%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV390^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n017.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 09:41:09 AM UTC 2026
% Result : Theorem 1.18s 1.07s
% Output : Refutation 1.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 2
% Syntax : Number of formulae : 18 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 119 ( 31 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 90 ( 9 ~; 3 |; 17 &; 50 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 20 ( 9 ^; 9 !; 2 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cS: $i > $o ).
thf(func_def_1,type,
cR: $i > $o ).
thf(func_def_10,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f24,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f23,f11]) ).
thf(f11,plain,
( ( cS @ sK0 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ( cR
= ( ^ [Y0: $i] :
( ( cR @ Y0 )
& ( cS @ Y0 ) ) ) )
& ( ( cS @ sK0 )
!= $true )
& ( ( cR @ sK0 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8]) ).
thf(f8,plain,
( ? [X0: $i] :
( ( ( cS @ X0 )
!= $true )
& ( ( cR @ X0 )
= $true ) )
=> ( ( ( cS @ sK0 )
!= $true )
& ( ( cR @ sK0 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
( ( cR
= ( ^ [Y0: $i] :
( ( cR @ Y0 )
& ( cS @ Y0 ) ) ) )
& ? [X0: $i] :
( ( ( cS @ X0 )
!= $true )
& ( ( cR @ X0 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ( cR
= ( ^ [Y0: $i] :
( ( cR @ Y0 )
& ( cS @ Y0 ) ) ) )
=> ! [X0: $i] :
( ( ( cR @ X0 )
= $true )
=> ( ( cS @ X0 )
= $true ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( cR
= ( ^ [Y0: $i] :
( ( cR @ Y0 )
& ( cS @ Y0 ) ) ) )
=> ! [X1: $i] :
( ( $true
= ( cR @ X1 ) )
=> ( ( cS @ X1 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ( ^ [X0: $i] :
( ( cS @ X0 )
& ( cR @ X0 ) ) )
= cR )
=> ! [X1: $i] :
( ( cR @ X1 )
=> ( cS @ X1 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ( ^ [X0: $i] :
( ( cS @ X0 )
& ( cR @ X0 ) ) )
= cR )
=> ! [X0: $i] :
( ( cR @ X0 )
=> ( cS @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ( ^ [X0: $i] :
( ( cS @ X0 )
& ( cR @ X0 ) ) )
= cR )
=> ! [X0: $i] :
( ( cR @ X0 )
=> ( cS @ X0 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.7RjSvr9kty/DTF2THF_6085.p',cTHM35_pme) ).
thf(f23,plain,
( ( cS @ sK0 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ( cS @ sK0 )
= $true )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f10,f17]) ).
thf(f17,plain,
! [X1: $i] :
( ( ( cR @ X1 )
= $false )
| ( ( cS @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
! [X1: $i] :
( ( $true
= ( ( cR @ X1 )
& ( cS @ X1 ) ) )
| ( ( cR @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
! [X1: $i] :
( ( cR @ X1 )
= ( ( cR @ X1 )
& ( cS @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f13]) ).
thf(f13,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( cR @ Y0 )
& ( cS @ Y0 ) )
@ X1 )
= ( cR @ X1 ) ),
inference(argument_congruence,[status(thm)],[f12]) ).
thf(f12,plain,
( cR
= ( ^ [Y0: $i] :
( ( cR @ Y0 )
& ( cS @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f10,plain,
( ( cR @ sK0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SEV390^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.27 % Computer : n017.cluster.edu
% 0.08/0.27 % Model : x86_64 x86_64
% 0.08/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.27 % Memory : 8042.1875MB
% 0.08/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.27 % CPULimit : 300
% 0.08/0.27 % WCLimit : 300
% 0.08/0.27 % DateTime : Tue Feb 24 12:44:26 EST 2026
% 0.08/0.27 % CPUTime :
% 0.08/0.27 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.13/0.35 ---- Original DTF file ---
% 0.13/0.35 thf(spec,logic,$$dhol).
% 0.13/0.35 %------------------------------------------------------------------------------
% 0.13/0.35 % File : SEV390^5 : TPTP v9.2.1. Released v4.0.0.
% 0.13/0.35 % Domain : Set Theory
% 0.13/0.35 % Problem : TPS problem THM35
% 0.13/0.35 % Version : Especial.
