%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO514^1 : 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 : n003.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 09:54:26 AM UTC 2026
% Result : Theorem 1.50s 1.22s
% Output : Refutation 1.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 65 ( 20 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 80 ( 9 ~; 2 |; 4 &; 56 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 70 ( 70 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 4 usr; 3 con; 0-2 aty)
% ( 0 !!; 0 ??; 3 @@+; 0 @@-)
% Number of variables : 28 ( 0 ^; 14 !; 14 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_4,type,
sK0: ( ( ( $o > $o ) > $o ) > $o > $o ) > ( $o > $o ) > $o ).
thf(func_def_5,type,
sK1: ( ( ( $o > $o ) > $o ) > $o > $o ) > $o > $o ).
thf(func_def_7,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f22,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f18]) ).
thf(f18,plain,
$true = $false,
inference(superposition,[status(thm)],[f16,f11]) ).
thf(f11,plain,
! [X0: ( ( $o > $o ) > $o ) > $o > $o] :
( ( sK0 @ X0 @ ( sK1 @ X0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: ( ( $o > $o ) > $o ) > $o > $o] :
( ( ( sK0 @ X0 @ ( sK1 @ X0 ) )
= $true )
& ( $true
!= ( sK0 @ X0 @ ( X0 @ ( sK0 @ X0 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f8,f7]) ).
thf(f7,plain,
! [X0: ( ( $o > $o ) > $o ) > $o > $o] :
( ? [X1: ( $o > $o ) > $o] :
( ? [X2: $o > $o] :
( ( X1 @ X2 )
= $true )
& ( ( X1 @ ( X0 @ X1 ) )
!= $true ) )
=> ( ? [X2: $o > $o] :
( $true
= ( sK0 @ X0 @ X2 ) )
& ( $true
!= ( sK0 @ X0 @ ( X0 @ ( sK0 @ X0 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
! [X0: ( ( $o > $o ) > $o ) > $o > $o] :
( ? [X2: $o > $o] :
( $true
= ( sK0 @ X0 @ X2 ) )
=> ( ( sK0 @ X0 @ ( sK1 @ X0 ) )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
! [X0: ( ( $o > $o ) > $o ) > $o > $o] :
? [X1: ( $o > $o ) > $o] :
( ? [X2: $o > $o] :
( ( X1 @ X2 )
= $true )
& ( ( X1 @ ( X0 @ X1 ) )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ? [X0: ( ( $o > $o ) > $o ) > $o > $o] :
! [X1: ( $o > $o ) > $o] :
( ? [X2: $o > $o] :
( ( X1 @ X2 )
= $true )
=> ( ( X1 @ ( X0 @ X1 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: ( ( $o > $o ) > $o ) > $o > $o] :
! [X1: ( $o > $o ) > $o] :
( ? [X2: $o > $o] : ( X1 @ X2 )
=> ( X1 @ ( X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X0: ( ( $o > $o ) > $o ) > $o > $o] :
! [X1: ( $o > $o ) > $o] :
( ? [X2: $o > $o] : ( X1 @ X2 )
=> ( X1 @ ( X0 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X0: ( ( $o > $o ) > $o ) > $o > $o] :
! [X1: ( $o > $o ) > $o] :
( ? [X2: $o > $o] : ( X1 @ X2 )
=> ( X1 @ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.bRLXHrXN8R/DTF2THF_29312.p',choiceoo) ).
thf(f16,plain,
! [X0: $o > $o] :
( $false
= ( sK0 @ @@+ @ ( $o > $o ) @ X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: $o > $o] :
( ( $true != $true )
| ( $false
= ( sK0 @ @@+ @ ( $o > $o ) @ X0 ) ) ),
inference(superposition,[status(thm)],[f10,f12]) ).
thf(f12,plain,
! [X0: ( ( $o > $o ) > $o ) > $o > $o,X1: $o > $o] :
( ( $true
= ( sK0 @ X0 @ ( @@+ @ ( $o > $o ) @ ( sK0 @ X0 ) ) ) )
| ( ( sK0 @ X0 @ X1 )
= $false ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
! [X0: ( ( $o > $o ) > $o ) > $o > $o] :
( $true
!= ( sK0 @ X0 @ ( X0 @ ( sK0 @ X0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SYO514^1 : TPTP v9.2.1. Released v4.1.0.
