%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU546^2 : 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 : n010.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 09:35:12 AM UTC 2026
% Result : Theorem 1.63s 1.31s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 4
% Syntax : Number of formulae : 35 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 229 ( 91 equ; 0 cnn)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 218 ( 28 ~; 25 |; 22 &; 106 @)
% ( 5 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 72 ( 29 ^; 29 !; 14 ?; 72 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
exu: ( $i > $o ) > $o ).
thf(func_def_3,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_15,type,
sK0: $i > $o ).
thf(func_def_18,type,
sK3: $i > $i ).
thf(func_def_20,type,
sK4: ( $i > $o ) > $i ).
thf(func_def_21,type,
sK5: ( $i > $o ) > $i > $i ).
thf(func_def_22,type,
sK6: ( $i > $o ) > $i > $i ).
thf(f83,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f81]) ).
thf(f81,plain,
$false = $true,
inference(backward_demodulation,[status(thm)],[f26,f80]) ).
thf(f80,plain,
( ( sK0 @ sK1 )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f79]) ).
thf(f79,plain,
( ( ( sK0 @ sK1 )
= $false )
| ( sK1 != sK1 ) ),
inference(superposition,[status(thm)],[f35,f74]) ).
thf(f74,plain,
( ( sK3 @ sK1 )
= sK1 ),
inference(trivial_inequality_removal,[status(thm)],[f69]) ).
thf(f69,plain,
( ( $false = $true )
| ( ( sK3 @ sK1 )
= sK1 ) ),
inference(superposition,[status(thm)],[f68,f26]) ).
thf(f68,plain,
! [X0: $i] :
( ( $false
= ( sK0 @ X0 ) )
| ( ( sK3 @ X0 )
= sK1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f67]) ).
thf(f67,plain,
! [X0: $i] :
( ( $false
= ( sK0 @ X0 ) )
| ( ( sK3 @ X0 )
= sK1 )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f20,f34]) ).
thf(f34,plain,
! [X1: $i] :
( ( ( sK0 @ ( sK3 @ X1 ) )
= $true )
| ( $false
= ( sK0 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ X1 ) )
| ( ( ( sK0 @ ( sK3 @ X1 ) )
=> ( X1
= ( sK3 @ X1 ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f31]) ).
thf(f31,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( X1 = Y0 ) )
@ ( sK3 @ X1 ) )
= $false )
| ( $false
= ( sK0 @ X1 ) ) ),
inference(sigma_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( X1 = Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
! [X1: $i] :
( ( ( sK0 @ X1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( X1 = Y0 ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f28]) ).
thf(f28,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) ) )
@ X1 )
= $false ),
inference(pi_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
@ ^ [Y0: $i] : ( sK0 @ Y0 ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f21,f22]) ).
thf(f22,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,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/sandbox/tmp/tmp.L5SDdB5SSQ/DTF2THF_26446.p',exu) ).
thf(f21,plain,
( ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) )
!= $true )
& ! [X2: $i] :
( ( ( sK1 = X2 )
| ( $true
!= ( sK0 @ X2 ) ) )
& ( ( $true
= ( sK0 @ X2 ) )
| ( sK1 != X2 ) ) )
& ( exuI1 = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f15,f14]) ).
