%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO032^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n019.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 09:53:11 AM UTC 2026
% Result : Theorem 1.50s 1.26s
% Output : Refutation 1.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 47 ( 1 unt; 0 typ; 4 def)
% Number of atoms : 293 ( 88 equ; 0 cnn)
% Maximal formula atoms : 12 ( 6 avg)
% Number of connectives : 318 ( 52 ~; 125 |; 10 &; 121 @)
% ( 8 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 136 ( 108 ^; 16 !; 12 ?; 136 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_3,type,
sK0: ( $o > $o > $o ) > $o ).
thf(func_def_4,type,
sK1: ( $o > $o > $o ) > $o ).
thf(func_def_6,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f312,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f88,f152,f229,f304,f308]) ).
thf(f308,plain,
( ~ spl2_11
| ~ spl2_17 ),
inference(avatar_contradiction_clause,[status(thm)],[f307]) ).
thf(f307,plain,
( $false
| ~ spl2_11
| ~ spl2_17 ),
inference(trivial_inequality_removal,[status(thm)],[f306]) ).
thf(f306,plain,
( ( $false = $true )
| ~ spl2_11
| ~ spl2_17 ),
inference(forward_demodulation,[status(thm)],[f149,f92]) ).
thf(f92,plain,
( ( $false
= ( sK0
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) ) )
| ~ spl2_11 ),
inference(avatar_component_clause,[status(thm)],[f90]) ).
thf(f90,definition,
( spl2_11
<=> ( $false
= ( sK0
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl2_11])],[avatar_definition]) ).
thf(f149,plain,
( ( $true
= ( sK0
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) ) )
| ~ spl2_17 ),
inference(avatar_component_clause,[status(thm)],[f148]) ).
thf(f148,definition,
( spl2_17
<=> ( $true
= ( sK0
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl2_17])],[avatar_definition]) ).
thf(f304,plain,
( ~ spl2_9
| spl2_17 ),
inference(avatar_contradiction_clause,[status(thm)],[f303]) ).
thf(f303,plain,
( $false
| ~ spl2_9
| spl2_17 ),
inference(subsumption_resolution,[status(thm)],[f297,f150]) ).
thf(f150,plain,
( ( $true
!= ( sK0
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) ) )
| spl2_17 ),
inference(avatar_component_clause,[status(thm)],[f148]) ).
thf(f297,plain,
( ( $true
= ( sK0
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) ) )
| ~ spl2_9 ),
inference(duplicate_literal_removal,[status(thm)],[f296]) ).
thf(f296,plain,
( ( $true
= ( sK0
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) ) )
| ( $true
= ( sK0
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) ) )
| ~ spl2_9 ),
inference(boolean_simplification,[status(thm)],[f295]) ).
thf(f295,plain,
( ( $true
= ( sK0
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) ) )
| ( $true
= ( ( sK0
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) )
| $false ) )
| ~ spl2_9 ),
inference(beta_eta_normalization,[status(thm)],[f294]) ).
thf(f294,plain,
( ( $true
= ( sK0
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) ) )
| ( ( ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 )
@ $false
@ ( sK0
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) ) )
= $true )
| ~ spl2_9 ),
inference(trivial_inequality_removal,[status(thm)],[f291]) ).
thf(f291,plain,
( ( ( ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 )
@ $false
@ ( sK0
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) ) )
= $true )
| ( $true
= ( sK0
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) ) )
| ( $false = $true )
| ~ spl2_9 ),
inference(superposition,[status(thm)],[f11,f83]) ).
thf(f83,plain,
( ( ( sK1
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) )
= $false )
| ~ spl2_9 ),
inference(avatar_component_clause,[status(thm)],[f81]) ).
thf(f81,definition,
( spl2_9
<=> ( ( sK1
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl2_9])],[avatar_definition]) ).
thf(f11,plain,
! [X0: $o > $o > $o] :
( ( ( X0 @ ( sK1 @ X0 ) @ ( sK0 @ X0 ) )
= $true )
| ( ( sK0 @ X0 )
= $true )
| ( $true
= ( sK1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $o > $o > $o] :
( ( ( ( ( sK0 @ X0 )
!= $true )
& ( $true
!= ( sK1 @ X0 ) ) )
| ( ( X0 @ ( sK1 @ X0 ) @ ( sK0 @ X0 ) )
!= $true ) )
& ( ( ( sK0 @ X0 )
= $true )
| ( $true
= ( sK1 @ X0 ) )
| ( ( X0 @ ( sK1 @ X0 ) @ ( sK0 @ X0 ) )
= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f8,f9]) ).
