%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO520^1 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n017.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 09:54:27 AM UTC 2026
% Result : Unsatisfiable 1.49s 1.28s
% Output : Refutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 8 unt; 0 typ; 2 def)
% Number of atoms : 70 ( 13 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 59 ( 18 ~; 8 |; 0 &; 31 @)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 7 ( 4 ^; 3 !; 0 ?; 7 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
eps: ( $i > $o ) > $i ).
thf(func_def_2,type,
p: $i > $o ).
thf(func_def_3,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_10,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f34,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f28,f29,f33]) ).
thf(f33,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f32]) ).
thf(f32,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f31]) ).
thf(f31,plain,
( ( $false = $true )
| ~ spl0_1 ),
inference(forward_demodulation,[status(thm)],[f13,f19]) ).
thf(f19,plain,
( ! [X1: $i] :
( ( p @ X1 )
= $false )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f18]) ).
thf(f18,definition,
( spl0_1
<=> ! [X1: $i] :
( ( p @ X1 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f13,plain,
( $true
= ( p
@ ( eps
@ ^ [Y0: $i] :
~ ( p @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( $true
= ( p
@ ( eps
@ ^ [Y0: $i] :
~ ( p @ Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
( p
@ ( eps
@ ^ [X0: $i] :
~ ( p @ X0 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( p
@ ( eps
@ ^ [X1: $i] :
~ ( p @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CLEkmRWt7v/DTF2THF_3296.p',ax1) ).
thf(f29,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f25,f21,f18]) ).
thf(f21,definition,
( spl0_2
<=> ( ( p @ ( eps @ p ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f25,plain,
! [X1: $i] :
( ( ( p @ X1 )
= $false )
| ( ( p @ ( eps @ p ) )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f28,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f27]) ).
thf(f27,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f26]) ).
thf(f26,plain,
( ( $true != $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f15,f23]) ).
thf(f23,plain,
( ( ( p @ ( eps @ p ) )
= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f21]) ).
thf(f15,plain,
( ( p @ ( eps @ p ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( p @ ( eps @ p ) )
!= $true ),
inference(flattening,[status(thm)],[f10]) ).
thf(f10,plain,
( ( p @ ( eps @ p ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( p @ ( eps @ p ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
~ ( p @ ( eps @ p ) ),
file('/export/starexec/sandbox2/tmp/tmp.CLEkmRWt7v/DTF2THF_3296.p',ax2) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO520^1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n017.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 14:37:26 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.45 ---- Original DTF file ---
% 0.18/0.45 thf(spec,logic,$$dhol).
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 % File : SYO520^1 : TPTP v9.2.1. Released v4.1.0.
% 0.18/0.45 % Domain : Syntactic
% 0.18/0.45 % Problem : A simple problem with a choice operator
% 0.18/0.45 % Version : Especial.
% 0.18/0.45 % English :
% 0.18/0.45
% 0.18/0.45 % Refs : [Bro10] Brown E. (2010), Email to Geoff Sutcliffe
% 0.18/0.45 % Source : [Bro10]
% 0.18/0.45 % Names :
% 0.18/0.45
% 0.18/0.45 % Status : Unsatisfiable
% 0.18/0.45 % Rating : 0.00 v4.1.0
% 0.18/0.45 % Syntax : Number of formulae : 5 ( 0 unt; 2 typ; 0 def)
% 0.18/0.45 % Number of atoms : 4 ( 0 equ; 0 cnn)
% 0.18/0.45 % Maximal formula atoms : 2 ( 1 avg)
% 0.18/0.45 % Number of connectives : 11 ( 2 ~; 0 |; 0 &; 8 @)
% 0.18/0.45 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.18/0.45 % Maximal formula depth : 6 ( 5 avg)
% 0.18/0.45 % Number of types : 2 ( 0 usr)
% 0.18/0.45 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.18/0.45 % Number of symbols : 2 ( 2 usr; 0 con; 1-1 aty)
% 0.18/0.45 % Number of variables : 3 ( 1 ^; 1 !; 1 ?; 3 :)
% 0.18/0.45 % SPC : TH0_UNS_NEQ_NAR
% 0.18/0.45
% 0.18/0.45 % Comments : The operator eps for type i is given, and assumed to be a choice
% 0.18/0.45 % operator. This is to get around using the choice operator @+ in
% 0.18/0.45 % TH0 syntax (since it is not ). eps maybe semantically
% 0.18/0.45 % different from the choice operator @+ but a theorem prover may
% 0.18/0.45 % recognize eps is a choice operator and treat it accordingly.
