%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV389^5 : 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 : n014.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 1.27s 1.14s
% Output : Refutation 1.27s
% 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,f12]) ).
thf(f12,plain,
( ( cS @ sK0 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ( cS @ sK0 )
!= $true )
& ( ( cR @ sK0 )
= $true )
& ( cR
= ( ^ [Y0: $i] :
( ( cR @ Y0 )
& ( cS @ Y0 ) ) ) ) ),
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,
( ? [X0: $i] :
( ( ( cS @ X0 )
!= $true )
& ( ( cR @ X0 )
= $true ) )
& ( cR
= ( ^ [Y0: $i] :
( ( cR @ Y0 )
& ( cS @ Y0 ) ) ) ) ),
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/sandbox/tmp/tmp.VFMv8KFZpO/DTF2THF_18728.p',cTHM37_pme) ).
thf(f23,plain,
( ( cS @ sK0 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f20]) ).
thf(f20,plain,
( ( $true = $false )
| ( ( cS @ sK0 )
= $true ) ),
inference(superposition,[status(thm)],[f18,f11]) ).
thf(f11,plain,
( ( cR @ sK0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f18,plain,
! [X1: $i] :
( ( $false
= ( cR @ X1 ) )
| ( ( cS @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
! [X1: $i] :
( ( $true
= ( ( cR @ X1 )
& ( cS @ X1 ) ) )
| ( $false
= ( cR @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
! [X1: $i] :
( ( ( cR @ X1 )
& ( cS @ X1 ) )
= ( cR @ 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)],[f10]) ).
thf(f10,plain,
( cR
= ( ^ [Y0: $i] :
( ( cR @ Y0 )
& ( cS @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV389^5 : 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
% 0.14/0.32 % Computer : n014.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue Feb 24 12:45:57 EST 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.32 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.42 ---- Original DTF file ---
% 0.16/0.42 thf(spec,logic,$$dhol).
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 % File : SEV389^5 : TPTP v9.2.1. Released v4.0.0.
% 0.16/0.42 % Domain : Set Theory
% 0.16/0.42 % Problem : TPS problem THM37
% 0.16/0.42 % Version : Especial.
% 0.16/0.42 % English :
% 0.16/0.42
% 0.16/0.42 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.42 % Source : [Bro09]
% 0.16/0.42 % Names : tps_0183 [Bro09]
% 0.16/0.42 % : THM37 [TPS]
% 0.16/0.42
% 0.16/0.42 % Status : Theorem
% 0.16/0.42 % 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 v6.1.0, 0.00 v6.0.0, 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
% 0.16/0.42 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.16/0.42 % Number of atoms : 6 ( 1 equ; 0 cnn)
% 0.16/0.42 % Maximal formula atoms : 3 ( 6 avg)
% 0.16/0.42 % Number of connectives : 7 ( 0 ~; 0 |; 1 &; 4 @)
% 0.16/0.42 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.16/0.42 % Maximal formula depth : 5 ( 5 avg)
% 0.16/0.42 % Number of types : 2 ( 0 usr)
% 0.16/0.42 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.16/0.42 % Number of symbols : 3 ( 2 usr; 0 con; 1-2 aty)
% 0.16/0.42 % Number of variables : 2 ( 1 ^; 1 !; 0 ?; 2 :)
% 0.16/0.42 % SPC : TH0_THM_EQU_NAR
% 0.16/0.42
% 0.16/0.42 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.42 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.42 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.42 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.42 % : Polymorphic definitions expanded.
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 thf(cS,type,
% 0.16/0.42 cS: $i > $o ).
% 0.16/0.42
% 0.16/0.42 thf(cR,type,
% 0.16/0.42 cR: $i > $o ).
% 0.16/0.42
% 0.16/0.42 thf(cTHM37_pme,conjecture,
% 0.16/0.42 ( ( cR
% 0.16/0.42 = ( ^ [Xx: $i] :
% 0.16/0.42 ( ( cR @ Xx )
% 0.16/0.42 & ( cS @ Xx ) ) ) )
% 0.16/0.42 => ! [Xx: $i] :
% 0.16/0.42 ( ( cR @ Xx )
% 0.16/0.42 => ( cS @ Xx ) ) ) ).
% 0.16/0.42
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 ------------------------
% 1.09/1.11 ---- Embedded in THF ---
% 1.09/1.11 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.09/1.11 %%% Generated on Tue Feb 24 12:45:58 EST 2026
% 1.09/1.11 %%% using '$$dhol' embedding, version 1.3.0.
% 1.09/1.11 %%% Logic specification used:
% 1.09/1.11 %%% thf(spec, logic, $$dhol).
