%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO527^1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n015.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 : Theorem 1.50s 1.29s
% Output : Refutation 1.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 42 ( 12 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 61 ( 9 ~; 0 |; 0 &; 50 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 24 ( 0 ^; 14 !; 10 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
b: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
b: $tType ).
thf(func_def_2,type,
r: a > b > $o ).
thf(func_def_6,type,
sK0: a > b ).
thf(func_def_7,type,
sK1: ( a > b ) > a ).
thf(func_def_9,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f17,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f16]) ).
thf(f16,plain,
$true != $true,
inference(superposition,[status(thm)],[f15,f14]) ).
thf(f14,plain,
! [X0: a] :
( ( r @ X0 @ ( sK0 @ X0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: a] :
( ( r @ X0 @ ( sK0 @ X0 ) )
= $true ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f10]) ).
thf(f10,plain,
! [X0: a] :
( ? [X1: b] :
( ( r @ X0 @ X1 )
= $true )
=> ( ( r @ X0 @ ( sK0 @ X0 ) )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
! [X0: a] :
? [X1: b] :
( ( r @ X0 @ X1 )
= $true ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: a] :
? [X1: b] : ( r @ X0 @ X1 ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: a] :
? [X1: b] : ( r @ X0 @ X1 ),
file('/export/starexec/sandbox/tmp/tmp.OvTwChR7eM/DTF2THF_20767.p',rtotal) ).
thf(f15,plain,
! [X0: a > b] :
( ( r @ ( sK1 @ X0 ) @ ( X0 @ ( sK1 @ X0 ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: a > b] :
( ( r @ ( sK1 @ X0 ) @ ( X0 @ ( sK1 @ X0 ) ) )
!= $true ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f9,f12]) ).
thf(f12,plain,
! [X0: a > b] :
( ? [X1: a] :
( $true
!= ( r @ X1 @ ( X0 @ X1 ) ) )
=> ( ( r @ ( sK1 @ X0 ) @ ( X0 @ ( sK1 @ X0 ) ) )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
! [X0: a > b] :
? [X1: a] :
( $true
!= ( r @ X1 @ ( X0 @ X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ? [X0: a > b] :
! [X1: a] :
( $true
= ( r @ X1 @ ( X0 @ X1 ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ? [X0: a > b] :
! [X1: a] : ( r @ X1 @ ( X0 @ X1 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ? [X2: a > b] :
! [X0: a] : ( r @ X0 @ ( X2 @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
? [X2: a > b] :
! [X0: a] : ( r @ X0 @ ( X2 @ X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.OvTwChR7eM/DTF2THF_20767.p',skolem) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO527^1 : TPTP v9.2.1. Released v5.2.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n015.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 14:33:31 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.47 thf(spec,logic,$$dhol).
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 % File : SYO527^1 : TPTP v9.2.1. Released v5.2.0.
% 0.20/0.47 % Domain : Syntactic
% 0.20/0.47 % Problem : Skolem Property on two types
% 0.20/0.47 % Version : Especial.
% 0.20/0.47 % English : For every total relation r on a * b, there is a corresponding
% 0.20/0.47 % function from a to b.
% 0.20/0.47
% 0.20/0.47 % Refs : [Bro11] Brown E. (2011), Email to Geoff Sutcliffe
% 0.20/0.47 % Source : [Bro11]
% 0.20/0.47 % Names : CHOICE3 [Bro11]
% 0.20/0.47
% 0.20/0.47 % Status : Theorem
% 0.20/0.47 % Rating : 0.25 v9.0.0, 0.17 v8.2.0, 0.18 v8.1.0, 0.17 v7.4.0, 0.11 v7.3.0, 0.20 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, 0.50 v6.1.0, 0.17 v5.5.0, 0.20 v5.4.0, 0.25 v5.2.0
% 0.20/0.47 % Syntax : Number of formulae : 5 ( 2 unt; 3 typ; 0 def)
% 0.20/0.47 % Number of atoms : 2 ( 0 equ; 0 cnn)
% 0.20/0.47 % Maximal formula atoms : 1 ( 1 avg)
% 0.20/0.47 % Number of connectives : 5 ( 0 ~; 0 |; 0 &; 5 @)
% 0.20/0.47 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.20/0.47 % Maximal formula depth : 5 ( 5 avg)
% 0.20/0.47 % Number of types : 3 ( 2 usr)
% 0.20/0.47 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.20/0.47 % Number of symbols : 1 ( 1 usr; 0 con; 2-2 aty)
% 0.20/0.47 % Number of variables : 4 ( 0 ^; 2 !; 2 ?; 4 :)
% 0.20/0.47 % SPC : TH0_THM_NEQ_NAR
% 0.20/0.47
% 0.20/0.47 % Comments : This is similar to SYN996^1 and SYO508^1, but since we use two
% 0.20/0.47 % different types there are fewer candidate instantiations. Hence
% 0.20/0.47 % this version should be easier to solve.
