%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO517^1 : 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 : n001.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 1.42s 1.25s
% Output : Refutation 1.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 90 ( 37 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 122 ( 15 ~; 8 |; 14 &; 72 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 4 usr; 3 con; 0-2 aty)
% ( 0 !!; 0 ??; 3 @@+; 0 @@-)
% Number of variables : 38 ( 0 ^; 24 !; 14 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_4,type,
sK0: ( ( $i > $o ) > $i ) > $i > $o ).
thf(func_def_5,type,
sK1: ( ( $i > $o ) > $i ) > $i ).
thf(func_def_7,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f29,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f23]) ).
thf(f23,plain,
$true = $false,
inference(superposition,[status(thm)],[f11,f19]) ).
thf(f19,plain,
! [X0: $i] :
( ( sK0 @ @@+ @ $i @ X0 )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( sK0 @ @@+ @ $i @ X0 )
= $false ) ),
inference(superposition,[status(thm)],[f12,f14]) ).
thf(f14,plain,
! [X0: ( $i > $o ) > $i,X1: $i] :
( ( $true
= ( sK0 @ X0 @ ( @@+ @ $i @ ( sK0 @ X0 ) ) ) )
| ( ( sK0 @ X0 @ X1 )
= $false ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
! [X0: ( $i > $o ) > $i] :
( $true
!= ( sK0 @ X0 @ ( X0 @ ( sK0 @ X0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: ( $i > $o ) > $i] :
( ( $true
!= ( sK0 @ X0 @ ( X0 @ ( sK0 @ X0 ) ) ) )
& ( $true
= ( sK0 @ X0 @ ( sK1 @ X0 ) ) )
& ! [X3: $i] :
( ( $true
!= ( sK0 @ X0 @ X3 ) )
| ( ( sK1 @ X0 )
= X3 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f8,f7]) ).
thf(f7,plain,
! [X0: ( $i > $o ) > $i] :
( ? [X1: $i > $o] :
( ( ( X1 @ ( X0 @ X1 ) )
!= $true )
& ? [X2: $i] :
( ( ( X1 @ X2 )
= $true )
& ! [X3: $i] :
( ( ( X1 @ X3 )
!= $true )
| ( X2 = X3 ) ) ) )
=> ( ( $true
!= ( sK0 @ X0 @ ( X0 @ ( sK0 @ X0 ) ) ) )
& ? [X2: $i] :
( ( $true
= ( sK0 @ X0 @ X2 ) )
& ! [X3: $i] :
( ( $true
!= ( sK0 @ X0 @ X3 ) )
| ( X2 = X3 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
! [X0: ( $i > $o ) > $i] :
( ? [X2: $i] :
( ( $true
= ( sK0 @ X0 @ X2 ) )
& ! [X3: $i] :
( ( $true
!= ( sK0 @ X0 @ X3 ) )
| ( X2 = X3 ) ) )
=> ( ( $true
= ( sK0 @ X0 @ ( sK1 @ X0 ) ) )
& ! [X3: $i] :
( ( $true
!= ( sK0 @ X0 @ X3 ) )
| ( ( sK1 @ X0 )
= X3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
! [X0: ( $i > $o ) > $i] :
? [X1: $i > $o] :
( ( ( X1 @ ( X0 @ X1 ) )
!= $true )
& ? [X2: $i] :
( ( ( X1 @ X2 )
= $true )
& ! [X3: $i] :
( ( ( X1 @ X3 )
!= $true )
| ( X2 = X3 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ? [X0: ( $i > $o ) > $i] :
! [X1: $i > $o] :
( ? [X2: $i] :
( ( ( X1 @ X2 )
= $true )
& ! [X3: $i] :
( ( ( X1 @ X3 )
= $true )
=> ( X2 = X3 ) ) )
=> ( ( X1 @ ( X0 @ X1 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: ( $i > $o ) > $i] :
! [X1: $i > $o] :
( ? [X2: $i] :
( ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) )
& ( X1 @ X2 ) )
=> ( X1 @ ( X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X0: ( $i > $o ) > $i] :
! [X1: $i > $o] :
( ? [X2: $i] :
( ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) )
& ( X1 @ X2 ) )
=> ( X1 @ ( X0 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X0: ( $i > $o ) > $i] :
! [X1: $i > $o] :
( ? [X2: $i] :
( ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) )
& ( X1 @ X2 ) )
=> ( X1 @ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YE3VKFy6LL/DTF2THF_6863.p',descri) ).
