%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU884^5 : 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 : n011.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 1.47s 1.29s
% Output : Refutation 1.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 133 ( 52 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 123 ( 24 ~; 14 |; 18 &; 53 @)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 33 ( 0 ^; 21 !; 12 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
cS: a > $o ).
thf(func_def_2,type,
cR: a > $o ).
thf(func_def_6,type,
sK0: a > a ).
thf(func_def_7,type,
sK1: a ).
thf(f20,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f19,f10]) ).
thf(f10,plain,
( $true
= ( cR @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X0: a] :
( ! [X1: a] :
( ( X0 != X1 )
| ( ( cR @ X1 )
!= $true ) )
| ( ( ( sK0 @ X0 )
= X0 )
& ( $true
= ( cS @ ( sK0 @ X0 ) ) ) ) )
& ( $true
!= ( cS @ sK1 ) )
& ( $true
= ( cR @ sK1 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f8,f7]) ).
thf(f7,plain,
! [X0: a] :
( ? [X2: a] :
( ( X0 = X2 )
& ( ( cS @ X2 )
= $true ) )
=> ( ( ( sK0 @ X0 )
= X0 )
& ( $true
= ( cS @ ( sK0 @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ? [X3: a] :
( ( $true
!= ( cS @ X3 ) )
& ( ( cR @ X3 )
= $true ) )
=> ( ( $true
!= ( cS @ sK1 ) )
& ( $true
= ( cR @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
( ! [X0: a] :
( ! [X1: a] :
( ( X0 != X1 )
| ( ( cR @ X1 )
!= $true ) )
| ? [X2: a] :
( ( X0 = X2 )
& ( ( cS @ X2 )
= $true ) ) )
& ? [X3: a] :
( ( $true
!= ( cS @ X3 ) )
& ( ( cR @ X3 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X0: a] :
( ? [X1: a] :
( ( ( cR @ X1 )
= $true )
& ( X0 = X1 ) )
=> ? [X2: a] :
( ( X0 = X2 )
& ( ( cS @ X2 )
= $true ) ) )
=> ! [X3: a] :
( ( ( cR @ X3 )
= $true )
=> ( $true
= ( cS @ X3 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: a] :
( ? [X1: a] :
( ( X0 = X1 )
& ( cR @ X1 ) )
=> ? [X2: a] :
( ( cS @ X2 )
& ( X0 = X2 ) ) )
=> ! [X3: a] :
( ( cR @ X3 )
=> ( cS @ X3 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: a] :
( ? [X1: a] :
( ( X0 = X1 )
& ( cR @ X1 ) )
=> ? [X1: a] :
( ( cS @ X1 )
& ( X0 = X1 ) ) )
=> ! [X0: a] :
( ( cR @ X0 )
=> ( cS @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X0: a] :
( ? [X1: a] :
( ( X0 = X1 )
& ( cR @ X1 ) )
=> ? [X1: a] :
( ( cS @ X1 )
& ( X0 = X1 ) ) )
=> ! [X0: a] :
( ( cR @ X0 )
=> ( cS @ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0Wcdqfa79k/DTF2THF_8416.p',cTHM30B_pme) ).
thf(f19,plain,
( $true
!= ( cR @ sK1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f18]) ).
thf(f18,plain,
( ( $true != $true )
| ( $true
!= ( cR @ sK1 ) ) ),
inference(superposition,[status(thm)],[f11,f17]) ).
thf(f17,plain,
! [X0: a] :
( ( ( cS @ X0 )
= $true )
| ( ( cR @ X0 )
!= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: a] :
( ( ( cS @ X0 )
= $true )
| ( ( cR @ X0 )
!= $true )
| ( ( cR @ X0 )
!= $true ) ),
inference(superposition,[status(thm)],[f15,f14]) ).
thf(f14,plain,
! [X1: a] :
( ( ( sK0 @ X1 )
= X1 )
| ( ( cR @ X1 )
!= $true ) ),
inference(equality_resolution,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: a,X1: a] :
( ( X0 != X1 )
| ( ( cR @ X1 )
!= $true )
| ( ( sK0 @ X0 )
= X0 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f15,plain,
! [X1: a] :
( ( $true
= ( cS @ ( sK0 @ X1 ) ) )
| ( ( cR @ X1 )
!= $true ) ),
inference(equality_resolution,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: a,X1: a] :
( ( X0 != X1 )
| ( ( cR @ X1 )
!= $true )
| ( $true
= ( cS @ ( sK0 @ X0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f11,plain,
( $true
!= ( cS @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU884^5 : 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
% 0.15/0.33 % Computer : n011.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 12:35:47 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
% 0.18/0.45 ---- Original DTF file ---
% 0.29/0.45 thf(spec,logic,$$dhol).