% 1.09/1.11
% 1.09/1.11 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.VFMv8KFZpO/DTF2DTF18728.p
% See solution above
% 1.09/1.11 ------------------------
% 1.27/1.12 ---- Cleaned THF ---
% 1.27/1.12 thf(cS,type,
% 1.27/1.12 cS: $i > $o ).
% 1.27/1.12
% 1.27/1.12 thf(cR,type,
% 1.27/1.12 cR: $i > $o ).
% 1.27/1.12
% 1.27/1.12 thf(cTHM37_pme,conjecture,
% 1.27/1.12 ( ( cR
% 1.27/1.12 = ( ^ [Xx: $i] :
% 1.27/1.12 ( ( cR @ Xx )
% 1.27/1.12 & ( cS @ Xx ) ) ) )
% 1.27/1.12 => ! [Xx: $i] :
% 1.27/1.12 ( ( cR @ Xx )
% 1.27/1.12 => ( cS @ Xx ) ) ) ).
% 1.27/1.12 ------------------------
% 1.27/1.14 % (18825)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_18728 for (3000ds/183Mi)
% 1.27/1.14 % (18826)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_18728 for (3000ds/4Mi)
% 1.27/1.14 % (18830)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_18728 for (3000ds/275Mi)
% 1.27/1.14 % (18827)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_18728 for (3000ds/27Mi)
% 1.27/1.14 % (18828)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_18728 for (3000ds/2Mi)
% 1.27/1.14 % (18829)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_18728 for (3000ds/2Mi)
% 1.27/1.14 % (18831)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_18728 for (3000ds/18Mi)
% 1.27/1.14 % (18828)Instruction limit reached!
% 1.27/1.14 % (18828)------------------------------
% 1.27/1.14 % (18828)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.14 % (18828)Termination reason: Unknown
% 1.27/1.14 % (18828)Termination phase: Saturation
% 1.27/1.14
% 1.27/1.14 % (18828)Memory used [KB]: 5500
% 1.27/1.14 % (18828)Time elapsed: 0.003 s
% 1.27/1.14 % (18828)Instructions burned: 2 (million)
% 1.27/1.14 % (18828)------------------------------
% 1.27/1.14 % (18828)------------------------------
% 1.27/1.14 % (18829)Instruction limit reached!
% 1.27/1.14 % (18829)------------------------------
% 1.27/1.14 % (18829)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.14 % (18829)Termination reason: Unknown
% 1.27/1.14 % (18829)Termination phase: Saturation
% 1.27/1.14
% 1.27/1.14 % (18829)Memory used [KB]: 5500
% 1.27/1.14 % (18829)Time elapsed: 0.003 s
% 1.27/1.14 % (18829)Instructions burned: 2 (million)
% 1.27/1.14 % (18829)------------------------------
% 1.27/1.14 % (18829)------------------------------
% 1.27/1.14 % (18830)First to succeed.
% 1.27/1.14 % (18825)Also succeeded, but the first one will report.
% 1.27/1.14 % (18830)Refutation found. Thanks to Tanya!
% 1.27/1.14 % SZS status Theorem for DTF2THF_18728
% 1.27/1.14 % SZS output start Proof for DTF2THF_18728
% 1.27/1.14 thf(func_def_0, type, cS: $i > $o).
% 1.27/1.14 thf(func_def_1, type, cR: $i > $o).
% 1.27/1.14 thf(func_def_10, type, ph2: !>[X0: $tType]:(X0)).
% 1.27/1.14 thf(f24,plain,(
% 1.27/1.14 $false),
% 1.27/1.14 inference(subsumption_resolution,[status(thm)],[f23,f12])).
% 1.27/1.14 thf(f12,plain,(
% 1.27/1.14 ((cS @ sK0) != $true)),
% 1.27/1.14 inference(cnf_transformation,[status(thm)],[f9])).
% 1.27/1.14 thf(f9,plain,(
% 1.27/1.14 (((cS @ sK0) != $true) & ((cR @ sK0) = $true)) & (cR = (^[Y0 : $i]: ((cR @ Y0) & (cS @ Y0))))),
% 1.27/1.14 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8])).
% 1.27/1.14 thf(f8,plain,(
% 1.27/1.14 ? [X0 : $i] : (((cS @ X0) != $true) & ((cR @ X0) = $true)) => (((cS @ sK0) != $true) & ((cR @ sK0) = $true))),
% 1.27/1.14 introduced(definition,[],[choice_axiom])).
