%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV288^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n022.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 09:40:45 AM UTC 2026
% Result : Theorem 1.64s 1.30s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 40 ( 12 unt; 0 typ; 4 def)
% Number of atoms : 142 ( 62 equ; 3 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 178 ( 32 ~; 33 |; 0 &; 79 @)
% ( 4 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 8 usr; 10 con; 0-2 aty)
% ( 11 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 51 ( 43 ^; 8 !; 0 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_13,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
sK2: a ).
thf(func_def_15,type,
sK3: a ).
thf(func_def_16,type,
sK4: a > $o ).
thf(f69,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f31,f36,f41,f62,f68]) ).
thf(f68,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f67]) ).
thf(f67,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f66]) ).
thf(f66,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f40,f65]) ).
thf(f65,plain,
( ( ( sK4 @ sK2 )
= $false )
| ~ spl0_1
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f35,f27]) ).
thf(f27,plain,
( ( sK3 = sK2 )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f25]) ).
thf(f25,definition,
( spl0_1
<=> ( sK3 = sK2 ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f35,plain,
( ( ( sK4 @ sK3 )
= $false )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f33]) ).
thf(f33,definition,
( spl0_3
<=> ( ( sK4 @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f40,plain,
( ( $true
= ( sK4 @ sK2 ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f38]) ).
thf(f38,definition,
( spl0_4
<=> ( $true
= ( sK4 @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f62,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f43,f29,f25]) ).
thf(f29,definition,
( spl0_2
<=> ! [X1: a > $o] :
( ( ( X1 @ sK3 )
= $true )
| ( ( X1 @ sK2 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f43,plain,
( ( sK3 = sK2 )
| ~ spl0_2 ),
inference(leibniz_equality_elimination,[status(thm)],[f30]) ).
thf(f30,plain,
( ! [X1: a > $o] :
( ( ( X1 @ sK3 )
= $true )
| ( ( X1 @ sK2 )
= $false ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f29]) ).
thf(f41,plain,
( spl0_4
| ~ spl0_1 ),
inference(avatar_split_clause,[status(thm)],[f19,f25,f38]) ).
thf(f19,plain,
( ( sK3 != sK2 )
| ( $true
= ( sK4 @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( sK3 != sK2 )
| ( ( ( sK4 @ sK2 )
=> ( sK4 @ sK3 ) )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( ( $false
= ( sK2 = sK3 ) )
| ( ( ( sK4 @ sK2 )
=> ( sK4 @ sK3 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ( ^ [Y0: a > $o] :
( ( Y0 @ sK2 )
=> ( Y0 @ sK3 ) )
@ sK4 )
= $false )
| ( $false
= ( sK2 = sK3 ) ) ),
inference(sigma_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK2 )
=> ( Y0 @ sK3 ) ) )
= $false )
| ( $false
= ( sK2 = sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK2 )
=> ( Y0 @ sK3 ) ) )
!= ( sK2 = sK3 ) ),
inference(beta_eta_normalization,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ sK2 )
=> ( Y1 @ Y0 ) ) )
@ sK3 )
!= ( sK2 = sK3 ) ),
inference(negative_extensionality,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ sK2 )
=> ( Y1 @ Y0 ) ) ) )
!= ( (=) @ sK2 ) ),
inference(beta_eta_normalization,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) )
@ sK2 )
!= ( (=) @ sK2 ) ),
inference(negative_extensionality,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) )
!= (=) ),
inference(beta_eta_normalization,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 ) )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 ) )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ^ [Y0: a,Y1: a] : ( Y0 = Y1 ) )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
( ( ^ [X0: a,X1: a] : ( X0 = X1 ) )
!= ( ^ [X2: a,X3: a] :
! [X4: a > $o] :
( ( X4 @ X2 )
=> ( X4 @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
( ( ^ [X0: a,X1: a] : ( X0 = X1 ) )
!= ( ^ [X0: a,X1: a] :
! [X2: a > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ^ [X0: a,X1: a] : ( X0 = X1 ) )
= ( ^ [X0: a,X1: a] :
! [X2: a > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.gEeValPkpj/DTF2THF_30045.p',cE1_eq__pme) ).
thf(f36,plain,
( ~ spl0_1
| spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f18,f33,f25]) ).
