%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU545^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n020.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 1.66s 1.33s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 4
% Syntax : Number of formulae : 36 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 241 ( 93 equ; 0 cnn)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 240 ( 29 ~; 26 |; 21 &; 120 @)
% ( 0 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 9 usr; 6 con; 0-2 aty)
% ( 7 !!; 4 ??; 0 @@+; 0 @@-)
% Number of variables : 81 ( 29 ^; 38 !; 14 ?; 81 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
exu: ( $i > $o ) > $o ).
thf(func_def_14,type,
sK0: $i > $o ).
thf(func_def_16,type,
sK2: $i > $o ).
thf(func_def_18,type,
sK4: $i > ( $i > $o ) > $i ).
thf(func_def_20,type,
sK6: $i > $i ).
thf(func_def_21,type,
sK7: ( $i > $o ) > $i ).
thf(func_def_22,type,
sK8: ( $i > $o ) > $i ).
thf(f90,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f89]) ).
thf(f89,plain,
$true = $false,
inference(backward_demodulation,[status(thm)],[f25,f88]) ).
thf(f88,plain,
( ( sK0 @ sK1 )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f87]) ).
thf(f87,plain,
( ( ( sK0 @ sK1 )
= $false )
| ( sK1 != sK1 ) ),
inference(superposition,[status(thm)],[f48,f84]) ).
thf(f84,plain,
( ( sK6 @ sK1 )
= sK1 ),
inference(trivial_inequality_removal,[status(thm)],[f78]) ).
thf(f78,plain,
( ( ( sK6 @ sK1 )
= sK1 )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f25,f74]) ).
thf(f74,plain,
! [X0: $i] :
( ( ( sK0 @ X0 )
= $false )
| ( ( sK6 @ X0 )
= sK1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f72]) ).
thf(f72,plain,
! [X0: $i] :
( ( ( sK6 @ X0 )
= sK1 )
| ( ( sK0 @ X0 )
= $false )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f70,f47]) ).
thf(f47,plain,
! [X1: $i] :
( ( ( sK0 @ ( sK6 @ X1 ) )
= $true )
| ( ( sK0 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
! [X1: $i] :
( ( ( sK0 @ X1 )
= $false )
| ( ( ( sK0 @ ( sK6 @ X1 ) )
=> ( X1
= ( sK6 @ X1 ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f44]) ).
thf(f44,plain,
! [X1: $i] :
( ( ( sK0 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( X1 = Y0 ) )
@ ( sK6 @ X1 ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( X1 = Y0 ) ) )
= $false )
| ( ( sK0 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
! [X1: $i] :
( ( ( sK0 @ X1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( X1 = Y0 ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f41]) ).
thf(f41,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) ) )
@ X1 )
= $false ),
inference(pi_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
( $true
!= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f34]) ).
thf(f34,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)],[f26,f28]) ).
thf(f28,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [X0: $i > $o] :
? [X1: $i] :
( ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) )
& ( X0 @ X1 ) ) )
= exu ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: $i > $o] :
? [X1: $i] :
( ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) )
& ( X0 @ X1 ) ) )
= exu ),
file('/export/starexec/sandbox2/tmp/tmp.EkfjRFc6r6/DTF2THF_18589.p',exu) ).
thf(f26,plain,
( $true
!= ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( exuI1 = $true )
& ( $true
!= ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) )
& ( $true
= ( sK0 @ sK1 ) )
& ! [X2: $i,X3: $i] :
( ( $true
!= ( sK0 @ X3 ) )
| ( $true
!= ( sK0 @ X2 ) )
| ( X2 = X3 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f16,f15]) ).
