%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO351^5 : 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 : n014.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 09:54:01 AM UTC 2026
% Result : Theorem 0.23s 1.33s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 40 ( 11 unt; 0 typ; 3 def)
% Number of atoms : 187 ( 57 equ; 2 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 142 ( 38 ~; 29 |; 0 &; 55 @)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 7 usr; 9 con; 0-2 aty)
% ( 10 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 62 ( 52 ^; 10 !; 0 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_12,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
sK2: a > $o ).
thf(func_def_14,type,
sK3: a ).
thf(func_def_15,type,
sK4: a ).
thf(f48,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f29,f34,f38,f44,f47]) ).
thf(f47,plain,
( spl0_2
| ~ spl0_1 ),
inference(avatar_split_clause,[status(thm)],[f46,f23,f27]) ).
thf(f27,definition,
( spl0_2
<=> ! [X1: a] :
( $false
= ( sK2 @ X1 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f23,definition,
( spl0_1
<=> ( sK2
= ( ^ [Y0: a] : $false ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f46,plain,
( ! [X1: a] :
( $false
= ( sK2 @ X1 ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f45]) ).
thf(f45,plain,
( ! [X1: a] :
( ( sK2 @ X1 )
= ( ^ [Y0: a] : $false
@ X1 ) )
| ~ spl0_1 ),
inference(argument_congruence,[status(thm)],[f25]) ).
thf(f25,plain,
( ( sK2
= ( ^ [Y0: a] : $false ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f23]) ).
thf(f44,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f43]) ).
thf(f43,plain,
( $false
| ~ spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f40]) ).
thf(f40,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f28,f33]) ).
thf(f33,plain,
( ( ( sK2 @ sK3 )
= $true )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f31]) ).
thf(f31,definition,
( spl0_3
<=> ( ( sK2 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f28,plain,
( ! [X1: a] :
( $false
= ( sK2 @ X1 ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f27]) ).
thf(f38,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_contradiction_clause,[status(thm)],[f37]) ).
thf(f37,plain,
( $false
| spl0_1
| ~ spl0_2 ),
inference(subsumption_resolution,[status(thm)],[f36,f28]) ).
thf(f36,plain,
( ( $false
!= ( sK2 @ sK4 ) )
| spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ( sK2 @ sK4 )
!= ( ^ [Y0: a] : $false
@ sK4 ) )
| spl0_1 ),
inference(negative_extensionality,[status(thm)],[f24]) ).
thf(f24,plain,
( ( sK2
!= ( ^ [Y0: a] : $false ) )
| spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f23]) ).
thf(f34,plain,
( spl0_3
| ~ spl0_1 ),
inference(avatar_split_clause,[status(thm)],[f17,f23,f31]) ).
thf(f17,plain,
( ( sK2
!= ( ^ [Y0: a] : $false ) )
| ( ( sK2 @ sK3 )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ( sK2 @ sK3 )
= $true )
| ( $false
= ( ( ^ [Y0: a] : $false )
= sK2 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( $false
= ( ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( ( ^ [Y0: a] : $false )
= sK2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
( ( $false
= ( ( ^ [Y0: a] : $false )
= sK2 ) )
| ( $false
= ( ^ [Y0: a] :
~ ( sK2 @ Y0 )
@ sK3 ) ) ),
inference(sigma_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
~ ( sK2 @ Y0 ) ) )
| ( $false
= ( ( ^ [Y0: a] : $false )
= sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( !! @ a
@ ^ [Y0: a] :
~ ( sK2 @ Y0 ) )
!= ( ( ^ [Y0: a] : $false )
= sK2 ) ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ( ^ [Y0: a] : $false )
= sK2 )
!= ( ^ [Y0: a > $o] :
( !! @ a
@ ^ [Y1: a] :
~ ( Y0 @ Y1 ) )
@ sK2 ) ),
inference(negative_extensionality,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ^ [Y0: a > $o] :
( !! @ a
@ ^ [Y1: a] :
~ ( Y0 @ Y1 ) ) )
!= ( (=)
@ ^ [Y0: a] : $false ) ),
inference(boolean_simplification,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [Y0: a > $o] :
( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> $false ) ) )
!= ( (=)
@ ^ [Y0: a] : $false ) ),
inference(beta_eta_normalization,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ^ [Y0: a > $o] :
( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> $false ) ) )
!= ( ^ [Y0: a > $o] :
( ( ^ [Y1: a] : $false )
= Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ^ [Y0: a > $o] :
( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> $false ) ) )
!= ( ^ [Y0: a > $o] :
( ( ^ [Y1: a] : $false )
= Y0 ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ^ [Y0: a > $o] :
( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> $false ) ) )
!= ( ^ [Y0: a > $o] :
( ( ^ [Y1: a] : $false )
= Y0 ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
( ( ^ [X0: a > $o] :
( ( ^ [X1: a] : $false )
= X0 ) )
!= ( ^ [X2: a > $o] :
! [X3: a] :
( ( X2 @ X3 )
=> $false ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
( ( ^ [X2: a > $o] :
( ( ^ [X1: a] : $false )
= X2 ) )
!= ( ^ [X0: a > $o] :
! [X1: a] :
( ( X0 @ X1 )
=> $false ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ^ [X2: a > $o] :
( ( ^ [X1: a] : $false )
= X2 ) )
= ( ^ [X0: a > $o] :
! [X1: a] :
( ( X0 @ X1 )
=> $false ) ) ),
file('/export/starexec/sandbox/tmp/tmp.goQFX6n1vp/DTF2THF_8561.p',cE6EXT_pme) ).
thf(f29,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f21,f27,f23]) ).
thf(f21,plain,
! [X1: a] :
( ( $false
= ( sK2 @ X1 ) )
| ( sK2
= ( ^ [Y0: a] : $false ) ) ),
inference(not_proxy_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
! [X1: a] :
( ( ( ~ ( sK2 @ X1 ) )
= $true )
| ( sK2
= ( ^ [Y0: a] : $false ) ) ),
inference(beta_eta_normalization,[status(thm)],[f19]) ).
thf(f19,plain,
! [X1: a] :
( ( ( ^ [Y0: a] :
~ ( sK2 @ Y0 )
@ X1 )
= $true )
| ( sK2
= ( ^ [Y0: a] : $false ) ) ),
inference(pi_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
~ ( sK2 @ Y0 ) )
= $true )
| ( sK2
= ( ^ [Y0: a] : $false ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( ( ^ [Y0: a] : $false )
= sK2 )
= $true )
| ( ( !! @ a
@ ^ [Y0: a] :
~ ( sK2 @ Y0 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYO351^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n014.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 14:28:27 EST 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.40 ---- Original DTF file ---
% 0.16/0.40 thf(spec,logic,$$dhol).
% 0.16/0.40 %------------------------------------------------------------------------------
% 0.16/0.40 % File : SYO351^5 : TPTP v9.2.1. Released v4.0.0.
% 0.16/0.40 % Domain : Syntactic
% 0.16/0.40 % Problem : TPS problem E6EXT
% 0.16/0.40 % Version : Especial.
% 0.16/0.40 % English : Example from [Ben99] p.116.
% 0.16/0.40
% 0.16/0.40 % Refs : [Ben99] Benzmueller (1999), Equality and Extensionality in Hig
% 0.16/0.40 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.40 % Source : [Bro09]
% 0.16/0.40 % Names : tps_0091 [Bro09]
% 0.16/0.40 % : E6ext [Ben99]
% 0.16/0.40 % : E6EXT [TPS]
% 0.16/0.40
% 0.16/0.40 % Status : Theorem
% 0.16/0.40 % Rating : 0.00 v8.2.0, 0.15 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.16/0.40 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.16/0.40 % Number of atoms : 4 ( 2 equ; 0 cnn)
% 0.16/0.40 % Maximal formula atoms : 1 ( 4 avg)
% 0.16/0.40 % Number of connectives : 2 ( 0 ~; 0 |; 0 &; 1 @)
% 0.16/0.40 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.16/0.40 % Maximal formula depth : 1 ( 1 avg)
% 0.16/0.40 % Number of types : 2 ( 1 usr)
% 0.16/0.40 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.16/0.40 % Number of symbols : 2 ( 0 usr; 1 con; 0-2 aty)
% 0.16/0.40 % Number of variables : 4 ( 3 ^; 1 !; 0 ?; 4 :)
% 0.16/0.40 % SPC : TH0_THM_EQU_NAR
% 0.16/0.40
% 0.16/0.40 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.40 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.40 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.40 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.40 % : Polymorphic definitions expanded.
