%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV409^5 : 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 : n029.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 09:41:11 AM UTC 2026
% Result : Theorem 1.39s 1.18s
% Output : Refutation 1.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 68 ( 26 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 128 ( 11 ~; 0 |; 16 &; 92 @)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 66 ( 66 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 43 ( 6 ^; 19 !; 18 ?; 43 :)
% 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 ).
thf(func_def_8,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f27,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f26]) ).
thf(f26,plain,
$true = $false,
inference(beta_eta_normalization,[status(thm)],[f21]) ).
thf(f21,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)],[f12]) ).
thf(f12,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( X0 @ ( sK0 @ X0 ) @ ( sK1 @ X0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( $true
= ( X0 @ ( sK1 @ X0 ) @ ( sK0 @ X0 ) ) )
& ( ( sK0 @ X0 @ ( sK2 @ X0 ) )
!= ( sK1 @ X0 @ ( sK2 @ X0 ) ) )
& ( ( X0 @ ( sK0 @ X0 ) @ ( sK1 @ X0 ) )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f10,f9]) ).
thf(f9,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X1: $i > $o,X2: $i > $o] :
( ( ( X0 @ X2 @ X1 )
= $true )
& ? [X3: $i] :
( ( X1 @ X3 )
!= ( X2 @ X3 ) )
& ( ( X0 @ X1 @ X2 )
= $true ) )
=> ( ( $true
= ( X0 @ ( sK1 @ X0 ) @ ( sK0 @ X0 ) ) )
& ? [X3: $i] :
( ( sK1 @ X0 @ X3 )
!= ( sK0 @ X0 @ X3 ) )
& ( ( X0 @ ( sK0 @ X0 ) @ ( sK1 @ X0 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X3: $i] :
( ( sK1 @ X0 @ X3 )
!= ( sK0 @ X0 @ X3 ) )
=> ( ( sK0 @ X0 @ ( sK2 @ X0 ) )
!= ( sK1 @ X0 @ ( sK2 @ X0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
? [X1: $i > $o,X2: $i > $o] :
( ( ( X0 @ X2 @ X1 )
= $true )
& ? [X3: $i] :
( ( X1 @ X3 )
!= ( X2 @ X3 ) )
& ( ( X0 @ X1 @ X2 )
= $true ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
? [X2: $i > $o,X1: $i > $o] :
( ( ( X0 @ X1 @ X2 )
= $true )
& ? [X3: $i] :
( ( X1 @ X3 )
!= ( X2 @ X3 ) )
& ( ( X0 @ X2 @ X1 )
= $true ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
? [X1: $i > $o,X2: $i > $o] :
( ? [X3: $i] :
( ( X1 @ X3 )
!= ( X2 @ X3 ) )
& ( ( X0 @ X1 @ X2 )
= $true )
& ( ( X0 @ X2 @ X1 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
! [X1: $i > $o,X2: $i > $o] :
( ( ( ( X0 @ X1 @ X2 )
= $true )
& ( ( X0 @ X2 @ X1 )
= $true ) )
=> ! [X3: $i] :
( ( X1 @ X3 )
= ( X2 @ X3 ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
! [X1: $i > $o,X2: $i > $o] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X1 ) )
=> ! [X3: $i] :
( ( X2 @ X3 )
<=> ( X1 @ X3 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
! [X2: $i > $o,X1: $i > $o] :
( ( ( X0 @ X2 @ X1 )
& ( X0 @ X1 @ X2 ) )
=> ! [X3: $i] :
( ( X1 @ X3 )
<=> ( X2 @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
! [X2: $i > $o,X1: $i > $o] :
( ( ( X0 @ X2 @ X1 )
& ( X0 @ X1 @ X2 ) )
=> ! [X3: $i] :
( ( X1 @ X3 )
<=> ( X2 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Vzzw2Rn1jF/DTF2THF_31615.p',cTHM120_BUG_pme) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV409^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.32 % Computer : n029.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue Feb 24 12:46:29 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.45 ---- Original DTF file ---
% 0.28/0.45 thf(spec,logic,$$dhol).
% 0.28/0.45 %------------------------------------------------------------------------------
% 0.28/0.45 % File : SEV409^5 : TPTP v9.2.1. Released v4.0.0.
% 0.28/0.45 % Domain : Set Theory
% 0.28/0.45 % Problem : TPS problem from SETS-THMS
% 0.28/0.45 % Version : Especial.
