%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO259^5 : 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 : n025.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 09:53:47 AM UTC 2026
% Result : Theorem 1.64s 1.34s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 3 unt; 0 typ; 2 def)
% Number of atoms : 161 ( 56 equ; 0 cnn)
% Maximal formula atoms : 12 ( 6 avg)
% Number of connectives : 201 ( 60 ~; 39 |; 25 &; 74 @)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 37 ( 37 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 7 con; 0-2 aty)
% Number of variables : 63 ( 2 ^; 39 !; 22 ?; 63 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_4,type,
sK1: $i > $o ).
thf(func_def_9,type,
ph5:
!>[X0: $tType] : X0 ).
thf(f87,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f38,f65,f79]) ).
thf(f79,plain,
~ spl4_5,
inference(avatar_contradiction_clause,[status(thm)],[f78]) ).
thf(f78,plain,
( $false
| ~ spl4_5 ),
inference(trivial_inequality_removal,[status(thm)],[f77]) ).
thf(f77,plain,
( ( $true != $true )
| ~ spl4_5 ),
inference(beta_eta_normalization,[status(thm)],[f70]) ).
thf(f70,plain,
( ( ( ^ [Y0: $i] : $true
@ sK3 )
!= $true )
| ~ spl4_5 ),
inference(equality_resolution,[status(thm)],[f37]) ).
thf(f37,plain,
( ! [X5: $i > $o] :
( ( $true
!= ( X5 @ sK0 ) )
| ( ( X5 @ sK3 )
!= $true ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[status(thm)],[f36]) ).
thf(f36,definition,
( spl4_5
<=> ! [X5: $i > $o] :
( ( $true
!= ( X5 @ sK0 ) )
| ( ( X5 @ sK3 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl4_5])],[avatar_definition]) ).
thf(f65,plain,
~ spl4_4,
inference(avatar_contradiction_clause,[status(thm)],[f64]) ).
thf(f64,plain,
( $false
| ~ spl4_4 ),
inference(subsumption_resolution,[status(thm)],[f56,f34]) ).
thf(f34,plain,
( ! [X4: $i > $o] :
( $true
!= ( X4 @ sK2 ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[status(thm)],[f33]) ).
thf(f33,definition,
( spl4_4
<=> ! [X4: $i > $o] :
( $true
!= ( X4 @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition]) ).
thf(f56,plain,
( ! [X7: $i > $o] :
( ( X7 @ sK2 )
= $true )
| ~ spl4_4 ),
inference(not_proxy_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
( ! [X7: $i > $o] :
( ( ~ ( X7 @ sK2 ) )
!= $true )
| ~ spl4_4 ),
inference(beta_eta_normalization,[status(thm)],[f52]) ).
thf(f52,plain,
( ! [X7: $i > $o] :
( ( ^ [Y0: $i] :
~ ( X7 @ Y0 )
@ sK2 )
!= $true )
| ~ spl4_4 ),
inference(primitive_instantiation,[status(thm)],[f34]) ).
thf(f38,plain,
( spl4_4
| spl4_5 ),
inference(avatar_split_clause,[status(thm)],[f18,f36,f33]) ).
thf(f18,plain,
! [X4: $i > $o,X5: $i > $o] :
( ( $true
!= ( X5 @ sK0 ) )
| ( $true
!= ( X4 @ sK2 ) )
| ( ( X5 @ sK3 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
! [X4: $i > $o,X5: $i > $o] :
( ( ( ( X5 @ sK3 )
!= $true )
& ( ( X4 @ sK3 )
!= $true ) )
| ( ( $true
!= ( X4 @ sK2 ) )
& ( ( sK1 @ sK2 )
= $true ) )
| ( ( $true
!= ( X5 @ sK0 ) )
& ( ( sK1 @ sK0 )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f9]) ).