% 1.27/1.14 thf(f7,plain,(
% 1.27/1.14 ? [X0 : $i] : (((cS @ X0) != $true) & ((cR @ X0) = $true)) & (cR = (^[Y0 : $i]: ((cR @ Y0) & (cS @ Y0))))),
% 1.27/1.14 inference(ennf_transformation,[status(thm)],[f6])).
% 1.27/1.14 thf(f6,plain,(
% 1.27/1.14 ~((cR = (^[Y0 : $i]: ((cR @ Y0) & (cS @ Y0)))) => ! [X0 : $i] : (((cR @ X0) = $true) => ((cS @ X0) = $true)))),
% 1.27/1.14 inference(rectify,[status(thm)],[f5])).
% 1.27/1.14 thf(f5,plain,(
% 1.27/1.14 ~((cR = (^[Y0 : $i]: ((cR @ Y0) & (cS @ Y0)))) => ! [X1 : $i] : (($true = (cR @ X1)) => ((cS @ X1) = $true)))),
% 1.27/1.14 inference(fool_elimination,[status(thm)],[f4])).
% 1.27/1.14 thf(f4,plain,(
% 1.27/1.14 ~(((^[X0 : $i] : ((cS @ X0) & (cR @ X0))) = cR) => ! [X1 : $i] : ((cR @ X1) => (cS @ X1)))),
% 1.27/1.14 inference(rectify,[status(thm)],[f2])).
% 1.27/1.14 thf(f2,negated_conjecture,(
% 1.27/1.14 ~(((^[X0 : $i] : ((cS @ X0) & (cR @ X0))) = cR) => ! [X0 : $i] : ((cR @ X0) => (cS @ X0)))),
% 1.27/1.14 inference(negated_conjecture,[status(cth)],[f1])).
% 1.27/1.14 thf(f1,conjecture,(
% 1.27/1.14 ((^[X0 : $i] : ((cS @ X0) & (cR @ X0))) = cR) => ! [X0 : $i] : ((cR @ X0) => (cS @ X0))),
% 1.27/1.14 file('/export/starexec/sandbox/tmp/tmp.VFMv8KFZpO/DTF2THF_18728.p',cTHM37_pme)).
% 1.27/1.14 thf(f23,plain,(
% 1.27/1.14 ((cS @ sK0) = $true)),
% 1.27/1.14 inference(trivial_inequality_removal,[status(thm)],[f20])).
% 1.27/1.14 thf(f20,plain,(
% 1.27/1.14 ($true = $false) | ((cS @ sK0) = $true)),
% 1.27/1.14 inference(superposition,[status(thm)],[f18,f11])).
% 1.27/1.14 thf(f11,plain,(
% 1.27/1.14 ((cR @ sK0) = $true)),
% 1.27/1.14 inference(cnf_transformation,[status(thm)],[f9])).
% 1.27/1.14 thf(f18,plain,(
% 1.27/1.14 ( ! [X1 : $i] : (($false = (cR @ X1)) | ((cS @ X1) = $true)) )),
% 1.27/1.14 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.27/1.14 thf(f15,plain,(
% 1.27/1.14 ( ! [X1 : $i] : (($true = ((cR @ X1) & (cS @ X1))) | ($false = (cR @ X1))) )),
% 1.27/1.14 inference(binary_proxy_clausification,[status(thm)],[f14])).
% 1.27/1.14 thf(f14,plain,(
% 1.27/1.14 ( ! [X1 : $i] : ((((cR @ X1) & (cS @ X1)) = (cR @ X1))) )),
% 1.27/1.14 inference(beta_eta_normalization,[status(thm)],[f13])).
% 1.27/1.14 thf(f13,plain,(
% 1.27/1.14 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((cR @ Y0) & (cS @ Y0))) @ X1) = (cR @ X1))) )),
% 1.27/1.14 inference(argument_congruence,[status(thm)],[f10])).
% 1.27/1.14 thf(f10,plain,(
% 1.27/1.14 (cR = (^[Y0 : $i]: ((cR @ Y0) & (cS @ Y0))))),
% 1.27/1.14 inference(cnf_transformation,[status(thm)],[f9])).
% 1.27/1.14 % SZS output end Proof for DTF2THF_18728
% 1.27/1.14 % (18830)------------------------------
% 1.27/1.14 % (18830)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.27/1.14 % (18830)Termination reason: Refutation
% 1.27/1.14
% 1.27/1.14 % (18830)Memory used [KB]: 5500
% 1.27/1.14 % (18830)Time elapsed: 0.004 s
% 1.27/1.14 % (18830)Instructions burned: 2 (million)
% 1.27/1.14 % (18830)------------------------------
% 1.27/1.14 % (18830)------------------------------
% 1.27/1.14 % (18824)Success in time 0.018 s
%------------------------------------------------------------------------------