% 0.28/0.45 % English :
% 0.28/0.45
% 0.28/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.28/0.45 % Source : [Bro09]
% 0.28/0.45 % Names : tps_0783 [Bro09]
% 0.28/0.45
% 0.28/0.45 % Status : Theorem
% 0.28/0.45 % 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 v4.0.1, 0.33 v4.0.0
% 0.28/0.45 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.28/0.45 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.28/0.45 % Maximal formula atoms : 0 ( 0 avg)
% 0.28/0.45 % Number of connectives : 9 ( 0 ~; 0 |; 1 &; 6 @)
% 0.28/0.45 % ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% 0.28/0.45 % Maximal formula depth : 8 ( 8 avg)
% 0.28/0.45 % Number of types : 2 ( 0 usr)
% 0.28/0.45 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.28/0.45 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.28/0.45 % Number of variables : 4 ( 0 ^; 3 !; 1 ?; 4 :)
% 0.28/0.45 % SPC : TH0_THM_NEQ_NAR
% 0.28/0.45
% 0.28/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.28/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.28/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.28/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.28/0.45 %------------------------------------------------------------------------------
% 0.28/0.45 thf(cTHM120_BUG_pme,conjecture,
% 0.28/0.45 ? [R: ( $i > $o ) > ( $i > $o ) > $o] :
% 0.28/0.45 ! [X: $i > $o,Y: $i > $o] :
% 0.28/0.45 ( ( ( R @ X @ Y )
% 0.28/0.45 & ( R @ Y @ X ) )
% 0.28/0.45 => ! [Xx: $i] :
% 0.28/0.45 ( ( X @ Xx )
% 0.28/0.45 <=> ( Y @ Xx ) ) ) ).
% 0.28/0.45
% 0.28/0.45 %------------------------------------------------------------------------------
% 0.28/0.45 ------------------------
% 1.39/1.15 ---- Embedded in THF ---
% 1.39/1.15 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.39/1.15 %%% Generated on Tue Feb 24 12:46:30 EST 2026
% 1.39/1.15 %%% using '$$dhol' embedding, version 1.3.0.
% 1.39/1.15 %%% Logic specification used:
% 1.39/1.15 %%% thf(spec, logic, $$dhol).
% 1.39/1.15
% 1.39/1.15 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.Vzzw2Rn1jF/DTF2DTF31615.p
% See solution above
% 1.39/1.15 ------------------------
% 1.39/1.16 ---- Cleaned THF ---
% 1.39/1.16 thf(cTHM120_BUG_pme,conjecture,
% 1.39/1.16 ? [R: ( $i > $o ) > ( $i > $o ) > $o] :
% 1.39/1.16 ! [X: $i > $o,Y: $i > $o] :
% 1.39/1.16 ( ( ( R @ X @ Y )
% 1.39/1.16 & ( R @ Y @ X ) )
% 1.39/1.16 => ! [Xx: $i] :
% 1.39/1.16 ( ( X @ Xx )
% 1.39/1.16 <=> ( Y @ Xx ) ) ) ).
% 1.39/1.16 ------------------------
% 1.39/1.18 % (31909)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_31615 for (2999ds/4Mi)
% 1.39/1.18 % (31908)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_31615 for (2999ds/183Mi)
% 1.39/1.18 % (31909)First to succeed.
% 1.39/1.18 % (31908)Also succeeded, but the first one will report.
% 1.39/1.18 % (31909)Refutation found. Thanks to Tanya!
% 1.39/1.18 % SZS status Theorem for DTF2THF_31615
% 1.39/1.18 % SZS output start Proof for DTF2THF_31615
% 1.39/1.18 thf(func_def_3, type, sK0: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 1.39/1.18 thf(func_def_4, type, sK1: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 1.39/1.18 thf(func_def_5, type, sK2: (($i > $o) > ($i > $o) > $o) > $i).
% 1.39/1.18 thf(func_def_8, type, ph4: !>[X0: $tType]:(X0)).
% 1.39/1.18 thf(f27,plain,(
% 1.39/1.18 $false),
% 1.39/1.18 inference(trivial_inequality_removal,[status(thm)],[f26])).
% 1.39/1.18 thf(f26,plain,(
% 1.39/1.18 ($true = $false)),
% 1.39/1.18 inference(beta_eta_normalization,[status(thm)],[f21])).
% 1.39/1.18 thf(f21,plain,(
% 1.39/1.18 ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($false)))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($false))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($false)))))))),
% 1.39/1.18 inference(primitive_instantiation,[status(thm)],[f12])).
% 1.39/1.18 thf(f12,plain,(
% 1.39/1.18 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (((X0 @ (sK0 @ X0) @ (sK1 @ X0)) = $true)) )),
% 1.39/1.18 inference(cnf_transformation,[status(thm)],[f11])).
% 1.39/1.18 thf(f11,plain,(
% 1.39/1.18 ! [X0 : ($i > $o) > ($i > $o) > $o] : (($true = (X0 @ (sK1 @ X0) @ (sK0 @ X0))) & ((sK0 @ X0 @ (sK2 @ X0)) != (sK1 @ X0 @ (sK2 @ X0))) & ((X0 @ (sK0 @ X0) @ (sK1 @ X0)) = $true))),
% 1.39/1.18 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f10,f9])).