thf(f11,plain,
! [X0: ( $i > $o ) > $i] :
( $true
= ( sK0 @ X0 @ ( sK1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SYO517^1 : TPTP v9.2.1. Released v4.1.0.
% 0.11/0.14 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n001.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 14:34:05 EST 2026
% 0.15/0.35 % CPUTime :
% 0.15/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.28/0.45 ---- Original DTF file ---
% 0.28/0.45 thf(spec,logic,$$dhol).
% 0.28/0.45 %------------------------------------------------------------------------------
% 0.28/0.45 % File : SYO517^1 : TPTP v9.2.1. Released v4.1.0.
% 0.28/0.45 % Domain : Syntactic
% 0.28/0.45 % Problem : A description operator at type i
% 0.28/0.45 % Version : Especial.
% 0.28/0.45 % English :
% 0.28/0.45
% 0.28/0.45 % Refs : [Bro09] Brown E. (2009), Email to Geoff Sutcliffe
% 0.28/0.45 % Source : [Bro09]
% 0.28/0.45 % Names : basic18 [Bro09]
% 0.28/0.45
% 0.28/0.45 % Status : Theorem
% 0.28/0.45 % Rating : 0.22 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.46 v8.1.0, 0.45 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.43 v6.1.0, 0.29 v6.0.0, 0.57 v5.5.0, 0.83 v5.4.0, 0.80 v4.1.0
% 0.28/0.45 % Syntax : Number of formulae : 1 ( 1 unt; 0 typ; 0 def)
% 0.28/0.45 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.28/0.45 % Maximal formula atoms : 1 ( 1 avg)
% 0.28/0.45 % Number of connectives : 7 ( 0 ~; 0 |; 1 &; 4 @)
% 0.28/0.45 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.28/0.45 % Maximal formula depth : 9 ( 9 avg)
% 0.28/0.45 % Number of types : 2 ( 0 usr)
% 0.28/0.45 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.28/0.45 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.28/0.45 % Number of variables : 4 ( 0 ^; 2 !; 2 ?; 4 :)
% 0.28/0.45 % SPC : TH0_THM_EQU_NAR
% 0.28/0.45
% 0.28/0.45 % Comments : This is a theorem because the default semantics is Henkin with
% 0.28/0.45 % choice.
% 0.28/0.45 %------------------------------------------------------------------------------
% 0.28/0.45 thf(descri,conjecture,
% 0.28/0.45 ? [D: ( $i > $o ) > $i] :
% 0.28/0.45 ! [P: $i > $o] :
% 0.28/0.45 ( ? [X: $i] :
% 0.28/0.45 ( ( P @ X )
% 0.28/0.45 & ! [Y: $i] :
% 0.28/0.45 ( ( P @ Y )
% 0.28/0.45 => ( X = Y ) ) )
% 0.28/0.45 => ( P @ ( D @ P ) ) ) ).
% 0.28/0.45
% 0.28/0.45 %------------------------------------------------------------------------------
% 0.28/0.45 ------------------------
% 1.42/1.23 ---- Embedded in THF ---
% 1.42/1.23 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.42/1.23 %%% Generated on Tue Feb 24 14:34:06 EST 2026
% 1.42/1.23 %%% using '$$dhol' embedding, version 1.3.0.
% 1.42/1.23 %%% Logic specification used:
% 1.42/1.23 %%% thf(spec, logic, $$dhol).