thf(f9,plain,
( ? [X0: $i,X1: $i > $o,X2: $i,X3: $i] :
! [X4: $i > $o,X5: $i > $o] :
( ( ( $true
!= ( X5 @ X3 ) )
& ( ( X4 @ X3 )
!= $true ) )
| ( ( ( X4 @ X2 )
!= $true )
& ( ( X1 @ X2 )
= $true ) )
| ( ( ( X5 @ X0 )
!= $true )
& ( ( X1 @ X0 )
!= $true ) ) )
=> ! [X5: $i > $o,X4: $i > $o] :
( ( ( ( X5 @ sK3 )
!= $true )
& ( ( X4 @ sK3 )
!= $true ) )
| ( ( $true
!= ( X4 @ sK2 ) )
& ( ( sK1 @ sK2 )
= $true ) )
| ( ( $true
!= ( X5 @ sK0 ) )
& ( ( sK1 @ sK0 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: $i,X1: $i > $o,X2: $i,X3: $i] :
! [X4: $i > $o,X5: $i > $o] :
( ( ( $true
!= ( X5 @ X3 ) )
& ( ( X4 @ X3 )
!= $true ) )
| ( ( ( X4 @ X2 )
!= $true )
& ( ( X1 @ X2 )
= $true ) )
| ( ( ( X5 @ X0 )
!= $true )
& ( ( X1 @ X0 )
!= $true ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X3: $i,X1: $i > $o,X0: $i,X2: $i] :
! [X4: $i > $o,X5: $i > $o] :
( ( ( ( X5 @ X2 )
!= $true )
& ( ( X4 @ X2 )
!= $true ) )
| ( ( ( X4 @ X0 )
!= $true )
& ( ( X1 @ X0 )
= $true ) )
| ( ( $true
!= ( X5 @ X3 ) )
& ( $true
!= ( X1 @ X3 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: $i,X1: $i > $o,X2: $i,X3: $i] :
? [X5: $i > $o,X4: $i > $o] :
( ( ( ( X1 @ X0 )
!= $true )
| ( ( X4 @ X0 )
= $true ) )
& ( ( ( X5 @ X2 )
= $true )
| ( ( X4 @ X2 )
= $true ) )
& ( ( $true
= ( X5 @ X3 ) )
| ( $true
= ( X1 @ X3 ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: $i,X1: $i > $o,X2: $i,X3: $i] :
? [X4: $i > $o,X5: $i > $o] :
( ( ( ( X4 @ X0 )
= $true )
| ( ( X1 @ X0 )
!= $true ) )
& ( ( ( X5 @ X2 )
= $true )
| ( ( X4 @ X2 )
= $true ) )
& ( ( $true
= ( X5 @ X3 ) )
| ( $true
= ( X1 @ X3 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: $i,X1: $i > $o,X2: $i,X3: $i] :
? [X4: $i > $o,X5: $i > $o] :
( ( ( X4 @ X0 )
| ~ ( X1 @ X0 ) )
& ( ( X5 @ X2 )
| ( X4 @ X2 ) )
& ( ( X1 @ X3 )
| ( X5 @ X3 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X2: $i,X3: $i > $o,X0: $i,X1: $i] :
? [X4: $i > $o,X5: $i > $o] :
( ( ( X4 @ X2 )
| ~ ( X3 @ X2 ) )
& ( ( X5 @ X0 )
| ( X4 @ X0 ) )
& ( ( X3 @ X1 )
| ( X5 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X2: $i,X3: $i > $o,X0: $i,X1: $i] :
? [X4: $i > $o,X5: $i > $o] :
( ( ( X4 @ X2 )
| ~ ( X3 @ X2 ) )
& ( ( X5 @ X0 )
| ( X4 @ X0 ) )
& ( ( X3 @ X1 )
| ( X5 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.uggoABYEie/DTF2THF_11898.p',cTHM125B) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO259^5 : TPTP v9.2.1. Released v4.0.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n025.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 14:27:12 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.31/0.47 ---- Original DTF file ---
% 0.31/0.47 thf(spec,logic,$$dhol).
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 % File : SYO259^5 : TPTP v9.2.1. Released v4.0.0.
% 0.31/0.47 % Domain : Syntactic
% 0.31/0.47 % Problem : TPS problem THM125B
% 0.31/0.47 % Version : Especial.
% 0.31/0.47 % English : Trivial theorem to test flexible-flexible pairs.
