%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU885^5 : 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 : n002.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 09:37:40 AM UTC 2026
% Result : Theorem 1.60s 1.35s
% Output : Refutation 1.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 129 ( 54 equ; 0 cnn)
% Maximal formula atoms : 8 ( 7 avg)
% Number of connectives : 138 ( 23 ~; 12 |; 23 &; 66 @)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 35 ( 0 ^; 19 !; 16 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(type_def_6,type,
a: $tType ).
thf(func_def_0,type,
b: $tType ).
thf(func_def_1,type,
a: $tType ).
thf(func_def_2,type,
cF: b > a ).
thf(func_def_3,type,
cV: b > $o ).
thf(func_def_4,type,
cU: b > $o ).
thf(func_def_8,type,
sK0: a ).
thf(func_def_9,type,
sK1: b ).
thf(f22,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f21,f20]) ).
thf(f20,plain,
( $true
= ( cV @ sK1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f18]) ).
thf(f18,plain,
( ( $true
= ( cV @ sK1 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f11,f14]) ).
thf(f14,plain,
( $true
= ( cU @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( $true
= ( cU @ sK1 ) )
& ( sK0
= ( cF @ sK1 ) )
& ! [X2: b] :
( ( sK0
!= ( cF @ X2 ) )
| ( ( cV @ X2 )
!= $true ) )
& ! [X3: b] :
( ( $true
!= ( cU @ X3 ) )
| ( ( cV @ X3 )
= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f9,f8]) ).
thf(f8,plain,
( ? [X0: a] :
( ? [X1: b] :
( ( ( cU @ X1 )
= $true )
& ( ( cF @ X1 )
= X0 ) )
& ! [X2: b] :
( ( ( cF @ X2 )
!= X0 )
| ( ( cV @ X2 )
!= $true ) ) )
=> ( ? [X1: b] :
( ( ( cU @ X1 )
= $true )
& ( ( cF @ X1 )
= sK0 ) )
& ! [X2: b] :
( ( sK0
!= ( cF @ X2 ) )
| ( ( cV @ X2 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ? [X1: b] :
( ( ( cU @ X1 )
= $true )
& ( ( cF @ X1 )
= sK0 ) )
=> ( ( $true
= ( cU @ sK1 ) )
& ( sK0
= ( cF @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
( ? [X0: a] :
( ? [X1: b] :
( ( ( cU @ X1 )
= $true )
& ( ( cF @ X1 )
= X0 ) )
& ! [X2: b] :
( ( ( cF @ X2 )
!= X0 )
| ( ( cV @ X2 )
!= $true ) ) )
& ! [X3: b] :
( ( $true
!= ( cU @ X3 ) )
| ( ( cV @ X3 )
= $true ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
( ? [X1: a] :
( ? [X2: b] :
( ( $true
= ( cU @ X2 ) )
& ( ( cF @ X2 )
= X1 ) )
& ! [X3: b] :
( ( ( cF @ X3 )
!= X1 )
| ( ( cV @ X3 )
!= $true ) ) )
& ! [X0: b] :
( ( ( cU @ X0 )
!= $true )
| ( ( cV @ X0 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X0: b] :
( ( ( cU @ X0 )
= $true )
=> ( ( cV @ X0 )
= $true ) )
=> ! [X1: a] :
( ? [X2: b] :
( ( $true
= ( cU @ X2 ) )
& ( ( cF @ X2 )
= X1 ) )
=> ? [X3: b] :
( ( ( cV @ X3 )
= $true )
& ( ( cF @ X3 )
= X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: b] :
( ( cU @ X0 )
=> ( cV @ X0 ) )
=> ! [X1: a] :
( ? [X2: b] :
( ( cU @ X2 )
& ( ( cF @ X2 )
= X1 ) )
=> ? [X3: b] :
( ( cV @ X3 )
& ( ( cF @ X3 )
= X1 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: b] :
( ( cU @ X0 )
=> ( cV @ X0 ) )
=> ! [X0: a] :
( ? [X1: b] :
( ( cU @ X1 )
& ( ( cF @ X1 )
= X0 ) )
=> ? [X1: b] :
( ( cV @ X1 )
& ( ( cF @ X1 )
= X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X0: b] :
( ( cU @ X0 )
=> ( cV @ X0 ) )
=> ! [X0: a] :
( ? [X1: b] :
( ( cU @ X1 )
& ( ( cF @ X1 )
= X0 ) )
=> ? [X1: b] :
( ( cV @ X1 )
& ( ( cF @ X1 )
= X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.FBQpOuZx1Y/DTF2THF_23623.p',cTHM30A_pme) ).