% 0.13/0.35 % English :
% 0.13/0.35
% 0.13/0.35 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.13/0.35 % Source : [Bro09]
% 0.13/0.35 % Names : tps_0184 [Bro09]
% 0.13/0.35 % : THM35 [TPS]
% 0.13/0.35
% 0.13/0.35 % Status : Theorem
% 0.13/0.35 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 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, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.13/0.35 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.13/0.35 % Number of atoms : 6 ( 1 equ; 0 cnn)
% 0.13/0.35 % Maximal formula atoms : 3 ( 6 avg)
% 0.13/0.35 % Number of connectives : 7 ( 0 ~; 0 |; 1 &; 4 @)
% 0.13/0.35 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.13/0.35 % Maximal formula depth : 5 ( 5 avg)
% 0.13/0.35 % Number of types : 2 ( 0 usr)
% 0.13/0.35 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.13/0.35 % Number of symbols : 3 ( 2 usr; 0 con; 1-2 aty)
% 0.13/0.35 % Number of variables : 2 ( 1 ^; 1 !; 0 ?; 2 :)
% 0.13/0.35 % SPC : TH0_THM_EQU_NAR
% 0.13/0.35
% 0.13/0.35 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.13/0.35 % project in the Department of Mathematical Sciences at Carnegie
% 0.13/0.35 % Mellon University. Distributed under the Creative Commons copyleft
% 0.13/0.35 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.13/0.35 % : Polymorphic definitions expanded.
% 0.13/0.35 %------------------------------------------------------------------------------
% 0.13/0.35 thf(cS,type,
% 0.13/0.35 cS: $i > $o ).
% 0.13/0.35
% 0.13/0.35 thf(cR,type,
% 0.13/0.35 cR: $i > $o ).
% 0.13/0.35
% 0.13/0.35 thf(cTHM35_pme,conjecture,
% 0.13/0.35 ( ( ( ^ [Xx: $i] :
% 0.13/0.35 ( ( cR @ Xx )
% 0.13/0.35 & ( cS @ Xx ) ) )
% 0.13/0.35 = cR )
% 0.13/0.35 => ! [Xx: $i] :
% 0.13/0.35 ( ( cR @ Xx )
% 0.13/0.35 => ( cS @ Xx ) ) ) ).
% 0.13/0.35
% 0.13/0.35 %------------------------------------------------------------------------------
% 0.13/0.35 ------------------------
% 1.18/1.04 ---- Embedded in THF ---
% 1.18/1.04 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.18/1.04 %%% Generated on Tue Feb 24 12:44:26 EST 2026
% 1.18/1.04 %%% using '$$dhol' embedding, version 1.3.0.
% 1.18/1.04 %%% Logic specification used:
% 1.18/1.04 %%% thf(spec, logic, $$dhol).
% 1.18/1.04
% 1.18/1.04 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.7RjSvr9kty/DTF2DTF6085.p
% See solution above
% 1.18/1.04 ------------------------
% 1.18/1.05 ---- Cleaned THF ---
% 1.18/1.05 thf(cS,type,
% 1.18/1.05 cS: $i > $o ).
% 1.18/1.05
% 1.18/1.05 thf(cR,type,
% 1.18/1.05 cR: $i > $o ).
% 1.18/1.05
% 1.18/1.05 thf(cTHM35_pme,conjecture,
% 1.18/1.05 ( ( ( ^ [Xx: $i] :
% 1.18/1.05 ( ( cR @ Xx )
% 1.18/1.05 & ( cS @ Xx ) ) )
% 1.18/1.05 = cR )
% 1.18/1.05 => ! [Xx: $i] :
% 1.18/1.05 ( ( cR @ Xx )
% 1.18/1.05 => ( cS @ Xx ) ) ) ).
% 1.18/1.05 ------------------------
% 1.18/1.06 % (6228)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6085 for (3000ds/183Mi)
% 1.18/1.06 % (6228)First to succeed.
% 1.18/1.07 % (6228)Refutation found. Thanks to Tanya!
% 1.18/1.07 % SZS status Theorem for DTF2THF_6085
% 1.18/1.07 % SZS output start Proof for DTF2THF_6085
% 1.18/1.07 thf(func_def_0, type, cS: $i > $o).
% 1.18/1.07 thf(func_def_1, type, cR: $i > $o).
% 1.18/1.07 thf(func_def_10, type, ph2: !>[X0: $tType]:(X0)).
% 1.18/1.07 thf(f24,plain,(
% 1.18/1.07 $false),
% 1.18/1.07 inference(subsumption_resolution,[status(thm)],[f23,f11])).
% 1.18/1.07 thf(f11,plain,(
% 1.18/1.07 ((cS @ sK0) != $true)),
% 1.18/1.07 inference(cnf_transformation,[status(thm)],[f9])).
% 1.18/1.07 thf(f9,plain,(
% 1.18/1.07 (cR = (^[Y0 : $i]: ((cR @ Y0) & (cS @ Y0)))) & (((cS @ sK0) != $true) & ((cR @ sK0) = $true))),
% 1.18/1.07 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8])).
% 1.18/1.07 thf(f8,plain,(
% 1.18/1.07 ? [X0 : $i] : (((cS @ X0) != $true) & ((cR @ X0) = $true)) => (((cS @ sK0) != $true) & ((cR @ sK0) = $true))),
% 1.18/1.07 introduced(definition,[],[choice_axiom])).