thf(f9,plain,
! [X0: $o > $o > $o] :
( ? [X1: $o,X2: $o] :
( ( ( ( $true != X1 )
& ( $true != X2 ) )
| ( $true
!= ( X0 @ X2 @ X1 ) ) )
& ( ( $true = X1 )
| ( $true = X2 )
| ( $true
= ( X0 @ X2 @ X1 ) ) ) )
=> ( ( ( ( ( sK0 @ X0 )
!= $true )
& ( $true
!= ( sK1 @ X0 ) ) )
| ( ( X0 @ ( sK1 @ X0 ) @ ( sK0 @ X0 ) )
!= $true ) )
& ( ( ( sK0 @ X0 )
= $true )
| ( $true
= ( sK1 @ X0 ) )
| ( ( X0 @ ( sK1 @ X0 ) @ ( sK0 @ X0 ) )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
! [X0: $o > $o > $o] :
? [X1: $o,X2: $o] :
( ( ( ( $true != X1 )
& ( $true != X2 ) )
| ( $true
!= ( X0 @ X2 @ X1 ) ) )
& ( ( $true = X1 )
| ( $true = X2 )
| ( $true
= ( X0 @ X2 @ X1 ) ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: $o > $o > $o] :
? [X1: $o,X2: $o] :
( ( ( ( $true != X1 )
& ( $true != X2 ) )
| ( $true
!= ( X0 @ X2 @ X1 ) ) )
& ( ( $true = X1 )
| ( $true = X2 )
| ( $true
= ( X0 @ X2 @ X1 ) ) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: $o > $o > $o] :
? [X1: $o,X2: $o] :
( ( $true
= ( X0 @ X2 @ X1 ) )
<~> ( ( $true = X1 )
| ( $true = X2 ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ? [X0: $o > $o > $o] :
! [X2: $o,X1: $o] :
( ( $true
= ( X0 @ X2 @ X1 ) )
<=> ( ( $true = X1 )
| ( $true = X2 ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: $o > $o > $o] :
! [X1: $o,X2: $o] :
( ( X2
| X1 )
<=> ( X0 @ X2 @ X1 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X0: $o > $o > $o] :
! [X2: $o,X1: $o] :
( ( X1
| X2 )
<=> ( X0 @ X1 @ X2 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X0: $o > $o > $o] :
! [X2: $o,X1: $o] :
( ( X1
| X2 )
<=> ( X0 @ X1 @ X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.ChxRi0Un2l/DTF2THF_6450.p',conj) ).
thf(f229,plain,
( spl2_10
| spl2_17 ),
inference(avatar_contradiction_clause,[status(thm)],[f228]) ).
thf(f228,plain,
( $false
| spl2_10
| spl2_17 ),
inference(subsumption_resolution,[status(thm)],[f227,f87]) ).
thf(f87,plain,
( ( ( sK1
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) )
!= $true )
| spl2_10 ),
inference(avatar_component_clause,[status(thm)],[f85]) ).
thf(f85,definition,
( spl2_10
<=> ( ( sK1
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_10])],[avatar_definition]) ).
thf(f227,plain,
( ( ( sK1
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) )
= $true )
| spl2_17 ),
inference(subsumption_resolution,[status(thm)],[f195,f150]) ).
thf(f195,plain,
( ( ( sK1
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) )
= $true )
| ( $true
= ( sK0
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f194]) ).
thf(f194,plain,
( ( $true
= ( sK0
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) ) )
| ( ( sK1
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) )
= $true )
| ( ( sK1
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) )
= $true )
| ( $true
= ( sK0
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f193]) ).
thf(f193,plain,
( ( $true
= ( sK0
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) ) )
| ( ( sK1
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) )
= $true )
| ( ( ( sK0
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) )
| ( sK1
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f174]) ).
thf(f174,plain,
( ( $true
= ( sK0
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) ) )
| ( ( sK1
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) )
= $true )
| ( $true
= ( ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 )
@ ( sK1
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) )
@ ( sK0
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) ) ) ) ),
inference(primitive_instantiation,[status(thm)],[f11]) ).