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 thf(eps,type,
% 0.18/0.45 eps: ( $i > $o ) > $i ).
% 0.18/0.45
% 0.18/0.45 thf(epschoice,axiom,
% 0.18/0.45 ! [P: $i > $o] :
% 0.18/0.45 ( ? [X: $i] : ( P @ X )
% 0.18/0.45 => ( P @ ( eps @ P ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(p,type,
% 0.18/0.45 p: $i > $o ).
% 0.18/0.45
% 0.18/0.45 thf(ax1,axiom,
% 0.18/0.45 ( p
% 0.18/0.45 @ ( eps
% 0.18/0.45 @ ^ [X: $i] :
% 0.18/0.45 ~ ( p @ X ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(ax2,axiom,
% 0.18/0.45 ~ ( p @ ( eps @ p ) ) ).
% 0.18/0.45
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 ------------------------
% 1.49/1.24 ---- Embedded in THF ---
% 1.49/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.24 %%% Generated on Tue Feb 24 14:37:26 EST 2026
% 1.49/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.24 %%% Logic specification used:
% 1.49/1.24 %%% thf(spec, logic, $$dhol).
% 1.49/1.24
% 1.49/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.CLEkmRWt7v/DTF2DTF3296.p
% See solution above
% 1.49/1.24 ------------------------
% 1.49/1.25 ---- Cleaned THF ---
% 1.49/1.25 thf(eps,type,
% 1.49/1.25 eps: ( $i > $o ) > $i ).
% 1.49/1.25
% 1.49/1.25 thf(epschoice,axiom,
% 1.49/1.25 ! [P: $i > $o] :
% 1.49/1.25 ( ? [X: $i] : ( P @ X )
% 1.49/1.25 => ( P @ ( eps @ P ) ) ) ).
% 1.49/1.25
% 1.49/1.25 thf(p,type,
% 1.49/1.25 p: $i > $o ).
% 1.49/1.25
% 1.49/1.25 thf(ax1,axiom,
% 1.49/1.25 ( p
% 1.49/1.25 @ ( eps
% 1.49/1.25 @ ^ [X: $i] :
% 1.49/1.25 ~ ( p @ X ) ) ) ).
% 1.49/1.25
% 1.49/1.25 thf(ax2,axiom,
% 1.49/1.25 ~ ( p @ ( eps @ p ) ) ).
% 1.49/1.25 ------------------------
% 1.49/1.27 % (3401)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_3296 for (3000ds/275Mi)
% 1.49/1.27 % (3401)Refutation not found, incomplete strategy
% 1.49/1.27 % (3401)------------------------------
% 1.49/1.27 % (3401)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.27 % (3401)Termination reason: Refutation not found, incomplete strategy
% 1.49/1.27
% 1.49/1.27
% 1.49/1.27 % (3401)Memory used [KB]: 5373
% 1.49/1.27 % (3401)Time elapsed: 0.001 s
% 1.49/1.27 % (3401)------------------------------
% 1.49/1.27 % (3401)------------------------------
% 1.49/1.27 % (3400)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_3296 for (3000ds/2Mi)
% 1.49/1.27 % (3400)Refutation not found, incomplete strategy
% 1.49/1.27 % (3400)------------------------------
% 1.49/1.27 % (3400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.27 % (3400)Termination reason: Refutation not found, incomplete strategy
% 1.49/1.27
% 1.49/1.27
% 1.49/1.27 % (3400)Memory used [KB]: 5500
% 1.49/1.27 % (3400)Time elapsed: 0.001 s
% 1.49/1.27 % (3400)------------------------------
% 1.49/1.27 % (3400)------------------------------
% 1.49/1.27 % (3399)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3296 for (3000ds/2Mi)
% 1.49/1.27 % (3397)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_3296 for (3000ds/4Mi)
% 1.49/1.27 % (3398)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_3296 for (3000ds/27Mi)
% 1.49/1.27 % (3396)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3296 for (3000ds/183Mi)
% 1.49/1.28 % (3399)Instruction limit reached!
