%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV256^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n023.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 09:40:41 AM UTC 2026
% Result : Theorem 1.66s 1.48s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 2
% Syntax : Number of formulae : 20 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 142 ( 39 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 177 ( 15 ~; 13 |; 19 &; 109 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 60 ( 60 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 5 usr; 3 con; 0-2 aty)
% ( 0 !!; 8 ??; 0 @@+; 0 @@-)
% Number of variables : 57 ( 33 ^; 19 !; 5 ?; 57 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
cOPEN: ( a > $o ) > $o ).
thf(func_def_10,type,
sK0: ( ( a > $o ) > $o ) > a > $o ).
thf(func_def_13,type,
ph2:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
sK3: ( ( a > $o ) > $o ) > a ).
thf(func_def_15,type,
sK4: ( ( a > $o ) > $o ) > a > $o ).
thf(f45,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f44]) ).
thf(f44,plain,
$true = $false,
inference(duplicate_literal_removal,[status(thm)],[f43]) ).
thf(f43,plain,
( ( $true = $false )
| ( $true = $false ) ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ( ^ [Y0: a > $o] : $false
@ ( sK4
@ ^ [Y0: a > $o] : $false ) )
= $true )
| ( $true
= ( ^ [Y0: a > $o] : $false
@ ( sK0
@ ^ [Y0: a > $o] : $false ) ) ) ),
inference(primitive_instantiation,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: ( a > $o ) > $o] :
( ( ( X0 @ ( sK4 @ X0 ) )
= $true )
| ( ( X0 @ ( sK0 @ X0 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: ( a > $o ) > $o] :
( ( ( X0 @ ( sK0 @ X0 ) )
= $true )
| ( ( ( sK4 @ X0 @ ( sK3 @ X0 ) )
& ( X0 @ ( sK4 @ X0 ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: ( a > $o ) > $o] :
( ( ( X0 @ ( sK0 @ X0 ) )
= $true )
| ( $true
= ( ^ [Y0: a > $o] :
( ( Y0 @ ( sK3 @ X0 ) )
& ( X0 @ Y0 ) )
@ ( sK4 @ X0 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: ( a > $o ) > $o] :
( ( ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ ( sK3 @ X0 ) )
& ( X0 @ Y0 ) ) )
!= $false )
| ( ( X0 @ ( sK0 @ X0 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: ( a > $o ) > $o] :
( ( ( ^ [Y0: a] : $false
@ ( sK3 @ X0 ) )
!= ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( X0 @ Y1 ) ) )
@ ( sK3 @ X0 ) ) )
| ( ( X0 @ ( sK0 @ X0 ) )
= $true ) ),
inference(negative_extensionality,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: ( a > $o ) > $o] :
( ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( X0 @ Y1 ) ) ) ) )
| ( ( X0 @ ( sK0 @ X0 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: ( a > $o ) > $o] :
( ( ( X0 @ ( sK0 @ X0 ) )
= $true )
| ( $true != $true )
| ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( X0 @ Y1 ) ) ) ) ) ),
inference(constrained_superposition,[status(thm)],[f9,f11]) ).
thf(f11,plain,
! [X0: ( a > $o ) > $o] :
( ( ( cOPEN
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( X0 @ Y1 ) ) ) )
= $true )
| ( ( X0 @ ( sK0 @ X0 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ! [X0: ( a > $o ) > $o] :
( ( ( cOPEN
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( X0 @ Y1 ) ) ) )
= $true )
| ( ( ( X0 @ ( sK0 @ X0 ) )
= $true )
& ( $true
!= ( cOPEN @ ( sK0 @ X0 ) ) ) ) )
& ( $true
!= ( cOPEN
@ ^ [Y0: a] : $false ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f6,f7]) ).