% 1.18/1.07 thf(f7,plain,(
% 1.18/1.07 (cR = (^[Y0 : $i]: ((cR @ Y0) & (cS @ Y0)))) & ? [X0 : $i] : (((cS @ X0) != $true) & ((cR @ X0) = $true))),
% 1.18/1.07 inference(ennf_transformation,[status(thm)],[f6])).
% 1.18/1.07 thf(f6,plain,(
% 1.18/1.07 ~((cR = (^[Y0 : $i]: ((cR @ Y0) & (cS @ Y0)))) => ! [X0 : $i] : (((cR @ X0) = $true) => ((cS @ X0) = $true)))),
% 1.18/1.07 inference(rectify,[status(thm)],[f5])).
% 1.18/1.07 thf(f5,plain,(
% 1.18/1.07 ~((cR = (^[Y0 : $i]: ((cR @ Y0) & (cS @ Y0)))) => ! [X1 : $i] : (($true = (cR @ X1)) => ((cS @ X1) = $true)))),
% 1.18/1.07 inference(fool_elimination,[status(thm)],[f4])).
% 1.18/1.07 thf(f4,plain,(
% 1.18/1.07 ~(((^[X0 : $i] : ((cS @ X0) & (cR @ X0))) = cR) => ! [X1 : $i] : ((cR @ X1) => (cS @ X1)))),
% 1.18/1.07 inference(rectify,[status(thm)],[f2])).
% 1.18/1.07 thf(f2,negated_conjecture,(
% 1.18/1.07 ~(((^[X0 : $i] : ((cS @ X0) & (cR @ X0))) = cR) => ! [X0 : $i] : ((cR @ X0) => (cS @ X0)))),
% 1.18/1.07 inference(negated_conjecture,[status(cth)],[f1])).
% 1.18/1.07 thf(f1,conjecture,(
% 1.18/1.07 ((^[X0 : $i] : ((cS @ X0) & (cR @ X0))) = cR) => ! [X0 : $i] : ((cR @ X0) => (cS @ X0))),
% 1.18/1.07 file('/export/starexec/sandbox2/tmp/tmp.7RjSvr9kty/DTF2THF_6085.p',cTHM35_pme)).
% 1.18/1.07 thf(f23,plain,(
% 1.18/1.07 ((cS @ sK0) = $true)),
% 1.18/1.07 inference(trivial_inequality_removal,[status(thm)],[f21])).
% 1.18/1.07 thf(f21,plain,(
% 1.18/1.07 ((cS @ sK0) = $true) | ($true = $false)),
% 1.18/1.07 inference(superposition,[status(thm)],[f10,f17])).
% 1.18/1.07 thf(f17,plain,(
% 1.18/1.07 ( ! [X1 : $i] : (((cR @ X1) = $false) | ((cS @ X1) = $true)) )),
% 1.18/1.07 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.18/1.07 thf(f16,plain,(
% 1.18/1.07 ( ! [X1 : $i] : (($true = ((cR @ X1) & (cS @ X1))) | ((cR @ X1) = $false)) )),
% 1.18/1.07 inference(binary_proxy_clausification,[status(thm)],[f14])).
% 1.18/1.07 thf(f14,plain,(
% 1.18/1.07 ( ! [X1 : $i] : (((cR @ X1) = ((cR @ X1) & (cS @ X1)))) )),
% 1.18/1.07 inference(beta_eta_normalization,[status(thm)],[f13])).
% 1.18/1.07 thf(f13,plain,(
% 1.18/1.07 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((cR @ Y0) & (cS @ Y0))) @ X1) = (cR @ X1))) )),
% 1.18/1.07 inference(argument_congruence,[status(thm)],[f12])).
% 1.18/1.07 thf(f12,plain,(
% 1.18/1.07 (cR = (^[Y0 : $i]: ((cR @ Y0) & (cS @ Y0))))),
% 1.18/1.07 inference(cnf_transformation,[status(thm)],[f9])).
% 1.18/1.07 thf(f10,plain,(
% 1.18/1.07 ((cR @ sK0) = $true)),
% 1.18/1.07 inference(cnf_transformation,[status(thm)],[f9])).
% 1.18/1.07 % SZS output end Proof for DTF2THF_6085
% 1.18/1.07 % (6228)------------------------------
% 1.18/1.07 % (6228)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.18/1.07 % (6228)Termination reason: Refutation
% 1.18/1.07
% 1.18/1.07 % (6228)Memory used [KB]: 5500
% 1.18/1.07 % (6228)Time elapsed: 0.003 s
% 1.18/1.07 % (6228)Instructions burned: 1 (million)
% 1.18/1.07 % (6228)------------------------------
% 1.18/1.07 % (6228)------------------------------
% 1.18/1.07 % (6227)Success in time 0.012 s
%------------------------------------------------------------------------------