thf(f18,plain,
( ( ( sK4 @ sK3 )
= $false )
| ( sK3 != sK2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f31,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f23,f29,f25]) ).
thf(f23,plain,
! [X1: a > $o] :
( ( ( X1 @ sK3 )
= $true )
| ( ( X1 @ sK2 )
= $false )
| ( sK3 = sK2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
! [X1: a > $o] :
( ( $true
= ( ( X1 @ sK2 )
=> ( X1 @ sK3 ) ) )
| ( sK3 = sK2 ) ),
inference(beta_eta_normalization,[status(thm)],[f21]) ).
thf(f21,plain,
! [X1: a > $o] :
( ( sK3 = sK2 )
| ( $true
= ( ^ [Y0: a > $o] :
( ( Y0 @ sK2 )
=> ( Y0 @ sK3 ) )
@ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK2 )
=> ( Y0 @ sK3 ) ) )
= $true )
| ( sK3 = sK2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( $true
= ( sK2 = sK3 ) )
| ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK2 )
=> ( Y0 @ sK3 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV288^5 : TPTP v9.2.1. Released v4.0.0.
% 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n022.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 12:43:06 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.47 thf(spec,logic,$$dhol).
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 % File : SEV288^5 : TPTP v9.2.1. Released v4.0.0.
% 0.20/0.47 % Domain : Set Theory
% 0.20/0.47 % Problem : TPS problem from TTTP-NATS-THMS
% 0.20/0.47 % Version : Especial.
% 0.20/0.47 % English :
% 0.20/0.47
% 0.20/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.47 % Source : [Bro09]
% 0.20/0.47 % Names : tps_0102 [Bro09]
% 0.20/0.47
% 0.20/0.47 % Status : Theorem
% 0.20/0.47 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0, 0.29 v7.4.0, 0.00 v6.2.0, 0.29 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% 0.20/0.47 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.20/0.47 % Number of atoms : 2 ( 2 equ; 0 cnn)
% 0.20/0.47 % Maximal formula atoms : 1 ( 2 avg)
% 0.20/0.47 % Number of connectives : 3 ( 0 ~; 0 |; 0 &; 2 @)
% 0.20/0.47 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.20/0.47 % Maximal formula depth : 1 ( 1 avg)
% 0.20/0.47 % Number of types : 2 ( 1 usr)
% 0.20/0.47 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.20/0.47 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.20/0.47 % Number of variables : 5 ( 4 ^; 1 !; 0 ?; 5 :)
% 0.20/0.47 % SPC : TH0_THM_EQU_NAR
% 0.20/0.47
% 0.20/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 thf(a_type,type,
% 0.20/0.47 a: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(cE1_eq__pme,conjecture,
% 0.20/0.47 ( ( ^ [X: a,Y: a] :
% 0.20/0.47 ! [Xq: a > $o] :
% 0.20/0.47 ( ( Xq @ X )
% 0.20/0.47 => ( Xq @ Y ) ) )
% 0.20/0.47 = ( ^ [X: a,Y: a] : ( X = Y ) ) ) ).
% 0.20/0.47
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 ------------------------
% 1.46/1.27 ---- Embedded in THF ---
% 1.46/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.27 %%% Generated on Tue Feb 24 12:43:07 EST 2026
% 1.46/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.27 %%% Logic specification used:
% 1.46/1.27 %%% thf(spec, logic, $$dhol).
% 1.46/1.27
% 1.46/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.gEeValPkpj/DTF2DTF30045.p
% See solution above
% 1.46/1.27 ------------------------
% 1.46/1.28 ---- Cleaned THF ---
% 1.46/1.28 thf(a_type,type,
% 1.46/1.28 a: $tType ).
% 1.46/1.28
% 1.46/1.28 thf(cE1_eq__pme,conjecture,
% 1.46/1.28 ( ( ^ [X: a,Y: a] :
% 1.46/1.28 ! [Xq: a > $o] :
% 1.46/1.28 ( ( Xq @ X )
% 1.46/1.28 => ( Xq @ Y ) ) )
% 1.46/1.28 = ( ^ [X: a,Y: a] : ( X = Y ) ) ) ).