thf(f152,plain,
( spl2_11
| ~ spl2_17 ),
inference(avatar_split_clause,[status(thm)],[f146,f148,f90]) ).
thf(f146,plain,
( ( $false
= ( sK0
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) ) )
| ( $true
!= ( sK0
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f144]) ).
thf(f144,plain,
( ( $true
!= ( sK0
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) ) )
| ( ( ( sK0
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) )
| ( sK1
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) ) )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f120]) ).
thf(f120,plain,
( ( $true
!= ( ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 )
@ ( sK1
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) )
@ ( sK0
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) ) ) )
| ( $true
!= ( sK0
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) ) ) ),
inference(primitive_instantiation,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: $o > $o > $o] :
( ( ( X0 @ ( sK1 @ X0 ) @ ( sK0 @ X0 ) )
!= $true )
| ( ( sK0 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f88,plain,
( spl2_9
| ~ spl2_10 ),
inference(avatar_split_clause,[status(thm)],[f31,f85,f81]) ).
thf(f31,plain,
( ( ( sK1
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) )
!= $true )
| ( ( sK1
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ( ( sK0
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) )
| ( sK1
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) ) )
!= $true )
| ( ( sK1
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f18]) ).
thf(f18,plain,
( ( $true
!= ( ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 )
@ ( sK1
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) )
@ ( sK0
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) ) ) )
| ( ( sK1
@ ^ [Y0: $o,Y1: $o] :
( Y1
| Y0 ) )
!= $true ) ),
inference(primitive_instantiation,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: $o > $o > $o] :
( ( ( X0 @ ( sK1 @ X0 ) @ ( sK0 @ X0 ) )
!= $true )
| ( $true
!= ( sK1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO032^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.33 % Computer : n019.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
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue Feb 24 14:22:09 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
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.45 thf(spec,logic,$$dhol).
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 % File : SYO032^1 : TPTP v9.2.1. Released v3.7.0.
% 0.19/0.45 % Domain : Syntactic
% 0.19/0.45 % Problem : There is a disjunction connective
% 0.19/0.45 % Version : Especial.
% 0.19/0.45 % English :
% 0.19/0.45
% 0.19/0.45 % Refs : [BB05] Benzmueller & Brown (2005), A Structured Set of Higher
% 0.19/0.45 % : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% 0.19/0.45 % Source : [Ben09]
% 0.19/0.45 % Names : Example 27 [BB05]
% 0.19/0.45
% 0.19/0.45 % Status : Theorem
% 0.19/0.45 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.00 v8.1.0, 0.08 v7.4.0, 0.00 v7.3.0, 0.10 v7.2.0, 0.00 v6.2.0, 0.33 v6.1.0, 0.00 v5.1.0, 0.25 v4.1.0, 0.33 v4.0.1, 0.00 v4.0.0, 0.33 v3.7.0
% 0.19/0.45 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.19/0.45 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.19/0.45 % Maximal formula atoms : 0 ( 0 avg)
% 0.19/0.45 % Number of connectives : 4 ( 0 ~; 1 |; 0 &; 2 @)
% 0.19/0.45 % ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% 0.19/0.45 % Maximal formula depth : 7 ( 7 avg)
% 0.19/0.45 % Number of types : 1 ( 0 usr)
% 0.19/0.45 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.19/0.45 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.19/0.45 % Number of variables : 3 ( 0 ^; 2 !; 1 ?; 3 :)
% 0.19/0.45 % SPC : TH0_THM_NEQ_NAR
% 0.19/0.45
% 0.19/0.45 % Comments : Requires set comprehension
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 thf(conj,conjecture,
% 0.19/0.45 ? [D: $o > $o > $o] :
% 0.19/0.45 ! [P: $o,Q: $o] :
% 0.19/0.45 ( ( D @ P @ Q )
% 0.19/0.45 <=> ( P
% 0.19/0.45 | Q ) ) ).
% 0.19/0.45
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 ------------------------
% 1.50/1.23 ---- Embedded in THF ---
% 1.50/1.23 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.23 %%% Generated on Tue Feb 24 14:22:10 EST 2026
% 1.50/1.23 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.23 %%% Logic specification used:
% 1.50/1.23 %%% thf(spec, logic, $$dhol).