% 0.16/0.40 %------------------------------------------------------------------------------
% 0.16/0.40 thf(a_type,type,
% 0.16/0.40 a: $tType ).
% 0.16/0.40
% 0.16/0.40 thf(cE6EXT_pme,conjecture,
% 0.16/0.40 ( ( ^ [R: a > $o] :
% 0.16/0.40 ! [Xx: a] :
% 0.16/0.40 ( ( R @ Xx )
% 0.16/0.40 => $false ) )
% 0.16/0.40 = ( ^ [Xy: a > $o] :
% 0.16/0.40 ( ( ^ [Xx: a] : $false )
% 0.16/0.40 = Xy ) ) ) ).
% 0.16/0.40
% 0.16/0.40 %------------------------------------------------------------------------------
% 0.16/0.40 ------------------------
% 0.23/1.30 ---- Embedded in THF ---
% 0.23/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.23/1.30 %%% Generated on Tue Feb 24 14:28:28 EST 2026
% 0.23/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 0.23/1.30 %%% Logic specification used:
% 0.23/1.30 %%% thf(spec, logic, $$dhol).
% 0.23/1.30
% 0.23/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.goQFX6n1vp/DTF2DTF8561.p
% See solution above
% 0.23/1.30 ------------------------
% 0.23/1.31 ---- Cleaned THF ---
% 0.23/1.31 thf(a_type,type,
% 0.23/1.31 a: $tType ).
% 0.23/1.31
% 0.23/1.31 thf(cE6EXT_pme,conjecture,
% 0.23/1.31 ( ( ^ [R: a > $o] :
% 0.23/1.31 ! [Xx: a] :
% 0.23/1.31 ( ( R @ Xx )
% 0.23/1.31 => $false ) )
% 0.23/1.31 = ( ^ [Xy: a > $o] :
% 0.23/1.31 ( ( ^ [Xx: a] : $false )
% 0.23/1.31 = Xy ) ) ) ).
% 0.23/1.31 ------------------------
% 0.23/1.33 % (8661)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_8561 for (3000ds/2Mi)
% 0.23/1.33 % (8660)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_8561 for (3000ds/27Mi)
% 0.23/1.33 % (8658)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_8561 for (3000ds/183Mi)
% 0.23/1.33 % (8659)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_8561 for (3000ds/4Mi)
% 0.23/1.33 % (8662)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_8561 for (3000ds/2Mi)
% 0.23/1.33 % (8663)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_8561 for (3000ds/275Mi)
% 0.23/1.33 % (8664)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_8561 for (3000ds/18Mi)
% 0.23/1.33 % (8662)Refutation not found, incomplete strategy
% 0.23/1.33 % (8662)------------------------------
% 0.23/1.33 % (8662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.23/1.33 % (8662)Termination reason: Refutation not found, incomplete strategy
% 0.23/1.33
% 0.23/1.33
% 0.23/1.33 % (8662)Memory used [KB]: 5500
% 0.23/1.33 % (8662)Time elapsed: 0.003 s
% 0.23/1.33 % (8662)Instructions burned: 1 (million)
% 0.23/1.33 % (8662)------------------------------
% 0.23/1.33 % (8662)------------------------------
% 0.23/1.33 % (8658)First to succeed.
% 0.23/1.33 % (8659)Instruction limit reached!
% 0.23/1.33 % (8659)------------------------------
% 0.23/1.33 % (8659)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.23/1.33 % (8659)Termination reason: Unknown
% 0.23/1.33 % (8659)Termination phase: Saturation
% 0.23/1.33
% 0.23/1.33 % (8659)Memory used [KB]: 5500
% 0.23/1.33 % (8659)Time elapsed: 0.005 s
% 0.23/1.33 % (8659)Instructions burned: 4 (million)
% 0.23/1.33 % (8659)------------------------------
% 0.23/1.33 % (8659)------------------------------
% 0.23/1.33 % (8661)Instruction limit reached!