% 0.31/0.47
% 0.31/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.31/0.47 % Source : [Bro09]
% 0.31/0.47 % Names : tps_0146 [Bro09]
% 0.31/0.47 % : THM125B [TPS]
% 0.31/0.47
% 0.31/0.47 % Status : Theorem
% 0.31/0.47 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.17 v7.4.0, 0.11 v7.3.0, 0.10 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.2.0, 0.33 v6.1.0, 0.17 v6.0.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.31/0.47 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.31/0.47 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.31/0.47 % Maximal formula atoms : 0 ( 0 avg)
% 0.31/0.47 % Number of connectives : 12 ( 1 ~; 3 |; 2 &; 6 @)
% 0.31/0.47 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.31/0.47 % Maximal formula depth : 12 ( 12 avg)
% 0.31/0.47 % Number of types : 2 ( 0 usr)
% 0.31/0.47 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.31/0.47 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.31/0.47 % Number of variables : 6 ( 0 ^; 4 !; 2 ?; 6 :)
% 0.31/0.47 % SPC : TH0_THM_NEQ_NAR
% 0.31/0.47
% 0.31/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.31/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.31/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.31/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 thf(cTHM125B,conjecture,
% 0.31/0.47 ! [Xa: $i,Xb: $i,Xc: $i,P: $i > $o] :
% 0.31/0.47 ? [Xm: $i > $o,Xn: $i > $o] :
% 0.31/0.47 ( ( ( Xn @ Xa )
% 0.31/0.47 | ( Xm @ Xa ) )
% 0.31/0.47 & ( ( P @ Xb )
% 0.31/0.47 | ( Xn @ Xb ) )
% 0.31/0.47 & ( ( Xm @ Xc )
% 0.31/0.47 | ~ ( P @ Xc ) ) ) ).
% 0.31/0.47
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 ------------------------
% 1.64/1.31 ---- Embedded in THF ---
% 1.64/1.31 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.64/1.31 %%% Generated on Tue Feb 24 14:27:13 EST 2026
% 1.64/1.31 %%% using '$$dhol' embedding, version 1.3.0.
% 1.64/1.31 %%% Logic specification used:
% 1.64/1.31 %%% thf(spec, logic, $$dhol).
% 1.64/1.31
% 1.64/1.31 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.uggoABYEie/DTF2DTF11898.p
% See solution above
% 1.64/1.31 ------------------------
% 1.64/1.32 ---- Cleaned THF ---
% 1.64/1.32 thf(cTHM125B,conjecture,
% 1.64/1.32 ! [Xa: $i,Xb: $i,Xc: $i,P: $i > $o] :
% 1.64/1.32 ? [Xm: $i > $o,Xn: $i > $o] :
% 1.64/1.32 ( ( ( Xn @ Xa )
% 1.64/1.32 | ( Xm @ Xa ) )
% 1.64/1.32 & ( ( P @ Xb )
% 1.64/1.32 | ( Xn @ Xb ) )
% 1.64/1.32 & ( ( Xm @ Xc )
% 1.64/1.32 | ~ ( P @ Xc ) ) ) ).
% 1.64/1.32 ------------------------
% 1.64/1.33 % (12090)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_11898 for (2999ds/2Mi)
% 1.64/1.33 % (12090)Instruction limit reached!
% 1.64/1.33 % (12090)------------------------------
% 1.64/1.33 % (12090)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.33 % (12090)Termination reason: Unknown
% 1.64/1.33 % (12090)Termination phase: Saturation
% 1.64/1.33
% 1.64/1.33 % (12090)Memory used [KB]: 5373
% 1.64/1.33 % (12090)Time elapsed: 0.002 s
% 1.64/1.33 % (12090)Instructions burned: 2 (million)
% 1.64/1.33 % (12090)------------------------------
% 1.64/1.33 % (12090)------------------------------
% 1.64/1.34 % (12087)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_11898 for (2999ds/183Mi)
% 1.64/1.34 % (12087)First to succeed.
% 1.64/1.34 % (12088)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_11898 for (2999ds/4Mi)
% 1.64/1.34 % (12089)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_11898 for (2999ds/27Mi)
% 1.64/1.34 % (12087)Refutation found. Thanks to Tanya!
% 1.64/1.34 % SZS status Theorem for DTF2THF_11898
% 1.64/1.34 % SZS output start Proof for DTF2THF_11898
% 1.64/1.34 thf(func_def_4, type, sK1: $i > $o).
% 1.64/1.34 thf(func_def_9, type, ph5: !>[X0: $tType]:(X0)).
% 1.64/1.34 thf(f87,plain,(
% 1.64/1.34 $false),
% 1.64/1.34 inference(avatar_sat_refutation,[status(thm)],[f38,f65,f79])).
% 1.64/1.34 thf(f79,plain,(
% 1.64/1.34 ~spl4_5),
% 1.64/1.34 inference(avatar_contradiction_clause,[status(thm)],[f78])).
% 1.64/1.34 thf(f78,plain,(
% 1.64/1.34 $false | ~spl4_5),
% 1.64/1.34 inference(trivial_inequality_removal,[status(thm)],[f77])).
% 1.64/1.34 thf(f77,plain,(
% 1.64/1.34 ($true != $true) | ~spl4_5),
% 1.64/1.34 inference(beta_eta_normalization,[status(thm)],[f70])).
