%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU559^2 : TPTP v9.2.1. Released v3.7.0.
% 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 09:35:16 AM UTC 2026
% Result : Theorem 1.55s 1.31s
% Output : Refutation 1.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 2
% Syntax : Number of formulae : 18 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 90 ( 14 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 159 ( 7 ~; 0 |; 0 &; 110 @)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 5 usr; 5 con; 0-2 aty)
% ( 22 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 45 ( 34 ^; 11 !; 0 ?; 45 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
subset: $i > $i > $o ).
thf(func_def_14,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f19,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f18]) ).
thf(f18,plain,
$true = $false,
inference(beta_eta_normalization,[status(thm)],[f17]) ).
thf(f17,plain,
( $false
= ( ^ [Y0: $i] : $true
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] : $true ) ),
inference(beta_eta_normalization,[status(thm)],[f15]) ).
thf(f15,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : $true )
@ sK2 ) ),
inference(sigma_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : $true ) ) ),
inference(not_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : $true ) ) ) ),
inference(boolean_simplification,[status(thm)],[f12]) ).
thf(f12,plain,
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f11]) ).
thf(f11,plain,
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ^ [Y2: $i,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( in @ Y4 @ Y3 ) ) )
@ Y0
@ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f9,f10]) ).
thf(f10,plain,
( subset
= ( ^ [Y0: $i,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( subset
= ( ^ [Y0: $i,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ^ [X0: $i,X1: $i] :
! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) )
= subset ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: $i,X1: $i] :
! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) )
= subset ),
file('/export/starexec/sandbox/tmp/tmp.o2dWN1FRHB/DTF2THF_18328.p',subset) ).
thf(f9,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( subset @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( subset @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( subset @ X1 @ X0 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.o2dWN1FRHB/DTF2THF_18328.p',subsetI1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU559^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.29 % Computer : n014.cluster.edu
% 0.12/0.29 % Model : x86_64 x86_64
% 0.12/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.29 % Memory : 8042.1875MB
% 0.12/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.29 % CPULimit : 300
% 0.12/0.29 % WCLimit : 300
% 0.12/0.29 % DateTime : Tue Feb 24 12:26:57 EST 2026
% 0.12/0.29 % CPUTime :
% 0.12/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.38 ---- Original DTF file ---
% 0.19/0.38 thf(spec,logic,$$dhol).
% 0.19/0.38 %------------------------------------------------------------------------------
% 0.19/0.38 % File : SEU559^2 : TPTP v9.2.1. Released v3.7.0.
% 0.19/0.38 % Domain : Set Theory
% 0.19/0.38 % Problem : Preliminary Notions - Relations on Sets - Subsets
% 0.19/0.38 % Version : Especial > Reduced > Especial.
% 0.19/0.38 % English : (! A:i.! B:i.(! x:i.in x A -> in x B) -> subset A B)
% 0.19/0.38
% 0.19/0.38 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.19/0.38 % Source : [Bro08]
% 0.19/0.38 % Names : ZFC061l [Bro08]
% 0.19/0.38
% 0.19/0.38 % Status : Theorem
% 0.19/0.38 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v5.0.0, 0.40 v4.1.0, 0.00 v3.7.0
% 0.19/0.38 % Syntax : Number of formulae : 4 ( 1 unt; 2 typ; 1 def)
% 0.19/0.38 % Number of atoms : 7 ( 1 equ; 0 cnn)
% 0.19/0.38 % Maximal formula atoms : 3 ( 3 avg)
% 0.19/0.38 % Number of connectives : 13 ( 0 ~; 0 |; 0 &; 10 @)
% 0.19/0.38 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.19/0.38 % Maximal formula depth : 8 ( 5 avg)
% 0.19/0.38 % Number of types : 2 ( 0 usr)
% 0.19/0.38 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.19/0.38 % Number of symbols : 3 ( 2 usr; 0 con; 2-2 aty)
% 0.19/0.38 % Number of variables : 6 ( 2 ^; 4 !; 0 ?; 6 :)
% 0.19/0.38 % SPC : TH0_THM_EQU_NAR
% 0.19/0.38
% 0.19/0.38 % Comments : http://mathgate.info/detsetitem.php?id=150
% 0.19/0.38 %------------------------------------------------------------------------------
% 0.19/0.38 thf(in_type,type,
% 0.19/0.38 in: $i > $i > $o ).
% 0.19/0.38
% 0.19/0.38 thf(subset_type,type,
% 0.19/0.38 subset: $i > $i > $o ).
