%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO558^1 : TPTP v9.2.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n005.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 09:54:32 AM UTC 2026
% Result : Theorem 1.50s 1.24s
% Output : Refutation 1.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 9 unt; 0 typ; 4 def)
% Number of atoms : 157 ( 36 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 198 ( 56 ~; 30 |; 0 &; 97 @)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 9 usr; 8 con; 0-2 aty)
% ( 11 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 44 ( 37 ^; 7 !; 0 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
eps: ( $i > $o ) > $i ).
thf(func_def_3,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_11,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
sK2: $i > $o ).
thf(f62,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f27,f36,f41,f48,f59,f61]) ).
thf(f61,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f60]) ).
thf(f60,plain,
( $false
| ~ spl0_1
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f52]) ).
thf(f52,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f31,f22]) ).
thf(f22,plain,
( ! [X1: $i] :
( ( sK2 @ X1 )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f21]) ).
thf(f21,definition,
( spl0_1
<=> ! [X1: $i] :
( ( sK2 @ X1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f31,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f29]) ).
thf(f29,definition,
( spl0_3
<=> ( $false
= ( sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f59,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f58]) ).
thf(f58,plain,
( $false
| ~ spl0_1
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f53]) ).
thf(f53,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f35,f22]) ).
thf(f35,plain,
( ( $false
= ( sK2
@ ( eps
@ ^ [Y0: $i] :
~ ( sK2 @ Y0 ) ) ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f33]) ).
thf(f33,definition,
( spl0_4
<=> ( $false
= ( sK2
@ ( eps
@ ^ [Y0: $i] :
~ ( sK2 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f48,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f47]) ).
thf(f47,plain,
( $false
| ~ spl0_2
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f42]) ).
thf(f42,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f26,f35]) ).
thf(f26,plain,
( ( $true
= ( sK2
@ ( eps
@ ^ [Y0: $i] :
~ ( sK2 @ Y0 ) ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f24]) ).
thf(f24,definition,
( spl0_2
<=> ( $true
= ( sK2
@ ( eps
@ ^ [Y0: $i] :
~ ( sK2 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f41,plain,
( spl0_1
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f40,f33,f21]) ).
thf(f40,plain,
! [X1: $i] :
( ( ( sK2 @ X1 )
= $true )
| ( $false
= ( sK2
@ ( eps
@ ^ [Y0: $i] :
~ ( sK2 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
! [X1: $i] :
( ( $false
= ( sK2
@ ( eps
@ ^ [Y0: $i] :
~ ( sK2 @ Y0 ) ) ) )
| ( $false
= ( ~ ( sK2 @ X1 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
! [X1: $i] :
( ( ( ~ ( sK2
@ ( eps
@ ^ [Y0: $i] :
~ ( sK2 @ Y0 ) ) ) )
= $true )
| ( $false
= ( ~ ( sK2 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f37]) ).
thf(f37,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
~ ( sK2 @ Y0 )
@ ( eps
@ ^ [Y0: $i] :
~ ( sK2 @ Y0 ) ) )
= $true )
| ( $false
= ( ^ [Y0: $i] :
~ ( sK2 @ Y0 )
@ X1 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f36,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f18,f33,f29]) ).
thf(f18,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2
@ ( eps
@ ^ [Y0: $i] :
~ ( sK2 @ Y0 ) ) ) ) ),
inference(sigma_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( $false
= ( !! @ $i @ sK2 ) )
| ( $false
= ( sK2
@ ( eps
@ ^ [Y0: $i] :
~ ( sK2 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( !! @ $i @ sK2 )
!= ( sK2
@ ( eps
@ ^ [Y0: $i] :
~ ( sK2 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ^ [Y0: $i > $o] :
( Y0
@ ( eps
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) )
@ sK2 )
!= ( !! @ $i @ sK2 ) ),
inference(negative_extensionality,[status(thm)],[f13]) ).
thf(f13,plain,
( !!