% 1.42/1.23
% 1.42/1.23 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.YE3VKFy6LL/DTF2DTF6863.p
% See solution above
% 1.42/1.23 ------------------------
% 1.42/1.24 ---- Cleaned THF ---
% 1.42/1.24 thf(descri,conjecture,
% 1.42/1.24 ? [D: ( $i > $o ) > $i] :
% 1.42/1.24 ! [P: $i > $o] :
% 1.42/1.24 ( ? [X: $i] :
% 1.42/1.24 ( ( P @ X )
% 1.42/1.24 & ! [Y: $i] :
% 1.42/1.24 ( ( P @ Y )
% 1.42/1.24 => ( X = Y ) ) )
% 1.42/1.24 => ( P @ ( D @ P ) ) ) ).
% 1.42/1.24 ------------------------
% 1.42/1.25 % (6962)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6863 for (3000ds/183Mi)
% 1.42/1.25 % (6964)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_6863 for (3000ds/27Mi)
% 1.42/1.25 % (6964)First to succeed.
% 1.42/1.25 % (6964)Refutation found. Thanks to Tanya!
% 1.42/1.25 % SZS status Theorem for DTF2THF_6863
% 1.42/1.25 % SZS output start Proof for DTF2THF_6863
% 1.42/1.25 thf(func_def_1, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.42/1.25 thf(func_def_4, type, sK0: (($i > $o) > $i) > $i > $o).
% 1.42/1.25 thf(func_def_5, type, sK1: (($i > $o) > $i) > $i).
% 1.42/1.25 thf(func_def_7, type, ph3: !>[X0: $tType]:(X0)).
% 1.42/1.25 thf(f29,plain,(
% 1.42/1.25 $false),
% 1.42/1.25 inference(trivial_inequality_removal,[status(thm)],[f23])).
% 1.42/1.25 thf(f23,plain,(
% 1.42/1.25 ($true = $false)),
% 1.42/1.25 inference(superposition,[status(thm)],[f11,f19])).
% 1.42/1.25 thf(f19,plain,(
% 1.42/1.25 ( ! [X0 : $i] : (((sK0 @ @@+ @ $i @ X0) = $false)) )),
% 1.42/1.25 inference(trivial_inequality_removal,[status(thm)],[f17])).
% 1.42/1.25 thf(f17,plain,(
% 1.42/1.25 ( ! [X0 : $i] : (($true != $true) | ((sK0 @ @@+ @ $i @ X0) = $false)) )),
% 1.42/1.25 inference(superposition,[status(thm)],[f12,f14])).
% 1.42/1.25 thf(f14,plain,(
% 1.42/1.25 ( ! [X0 : ($i > $o) > $i,X1 : $i] : (($true = (sK0 @ X0 @ (@@+ @ $i @ (sK0 @ X0)))) | ((sK0 @ X0 @ X1) = $false)) )),
% 1.42/1.25 introduced(definition,[],[choice_axiom])).
% 1.42/1.25 thf(f12,plain,(
% 1.42/1.25 ( ! [X0 : ($i > $o) > $i] : (($true != (sK0 @ X0 @ (X0 @ (sK0 @ X0))))) )),
% 1.42/1.25 inference(cnf_transformation,[status(thm)],[f9])).
% 1.42/1.25 thf(f9,plain,(
% 1.42/1.25 ! [X0 : ($i > $o) > $i] : (($true != (sK0 @ X0 @ (X0 @ (sK0 @ X0)))) & (($true = (sK0 @ X0 @ (sK1 @ X0))) & ! [X3 : $i] : (($true != (sK0 @ X0 @ X3)) | ((sK1 @ X0) = X3))))),
% 1.42/1.25 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f8,f7])).
% 1.42/1.25 thf(f7,plain,(
% 1.42/1.25 ! [X0 : ($i > $o) > $i] : (? [X1 : $i > $o] : (((X1 @ (X0 @ X1)) != $true) & ? [X2 : $i] : (((X1 @ X2) = $true) & ! [X3 : $i] : (((X1 @ X3) != $true) | (X2 = X3)))) => (($true != (sK0 @ X0 @ (X0 @ (sK0 @ X0)))) & ? [X2 : $i] : (($true = (sK0 @ X0 @ X2)) & ! [X3 : $i] : (($true != (sK0 @ X0 @ X3)) | (X2 = X3)))))),
% 1.42/1.25 introduced(definition,[],[choice_axiom])).
