%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU544^2 : 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 : n015.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 09:35:11 AM UTC 2026
% Result : Theorem 1.48s 1.29s
% Output : Refutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 196 ( 77 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 200 ( 21 ~; 19 |; 22 &; 106 @)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 4 usr; 5 con; 0-2 aty)
% ( 7 !!; 4 ??; 0 @@+; 0 @@-)
% Number of variables : 69 ( 28 ^; 29 !; 12 ?; 69 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
exu: ( $i > $o ) > $o ).
thf(func_def_13,type,
sK0: $i > $o ).
thf(func_def_16,type,
sK3: $i > $i ).
thf(f36,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f35]) ).
thf(f35,plain,
$false = $true,
inference(backward_demodulation,[status(thm)],[f14,f34]) ).
thf(f34,plain,
( ( sK0 @ sK1 )
= $false ),
inference(equality_resolution,[status(thm)],[f33]) ).
thf(f33,plain,
! [X0: $i] :
( ( sK1 != X0 )
| ( $false
= ( sK0 @ X0 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f31]) ).
thf(f31,plain,
! [X0: $i] :
( ( $false
= ( sK0 @ X0 ) )
| ( sK1 != X0 )
| ( $false
= ( sK0 @ X0 ) ) ),
inference(superposition,[status(thm)],[f26,f29]) ).
thf(f29,plain,
! [X0: $i] :
( ( sK1
= ( sK3 @ X0 ) )
| ( $false
= ( sK0 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f28]) ).
thf(f28,plain,
! [X0: $i] :
( ( sK1
= ( sK3 @ X0 ) )
| ( $true != $true )
| ( $false
= ( sK0 @ X0 ) ) ),
inference(superposition,[status(thm)],[f15,f25]) ).
thf(f25,plain,
! [X1: $i] :
( ( ( sK0 @ ( sK3 @ X1 ) )
= $true )
| ( $false
= ( sK0 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
! [X1: $i] :
( ( ( ( sK0 @ ( sK3 @ X1 ) )
=> ( X1
= ( sK3 @ X1 ) ) )
= $false )
| ( $false
= ( sK0 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f22]) ).
thf(f22,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( X1 = Y0 ) )
@ ( sK3 @ X1 ) )
= $false )
| ( $false
= ( sK0 @ X1 ) ) ),
inference(sigma_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ X1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( X1 = Y0 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
! [X1: $i] :
( ( ( sK0 @ X1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( X1 = Y0 ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f19]) ).
thf(f19,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) ) )
@ X1 )
= $false ),
inference(pi_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f17]) ).
thf(f17,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) ),
inference(definition_unfolding,[status(thm)],[f16,f13]) ).
thf(f13,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
( exu
= ( ^ [X0: $i > $o] :
? [X1: $i] :
( ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) )
& ( X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( exu
= ( ^ [X0: $i > $o] :
? [X1: $i] :
( ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) )
& ( X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.aLh2Wo5XQg/DTF2THF_23338.p',exu) ).
thf(f16,plain,
( ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) )
!= $true )
& ! [X2: $i] :
( ( $true
!= ( sK0 @ X2 ) )
| ( sK1 = X2 ) )
& ( ( sK0 @ sK1 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f11,f10]) ).
thf(f10,plain,
( ? [X0: $i > $o] :
( ( ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
!= $true )
& ? [X1: $i] :
( ! [X2: $i] :
( ( ( X0 @ X2 )
!= $true )
| ( X1 = X2 ) )
& ( ( X0 @ X1 )
= $true ) ) )
=> ( ( ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) )
!= $true )
& ? [X1: $i] :
( ! [X2: $i] :
( ( $true
!= ( sK0 @ X2 ) )
| ( X1 = X2 ) )
& ( ( sK0 @ X1 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X1: $i] :
( ! [X2: $i] :
( ( $true
!= ( sK0 @ X2 ) )
| ( X1 = X2 ) )
& ( ( sK0 @ X1 )
= $true ) )
=> ( ! [X2: $i] :
( ( $true
!= ( sK0 @ X2 ) )
| ( sK1 = X2 ) )
& ( ( sK0 @ sK1 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
? [X0: $i > $o] :
( ( ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
!= $true )
& ? [X1: $i] :
( ! [X2: $i] :
( ( ( X0 @ X2 )
!= $true )
| ( X1 = X2 ) )
& ( ( X0 @ X1 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ! [X0: $i > $o] :
( ? [X1: $i] :
( ! [X2: $i] :
( ( ( X0 @ X2 )
= $true )
=> ( X1 = X2 ) )
& ( ( X0 @ X1 )
= $true ) )
=> ( ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ! [X0: $i > $o] :
( ? [X1: $i] :
( ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) )
& ( X0 @ X1 ) )
=> ( exu
@ ^ [X3: $i] : ( X0 @ X3 ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ! [X0: $i > $o] :
( ? [X1: $i] :
( ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) )
& ( X0 @ X1 ) )
=> ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
! [X0: $i > $o] :
( ? [X1: $i] :
( ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) )
& ( X0 @ X1 ) )
=> ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.aLh2Wo5XQg/DTF2THF_23338.p',exuI1) ).