thf(f15,plain,
( ? [X0: $i > $o] :
( ( $true
!= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
& ? [X1: $i] :
( ( X0 @ X1 )
= $true )
& ! [X2: $i,X3: $i] :
( ( $true
!= ( X0 @ X3 ) )
| ( ( X0 @ X2 )
!= $true )
| ( X2 = X3 ) ) )
=> ( ( $true
!= ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) )
& ? [X1: $i] :
( $true
= ( sK0 @ X1 ) )
& ! [X3: $i,X2: $i] :
( ( $true
!= ( sK0 @ X3 ) )
| ( $true
!= ( sK0 @ X2 ) )
| ( X2 = X3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
( ? [X1: $i] :
( $true
= ( sK0 @ X1 ) )
=> ( $true
= ( sK0 @ sK1 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ( exuI1 = $true )
& ? [X0: $i > $o] :
( ( $true
!= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
& ? [X1: $i] :
( ( X0 @ X1 )
= $true )
& ! [X2: $i,X3: $i] :
( ( $true
!= ( X0 @ X3 ) )
| ( ( X0 @ X2 )
!= $true )
| ( X2 = X3 ) ) ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ? [X0: $i > $o] :
( ( $true
!= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
& ! [X2: $i,X3: $i] :
( ( X2 = X3 )
| ( $true
!= ( X0 @ X3 ) )
| ( ( X0 @ X2 )
!= $true ) )
& ? [X1: $i] :
( ( X0 @ X1 )
= $true ) )
& ( exuI1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( ( exuI1 = $true )
=> ! [X0: $i > $o] :
( ? [X1: $i] :
( ( X0 @ X1 )
= $true )
=> ( ! [X2: $i,X3: $i] :
( ( ( X0 @ X2 )
= $true )
=> ( ( $true
= ( X0 @ X3 ) )
=> ( X2 = X3 ) ) )
=> ( $true
= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( exuI1
=> ! [X0: $i > $o] :
( ? [X1: $i] : ( X0 @ X1 )
=> ( ! [X2: $i,X3: $i] :
( ( X0 @ X2 )
=> ( ( X0 @ X3 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X4: $i] : ( X0 @ X4 ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( exuI1
=> ! [X0: $i > $o] :
( ? [X1: $i] : ( X0 @ X1 )
=> ( ! [X1: $i,X2: $i] :
( ( X0 @ X1 )
=> ( ( X0 @ X2 )
=> ( X1 = X2 ) ) )
=> ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( exuI1
=> ! [X0: $i > $o] :
( ? [X1: $i] : ( X0 @ X1 )
=> ( ! [X1: $i,X2: $i] :
( ( X0 @ X1 )
=> ( ( X0 @ X2 )
=> ( X1 = X2 ) ) )
=> ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.EkfjRFc6r6/DTF2THF_18589.p',exuI3) ).
thf(f70,plain,
! [X0: $i] :
( ( $true
!= ( sK0 @ X0 ) )
| ( sK1 = X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f69]) ).
thf(f69,plain,
! [X0: $i] :
( ( $true != $true )
| ( sK1 = X0 )
| ( $true
!= ( sK0 @ X0 ) ) ),
inference(superposition,[status(thm)],[f24,f25]) ).
thf(f24,plain,
! [X2: $i,X3: $i] :
( ( $true
!= ( sK0 @ X3 ) )
| ( $true
!= ( sK0 @ X2 ) )
| ( X2 = X3 ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f48,plain,
! [X1: $i] :
( ( ( sK6 @ X1 )
!= X1 )
| ( ( sK0 @ X1 )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
! [X1: $i] :
( ( ( sK0 @ X1 )
= $false )
| ( ( X1
= ( sK6 @ X1 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f45]) ).
thf(f25,plain,
( $true
= ( sK0 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU545^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n020.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:26:42 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
% 0.27/0.47 ---- Original DTF file ---
% 0.27/0.47 thf(spec,logic,$$dhol).
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 % File : SEU545^2 : TPTP v9.2.1. Released v3.7.0.
% 0.27/0.47 % Domain : Set Theory
% 0.27/0.47 % Problem : Preliminary Notions - Equivalence Laws
% 0.27/0.47 % Version : Especial > Reduced > Especial.
% 0.27/0.47 % English : (! phi:i>o.(? x:i.phi x) -> (! x:i.! y:i.phi x -> phi y ->
% 0.27/0.47 % x = y) -> exu (^ x:i.phi x))
% 0.27/0.47
% 0.27/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.27/0.47 % Source : [Bro08]
% 0.27/0.47 % Names : ZFC047l [Bro08]
% 0.27/0.47
% 0.27/0.47 % Status : Theorem
% 0.27/0.47 % 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
% 0.27/0.47 % Syntax : Number of formulae : 5 ( 2 unt; 2 typ; 2 def)
% 0.27/0.47 % Number of atoms : 10 ( 5 equ; 0 cnn)
% 0.27/0.47 % Maximal formula atoms : 3 ( 3 avg)
% 0.27/0.47 % Number of connectives : 21 ( 0 ~; 0 |; 2 &; 11 @)
% 0.27/0.47 % ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% 0.27/0.47 % Maximal formula depth : 10 ( 4 avg)
% 0.27/0.47 % Number of types : 2 ( 0 usr)
% 0.27/0.47 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.27/0.47 % Number of symbols : 3 ( 2 usr; 1 con; 0-2 aty)
% 0.27/0.47 % Number of variables : 12 ( 3 ^; 6 !; 3 ?; 12 :)
% 0.27/0.47 % SPC : TH0_THM_EQU_NAR
% 0.27/0.47
% 0.27/0.47 % Comments : http://mathgate.info/detsetitem.php?id=410
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 thf(exu_type,type,
% 0.27/0.47 exu: ( $i > $o ) > $o ).