% 1.39/1.18 thf(f9,plain,(
% 1.39/1.18 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o,X2 : $i > $o] : (((X0 @ X2 @ X1) = $true) & ? [X3 : $i] : ((X1 @ X3) != (X2 @ X3)) & ((X0 @ X1 @ X2) = $true)) => (($true = (X0 @ (sK1 @ X0) @ (sK0 @ X0))) & ? [X3 : $i] : ((sK1 @ X0 @ X3) != (sK0 @ X0 @ X3)) & ((X0 @ (sK0 @ X0) @ (sK1 @ X0)) = $true)))),
% 1.39/1.18 introduced(definition,[],[choice_axiom])).
% 1.39/1.18 thf(f10,plain,(
% 1.39/1.18 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X3 : $i] : ((sK1 @ X0 @ X3) != (sK0 @ X0 @ X3)) => ((sK0 @ X0 @ (sK2 @ X0)) != (sK1 @ X0 @ (sK2 @ X0))))),
% 1.39/1.18 introduced(definition,[],[choice_axiom])).
% 1.39/1.18 thf(f8,plain,(
% 1.39/1.18 ! [X0 : ($i > $o) > ($i > $o) > $o] : ? [X1 : $i > $o,X2 : $i > $o] : (((X0 @ X2 @ X1) = $true) & ? [X3 : $i] : ((X1 @ X3) != (X2 @ X3)) & ((X0 @ X1 @ X2) = $true))),
% 1.39/1.18 inference(rectify,[status(thm)],[f7])).
% 1.39/1.18 thf(f7,plain,(
% 1.39/1.18 ! [X0 : ($i > $o) > ($i > $o) > $o] : ? [X2 : $i > $o,X1 : $i > $o] : (((X0 @ X1 @ X2) = $true) & ? [X3 : $i] : ((X1 @ X3) != (X2 @ X3)) & ((X0 @ X2 @ X1) = $true))),
% 1.39/1.18 inference(flattening,[status(thm)],[f6])).
% 1.39/1.18 thf(f6,plain,(
% 1.39/1.18 ! [X0 : ($i > $o) > ($i > $o) > $o] : ? [X1 : $i > $o,X2 : $i > $o] : (? [X3 : $i] : ((X1 @ X3) != (X2 @ X3)) & (((X0 @ X1 @ X2) = $true) & ((X0 @ X2 @ X1) = $true)))),
% 1.39/1.18 inference(ennf_transformation,[status(thm)],[f5])).
% 1.39/1.18 thf(f5,plain,(
% 1.39/1.18 ~? [X0 : ($i > $o) > ($i > $o) > $o] : ! [X1 : $i > $o,X2 : $i > $o] : ((((X0 @ X1 @ X2) = $true) & ((X0 @ X2 @ X1) = $true)) => ! [X3 : $i] : ((X1 @ X3) = (X2 @ X3)))),
% 1.39/1.18 inference(fool_elimination,[status(thm)],[f4])).
% 1.39/1.18 thf(f4,plain,(
% 1.39/1.18 ~? [X0 : ($i > $o) > ($i > $o) > $o] : ! [X1 : $i > $o,X2 : $i > $o] : (((X0 @ X1 @ X2) & (X0 @ X2 @ X1)) => ! [X3 : $i] : ((X2 @ X3) <=> (X1 @ X3)))),
% 1.39/1.18 inference(rectify,[status(thm)],[f2])).
% 1.39/1.18 thf(f2,negated_conjecture,(
% 1.39/1.18 ~? [X0 : ($i > $o) > ($i > $o) > $o] : ! [X2 : $i > $o,X1 : $i > $o] : (((X0 @ X2 @ X1) & (X0 @ X1 @ X2)) => ! [X3 : $i] : ((X1 @ X3) <=> (X2 @ X3)))),
% 1.39/1.18 inference(negated_conjecture,[status(cth)],[f1])).
% 1.39/1.18 thf(f1,conjecture,(
% 1.39/1.18 ? [X0 : ($i > $o) > ($i > $o) > $o] : ! [X2 : $i > $o,X1 : $i > $o] : (((X0 @ X2 @ X1) & (X0 @ X1 @ X2)) => ! [X3 : $i] : ((X1 @ X3) <=> (X2 @ X3)))),
% 1.39/1.18 file('/export/starexec/sandbox/tmp/tmp.Vzzw2Rn1jF/DTF2THF_31615.p',cTHM120_BUG_pme)).
% 1.39/1.18 % SZS output end Proof for DTF2THF_31615
% 1.39/1.18 % (31909)------------------------------
% 1.39/1.18 % (31909)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.39/1.18 % (31909)Termination reason: Refutation
% 1.39/1.18
% 1.39/1.18 % (31909)Memory used [KB]: 5500
% 1.39/1.18 % (31909)Time elapsed: 0.003 s
% 1.39/1.18 % (31909)Instructions burned: 2 (million)
% 1.39/1.18 % (31909)------------------------------
% 1.39/1.18 % (31909)------------------------------
% 1.39/1.18 % (31907)Success in time 0.013 s
%------------------------------------------------------------------------------