%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV048^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/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 09:40:09 AM UTC 2026
% Result : Theorem 1.45s 1.28s
% Output : Refutation 1.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 13 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 69 ( 24 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 110 ( 9 ~; 0 |; 16 &; 80 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 70 ( 70 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 40 ( 6 ^; 18 !; 16 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_3,type,
sK0: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_4,type,
sK1: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_5,type,
sK2: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_8,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f22,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f21]) ).
thf(f21,plain,
$false = $true,
inference(beta_eta_normalization,[status(thm)],[f17]) ).
thf(f17,plain,
( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o] : $false
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o] : $false )
@ ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : $false ) ) ),
inference(primitive_instantiation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( $true
= ( X0 @ ( sK0 @ X0 ) @ ( sK1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( $true
!= ( X0 @ ( sK2 @ X0 ) @ ( sK1 @ X0 ) ) )
& ( ( X0 @ ( sK2 @ X0 ) @ ( sK0 @ X0 ) )
= $true )
& ( $true
= ( X0 @ ( sK0 @ X0 ) @ ( sK1 @ X0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f9]) ).
thf(f9,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ( ( X0 @ X3 @ X2 )
!= $true )
& ( ( X0 @ X3 @ X1 )
= $true )
& ( ( X0 @ X1 @ X2 )
= $true ) )
=> ( ( $true
!= ( X0 @ ( sK2 @ X0 ) @ ( sK1 @ X0 ) ) )
& ( ( X0 @ ( sK2 @ X0 ) @ ( sK0 @ X0 ) )
= $true )
& ( $true
= ( X0 @ ( sK0 @ X0 ) @ ( sK1 @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
? [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ( ( X0 @ X3 @ X2 )
!= $true )
& ( ( X0 @ X3 @ X1 )
= $true )
& ( ( X0 @ X1 @ X2 )
= $true ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
? [X2: $i > $o,X3: $i > $o,X1: $i > $o] :
( ( ( X0 @ X1 @ X3 )
!= $true )
& ( ( X0 @ X1 @ X2 )
= $true )
& ( ( X0 @ X2 @ X3 )
= $true ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
? [X1: $i > $o,X3: $i > $o,X2: $i > $o] :
( ( ( X0 @ X1 @ X3 )
!= $true )
& ( ( X0 @ X1 @ X2 )
= $true )
& ( ( X0 @ X2 @ X3 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
! [X1: $i > $o,X3: $i > $o,X2: $i > $o] :
( ( ( ( X0 @ X1 @ X2 )
= $true )
& ( ( X0 @ X2 @ X3 )
= $true ) )
=> ( ( X0 @ X1 @ X3 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
! [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X1 @ X3 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
! [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X1 @ X3 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
! [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X1 @ X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.RmnEg0cQ2g/DTF2THF_20546.p',cTHM120_pme) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV048^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n003.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 12:39:10 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 : SEV048^5 : TPTP v9.2.1. Released v4.0.0.
% 0.28/0.46 % Domain : Set Theory (Relations)
% 0.28/0.46 % Problem : TPS problem THM120
% 0.28/0.46 % Version : Especial.
% 0.28/0.46 % English : There exists a transitive relation on sets.
% 0.28/0.46
% 0.28/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.28/0.46 % Source : [Bro09]
% 0.28/0.46 % Names : tps_0107 [Bro09]
% 0.28/0.46 % : THM120 [TPS]
% 0.28/0.46
% 0.28/0.46 % Status : Theorem
% 0.28/0.46 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 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, 0.33 v6.1.0, 0.17 v6.0.0, 0.00 v4.0.0
% 0.28/0.46 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.28/0.46 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.28/0.46 % Maximal formula atoms : 0 ( 0 avg)
% 0.28/0.46 % Number of connectives : 8 ( 0 ~; 0 |; 1 &; 6 @)
% 0.28/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.28/0.46 % Maximal formula depth : 9 ( 9 avg)
% 0.28/0.46 % Number of types : 2 ( 0 usr)
% 0.28/0.46 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.28/0.46 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.28/0.46 % Number of variables : 4 ( 0 ^; 3 !; 1 ?; 4 :)
% 0.28/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.28/0.46
% 0.28/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.28/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.28/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.28/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.28/0.46 % : Polymorphic definitions expanded.