% 0.27/0.47
% 0.27/0.47 thf(exu,definition,
% 0.27/0.47 ( exu
% 0.27/0.47 = ( ^ [Xphi: $i > $o] :
% 0.27/0.47 ? [Xx: $i] :
% 0.27/0.47 ( ( Xphi @ Xx )
% 0.27/0.47 & ! [Xy: $i] :
% 0.27/0.47 ( ( Xphi @ Xy )
% 0.27/0.47 => ( Xx = Xy ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(exuI1_type,type,
% 0.27/0.47 exuI1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(exuI1,definition,
% 0.27/0.47 ( exuI1
% 0.27/0.47 = ( ! [Xphi: $i > $o] :
% 0.27/0.47 ( ? [Xx: $i] :
% 0.27/0.47 ( ( Xphi @ Xx )
% 0.27/0.47 & ! [Xy: $i] :
% 0.27/0.47 ( ( Xphi @ Xy )
% 0.27/0.47 => ( Xx = Xy ) ) )
% 0.27/0.47 => ( exu
% 0.27/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(exuI3,conjecture,
% 0.27/0.47 ( exuI1
% 0.27/0.47 => ! [Xphi: $i > $o] :
% 0.27/0.47 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.27/0.47 => ( ! [Xx: $i,Xy: $i] :
% 0.27/0.47 ( ( Xphi @ Xx )
% 0.27/0.47 => ( ( Xphi @ Xy )
% 0.27/0.47 => ( Xx = Xy ) ) )
% 0.27/0.47 => ( exu
% 0.27/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 ------------------------
% 1.46/1.29 ---- Embedded in THF ---
% 1.46/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.29 %%% Generated on Tue Feb 24 12:26:43 EST 2026
% 1.46/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.29 %%% Logic specification used:
% 1.46/1.29 %%% thf(spec, logic, $$dhol).
% 1.46/1.29
% 1.46/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.EkfjRFc6r6/DTF2DTF18589.p
% See solution above
% 1.46/1.29 ------------------------
% 1.66/1.30 ---- Cleaned THF ---
% 1.66/1.31 thf(exu_type,type,
% 1.66/1.31 exu: ( $i > $o ) > $o ).
% 1.66/1.31
% 1.66/1.31 thf(exu,definition,
% 1.66/1.31 ( exu
% 1.66/1.31 = ( ^ [Xphi: $i > $o] :
% 1.66/1.31 ? [Xx: $i] :
% 1.66/1.31 ( ( Xphi @ Xx )
% 1.66/1.31 & ! [Xy: $i] :
% 1.66/1.31 ( ( Xphi @ Xy )
% 1.66/1.31 => ( Xx = Xy ) ) ) ) ) ).
% 1.66/1.31
% 1.66/1.31 thf(exuI1_type,type,
% 1.66/1.31 exuI1: $o ).
% 1.66/1.31
% 1.66/1.31 thf(exuI1,definition,
% 1.66/1.31 ( exuI1
% 1.66/1.31 = ( ! [Xphi: $i > $o] :
% 1.66/1.31 ( ? [Xx: $i] :
% 1.66/1.31 ( ( Xphi @ Xx )
% 1.66/1.31 & ! [Xy: $i] :
% 1.66/1.31 ( ( Xphi @ Xy )
% 1.66/1.31 => ( Xx = Xy ) ) )
% 1.66/1.31 => ( exu
% 1.66/1.31 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 1.66/1.31
% 1.66/1.31 thf(exuI3,conjecture,
% 1.66/1.31 ( exuI1
% 1.66/1.31 => ! [Xphi: $i > $o] :
% 1.66/1.31 ( ? [Xx: $i] : ( Xphi @ Xx )
% 1.66/1.31 => ( ! [Xx: $i,Xy: $i] :
% 1.66/1.31 ( ( Xphi @ Xx )
% 1.66/1.31 => ( ( Xphi @ Xy )
% 1.66/1.31 => ( Xx = Xy ) ) )
% 1.66/1.31 => ( exu
% 1.66/1.31 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 1.66/1.31 ------------------------
% 1.66/1.32 % (18705)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_18589 for (2999ds/27Mi)
% 1.66/1.32 % (18709)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_18589 for (2999ds/18Mi)
% 1.66/1.32 % (18709)First to succeed.