@ ( $i
!= ( ^ [Y0: $i > $o] :
( Y0
@ ( eps
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ^ [Y0: $i > $o] :
( Y0
@ ( eps
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: $i > $o] : ( !! @ $i @ Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ^ [Y0: $i > $o] :
( Y0
@ ( eps
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: $i > $o] : ( !! @ $i @ Y0 ) ) ),
inference(flattening,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [Y0: $i > $o] :
( Y0
@ ( eps
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: $i > $o] : ( !! @ $i @ Y0 ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ^ [X0: $i > $o] :
( X0
@ ( eps
@ ^ [X1: $i] :
~ ( X0 @ X1 ) ) ) )
!= ( ^ [X2: $i > $o] : ( !! @ $i @ X2 ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
( ( ^ [X0: $i > $o] :
( X0
@ ( eps
@ ^ [X1: $i] :
~ ( X0 @ X1 ) ) ) )
!= ( ^ [X0: $i > $o] : ( !! @ $i @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( ( ^ [X0: $i > $o] :
( X0
@ ( eps
@ ^ [X1: $i] :
~ ( X0 @ X1 ) ) ) )
= ( ^ [X0: $i > $o] : ( !! @ $i @ X0 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.RlLqLZtRA5/DTF2THF_21074.p',conj) ).
thf(f27,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f19,f24,f21]) ).
thf(f19,plain,
! [X1: $i] :
( ( ( sK2 @ X1 )
= $true )
| ( $true
= ( sK2
@ ( eps
@ ^ [Y0: $i] :
~ ( sK2 @ Y0 ) ) ) ) ),
inference(pi_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( ( $true
= ( !! @ $i @ sK2 ) )
| ( $true
= ( sK2
@ ( eps
@ ^ [Y0: $i] :
~ ( sK2 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO558^1 : TPTP v9.2.1. Bugfixed v7.5.0.
% 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.33 % Computer : n005.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % 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 14:33:44 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
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : SYO558^1 : TPTP v9.2.1. Bugfixed v7.5.0.
% 0.29/0.46 % Domain : Syntactic
% 0.29/0.46 % Problem : Forall on $i can be expressed in terms of choice on $
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English :
% 0.29/0.46
% 0.29/0.46 % Refs : [Bro11] Brown (2011), Email to Geoff Sutcliffe
% 0.29/0.46 % Source : [Bro11]
% 0.29/0.46 % Names : CHOICE30 [Bro11]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % Rating : 0.33 v8.1.0, 0.50 v7.5.0
% 0.29/0.46 % Syntax : Number of formulae : 3 ( 1 unt; 1 typ; 0 def)
% 0.29/0.46 % Number of atoms : 2 ( 1 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 1 ( 1 avg)
% 0.29/0.46 % Number of connectives : 11 ( 1 ~; 0 |; 0 &; 8 @)
% 0.29/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 5 ( 3 avg)
% 0.29/0.46 % Number of types : 2 ( 0 usr)
% 0.29/0.46 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 3 ( 1 usr; 1 con; 0-2 aty)
% 0.29/0.46 % ( 1 !!; 0 ??; 0 @@+; 0 @@-)
% 0.29/0.46 % Number of variables : 5 ( 3 ^; 1 !; 1 ?; 5 :)
% 0.29/0.46 % SPC : TH1_THM_EQU_NAR
% 0.29/0.46
% 0.29/0.46 % Comments : (eps (complement P)) can only satisfy P if everything satisfies P.
% 0.29/0.46 % Hence (^P.P(eps (^x.~Px))) = (^P.!! P).
% 0.29/0.46 % : Note that this problem uses !! for forall instead of the !
% 0.29/0.46 % quantifier.
% 0.29/0.46 % Bugfixes : Added type argument to !!.
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf(eps,type,
% 0.29/0.46 eps: ( $i > $o ) > $i ).
% 0.29/0.46
% 0.29/0.46 thf(choiceax,axiom,
% 0.29/0.46 ! [P: $i > $o] :
% 0.29/0.46 ( ? [X: $i] : ( P @ X )
% 0.29/0.46 => ( P @ ( eps @ P ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(conj,conjecture,
% 0.29/0.46 ( ( ^ [P: $i > $o] :
% 0.29/0.46 ( P
% 0.29/0.46 @ ( eps
% 0.29/0.46 @ ^ [X: $i] :
% 0.29/0.46 ~ ( P @ X ) ) ) )
% 0.29/0.46 = ( ^ [P: $i > $o] : ( !! @ $i @ P ) ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 1.50/1.21 ---- Embedded in THF ---
% 1.50/1.21 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.21 %%% Generated on Tue Feb 24 14:33:45 EST 2026
% 1.50/1.21 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.21 %%% Logic specification used:
% 1.50/1.21 %%% thf(spec, logic, $$dhol).