thf(f15,plain,
! [X2: $i] :
( ( $true
!= ( sK0 @ X2 ) )
| ( sK1 = X2 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f26,plain,
! [X1: $i] :
( ( ( sK3 @ X1 )
!= X1 )
| ( $false
= ( sK0 @ X1 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
! [X1: $i] :
( ( $false
= ( X1
= ( sK3 @ X1 ) ) )
| ( $false
= ( sK0 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
thf(f14,plain,
( ( sK0 @ sK1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU544^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n015.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 12:26:46 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
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.46 thf(spec,logic,$$dhol).
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % File : SEU544^2 : TPTP v9.2.1. Released v3.7.0.
% 0.31/0.46 % Domain : Set Theory
% 0.31/0.46 % Problem : Preliminary Notions - Equivalence Laws
% 0.31/0.46 % Version : Especial > Reduced > Especial.
% 0.31/0.46 % English : (! phi:i>o.(? x:i.phi x & (! y:i.phi y -> x = y)) ->
% 0.31/0.46 % exu (^ x:i.phi x))
% 0.31/0.46
% 0.31/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.31/0.46 % Source : [Bro08]
% 0.31/0.46 % Names : ZFC046l [Bro08]
% 0.31/0.46
% 0.31/0.46 % Status : Theorem
% 0.31/0.46 % Rating : 0.00 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v3.7.0
% 0.31/0.46 % Syntax : Number of formulae : 3 ( 1 unt; 1 typ; 1 def)
% 0.31/0.46 % Number of atoms : 5 ( 3 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 2 ( 2 avg)
% 0.31/0.46 % Number of connectives : 11 ( 0 ~; 0 |; 2 &; 6 @)
% 0.31/0.46 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.31/0.46 % Maximal formula depth : 8 ( 5 avg)
% 0.31/0.46 % Number of types : 2 ( 0 usr)
% 0.31/0.46 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 2 ( 1 usr; 0 con; 1-2 aty)
% 0.31/0.46 % Number of variables : 7 ( 2 ^; 3 !; 2 ?; 7 :)
% 0.31/0.46 % SPC : TH0_THM_EQU_NAR
% 0.31/0.46
% 0.31/0.46 % Comments : http://mathgate.info/detsetitem.php?id=408
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 thf(exu_type,type,
% 0.31/0.46 exu: ( $i > $o ) > $o ).
% 0.31/0.46
% 0.31/0.46 thf(exu,definition,
% 0.31/0.46 ( exu
% 0.31/0.46 = ( ^ [Xphi: $i > $o] :
% 0.31/0.46 ? [Xx: $i] :
% 0.31/0.46 ( ( Xphi @ Xx )
% 0.31/0.46 & ! [Xy: $i] :
% 0.31/0.46 ( ( Xphi @ Xy )
% 0.31/0.46 => ( Xx = Xy ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(exuI1,conjecture,
% 0.31/0.46 ! [Xphi: $i > $o] :
% 0.31/0.46 ( ? [Xx: $i] :
% 0.31/0.46 ( ( Xphi @ Xx )
% 0.31/0.46 & ! [Xy: $i] :
% 0.31/0.46 ( ( Xphi @ Xy )
% 0.31/0.46 => ( Xx = Xy ) ) )
% 0.31/0.46 => ( exu
% 0.31/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ).