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 thf(a,type,
% 0.20/0.47 a: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(b,type,
% 0.20/0.47 b: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(r,type,
% 0.20/0.47 r: a > b > $o ).
% 0.20/0.47
% 0.20/0.47 thf(rtotal,axiom,
% 0.20/0.47 ! [X: a] :
% 0.20/0.47 ? [Y: b] : ( r @ X @ Y ) ).
% 0.20/0.47
% 0.20/0.47 thf(skolem,conjecture,
% 0.20/0.47 ? [F: a > b] :
% 0.20/0.47 ! [X: a] : ( r @ X @ ( F @ X ) ) ).
% 0.20/0.47
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 ------------------------
% 1.50/1.26 ---- Embedded in THF ---
% 1.50/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.26 %%% Generated on Tue Feb 24 14:33:32 EST 2026
% 1.50/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.26 %%% Logic specification used:
% 1.50/1.26 %%% thf(spec, logic, $$dhol).
% 1.50/1.26
% 1.50/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.OvTwChR7eM/DTF2DTF20767.p
% See solution above
% 1.50/1.26 ------------------------
% 1.50/1.27 ---- Cleaned THF ---
% 1.50/1.27 thf(a,type,
% 1.50/1.27 a: $tType ).
% 1.50/1.27
% 1.50/1.27 thf(b,type,
% 1.50/1.27 b: $tType ).
% 1.50/1.27
% 1.50/1.27 thf(r,type,
% 1.50/1.27 r: a > b > $o ).
% 1.50/1.27
% 1.50/1.27 thf(rtotal,axiom,
% 1.50/1.27 ! [X: a] :
% 1.50/1.27 ? [Y: b] : ( r @ X @ Y ) ).
% 1.50/1.27
% 1.50/1.27 thf(skolem,conjecture,
% 1.50/1.27 ? [F: a > b] :
% 1.50/1.27 ! [X: a] : ( r @ X @ ( F @ X ) ) ).
% 1.50/1.28 ------------------------
% 1.50/1.29 % (20955)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_20767 for (2999ds/183Mi)
% 1.50/1.29 % (20955)First to succeed.
% 1.50/1.29 % (20955)Refutation found. Thanks to Tanya!
% 1.50/1.29 % SZS status Theorem for DTF2THF_20767
% 1.50/1.29 % SZS output start Proof for DTF2THF_20767
% 1.50/1.29 thf(type_def_5, type, a: $tType).
% 1.50/1.29 thf(type_def_6, type, b: $tType).
% 1.50/1.29 thf(func_def_0, type, a: $tType).
% 1.50/1.29 thf(func_def_1, type, b: $tType).
% 1.50/1.29 thf(func_def_2, type, r: a > b > $o).
% 1.50/1.29 thf(func_def_6, type, sK0: a > b).
% 1.50/1.29 thf(func_def_7, type, sK1: (a > b) > a).
% 1.50/1.29 thf(func_def_9, type, ph3: !>[X0: $tType]:(X0)).
% 1.50/1.29 thf(f17,plain,(
% 1.50/1.29 $false),
% 1.50/1.29 inference(trivial_inequality_removal,[status(thm)],[f16])).
% 1.50/1.29 thf(f16,plain,(
% 1.50/1.29 ($true != $true)),
% 1.50/1.29 inference(superposition,[status(thm)],[f15,f14])).
% 1.50/1.29 thf(f14,plain,(
% 1.50/1.29 ( ! [X0 : a] : (((r @ X0 @ (sK0 @ X0)) = $true)) )),
% 1.50/1.29 inference(cnf_transformation,[status(thm)],[f11])).