% 1.50/1.23
% 1.50/1.23 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.ChxRi0Un2l/DTF2DTF6450.p
% See solution above
% 1.50/1.23 ------------------------
% 1.50/1.24 ---- Cleaned THF ---
% 1.50/1.24 thf(conj,conjecture,
% 1.50/1.24 ? [D: $o > $o > $o] :
% 1.50/1.24 ! [P: $o,Q: $o] :
% 1.50/1.24 ( ( D @ P @ Q )
% 1.50/1.24 <=> ( P
% 1.50/1.24 | Q ) ) ).
% 1.50/1.24 ------------------------
% 1.50/1.25 % (6611)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_6450 for (3000ds/275Mi)
% 1.50/1.25 % (6607)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_6450 for (3000ds/4Mi)
% 1.50/1.25 % (6610)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_6450 for (3000ds/2Mi)
% 1.50/1.25 % (6610)Instruction limit reached!
% 1.50/1.25 % (6610)------------------------------
% 1.50/1.25 % (6610)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.25 % (6610)Termination reason: Unknown
% 1.50/1.25 % (6610)Termination phase: Saturation
% 1.50/1.25
% 1.50/1.25 % (6610)Memory used [KB]: 5500
% 1.50/1.25 % (6610)Time elapsed: 0.002 s
% 1.50/1.25 % (6610)Instructions burned: 2 (million)
% 1.50/1.25 % (6610)------------------------------
% 1.50/1.25 % (6610)------------------------------
% 1.50/1.25 % (6607)Instruction limit reached!
% 1.50/1.25 % (6607)------------------------------
% 1.50/1.25 % (6607)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.25 % (6607)Termination reason: Unknown
% 1.50/1.25 % (6607)Termination phase: Saturation
% 1.50/1.25
% 1.50/1.25 % (6607)Memory used [KB]: 5500
% 1.50/1.25 % (6607)Time elapsed: 0.003 s
% 1.50/1.25 % (6607)Instructions burned: 5 (million)
% 1.50/1.25 % (6607)------------------------------
% 1.50/1.25 % (6607)------------------------------
% 1.50/1.26 % (6611)First to succeed.
% 1.50/1.26 % (6606)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6450 for (3000ds/183Mi)
% 1.50/1.26 % (6608)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_6450 for (3000ds/27Mi)
% 1.50/1.26 % (6609)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6450 for (3000ds/2Mi)
% 1.50/1.26 % (6612)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6450 for (3000ds/18Mi)
% 1.50/1.26 % (6611)Refutation found. Thanks to Tanya!
% 1.50/1.26 % SZS status Theorem for DTF2THF_6450
% 1.50/1.26 % SZS output start Proof for DTF2THF_6450
% 1.50/1.26 thf(func_def_3, type, sK0: ($o > $o > $o) > $o).
% 1.50/1.26 thf(func_def_4, type, sK1: ($o > $o > $o) > $o).
% 1.50/1.26 thf(func_def_6, type, ph3: !>[X0: $tType]:(X0)).
% 1.50/1.26 thf(f312,plain,(
% 1.50/1.26 $false),
% 1.50/1.26 inference(avatar_sat_refutation,[status(thm)],[f88,f152,f229,f304,f308])).
% 1.50/1.26 thf(f308,plain,(
% 1.50/1.26 ~spl2_11 | ~spl2_17),
% 1.50/1.26 inference(avatar_contradiction_clause,[status(thm)],[f307])).
% 1.50/1.26 thf(f307,plain,(
% 1.50/1.26 $false | (~spl2_11 | ~spl2_17)),
% 1.50/1.26 inference(trivial_inequality_removal,[status(thm)],[f306])).
% 1.50/1.26 thf(f306,plain,(
% 1.50/1.26 ($false = $true) | (~spl2_11 | ~spl2_17)),
% 1.50/1.26 inference(forward_demodulation,[status(thm)],[f149,f92])).
% 1.50/1.26 thf(f92,plain,(
% 1.50/1.26 ($false = (sK0 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0)))))) | ~spl2_11),
% 1.50/1.26 inference(avatar_component_clause,[status(thm)],[f90])).
% 1.50/1.26 thf(f90,definition,(
% 1.50/1.26 spl2_11 <=> ($false = (sK0 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0))))))),
% 1.50/1.26 introduced(definition,[new_symbols(naming,[spl2_11])],[avatar_definition])).
% 1.50/1.26 thf(f149,plain,(
% 1.50/1.26 ($true = (sK0 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0)))))) | ~spl2_17),
% 1.50/1.26 inference(avatar_component_clause,[status(thm)],[f148])).