% 0.19/0.38
% 0.19/0.38 thf(subset,definition,
% 0.19/0.38 ( subset
% 0.19/0.38 = ( ^ [A: $i,B: $i] :
% 0.19/0.38 ! [Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ A )
% 0.19/0.38 => ( in @ Xx @ B ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(subsetI1,conjecture,
% 0.19/0.38 ! [A: $i,B: $i] :
% 0.19/0.38 ( ! [Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ A )
% 0.19/0.38 => ( in @ Xx @ B ) )
% 0.19/0.38 => ( subset @ A @ B ) ) ).
% 0.19/0.38
% 0.19/0.38 %------------------------------------------------------------------------------
% 0.19/0.38 ------------------------
% 1.37/1.28 ---- Embedded in THF ---
% 1.37/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.37/1.28 %%% Generated on Tue Feb 24 12:26:58 EST 2026
% 1.37/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.37/1.28 %%% Logic specification used:
% 1.37/1.28 %%% thf(spec, logic, $$dhol).
% 1.37/1.28
% 1.37/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.o2dWN1FRHB/DTF2DTF18328.p
% See solution above
% 1.37/1.28 ------------------------
% 1.37/1.29 ---- Cleaned THF ---
% 1.37/1.29 thf(in_type,type,
% 1.37/1.29 in: $i > $i > $o ).
% 1.37/1.29
% 1.37/1.29 thf(subset_type,type,
% 1.37/1.29 subset: $i > $i > $o ).
% 1.37/1.29
% 1.37/1.29 thf(subset,definition,
% 1.37/1.29 ( subset
% 1.37/1.29 = ( ^ [A: $i,B: $i] :
% 1.37/1.29 ! [Xx: $i] :
% 1.37/1.29 ( ( in @ Xx @ A )
% 1.37/1.29 => ( in @ Xx @ B ) ) ) ) ).
% 1.37/1.29
% 1.37/1.29 thf(subsetI1,conjecture,
% 1.37/1.29 ! [A: $i,B: $i] :
% 1.37/1.29 ( ! [Xx: $i] :
% 1.37/1.29 ( ( in @ Xx @ A )
% 1.37/1.29 => ( in @ Xx @ B ) )
% 1.37/1.29 => ( subset @ A @ B ) ) ).
% 1.37/1.29 ------------------------
% 1.55/1.31 % (18430)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_18328 for (2999ds/2Mi)
% 1.55/1.31 % (18429)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_18328 for (2999ds/27Mi)
% 1.55/1.31 % (18427)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_18328 for (2999ds/183Mi)
% 1.55/1.31 % (18428)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_18328 for (2999ds/4Mi)
% 1.55/1.31 % (18431)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_18328 for (2999ds/2Mi)
% 1.55/1.31 % (18432)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_18328 for (2999ds/275Mi)
% 1.55/1.31 % (18433)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_18328 for (2999ds/18Mi)
% 1.55/1.31 % (18432)Refutation not found, incomplete strategy
% 1.55/1.31 % (18432)------------------------------
% 1.55/1.31 % (18432)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.31 % (18432)Termination reason: Refutation not found, incomplete strategy
% 1.55/1.31
% 1.55/1.31
% 1.55/1.31 % (18432)Memory used [KB]: 5500
% 1.55/1.31 % (18432)Time elapsed: 0.002 s
% 1.55/1.31 % (18432)Instructions burned: 1 (million)
% 1.55/1.31 % (18432)------------------------------
% 1.55/1.31 % (18432)------------------------------
% 1.55/1.31 % (18431)First to succeed.
% 1.55/1.31 % (18430)Instruction limit reached!
% 1.55/1.31 % (18430)------------------------------
% 1.55/1.31 % (18430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.31 % (18430)Termination reason: Unknown
% 1.55/1.31 % (18430)Termination phase: Saturation
% 1.55/1.31
% 1.55/1.31 % (18430)Memory used [KB]: 5500
% 1.55/1.31 % (18430)Time elapsed: 0.003 s
% 1.55/1.31 % (18430)Instructions burned: 2 (million)
% 1.55/1.31 % (18430)------------------------------
% 1.55/1.31 % (18430)------------------------------
% 1.55/1.31 % (18427)Also succeeded, but the first one will report.
% 1.55/1.31 % (18431)Refutation found. Thanks to Tanya!
% 1.55/1.31 % SZS status Theorem for DTF2THF_18328
% 1.55/1.31 % SZS output start Proof for DTF2THF_18328
% 1.55/1.31 thf(func_def_0, type, in: $i > $i > $o).
% 1.55/1.31 thf(func_def_1, type, subset: $i > $i > $o).