thf(f11,plain,
! [X3: b] :
( ( $true
!= ( cU @ X3 ) )
| ( ( cV @ X3 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f21,plain,
( $true
!= ( cV @ sK1 ) ),
inference(equality_resolution,[status(thm)],[f15]) ).
thf(f15,plain,
! [X2: b] :
( ( ( cF @ X2 )
!= ( cF @ sK1 ) )
| ( ( cV @ X2 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f12,f13]) ).
thf(f13,plain,
( sK0
= ( cF @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f12,plain,
! [X2: b] :
( ( sK0
!= ( cF @ X2 ) )
| ( ( cV @ X2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU885^5 : 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
% 0.16/0.33 % Computer : n002.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 12:36:18 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.46 ---- Original DTF file ---
% 0.18/0.46 thf(spec,logic,$$dhol).
% 0.18/0.46 %------------------------------------------------------------------------------
% 0.18/0.46 % File : SEU885^5 : TPTP v9.2.1. Released v4.0.0.
% 0.18/0.46 % Domain : Set Theory
% 0.18/0.46 % Problem : TPS problem THM30A
% 0.18/0.46 % Version : Especial.
% 0.18/0.46 % English :
% 0.18/0.46
% 0.18/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.18/0.46 % Source : [Bro09]
% 0.18/0.46 % Names : tps_0241 [Bro09]
% 0.18/0.46 % : THM30A [TPS]
% 0.18/0.46
% 0.18/0.46 % Status : Theorem
% 0.18/0.46 % Rating : 0.00 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.0
% 0.18/0.46 % Syntax : Number of formulae : 6 ( 0 unt; 5 typ; 0 def)
% 0.18/0.46 % Number of atoms : 6 ( 2 equ; 0 cnn)
% 0.18/0.46 % Maximal formula atoms : 6 ( 6 avg)
% 0.18/0.46 % Number of connectives : 11 ( 0 ~; 0 |; 2 &; 6 @)
% 0.18/0.46 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.18/0.46 % Maximal formula depth : 7 ( 7 avg)
% 0.18/0.46 % Number of types : 3 ( 2 usr)
% 0.18/0.46 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.18/0.46 % Number of symbols : 4 ( 3 usr; 0 con; 1-2 aty)
% 0.18/0.46 % Number of variables : 4 ( 0 ^; 2 !; 2 ?; 4 :)
% 0.18/0.46 % SPC : TH0_THM_EQU_NAR
% 0.18/0.46
% 0.18/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.18/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.18/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.18/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.18/0.46 % : Polymorphic definitions expanded.
% 0.18/0.46 %------------------------------------------------------------------------------
% 0.18/0.46 thf(b_type,type,
% 0.18/0.46 b: $tType ).
% 0.18/0.46
% 0.18/0.46 thf(a_type,type,
% 0.18/0.46 a: $tType ).
% 0.18/0.46
% 0.18/0.46 thf(cF,type,
% 0.18/0.46 cF: b > a ).
% 0.18/0.46
% 0.18/0.46 thf(cV,type,
% 0.18/0.46 cV: b > $o ).
% 0.18/0.46
% 0.18/0.46 thf(cU,type,
% 0.18/0.46 cU: b > $o ).