% 0.23/1.33 % (8661)------------------------------
% 0.23/1.33 % (8661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.23/1.33 % (8661)Termination reason: Unknown
% 0.23/1.33 % (8661)Termination phase: Saturation
% 0.23/1.33
% 0.23/1.33 % (8661)Memory used [KB]: 5500
% 0.23/1.33 % (8661)Time elapsed: 0.005 s
% 0.23/1.33 % (8661)Instructions burned: 2 (million)
% 0.23/1.33 % (8661)------------------------------
% 0.23/1.33 % (8661)------------------------------
% 0.23/1.33 % (8663)Also succeeded, but the first one will report.
% 0.23/1.33 % (8658)Refutation found. Thanks to Tanya!
% 0.23/1.33 % SZS status Theorem for DTF2THF_8561
% 0.23/1.33 % SZS output start Proof for DTF2THF_8561
% 0.23/1.33 thf(type_def_5, type, a: $tType).
% 0.23/1.33 thf(func_def_0, type, a: $tType).
% 0.23/1.33 thf(func_def_12, type, ph1: !>[X0: $tType]:(X0)).
% 0.23/1.33 thf(func_def_13, type, sK2: a > $o).
% 0.23/1.33 thf(func_def_14, type, sK3: a).
% 0.23/1.33 thf(func_def_15, type, sK4: a).
% 0.23/1.33 thf(f48,plain,(
% 0.23/1.33 $false),
% 0.23/1.33 inference(avatar_sat_refutation,[status(thm)],[f29,f34,f38,f44,f47])).
% 0.23/1.33 thf(f47,plain,(
% 0.23/1.33 spl0_2 | ~spl0_1),
% 0.23/1.33 inference(avatar_split_clause,[status(thm)],[f46,f23,f27])).
% 0.23/1.33 thf(f27,definition,(
% 0.23/1.33 spl0_2 <=> ! [X1 : a] : ($false = (sK2 @ X1))),
% 0.23/1.33 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 0.23/1.33 thf(f23,definition,(
% 0.23/1.33 spl0_1 <=> (sK2 = (^[Y0 : a]: ($false)))),
% 0.23/1.33 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 0.23/1.33 thf(f46,plain,(
% 0.23/1.33 ( ! [X1 : a] : (($false = (sK2 @ X1))) ) | ~spl0_1),
% 0.23/1.33 inference(beta_eta_normalization,[status(thm)],[f45])).
% 0.23/1.33 thf(f45,plain,(
% 0.23/1.33 ( ! [X1 : a] : (((sK2 @ X1) = ((^[Y0 : a]: ($false)) @ X1))) ) | ~spl0_1),
% 0.23/1.33 inference(argument_congruence,[status(thm)],[f25])).
% 0.23/1.33 thf(f25,plain,(
% 0.23/1.33 (sK2 = (^[Y0 : a]: ($false))) | ~spl0_1),
% 0.23/1.33 inference(avatar_component_clause,[status(thm)],[f23])).
% 0.23/1.33 thf(f44,plain,(
% 0.23/1.33 ~spl0_2 | ~spl0_3),
% 0.23/1.33 inference(avatar_contradiction_clause,[status(thm)],[f43])).
% 0.23/1.33 thf(f43,plain,(
% 0.23/1.33 $false | (~spl0_2 | ~spl0_3)),
% 0.23/1.33 inference(trivial_inequality_removal,[status(thm)],[f40])).
% 0.23/1.33 thf(f40,plain,(
% 0.23/1.33 ($false = $true) | (~spl0_2 | ~spl0_3)),
% 0.23/1.33 inference(superposition,[status(thm)],[f28,f33])).
% 0.23/1.33 thf(f33,plain,(
% 0.23/1.33 ((sK2 @ sK3) = $true) | ~spl0_3),
% 0.23/1.33 inference(avatar_component_clause,[status(thm)],[f31])).
% 0.23/1.33 thf(f31,definition,(
% 0.23/1.33 spl0_3 <=> ((sK2 @ sK3) = $true)),
% 0.23/1.33 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 0.23/1.33 thf(f28,plain,(
% 0.23/1.33 ( ! [X1 : a] : (($false = (sK2 @ X1))) ) | ~spl0_2),
% 0.23/1.33 inference(avatar_component_clause,[status(thm)],[f27])).
% 0.23/1.33 thf(f38,plain,(
% 0.23/1.33 spl0_1 | ~spl0_2),
% 0.23/1.33 inference(avatar_contradiction_clause,[status(thm)],[f37])).