% 1.46/1.28 ------------------------
% 1.64/1.30 % (30204)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30045 for (2999ds/18Mi)
% 1.64/1.30 % (30202)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_30045 for (2999ds/2Mi)
% 1.64/1.30 % (30201)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30045 for (2999ds/2Mi)
% 1.64/1.30 % (30202)Refutation not found, incomplete strategy
% 1.64/1.30 % (30202)------------------------------
% 1.64/1.30 % (30202)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.30 % (30202)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.30
% 1.64/1.30
% 1.64/1.30 % (30202)Memory used [KB]: 5500
% 1.64/1.30 % (30202)Time elapsed: 0.002 s
% 1.64/1.30 % (30202)Instructions burned: 1 (million)
% 1.64/1.30 % (30202)------------------------------
% 1.64/1.30 % (30202)------------------------------
% 1.64/1.30 % (30201)Instruction limit reached!
% 1.64/1.30 % (30201)------------------------------
% 1.64/1.30 % (30201)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.30 % (30201)Termination reason: Unknown
% 1.64/1.30 % (30201)Termination phase: Saturation
% 1.64/1.30
% 1.64/1.30 % (30201)Memory used [KB]: 5500
% 1.64/1.30 % (30201)Time elapsed: 0.002 s
% 1.64/1.30 % (30201)Instructions burned: 2 (million)
% 1.64/1.30 % (30201)------------------------------
% 1.64/1.30 % (30201)------------------------------
% 1.64/1.30 % (30204)First to succeed.
% 1.64/1.30 % (30204)Refutation found. Thanks to Tanya!
% 1.64/1.30 % SZS status Theorem for DTF2THF_30045
% 1.64/1.30 % SZS output start Proof for DTF2THF_30045
% 1.64/1.30 thf(type_def_5, type, a: $tType).
% 1.64/1.30 thf(func_def_0, type, a: $tType).
% 1.64/1.30 thf(func_def_13, type, ph1: !>[X0: $tType]:(X0)).
% 1.64/1.30 thf(func_def_14, type, sK2: a).
% 1.64/1.30 thf(func_def_15, type, sK3: a).
% 1.64/1.30 thf(func_def_16, type, sK4: a > $o).
% 1.64/1.30 thf(f69,plain,(
% 1.64/1.30 $false),
% 1.64/1.30 inference(avatar_sat_refutation,[status(thm)],[f31,f36,f41,f62,f68])).
% 1.64/1.30 thf(f68,plain,(
% 1.64/1.30 ~spl0_1 | ~spl0_3 | ~spl0_4),
% 1.64/1.30 inference(avatar_contradiction_clause,[status(thm)],[f67])).
% 1.64/1.30 thf(f67,plain,(
% 1.64/1.30 $false | (~spl0_1 | ~spl0_3 | ~spl0_4)),
% 1.64/1.30 inference(trivial_inequality_removal,[status(thm)],[f66])).
% 1.64/1.30 thf(f66,plain,(
% 1.64/1.30 ($true = $false) | (~spl0_1 | ~spl0_3 | ~spl0_4)),
% 1.64/1.30 inference(backward_demodulation,[status(thm)],[f40,f65])).
% 1.64/1.30 thf(f65,plain,(
% 1.64/1.30 ((sK4 @ sK2) = $false) | (~spl0_1 | ~spl0_3)),
% 1.64/1.30 inference(forward_demodulation,[status(thm)],[f35,f27])).
% 1.64/1.30 thf(f27,plain,(
% 1.64/1.30 (sK3 = sK2) | ~spl0_1),
% 1.64/1.30 inference(avatar_component_clause,[status(thm)],[f25])).
% 1.64/1.30 thf(f25,definition,(
% 1.64/1.30 spl0_1 <=> (sK3 = sK2)),
% 1.64/1.30 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.64/1.30 thf(f35,plain,(
% 1.64/1.30 ((sK4 @ sK3) = $false) | ~spl0_3),
% 1.64/1.30 inference(avatar_component_clause,[status(thm)],[f33])).
% 1.64/1.30 thf(f33,definition,(
% 1.64/1.30 spl0_3 <=> ((sK4 @ sK3) = $false)),
% 1.64/1.30 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.64/1.30 thf(f40,plain,(
% 1.64/1.30 ($true = (sK4 @ sK2)) | ~spl0_4),
% 1.64/1.30 inference(avatar_component_clause,[status(thm)],[f38])).