% 1.50/1.21
% 1.50/1.21 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.RlLqLZtRA5/DTF2DTF21074.p
% See solution above
% 1.50/1.21 ------------------------
% 1.50/1.22 ---- Cleaned THF ---
% 1.50/1.22 thf(eps,type,
% 1.50/1.22 eps: ( $i > $o ) > $i ).
% 1.50/1.22
% 1.50/1.22 thf(choiceax,axiom,
% 1.50/1.22 ! [P: $i > $o] :
% 1.50/1.22 ( ? [X: $i] : ( P @ X )
% 1.50/1.22 => ( P @ ( eps @ P ) ) ) ).
% 1.50/1.22
% 1.50/1.22 thf(conj,conjecture,
% 1.50/1.22 ( ( ^ [P: $i > $o] :
% 1.50/1.22 ( P
% 1.50/1.22 @ ( eps
% 1.50/1.22 @ ^ [X: $i] :
% 1.50/1.22 ~ ( P @ X ) ) ) )
% 1.50/1.22 = ( ^ [P: $i > $o] : ( !! @ $i @ P ) ) ) ).
% 1.50/1.22 ------------------------
% 1.50/1.23 % (21292)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_21074 for (2999ds/4Mi)
% 1.50/1.23 % (21294)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_21074 for (2999ds/2Mi)
% 1.50/1.23 % (21292)Instruction limit reached!
% 1.50/1.23 % (21292)------------------------------
% 1.50/1.23 % (21292)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.23 % (21292)Termination reason: Unknown
% 1.50/1.23 % (21292)Termination phase: Saturation
% 1.50/1.23
% 1.50/1.23 % (21292)Memory used [KB]: 5500
% 1.50/1.23 % (21292)Time elapsed: 0.003 s
% 1.50/1.23 % (21292)Instructions burned: 4 (million)
% 1.50/1.23 % (21292)------------------------------
% 1.50/1.23 % (21292)------------------------------
% 1.50/1.23 % (21294)Instruction limit reached!
% 1.50/1.23 % (21294)------------------------------
% 1.50/1.23 % (21294)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.23 % (21294)Termination reason: Unknown
% 1.50/1.23 % (21294)Termination phase: Saturation
% 1.50/1.23
% 1.50/1.23 % (21294)Memory used [KB]: 5500
% 1.50/1.23 % (21294)Time elapsed: 0.002 s
% 1.50/1.23 % (21294)Instructions burned: 2 (million)
% 1.50/1.23 % (21294)------------------------------
% 1.50/1.23 % (21294)------------------------------
% 1.50/1.24 % (21291)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_21074 for (2999ds/183Mi)
% 1.50/1.24 % (21293)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_21074 for (2999ds/27Mi)
% 1.50/1.24 % (21295)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_21074 for (2999ds/2Mi)
% 1.50/1.24 % (21297)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_21074 for (2999ds/18Mi)
% 1.50/1.24 % (21296)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_21074 for (2999ds/275Mi)
% 1.50/1.24 % (21295)Refutation not found, incomplete strategy
% 1.50/1.24 % (21295)------------------------------
% 1.50/1.24 % (21295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.24 % (21295)Termination reason: Refutation not found, incomplete strategy
% 1.50/1.24
% 1.50/1.24
% 1.50/1.24 % (21295)Memory used [KB]: 5500
% 1.50/1.24 % (21295)Time elapsed: 0.004 s
% 1.50/1.24 % (21295)Instructions burned: 1 (million)
% 1.50/1.24 % (21295)------------------------------
% 1.50/1.24 % (21295)------------------------------
% 1.50/1.24 % (21296)Refutation not found, incomplete strategy
% 1.50/1.24 % (21296)------------------------------
% 1.50/1.24 % (21296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.24 % (21296)Termination reason: Refutation not found, incomplete strategy
% 1.50/1.24
% 1.50/1.24
% 1.50/1.24 % (21296)Memory used [KB]: 5500
% 1.50/1.24 % (21296)Time elapsed: 0.004 s
% 1.50/1.24 % (21296)Instructions burned: 2 (million)
% 1.50/1.24 % (21296)------------------------------
% 1.50/1.24 % (21296)------------------------------
% 1.50/1.24 % (21293)First to succeed.