% 0.31/0.46
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.47 ------------------------
% 1.48/1.27 ---- Embedded in THF ---
% 1.48/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.27 %%% Generated on Tue Feb 24 12:26:47 EST 2026
% 1.48/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.27 %%% Logic specification used:
% 1.48/1.27 %%% thf(spec, logic, $$dhol).
% 1.48/1.27
% 1.48/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.aLh2Wo5XQg/DTF2DTF23338.p
% See solution above
% 1.48/1.27 ------------------------
% 1.48/1.28 ---- Cleaned THF ---
% 1.48/1.28 thf(exu_type,type,
% 1.48/1.28 exu: ( $i > $o ) > $o ).
% 1.48/1.28
% 1.48/1.28 thf(exu,definition,
% 1.48/1.28 ( exu
% 1.48/1.28 = ( ^ [Xphi: $i > $o] :
% 1.48/1.28 ? [Xx: $i] :
% 1.48/1.28 ( ( Xphi @ Xx )
% 1.48/1.28 & ! [Xy: $i] :
% 1.48/1.28 ( ( Xphi @ Xy )
% 1.48/1.28 => ( Xx = Xy ) ) ) ) ) ).
% 1.48/1.28
% 1.48/1.28 thf(exuI1,conjecture,
% 1.48/1.28 ! [Xphi: $i > $o] :
% 1.48/1.28 ( ? [Xx: $i] :
% 1.48/1.28 ( ( Xphi @ Xx )
% 1.48/1.28 & ! [Xy: $i] :
% 1.48/1.28 ( ( Xphi @ Xy )
% 1.48/1.28 => ( Xx = Xy ) ) )
% 1.48/1.28 => ( exu
% 1.48/1.28 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ).
% 1.48/1.28 ------------------------
% 1.48/1.29 % (23458)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_23338 for (3000ds/18Mi)
% 1.48/1.29 % (23454)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_23338 for (3000ds/27Mi)
% 1.48/1.29 % (23458)First to succeed.
% 1.48/1.29 % (23454)Also succeeded, but the first one will report.
% 1.48/1.29 % (23458)Refutation found. Thanks to Tanya!
% 1.48/1.29 % SZS status Theorem for DTF2THF_23338
% 1.48/1.29 % SZS output start Proof for DTF2THF_23338
% 1.48/1.29 thf(func_def_0, type, exu: ($i > $o) > $o).
% 1.48/1.29 thf(func_def_13, type, sK0: $i > $o).
% 1.48/1.29 thf(func_def_16, type, sK3: $i > $i).
% 1.48/1.29 thf(f36,plain,(
% 1.48/1.29 $false),
% 1.48/1.29 inference(trivial_inequality_removal,[status(thm)],[f35])).
% 1.48/1.29 thf(f35,plain,(
% 1.48/1.29 ($false = $true)),
% 1.48/1.29 inference(backward_demodulation,[status(thm)],[f14,f34])).
% 1.48/1.29 thf(f34,plain,(
% 1.48/1.29 ((sK0 @ sK1) = $false)),
% 1.48/1.29 inference(equality_resolution,[status(thm)],[f33])).
% 1.48/1.29 thf(f33,plain,(
% 1.48/1.29 ( ! [X0 : $i] : ((sK1 != X0) | ($false = (sK0 @ X0))) )),
% 1.48/1.29 inference(duplicate_literal_removal,[status(thm)],[f31])).
% 1.48/1.29 thf(f31,plain,(
% 1.48/1.29 ( ! [X0 : $i] : (($false = (sK0 @ X0)) | (sK1 != X0) | ($false = (sK0 @ X0))) )),
% 1.48/1.29 inference(superposition,[status(thm)],[f26,f29])).
% 1.48/1.29 thf(f29,plain,(
% 1.48/1.29 ( ! [X0 : $i] : ((sK1 = (sK3 @ X0)) | ($false = (sK0 @ X0))) )),
% 1.48/1.29 inference(trivial_inequality_removal,[status(thm)],[f28])).
% 1.48/1.29 thf(f28,plain,(
% 1.48/1.29 ( ! [X0 : $i] : ((sK1 = (sK3 @ X0)) | ($true != $true) | ($false = (sK0 @ X0))) )),
% 1.48/1.29 inference(superposition,[status(thm)],[f15,f25])).