% 1.64/1.30 thf(f38,definition,(
% 1.64/1.30 spl0_4 <=> ($true = (sK4 @ sK2))),
% 1.64/1.30 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.64/1.30 thf(f62,plain,(
% 1.64/1.30 spl0_1 | ~spl0_2),
% 1.64/1.30 inference(avatar_split_clause,[status(thm)],[f43,f29,f25])).
% 1.64/1.30 thf(f29,definition,(
% 1.64/1.30 spl0_2 <=> ! [X1 : a > $o] : (((X1 @ sK3) = $true) | ((X1 @ sK2) = $false))),
% 1.64/1.30 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.64/1.30 thf(f43,plain,(
% 1.64/1.30 (sK3 = sK2) | ~spl0_2),
% 1.64/1.30 inference(leibniz_equality_elimination,[status(thm)],[f30])).
% 1.64/1.30 thf(f30,plain,(
% 1.64/1.30 ( ! [X1 : a > $o] : (((X1 @ sK3) = $true) | ((X1 @ sK2) = $false)) ) | ~spl0_2),
% 1.64/1.30 inference(avatar_component_clause,[status(thm)],[f29])).
% 1.64/1.30 thf(f41,plain,(
% 1.64/1.30 spl0_4 | ~spl0_1),
% 1.64/1.30 inference(avatar_split_clause,[status(thm)],[f19,f25,f38])).
% 1.64/1.30 thf(f19,plain,(
% 1.64/1.30 (sK3 != sK2) | ($true = (sK4 @ sK2))),
% 1.64/1.30 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.64/1.30 thf(f17,plain,(
% 1.64/1.30 (sK3 != sK2) | (((sK4 @ sK2) => (sK4 @ sK3)) = $false)),
% 1.64/1.30 inference(equality_proxy_clausification,[status(thm)],[f16])).
% 1.64/1.30 thf(f16,plain,(
% 1.64/1.30 ($false = (sK2 = sK3)) | (((sK4 @ sK2) => (sK4 @ sK3)) = $false)),
% 1.64/1.30 inference(beta_eta_normalization,[status(thm)],[f15])).
% 1.64/1.30 thf(f15,plain,(
% 1.64/1.30 (((^[Y0 : a > $o]: ((Y0 @ sK2) => (Y0 @ sK3))) @ sK4) = $false) | ($false = (sK2 = sK3))),
% 1.64/1.30 inference(sigma_clausification,[status(thm)],[f14])).
% 1.64/1.30 thf(f14,plain,(
% 1.64/1.30 ((!! @ (a > $o) @ (^[Y0 : a > $o]: ((Y0 @ sK2) => (Y0 @ sK3)))) = $false) | ($false = (sK2 = sK3))),
% 1.64/1.30 inference(binary_proxy_clausification,[status(thm)],[f12])).
% 1.64/1.30 thf(f12,plain,(
% 1.64/1.30 ((!! @ (a > $o) @ (^[Y0 : a > $o]: ((Y0 @ sK2) => (Y0 @ sK3)))) != (sK2 = sK3))),
% 1.64/1.30 inference(beta_eta_normalization,[status(thm)],[f11])).
% 1.64/1.30 thf(f11,plain,(
% 1.64/1.30 (((^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ sK2) => (Y1 @ Y0))))) @ sK3) != (sK2 = sK3))),
% 1.64/1.30 inference(negative_extensionality,[status(thm)],[f10])).
% 1.64/1.30 thf(f10,plain,(
% 1.64/1.30 ((^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ sK2) => (Y1 @ Y0))))) != (= @ sK2))),
% 1.64/1.30 inference(beta_eta_normalization,[status(thm)],[f9])).
% 1.64/1.30 thf(f9,plain,(
% 1.64/1.30 (((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))) @ sK2) != (= @ sK2))),
% 1.64/1.30 inference(negative_extensionality,[status(thm)],[f8])).
% 1.64/1.30 thf(f8,plain,(
% 1.64/1.30 ((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))) != =)),
% 1.64/1.30 inference(beta_eta_normalization,[status(thm)],[f7])).
% 1.64/1.30 thf(f7,plain,(
% 1.64/1.30 ((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) != (^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 1.64/1.30 inference(cnf_transformation,[status(thm)],[f6])).
% 1.64/1.30 thf(f6,plain,(
% 1.64/1.30 ((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) != (^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 1.64/1.30 inference(flattening,[status(thm)],[f5])).
