%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV228^5 : 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 : n005.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 09:40:36 AM UTC 2026
% Result : Theorem 1.66s 1.46s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 102 ( 36 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 106 ( 21 ~; 8 |; 14 &; 53 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 25 ( 0 ^; 15 !; 10 ?; 25 :)
% 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_3,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_6,type,
sK0: a ).
thf(func_def_7,type,
sK1: ( a > $o ) > a ).
thf(func_def_9,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f18,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f17]) ).
thf(f17,plain,
$true != $true,
inference(superposition,[status(thm)],[f16,f10]) ).
thf(f10,plain,
( $true
= ( cS @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X1: a > $o] :
( ( ( ( X1 @ ( sK1 @ X1 ) )
= $true )
& ( ( cS @ ( sK1 @ X1 ) )
!= $true ) )
| ( ( X1 @ sK0 )
!= $true ) )
& ( $true
= ( cS @ sK0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f8,f7]) ).
thf(f7,plain,
( ? [X0: a] :
( ! [X1: a > $o] :
( ? [X2: a] :
( ( ( X1 @ X2 )
= $true )
& ( ( cS @ X2 )
!= $true ) )
| ( ( X1 @ X0 )
!= $true ) )
& ( ( cS @ X0 )
= $true ) )
=> ( ! [X1: a > $o] :
( ? [X2: a] :
( ( ( X1 @ X2 )
= $true )
& ( ( cS @ X2 )
!= $true ) )
| ( ( X1 @ sK0 )
!= $true ) )
& ( $true
= ( cS @ sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
! [X1: a > $o] :
( ? [X2: a] :
( ( ( X1 @ X2 )
= $true )
& ( ( cS @ X2 )
!= $true ) )
=> ( ( ( X1 @ ( sK1 @ X1 ) )
= $true )
& ( ( cS @ ( sK1 @ X1 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
? [X0: a] :
( ! [X1: a > $o] :
( ? [X2: a] :
( ( ( X1 @ X2 )
= $true )
& ( ( cS @ X2 )
!= $true ) )
| ( ( X1 @ X0 )
!= $true ) )
& ( ( cS @ X0 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a] :
( ( ( cS @ X0 )
= $true )
=> ? [X1: a > $o] :
( ! [X2: a] :
( ( ( X1 @ X2 )
= $true )
=> ( ( cS @ X2 )
= $true ) )
& ( ( X1 @ X0 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a] :
( ( cS @ X0 )
=> ? [X1: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ( cS @ X2 ) )
& ( X1 @ X0 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a] :
( ( cS @ X0 )
=> ? [X1: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ( cS @ X2 ) )
& ( X1 @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a] :
( ( cS @ X0 )
=> ? [X1: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ( cS @ X2 ) )
& ( X1 @ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.17vcSoXKJp/DTF2THF_20667.p',cTHM91A_pme) ).
thf(f16,plain,
( $true
!= ( cS @ sK0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f15]) ).
thf(f15,plain,
( ( $true
!= ( cS @ sK0 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f11,f14]) ).
thf(f14,plain,
( ( cS @ ( sK1 @ cS ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f13]) ).
thf(f13,plain,
( ( $true != $true )
| ( ( cS @ ( sK1 @ cS ) )
= $true ) ),
inference(superposition,[status(thm)],[f12,f10]) ).
thf(f12,plain,
! [X1: a > $o] :
( ( ( X1 @ sK0 )
!= $true )
| ( ( X1 @ ( sK1 @ X1 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f11,plain,
! [X1: a > $o] :
( ( ( cS @ ( sK1 @ X1 ) )
!= $true )
| ( ( X1 @ sK0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV228^5 : TPTP v9.2.1. Released v4.0.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n005.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 12:42:14 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.47 ---- Original DTF file ---
% 0.20/0.47 thf(spec,logic,$$dhol).
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 % File : SEV228^5 : TPTP v9.2.1. Released v4.0.0.
% 0.20/0.47 % Domain : Set Theory (Sets of sets)
% 0.20/0.47 % Problem : TPS problem THM91A
% 0.20/0.47 % Version : Especial.