thf(f14,plain,
( ? [X0: $i > $o] :
( ( $true
!= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
& ? [X1: $i] :
! [X2: $i] :
( ( ( X1 = X2 )
| ( ( X0 @ X2 )
!= $true ) )
& ( ( ( X0 @ X2 )
= $true )
| ( X1 != X2 ) ) ) )
=> ( ( ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) )
!= $true )
& ? [X1: $i] :
! [X2: $i] :
( ( ( X1 = X2 )
| ( $true
!= ( sK0 @ X2 ) ) )
& ( ( $true
= ( sK0 @ X2 ) )
| ( X1 != X2 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
( ? [X1: $i] :
! [X2: $i] :
( ( ( X1 = X2 )
| ( $true
!= ( sK0 @ X2 ) ) )
& ( ( $true
= ( sK0 @ X2 ) )
| ( X1 != X2 ) ) )
=> ! [X2: $i] :
( ( ( sK1 = X2 )
| ( $true
!= ( sK0 @ X2 ) ) )
& ( ( $true
= ( sK0 @ X2 ) )
| ( sK1 != X2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ? [X0: $i > $o] :
( ( $true
!= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
& ? [X1: $i] :
! [X2: $i] :
( ( ( X1 = X2 )
| ( ( X0 @ X2 )
!= $true ) )
& ( ( ( X0 @ X2 )
= $true )
| ( X1 != X2 ) ) ) )
& ( exuI1 = $true ) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ? [X0: $i > $o] :
( ( $true
!= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
& ? [X1: $i] :
! [X2: $i] :
( ( X1 = X2 )
<=> ( ( X0 @ X2 )
= $true ) ) )
& ( exuI1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( ( exuI1 = $true )
=> ! [X0: $i > $o] :
( ? [X1: $i] :
! [X2: $i] :
( ( X1 = X2 )
<=> ( ( X0 @ X2 )
= $true ) )
=> ( $true
= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( exuI1
=> ! [X0: $i > $o] :
( ? [X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
<=> ( X1 = X2 ) )
=> ( exu
@ ^ [X3: $i] : ( X0 @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( exuI1
=> ! [X0: $i > $o] :
( ? [X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
<=> ( X1 = X2 ) )
=> ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( exuI1
=> ! [X0: $i > $o] :
( ? [X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
<=> ( X1 = X2 ) )
=> ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.L5SDdB5SSQ/DTF2THF_26446.p',exuI2) ).
thf(f20,plain,
! [X2: $i] :
( ( $true
!= ( sK0 @ X2 ) )
| ( sK1 = X2 ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f35,plain,
! [X1: $i] :
( ( ( sK3 @ X1 )
!= X1 )
| ( $false
= ( sK0 @ X1 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
! [X1: $i] :
( ( $false
= ( X1
= ( sK3 @ X1 ) ) )
| ( $false
= ( sK0 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f32]) ).
thf(f26,plain,
( ( sK0 @ sK1 )
= $true ),
inference(equality_resolution,[status(thm)],[f19]) ).
thf(f19,plain,
! [X2: $i] :
( ( $true
= ( sK0 @ X2 ) )
| ( sK1 != X2 ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU546^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n010.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 12:26:18 EST 2026
% 0.17/0.35 % CPUTime :
% 0.17/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.32/0.47 ---- Original DTF file ---
% 0.32/0.47 thf(spec,logic,$$dhol).
% 0.32/0.47 %------------------------------------------------------------------------------
% 0.32/0.47 % File : SEU546^2 : TPTP v9.2.1. Released v3.7.0.
% 0.32/0.47 % Domain : Set Theory
% 0.32/0.47 % Problem : Preliminary Notions - Equivalence Laws
% 0.32/0.47 % Version : Especial > Reduced > Especial.
% 0.32/0.47 % English : (! phi:i>o.(? x:i.! y:i.phi y <-> y = x) -> exu (^ x:i.phi x))
% 0.32/0.47
% 0.32/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.32/0.47 % Source : [Bro08]
% 0.32/0.47 % Names : ZFC048l [Bro08]
% 0.32/0.47
% 0.32/0.47 % Status : Theorem
% 0.32/0.47 % Rating : 0.00 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 0.00 v6.1.0, 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 v4.0.1, 0.33 v4.0.0, 0.00 v3.7.0
% 0.32/0.47 % Syntax : Number of formulae : 5 ( 2 unt; 2 typ; 2 def)
% 0.32/0.47 % Number of atoms : 10 ( 5 equ; 0 cnn)
% 0.32/0.47 % Maximal formula atoms : 3 ( 3 avg)
% 0.32/0.47 % Number of connectives : 17 ( 0 ~; 0 |; 2 &; 9 @)
% 0.32/0.47 % ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% 0.32/0.47 % Maximal formula depth : 8 ( 3 avg)
% 0.32/0.47 % Number of types : 2 ( 0 usr)
% 0.32/0.47 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.32/0.47 % Number of symbols : 3 ( 2 usr; 1 con; 0-2 aty)
% 0.32/0.47 % Number of variables : 11 ( 3 ^; 5 !; 3 ?; 11 :)
% 0.32/0.47 % SPC : TH0_THM_EQU_NAR
% 0.32/0.47
% 0.32/0.47 % Comments : http://mathgate.info/detsetitem.php?id=409
% 0.32/0.47 %------------------------------------------------------------------------------
% 0.32/0.47 thf(exu_type,type,
% 0.32/0.47 exu: ( $i > $o ) > $o ).