% 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n003.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 14:32:55 EST 2026
% 0.16/0.35 % CPUTime :
% 0.16/0.35 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 : SYO514^1 : TPTP v9.2.1. Released v4.1.0.
% 0.29/0.46 % Domain : Syntactic
% 0.29/0.46 % Problem : A choice operator at type oo
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English :
% 0.29/0.46
% 0.29/0.46 % Refs : [Bro09] Brown E. (2009), Email to Geoff Sutcliffe
% 0.29/0.46 % : [Hoe09] Hoeschele (2009), Towards a Semi-Automatic Higher-Orde
% 0.29/0.46 % Source : [Bro09]
% 0.29/0.46 % Names : choiceoo [Bro09]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % : Without choice : Theorem
% 0.29/0.46 % Rating : 0.17 v9.1.0, 0.25 v8.2.0, 0.27 v8.1.0, 0.33 v7.4.0, 0.22 v7.3.0, 0.30 v7.2.0, 0.25 v7.1.0, 0.29 v7.0.0, 0.25 v6.4.0, 0.29 v6.3.0, 0.17 v6.2.0, 0.50 v6.1.0, 0.17 v6.0.0, 0.50 v5.5.0, 0.80 v5.4.0, 1.00 v4.1.0
% 0.29/0.46 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.29/0.46 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 0 ( 0 avg)
% 0.29/0.46 % Number of connectives : 4 ( 0 ~; 0 |; 0 &; 3 @)
% 0.29/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 6 ( 6 avg)
% 0.29/0.46 % Number of types : 1 ( 0 usr)
% 0.29/0.46 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.29/0.46 % Number of variables : 3 ( 0 ^; 1 !; 2 ?; 3 :)
% 0.29/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.29/0.46
% 0.29/0.46 % Comments : This theorem is in a sense trivial because the semantics is Henkin
% 0.29/0.46 % with choice. It is also a theorem if we do not assume choice
% 0.29/0.46 % because a choice operator can be defined.
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf(choiceoo,conjecture,
% 0.29/0.46 ? [C: ( ( $o > $o ) > $o ) > $o > $o] :
% 0.29/0.46 ! [P: ( $o > $o ) > $o] :
% 0.29/0.46 ( ? [X: $o > $o] : ( P @ X )
% 0.29/0.46 => ( P @ ( C @ P ) ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 1.38/1.18 ---- Embedded in THF ---
% 1.38/1.18 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.38/1.18 %%% Generated on Tue Feb 24 14:32:56 EST 2026
% 1.38/1.18 %%% using '$$dhol' embedding, version 1.3.0.
% 1.38/1.18 %%% Logic specification used:
% 1.38/1.18 %%% thf(spec, logic, $$dhol).
% 1.38/1.18
% 1.38/1.18 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.bRLXHrXN8R/DTF2DTF29312.p
% See solution above
% 1.38/1.18 ------------------------
% 1.38/1.19 ---- Cleaned THF ---
% 1.38/1.19 thf(choiceoo,conjecture,
% 1.38/1.19 ? [C: ( ( $o > $o ) > $o ) > $o > $o] :
% 1.38/1.19 ! [P: ( $o > $o ) > $o] :
% 1.38/1.19 ( ? [X: $o > $o] : ( P @ X )
% 1.38/1.19 => ( P @ ( C @ P ) ) ) ).
% 1.38/1.19 ------------------------
% 1.50/1.21 % (29410)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_29312 for (3000ds/183Mi)
% 1.50/1.21 % (29412)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_29312 for (3000ds/27Mi)
% 1.50/1.21 % (29416)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_29312 for (3000ds/18Mi)
% 1.50/1.21 % (29411)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_29312 for (3000ds/4Mi)
% 1.50/1.21 % (29414)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_29312 for (3000ds/2Mi)
% 1.50/1.22 % (29413)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_29312 for (3000ds/2Mi)
% 1.50/1.22 % (29415)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_29312 for (3000ds/275Mi)
% 1.50/1.22 % (29414)Instruction limit reached!