% 1.48/1.29 thf(f25,plain,(
% 1.48/1.29 ( ! [X1 : $i] : (((sK0 @ (sK3 @ X1)) = $true) | ($false = (sK0 @ X1))) )),
% 1.48/1.29 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 1.48/1.29 thf(f23,plain,(
% 1.48/1.29 ( ! [X1 : $i] : ((((sK0 @ (sK3 @ X1)) => (X1 = (sK3 @ X1))) = $false) | ($false = (sK0 @ X1))) )),
% 1.48/1.29 inference(beta_eta_normalization,[status(thm)],[f22])).
% 1.48/1.29 thf(f22,plain,(
% 1.48/1.29 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((sK0 @ Y0) => (X1 = Y0))) @ (sK3 @ X1)) = $false) | ($false = (sK0 @ X1))) )),
% 1.48/1.29 inference(sigma_clausification,[status(thm)],[f21])).
% 1.48/1.29 thf(f21,plain,(
% 1.48/1.29 ( ! [X1 : $i] : (($false = (sK0 @ X1)) | ((!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (X1 = Y0)))) = $false)) )),
% 1.48/1.29 inference(binary_proxy_clausification,[status(thm)],[f20])).
% 1.48/1.29 thf(f20,plain,(
% 1.48/1.29 ( ! [X1 : $i] : ((((sK0 @ X1) & (!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (X1 = Y0))))) = $false)) )),
% 1.48/1.29 inference(beta_eta_normalization,[status(thm)],[f19])).
% 1.48/1.29 thf(f19,plain,(
% 1.48/1.29 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((sK0 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1)))))) @ X1) = $false)) )),
% 1.48/1.29 inference(pi_clausification,[status(thm)],[f18])).
% 1.48/1.29 thf(f18,plain,(
% 1.48/1.29 ((?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1))))))) != $true)),
% 1.48/1.29 inference(beta_eta_normalization,[status(thm)],[f17])).
% 1.48/1.29 thf(f17,plain,(
% 1.48/1.29 ($true != ((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))) @ (^[Y0 : $i]: (sK0 @ Y0))))),
% 1.48/1.29 inference(definition_unfolding,[status(thm)],[f16,f13])).
% 1.48/1.29 thf(f13,plain,(
% 1.48/1.29 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))),
% 1.48/1.29 inference(cnf_transformation,[status(thm)],[f6])).
% 1.48/1.29 thf(f6,plain,(
% 1.48/1.29 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))),
% 1.48/1.29 inference(fool_elimination,[status(thm)],[f5])).
% 1.48/1.29 thf(f5,plain,(
% 1.48/1.29 (exu = (^[X0 : $i > $o] : (? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))))),
% 1.48/1.29 inference(rectify,[status(thm)],[f1])).
% 1.48/1.29 thf(f1,axiom,(
% 1.48/1.29 (exu = (^[X0 : $i > $o] : (? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))))),
% 1.48/1.29 file('/export/starexec/sandbox/tmp/tmp.aLh2Wo5XQg/DTF2THF_23338.p',exu)).
% 1.48/1.29 thf(f16,plain,(
% 1.48/1.29 ((exu @ (^[Y0 : $i]: (sK0 @ Y0))) != $true)),
% 1.48/1.29 inference(cnf_transformation,[status(thm)],[f12])).
% 1.48/1.29 thf(f12,plain,(
% 1.48/1.29 ((exu @ (^[Y0 : $i]: (sK0 @ Y0))) != $true) & (! [X2 : $i] : (($true != (sK0 @ X2)) | (sK1 = X2)) & ((sK0 @ sK1) = $true))),
% 1.48/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f11,f10])).
% 1.48/1.29 thf(f10,plain,(
% 1.48/1.29 ? [X0 : $i > $o] : (((exu @ (^[Y0 : $i]: (X0 @ Y0))) != $true) & ? [X1 : $i] : (! [X2 : $i] : (((X0 @ X2) != $true) | (X1 = X2)) & ((X0 @ X1) = $true))) => (((exu @ (^[Y0 : $i]: (sK0 @ Y0))) != $true) & ? [X1 : $i] : (! [X2 : $i] : (($true != (sK0 @ X2)) | (X1 = X2)) & ((sK0 @ X1) = $true)))),
% 1.48/1.29 introduced(definition,[],[choice_axiom])).