% 0.18/0.46
% 0.18/0.46 thf(cTHM30A_pme,conjecture,
% 0.18/0.46 ( ! [Xx: b] :
% 0.18/0.46 ( ( cU @ Xx )
% 0.18/0.46 => ( cV @ Xx ) )
% 0.18/0.46 => ! [Xx: a] :
% 0.18/0.46 ( ? [Xt: b] :
% 0.18/0.46 ( ( cU @ Xt )
% 0.18/0.46 & ( Xx
% 0.18/0.46 = ( cF @ Xt ) ) )
% 0.18/0.46 => ? [Xt: b] :
% 0.18/0.46 ( ( cV @ Xt )
% 0.18/0.46 & ( Xx
% 0.18/0.46 = ( cF @ Xt ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 %------------------------------------------------------------------------------
% 0.18/0.46 ------------------------
% 1.60/1.31 ---- Embedded in THF ---
% 1.60/1.32 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.60/1.32 %%% Generated on Tue Feb 24 12:36:19 EST 2026
% 1.60/1.32 %%% using '$$dhol' embedding, version 1.3.0.
% 1.60/1.32 %%% Logic specification used:
% 1.60/1.32 %%% thf(spec, logic, $$dhol).
% 1.60/1.32
% 1.60/1.32 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.FBQpOuZx1Y/DTF2DTF23623.p
% See solution above
% 1.60/1.32 ------------------------
% 1.60/1.33 ---- Cleaned THF ---
% 1.60/1.33 thf(b_type,type,
% 1.60/1.33 b: $tType ).
% 1.60/1.33
% 1.60/1.33 thf(a_type,type,
% 1.60/1.33 a: $tType ).
% 1.60/1.33
% 1.60/1.33 thf(cF,type,
% 1.60/1.33 cF: b > a ).
% 1.60/1.33
% 1.60/1.33 thf(cV,type,
% 1.60/1.33 cV: b > $o ).
% 1.60/1.33
% 1.60/1.33 thf(cU,type,
% 1.60/1.33 cU: b > $o ).
% 1.60/1.33
% 1.60/1.33 thf(cTHM30A_pme,conjecture,
% 1.60/1.33 ( ! [Xx: b] :
% 1.60/1.33 ( ( cU @ Xx )
% 1.60/1.33 => ( cV @ Xx ) )
% 1.60/1.33 => ! [Xx: a] :
% 1.60/1.33 ( ? [Xt: b] :
% 1.60/1.33 ( ( cU @ Xt )
% 1.60/1.33 & ( Xx
% 1.60/1.33 = ( cF @ Xt ) ) )
% 1.60/1.33 => ? [Xt: b] :
% 1.60/1.33 ( ( cV @ Xt )
% 1.60/1.33 & ( Xx
% 1.60/1.33 = ( cF @ Xt ) ) ) ) ) ).
% 1.60/1.33 ------------------------
% 1.60/1.34 % (23827)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_23623 for (2999ds/4Mi)
% 1.60/1.34 % (23830)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_23623 for (2999ds/2Mi)
% 1.60/1.34 % (23830)Instruction limit reached!
% 1.60/1.34 % (23830)------------------------------
% 1.60/1.34 % (23830)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.34 % (23830)Termination reason: Unknown
% 1.60/1.34 % (23830)Termination phase: Saturation
% 1.60/1.34
% 1.60/1.34 % (23830)Memory used [KB]: 5500
% 1.60/1.34 % (23830)Time elapsed: 0.002 s
% 1.60/1.34 % (23830)Instructions burned: 2 (million)
% 1.60/1.34 % (23830)------------------------------
% 1.60/1.34 % (23830)------------------------------
% 1.60/1.34 % (23828)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_23623 for (2999ds/27Mi)
% 1.60/1.34 % (23827)First to succeed.
% 1.60/1.35 % (23828)Also succeeded, but the first one will report.