% 1.50/1.22 % (29414)------------------------------
% 1.50/1.22 % (29414)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.22 % (29414)Termination reason: Unknown
% 1.50/1.22 % (29414)Termination phase: Saturation
% 1.50/1.22
% 1.50/1.22 % (29414)Memory used [KB]: 5373
% 1.50/1.22 % (29414)Time elapsed: 0.003 s
% 1.50/1.22 % (29414)Instructions burned: 2 (million)
% 1.50/1.22 % (29414)------------------------------
% 1.50/1.22 % (29414)------------------------------
% 1.50/1.22 % (29412)First to succeed.
% 1.50/1.22 % (29413)Refutation not found, incomplete strategy
% 1.50/1.22 % (29413)------------------------------
% 1.50/1.22 % (29413)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.22 % (29413)Termination reason: Refutation not found, incomplete strategy
% 1.50/1.22
% 1.50/1.22
% 1.50/1.22 % (29413)Memory used [KB]: 5500
% 1.50/1.22 % (29413)Time elapsed: 0.002 s
% 1.50/1.22 % (29413)Instructions burned: 1 (million)
% 1.50/1.22 % (29413)------------------------------
% 1.50/1.22 % (29413)------------------------------
% 1.50/1.22 % (29415)Refutation not found, incomplete strategy
% 1.50/1.22 % (29415)------------------------------
% 1.50/1.22 % (29415)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.22 % (29415)Termination reason: Refutation not found, incomplete strategy
% 1.50/1.22
% 1.50/1.22
% 1.50/1.22 % (29415)Memory used [KB]: 5500
% 1.50/1.22 % (29415)Time elapsed: 0.002 s
% 1.50/1.22 % (29415)Instructions burned: 1 (million)
% 1.50/1.22 % (29415)------------------------------
% 1.50/1.22 % (29415)------------------------------
% 1.50/1.22 % (29412)Refutation found. Thanks to Tanya!
% 1.50/1.22 % SZS status Theorem for DTF2THF_29312
% 1.50/1.22 % SZS output start Proof for DTF2THF_29312
% 1.50/1.22 thf(func_def_1, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.50/1.22 thf(func_def_4, type, sK0: ((($o > $o) > $o) > $o > $o) > ($o > $o) > $o).
% 1.50/1.22 thf(func_def_5, type, sK1: ((($o > $o) > $o) > $o > $o) > $o > $o).
% 1.50/1.22 thf(func_def_7, type, ph3: !>[X0: $tType]:(X0)).
% 1.50/1.22 thf(f22,plain,(
% 1.50/1.22 $false),
% 1.50/1.22 inference(trivial_inequality_removal,[status(thm)],[f18])).
% 1.50/1.22 thf(f18,plain,(
% 1.50/1.22 ($true = $false)),
% 1.50/1.22 inference(superposition,[status(thm)],[f16,f11])).
% 1.50/1.22 thf(f11,plain,(
% 1.50/1.22 ( ! [X0 : (($o > $o) > $o) > $o > $o] : (((sK0 @ X0 @ (sK1 @ X0)) = $true)) )),
% 1.50/1.22 inference(cnf_transformation,[status(thm)],[f9])).
% 1.50/1.22 thf(f9,plain,(
% 1.50/1.22 ! [X0 : (($o > $o) > $o) > $o > $o] : (((sK0 @ X0 @ (sK1 @ X0)) = $true) & ($true != (sK0 @ X0 @ (X0 @ (sK0 @ X0)))))),
% 1.50/1.22 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f8,f7])).
% 1.50/1.22 thf(f7,plain,(
% 1.50/1.22 ! [X0 : (($o > $o) > $o) > $o > $o] : (? [X1 : ($o > $o) > $o] : (? [X2 : $o > $o] : ((X1 @ X2) = $true) & ((X1 @ (X0 @ X1)) != $true)) => (? [X2 : $o > $o] : ($true = (sK0 @ X0 @ X2)) & ($true != (sK0 @ X0 @ (X0 @ (sK0 @ X0))))))),
% 1.50/1.22 introduced(definition,[],[choice_axiom])).
% 1.50/1.22 thf(f8,plain,(
% 1.50/1.22 ! [X0 : (($o > $o) > $o) > $o > $o] : (? [X2 : $o > $o] : ($true = (sK0 @ X0 @ X2)) => ((sK0 @ X0 @ (sK1 @ X0)) = $true))),
% 1.50/1.22 introduced(definition,[],[choice_axiom])).