% 1.64/1.34 thf(f70,plain,(
% 1.64/1.34 (((^[Y0 : $i]: ($true)) @ sK3) != $true) | ~spl4_5),
% 1.64/1.34 inference(equality_resolution,[status(thm)],[f37])).
% 1.64/1.34 thf(f37,plain,(
% 1.64/1.34 ( ! [X5 : $i > $o] : (($true != (X5 @ sK0)) | ((X5 @ sK3) != $true)) ) | ~spl4_5),
% 1.64/1.34 inference(avatar_component_clause,[status(thm)],[f36])).
% 1.64/1.34 thf(f36,definition,(
% 1.64/1.34 spl4_5 <=> ! [X5 : $i > $o] : (($true != (X5 @ sK0)) | ((X5 @ sK3) != $true))),
% 1.64/1.34 introduced(definition,[new_symbols(naming,[spl4_5])],[avatar_definition])).
% 1.64/1.34 thf(f65,plain,(
% 1.64/1.34 ~spl4_4),
% 1.64/1.34 inference(avatar_contradiction_clause,[status(thm)],[f64])).
% 1.64/1.34 thf(f64,plain,(
% 1.64/1.34 $false | ~spl4_4),
% 1.64/1.34 inference(subsumption_resolution,[status(thm)],[f56,f34])).
% 1.64/1.34 thf(f34,plain,(
% 1.64/1.34 ( ! [X4 : $i > $o] : (($true != (X4 @ sK2))) ) | ~spl4_4),
% 1.64/1.34 inference(avatar_component_clause,[status(thm)],[f33])).
% 1.64/1.34 thf(f33,definition,(
% 1.64/1.34 spl4_4 <=> ! [X4 : $i > $o] : ($true != (X4 @ sK2))),
% 1.64/1.34 introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition])).
% 1.64/1.34 thf(f56,plain,(
% 1.64/1.34 ( ! [X7 : $i > $o] : (((X7 @ sK2) = $true)) ) | ~spl4_4),
% 1.64/1.34 inference(not_proxy_clausification,[status(thm)],[f55])).
% 1.64/1.34 thf(f55,plain,(
% 1.64/1.34 ( ! [X7 : $i > $o] : (((~ (X7 @ sK2)) != $true)) ) | ~spl4_4),
% 1.64/1.34 inference(beta_eta_normalization,[status(thm)],[f52])).
% 1.64/1.34 thf(f52,plain,(
% 1.64/1.34 ( ! [X7 : $i > $o] : ((((^[Y0 : $i]: (~ (X7 @ Y0))) @ sK2) != $true)) ) | ~spl4_4),
% 1.64/1.34 inference(primitive_instantiation,[status(thm)],[f34])).
% 1.64/1.34 thf(f38,plain,(
% 1.64/1.34 spl4_4 | spl4_5),
% 1.64/1.34 inference(avatar_split_clause,[status(thm)],[f18,f36,f33])).
% 1.64/1.34 thf(f18,plain,(
% 1.64/1.34 ( ! [X4 : $i > $o,X5 : $i > $o] : (($true != (X5 @ sK0)) | ($true != (X4 @ sK2)) | ((X5 @ sK3) != $true)) )),
% 1.64/1.34 inference(cnf_transformation,[status(thm)],[f10])).
% 1.64/1.34 thf(f10,plain,(
% 1.64/1.34 ! [X4 : $i > $o,X5 : $i > $o] : ((((X5 @ sK3) != $true) & ((X4 @ sK3) != $true)) | (($true != (X4 @ sK2)) & ((sK1 @ sK2) = $true)) | (($true != (X5 @ sK0)) & ((sK1 @ sK0) != $true)))),
% 1.64/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f9])).
% 1.64/1.34 thf(f9,plain,(
% 1.64/1.34 ? [X0 : $i,X1 : $i > $o,X2 : $i,X3 : $i] : ! [X4 : $i > $o,X5 : $i > $o] : ((($true != (X5 @ X3)) & ((X4 @ X3) != $true)) | (((X4 @ X2) != $true) & ((X1 @ X2) = $true)) | (((X5 @ X0) != $true) & ((X1 @ X0) != $true))) => ! [X5 : $i > $o,X4 : $i > $o] : ((((X5 @ sK3) != $true) & ((X4 @ sK3) != $true)) | (($true != (X4 @ sK2)) & ((sK1 @ sK2) = $true)) | (($true != (X5 @ sK0)) & ((sK1 @ sK0) != $true)))),
% 1.64/1.34 introduced(definition,[],[choice_axiom])).