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 % File : SEU884^5 : TPTP v9.2.1. Released v4.0.0.
% 0.29/0.45 % Domain : Set Theory
% 0.29/0.45 % Problem : TPS problem THM30B
% 0.29/0.45 % Version : Especial.
% 0.29/0.45 % English :
% 0.29/0.45
% 0.29/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.45 % Source : [Bro09]
% 0.29/0.45 % Names : tps_0234 [Bro09]
% 0.29/0.45 % : THM30B [TPS]
% 0.29/0.45
% 0.29/0.45 % Status : Theorem
% 0.29/0.45 % Rating : 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 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 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.0
% 0.29/0.45 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.29/0.45 % Number of atoms : 6 ( 2 equ; 0 cnn)
% 0.29/0.45 % Maximal formula atoms : 6 ( 6 avg)
% 0.29/0.45 % Number of connectives : 9 ( 0 ~; 0 |; 2 &; 4 @)
% 0.29/0.45 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.29/0.45 % Maximal formula depth : 7 ( 7 avg)
% 0.29/0.45 % Number of types : 2 ( 1 usr)
% 0.29/0.45 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.29/0.45 % Number of symbols : 3 ( 2 usr; 0 con; 1-2 aty)
% 0.29/0.45 % Number of variables : 4 ( 0 ^; 2 !; 2 ?; 4 :)
% 0.29/0.45 % SPC : TH0_THM_EQU_NAR
% 0.29/0.45
% 0.29/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.29/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.29/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.29/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.29/0.45 % : Polymorphic definitions expanded.
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 thf(a_type,type,
% 0.29/0.45 a: $tType ).
% 0.29/0.45
% 0.29/0.45 thf(cS,type,
% 0.29/0.45 cS: a > $o ).
% 0.29/0.45
% 0.29/0.45 thf(cR,type,
% 0.29/0.45 cR: a > $o ).
% 0.29/0.45
% 0.29/0.45 thf(cTHM30B_pme,conjecture,
% 0.29/0.45 ( ! [Xx: a] :
% 0.29/0.45 ( ? [Xt: a] :
% 0.29/0.45 ( ( cR @ Xt )
% 0.29/0.45 & ( Xx = Xt ) )
% 0.29/0.45 => ? [Xt: a] :
% 0.29/0.45 ( ( cS @ Xt )
% 0.29/0.45 & ( Xx = Xt ) ) )
% 0.29/0.45 => ! [Xx: a] :
% 0.29/0.45 ( ( cR @ Xx )
% 0.29/0.45 => ( cS @ Xx ) ) ) ).
% 0.29/0.45
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 ------------------------
% 1.47/1.26 ---- Embedded in THF ---
% 1.47/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.26 %%% Generated on Tue Feb 24 12:35:48 EST 2026
% 1.47/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.26 %%% Logic specification used:
% 1.47/1.26 %%% thf(spec, logic, $$dhol).
% 1.47/1.26
% 1.47/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.0Wcdqfa79k/DTF2DTF8416.p
% See solution above
% 1.47/1.26 ------------------------
% 1.47/1.27 ---- Cleaned THF ---
% 1.47/1.27 thf(a_type,type,
% 1.47/1.27 a: $tType ).
% 1.47/1.27
% 1.47/1.27 thf(cS,type,
% 1.47/1.27 cS: a > $o ).
% 1.47/1.27
% 1.47/1.27 thf(cR,type,
% 1.47/1.27 cR: a > $o ).
% 1.47/1.27
% 1.47/1.27 thf(cTHM30B_pme,conjecture,
% 1.47/1.27 ( ! [Xx: a] :
% 1.47/1.27 ( ? [Xt: a] :
% 1.47/1.27 ( ( cR @ Xt )
% 1.47/1.27 & ( Xx = Xt ) )
% 1.47/1.27 => ? [Xt: a] :
% 1.47/1.27 ( ( cS @ Xt )
% 1.47/1.27 & ( Xx = Xt ) ) )
% 1.47/1.27 => ! [Xx: a] :
% 1.47/1.27 ( ( cR @ Xx )
% 1.47/1.27 => ( cS @ Xx ) ) ) ).