% 1.64/1.30 thf(f5,plain,(
% 1.64/1.30 ~((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) = (^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 1.64/1.30 inference(fool_elimination,[status(thm)],[f4])).
% 1.64/1.30 thf(f4,plain,(
% 1.64/1.30 ~((^[X0 : a, X1 : a] : ((X0 = X1))) = (^[X2 : a, X3 : a] : (! [X4 : a > $o] : ((X4 @ X2) => (X4 @ X3)))))),
% 1.64/1.30 inference(rectify,[status(thm)],[f2])).
% 1.64/1.30 thf(f2,negated_conjecture,(
% 1.64/1.30 ~((^[X0 : a, X1 : a] : ((X0 = X1))) = (^[X0 : a, X1 : a] : (! [X2 : a > $o] : ((X2 @ X0) => (X2 @ X1)))))),
% 1.64/1.30 inference(negated_conjecture,[status(cth)],[f1])).
% 1.64/1.30 thf(f1,conjecture,(
% 1.64/1.30 ((^[X0 : a, X1 : a] : ((X0 = X1))) = (^[X0 : a, X1 : a] : (! [X2 : a > $o] : ((X2 @ X0) => (X2 @ X1)))))),
% 1.64/1.30 file('/export/starexec/sandbox2/tmp/tmp.gEeValPkpj/DTF2THF_30045.p',cE1_eq__pme)).
% 1.64/1.30 thf(f36,plain,(
% 1.64/1.30 ~spl0_1 | spl0_3),
% 1.64/1.30 inference(avatar_split_clause,[status(thm)],[f18,f33,f25])).
% 1.64/1.30 thf(f18,plain,(
% 1.64/1.30 ((sK4 @ sK3) = $false) | (sK3 != sK2)),
% 1.64/1.30 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.64/1.30 thf(f31,plain,(
% 1.64/1.30 spl0_1 | spl0_2),
% 1.64/1.30 inference(avatar_split_clause,[status(thm)],[f23,f29,f25])).
% 1.64/1.30 thf(f23,plain,(
% 1.64/1.30 ( ! [X1 : a > $o] : (((X1 @ sK3) = $true) | ((X1 @ sK2) = $false) | (sK3 = sK2)) )),
% 1.64/1.30 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 1.64/1.30 thf(f22,plain,(
% 1.64/1.30 ( ! [X1 : a > $o] : (($true = ((X1 @ sK2) => (X1 @ sK3))) | (sK3 = sK2)) )),
% 1.64/1.30 inference(beta_eta_normalization,[status(thm)],[f21])).
% 1.64/1.30 thf(f21,plain,(
% 1.64/1.30 ( ! [X1 : a > $o] : ((sK3 = sK2) | ($true = ((^[Y0 : a > $o]: ((Y0 @ sK2) => (Y0 @ sK3))) @ X1))) )),
% 1.64/1.30 inference(pi_clausification,[status(thm)],[f20])).
% 1.64/1.30 thf(f20,plain,(
% 1.64/1.30 ((!! @ (a > $o) @ (^[Y0 : a > $o]: ((Y0 @ sK2) => (Y0 @ sK3)))) = $true) | (sK3 = sK2)),
% 1.64/1.30 inference(equality_proxy_clausification,[status(thm)],[f13])).
% 1.64/1.30 thf(f13,plain,(
% 1.64/1.30 ($true = (sK2 = sK3)) | ((!! @ (a > $o) @ (^[Y0 : a > $o]: ((Y0 @ sK2) => (Y0 @ sK3)))) = $true)),
% 1.64/1.30 inference(binary_proxy_clausification,[status(thm)],[f12])).
% 1.64/1.30 % SZS output end Proof for DTF2THF_30045
% 1.64/1.30 % (30204)------------------------------
% 1.64/1.30 % (30204)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.30 % (30204)Termination reason: Refutation
% 1.64/1.30
% 1.64/1.30 % (30204)Memory used [KB]: 5500
% 1.64/1.30 % (30204)Time elapsed: 0.004 s
% 1.64/1.30 % (30204)Instructions burned: 3 (million)
% 1.64/1.30 % (30204)------------------------------
% 1.64/1.30 % (30204)------------------------------
% 1.64/1.30 % (30197)Success in time 0.014 s
%------------------------------------------------------------------------------