% 1.49/1.28 % (3399)------------------------------
% 1.49/1.28 % (3399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.28 % (3399)Termination reason: Unknown
% 1.49/1.28 % (3399)Termination phase: Saturation
% 1.49/1.28
% 1.49/1.28 % (3399)Memory used [KB]: 5500
% 1.49/1.28 % (3399)Time elapsed: 0.004 s
% 1.49/1.28 % (3399)Instructions burned: 2 (million)
% 1.49/1.28 % (3399)------------------------------
% 1.49/1.28 % (3399)------------------------------
% 1.49/1.28 % (3398)First to succeed.
% 1.49/1.28 % (3397)Instruction limit reached!
% 1.49/1.28 % (3397)------------------------------
% 1.49/1.28 % (3397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.28 % (3397)Termination reason: Unknown
% 1.49/1.28 % (3403)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_3296 for (2999ds/3Mi)
% 1.49/1.28 % (3397)Termination phase: Saturation
% 1.49/1.28
% 1.49/1.28 % (3397)Memory used [KB]: 5500
% 1.49/1.28 % (3397)Time elapsed: 0.005 s
% 1.49/1.28 % (3397)Instructions burned: 4 (million)
% 1.49/1.28 % (3397)------------------------------
% 1.49/1.28 % (3397)------------------------------
% 1.49/1.28 % (3398)Refutation found. Thanks to Tanya!
% 1.49/1.28 % SZS status Unsatisfiable for DTF2THF_3296
% 1.49/1.28 % SZS output start Proof for DTF2THF_3296
% 1.49/1.28 thf(func_def_0, type, eps: ($i > $o) > $i).
% 1.49/1.28 thf(func_def_2, type, p: $i > $o).
% 1.49/1.28 thf(func_def_3, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.49/1.28 thf(func_def_10, type, ph1: !>[X0: $tType]:(X0)).
% 1.49/1.28 thf(f34,plain,(
% 1.49/1.28 $false),
% 1.49/1.28 inference(avatar_sat_refutation,[status(thm)],[f28,f29,f33])).
% 1.49/1.28 thf(f33,plain,(
% 1.49/1.28 ~spl0_1),
% 1.49/1.28 inference(avatar_contradiction_clause,[status(thm)],[f32])).
% 1.49/1.28 thf(f32,plain,(
% 1.49/1.28 $false | ~spl0_1),
% 1.49/1.28 inference(trivial_inequality_removal,[status(thm)],[f31])).
% 1.49/1.28 thf(f31,plain,(
% 1.49/1.28 ($false = $true) | ~spl0_1),
% 1.49/1.28 inference(forward_demodulation,[status(thm)],[f13,f19])).
% 1.49/1.28 thf(f19,plain,(
% 1.49/1.28 ( ! [X1 : $i] : (((p @ X1) = $false)) ) | ~spl0_1),
% 1.49/1.28 inference(avatar_component_clause,[status(thm)],[f18])).
% 1.49/1.28 thf(f18,definition,(
% 1.49/1.28 spl0_1 <=> ! [X1 : $i] : ((p @ X1) = $false)),
% 1.49/1.28 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.49/1.28 thf(f13,plain,(
% 1.49/1.28 ($true = (p @ (eps @ (^[Y0 : $i]: (~ (p @ Y0))))))),
% 1.49/1.28 inference(cnf_transformation,[status(thm)],[f6])).