thf(f7,plain,
! [X0: ( a > $o ) > $o] :
( ? [X1: a > $o] :
( ( ( X0 @ X1 )
= $true )
& ( ( cOPEN @ X1 )
!= $true ) )
=> ( ( ( X0 @ ( sK0 @ X0 ) )
= $true )
& ( $true
!= ( cOPEN @ ( sK0 @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
( ! [X0: ( a > $o ) > $o] :
( ( ( cOPEN
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( X0 @ Y1 ) ) ) )
= $true )
| ? [X1: a > $o] :
( ( ( X0 @ X1 )
= $true )
& ( ( cOPEN @ X1 )
!= $true ) ) )
& ( $true
!= ( cOPEN
@ ^ [Y0: a] : $false ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X0: ( a > $o ) > $o] :
( ! [X1: a > $o] :
( ( ( X0 @ X1 )
= $true )
=> ( ( cOPEN @ X1 )
= $true ) )
=> ( ( cOPEN
@ ^ [Y0: a] :
( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ Y0 )
& ( X0 @ Y1 ) ) ) )
= $true ) )
=> ( $true
= ( cOPEN
@ ^ [Y0: a] : $false ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: ( a > $o ) > $o] :
( ! [X1: a > $o] :
( ( X0 @ X1 )
=> ( cOPEN @ X1 ) )
=> ( cOPEN
@ ^ [X2: a] :
? [X3: a > $o] :
( ( X0 @ X3 )
& ( X3 @ X2 ) ) ) )
=> ( cOPEN
@ ^ [X4: a] : $false ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: ( a > $o ) > $o] :
( ! [X1: a > $o] :
( ( X0 @ X1 )
=> ( cOPEN @ X1 ) )
=> ( cOPEN
@ ^ [X1: a] :
? [X2: a > $o] :
( ( X0 @ X2 )
& ( X2 @ X1 ) ) ) )
=> ( cOPEN
@ ^ [X1: a] : $false ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X0: ( a > $o ) > $o] :
( ! [X1: a > $o] :
( ( X0 @ X1 )
=> ( cOPEN @ X1 ) )
=> ( cOPEN
@ ^ [X1: a] :
? [X2: a > $o] :
( ( X0 @ X2 )
& ( X2 @ X1 ) ) ) )
=> ( cOPEN
@ ^ [X1: a] : $false ) ),
file('/export/starexec/sandbox/tmp/tmp.41Qi5JIaKo/DTF2THF_12304.p',cTHM625A_pme) ).
thf(f9,plain,
( $true
!= ( cOPEN
@ ^ [Y0: a] : $false ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV256^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n023.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 12:43:34 EST 2026
% 0.16/0.35 % CPUTime :
% 0.16/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.46 ---- Original DTF file ---
% 0.19/0.46 thf(spec,logic,$$dhol).
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % File : SEV256^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.46 % Domain : Set Theory (Sets of sets)
% 0.19/0.46 % Problem : TPS problem THM625A
% 0.19/0.46 % Version : Especial.
% 0.19/0.46 % English : THM625 without assuming full topology axioms.
% 0.19/0.46
% 0.19/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.46 % Source : [Bro09]
% 0.19/0.46 % Names : tps_0124 [Bro09]
% 0.19/0.46 % : THM625A [TPS]
% 0.19/0.46
% 0.19/0.46 % Status : Theorem
% 0.19/0.46 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.17 v7.4.0, 0.11 v7.3.0, 0.20 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.2.0, 0.33 v6.1.0, 0.17 v6.0.0, 0.00 v5.5.0, 0.20 v5.4.0, 0.50 v5.3.0, 0.75 v5.2.0, 0.50 v5.0.0, 0.25 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% 0.19/0.46 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.19/0.46 % Number of atoms : 4 ( 0 equ; 0 cnn)
% 0.19/0.46 % Maximal formula atoms : 4 ( 4 avg)
% 0.19/0.46 % Number of connectives : 10 ( 0 ~; 0 |; 1 &; 6 @)
% 0.19/0.46 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.19/0.46 % Maximal formula depth : 9 ( 9 avg)
% 0.19/0.46 % Number of types : 2 ( 1 usr)
% 0.19/0.46 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.19/0.46 % Number of symbols : 2 ( 1 usr; 1 con; 0-1 aty)
% 0.19/0.46 % Number of variables : 5 ( 2 ^; 2 !; 1 ?; 5 :)
% 0.19/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.19/0.46
% 0.19/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.46 % : Polymorphic definitions expanded.