% 1.50/1.29 thf(f11,plain,(
% 1.50/1.29 ! [X0 : a] : ((r @ X0 @ (sK0 @ X0)) = $true)),
% 1.50/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f10])).
% 1.50/1.29 thf(f10,plain,(
% 1.50/1.29 ! [X0 : a] : (? [X1 : b] : ((r @ X0 @ X1) = $true) => ((r @ X0 @ (sK0 @ X0)) = $true))),
% 1.50/1.29 introduced(definition,[],[choice_axiom])).
% 1.50/1.29 thf(f8,plain,(
% 1.50/1.29 ! [X0 : a] : ? [X1 : b] : ((r @ X0 @ X1) = $true)),
% 1.50/1.29 inference(fool_elimination,[status(thm)],[f7])).
% 1.50/1.29 thf(f7,plain,(
% 1.50/1.29 ! [X0 : a] : ? [X1 : b] : (r @ X0 @ X1)),
% 1.50/1.29 inference(rectify,[status(thm)],[f1])).
% 1.50/1.29 thf(f1,axiom,(
% 1.50/1.29 ! [X0 : a] : ? [X1 : b] : (r @ X0 @ X1)),
% 1.50/1.29 file('/export/starexec/sandbox/tmp/tmp.OvTwChR7eM/DTF2THF_20767.p',rtotal)).
% 1.50/1.29 thf(f15,plain,(
% 1.50/1.29 ( ! [X0 : a > b] : (((r @ (sK1 @ X0) @ (X0 @ (sK1 @ X0))) != $true)) )),
% 1.50/1.29 inference(cnf_transformation,[status(thm)],[f13])).
% 1.50/1.29 thf(f13,plain,(
% 1.50/1.29 ! [X0 : a > b] : ((r @ (sK1 @ X0) @ (X0 @ (sK1 @ X0))) != $true)),
% 1.50/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f9,f12])).
% 1.50/1.29 thf(f12,plain,(
% 1.50/1.29 ! [X0 : a > b] : (? [X1 : a] : ($true != (r @ X1 @ (X0 @ X1))) => ((r @ (sK1 @ X0) @ (X0 @ (sK1 @ X0))) != $true))),
% 1.50/1.29 introduced(definition,[],[choice_axiom])).
% 1.50/1.29 thf(f9,plain,(
% 1.50/1.29 ! [X0 : a > b] : ? [X1 : a] : ($true != (r @ X1 @ (X0 @ X1)))),
% 1.50/1.29 inference(ennf_transformation,[status(thm)],[f6])).
% 1.50/1.29 thf(f6,plain,(
% 1.50/1.29 ~? [X0 : a > b] : ! [X1 : a] : ($true = (r @ X1 @ (X0 @ X1)))),
% 1.50/1.29 inference(fool_elimination,[status(thm)],[f5])).
% 1.50/1.29 thf(f5,plain,(
% 1.50/1.29 ~? [X0 : a > b] : ! [X1 : a] : (r @ X1 @ (X0 @ X1))),
% 1.50/1.29 inference(rectify,[status(thm)],[f3])).
% 1.50/1.29 thf(f3,negated_conjecture,(
% 1.50/1.29 ~? [X2 : a > b] : ! [X0 : a] : (r @ X0 @ (X2 @ X0))),
% 1.50/1.29 inference(negated_conjecture,[status(cth)],[f2])).
% 1.50/1.29 thf(f2,conjecture,(
% 1.50/1.29 ? [X2 : a > b] : ! [X0 : a] : (r @ X0 @ (X2 @ X0))),
% 1.50/1.29 file('/export/starexec/sandbox/tmp/tmp.OvTwChR7eM/DTF2THF_20767.p',skolem)).
% 1.50/1.29 % SZS output end Proof for DTF2THF_20767
% 1.50/1.29 % (20955)------------------------------
% 1.50/1.29 % (20955)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.29 % (20955)Termination reason: Refutation
% 1.50/1.29
% 1.50/1.29 % (20955)Memory used [KB]: 5500
% 1.50/1.29 % (20955)Time elapsed: 0.002 s
% 1.50/1.29 % (20955)Instructions burned: 2 (million)
% 1.50/1.29 % (20955)------------------------------
% 1.50/1.29 % (20955)------------------------------
% 1.50/1.29 % (20954)Success in time 0.011 s
%------------------------------------------------------------------------------