% 1.49/1.28 thf(f6,plain,(
% 1.49/1.28 ($true = (p @ (eps @ (^[Y0 : $i]: (~ (p @ Y0))))))),
% 1.49/1.28 inference(fool_elimination,[status(thm)],[f5])).
% 1.49/1.28 thf(f5,plain,(
% 1.49/1.28 (p @ (eps @ (^[X0 : $i] : (~(p @ X0)))))),
% 1.49/1.28 inference(rectify,[status(thm)],[f2])).
% 1.49/1.28 thf(f2,axiom,(
% 1.49/1.28 (p @ (eps @ (^[X1 : $i] : (~(p @ X1)))))),
% 1.49/1.28 file('/export/starexec/sandbox2/tmp/tmp.CLEkmRWt7v/DTF2THF_3296.p',ax1)).
% 1.49/1.28 thf(f29,plain,(
% 1.49/1.28 spl0_1 | spl0_2),
% 1.49/1.28 inference(avatar_split_clause,[status(thm)],[f25,f21,f18])).
% 1.49/1.28 thf(f21,definition,(
% 1.49/1.28 spl0_2 <=> ((p @ (eps @ p)) = $true)),
% 1.49/1.28 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.49/1.28 thf(f25,plain,(
% 1.49/1.28 ( ! [X1 : $i] : (((p @ X1) = $false) | ((p @ (eps @ p)) = $true)) )),
% 1.49/1.28 introduced(definition,[],[choice_axiom])).
% 1.49/1.28 thf(f28,plain,(
% 1.49/1.28 ~spl0_2),
% 1.49/1.28 inference(avatar_contradiction_clause,[status(thm)],[f27])).
% 1.49/1.28 thf(f27,plain,(
% 1.49/1.28 $false | ~spl0_2),
% 1.49/1.28 inference(trivial_inequality_removal,[status(thm)],[f26])).
% 1.49/1.28 thf(f26,plain,(
% 1.49/1.28 ($true != $true) | ~spl0_2),
% 1.49/1.28 inference(superposition,[status(thm)],[f15,f23])).
% 1.49/1.28 thf(f23,plain,(
% 1.49/1.28 ((p @ (eps @ p)) = $true) | ~spl0_2),
% 1.49/1.28 inference(avatar_component_clause,[status(thm)],[f21])).
% 1.49/1.28 thf(f15,plain,(
% 1.49/1.28 ((p @ (eps @ p)) != $true)),
% 1.49/1.28 inference(cnf_transformation,[status(thm)],[f11])).
% 1.49/1.28 thf(f11,plain,(
% 1.49/1.28 ((p @ (eps @ p)) != $true)),
% 1.49/1.28 inference(flattening,[status(thm)],[f10])).
% 1.49/1.28 thf(f10,plain,(
% 1.49/1.28 ~((p @ (eps @ p)) = $true)),
% 1.49/1.28 inference(fool_elimination,[status(thm)],[f9])).
% 1.49/1.28 thf(f9,plain,(
% 1.49/1.28 ~(p @ (eps @ p))),
% 1.49/1.28 inference(rectify,[status(thm)],[f3])).
% 1.49/1.28 thf(f3,axiom,(
% 1.49/1.28 ~(p @ (eps @ p))),
% 1.49/1.28 file('/export/starexec/sandbox2/tmp/tmp.CLEkmRWt7v/DTF2THF_3296.p',ax2)).
% 1.49/1.28 % SZS output end Proof for DTF2THF_3296
% 1.49/1.28 % (3398)------------------------------
% 1.49/1.28 % (3398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.28 % (3398)Termination reason: Refutation
% 1.49/1.28
% 1.49/1.28 % (3398)Memory used [KB]: 5500
% 1.49/1.28 % (3398)Time elapsed: 0.005 s
% 1.49/1.28 % (3398)Instructions burned: 2 (million)
% 1.49/1.28 % (3398)------------------------------
% 1.49/1.28 % (3398)------------------------------
% 1.49/1.28 % (3395)Success in time 0.01 s
%------------------------------------------------------------------------------