = X1)),
% 1.63/1.32 file('/export/starexec/sandbox2/tmp/tmp.rg1nfRGPID/DTF2THF_19592.p',conj)).
% 1.63/1.32 thf(f86,plain,(
% 1.63/1.32 spl2_1 | spl2_2 | spl2_3),
% 1.63/1.32 inference(avatar_split_clause,[status(thm)],[f60,f76,f72,f69])).
% 1.63/1.32 thf(f60,plain,(
% 1.63/1.32 ( ! [X1 : $i > $i] : ((sK0 != X1) | ((epsii @ (^[Y0 : $i > $i]: (((~ sK1) & (sK0 = Y0)) | ((sK0 = Y0) & sK1)))) = sK0) | ($false = sK1)) )),
% 1.63/1.32 inference(duplicate_literal_removal,[status(thm)],[f59])).
% 1.63/1.32 thf(f59,plain,(
% 1.63/1.32 ( ! [X1 : $i > $i] : (((epsii @ (^[Y0 : $i > $i]: (((~ sK1) & (sK0 = Y0)) | ((sK0 = Y0) & sK1)))) = sK0) | ($false = sK1) | ($false = sK1) | (sK0 != X1)) )),
% 1.63/1.32 inference(not_proxy_clausification,[status(thm)],[f58])).
% 1.63/1.32 thf(f58,plain,(
% 1.63/1.32 ( ! [X1 : $i > $i] : ((sK0 != X1) | ($false = sK1) | ($true = (~ sK1)) | ((epsii @ (^[Y0 : $i > $i]: (((~ sK1) & (sK0 = Y0)) | ((sK0 = Y0) & sK1)))) = sK0)) )),
% 1.63/1.32 inference(binary_proxy_clausification,[status(thm)],[f56])).
% 1.63/1.32 thf(f56,plain,(
% 1.63/1.32 ( ! [X1 : $i > $i] : (($false = sK1) | ((epsii @ (^[Y0 : $i > $i]: (((~ sK1) & (sK0 = Y0)) | ((sK0 = Y0) & sK1)))) = sK0) | (sK0 != X1) | ($true = ((~ sK1) & (sK0 = (epsii @ (^[Y0 : $i > $i]: (((~ sK1) & (sK0 = Y0)) | ((sK0 = Y0) & sK1)))))))) )),
% 1.63/1.32 inference(equality_proxy_clausification,[status(thm)],[f55])).
% 1.63/1.32 thf(f55,plain,(
% 1.63/1.32 ( ! [X1 : $i > $i] : (($true = (sK0 = (epsii @ (^[Y0 : $i > $i]: (((~ sK1) & (sK0 = Y0)) | ((sK0 = Y0) & sK1)))))) | ($false = sK1) | ($true = ((~ sK1) & (sK0 = (epsii @ (^[Y0 : $i > $i]: (((~ sK1) & (sK0 = Y0)) | ((sK0 = Y0) & sK1))))))) | (sK0 != X1)) )),
% 1.63/1.32 inference(binary_proxy_clausification,[status(thm)],[f53])).
% 1.63/1.32 thf(f53,plain,(
% 1.63/1.32 ( ! [X1 : $i > $i] : (($true = ((sK0 = (epsii @ (^[Y0 : $i > $i]: (((~ sK1) & (sK0 = Y0)) | ((sK0 = Y0) & sK1))))) & sK1)) | ($false = sK1) | ($true = ((~ sK1) & (sK0 = (epsii @ (^[Y0 : $i > $i]: (((~ sK1) & (sK0 = Y0)) | ((sK0 = Y0) & sK1))))))) | (sK0 != X1)) )),
% 1.63/1.32 inference(equality_proxy_clausification,[status(thm)],[f52])).
% 1.63/1.32 thf(f52,plain,(
% 1.63/1.32 ( ! [X1 : $i > $i] : (($false = (sK0 = X1)) | ($true = ((sK0 = (epsii @ (^[Y0 : $i > $i]: (((~ sK1) & (sK0 = Y0)) | ((sK0 = Y0) & sK1))))) & sK1)) | ($false = sK1) | ($true = ((~ sK1) & (sK0 = (epsii @ (^[Y0 : $i > $i]: (((~ sK1) & (sK0 = Y0)) | ((sK0 = Y0) & sK1)))))))) )),
% 1.63/1.32 inference(binary_proxy_clausification,[status(thm)],[f24])).
% 1.63/1.32 thf(f24,plain,(
% 1.63/1.32 ( ! [X1 : $i > $i] : (($false = ((sK0 = X1) & sK1)) | ($true = ((~ sK1) & (sK0 = (epsii @ (^[Y0 : $i > $i]: (((~ sK1) & (sK0 = Y0)) | ((sK0 = Y0) & sK1))))))) | ($true = ((sK0 = (epsii @ (^[Y0 : $i > $i]: (((~ sK1) & (sK0 = Y0)) | ((sK0 = Y0) & sK1))))) & sK1))) )),
% 1.63/1.32 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 1.63/1.32 thf(f23,plain,(
% 1.63/1.32 ( ! [X1 : $i > $i] : (($false = (((~ sK1) & (sK0 = X1)) | ((sK0 = X1) & sK1))) | ($true = ((sK0 = (epsii @ (^[Y0 : $i > $i]: (((~ sK1) & (sK0 = Y0)) | ((sK0 = Y0) & sK1))))) & sK1)) | ($true = ((~ sK1) & (sK0 = (epsii @ (^[Y0 : $i > $i]: (((~ sK1) & (sK0 = Y0)) | ((sK0 = Y0) & sK1)))))))) )),
% 1.63/1.32 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 1.63/1.32 thf(f22,plain,(
% 1.63/1.32 ( ! [X1 : $i > $i] : (($true = (((~ sK1) & (sK0 = (epsii @ (^[Y0 : $i > $i]: (((~ sK1) & (sK0 = Y0)) | ((sK0 = Y0) & sK1)))))) | ((sK0 = (epsii @ (^[Y0 : $i > $i]: (((~ sK1) & (sK0 = Y0)) | ((sK0 = Y0) & sK1))))) & sK1))) | ($false = (((~ sK1) & (sK0 = X1)) | ((sK0 = X1) & sK1)))) )),
% 1.63/1.32 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.63/1.32 thf(f20,plain,(
% 1.63/1.32 ( ! [X1 : $i > $i] : (($true = ((^[Y0 : $i > $i]: (((~ sK1) & (sK0 = Y0)) | ((sK0 = Y0) & sK1))) @ (epsii @ (^[Y0 : $i > $i]: (((~ sK1) & (sK0 = Y0)) | ((sK0 = Y0) & sK1)))))) | ($false = ((^[Y0 : $i > $i]: (((~ sK1) & (sK0 = Y0)) | ((sK0 = Y0) & sK1))) @ X1))) )),
% 1.63/1.32 introduced(definition,[],[choice_axiom])).
% 1.63/1.32 % SZS output end Proof for DTF2THF_19592
% 1.63/1.32 % (19755)------------------------------
% 1.63/1.32 % (19755)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.32 % (19755)Termination reason: Refutation
% 1.63/1.32
% 1.63/1.32 % (19755)Memory used [KB]: 5500
% 1.63/1.32 % (19755)Time elapsed: 0.008 s
% 1.63/1.32 % (19755)Instructions burned: 9 (million)
% 1.63/1.32 % (19755)------------------------------
% 1.63/1.32 % (19755)------------------------------
% 1.63/1.32 % (19752)Success in time 0.015 s
%------------------------------------------------------------------------------