% 0.32/0.47
% 0.32/0.47 thf(exu,definition,
% 0.32/0.47 ( exu
% 0.32/0.47 = ( ^ [Xphi: $i > $o] :
% 0.32/0.47 ? [Xx: $i] :
% 0.32/0.47 ( ( Xphi @ Xx )
% 0.32/0.47 & ! [Xy: $i] :
% 0.32/0.47 ( ( Xphi @ Xy )
% 0.32/0.47 => ( Xx = Xy ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 thf(exuI1_type,type,
% 0.32/0.47 exuI1: $o ).
% 0.32/0.47
% 0.32/0.47 thf(exuI1,definition,
% 0.32/0.47 ( exuI1
% 0.32/0.47 = ( ! [Xphi: $i > $o] :
% 0.32/0.47 ( ? [Xx: $i] :
% 0.32/0.47 ( ( Xphi @ Xx )
% 0.32/0.47 & ! [Xy: $i] :
% 0.32/0.47 ( ( Xphi @ Xy )
% 0.32/0.47 => ( Xx = Xy ) ) )
% 0.32/0.47 => ( exu
% 0.32/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 thf(exuI2,conjecture,
% 0.32/0.47 ( exuI1
% 0.32/0.47 => ! [Xphi: $i > $o] :
% 0.32/0.47 ( ? [Xx: $i] :
% 0.32/0.47 ! [Xy: $i] :
% 0.32/0.47 ( ( Xphi @ Xy )
% 0.32/0.47 <=> ( Xy = Xx ) )
% 0.32/0.47 => ( exu
% 0.32/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 %------------------------------------------------------------------------------
% 0.32/0.47 ------------------------
% 1.47/1.27 ---- Embedded in THF ---
% 1.47/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.28 %%% Generated on Tue Feb 24 12:26:19 EST 2026
% 1.47/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.28 %%% Logic specification used:
% 1.47/1.28 %%% thf(spec, logic, $$dhol).
% 1.47/1.28
% 1.47/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.L5SDdB5SSQ/DTF2DTF26446.p
% See solution above
% 1.47/1.28 ------------------------
% 1.47/1.29 ---- Cleaned THF ---
% 1.47/1.29 thf(exu_type,type,
% 1.47/1.29 exu: ( $i > $o ) > $o ).
% 1.47/1.29
% 1.47/1.29 thf(exu,definition,
% 1.47/1.29 ( exu
% 1.47/1.29 = ( ^ [Xphi: $i > $o] :
% 1.47/1.29 ? [Xx: $i] :
% 1.47/1.29 ( ( Xphi @ Xx )
% 1.47/1.29 & ! [Xy: $i] :
% 1.47/1.29 ( ( Xphi @ Xy )
% 1.47/1.29 => ( Xx = Xy ) ) ) ) ) ).
% 1.47/1.29
% 1.47/1.29 thf(exuI1_type,type,
% 1.47/1.29 exuI1: $o ).
% 1.47/1.29
% 1.47/1.29 thf(exuI1,definition,
% 1.47/1.29 ( exuI1
% 1.47/1.29 = ( ! [Xphi: $i > $o] :
% 1.47/1.29 ( ? [Xx: $i] :
% 1.47/1.29 ( ( Xphi @ Xx )
% 1.47/1.29 & ! [Xy: $i] :
% 1.47/1.29 ( ( Xphi @ Xy )
% 1.47/1.29 => ( Xx = Xy ) ) )
% 1.47/1.29 => ( exu
% 1.47/1.29 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 1.47/1.29
% 1.47/1.29 thf(exuI2,conjecture,
% 1.47/1.29 ( exuI1
% 1.47/1.29 => ! [Xphi: $i > $o] :
% 1.47/1.29 ( ? [Xx: $i] :
% 1.47/1.29 ! [Xy: $i] :
% 1.47/1.29 ( ( Xphi @ Xy )
% 1.47/1.29 <=> ( Xy = Xx ) )
% 1.47/1.29 => ( exu
% 1.47/1.29 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 1.47/1.29 ------------------------
% 1.63/1.30 % (26777)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_26446 for (2999ds/2Mi)
% 1.63/1.30 % (26777)Instruction limit reached!