% 0.23/1.33 thf(f37,plain,(
% 0.23/1.33 $false | (spl0_1 | ~spl0_2)),
% 0.23/1.33 inference(subsumption_resolution,[status(thm)],[f36,f28])).
% 0.23/1.33 thf(f36,plain,(
% 0.23/1.33 ($false != (sK2 @ sK4)) | spl0_1),
% 0.23/1.33 inference(beta_eta_normalization,[status(thm)],[f35])).
% 0.23/1.33 thf(f35,plain,(
% 0.23/1.33 ((sK2 @ sK4) != ((^[Y0 : a]: ($false)) @ sK4)) | spl0_1),
% 0.23/1.33 inference(negative_extensionality,[status(thm)],[f24])).
% 0.23/1.33 thf(f24,plain,(
% 0.23/1.33 (sK2 != (^[Y0 : a]: ($false))) | spl0_1),
% 0.23/1.33 inference(avatar_component_clause,[status(thm)],[f23])).
% 0.23/1.33 thf(f34,plain,(
% 0.23/1.33 spl0_3 | ~spl0_1),
% 0.23/1.33 inference(avatar_split_clause,[status(thm)],[f17,f23,f31])).
% 0.23/1.33 thf(f17,plain,(
% 0.23/1.33 (sK2 != (^[Y0 : a]: ($false))) | ((sK2 @ sK3) = $true)),
% 0.23/1.33 inference(equality_proxy_clausification,[status(thm)],[f16])).
% 0.23/1.33 thf(f16,plain,(
% 0.23/1.33 ((sK2 @ sK3) = $true) | ($false = ((^[Y0 : a]: ($false)) = sK2))),
% 0.23/1.33 inference(not_proxy_clausification,[status(thm)],[f15])).
% 0.23/1.33 thf(f15,plain,(
% 0.23/1.33 ($false = (~ (sK2 @ sK3))) | ($false = ((^[Y0 : a]: ($false)) = sK2))),
% 0.23/1.33 inference(beta_eta_normalization,[status(thm)],[f14])).
% 0.23/1.33 thf(f14,plain,(
% 0.23/1.33 ($false = ((^[Y0 : a]: ($false)) = sK2)) | ($false = ((^[Y0 : a]: (~ (sK2 @ Y0))) @ sK3))),
% 0.23/1.33 inference(sigma_clausification,[status(thm)],[f13])).
% 0.23/1.33 thf(f13,plain,(
% 0.23/1.33 ($false = (!! @ a @ (^[Y0 : a]: (~ (sK2 @ Y0))))) | ($false = ((^[Y0 : a]: ($false)) = sK2))),
% 0.23/1.33 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 0.23/1.33 thf(f11,plain,(
% 0.23/1.33 ((!! @ a @ (^[Y0 : a]: (~ (sK2 @ Y0)))) != ((^[Y0 : a]: ($false)) = sK2))),
% 0.23/1.33 inference(beta_eta_normalization,[status(thm)],[f10])).
% 0.23/1.33 thf(f10,plain,(
% 0.23/1.33 (((^[Y0 : a]: ($false)) = sK2) != ((^[Y0 : a > $o]: (!! @ a @ (^[Y1 : a]: (~ (Y0 @ Y1))))) @ sK2))),
% 0.23/1.33 inference(negative_extensionality,[status(thm)],[f9])).
% 0.23/1.33 thf(f9,plain,(
% 0.23/1.33 ((^[Y0 : a > $o]: (!! @ a @ (^[Y1 : a]: (~ (Y0 @ Y1))))) != (= @ (^[Y0 : a]: ($false))))),
% 0.23/1.33 inference(boolean_simplification,[status(thm)],[f8])).
% 0.23/1.33 thf(f8,plain,(
% 0.23/1.33 ((^[Y0 : a > $o]: (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => $false)))) != (= @ (^[Y0 : a]: ($false))))),
% 0.23/1.33 inference(beta_eta_normalization,[status(thm)],[f7])).
% 0.23/1.33 thf(f7,plain,(
% 0.23/1.33 ((^[Y0 : a > $o]: (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => $false)))) != (^[Y0 : a > $o]: ((^[Y1 : a]: ($false)) = Y0)))),
% 0.23/1.33 inference(cnf_transformation,[status(thm)],[f6])).