% 1.50/1.24 % (21298)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_21074 for (2999ds/3Mi)
% 1.50/1.24 % (21299)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_21074 for (2999ds/37Mi)
% 1.50/1.24 % (21298)Instruction limit reached!
% 1.50/1.24 % (21298)------------------------------
% 1.50/1.24 % (21298)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.24 % (21298)Termination reason: Unknown
% 1.50/1.24 % (21298)Termination phase: Saturation
% 1.50/1.24
% 1.50/1.24 % (21298)Memory used [KB]: 5500
% 1.50/1.24 % (21298)Time elapsed: 0.002 s
% 1.50/1.24 % (21298)Instructions burned: 3 (million)
% 1.50/1.24 % (21298)------------------------------
% 1.50/1.24 % (21298)------------------------------
% 1.50/1.24 % (21293)Refutation found. Thanks to Tanya!
% 1.50/1.24 % SZS status Theorem for DTF2THF_21074
% 1.50/1.24 % SZS output start Proof for DTF2THF_21074
% 1.50/1.24 thf(func_def_0, type, eps: ($i > $o) > $i).
% 1.50/1.24 thf(func_def_3, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.50/1.24 thf(func_def_11, type, ph1: !>[X0: $tType]:(X0)).
% 1.50/1.24 thf(func_def_12, type, sK2: $i > $o).
% 1.50/1.24 thf(f62,plain,(
% 1.50/1.24 $false),
% 1.50/1.24 inference(avatar_sat_refutation,[status(thm)],[f27,f36,f41,f48,f59,f61])).
% 1.50/1.24 thf(f61,plain,(
% 1.50/1.24 ~spl0_1 | ~spl0_3),
% 1.50/1.24 inference(avatar_contradiction_clause,[status(thm)],[f60])).
% 1.50/1.24 thf(f60,plain,(
% 1.50/1.24 $false | (~spl0_1 | ~spl0_3)),
% 1.50/1.24 inference(trivial_inequality_removal,[status(thm)],[f52])).
% 1.50/1.24 thf(f52,plain,(
% 1.50/1.24 ($false = $true) | (~spl0_1 | ~spl0_3)),
% 1.50/1.24 inference(superposition,[status(thm)],[f31,f22])).
% 1.50/1.24 thf(f22,plain,(
% 1.50/1.24 ( ! [X1 : $i] : (((sK2 @ X1) = $true)) ) | ~spl0_1),
% 1.50/1.24 inference(avatar_component_clause,[status(thm)],[f21])).
% 1.50/1.24 thf(f21,definition,(
% 1.50/1.24 spl0_1 <=> ! [X1 : $i] : ((sK2 @ X1) = $true)),
% 1.50/1.24 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.50/1.24 thf(f31,plain,(
% 1.50/1.24 ($false = (sK2 @ sK3)) | ~spl0_3),
% 1.50/1.24 inference(avatar_component_clause,[status(thm)],[f29])).
% 1.50/1.24 thf(f29,definition,(
% 1.50/1.24 spl0_3 <=> ($false = (sK2 @ sK3))),
% 1.50/1.24 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.50/1.24 thf(f59,plain,(
% 1.50/1.24 ~spl0_1 | ~spl0_4),
% 1.50/1.24 inference(avatar_contradiction_clause,[status(thm)],[f58])).
% 1.50/1.24 thf(f58,plain,(
% 1.50/1.24 $false | (~spl0_1 | ~spl0_4)),
% 1.50/1.24 inference(trivial_inequality_removal,[status(thm)],[f53])).
% 1.50/1.24 thf(f53,plain,(
% 1.50/1.24 ($false = $true) | (~spl0_1 | ~spl0_4)),
% 1.50/1.24 inference(superposition,[status(thm)],[f35,f22])).
% 1.50/1.24 thf(f35,plain,(
% 1.50/1.24 ($false = (sK2 @ (eps @ (^[Y0 : $i]: (~ (sK2 @ Y0)))))) | ~spl0_4),
% 1.50/1.24 inference(avatar_component_clause,[status(thm)],[f33])).