% 1.63/1.30 % (26777)------------------------------
% 1.63/1.30 % (26777)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.30 % (26777)Termination reason: Unknown
% 1.63/1.30 % (26777)Termination phase: Saturation
% 1.63/1.30
% 1.63/1.30 % (26777)Memory used [KB]: 895
% 1.63/1.30 % (26777)Time elapsed: 0.002 s
% 1.63/1.30 % (26777)Instructions burned: 2 (million)
% 1.63/1.30 % (26777)------------------------------
% 1.63/1.30 % (26777)------------------------------
% 1.63/1.30 % (26775)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_26446 for (2999ds/27Mi)
% 1.63/1.31 % (26775)First to succeed.
% 1.63/1.31 % (26775)Refutation found. Thanks to Tanya!
% 1.63/1.31 % SZS status Theorem for DTF2THF_26446
% 1.63/1.31 % SZS output start Proof for DTF2THF_26446
% 1.63/1.31 thf(func_def_0, type, exu: ($i > $o) > $o).
% 1.63/1.31 thf(func_def_3, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.63/1.31 thf(func_def_15, type, sK0: $i > $o).
% 1.63/1.31 thf(func_def_18, type, sK3: $i > $i).
% 1.63/1.31 thf(func_def_20, type, sK4: ($i > $o) > $i).
% 1.63/1.31 thf(func_def_21, type, sK5: ($i > $o) > $i > $i).
% 1.63/1.31 thf(func_def_22, type, sK6: ($i > $o) > $i > $i).
% 1.63/1.31 thf(f83,plain,(
% 1.63/1.31 $false),
% 1.63/1.31 inference(trivial_inequality_removal,[status(thm)],[f81])).
% 1.63/1.31 thf(f81,plain,(
% 1.63/1.31 ($false = $true)),
% 1.63/1.31 inference(backward_demodulation,[status(thm)],[f26,f80])).
% 1.63/1.31 thf(f80,plain,(
% 1.63/1.31 ((sK0 @ sK1) = $false)),
% 1.63/1.31 inference(trivial_inequality_removal,[status(thm)],[f79])).
% 1.63/1.31 thf(f79,plain,(
% 1.63/1.31 ((sK0 @ sK1) = $false) | (sK1 != sK1)),
% 1.63/1.31 inference(superposition,[status(thm)],[f35,f74])).
% 1.63/1.31 thf(f74,plain,(
% 1.63/1.31 ((sK3 @ sK1) = sK1)),
% 1.63/1.31 inference(trivial_inequality_removal,[status(thm)],[f69])).
% 1.63/1.31 thf(f69,plain,(
% 1.63/1.31 ($false = $true) | ((sK3 @ sK1) = sK1)),
% 1.63/1.31 inference(superposition,[status(thm)],[f68,f26])).
% 1.63/1.31 thf(f68,plain,(
% 1.63/1.31 ( ! [X0 : $i] : (($false = (sK0 @ X0)) | ((sK3 @ X0) = sK1)) )),
% 1.63/1.31 inference(trivial_inequality_removal,[status(thm)],[f67])).
% 1.63/1.31 thf(f67,plain,(
% 1.63/1.31 ( ! [X0 : $i] : (($false = (sK0 @ X0)) | ((sK3 @ X0) = sK1) | ($true != $true)) )),
% 1.63/1.31 inference(superposition,[status(thm)],[f20,f34])).
% 1.63/1.31 thf(f34,plain,(
% 1.63/1.31 ( ! [X1 : $i] : (((sK0 @ (sK3 @ X1)) = $true) | ($false = (sK0 @ X1))) )),
% 1.63/1.31 inference(binary_proxy_clausification,[status(thm)],[f32])).
% 1.63/1.31 thf(f32,plain,(
% 1.63/1.31 ( ! [X1 : $i] : (($false = (sK0 @ X1)) | (((sK0 @ (sK3 @ X1)) => (X1 = (sK3 @ X1))) = $false)) )),
% 1.63/1.31 inference(beta_eta_normalization,[status(thm)],[f31])).
% 1.63/1.31 thf(f31,plain,(
% 1.63/1.31 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((sK0 @ Y0) => (X1 = Y0))) @ (sK3 @ X1)) = $false) | ($false = (sK0 @ X1))) )),
% 1.63/1.31 inference(sigma_clausification,[status(thm)],[f30])).