% 1.66/1.32 % (18705)Also succeeded, but the first one will report.
% 1.66/1.33 % (18709)Refutation found. Thanks to Tanya!
% 1.66/1.33 % SZS status Theorem for DTF2THF_18589
% 1.66/1.33 % SZS output start Proof for DTF2THF_18589
% 1.66/1.33 thf(func_def_0, type, exu: ($i > $o) > $o).
% 1.66/1.33 thf(func_def_14, type, sK0: $i > $o).
% 1.66/1.33 thf(func_def_16, type, sK2: $i > $o).
% 1.66/1.33 thf(func_def_18, type, sK4: $i > ($i > $o) > $i).
% 1.66/1.33 thf(func_def_20, type, sK6: $i > $i).
% 1.66/1.33 thf(func_def_21, type, sK7: ($i > $o) > $i).
% 1.66/1.33 thf(func_def_22, type, sK8: ($i > $o) > $i).
% 1.66/1.33 thf(f90,plain,(
% 1.66/1.33 $false),
% 1.66/1.33 inference(trivial_inequality_removal,[status(thm)],[f89])).
% 1.66/1.33 thf(f89,plain,(
% 1.66/1.33 ($true = $false)),
% 1.66/1.33 inference(backward_demodulation,[status(thm)],[f25,f88])).
% 1.66/1.33 thf(f88,plain,(
% 1.66/1.33 ((sK0 @ sK1) = $false)),
% 1.66/1.33 inference(trivial_inequality_removal,[status(thm)],[f87])).
% 1.66/1.33 thf(f87,plain,(
% 1.66/1.33 ((sK0 @ sK1) = $false) | (sK1 != sK1)),
% 1.66/1.33 inference(superposition,[status(thm)],[f48,f84])).
% 1.66/1.33 thf(f84,plain,(
% 1.66/1.33 ((sK6 @ sK1) = sK1)),
% 1.66/1.33 inference(trivial_inequality_removal,[status(thm)],[f78])).
% 1.66/1.33 thf(f78,plain,(
% 1.66/1.33 ((sK6 @ sK1) = sK1) | ($true = $false)),
% 1.66/1.33 inference(superposition,[status(thm)],[f25,f74])).
% 1.66/1.33 thf(f74,plain,(
% 1.66/1.33 ( ! [X0 : $i] : (((sK0 @ X0) = $false) | ((sK6 @ X0) = sK1)) )),
% 1.66/1.33 inference(trivial_inequality_removal,[status(thm)],[f72])).
% 1.66/1.33 thf(f72,plain,(
% 1.66/1.33 ( ! [X0 : $i] : (((sK6 @ X0) = sK1) | ((sK0 @ X0) = $false) | ($true != $true)) )),
% 1.66/1.33 inference(superposition,[status(thm)],[f70,f47])).
% 1.66/1.33 thf(f47,plain,(
% 1.66/1.33 ( ! [X1 : $i] : (((sK0 @ (sK6 @ X1)) = $true) | ((sK0 @ X1) = $false)) )),
% 1.66/1.33 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 1.66/1.33 thf(f45,plain,(
% 1.66/1.33 ( ! [X1 : $i] : (((sK0 @ X1) = $false) | (((sK0 @ (sK6 @ X1)) => (X1 = (sK6 @ X1))) = $false)) )),
% 1.66/1.33 inference(beta_eta_normalization,[status(thm)],[f44])).
% 1.66/1.33 thf(f44,plain,(
% 1.66/1.33 ( ! [X1 : $i] : (((sK0 @ X1) = $false) | (((^[Y0 : $i]: ((sK0 @ Y0) => (X1 = Y0))) @ (sK6 @ X1)) = $false)) )),
% 1.66/1.33 inference(sigma_clausification,[status(thm)],[f43])).
% 1.66/1.33 thf(f43,plain,(
% 1.66/1.33 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (X1 = Y0)))) = $false) | ((sK0 @ X1) = $false)) )),
% 1.66/1.33 inference(binary_proxy_clausification,[status(thm)],[f42])).