% 0.20/0.47 % English :
% 0.20/0.47
% 0.20/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.47 % Source : [Bro09]
% 0.20/0.47 % Names : tps_0187 [Bro09]
% 0.20/0.47 % : THM91A [TPS]
% 0.20/0.47
% 0.20/0.47 % Status : Theorem
% 0.20/0.47 % 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, 0.25 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, 0.00 v4.0.0
% 0.20/0.47 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.20/0.47 % Number of atoms : 2 ( 0 equ; 0 cnn)
% 0.20/0.47 % Maximal formula atoms : 2 ( 2 avg)
% 0.20/0.47 % Number of connectives : 7 ( 0 ~; 0 |; 1 &; 4 @)
% 0.20/0.47 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.20/0.47 % Maximal formula depth : 8 ( 8 avg)
% 0.20/0.47 % Number of types : 2 ( 1 usr)
% 0.20/0.47 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.20/0.47 % Number of symbols : 1 ( 1 usr; 0 con; 1-1 aty)
% 0.20/0.47 % Number of variables : 3 ( 0 ^; 2 !; 1 ?; 3 :)
% 0.20/0.47 % SPC : TH0_THM_NEQ_NAR
% 0.20/0.47
% 0.20/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.47 % : Polymorphic definitions expanded.
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 thf(a_type,type,
% 0.20/0.47 a: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(cS,type,
% 0.20/0.47 cS: a > $o ).
% 0.20/0.47
% 0.20/0.47 thf(cTHM91A_pme,conjecture,
% 0.20/0.47 ! [Xx: a] :
% 0.20/0.47 ( ( cS @ Xx )
% 0.20/0.47 => ? [S_11: a > $o] :
% 0.20/0.47 ( ! [Xx0: a] :
% 0.20/0.47 ( ( S_11 @ Xx0 )
% 0.20/0.47 => ( cS @ Xx0 ) )
% 0.20/0.47 & ( S_11 @ Xx ) ) ) ).
% 0.20/0.47
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 ------------------------
% 1.66/1.42 ---- Embedded in THF ---
% 1.66/1.42 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.66/1.42 %%% Generated on Tue Feb 24 12:42:15 EST 2026
% 1.66/1.42 %%% using '$$dhol' embedding, version 1.3.0.
% 1.66/1.42 %%% Logic specification used:
% 1.66/1.42 %%% thf(spec, logic, $$dhol).
% 1.66/1.42
% 1.66/1.42 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.17vcSoXKJp/DTF2DTF20667.p
% See solution above
% 1.66/1.42 ------------------------
% 1.66/1.43 ---- Cleaned THF ---
% 1.66/1.43 thf(a_type,type,
% 1.66/1.43 a: $tType ).
% 1.66/1.43
% 1.66/1.43 thf(cS,type,
% 1.66/1.43 cS: a > $o ).
% 1.66/1.43
% 1.66/1.43 thf(cTHM91A_pme,conjecture,
% 1.66/1.43 ! [Xx: a] :
% 1.66/1.43 ( ( cS @ Xx )
% 1.66/1.43 => ? [S_11: a > $o] :
% 1.66/1.43 ( ! [Xx0: a] :
% 1.66/1.43 ( ( S_11 @ Xx0 )
% 1.66/1.43 => ( cS @ Xx0 ) )
% 1.66/1.43 & ( S_11 @ Xx ) ) ) ).
% 1.66/1.43 ------------------------
% 1.66/1.45 % (20770)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_20667 for (3000ds/18Mi)
% 1.66/1.45 % (20764)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_20667 for (3000ds/183Mi)
% 1.66/1.45 % (20766)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_20667 for (3000ds/27Mi)
% 1.66/1.45 % (20768)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_20667 for (3000ds/2Mi)
% 1.66/1.45 % (20765)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_20667 for (3000ds/4Mi)
% 1.66/1.45 % (20767)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_20667 for (3000ds/2Mi)
% 1.66/1.45 % (20769)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_20667 for (3000ds/275Mi)
% 1.66/1.45 % (20767)Instruction limit reached!