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 thf(cTHM120_pme,conjecture,
% 0.28/0.46 ? [R: ( $i > $o ) > ( $i > $o ) > $o] :
% 0.28/0.46 ! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
% 0.28/0.46 ( ( ( R @ Xx @ Xy )
% 0.28/0.46 & ( R @ Xy @ Xz ) )
% 0.28/0.46 => ( R @ Xx @ Xz ) ) ).
% 0.28/0.46
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 ------------------------
% 1.45/1.25 ---- Embedded in THF ---
% 1.45/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.45/1.25 %%% Generated on Tue Feb 24 12:39:11 EST 2026
% 1.45/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.45/1.25 %%% Logic specification used:
% 1.45/1.25 %%% thf(spec, logic, $$dhol).
% 1.45/1.25
% 1.45/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.RmnEg0cQ2g/DTF2DTF20546.p
% See solution above
% 1.45/1.25 ------------------------
% 1.45/1.26 ---- Cleaned THF ---
% 1.45/1.27 thf(cTHM120_pme,conjecture,
% 1.45/1.27 ? [R: ( $i > $o ) > ( $i > $o ) > $o] :
% 1.45/1.27 ! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
% 1.45/1.27 ( ( ( R @ Xx @ Xy )
% 1.45/1.27 & ( R @ Xy @ Xz ) )
% 1.45/1.27 => ( R @ Xx @ Xz ) ) ).
% 1.45/1.27 ------------------------
% 1.45/1.28 % (20849)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_20546 for (2999ds/2Mi)
% 1.45/1.28 % (20849)First to succeed.
% 1.45/1.28 % (20849)Refutation found. Thanks to Tanya!
% 1.45/1.28 % SZS status Theorem for DTF2THF_20546
% 1.45/1.28 % SZS output start Proof for DTF2THF_20546
% 1.45/1.28 thf(func_def_3, type, sK0: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 1.45/1.28 thf(func_def_4, type, sK1: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 1.45/1.28 thf(func_def_5, type, sK2: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 1.45/1.28 thf(func_def_8, type, ph4: !>[X0: $tType]:(X0)).
% 1.45/1.28 thf(f22,plain,(
% 1.45/1.28 $false),
% 1.45/1.28 inference(trivial_inequality_removal,[status(thm)],[f21])).
% 1.45/1.28 thf(f21,plain,(
% 1.45/1.28 ($false = $true)),
% 1.45/1.28 inference(beta_eta_normalization,[status(thm)],[f17])).
% 1.45/1.28 thf(f17,plain,(
% 1.45/1.28 ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($false)))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($false))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($false)))))))),
% 1.45/1.28 inference(primitive_instantiation,[status(thm)],[f11])).
% 1.45/1.28 thf(f11,plain,(
% 1.45/1.28 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (($true = (X0 @ (sK0 @ X0) @ (sK1 @ X0)))) )),
% 1.45/1.28 inference(cnf_transformation,[status(thm)],[f10])).
% 1.45/1.28 thf(f10,plain,(
% 1.45/1.28 ! [X0 : ($i > $o) > ($i > $o) > $o] : (($true != (X0 @ (sK2 @ X0) @ (sK1 @ X0))) & ((X0 @ (sK2 @ X0) @ (sK0 @ X0)) = $true) & ($true = (X0 @ (sK0 @ X0) @ (sK1 @ X0))))),
% 1.45/1.28 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f9])).
% 1.45/1.28 thf(f9,plain,(
% 1.45/1.28 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o,X2 : $i > $o,X3 : $i > $o] : (((X0 @ X3 @ X2) != $true) & ((X0 @ X3 @ X1) = $true) & ((X0 @ X1 @ X2) = $true)) => (($true != (X0 @ (sK2 @ X0) @ (sK1 @ X0))) & ((X0 @ (sK2 @ X0) @ (sK0 @ X0)) = $true) & ($true = (X0 @ (sK0 @ X0) @ (sK1 @ X0)))))),
% 1.45/1.28 introduced(definition,[],[choice_axiom])).