% 1.42/1.25 thf(f8,plain,(
% 1.42/1.25 ! [X0 : ($i > $o) > $i] : (? [X2 : $i] : (($true = (sK0 @ X0 @ X2)) & ! [X3 : $i] : (($true != (sK0 @ X0 @ X3)) | (X2 = X3))) => (($true = (sK0 @ X0 @ (sK1 @ X0))) & ! [X3 : $i] : (($true != (sK0 @ X0 @ X3)) | ((sK1 @ X0) = X3))))),
% 1.42/1.25 introduced(definition,[],[choice_axiom])).
% 1.42/1.25 thf(f6,plain,(
% 1.42/1.25 ! [X0 : ($i > $o) > $i] : ? [X1 : $i > $o] : (((X1 @ (X0 @ X1)) != $true) & ? [X2 : $i] : (((X1 @ X2) = $true) & ! [X3 : $i] : (((X1 @ X3) != $true) | (X2 = X3))))),
% 1.42/1.25 inference(ennf_transformation,[status(thm)],[f5])).
% 1.42/1.25 thf(f5,plain,(
% 1.42/1.25 ~? [X0 : ($i > $o) > $i] : ! [X1 : $i > $o] : (? [X2 : $i] : (((X1 @ X2) = $true) & ! [X3 : $i] : (((X1 @ X3) = $true) => (X2 = X3))) => ((X1 @ (X0 @ X1)) = $true))),
% 1.42/1.25 inference(fool_elimination,[status(thm)],[f4])).
% 1.42/1.25 thf(f4,plain,(
% 1.42/1.25 ~? [X0 : ($i > $o) > $i] : ! [X1 : $i > $o] : (? [X2 : $i] : (! [X3 : $i] : ((X1 @ X3) => (X2 = X3)) & (X1 @ X2)) => (X1 @ (X0 @ X1)))),
% 1.42/1.25 inference(rectify,[status(thm)],[f2])).
% 1.42/1.25 thf(f2,negated_conjecture,(
% 1.42/1.25 ~? [X0 : ($i > $o) > $i] : ! [X1 : $i > $o] : (? [X2 : $i] : (! [X3 : $i] : ((X1 @ X3) => (X2 = X3)) & (X1 @ X2)) => (X1 @ (X0 @ X1)))),
% 1.42/1.25 inference(negated_conjecture,[status(cth)],[f1])).
% 1.42/1.25 thf(f1,conjecture,(
% 1.42/1.25 ? [X0 : ($i > $o) > $i] : ! [X1 : $i > $o] : (? [X2 : $i] : (! [X3 : $i] : ((X1 @ X3) => (X2 = X3)) & (X1 @ X2)) => (X1 @ (X0 @ X1)))),
% 1.42/1.25 file('/export/starexec/sandbox/tmp/tmp.YE3VKFy6LL/DTF2THF_6863.p',descri)).
% 1.42/1.25 thf(f11,plain,(
% 1.42/1.25 ( ! [X0 : ($i > $o) > $i] : (($true = (sK0 @ X0 @ (sK1 @ X0)))) )),
% 1.42/1.25 inference(cnf_transformation,[status(thm)],[f9])).
% 1.42/1.25 % SZS output end Proof for DTF2THF_6863
% 1.42/1.25 % (6964)------------------------------
% 1.42/1.25 % (6964)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.42/1.25 % (6964)Termination reason: Refutation
% 1.42/1.25
% 1.42/1.25 % (6964)Memory used [KB]: 5500
% 1.42/1.25 % (6964)Time elapsed: 0.003 s
% 1.42/1.25 % (6964)Instructions burned: 3 (million)
% 1.42/1.25 % (6964)------------------------------
% 1.42/1.25 % (6964)------------------------------
% 1.42/1.25 % (6961)Success in time 0.012 s
%------------------------------------------------------------------------------