% 1.66/1.45 % (20767)------------------------------
% 1.66/1.45 % (20767)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.45 % (20767)Termination reason: Unknown
% 1.66/1.45 % (20767)Termination phase: Saturation
% 1.66/1.45
% 1.66/1.45 % (20767)Memory used [KB]: 5500
% 1.66/1.45 % (20767)Time elapsed: 0.003 s
% 1.66/1.45 % (20767)Instructions burned: 2 (million)
% 1.66/1.45 % (20767)------------------------------
% 1.66/1.45 % (20767)------------------------------
% 1.66/1.45 % (20768)Instruction limit reached!
% 1.66/1.45 % (20768)------------------------------
% 1.66/1.45 % (20768)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.45 % (20768)Termination reason: Unknown
% 1.66/1.45 % (20768)Termination phase: Saturation
% 1.66/1.45
% 1.66/1.45 % (20768)Memory used [KB]: 5500
% 1.66/1.45 % (20768)Time elapsed: 0.003 s
% 1.66/1.45 % (20768)Instructions burned: 2 (million)
% 1.66/1.45 % (20768)------------------------------
% 1.66/1.45 % (20768)------------------------------
% 1.66/1.45 % (20766)First to succeed.
% 1.66/1.46 % (20764)Also succeeded, but the first one will report.
% 1.66/1.46 % (20770)Also succeeded, but the first one will report.
% 1.66/1.46 % (20766)Refutation found. Thanks to Tanya!
% 1.66/1.46 % SZS status Theorem for DTF2THF_20667
% 1.66/1.46 % SZS output start Proof for DTF2THF_20667
% 1.66/1.46 thf(type_def_5, type, a: $tType).
% 1.66/1.46 thf(func_def_0, type, a: $tType).
% 1.66/1.46 thf(func_def_1, type, cS: a > $o).
% 1.66/1.46 thf(func_def_3, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.66/1.46 thf(func_def_6, type, sK0: a).
% 1.66/1.46 thf(func_def_7, type, sK1: (a > $o) > a).
% 1.66/1.46 thf(func_def_9, type, ph3: !>[X0: $tType]:(X0)).
% 1.66/1.46 thf(f18,plain,(
% 1.66/1.46 $false),
% 1.66/1.46 inference(trivial_inequality_removal,[status(thm)],[f17])).
% 1.66/1.46 thf(f17,plain,(
% 1.66/1.46 ($true != $true)),
% 1.66/1.46 inference(superposition,[status(thm)],[f16,f10])).
% 1.66/1.46 thf(f10,plain,(
% 1.66/1.46 ($true = (cS @ sK0))),
% 1.66/1.46 inference(cnf_transformation,[status(thm)],[f9])).
% 1.66/1.46 thf(f9,plain,(
% 1.66/1.46 ! [X1 : a > $o] : ((((X1 @ (sK1 @ X1)) = $true) & ((cS @ (sK1 @ X1)) != $true)) | ((X1 @ sK0) != $true)) & ($true = (cS @ sK0))),
% 1.66/1.46 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f8,f7])).
% 1.66/1.46 thf(f7,plain,(
% 1.66/1.46 ? [X0 : a] : (! [X1 : a > $o] : (? [X2 : a] : (((X1 @ X2) = $true) & ((cS @ X2) != $true)) | ((X1 @ X0) != $true)) & ((cS @ X0) = $true)) => (! [X1 : a > $o] : (? [X2 : a] : (((X1 @ X2) = $true) & ((cS @ X2) != $true)) | ((X1 @ sK0) != $true)) & ($true = (cS @ sK0)))),
% 1.66/1.46 introduced(definition,[],[choice_axiom])).
% 1.66/1.46 thf(f8,plain,(
% 1.66/1.46 ! [X1 : a > $o] : (? [X2 : a] : (((X1 @ X2) = $true) & ((cS @ X2) != $true)) => (((X1 @ (sK1 @ X1)) = $true) & ((cS @ (sK1 @ X1)) != $true)))),
% 1.66/1.46 introduced(definition,[],[choice_axiom])).