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 thf(a_type,type,
% 0.19/0.46 a: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(cOPEN,type,
% 0.19/0.46 cOPEN: ( a > $o ) > $o ).
% 0.19/0.46
% 0.19/0.46 thf(cTHM625A_pme,conjecture,
% 0.19/0.46 ( ! [K: ( a > $o ) > $o] :
% 0.19/0.46 ( ! [Xx: a > $o] :
% 0.19/0.46 ( ( K @ Xx )
% 0.19/0.46 => ( cOPEN @ Xx ) )
% 0.19/0.46 => ( cOPEN
% 0.19/0.46 @ ^ [Xx: a] :
% 0.19/0.46 ? [S: a > $o] :
% 0.19/0.46 ( ( K @ S )
% 0.19/0.46 & ( S @ Xx ) ) ) )
% 0.19/0.46 => ( cOPEN
% 0.19/0.46 @ ^ [Xx: a] : $false ) ) ).
% 0.19/0.46
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 ------------------------
% 1.66/1.44 ---- Embedded in THF ---
% 1.66/1.45 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.66/1.45 %%% Generated on Tue Feb 24 12:43:35 EST 2026
% 1.66/1.45 %%% using '$$dhol' embedding, version 1.3.0.
% 1.66/1.45 %%% Logic specification used:
% 1.66/1.45 %%% thf(spec, logic, $$dhol).
% 1.66/1.45
% 1.66/1.45 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.41Qi5JIaKo/DTF2DTF12304.p
% See solution above
% 1.66/1.45 ------------------------
% 1.66/1.46 ---- Cleaned THF ---
% 1.66/1.46 thf(a_type,type,
% 1.66/1.46 a: $tType ).
% 1.66/1.46
% 1.66/1.46 thf(cOPEN,type,
% 1.66/1.46 cOPEN: ( a > $o ) > $o ).
% 1.66/1.46
% 1.66/1.46 thf(cTHM625A_pme,conjecture,
% 1.66/1.46 ( ! [K: ( a > $o ) > $o] :
% 1.66/1.46 ( ! [Xx: a > $o] :
% 1.66/1.46 ( ( K @ Xx )
% 1.66/1.46 => ( cOPEN @ Xx ) )
% 1.66/1.46 => ( cOPEN
% 1.66/1.46 @ ^ [Xx: a] :
% 1.66/1.46 ? [S: a > $o] :
% 1.66/1.46 ( ( K @ S )
% 1.66/1.46 & ( S @ Xx ) ) ) )
% 1.66/1.46 => ( cOPEN
% 1.66/1.46 @ ^ [Xx: a] : $false ) ) ).
% 1.66/1.46 ------------------------
% 1.66/1.48 % (12405)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_12304 for (3000ds/2Mi)
% 1.66/1.48 % (12407)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_12304 for (3000ds/18Mi)
% 1.66/1.48 % (12406)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_12304 for (3000ds/275Mi)
% 1.66/1.48 % (12404)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_12304 for (3000ds/2Mi)
% 1.66/1.48 % (12401)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_12304 for (3000ds/183Mi)
% 1.66/1.48 % (12402)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_12304 for (3000ds/4Mi)
% 1.66/1.48 % (12404)Instruction limit reached!
% 1.66/1.48 % (12404)------------------------------
% 1.66/1.48 % (12404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.48 % (12404)Termination reason: Unknown
% 1.66/1.48 % (12405)Instruction limit reached!
