%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO512^1 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n016.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 09:54:25 AM UTC 2026
% Result : Theorem 1.46s 1.29s
% Output : Refutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 80 ( 21 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 96 ( 12 ~; 3 |; 0 &; 76 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 28 ( 0 ^; 19 !; 9 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
eps: ( $i > $o ) > $i ).
thf(func_def_2,type,
r: $i > $i > $o ).
thf(func_def_6,type,
sK1: $i > $i ).
thf(func_def_9,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f34,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f32]) ).
thf(f32,plain,
$true != $true,
inference(superposition,[status(thm)],[f18,f28]) ).
thf(f28,plain,
! [X0: $i] :
( ( r @ X0 @ ( eps @ ( r @ X0 ) ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f25]) ).
thf(f25,plain,
! [X0: $i] :
( ( ( r @ X0 @ ( eps @ ( r @ X0 ) ) )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f19,f20]) ).
thf(f20,plain,
! [X0: $i] :
( ( r @ X0 @ ( sK1 @ X0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: $i] :
( ( r @ X0 @ ( sK1 @ X0 ) )
= $true ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f7,f16]) ).
thf(f16,plain,
! [X0: $i] :
( ? [X1: $i] :
( $true
= ( r @ X0 @ X1 ) )
=> ( ( r @ X0 @ ( sK1 @ X0 ) )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
! [X0: $i] :
? [X1: $i] :
( $true
= ( r @ X0 @ X1 ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: $i] :
? [X1: $i] : ( r @ X0 @ X1 ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X1: $i] :
? [X2: $i] : ( r @ X1 @ X2 ),
file('/export/starexec/sandbox/tmp/tmp.MyXM0UsJYF/DTF2THF_878.p',rtotal) ).
thf(f19,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ X1 )
!= $true )
| ( ( X0 @ ( eps @ X0 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: $i > $o] :
( ( ( X0 @ ( eps @ X0 ) )
= $true )
| ! [X1: $i] :
( ( X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $i > $o] :
( ? [X1: $i] :
( ( X0 @ X1 )
= $true )
=> ( ( X0 @ ( eps @ X0 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i > $o] :
( ? [X1: $i] : ( X0 @ X1 )
=> ( X0 @ ( eps @ X0 ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i > $o] :
( ? [X1: $i] : ( X0 @ X1 )
=> ( X0 @ ( eps @ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.MyXM0UsJYF/DTF2THF_878.p',epschoice) ).
thf(f18,plain,
( ( r @ sK0 @ ( eps @ ( r @ sK0 ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( r @ sK0 @ ( eps @ ( r @ sK0 ) ) )
!= $true ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f12,f14]) ).
thf(f14,plain,
( ? [X0: $i] :
( ( r @ X0 @ ( eps @ ( r @ X0 ) ) )
!= $true )
=> ( ( r @ sK0 @ ( eps @ ( r @ sK0 ) ) )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
? [X0: $i] :
( ( r @ X0 @ ( eps @ ( r @ X0 ) ) )
!= $true ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
~ ! [X0: $i] :
( ( r @ X0 @ ( eps @ ( r @ X0 ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ! [X0: $i] : ( r @ X0 @ ( eps @ ( r @ X0 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X1: $i] : ( r @ X1 @ ( eps @ ( r @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
! [X1: $i] : ( r @ X1 @ ( eps @ ( r @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.MyXM0UsJYF/DTF2THF_878.p',claim) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO512^1 : TPTP v9.2.1. Released v4.1.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n016.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 14:33:36 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.46 thf(spec,logic,$$dhol).
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 % File : SYO512^1 : TPTP v9.2.1. Released v4.1.0.
% 0.28/0.46 % Domain : Syntactic
% 0.28/0.46 % Problem : Choice operator used to obtain functions from total relations
% 0.28/0.46 % Version : Especial.
% 0.28/0.46 % English : A choice operator can be used to obtain functions from total
% 0.28/0.46 % relations.