% 1.47/1.27 ------------------------
% 1.47/1.29 % (8688)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_8416 for (2999ds/275Mi)
% 1.47/1.29 % (8687)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_8416 for (2999ds/2Mi)
% 1.47/1.29 % (8688)First to succeed.
% 1.47/1.29 % (8687)Instruction limit reached!
% 1.47/1.29 % (8687)------------------------------
% 1.47/1.29 % (8687)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.29 % (8687)Termination reason: Unknown
% 1.47/1.29 % (8687)Termination phase: Saturation
% 1.47/1.29
% 1.47/1.29 % (8687)Memory used [KB]: 5500
% 1.47/1.29 % (8687)Time elapsed: 0.002 s
% 1.47/1.29 % (8687)Instructions burned: 2 (million)
% 1.47/1.29 % (8687)------------------------------
% 1.47/1.29 % (8687)------------------------------
% 1.47/1.29 % (8688)Refutation found. Thanks to Tanya!
% 1.47/1.29 % SZS status Theorem for DTF2THF_8416
% 1.47/1.29 % SZS output start Proof for DTF2THF_8416
% 1.47/1.29 thf(type_def_5, type, a: $tType).
% 1.47/1.29 thf(func_def_0, type, a: $tType).
% 1.47/1.29 thf(func_def_1, type, cS: a > $o).
% 1.47/1.29 thf(func_def_2, type, cR: a > $o).
% 1.47/1.29 thf(func_def_6, type, sK0: a > a).
% 1.47/1.29 thf(func_def_7, type, sK1: a).
% 1.47/1.29 thf(f20,plain,(
% 1.47/1.29 $false),
% 1.47/1.29 inference(subsumption_resolution,[status(thm)],[f19,f10])).
% 1.47/1.29 thf(f10,plain,(
% 1.47/1.29 ($true = (cR @ sK1))),
% 1.47/1.29 inference(cnf_transformation,[status(thm)],[f9])).
% 1.47/1.29 thf(f9,plain,(
% 1.47/1.29 ! [X0 : a] : (! [X1 : a] : ((X0 != X1) | ((cR @ X1) != $true)) | (((sK0 @ X0) = X0) & ($true = (cS @ (sK0 @ X0))))) & (($true != (cS @ sK1)) & ($true = (cR @ sK1)))),
% 1.47/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f8,f7])).
% 1.47/1.29 thf(f7,plain,(
% 1.47/1.29 ! [X0 : a] : (? [X2 : a] : ((X0 = X2) & ((cS @ X2) = $true)) => (((sK0 @ X0) = X0) & ($true = (cS @ (sK0 @ X0)))))),
% 1.47/1.29 introduced(definition,[],[choice_axiom])).
% 1.47/1.29 thf(f8,plain,(
% 1.47/1.29 ? [X3 : a] : (($true != (cS @ X3)) & ((cR @ X3) = $true)) => (($true != (cS @ sK1)) & ($true = (cR @ sK1)))),
% 1.47/1.29 introduced(definition,[],[choice_axiom])).
% 1.47/1.29 thf(f6,plain,(
% 1.47/1.29 ! [X0 : a] : (! [X1 : a] : ((X0 != X1) | ((cR @ X1) != $true)) | ? [X2 : a] : ((X0 = X2) & ((cS @ X2) = $true))) & ? [X3 : a] : (($true != (cS @ X3)) & ((cR @ X3) = $true))),
% 1.47/1.29 inference(ennf_transformation,[status(thm)],[f5])).
% 1.47/1.29 thf(f5,plain,(
% 1.47/1.29 ~(! [X0 : a] : (? [X1 : a] : (((cR @ X1) = $true) & (X0 = X1)) => ? [X2 : a] : ((X0 = X2) & ((cS @ X2) = $true))) => ! [X3 : a] : (((cR @ X3) = $true) => ($true = (cS @ X3))))),
% 1.47/1.29 inference(fool_elimination,[status(thm)],[f4])).