% 1.48/1.29 thf(f11,plain,(
% 1.48/1.29 ? [X1 : $i] : (! [X2 : $i] : (($true != (sK0 @ X2)) | (X1 = X2)) & ((sK0 @ X1) = $true)) => (! [X2 : $i] : (($true != (sK0 @ X2)) | (sK1 = X2)) & ((sK0 @ sK1) = $true))),
% 1.48/1.29 introduced(definition,[],[choice_axiom])).
% 1.48/1.29 thf(f9,plain,(
% 1.48/1.29 ? [X0 : $i > $o] : (((exu @ (^[Y0 : $i]: (X0 @ Y0))) != $true) & ? [X1 : $i] : (! [X2 : $i] : (((X0 @ X2) != $true) | (X1 = X2)) & ((X0 @ X1) = $true)))),
% 1.48/1.29 inference(ennf_transformation,[status(thm)],[f8])).
% 1.48/1.29 thf(f8,plain,(
% 1.48/1.29 ~! [X0 : $i > $o] : (? [X1 : $i] : (! [X2 : $i] : (((X0 @ X2) = $true) => (X1 = X2)) & ((X0 @ X1) = $true)) => ((exu @ (^[Y0 : $i]: (X0 @ Y0))) = $true))),
% 1.48/1.29 inference(fool_elimination,[status(thm)],[f7])).
% 1.48/1.29 thf(f7,plain,(
% 1.48/1.29 ~! [X0 : $i > $o] : (? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)) => (exu @ (^[X3 : $i] : (X0 @ X3))))),
% 1.48/1.29 inference(rectify,[status(thm)],[f3])).
% 1.48/1.29 thf(f3,negated_conjecture,(
% 1.48/1.29 ~! [X0 : $i > $o] : (? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)) => (exu @ (^[X1 : $i] : (X0 @ X1))))),
% 1.48/1.29 inference(negated_conjecture,[status(cth)],[f2])).
% 1.48/1.29 thf(f2,conjecture,(
% 1.48/1.29 ! [X0 : $i > $o] : (? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)) => (exu @ (^[X1 : $i] : (X0 @ X1))))),
% 1.48/1.29 file('/export/starexec/sandbox/tmp/tmp.aLh2Wo5XQg/DTF2THF_23338.p',exuI1)).
% 1.48/1.29 thf(f15,plain,(
% 1.48/1.29 ( ! [X2 : $i] : (($true != (sK0 @ X2)) | (sK1 = X2)) )),
% 1.48/1.29 inference(cnf_transformation,[status(thm)],[f12])).
% 1.48/1.29 thf(f26,plain,(
% 1.48/1.29 ( ! [X1 : $i] : (((sK3 @ X1) != X1) | ($false = (sK0 @ X1))) )),
% 1.48/1.29 inference(equality_proxy_clausification,[status(thm)],[f24])).
% 1.48/1.29 thf(f24,plain,(
% 1.48/1.29 ( ! [X1 : $i] : (($false = (X1 = (sK3 @ X1))) | ($false = (sK0 @ X1))) )),
% 1.48/1.29 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 1.48/1.29 thf(f14,plain,(
% 1.48/1.29 ((sK0 @ sK1) = $true)),
% 1.48/1.29 inference(cnf_transformation,[status(thm)],[f12])).
% 1.48/1.29 % SZS output end Proof for DTF2THF_23338
% 1.48/1.29 % (23458)------------------------------
% 1.48/1.29 % (23458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.29 % (23458)Termination reason: Refutation
% 1.48/1.29
% 1.48/1.29 % (23458)Memory used [KB]: 5500
% 1.48/1.29 % (23458)Time elapsed: 0.003 s
% 1.48/1.29 % (23458)Instructions burned: 3 (million)
% 1.48/1.29 % (23458)------------------------------
% 1.48/1.29 % (23458)------------------------------
% 1.48/1.30 % (23451)Success in time 0.003 s
%------------------------------------------------------------------------------