% 0.28/0.46
% 0.28/0.46 % Refs : [Bro09] Brown E. (2009), Email to Geoff Sutcliffe
% 0.28/0.46 % : [Hoe09] Hoeschele (2009), Towards a Semi-Automatic Higher-Orde
% 0.28/0.46 % Source : [Bro09]
% 0.28/0.46 % Names : choiceiskolem [Bro09]
% 0.28/0.46
% 0.28/0.46 % Status : Theorem
% 0.28/0.46 % Rating : 0.00 v8.1.0, 0.08 v7.4.0, 0.00 v6.2.0, 0.17 v6.1.0, 0.00 v4.1.0
% 0.28/0.46 % Syntax : Number of formulae : 5 ( 1 unt; 2 typ; 0 def)
% 0.28/0.46 % Number of atoms : 3 ( 0 equ; 0 cnn)
% 0.28/0.46 % Maximal formula atoms : 2 ( 1 avg)
% 0.28/0.46 % Number of connectives : 10 ( 0 ~; 0 |; 0 &; 9 @)
% 0.28/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.28/0.46 % Maximal formula depth : 5 ( 5 avg)
% 0.28/0.46 % Number of types : 2 ( 0 usr)
% 0.28/0.46 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.28/0.46 % Number of symbols : 2 ( 2 usr; 0 con; 1-2 aty)
% 0.28/0.46 % Number of variables : 5 ( 0 ^; 3 !; 2 ?; 5 :)
% 0.28/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.28/0.46
% 0.28/0.46 % Comments : I have given a choice operator eps for type i and assumed it is a
% 0.28/0.46 % choice operator. This is to get around using the choice operator
% 0.28/0.46 % @+ in TH0 syntax (since it is not ). eps maybe
% 0.28/0.46 % semantically different from the choice operator @+ but a theorem
% 0.28/0.46 % prover may recognize eps is a choice operator and treat it
% 0.28/0.46 % accordingly.
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 thf(eps,type,
% 0.28/0.46 eps: ( $i > $o ) > $i ).
% 0.28/0.46
% 0.28/0.46 thf(epschoice,axiom,
% 0.28/0.46 ! [P: $i > $o] :
% 0.28/0.46 ( ? [X: $i] : ( P @ X )
% 0.28/0.46 => ( P @ ( eps @ P ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(r,type,
% 0.28/0.46 r: $i > $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(rtotal,axiom,
% 0.28/0.46 ! [X: $i] :
% 0.28/0.46 ? [Y: $i] : ( r @ X @ Y ) ).
% 0.28/0.46
% 0.28/0.46 thf(claim,conjecture,
% 0.28/0.46 ! [X: $i] : ( r @ X @ ( eps @ ( r @ X ) ) ) ).
% 0.28/0.46
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 ------------------------
% 1.46/1.26 ---- Embedded in THF ---
% 1.46/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.26 %%% Generated on Tue Feb 24 14:33:37 EST 2026
% 1.46/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.26 %%% Logic specification used:
% 1.46/1.26 %%% thf(spec, logic, $$dhol).
% 1.46/1.26
% 1.46/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.MyXM0UsJYF/DTF2DTF878.p
% See solution above
% 1.46/1.26 ------------------------
% 1.46/1.27 ---- Cleaned THF ---
% 1.46/1.27 thf(eps,type,
% 1.46/1.27 eps: ( $i > $o ) > $i ).
% 1.46/1.27
% 1.46/1.27 thf(epschoice,axiom,
% 1.46/1.27 ! [P: $i > $o] :
% 1.46/1.27 ( ? [X: $i] : ( P @ X )
% 1.46/1.27 => ( P @ ( eps @ P ) ) ) ).
% 1.46/1.27
% 1.46/1.27 thf(r,type,
% 1.46/1.27 r: $i > $i > $o ).
% 1.46/1.27
% 1.46/1.27 thf(rtotal,axiom,
% 1.46/1.27 ! [X: $i] :
% 1.46/1.27 ? [Y: $i] : ( r @ X @ Y ) ).
% 1.46/1.27
% 1.46/1.27 thf(claim,conjecture,
% 1.46/1.27 ! [X: $i] : ( r @ X @ ( eps @ ( r @ X ) ) ) ).