% 1.50/1.26 thf(f148,definition,(
% 1.50/1.26 spl2_17 <=> ($true = (sK0 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0))))))),
% 1.50/1.26 introduced(definition,[new_symbols(naming,[spl2_17])],[avatar_definition])).
% 1.50/1.26 thf(f304,plain,(
% 1.50/1.26 ~spl2_9 | spl2_17),
% 1.50/1.26 inference(avatar_contradiction_clause,[status(thm)],[f303])).
% 1.50/1.26 thf(f303,plain,(
% 1.50/1.26 $false | (~spl2_9 | spl2_17)),
% 1.50/1.26 inference(subsumption_resolution,[status(thm)],[f297,f150])).
% 1.50/1.26 thf(f150,plain,(
% 1.50/1.26 ($true != (sK0 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0)))))) | spl2_17),
% 1.50/1.26 inference(avatar_component_clause,[status(thm)],[f148])).
% 1.50/1.26 thf(f297,plain,(
% 1.50/1.26 ($true = (sK0 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0)))))) | ~spl2_9),
% 1.50/1.26 inference(duplicate_literal_removal,[status(thm)],[f296])).
% 1.50/1.26 thf(f296,plain,(
% 1.50/1.26 ($true = (sK0 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0)))))) | ($true = (sK0 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0)))))) | ~spl2_9),
% 1.50/1.26 inference(boolean_simplification,[status(thm)],[f295])).
% 1.50/1.26 thf(f295,plain,(
% 1.50/1.26 ($true = (sK0 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0)))))) | ($true = ((sK0 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0))))) | $false)) | ~spl2_9),
% 1.50/1.26 inference(beta_eta_normalization,[status(thm)],[f294])).
% 1.50/1.26 thf(f294,plain,(
% 1.50/1.26 ($true = (sK0 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0)))))) | (((^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0)))) @ $false @ (sK0 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0)))))) = $true) | ~spl2_9),
% 1.50/1.26 inference(trivial_inequality_removal,[status(thm)],[f291])).
% 1.50/1.26 thf(f291,plain,(
% 1.50/1.26 (((^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0)))) @ $false @ (sK0 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0)))))) = $true) | ($true = (sK0 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0)))))) | ($false = $true) | ~spl2_9),
% 1.50/1.26 inference(superposition,[status(thm)],[f11,f83])).
% 1.50/1.26 thf(f83,plain,(
% 1.50/1.26 ((sK1 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0))))) = $false) | ~spl2_9),
% 1.50/1.26 inference(avatar_component_clause,[status(thm)],[f81])).
% 1.50/1.26 thf(f81,definition,(
% 1.50/1.26 spl2_9 <=> ((sK1 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0))))) = $false)),
% 1.50/1.26 introduced(definition,[new_symbols(naming,[spl2_9])],[avatar_definition])).
% 1.50/1.26 thf(f11,plain,(
% 1.50/1.26 ( ! [X0 : $o > $o > $o] : (((X0 @ (sK1 @ X0) @ (sK0 @ X0)) = $true) | ((sK0 @ X0) = $true) | ($true = (sK1 @ X0))) )),
% 1.50/1.26 inference(cnf_transformation,[status(thm)],[f10])).
% 1.50/1.26 thf(f10,plain,(
% 1.50/1.26 ! [X0 : $o > $o > $o] : (((((sK0 @ X0) != $true) & ($true != (sK1 @ X0))) | ((X0 @ (sK1 @ X0) @ (sK0 @ X0)) != $true)) & (((sK0 @ X0) = $true) | ($true = (sK1 @ X0)) | ((X0 @ (sK1 @ X0) @ (sK0 @ X0)) = $true)))),
% 1.50/1.26 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f8,f9])).
% 1.50/1.26 thf(f9,plain,(
% 1.50/1.26 ! [X0 : $o > $o > $o] : (? [X1 : $o,X2 : $o] : (((($true != X1) & ($true != X2)) | ($true != (X0 @ X2 @ X1))) & (($true = X1) | ($true = X2) | ($true = (X0 @ X2 @ X1)))) => (((((sK0 @ X0) != $true) & ($true != (sK1 @ X0))) | ((X0 @ (sK1 @ X0) @ (sK0 @ X0)) != $true)) & (((sK0 @ X0) = $true) | ($true = (sK1 @ X0)) | ((X0 @ (sK1 @ X0) @ (sK0 @ X0)) = $true))))),
% 1.50/1.26 introduced(definition,[],[choice_axiom])).