% 1.45/1.28 thf(f8,plain,(
% 1.45/1.28 ! [X0 : ($i > $o) > ($i > $o) > $o] : ? [X1 : $i > $o,X2 : $i > $o,X3 : $i > $o] : (((X0 @ X3 @ X2) != $true) & ((X0 @ X3 @ X1) = $true) & ((X0 @ X1 @ X2) = $true))),
% 1.45/1.28 inference(rectify,[status(thm)],[f7])).
% 1.45/1.28 thf(f7,plain,(
% 1.45/1.28 ! [X0 : ($i > $o) > ($i > $o) > $o] : ? [X2 : $i > $o,X3 : $i > $o,X1 : $i > $o] : (((X0 @ X1 @ X3) != $true) & ((X0 @ X1 @ X2) = $true) & ((X0 @ X2 @ X3) = $true))),
% 1.45/1.28 inference(flattening,[status(thm)],[f6])).
% 1.45/1.28 thf(f6,plain,(
% 1.45/1.28 ! [X0 : ($i > $o) > ($i > $o) > $o] : ? [X1 : $i > $o,X3 : $i > $o,X2 : $i > $o] : (((X0 @ X1 @ X3) != $true) & (((X0 @ X1 @ X2) = $true) & ((X0 @ X2 @ X3) = $true)))),
% 1.45/1.28 inference(ennf_transformation,[status(thm)],[f5])).
% 1.45/1.28 thf(f5,plain,(
% 1.45/1.28 ~? [X0 : ($i > $o) > ($i > $o) > $o] : ! [X1 : $i > $o,X3 : $i > $o,X2 : $i > $o] : ((((X0 @ X1 @ X2) = $true) & ((X0 @ X2 @ X3) = $true)) => ((X0 @ X1 @ X3) = $true))),
% 1.45/1.28 inference(fool_elimination,[status(thm)],[f4])).
% 1.45/1.28 thf(f4,plain,(
% 1.45/1.28 ~? [X0 : ($i > $o) > ($i > $o) > $o] : ! [X1 : $i > $o,X2 : $i > $o,X3 : $i > $o] : (((X0 @ X1 @ X2) & (X0 @ X2 @ X3)) => (X0 @ X1 @ X3))),
% 1.45/1.28 inference(rectify,[status(thm)],[f2])).
% 1.45/1.28 thf(f2,negated_conjecture,(
% 1.45/1.28 ~? [X0 : ($i > $o) > ($i > $o) > $o] : ! [X1 : $i > $o,X2 : $i > $o,X3 : $i > $o] : (((X0 @ X1 @ X2) & (X0 @ X2 @ X3)) => (X0 @ X1 @ X3))),
% 1.45/1.28 inference(negated_conjecture,[status(cth)],[f1])).
% 1.45/1.28 thf(f1,conjecture,(
% 1.45/1.28 ? [X0 : ($i > $o) > ($i > $o) > $o] : ! [X1 : $i > $o,X2 : $i > $o,X3 : $i > $o] : (((X0 @ X1 @ X2) & (X0 @ X2 @ X3)) => (X0 @ X1 @ X3))),
% 1.45/1.28 file('/export/starexec/sandbox/tmp/tmp.RmnEg0cQ2g/DTF2THF_20546.p',cTHM120_pme)).
% 1.45/1.28 % SZS output end Proof for DTF2THF_20546
% 1.45/1.28 % (20849)------------------------------
% 1.45/1.28 % (20849)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.28 % (20849)Termination reason: Refutation
% 1.45/1.28
% 1.45/1.28 % (20849)Memory used [KB]: 5500
% 1.45/1.28 % (20849)Time elapsed: 0.003 s
% 1.45/1.28 % (20849)Instructions burned: 1 (million)
% 1.45/1.28 % (20849)------------------------------
% 1.45/1.28 % (20849)------------------------------
% 1.45/1.28 % (20845)Success in time 0.013 s
%------------------------------------------------------------------------------