% 1.46/1.27 ------------------------
% 1.46/1.29 % (1206)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_878 for (2999ds/2Mi)
% 1.46/1.29 % (1205)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_878 for (2999ds/2Mi)
% 1.46/1.29 % (1206)Refutation not found, incomplete strategy
% 1.46/1.29 % (1206)------------------------------
% 1.46/1.29 % (1206)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.29 % (1206)Termination reason: Refutation not found, incomplete strategy
% 1.46/1.29
% 1.46/1.29
% 1.46/1.29 % (1206)Memory used [KB]: 5500
% 1.46/1.29 % (1206)Time elapsed: 0.003 s
% 1.46/1.29 % (1206)Instructions burned: 1 (million)
% 1.46/1.29 % (1206)------------------------------
% 1.46/1.29 % (1206)------------------------------
% 1.46/1.29 % (1205)First to succeed.
% 1.46/1.29 % (1205)Refutation found. Thanks to Tanya!
% 1.46/1.29 % SZS status Theorem for DTF2THF_878
% 1.46/1.29 % SZS output start Proof for DTF2THF_878
% 1.46/1.29 thf(func_def_0, type, eps: ($i > $o) > $i).
% 1.46/1.29 thf(func_def_2, type, r: $i > $i > $o).
% 1.46/1.29 thf(func_def_6, type, sK1: $i > $i).
% 1.46/1.29 thf(func_def_9, type, ph3: !>[X0: $tType]:(X0)).
% 1.46/1.29 thf(f34,plain,(
% 1.46/1.29 $false),
% 1.46/1.29 inference(trivial_inequality_removal,[status(thm)],[f32])).
% 1.46/1.29 thf(f32,plain,(
% 1.46/1.29 ($true != $true)),
% 1.46/1.29 inference(superposition,[status(thm)],[f18,f28])).
% 1.46/1.29 thf(f28,plain,(
% 1.46/1.29 ( ! [X0 : $i] : (((r @ X0 @ (eps @ (r @ X0))) = $true)) )),
% 1.46/1.29 inference(trivial_inequality_removal,[status(thm)],[f25])).
% 1.46/1.29 thf(f25,plain,(
% 1.46/1.29 ( ! [X0 : $i] : (((r @ X0 @ (eps @ (r @ X0))) = $true) | ($true != $true)) )),
% 1.46/1.29 inference(superposition,[status(thm)],[f19,f20])).
% 1.46/1.29 thf(f20,plain,(
% 1.46/1.29 ( ! [X0 : $i] : (((r @ X0 @ (sK1 @ X0)) = $true)) )),
% 1.46/1.29 inference(cnf_transformation,[status(thm)],[f17])).
% 1.46/1.29 thf(f17,plain,(
% 1.46/1.29 ! [X0 : $i] : ((r @ X0 @ (sK1 @ X0)) = $true)),
% 1.46/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f7,f16])).
% 1.46/1.29 thf(f16,plain,(
% 1.46/1.29 ! [X0 : $i] : (? [X1 : $i] : ($true = (r @ X0 @ X1)) => ((r @ X0 @ (sK1 @ X0)) = $true))),
% 1.46/1.29 introduced(definition,[],[choice_axiom])).
% 1.46/1.29 thf(f7,plain,(
% 1.46/1.29 ! [X0 : $i] : ? [X1 : $i] : ($true = (r @ X0 @ X1))),
% 1.46/1.29 inference(fool_elimination,[status(thm)],[f6])).
% 1.46/1.29 thf(f6,plain,(
% 1.46/1.29 ! [X0 : $i] : ? [X1 : $i] : (r @ X0 @ X1)),
% 1.46/1.29 inference(rectify,[status(thm)],[f2])).
% 1.46/1.29 thf(f2,axiom,(
% 1.46/1.29 ! [X1 : $i] : ? [X2 : $i] : (r @ X1 @ X2)),
% 1.46/1.29 file('/export/starexec/sandbox/tmp/tmp.MyXM0UsJYF/DTF2THF_878.p',rtotal)).
% 1.46/1.29 thf(f19,plain,(
% 1.46/1.29 ( ! [X0 : $i > $o,X1 : $i] : (((X0 @ X1) != $true) | ((X0 @ (eps @ X0)) = $true)) )),
% 1.46/1.29 inference(cnf_transformation,[status(thm)],[f13])).