% 1.50/1.26 thf(f8,plain,(
% 1.50/1.26 ! [X0 : $o > $o > $o] : ? [X1 : $o,X2 : $o] : (((($true != X1) & ($true != X2)) | ($true != (X0 @ X2 @ X1))) & (($true = X1) | ($true = X2) | ($true = (X0 @ X2 @ X1))))),
% 1.50/1.26 inference(flattening,[status(thm)],[f7])).
% 1.50/1.26 thf(f7,plain,(
% 1.50/1.26 ! [X0 : $o > $o > $o] : ? [X1 : $o,X2 : $o] : (((($true != X1) & ($true != X2)) | ($true != (X0 @ X2 @ X1))) & ((($true = X1) | ($true = X2)) | ($true = (X0 @ X2 @ X1))))),
% 1.50/1.26 inference(nnf_transformation,[status(thm)],[f6])).
% 1.50/1.26 thf(f6,plain,(
% 1.50/1.26 ! [X0 : $o > $o > $o] : ? [X1 : $o,X2 : $o] : (($true = (X0 @ X2 @ X1)) <~> (($true = X1) | ($true = X2)))),
% 1.50/1.26 inference(ennf_transformation,[status(thm)],[f5])).
% 1.50/1.26 thf(f5,plain,(
% 1.50/1.26 ~? [X0 : $o > $o > $o] : ! [X2 : $o,X1 : $o] : (($true = (X0 @ X2 @ X1)) <=> (($true = X1) | ($true = X2)))),
% 1.50/1.26 inference(fool_elimination,[status(thm)],[f4])).
% 1.50/1.26 thf(f4,plain,(
% 1.50/1.26 ~? [X0 : $o > $o > $o] : ! [X1 : $o,X2 : $o] : ((X2 | X1) <=> (X0 @ X2 @ X1))),
% 1.50/1.26 inference(rectify,[status(thm)],[f2])).
% 1.50/1.26 thf(f2,negated_conjecture,(
% 1.50/1.26 ~? [X0 : $o > $o > $o] : ! [X2 : $o,X1 : $o] : ((X1 | X2) <=> (X0 @ X1 @ X2))),
% 1.50/1.26 inference(negated_conjecture,[status(cth)],[f1])).
% 1.50/1.26 thf(f1,conjecture,(
% 1.50/1.26 ? [X0 : $o > $o > $o] : ! [X2 : $o,X1 : $o] : ((X1 | X2) <=> (X0 @ X1 @ X2))),
% 1.50/1.26 file('/export/starexec/sandbox2/tmp/tmp.ChxRi0Un2l/DTF2THF_6450.p',conj)).
% 1.50/1.26 thf(f229,plain,(
% 1.50/1.26 spl2_10 | spl2_17),
% 1.50/1.26 inference(avatar_contradiction_clause,[status(thm)],[f228])).
% 1.50/1.26 thf(f228,plain,(
% 1.50/1.26 $false | (spl2_10 | spl2_17)),
% 1.50/1.26 inference(subsumption_resolution,[status(thm)],[f227,f87])).
% 1.50/1.26 thf(f87,plain,(
% 1.50/1.26 ((sK1 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0))))) != $true) | spl2_10),
% 1.50/1.26 inference(avatar_component_clause,[status(thm)],[f85])).
% 1.50/1.26 thf(f85,definition,(
% 1.50/1.26 spl2_10 <=> ((sK1 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0))))) = $true)),
% 1.50/1.26 introduced(definition,[new_symbols(naming,[spl2_10])],[avatar_definition])).
% 1.50/1.26 thf(f227,plain,(
% 1.50/1.26 ((sK1 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0))))) = $true) | spl2_17),
% 1.50/1.26 inference(subsumption_resolution,[status(thm)],[f195,f150])).
% 1.50/1.26 thf(f195,plain,(
% 1.50/1.26 ((sK1 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0))))) = $true) | ($true = (sK0 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0))))))),
% 1.50/1.26 inference(duplicate_literal_removal,[status(thm)],[f194])).