% 1.50/1.22 thf(f6,plain,(
% 1.50/1.22 ! [X0 : (($o > $o) > $o) > $o > $o] : ? [X1 : ($o > $o) > $o] : (? [X2 : $o > $o] : ((X1 @ X2) = $true) & ((X1 @ (X0 @ X1)) != $true))),
% 1.50/1.22 inference(ennf_transformation,[status(thm)],[f5])).
% 1.50/1.22 thf(f5,plain,(
% 1.50/1.22 ~? [X0 : (($o > $o) > $o) > $o > $o] : ! [X1 : ($o > $o) > $o] : (? [X2 : $o > $o] : ((X1 @ X2) = $true) => ((X1 @ (X0 @ X1)) = $true))),
% 1.50/1.22 inference(fool_elimination,[status(thm)],[f4])).
% 1.50/1.22 thf(f4,plain,(
% 1.50/1.22 ~? [X0 : (($o > $o) > $o) > $o > $o] : ! [X1 : ($o > $o) > $o] : (? [X2 : $o > $o] : (X1 @ X2) => (X1 @ (X0 @ X1)))),
% 1.50/1.22 inference(rectify,[status(thm)],[f2])).
% 1.50/1.22 thf(f2,negated_conjecture,(
% 1.50/1.22 ~? [X0 : (($o > $o) > $o) > $o > $o] : ! [X1 : ($o > $o) > $o] : (? [X2 : $o > $o] : (X1 @ X2) => (X1 @ (X0 @ X1)))),
% 1.50/1.22 inference(negated_conjecture,[status(cth)],[f1])).
% 1.50/1.22 thf(f1,conjecture,(
% 1.50/1.22 ? [X0 : (($o > $o) > $o) > $o > $o] : ! [X1 : ($o > $o) > $o] : (? [X2 : $o > $o] : (X1 @ X2) => (X1 @ (X0 @ X1)))),
% 1.50/1.22 file('/export/starexec/sandbox2/tmp/tmp.bRLXHrXN8R/DTF2THF_29312.p',choiceoo)).
% 1.50/1.22 thf(f16,plain,(
% 1.50/1.22 ( ! [X0 : $o > $o] : (($false = (sK0 @ @@+ @ ($o > $o) @ X0))) )),
% 1.50/1.22 inference(trivial_inequality_removal,[status(thm)],[f14])).
% 1.50/1.22 thf(f14,plain,(
% 1.50/1.22 ( ! [X0 : $o > $o] : (($true != $true) | ($false = (sK0 @ @@+ @ ($o > $o) @ X0))) )),
% 1.50/1.22 inference(superposition,[status(thm)],[f10,f12])).
% 1.50/1.22 thf(f12,plain,(
% 1.50/1.22 ( ! [X0 : (($o > $o) > $o) > $o > $o,X1 : $o > $o] : (($true = (sK0 @ X0 @ (@@+ @ ($o > $o) @ (sK0 @ X0)))) | ((sK0 @ X0 @ X1) = $false)) )),
% 1.50/1.22 introduced(definition,[],[choice_axiom])).
% 1.50/1.22 thf(f10,plain,(
% 1.50/1.22 ( ! [X0 : (($o > $o) > $o) > $o > $o] : (($true != (sK0 @ X0 @ (X0 @ (sK0 @ X0))))) )),
% 1.50/1.22 inference(cnf_transformation,[status(thm)],[f9])).
% 1.50/1.22 % SZS output end Proof for DTF2THF_29312
% 1.50/1.22 % (29412)------------------------------
% 1.50/1.22 % (29412)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.22 % (29412)Termination reason: Refutation
% 1.50/1.22
% 1.50/1.22 % (29412)Memory used [KB]: 5500
% 1.50/1.22 % (29412)Time elapsed: 0.005 s
% 1.50/1.22 % (29412)Instructions burned: 3 (million)
% 1.50/1.22 % (29412)------------------------------
% 1.50/1.22 % (29412)------------------------------
% 1.50/1.22 % (29409)Success in time 0.019 s
%------------------------------------------------------------------------------