% 1.66/1.48 % (12405)------------------------------
% 1.66/1.48 % (12405)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.48 % (12404)Termination phase: Saturation
% 1.66/1.48
% 1.66/1.48 % (12404)Memory used [KB]: 5500
% 1.66/1.48 % (12404)Time elapsed: 0.003 s
% 1.66/1.48 % (12404)Instructions burned: 2 (million)
% 1.66/1.48 % (12404)------------------------------
% 1.66/1.48 % (12404)------------------------------
% 1.66/1.48 % (12405)Termination reason: Unknown
% 1.66/1.48 % (12405)Termination phase: Saturation
% 1.66/1.48
% 1.66/1.48 % (12405)Memory used [KB]: 5500
% 1.66/1.48 % (12405)Time elapsed: 0.003 s
% 1.66/1.48 % (12405)Instructions burned: 2 (million)
% 1.66/1.48 % (12405)------------------------------
% 1.66/1.48 % (12405)------------------------------
% 1.66/1.48 % (12403)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_12304 for (3000ds/27Mi)
% 1.66/1.48 % (12406)Refutation not found, incomplete strategy
% 1.66/1.48 % (12406)------------------------------
% 1.66/1.48 % (12406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.48 % (12406)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.48
% 1.66/1.48
% 1.66/1.48 % (12406)Memory used [KB]: 5500
% 1.66/1.48 % (12406)Time elapsed: 0.003 s
% 1.66/1.48 % (12406)Instructions burned: 2 (million)
% 1.66/1.48 % (12406)------------------------------
% 1.66/1.48 % (12406)------------------------------
% 1.66/1.48 % (12403)Refutation not found, incomplete strategy
% 1.66/1.48 % (12403)------------------------------
% 1.66/1.48 % (12403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.48 % (12403)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.48
% 1.66/1.48
% 1.66/1.48 % (12403)Memory used [KB]: 5500
% 1.66/1.48 % (12403)Time elapsed: 0.002 s
% 1.66/1.48 % (12402)Instruction limit reached!
% 1.66/1.48 % (12402)------------------------------
% 1.66/1.48 % (12402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.48 % (12403)Instructions burned: 1 (million)
% 1.66/1.48 % (12403)------------------------------
% 1.66/1.48 % (12403)------------------------------
% 1.66/1.48 % (12402)Termination reason: Unknown
% 1.66/1.48 % (12402)Termination phase: Saturation
% 1.66/1.48
% 1.66/1.48 % (12402)Memory used [KB]: 5500
% 1.66/1.48 % (12402)Time elapsed: 0.005 s
% 1.66/1.48 % (12402)Instructions burned: 5 (million)
% 1.66/1.48 % (12402)------------------------------
% 1.66/1.48 % (12402)------------------------------
% 1.66/1.48 % (12407)First to succeed.
% 1.66/1.48 % (12407)Refutation found. Thanks to Tanya!
% 1.66/1.48 % SZS status Theorem for DTF2THF_12304
% 1.66/1.48 % SZS output start Proof for DTF2THF_12304
% 1.66/1.48 thf(type_def_5, type, a: $tType).
% 1.66/1.48 thf(func_def_0, type, a: $tType).
% 1.66/1.48 thf(func_def_1, type, cOPEN: (a > $o) > $o).
% 1.66/1.48 thf(func_def_10, type, sK0: ((a > $o) > $o) > a > $o).
% 1.66/1.48 thf(func_def_13, type, ph2: !>[X0: $tType]:(X0)).
% 1.66/1.48 thf(func_def_14, type, sK3: ((a > $o) > $o) > a).
% 1.66/1.48 thf(func_def_15, type, sK4: ((a > $o) > $o) > a > $o).
% 1.66/1.48 thf(f45,plain,(
% 1.66/1.48 $false),
% 1.66/1.48 inference(trivial_inequality_removal,[status(thm)],[f44])).
% 1.66/1.48 thf(f44,plain,(
% 1.66/1.48 ($true = $false)),
% 1.66/1.48 inference(duplicate_literal_removal,[status(thm)],[f43])).
% 1.66/1.48 thf(f43,plain,(
% 1.66/1.48 ($true = $false) | ($true = $false)),
% 1.66/1.48 inference(beta_eta_normalization,[status(thm)],[f26])).