% 1.50/1.26 thf(f194,plain,(
% 1.50/1.26 ($true = (sK0 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0)))))) | ((sK1 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0))))) = $true) | ((sK1 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0))))) = $true) | ($true = (sK0 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0))))))),
% 1.50/1.26 inference(binary_proxy_clausification,[status(thm)],[f193])).
% 1.50/1.26 thf(f193,plain,(
% 1.50/1.26 ($true = (sK0 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0)))))) | ((sK1 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0))))) = $true) | (((sK0 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0))))) | (sK1 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0)))))) = $true)),
% 1.50/1.26 inference(beta_eta_normalization,[status(thm)],[f174])).
% 1.50/1.26 thf(f174,plain,(
% 1.50/1.26 ($true = (sK0 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0)))))) | ((sK1 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0))))) = $true) | ($true = ((^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0)))) @ (sK1 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0))))) @ (sK0 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0)))))))),
% 1.50/1.26 inference(primitive_instantiation,[status(thm)],[f11])).
% 1.50/1.26 thf(f152,plain,(
% 1.50/1.26 spl2_11 | ~spl2_17),
% 1.50/1.26 inference(avatar_split_clause,[status(thm)],[f146,f148,f90])).
% 1.50/1.26 thf(f146,plain,(
% 1.50/1.26 ($false = (sK0 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0)))))) | ($true != (sK0 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0))))))),
% 1.50/1.26 inference(binary_proxy_clausification,[status(thm)],[f144])).
% 1.50/1.26 thf(f144,plain,(
% 1.50/1.26 ($true != (sK0 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0)))))) | (((sK0 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0))))) | (sK1 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0)))))) != $true)),
% 1.50/1.26 inference(beta_eta_normalization,[status(thm)],[f120])).
% 1.50/1.26 thf(f120,plain,(
% 1.50/1.26 ($true != ((^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0)))) @ (sK1 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0))))) @ (sK0 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0))))))) | ($true != (sK0 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0))))))),
% 1.50/1.26 inference(primitive_instantiation,[status(thm)],[f13])).
% 1.50/1.26 thf(f13,plain,(
% 1.50/1.26 ( ! [X0 : $o > $o > $o] : (((X0 @ (sK1 @ X0) @ (sK0 @ X0)) != $true) | ((sK0 @ X0) != $true)) )),
% 1.50/1.26 inference(cnf_transformation,[status(thm)],[f10])).
% 1.50/1.26 thf(f88,plain,(
% 1.50/1.26 spl2_9 | ~spl2_10),
% 1.50/1.26 inference(avatar_split_clause,[status(thm)],[f31,f85,f81])).
% 1.50/1.26 thf(f31,plain,(
% 1.50/1.26 ((sK1 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0))))) != $true) | ((sK1 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0))))) = $false)),
% 1.50/1.26 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.50/1.26 thf(f30,plain,(
% 1.50/1.26 (((sK0 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0))))) | (sK1 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0)))))) != $true) | ((sK1 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0))))) != $true)),
% 1.50/1.26 inference(beta_eta_normalization,[status(thm)],[f18])).
% 1.50/1.26 thf(f18,plain,(
% 1.50/1.26 ($true != ((^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0)))) @ (sK1 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0))))) @ (sK0 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0))))))) | ((sK1 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y1 | Y0))))) != $true)),
% 1.50/1.26 inference(primitive_instantiation,[status(thm)],[f12])).
% 1.50/1.26 thf(f12,plain,(
% 1.50/1.26 ( ! [X0 : $o > $o > $o] : (((X0 @ (sK1 @ X0) @ (sK0 @ X0)) != $true) | ($true != (sK1 @ X0))) )),
% 1.50/1.26 inference(cnf_transformation,[status(thm)],[f10])).
% 1.50/1.26 % SZS output end Proof for DTF2THF_6450
% 1.50/1.26 % (6611)------------------------------
% 1.50/1.26 % (6611)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.26 % (6611)Termination reason: Refutation
% 1.50/1.26
% 1.50/1.26 % (6611)Memory used [KB]: 5628
% 1.50/1.26 % (6611)Time elapsed: 0.009 s
% 1.50/1.26 % (6611)Instructions burned: 16 (million)
% 1.50/1.26 % (6611)------------------------------
% 1.50/1.26 % (6611)------------------------------
% 1.50/1.26 % (6605)Success in time 0.017 s
%------------------------------------------------------------------------------