% 1.66/1.46 thf(f6,plain,(
% 1.66/1.46 ? [X0 : a] : (! [X1 : a > $o] : (? [X2 : a] : (((X1 @ X2) = $true) & ((cS @ X2) != $true)) | ((X1 @ X0) != $true)) & ((cS @ X0) = $true))),
% 1.66/1.46 inference(ennf_transformation,[status(thm)],[f5])).
% 1.66/1.46 thf(f5,plain,(
% 1.66/1.46 ~! [X0 : a] : (((cS @ X0) = $true) => ? [X1 : a > $o] : (! [X2 : a] : (((X1 @ X2) = $true) => ((cS @ X2) = $true)) & ((X1 @ X0) = $true)))),
% 1.66/1.46 inference(fool_elimination,[status(thm)],[f4])).
% 1.66/1.46 thf(f4,plain,(
% 1.66/1.46 ~! [X0 : a] : ((cS @ X0) => ? [X1 : a > $o] : (! [X2 : a] : ((X1 @ X2) => (cS @ X2)) & (X1 @ X0)))),
% 1.66/1.46 inference(rectify,[status(thm)],[f2])).
% 1.66/1.46 thf(f2,negated_conjecture,(
% 1.66/1.46 ~! [X0 : a] : ((cS @ X0) => ? [X1 : a > $o] : (! [X2 : a] : ((X1 @ X2) => (cS @ X2)) & (X1 @ X0)))),
% 1.66/1.46 inference(negated_conjecture,[status(cth)],[f1])).
% 1.66/1.46 thf(f1,conjecture,(
% 1.66/1.46 ! [X0 : a] : ((cS @ X0) => ? [X1 : a > $o] : (! [X2 : a] : ((X1 @ X2) => (cS @ X2)) & (X1 @ X0)))),
% 1.66/1.46 file('/export/starexec/sandbox/tmp/tmp.17vcSoXKJp/DTF2THF_20667.p',cTHM91A_pme)).
% 1.66/1.46 thf(f16,plain,(
% 1.66/1.46 ($true != (cS @ sK0))),
% 1.66/1.46 inference(trivial_inequality_removal,[status(thm)],[f15])).
% 1.66/1.46 thf(f15,plain,(
% 1.66/1.46 ($true != (cS @ sK0)) | ($true != $true)),
% 1.66/1.46 inference(superposition,[status(thm)],[f11,f14])).
% 1.66/1.46 thf(f14,plain,(
% 1.66/1.46 ((cS @ (sK1 @ cS)) = $true)),
% 1.66/1.46 inference(trivial_inequality_removal,[status(thm)],[f13])).
% 1.66/1.46 thf(f13,plain,(
% 1.66/1.46 ($true != $true) | ((cS @ (sK1 @ cS)) = $true)),
% 1.66/1.46 inference(superposition,[status(thm)],[f12,f10])).
% 1.66/1.46 thf(f12,plain,(
% 1.66/1.46 ( ! [X1 : a > $o] : (((X1 @ sK0) != $true) | ((X1 @ (sK1 @ X1)) = $true)) )),
% 1.66/1.46 inference(cnf_transformation,[status(thm)],[f9])).
% 1.66/1.46 thf(f11,plain,(
% 1.66/1.46 ( ! [X1 : a > $o] : (((cS @ (sK1 @ X1)) != $true) | ((X1 @ sK0) != $true)) )),
% 1.66/1.46 inference(cnf_transformation,[status(thm)],[f9])).
% 1.66/1.46 % SZS output end Proof for DTF2THF_20667
% 1.66/1.46 % (20766)------------------------------
% 1.66/1.46 % (20766)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.46 % (20766)Termination reason: Refutation
% 1.66/1.46
% 1.66/1.46 % (20766)Memory used [KB]: 5500
% 1.66/1.46 % (20766)Time elapsed: 0.004 s
% 1.66/1.46 % (20766)Instructions burned: 2 (million)
% 1.66/1.46 % (20766)------------------------------
% 1.66/1.46 % (20766)------------------------------
% 1.66/1.46 % (20763)Success in time 0.014 s
%------------------------------------------------------------------------------