% 1.63/1.31 thf(f30,plain,(
% 1.63/1.31 ( ! [X1 : $i] : (($false = (sK0 @ X1)) | ($false = (!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (X1 = Y0)))))) )),
% 1.63/1.31 inference(binary_proxy_clausification,[status(thm)],[f29])).
% 1.63/1.31 thf(f29,plain,(
% 1.63/1.31 ( ! [X1 : $i] : ((((sK0 @ X1) & (!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (X1 = Y0))))) = $false)) )),
% 1.63/1.31 inference(beta_eta_normalization,[status(thm)],[f28])).
% 1.63/1.31 thf(f28,plain,(
% 1.63/1.31 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((sK0 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1)))))) @ X1) = $false)) )),
% 1.63/1.31 inference(pi_clausification,[status(thm)],[f27])).
% 1.63/1.31 thf(f27,plain,(
% 1.63/1.31 ((?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1))))))) != $true)),
% 1.63/1.31 inference(beta_eta_normalization,[status(thm)],[f24])).
% 1.63/1.31 thf(f24,plain,(
% 1.63/1.31 (((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))) @ (^[Y0 : $i]: (sK0 @ Y0))) != $true)),
% 1.63/1.31 inference(definition_unfolding,[status(thm)],[f21,f22])).
% 1.63/1.31 thf(f22,plain,(
% 1.63/1.31 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))),
% 1.63/1.31 inference(cnf_transformation,[status(thm)],[f7])).
% 1.63/1.31 thf(f7,plain,(
% 1.63/1.31 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))),
% 1.63/1.31 inference(fool_elimination,[status(thm)],[f6])).
% 1.63/1.31 thf(f6,plain,(
% 1.63/1.31 ((^[X0 : $i > $o] : (? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))) = exu)),
% 1.63/1.31 inference(rectify,[status(thm)],[f1])).
% 1.63/1.31 thf(f1,axiom,(
% 1.63/1.31 ((^[X0 : $i > $o] : (? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))) = exu)),
% 1.63/1.31 file('/export/starexec/sandbox/tmp/tmp.L5SDdB5SSQ/DTF2THF_26446.p',exu)).
% 1.63/1.31 thf(f21,plain,(
% 1.63/1.31 ((exu @ (^[Y0 : $i]: (sK0 @ Y0))) != $true)),
% 1.63/1.31 inference(cnf_transformation,[status(thm)],[f16])).
% 1.63/1.31 thf(f16,plain,(
% 1.63/1.31 (((exu @ (^[Y0 : $i]: (sK0 @ Y0))) != $true) & ! [X2 : $i] : (((sK1 = X2) | ($true != (sK0 @ X2))) & (($true = (sK0 @ X2)) | (sK1 != X2)))) & (exuI1 = $true)),
% 1.63/1.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f15,f14])).
% 1.63/1.31 thf(f14,plain,(
% 1.63/1.31 ? [X0 : $i > $o] : (($true != (exu @ (^[Y0 : $i]: (X0 @ Y0)))) & ? [X1 : $i] : ! [X2 : $i] : (((X1 = X2) | ((X0 @ X2) != $true)) & (((X0 @ X2) = $true) | (X1 != X2)))) => (((exu @ (^[Y0 : $i]: (sK0 @ Y0))) != $true) & ? [X1 : $i] : ! [X2 : $i] : (((X1 = X2) | ($true != (sK0 @ X2))) & (($true = (sK0 @ X2)) | (X1 != X2))))),
% 1.63/1.31 introduced(definition,[],[choice_axiom])).
% 1.63/1.31 thf(f15,plain,(
% 1.63/1.31 ? [X1 : $i] : ! [X2 : $i] : (((X1 = X2) | ($true != (sK0 @ X2))) & (($true = (sK0 @ X2)) | (X1 != X2))) => ! [X2 : $i] : (((sK1 = X2) | ($true != (sK0 @ X2))) & (($true = (sK0 @ X2)) | (sK1 != X2)))),
% 1.63/1.31 introduced(definition,[],[choice_axiom])).
% 1.63/1.31 thf(f13,plain,(
% 1.63/1.31 ? [X0 : $i > $o] : (($true != (exu @ (^[Y0 : $i]: (X0 @ Y0)))) & ? [X1 : $i] : ! [X2 : $i] : (((X1 = X2) | ((X0 @ X2) != $true)) & (((X0 @ X2) = $true) | (X1 != X2)))) & (exuI1 = $true)),
% 1.63/1.31 inference(nnf_transformation,[status(thm)],[f12])).