% 1.66/1.33 thf(f42,plain,(
% 1.66/1.33 ( ! [X1 : $i] : ((((sK0 @ X1) & (!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (X1 = Y0))))) = $false)) )),
% 1.66/1.33 inference(beta_eta_normalization,[status(thm)],[f41])).
% 1.66/1.33 thf(f41,plain,(
% 1.66/1.33 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((sK0 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1)))))) @ X1) = $false)) )),
% 1.66/1.33 inference(pi_clausification,[status(thm)],[f40])).
% 1.66/1.33 thf(f40,plain,(
% 1.66/1.33 ($true != (?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1))))))))),
% 1.66/1.33 inference(beta_eta_normalization,[status(thm)],[f34])).
% 1.66/1.33 thf(f34,plain,(
% 1.66/1.33 ($true != ((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))) @ (^[Y0 : $i]: (sK0 @ Y0))))),
% 1.66/1.33 inference(definition_unfolding,[status(thm)],[f26,f28])).
% 1.66/1.33 thf(f28,plain,(
% 1.66/1.33 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))),
% 1.66/1.33 inference(cnf_transformation,[status(thm)],[f11])).
% 1.66/1.33 thf(f11,plain,(
% 1.66/1.33 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))),
% 1.66/1.33 inference(fool_elimination,[status(thm)],[f10])).
% 1.66/1.33 thf(f10,plain,(
% 1.66/1.33 ((^[X0 : $i > $o] : (? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))) = exu)),
% 1.66/1.33 inference(rectify,[status(thm)],[f1])).
% 1.66/1.33 thf(f1,axiom,(
% 1.66/1.33 ((^[X0 : $i > $o] : (? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))) = exu)),
% 1.66/1.33 file('/export/starexec/sandbox2/tmp/tmp.EkfjRFc6r6/DTF2THF_18589.p',exu)).
% 1.66/1.33 thf(f26,plain,(
% 1.66/1.33 ($true != (exu @ (^[Y0 : $i]: (sK0 @ Y0))))),
% 1.66/1.33 inference(cnf_transformation,[status(thm)],[f17])).
% 1.66/1.33 thf(f17,plain,(
% 1.66/1.33 (exuI1 = $true) & (($true != (exu @ (^[Y0 : $i]: (sK0 @ Y0)))) & ($true = (sK0 @ sK1)) & ! [X2 : $i,X3 : $i] : (($true != (sK0 @ X3)) | ($true != (sK0 @ X2)) | (X2 = X3)))),
% 1.66/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f16,f15])).
% 1.66/1.33 thf(f15,plain,(
% 1.66/1.33 ? [X0 : $i > $o] : (($true != (exu @ (^[Y0 : $i]: (X0 @ Y0)))) & ? [X1 : $i] : ((X0 @ X1) = $true) & ! [X2 : $i,X3 : $i] : (($true != (X0 @ X3)) | ((X0 @ X2) != $true) | (X2 = X3))) => (($true != (exu @ (^[Y0 : $i]: (sK0 @ Y0)))) & ? [X1 : $i] : ($true = (sK0 @ X1)) & ! [X3 : $i,X2 : $i] : (($true != (sK0 @ X3)) | ($true != (sK0 @ X2)) | (X2 = X3)))),
% 1.66/1.33 introduced(definition,[],[choice_axiom])).
% 1.66/1.33 thf(f16,plain,(
% 1.66/1.33 ? [X1 : $i] : ($true = (sK0 @ X1)) => ($true = (sK0 @ sK1))),
% 1.66/1.33 introduced(definition,[],[choice_axiom])).
% 1.66/1.33 thf(f13,plain,(
% 1.66/1.33 (exuI1 = $true) & ? [X0 : $i > $o] : (($true != (exu @ (^[Y0 : $i]: (X0 @ Y0)))) & ? [X1 : $i] : ((X0 @ X1) = $true) & ! [X2 : $i,X3 : $i] : (($true != (X0 @ X3)) | ((X0 @ X2) != $true) | (X2 = X3)))),
% 1.66/1.33 inference(flattening,[status(thm)],[f12])).
% 1.66/1.33 thf(f12,plain,(
% 1.66/1.33 ? [X0 : $i > $o] : ((($true != (exu @ (^[Y0 : $i]: (X0 @ Y0)))) & ! [X2 : $i,X3 : $i] : (((X2 = X3) | ($true != (X0 @ X3))) | ((X0 @ X2) != $true))) & ? [X1 : $i] : ((X0 @ X1) = $true)) & (exuI1 = $true)),
% 1.66/1.33 inference(ennf_transformation,[status(thm)],[f7])).