% 1.64/1.34 thf(f8,plain,(
% 1.64/1.34 ? [X0 : $i,X1 : $i > $o,X2 : $i,X3 : $i] : ! [X4 : $i > $o,X5 : $i > $o] : ((($true != (X5 @ X3)) & ((X4 @ X3) != $true)) | (((X4 @ X2) != $true) & ((X1 @ X2) = $true)) | (((X5 @ X0) != $true) & ((X1 @ X0) != $true)))),
% 1.64/1.34 inference(rectify,[status(thm)],[f7])).
% 1.64/1.34 thf(f7,plain,(
% 1.64/1.34 ? [X3 : $i,X1 : $i > $o,X0 : $i,X2 : $i] : ! [X4 : $i > $o,X5 : $i > $o] : ((((X5 @ X2) != $true) & ((X4 @ X2) != $true)) | (((X4 @ X0) != $true) & ((X1 @ X0) = $true)) | (($true != (X5 @ X3)) & ($true != (X1 @ X3))))),
% 1.64/1.34 inference(ennf_transformation,[status(thm)],[f6])).
% 1.64/1.34 thf(f6,plain,(
% 1.64/1.34 ~! [X0 : $i,X1 : $i > $o,X2 : $i,X3 : $i] : ? [X5 : $i > $o,X4 : $i > $o] : ((((X1 @ X0) != $true) | ((X4 @ X0) = $true)) & (((X5 @ X2) = $true) | ((X4 @ X2) = $true)) & (($true = (X5 @ X3)) | ($true = (X1 @ X3))))),
% 1.64/1.34 inference(flattening,[status(thm)],[f5])).
% 1.64/1.34 thf(f5,plain,(
% 1.64/1.34 ~! [X0 : $i,X1 : $i > $o,X2 : $i,X3 : $i] : ? [X4 : $i > $o,X5 : $i > $o] : ((((X4 @ X0) = $true) | ~((X1 @ X0) = $true)) & (((X5 @ X2) = $true) | ((X4 @ X2) = $true)) & (($true = (X5 @ X3)) | ($true = (X1 @ X3))))),
% 1.64/1.34 inference(fool_elimination,[status(thm)],[f4])).
% 1.64/1.34 thf(f4,plain,(
% 1.64/1.34 ~! [X0 : $i,X1 : $i > $o,X2 : $i,X3 : $i] : ? [X4 : $i > $o,X5 : $i > $o] : (((X4 @ X0) | ~(X1 @ X0)) & ((X5 @ X2) | (X4 @ X2)) & ((X1 @ X3) | (X5 @ X3)))),
% 1.64/1.34 inference(rectify,[status(thm)],[f2])).
% 1.64/1.34 thf(f2,negated_conjecture,(
% 1.64/1.34 ~! [X2 : $i,X3 : $i > $o,X0 : $i,X1 : $i] : ? [X4 : $i > $o,X5 : $i > $o] : (((X4 @ X2) | ~(X3 @ X2)) & ((X5 @ X0) | (X4 @ X0)) & ((X3 @ X1) | (X5 @ X1)))),
% 1.64/1.34 inference(negated_conjecture,[status(cth)],[f1])).
% 1.64/1.34 thf(f1,conjecture,(
% 1.64/1.34 ! [X2 : $i,X3 : $i > $o,X0 : $i,X1 : $i] : ? [X4 : $i > $o,X5 : $i > $o] : (((X4 @ X2) | ~(X3 @ X2)) & ((X5 @ X0) | (X4 @ X0)) & ((X3 @ X1) | (X5 @ X1)))),
% 1.64/1.34 file('/export/starexec/sandbox/tmp/tmp.uggoABYEie/DTF2THF_11898.p',cTHM125B)).
% 1.64/1.34 % SZS output end Proof for DTF2THF_11898
% 1.64/1.34 % (12087)------------------------------
% 1.64/1.34 % (12087)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.34 % (12087)Termination reason: Refutation
% 1.64/1.34
% 1.64/1.34 % (12087)Memory used [KB]: 5500
% 1.64/1.34 % (12087)Time elapsed: 0.003 s
% 1.64/1.34 % (12087)Instructions burned: 3 (million)
% 1.64/1.34 % (12087)------------------------------
% 1.64/1.34 % (12087)------------------------------
% 1.64/1.34 % (12086)Success in time 0.017 s
%------------------------------------------------------------------------------