% 1.66/1.48 thf(f26,plain,(
% 1.66/1.48 (((^[Y0 : a > $o]: ($false)) @ (sK4 @ (^[Y0 : a > $o]: ($false)))) = $true) | ($true = ((^[Y0 : a > $o]: ($false)) @ (sK0 @ (^[Y0 : a > $o]: ($false)))))),
% 1.66/1.48 inference(primitive_instantiation,[status(thm)],[f23])).
% 1.66/1.48 thf(f23,plain,(
% 1.66/1.48 ( ! [X0 : (a > $o) > $o] : (((X0 @ (sK4 @ X0)) = $true) | ((X0 @ (sK0 @ X0)) = $true)) )),
% 1.66/1.48 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 1.66/1.48 thf(f22,plain,(
% 1.66/1.48 ( ! [X0 : (a > $o) > $o] : (((X0 @ (sK0 @ X0)) = $true) | (((sK4 @ X0 @ (sK3 @ X0)) & (X0 @ (sK4 @ X0))) = $true)) )),
% 1.66/1.48 inference(beta_eta_normalization,[status(thm)],[f21])).
% 1.66/1.48 thf(f21,plain,(
% 1.66/1.48 ( ! [X0 : (a > $o) > $o] : (((X0 @ (sK0 @ X0)) = $true) | ($true = ((^[Y0 : a > $o]: ((Y0 @ (sK3 @ X0)) & (X0 @ Y0))) @ (sK4 @ X0)))) )),
% 1.66/1.48 inference(sigma_clausification,[status(thm)],[f20])).
% 1.66/1.48 thf(f20,plain,(
% 1.66/1.48 ( ! [X0 : (a > $o) > $o] : (((?? @ (a > $o) @ (^[Y0 : a > $o]: ((Y0 @ (sK3 @ X0)) & (X0 @ Y0)))) != $false) | ((X0 @ (sK0 @ X0)) = $true)) )),
% 1.66/1.48 inference(beta_eta_normalization,[status(thm)],[f19])).
% 1.66/1.48 thf(f19,plain,(
% 1.66/1.48 ( ! [X0 : (a > $o) > $o] : ((((^[Y0 : a]: ($false)) @ (sK3 @ X0)) != ((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (X0 @ Y1))))) @ (sK3 @ X0))) | ((X0 @ (sK0 @ X0)) = $true)) )),
% 1.66/1.48 inference(negative_extensionality,[status(thm)],[f17])).
% 1.66/1.48 thf(f17,plain,(
% 1.66/1.48 ( ! [X0 : (a > $o) > $o] : (((^[Y0 : a]: ($false)) != (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (X0 @ Y1)))))) | ((X0 @ (sK0 @ X0)) = $true)) )),
% 1.66/1.48 inference(trivial_inequality_removal,[status(thm)],[f13])).
% 1.66/1.48 thf(f13,plain,(
% 1.66/1.48 ( ! [X0 : (a > $o) > $o] : (((X0 @ (sK0 @ X0)) = $true) | ($true != $true) | ((^[Y0 : a]: ($false)) != (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (X0 @ Y1))))))) )),
% 1.66/1.48 inference(constrained_superposition,[status(thm)],[f9,f11])).
% 1.66/1.48 thf(f11,plain,(
% 1.66/1.48 ( ! [X0 : (a > $o) > $o] : (((cOPEN @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (X0 @ Y1)))))) = $true) | ((X0 @ (sK0 @ X0)) = $true)) )),
% 1.66/1.48 inference(cnf_transformation,[status(thm)],[f8])).
% 1.66/1.48 thf(f8,plain,(
% 1.66/1.48 ! [X0 : (a > $o) > $o] : (((cOPEN @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (X0 @ Y1)))))) = $true) | (((X0 @ (sK0 @ X0)) = $true) & ($true != (cOPEN @ (sK0 @ X0))))) & ($true != (cOPEN @ (^[Y0 : a]: ($false))))),
% 1.66/1.48 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f6,f7])).