% 1.66/1.33 thf(f7,plain,(
% 1.66/1.33 ~((exuI1 = $true) => ! [X0 : $i > $o] : (? [X1 : $i] : ((X0 @ X1) = $true) => (! [X2 : $i,X3 : $i] : (((X0 @ X2) = $true) => (($true = (X0 @ X3)) => (X2 = X3))) => ($true = (exu @ (^[Y0 : $i]: (X0 @ Y0)))))))),
% 1.66/1.33 inference(fool_elimination,[status(thm)],[f6])).
% 1.66/1.33 thf(f6,plain,(
% 1.66/1.33 ~(exuI1 => ! [X0 : $i > $o] : (? [X1 : $i] : (X0 @ X1) => (! [X2 : $i,X3 : $i] : ((X0 @ X2) => ((X0 @ X3) => (X2 = X3))) => (exu @ (^[X4 : $i] : (X0 @ X4))))))),
% 1.66/1.33 inference(rectify,[status(thm)],[f4])).
% 1.66/1.33 thf(f4,negated_conjecture,(
% 1.66/1.33 ~(exuI1 => ! [X0 : $i > $o] : (? [X1 : $i] : (X0 @ X1) => (! [X1 : $i,X2 : $i] : ((X0 @ X1) => ((X0 @ X2) => (X1 = X2))) => (exu @ (^[X1 : $i] : (X0 @ X1))))))),
% 1.66/1.33 inference(negated_conjecture,[status(cth)],[f3])).
% 1.66/1.33 thf(f3,conjecture,(
% 1.66/1.33 exuI1 => ! [X0 : $i > $o] : (? [X1 : $i] : (X0 @ X1) => (! [X1 : $i,X2 : $i] : ((X0 @ X1) => ((X0 @ X2) => (X1 = X2))) => (exu @ (^[X1 : $i] : (X0 @ X1)))))),
% 1.66/1.33 file('/export/starexec/sandbox2/tmp/tmp.EkfjRFc6r6/DTF2THF_18589.p',exuI3)).
% 1.66/1.33 thf(f70,plain,(
% 1.66/1.33 ( ! [X0 : $i] : (($true != (sK0 @ X0)) | (sK1 = X0)) )),
% 1.66/1.33 inference(trivial_inequality_removal,[status(thm)],[f69])).
% 1.66/1.33 thf(f69,plain,(
% 1.66/1.33 ( ! [X0 : $i] : (($true != $true) | (sK1 = X0) | ($true != (sK0 @ X0))) )),
% 1.66/1.33 inference(superposition,[status(thm)],[f24,f25])).
% 1.66/1.33 thf(f24,plain,(
% 1.66/1.33 ( ! [X2 : $i,X3 : $i] : (($true != (sK0 @ X3)) | ($true != (sK0 @ X2)) | (X2 = X3)) )),
% 1.66/1.33 inference(cnf_transformation,[status(thm)],[f17])).
% 1.66/1.33 thf(f48,plain,(
% 1.66/1.33 ( ! [X1 : $i] : (((sK6 @ X1) != X1) | ((sK0 @ X1) = $false)) )),
% 1.66/1.33 inference(equality_proxy_clausification,[status(thm)],[f46])).
% 1.66/1.33 thf(f46,plain,(
% 1.66/1.33 ( ! [X1 : $i] : (((sK0 @ X1) = $false) | ((X1 = (sK6 @ X1)) = $false)) )),
% 1.66/1.33 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 1.66/1.33 thf(f25,plain,(
% 1.66/1.33 ($true = (sK0 @ sK1))),
% 1.66/1.33 inference(cnf_transformation,[status(thm)],[f17])).
% 1.66/1.33 % SZS output end Proof for DTF2THF_18589
% 1.66/1.33 % (18709)------------------------------
% 1.66/1.33 % (18709)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.33 % (18709)Termination reason: Refutation
% 1.66/1.33
% 1.66/1.33 % (18709)Memory used [KB]: 5500
% 1.66/1.33 % (18709)Time elapsed: 0.004 s
% 1.66/1.33 % (18709)Instructions burned: 5 (million)
% 1.66/1.33 % (18709)------------------------------
% 1.66/1.33 % (18709)------------------------------
% 1.66/1.33 % (18702)Success in time 0.011 s
%------------------------------------------------------------------------------