% 1.63/1.31 thf(f12,plain,(
% 1.63/1.31 ? [X0 : $i > $o] : (($true != (exu @ (^[Y0 : $i]: (X0 @ Y0)))) & ? [X1 : $i] : ! [X2 : $i] : ((X1 = X2) <=> ((X0 @ X2) = $true))) & (exuI1 = $true)),
% 1.63/1.31 inference(ennf_transformation,[status(thm)],[f9])).
% 1.63/1.31 thf(f9,plain,(
% 1.63/1.31 ~((exuI1 = $true) => ! [X0 : $i > $o] : (? [X1 : $i] : ! [X2 : $i] : ((X1 = X2) <=> ((X0 @ X2) = $true)) => ($true = (exu @ (^[Y0 : $i]: (X0 @ Y0))))))),
% 1.63/1.31 inference(fool_elimination,[status(thm)],[f8])).
% 1.63/1.31 thf(f8,plain,(
% 1.63/1.31 ~(exuI1 => ! [X0 : $i > $o] : (? [X1 : $i] : ! [X2 : $i] : ((X0 @ X2) <=> (X1 = X2)) => (exu @ (^[X3 : $i] : (X0 @ X3)))))),
% 1.63/1.31 inference(rectify,[status(thm)],[f4])).
% 1.63/1.31 thf(f4,negated_conjecture,(
% 1.63/1.31 ~(exuI1 => ! [X0 : $i > $o] : (? [X1 : $i] : ! [X2 : $i] : ((X0 @ X2) <=> (X1 = X2)) => (exu @ (^[X1 : $i] : (X0 @ X1)))))),
% 1.63/1.31 inference(negated_conjecture,[status(cth)],[f3])).
% 1.63/1.31 thf(f3,conjecture,(
% 1.63/1.31 exuI1 => ! [X0 : $i > $o] : (? [X1 : $i] : ! [X2 : $i] : ((X0 @ X2) <=> (X1 = X2)) => (exu @ (^[X1 : $i] : (X0 @ X1))))),
% 1.63/1.31 file('/export/starexec/sandbox/tmp/tmp.L5SDdB5SSQ/DTF2THF_26446.p',exuI2)).
% 1.63/1.31 thf(f20,plain,(
% 1.63/1.31 ( ! [X2 : $i] : (($true != (sK0 @ X2)) | (sK1 = X2)) )),
% 1.63/1.31 inference(cnf_transformation,[status(thm)],[f16])).
% 1.63/1.31 thf(f35,plain,(
% 1.63/1.31 ( ! [X1 : $i] : (((sK3 @ X1) != X1) | ($false = (sK0 @ X1))) )),
% 1.63/1.31 inference(equality_proxy_clausification,[status(thm)],[f33])).
% 1.63/1.31 thf(f33,plain,(
% 1.63/1.31 ( ! [X1 : $i] : (($false = (X1 = (sK3 @ X1))) | ($false = (sK0 @ X1))) )),
% 1.63/1.31 inference(binary_proxy_clausification,[status(thm)],[f32])).
% 1.63/1.31 thf(f26,plain,(
% 1.63/1.31 ((sK0 @ sK1) = $true)),
% 1.63/1.31 inference(equality_resolution,[status(thm)],[f19])).
% 1.63/1.31 thf(f19,plain,(
% 1.63/1.31 ( ! [X2 : $i] : (($true = (sK0 @ X2)) | (sK1 != X2)) )),
% 1.63/1.31 inference(cnf_transformation,[status(thm)],[f16])).
% 1.63/1.31 % SZS output end Proof for DTF2THF_26446
% 1.63/1.31 % (26775)------------------------------
% 1.63/1.31 % (26775)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.31 % (26775)Termination reason: Refutation
% 1.63/1.31
% 1.63/1.31 % (26775)Memory used [KB]: 5500
% 1.63/1.31 % (26775)Time elapsed: 0.004 s
% 1.63/1.31 % (26775)Instructions burned: 5 (million)
% 1.63/1.31 % (26775)------------------------------
% 1.63/1.31 % (26775)------------------------------
% 1.63/1.31 % (26772)Success in time 0.014 s
%------------------------------------------------------------------------------