% 1.50/1.24 thf(f33,definition,(
% 1.50/1.24 spl0_4 <=> ($false = (sK2 @ (eps @ (^[Y0 : $i]: (~ (sK2 @ Y0))))))),
% 1.50/1.24 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.50/1.24 thf(f48,plain,(
% 1.50/1.24 ~spl0_2 | ~spl0_4),
% 1.50/1.24 inference(avatar_contradiction_clause,[status(thm)],[f47])).
% 1.50/1.24 thf(f47,plain,(
% 1.50/1.24 $false | (~spl0_2 | ~spl0_4)),
% 1.50/1.25 inference(trivial_inequality_removal,[status(thm)],[f42])).
% 1.50/1.25 thf(f42,plain,(
% 1.50/1.25 ($false = $true) | (~spl0_2 | ~spl0_4)),
% 1.50/1.25 inference(backward_demodulation,[status(thm)],[f26,f35])).
% 1.50/1.25 thf(f26,plain,(
% 1.50/1.25 ($true = (sK2 @ (eps @ (^[Y0 : $i]: (~ (sK2 @ Y0)))))) | ~spl0_2),
% 1.50/1.25 inference(avatar_component_clause,[status(thm)],[f24])).
% 1.50/1.25 thf(f24,definition,(
% 1.50/1.25 spl0_2 <=> ($true = (sK2 @ (eps @ (^[Y0 : $i]: (~ (sK2 @ Y0))))))),
% 1.50/1.25 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.50/1.25 thf(f41,plain,(
% 1.50/1.25 spl0_1 | spl0_4),
% 1.50/1.25 inference(avatar_split_clause,[status(thm)],[f40,f33,f21])).
% 1.50/1.25 thf(f40,plain,(
% 1.50/1.25 ( ! [X1 : $i] : (((sK2 @ X1) = $true) | ($false = (sK2 @ (eps @ (^[Y0 : $i]: (~ (sK2 @ Y0))))))) )),
% 1.50/1.25 inference(not_proxy_clausification,[status(thm)],[f39])).
% 1.50/1.25 thf(f39,plain,(
% 1.50/1.25 ( ! [X1 : $i] : (($false = (sK2 @ (eps @ (^[Y0 : $i]: (~ (sK2 @ Y0)))))) | ($false = (~ (sK2 @ X1)))) )),
% 1.50/1.25 inference(not_proxy_clausification,[status(thm)],[f38])).
% 1.50/1.25 thf(f38,plain,(
% 1.50/1.25 ( ! [X1 : $i] : (((~ (sK2 @ (eps @ (^[Y0 : $i]: (~ (sK2 @ Y0)))))) = $true) | ($false = (~ (sK2 @ X1)))) )),
% 1.50/1.25 inference(beta_eta_normalization,[status(thm)],[f37])).
% 1.50/1.25 thf(f37,plain,(
% 1.50/1.25 ( ! [X1 : $i] : ((((^[Y0 : $i]: (~ (sK2 @ Y0))) @ (eps @ (^[Y0 : $i]: (~ (sK2 @ Y0))))) = $true) | ($false = ((^[Y0 : $i]: (~ (sK2 @ Y0))) @ X1))) )),
% 1.50/1.25 introduced(definition,[],[choice_axiom])).
% 1.50/1.25 thf(f36,plain,(
% 1.50/1.25 spl0_3 | spl0_4),
% 1.50/1.25 inference(avatar_split_clause,[status(thm)],[f18,f33,f29])).
% 1.50/1.25 thf(f18,plain,(
% 1.50/1.25 ($false = (sK2 @ sK3)) | ($false = (sK2 @ (eps @ (^[Y0 : $i]: (~ (sK2 @ Y0))))))),
% 1.50/1.25 inference(sigma_clausification,[status(thm)],[f17])).
% 1.50/1.25 thf(f17,plain,(
% 1.50/1.25 ($false = (!! @ $i @ sK2)) | ($false = (sK2 @ (eps @ (^[Y0 : $i]: (~ (sK2 @ Y0))))))),
% 1.50/1.25 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.50/1.25 thf(f15,plain,(
% 1.50/1.25 ((!! @ $i @ sK2) != (sK2 @ (eps @ (^[Y0 : $i]: (~ (sK2 @ Y0))))))),
% 1.50/1.25 inference(beta_eta_normalization,[status(thm)],[f14])).