% 1.60/1.35 % (23827)Refutation found. Thanks to Tanya!
% 1.60/1.35 % SZS status Theorem for DTF2THF_23623
% 1.60/1.35 % SZS output start Proof for DTF2THF_23623
% 1.60/1.35 thf(type_def_5, type, b: $tType).
% 1.60/1.35 thf(type_def_6, type, a: $tType).
% 1.60/1.35 thf(func_def_0, type, b: $tType).
% 1.60/1.35 thf(func_def_1, type, a: $tType).
% 1.60/1.35 thf(func_def_2, type, cF: b > a).
% 1.60/1.35 thf(func_def_3, type, cV: b > $o).
% 1.60/1.35 thf(func_def_4, type, cU: b > $o).
% 1.60/1.35 thf(func_def_8, type, sK0: a).
% 1.60/1.35 thf(func_def_9, type, sK1: b).
% 1.60/1.35 thf(f22,plain,(
% 1.60/1.35 $false),
% 1.60/1.35 inference(subsumption_resolution,[status(thm)],[f21,f20])).
% 1.60/1.35 thf(f20,plain,(
% 1.60/1.35 ($true = (cV @ sK1))),
% 1.60/1.35 inference(trivial_inequality_removal,[status(thm)],[f18])).
% 1.60/1.35 thf(f18,plain,(
% 1.60/1.35 ($true = (cV @ sK1)) | ($true != $true)),
% 1.60/1.35 inference(superposition,[status(thm)],[f11,f14])).
% 1.60/1.35 thf(f14,plain,(
% 1.60/1.35 ($true = (cU @ sK1))),
% 1.60/1.35 inference(cnf_transformation,[status(thm)],[f10])).
% 1.60/1.35 thf(f10,plain,(
% 1.60/1.35 ((($true = (cU @ sK1)) & (sK0 = (cF @ sK1))) & ! [X2 : b] : ((sK0 != (cF @ X2)) | ((cV @ X2) != $true))) & ! [X3 : b] : (($true != (cU @ X3)) | ((cV @ X3) = $true))),
% 1.60/1.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f9,f8])).
% 1.60/1.35 thf(f8,plain,(
% 1.60/1.35 ? [X0 : a] : (? [X1 : b] : (((cU @ X1) = $true) & ((cF @ X1) = X0)) & ! [X2 : b] : (((cF @ X2) != X0) | ((cV @ X2) != $true))) => (? [X1 : b] : (((cU @ X1) = $true) & ((cF @ X1) = sK0)) & ! [X2 : b] : ((sK0 != (cF @ X2)) | ((cV @ X2) != $true)))),
% 1.60/1.35 introduced(definition,[],[choice_axiom])).
% 1.60/1.35 thf(f9,plain,(
% 1.60/1.35 ? [X1 : b] : (((cU @ X1) = $true) & ((cF @ X1) = sK0)) => (($true = (cU @ sK1)) & (sK0 = (cF @ sK1)))),
% 1.60/1.35 introduced(definition,[],[choice_axiom])).
% 1.60/1.35 thf(f7,plain,(
% 1.60/1.35 ? [X0 : a] : (? [X1 : b] : (((cU @ X1) = $true) & ((cF @ X1) = X0)) & ! [X2 : b] : (((cF @ X2) != X0) | ((cV @ X2) != $true))) & ! [X3 : b] : (($true != (cU @ X3)) | ((cV @ X3) = $true))),
% 1.60/1.35 inference(rectify,[status(thm)],[f6])).
% 1.60/1.35 thf(f6,plain,(
% 1.60/1.35 ? [X1 : a] : (? [X2 : b] : (($true = (cU @ X2)) & ((cF @ X2) = X1)) & ! [X3 : b] : (((cF @ X3) != X1) | ((cV @ X3) != $true))) & ! [X0 : b] : (((cU @ X0) != $true) | ((cV @ X0) = $true))),
% 1.60/1.35 inference(ennf_transformation,[status(thm)],[f5])).