% 1.47/1.29 thf(f4,plain,(
% 1.47/1.29 ~(! [X0 : a] : (? [X1 : a] : ((X0 = X1) & (cR @ X1)) => ? [X2 : a] : ((cS @ X2) & (X0 = X2))) => ! [X3 : a] : ((cR @ X3) => (cS @ X3)))),
% 1.47/1.29 inference(rectify,[status(thm)],[f2])).
% 1.47/1.29 thf(f2,negated_conjecture,(
% 1.47/1.29 ~(! [X0 : a] : (? [X1 : a] : ((X0 = X1) & (cR @ X1)) => ? [X1 : a] : ((cS @ X1) & (X0 = X1))) => ! [X0 : a] : ((cR @ X0) => (cS @ X0)))),
% 1.47/1.29 inference(negated_conjecture,[status(cth)],[f1])).
% 1.47/1.29 thf(f1,conjecture,(
% 1.47/1.29 ! [X0 : a] : (? [X1 : a] : ((X0 = X1) & (cR @ X1)) => ? [X1 : a] : ((cS @ X1) & (X0 = X1))) => ! [X0 : a] : ((cR @ X0) => (cS @ X0))),
% 1.47/1.29 file('/export/starexec/sandbox/tmp/tmp.0Wcdqfa79k/DTF2THF_8416.p',cTHM30B_pme)).
% 1.47/1.29 thf(f19,plain,(
% 1.47/1.29 ($true != (cR @ sK1))),
% 1.47/1.29 inference(trivial_inequality_removal,[status(thm)],[f18])).
% 1.47/1.29 thf(f18,plain,(
% 1.47/1.29 ($true != $true) | ($true != (cR @ sK1))),
% 1.47/1.29 inference(superposition,[status(thm)],[f11,f17])).
% 1.47/1.29 thf(f17,plain,(
% 1.47/1.29 ( ! [X0 : a] : (((cS @ X0) = $true) | ((cR @ X0) != $true)) )),
% 1.47/1.29 inference(duplicate_literal_removal,[status(thm)],[f16])).
% 1.47/1.29 thf(f16,plain,(
% 1.47/1.29 ( ! [X0 : a] : (((cS @ X0) = $true) | ((cR @ X0) != $true) | ((cR @ X0) != $true)) )),
% 1.47/1.29 inference(superposition,[status(thm)],[f15,f14])).
% 1.47/1.29 thf(f14,plain,(
% 1.47/1.29 ( ! [X1 : a] : (((sK0 @ X1) = X1) | ((cR @ X1) != $true)) )),
% 1.47/1.29 inference(equality_resolution,[status(thm)],[f13])).
% 1.47/1.29 thf(f13,plain,(
% 1.47/1.29 ( ! [X0 : a,X1 : a] : ((X0 != X1) | ((cR @ X1) != $true) | ((sK0 @ X0) = X0)) )),
% 1.47/1.29 inference(cnf_transformation,[status(thm)],[f9])).
% 1.47/1.29 thf(f15,plain,(
% 1.47/1.29 ( ! [X1 : a] : (($true = (cS @ (sK0 @ X1))) | ((cR @ X1) != $true)) )),
% 1.47/1.29 inference(equality_resolution,[status(thm)],[f12])).
% 1.47/1.29 thf(f12,plain,(
% 1.47/1.29 ( ! [X0 : a,X1 : a] : ((X0 != X1) | ((cR @ X1) != $true) | ($true = (cS @ (sK0 @ X0)))) )),
% 1.47/1.29 inference(cnf_transformation,[status(thm)],[f9])).
% 1.47/1.29 thf(f11,plain,(
% 1.47/1.29 ($true != (cS @ sK1))),
% 1.47/1.29 inference(cnf_transformation,[status(thm)],[f9])).
% 1.47/1.29 % SZS output end Proof for DTF2THF_8416
% 1.47/1.29 % (8688)------------------------------
% 1.47/1.29 % (8688)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.29 % (8688)Termination reason: Refutation
% 1.47/1.29
% 1.47/1.29 % (8688)Memory used [KB]: 5500
% 1.47/1.29 % (8688)Time elapsed: 0.003 s
% 1.47/1.29 % (8688)Instructions burned: 1 (million)
% 1.47/1.29 % (8688)------------------------------
% 1.47/1.29 % (8688)------------------------------
% 1.47/1.29 % (8681)Success in time 0.012 s
%------------------------------------------------------------------------------