% 1.46/1.29 thf(f13,plain,(
% 1.46/1.29 ! [X0 : $i > $o] : (((X0 @ (eps @ X0)) = $true) | ! [X1 : $i] : ((X0 @ X1) != $true))),
% 1.46/1.29 inference(ennf_transformation,[status(thm)],[f9])).
% 1.46/1.29 thf(f9,plain,(
% 1.46/1.29 ! [X0 : $i > $o] : (? [X1 : $i] : ((X0 @ X1) = $true) => ((X0 @ (eps @ X0)) = $true))),
% 1.46/1.29 inference(fool_elimination,[status(thm)],[f8])).
% 1.46/1.29 thf(f8,plain,(
% 1.46/1.29 ! [X0 : $i > $o] : (? [X1 : $i] : (X0 @ X1) => (X0 @ (eps @ X0)))),
% 1.46/1.29 inference(rectify,[status(thm)],[f1])).
% 1.46/1.29 thf(f1,axiom,(
% 1.46/1.29 ! [X0 : $i > $o] : (? [X1 : $i] : (X0 @ X1) => (X0 @ (eps @ X0)))),
% 1.46/1.29 file('/export/starexec/sandbox/tmp/tmp.MyXM0UsJYF/DTF2THF_878.p',epschoice)).
% 1.46/1.29 thf(f18,plain,(
% 1.46/1.29 ((r @ sK0 @ (eps @ (r @ sK0))) != $true)),
% 1.46/1.29 inference(cnf_transformation,[status(thm)],[f15])).
% 1.46/1.29 thf(f15,plain,(
% 1.46/1.29 ((r @ sK0 @ (eps @ (r @ sK0))) != $true)),
% 1.46/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f12,f14])).
% 1.46/1.29 thf(f14,plain,(
% 1.46/1.29 ? [X0 : $i] : ((r @ X0 @ (eps @ (r @ X0))) != $true) => ((r @ sK0 @ (eps @ (r @ sK0))) != $true)),
% 1.46/1.29 introduced(definition,[],[choice_axiom])).
% 1.46/1.29 thf(f12,plain,(
% 1.46/1.29 ? [X0 : $i] : ((r @ X0 @ (eps @ (r @ X0))) != $true)),
% 1.46/1.29 inference(ennf_transformation,[status(thm)],[f11])).
% 1.46/1.29 thf(f11,plain,(
% 1.46/1.29 ~! [X0 : $i] : ((r @ X0 @ (eps @ (r @ X0))) = $true)),
% 1.46/1.29 inference(fool_elimination,[status(thm)],[f10])).
% 1.46/1.29 thf(f10,plain,(
% 1.46/1.29 ~! [X0 : $i] : (r @ X0 @ (eps @ (r @ X0)))),
% 1.46/1.29 inference(rectify,[status(thm)],[f4])).
% 1.46/1.29 thf(f4,negated_conjecture,(
% 1.46/1.29 ~! [X1 : $i] : (r @ X1 @ (eps @ (r @ X1)))),
% 1.46/1.29 inference(negated_conjecture,[status(cth)],[f3])).
% 1.46/1.29 thf(f3,conjecture,(
% 1.46/1.29 ! [X1 : $i] : (r @ X1 @ (eps @ (r @ X1)))),
% 1.46/1.29 file('/export/starexec/sandbox/tmp/tmp.MyXM0UsJYF/DTF2THF_878.p',claim)).
% 1.46/1.29 % SZS output end Proof for DTF2THF_878
% 1.46/1.29 % (1205)------------------------------
% 1.46/1.29 % (1205)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.29 % (1205)Termination reason: Refutation
% 1.46/1.29
% 1.46/1.29 % (1205)Memory used [KB]: 5500
% 1.46/1.29 % (1205)Time elapsed: 0.003 s
% 1.46/1.29 % (1205)Instructions burned: 1 (million)
% 1.46/1.29 % (1205)------------------------------
% 1.46/1.29 % (1205)------------------------------
% 1.46/1.29 % (1201)Success in time 0.013 s
%------------------------------------------------------------------------------