% 1.50/1.25 thf(f14,plain,(
% 1.50/1.25 (((^[Y0 : $i > $o]: (Y0 @ (eps @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) @ sK2) != (!! @ $i @ sK2))),
% 1.50/1.25 inference(negative_extensionality,[status(thm)],[f13])).
% 1.50/1.25 thf(f13,plain,(
% 1.50/1.25 (!! @ $i != (^[Y0 : $i > $o]: (Y0 @ (eps @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))))),
% 1.50/1.25 inference(beta_eta_normalization,[status(thm)],[f11])).
% 1.50/1.25 thf(f11,plain,(
% 1.50/1.25 ((^[Y0 : $i > $o]: (Y0 @ (eps @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) != (^[Y0 : $i > $o]: (!! @ $i @ Y0)))),
% 1.50/1.25 inference(cnf_transformation,[status(thm)],[f9])).
% 1.50/1.25 thf(f9,plain,(
% 1.50/1.25 ((^[Y0 : $i > $o]: (Y0 @ (eps @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) != (^[Y0 : $i > $o]: (!! @ $i @ Y0)))),
% 1.50/1.25 inference(flattening,[status(thm)],[f8])).
% 1.50/1.25 thf(f8,plain,(
% 1.50/1.25 ~((^[Y0 : $i > $o]: (Y0 @ (eps @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) = (^[Y0 : $i > $o]: (!! @ $i @ Y0)))),
% 1.50/1.25 inference(fool_elimination,[status(thm)],[f7])).
% 1.50/1.25 thf(f7,plain,(
% 1.50/1.25 ~((^[X0 : $i > $o] : (X0 @ (eps @ (^[X1 : $i] : (~(X0 @ X1)))))) = (^[X2 : $i > $o] : (!! @ $i @ X2)))),
% 1.50/1.25 inference(rectify,[status(thm)],[f3])).
% 1.50/1.25 thf(f3,negated_conjecture,(
% 1.50/1.25 ~((^[X0 : $i > $o] : (X0 @ (eps @ (^[X1 : $i] : (~(X0 @ X1)))))) = (^[X0 : $i > $o] : (!! @ $i @ X0)))),
% 1.50/1.25 inference(negated_conjecture,[status(cth)],[f2])).
% 1.50/1.25 thf(f2,conjecture,(
% 1.50/1.25 ((^[X0 : $i > $o] : (X0 @ (eps @ (^[X1 : $i] : (~(X0 @ X1)))))) = (^[X0 : $i > $o] : (!! @ $i @ X0)))),
% 1.50/1.25 file('/export/starexec/sandbox2/tmp/tmp.RlLqLZtRA5/DTF2THF_21074.p',conj)).
% 1.50/1.25 thf(f27,plain,(
% 1.50/1.25 spl0_1 | spl0_2),
% 1.50/1.25 inference(avatar_split_clause,[status(thm)],[f19,f24,f21])).
% 1.50/1.25 thf(f19,plain,(
% 1.50/1.25 ( ! [X1 : $i] : (((sK2 @ X1) = $true) | ($true = (sK2 @ (eps @ (^[Y0 : $i]: (~ (sK2 @ Y0))))))) )),
% 1.50/1.25 inference(pi_clausification,[status(thm)],[f16])).
% 1.50/1.25 thf(f16,plain,(
% 1.50/1.25 ($true = (!! @ $i @ sK2)) | ($true = (sK2 @ (eps @ (^[Y0 : $i]: (~ (sK2 @ Y0))))))),
% 1.50/1.25 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.50/1.25 % SZS output end Proof for DTF2THF_21074
% 1.50/1.25 % (21293)------------------------------
% 1.50/1.25 % (21293)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.25 % (21293)Termination reason: Refutation
% 1.50/1.25
% 1.50/1.25 % (21293)Memory used [KB]: 5500
% 1.50/1.25 % (21293)Time elapsed: 0.005 s
% 1.50/1.25 % (21293)Instructions burned: 3 (million)
% 1.50/1.25 % (21293)------------------------------
% 1.50/1.25 % (21293)------------------------------
% 1.50/1.25 % (21290)Success in time 0.019 s
%------------------------------------------------------------------------------