% 0.23/1.33 thf(f6,plain,(
% 0.23/1.33 ((^[Y0 : a > $o]: (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => $false)))) != (^[Y0 : a > $o]: ((^[Y1 : a]: ($false)) = Y0)))),
% 0.23/1.33 inference(flattening,[status(thm)],[f5])).
% 0.23/1.33 thf(f5,plain,(
% 0.23/1.33 ~((^[Y0 : a > $o]: (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => $false)))) = (^[Y0 : a > $o]: ((^[Y1 : a]: ($false)) = Y0)))),
% 0.23/1.33 inference(fool_elimination,[status(thm)],[f4])).
% 0.23/1.33 thf(f4,plain,(
% 0.23/1.33 ~((^[X0 : a > $o] : (((^[X1 : a] : ($false)) = X0))) = (^[X2 : a > $o] : (! [X3 : a] : ((X2 @ X3) => $false))))),
% 0.23/1.33 inference(rectify,[status(thm)],[f2])).
% 0.23/1.33 thf(f2,negated_conjecture,(
% 0.23/1.33 ~((^[X2 : a > $o] : (((^[X1 : a] : ($false)) = X2))) = (^[X0 : a > $o] : (! [X1 : a] : ((X0 @ X1) => $false))))),
% 0.23/1.33 inference(negated_conjecture,[status(cth)],[f1])).
% 0.23/1.33 thf(f1,conjecture,(
% 0.23/1.33 ((^[X2 : a > $o] : (((^[X1 : a] : ($false)) = X2))) = (^[X0 : a > $o] : (! [X1 : a] : ((X0 @ X1) => $false))))),
% 0.23/1.33 file('/export/starexec/sandbox/tmp/tmp.goQFX6n1vp/DTF2THF_8561.p',cE6EXT_pme)).
% 0.23/1.33 thf(f29,plain,(
% 0.23/1.33 spl0_1 | spl0_2),
% 0.23/1.33 inference(avatar_split_clause,[status(thm)],[f21,f27,f23])).
% 0.23/1.33 thf(f21,plain,(
% 0.23/1.33 ( ! [X1 : a] : (($false = (sK2 @ X1)) | (sK2 = (^[Y0 : a]: ($false)))) )),
% 0.23/1.33 inference(not_proxy_clausification,[status(thm)],[f20])).
% 0.23/1.33 thf(f20,plain,(
% 0.23/1.33 ( ! [X1 : a] : (((~ (sK2 @ X1)) = $true) | (sK2 = (^[Y0 : a]: ($false)))) )),
% 0.23/1.33 inference(beta_eta_normalization,[status(thm)],[f19])).
% 0.23/1.33 thf(f19,plain,(
% 0.23/1.33 ( ! [X1 : a] : ((((^[Y0 : a]: (~ (sK2 @ Y0))) @ X1) = $true) | (sK2 = (^[Y0 : a]: ($false)))) )),
% 0.23/1.33 inference(pi_clausification,[status(thm)],[f18])).
% 0.23/1.33 thf(f18,plain,(
% 0.23/1.33 ((!! @ a @ (^[Y0 : a]: (~ (sK2 @ Y0)))) = $true) | (sK2 = (^[Y0 : a]: ($false)))),
% 0.23/1.33 inference(equality_proxy_clausification,[status(thm)],[f12])).
% 0.23/1.33 thf(f12,plain,(
% 0.23/1.33 (((^[Y0 : a]: ($false)) = sK2) = $true) | ((!! @ a @ (^[Y0 : a]: (~ (sK2 @ Y0)))) = $true)),
% 0.23/1.33 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 0.23/1.33 % SZS output end Proof for DTF2THF_8561
% 0.23/1.33 % (8658)------------------------------
% 0.23/1.33 % (8658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.23/1.33 % (8658)Termination reason: Refutation
% 0.23/1.33
% 0.23/1.33 % (8658)Memory used [KB]: 5500
% 0.23/1.33 % (8658)Time elapsed: 0.005 s
% 0.23/1.33 % (8658)Instructions burned: 2 (million)
% 0.23/1.33 % (8658)------------------------------
% 0.23/1.33 % (8658)------------------------------
% 0.23/1.33 % (8657)Success in time 0.018 s
%------------------------------------------------------------------------------