% 1.66/1.48 thf(f7,plain,(
% 1.66/1.48 ! [X0 : (a > $o) > $o] : (? [X1 : a > $o] : (((X0 @ X1) = $true) & ((cOPEN @ X1) != $true)) => (((X0 @ (sK0 @ X0)) = $true) & ($true != (cOPEN @ (sK0 @ X0)))))),
% 1.66/1.48 introduced(definition,[],[choice_axiom])).
% 1.66/1.48 thf(f6,plain,(
% 1.66/1.48 ! [X0 : (a > $o) > $o] : (((cOPEN @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (X0 @ Y1)))))) = $true) | ? [X1 : a > $o] : (((X0 @ X1) = $true) & ((cOPEN @ X1) != $true))) & ($true != (cOPEN @ (^[Y0 : a]: ($false))))),
% 1.66/1.48 inference(ennf_transformation,[status(thm)],[f5])).
% 1.66/1.48 thf(f5,plain,(
% 1.66/1.48 ~(! [X0 : (a > $o) > $o] : (! [X1 : a > $o] : (((X0 @ X1) = $true) => ((cOPEN @ X1) = $true)) => ((cOPEN @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (X0 @ Y1)))))) = $true)) => ($true = (cOPEN @ (^[Y0 : a]: ($false)))))),
% 1.66/1.48 inference(fool_elimination,[status(thm)],[f4])).
% 1.66/1.48 thf(f4,plain,(
% 1.66/1.48 ~(! [X0 : (a > $o) > $o] : (! [X1 : a > $o] : ((X0 @ X1) => (cOPEN @ X1)) => (cOPEN @ (^[X2 : a] : (? [X3 : a > $o] : ((X0 @ X3) & (X3 @ X2)))))) => (cOPEN @ (^[X4 : a] : ($false))))),
% 1.66/1.48 inference(rectify,[status(thm)],[f2])).
% 1.66/1.48 thf(f2,negated_conjecture,(
% 1.66/1.48 ~(! [X0 : (a > $o) > $o] : (! [X1 : a > $o] : ((X0 @ X1) => (cOPEN @ X1)) => (cOPEN @ (^[X1 : a] : (? [X2 : a > $o] : ((X0 @ X2) & (X2 @ X1)))))) => (cOPEN @ (^[X1 : a] : ($false))))),
% 1.66/1.48 inference(negated_conjecture,[status(cth)],[f1])).
% 1.66/1.48 thf(f1,conjecture,(
% 1.66/1.48 ! [X0 : (a > $o) > $o] : (! [X1 : a > $o] : ((X0 @ X1) => (cOPEN @ X1)) => (cOPEN @ (^[X1 : a] : (? [X2 : a > $o] : ((X0 @ X2) & (X2 @ X1)))))) => (cOPEN @ (^[X1 : a] : ($false)))),
% 1.66/1.48 file('/export/starexec/sandbox/tmp/tmp.41Qi5JIaKo/DTF2THF_12304.p',cTHM625A_pme)).
% 1.66/1.48 thf(f9,plain,(
% 1.66/1.48 ($true != (cOPEN @ (^[Y0 : a]: ($false))))),
% 1.66/1.48 inference(cnf_transformation,[status(thm)],[f8])).
% 1.66/1.48 % SZS output end Proof for DTF2THF_12304
% 1.66/1.48 % (12407)------------------------------
% 1.66/1.48 % (12407)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.48 % (12407)Termination reason: Refutation
% 1.66/1.48
% 1.66/1.48 % (12407)Memory used [KB]: 5500
% 1.66/1.48 % (12407)Time elapsed: 0.006 s
% 1.66/1.48 % (12407)Instructions burned: 6 (million)
% 1.66/1.48 % (12407)------------------------------
% 1.66/1.48 % (12407)------------------------------
% 1.66/1.48 % (12400)Success in time 0.02 s
%------------------------------------------------------------------------------