% 1.60/1.35 thf(f5,plain,(
% 1.60/1.35 ~(! [X0 : b] : (((cU @ X0) = $true) => ((cV @ X0) = $true)) => ! [X1 : a] : (? [X2 : b] : (($true = (cU @ X2)) & ((cF @ X2) = X1)) => ? [X3 : b] : (((cV @ X3) = $true) & ((cF @ X3) = X1))))),
% 1.60/1.35 inference(fool_elimination,[status(thm)],[f4])).
% 1.60/1.35 thf(f4,plain,(
% 1.60/1.35 ~(! [X0 : b] : ((cU @ X0) => (cV @ X0)) => ! [X1 : a] : (? [X2 : b] : ((cU @ X2) & ((cF @ X2) = X1)) => ? [X3 : b] : ((cV @ X3) & ((cF @ X3) = X1))))),
% 1.60/1.35 inference(rectify,[status(thm)],[f2])).
% 1.60/1.35 thf(f2,negated_conjecture,(
% 1.60/1.35 ~(! [X0 : b] : ((cU @ X0) => (cV @ X0)) => ! [X0 : a] : (? [X1 : b] : ((cU @ X1) & ((cF @ X1) = X0)) => ? [X1 : b] : ((cV @ X1) & ((cF @ X1) = X0))))),
% 1.60/1.35 inference(negated_conjecture,[status(cth)],[f1])).
% 1.60/1.35 thf(f1,conjecture,(
% 1.60/1.35 ! [X0 : b] : ((cU @ X0) => (cV @ X0)) => ! [X0 : a] : (? [X1 : b] : ((cU @ X1) & ((cF @ X1) = X0)) => ? [X1 : b] : ((cV @ X1) & ((cF @ X1) = X0)))),
% 1.60/1.35 file('/export/starexec/sandbox/tmp/tmp.FBQpOuZx1Y/DTF2THF_23623.p',cTHM30A_pme)).
% 1.60/1.35 thf(f11,plain,(
% 1.60/1.35 ( ! [X3 : b] : (($true != (cU @ X3)) | ((cV @ X3) = $true)) )),
% 1.60/1.35 inference(cnf_transformation,[status(thm)],[f10])).
% 1.60/1.35 thf(f21,plain,(
% 1.60/1.35 ($true != (cV @ sK1))),
% 1.60/1.35 inference(equality_resolution,[status(thm)],[f15])).
% 1.60/1.35 thf(f15,plain,(
% 1.60/1.35 ( ! [X2 : b] : (((cF @ X2) != (cF @ sK1)) | ((cV @ X2) != $true)) )),
% 1.60/1.35 inference(definition_unfolding,[status(thm)],[f12,f13])).
% 1.60/1.35 thf(f13,plain,(
% 1.60/1.35 (sK0 = (cF @ sK1))),
% 1.60/1.35 inference(cnf_transformation,[status(thm)],[f10])).
% 1.60/1.35 thf(f12,plain,(
% 1.60/1.35 ( ! [X2 : b] : ((sK0 != (cF @ X2)) | ((cV @ X2) != $true)) )),
% 1.60/1.35 inference(cnf_transformation,[status(thm)],[f10])).
% 1.60/1.35 % SZS output end Proof for DTF2THF_23623
% 1.60/1.35 % (23827)------------------------------
% 1.60/1.35 % (23827)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.35 % (23827)Termination reason: Refutation
% 1.60/1.35
% 1.60/1.35 % (23827)Memory used [KB]: 5500
% 1.60/1.35 % (23827)Time elapsed: 0.004 s
% 1.60/1.35 % (23827)Instructions burned: 1 (million)
% 1.60/1.35 % (23827)------------------------------
% 1.60/1.35 % (23827)------------------------------
% 1.60/1.35 % (23825)Success in time 0.016 s
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