% 1.55/1.31 thf(func_def_14, type, ph1: !>[X0: $tType]:(X0)).
% 1.55/1.31 thf(f19,plain,(
% 1.55/1.31 $false),
% 1.55/1.31 inference(trivial_inequality_removal,[status(thm)],[f18])).
% 1.55/1.31 thf(f18,plain,(
% 1.55/1.31 ($true = $false)),
% 1.55/1.31 inference(beta_eta_normalization,[status(thm)],[f17])).
% 1.55/1.31 thf(f17,plain,(
% 1.55/1.31 ($false = ((^[Y0 : $i]: ($true)) @ sK3))),
% 1.55/1.31 inference(sigma_clausification,[status(thm)],[f16])).
% 1.55/1.31 thf(f16,plain,(
% 1.55/1.31 ($false = (!! @ $i @ (^[Y0 : $i]: ($true))))),
% 1.55/1.31 inference(beta_eta_normalization,[status(thm)],[f15])).
% 1.55/1.31 thf(f15,plain,(
% 1.55/1.31 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ($true)))) @ sK2))),
% 1.55/1.31 inference(sigma_clausification,[status(thm)],[f14])).
% 1.55/1.31 thf(f14,plain,(
% 1.55/1.31 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ($true))))))),
% 1.55/1.31 inference(not_proxy_clausification,[status(thm)],[f13])).
% 1.55/1.31 thf(f13,plain,(
% 1.55/1.31 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ($true)))))))),
% 1.55/1.31 inference(boolean_simplification,[status(thm)],[f12])).
% 1.55/1.31 thf(f12,plain,(
% 1.55/1.31 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))))))))))),
% 1.55/1.31 inference(beta_eta_normalization,[status(thm)],[f11])).
% 1.55/1.31 thf(f11,plain,(
% 1.55/1.31 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((^[Y2 : $i]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))) @ Y0 @ Y1))))))))),
% 1.55/1.31 inference(definition_unfolding,[status(thm)],[f9,f10])).
% 1.55/1.31 thf(f10,plain,(
% 1.55/1.31 (subset = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1))))))))),
% 1.55/1.31 inference(cnf_transformation,[status(thm)],[f8])).
% 1.55/1.31 thf(f8,plain,(
% 1.55/1.31 (subset = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1))))))))),
% 1.55/1.31 inference(fool_elimination,[status(thm)],[f7])).
% 1.55/1.31 thf(f7,plain,(
% 1.55/1.31 ((^[X0 : $i, X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)))) = subset)),
% 1.55/1.31 inference(rectify,[status(thm)],[f1])).
% 1.55/1.31 thf(f1,axiom,(
% 1.55/1.31 ((^[X0 : $i, X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)))) = subset)),
% 1.55/1.31 file('/export/starexec/sandbox/tmp/tmp.o2dWN1FRHB/DTF2THF_18328.p',subset)).
% 1.55/1.31 thf(f9,plain,(
% 1.55/1.31 ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1))))))) = $true)),
% 1.55/1.31 inference(cnf_transformation,[status(thm)],[f6])).
% 1.55/1.31 thf(f6,plain,(
% 1.55/1.31 ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1))))))) = $true)),
% 1.55/1.31 inference(fool_elimination,[status(thm)],[f5])).
% 1.55/1.31 thf(f5,plain,(
% 1.55/1.31 ~! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0))),
% 1.55/1.31 inference(rectify,[status(thm)],[f3])).
% 1.55/1.31 thf(f3,negated_conjecture,(
% 1.55/1.31 ~! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1))),
% 1.55/1.31 inference(negated_conjecture,[status(cth)],[f2])).
% 1.55/1.31 thf(f2,conjecture,(
% 1.55/1.31 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1))),
% 1.55/1.31 file('/export/starexec/sandbox/tmp/tmp.o2dWN1FRHB/DTF2THF_18328.p',subsetI1)).
% 1.55/1.31 % SZS output end Proof for DTF2THF_18328
% 1.55/1.31 % (18431)------------------------------
% 1.55/1.31 % (18431)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.31 % (18431)Termination reason: Refutation
% 1.55/1.31
% 1.55/1.31 % (18431)Memory used [KB]: 5500
% 1.55/1.31 % (18431)Time elapsed: 0.003 s
% 1.55/1.31 % (18431)Instructions burned: 1 (million)
% 1.55/1.31 % (18431)------------------------------
% 1.55/1.31 % (18431)------------------------------
% 1.55/1.31 % (18426)Success in time 0.007 s
%------------------------------------------------------------------------------