%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU693^2 : 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 : 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 09:36:27 AM UTC 2026
% Result : Theorem 1.71s 1.42s
% Output : Refutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 11 ( 2 unt; 0 typ; 0 def)
% Number of atoms : 109 ( 26 equ; 0 cnn)
% Maximal formula atoms : 6 ( 9 avg)
% Number of connectives : 187 ( 11 ~; 0 |; 12 &; 154 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-4 aty)
% Number of variables : 30 ( 0 ^; 16 !; 14 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
funcSet: $i > $i > $i ).
thf(func_def_2,type,
ap: $i > $i > $i > $i > $i ).
thf(f14,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ap @ sK0 @ sK2 @ sK1 @ sK3 )
!= ( ap @ sK0 @ sK2 @ sK1 @ sK3 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ( ap @ sK0 @ sK2 @ sK1 @ sK3 )
!= ( ap @ sK0 @ sK2 @ sK1 @ sK3 ) )
& ( ( in @ sK3 @ sK0 )
= $true )
& ( $true
= ( in @ sK1 @ ( funcSet @ sK0 @ sK2 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f7,f9,f8]) ).
thf(f8,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( ( ap @ X0 @ X2 @ X1 @ X3 )
!= ( ap @ X0 @ X2 @ X1 @ X3 ) )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X1 @ ( funcSet @ X0 @ X2 ) )
= $true ) )
=> ( ? [X3: $i] :
( ( ( ap @ sK0 @ sK2 @ sK1 @ X3 )
!= ( ap @ sK0 @ sK2 @ sK1 @ X3 ) )
& ( ( in @ X3 @ sK0 )
= $true ) )
& ( $true
= ( in @ sK1 @ ( funcSet @ sK0 @ sK2 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ? [X3: $i] :
( ( ( ap @ sK0 @ sK2 @ sK1 @ X3 )
!= ( ap @ sK0 @ sK2 @ sK1 @ X3 ) )
& ( ( in @ X3 @ sK0 )
= $true ) )
=> ( ( ( ap @ sK0 @ sK2 @ sK1 @ sK3 )
!= ( ap @ sK0 @ sK2 @ sK1 @ sK3 ) )
& ( ( in @ sK3 @ sK0 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( ( ap @ X0 @ X2 @ X1 @ X3 )
!= ( ap @ X0 @ X2 @ X1 @ X3 ) )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X1 @ ( funcSet @ X0 @ X2 ) )
= $true ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
? [X1: $i,X0: $i,X2: $i] :
( ? [X3: $i] :
( ( ( ap @ X1 @ X2 @ X0 @ X3 )
!= ( ap @ X1 @ X2 @ X0 @ X3 ) )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( ( in @ X0 @ ( funcSet @ X1 @ X2 ) )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X0 @ ( funcSet @ X1 @ X2 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( ap @ X1 @ X2 @ X0 @ X3 )
= ( ap @ X1 @ X2 @ X0 @ X3 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ ( funcSet @ X1 @ X2 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( ap @ X1 @ X2 @ X0 @ X3 )
= ( ap @ X1 @ X2 @ X0 @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X2: $i,X0: $i,X1: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( ap @ X0 @ X1 @ X2 @ X3 )
= ( ap @ X0 @ X1 @ X2 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X2: $i,X0: $i,X1: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( ap @ X0 @ X1 @ X2 @ X3 )
= ( ap @ X0 @ X1 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ATyxB2qjju/DTF2THF_24395.p',ap2apEq1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU693^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n017.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:29:41 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.33/0.49 ---- Original DTF file ---
% 0.33/0.49 thf(spec,logic,$$dhol).
% 0.33/0.49 %------------------------------------------------------------------------------
% 0.33/0.49 % File : SEU693^2 : TPTP v9.2.1. Released v3.7.0.
% 0.33/0.49 % Domain : Set Theory
% 0.33/0.49 % Problem : Functions - Extensionality and Beta Reduction
% 0.33/0.49 % Version : Especial > Reduced > Especial.
% 0.33/0.49 % English : (! A:i.! B:i.! f:i.in f (funcSet A B) -> (! x:i.in x A ->
% 0.33/0.49 % ap A B f x = ap A B f x))
% 0.33/0.49
% 0.33/0.49 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.33/0.49 % Source : [Bro08]
% 0.33/0.49 % Names : ZFC195l [Bro08]
% 0.33/0.49
% 0.33/0.49 % Status : Theorem
% 0.33/0.49 % Rating : 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 v4.1.0, 0.00 v3.7.0
% 0.33/0.49 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.33/0.49 % Number of atoms : 3 ( 1 equ; 0 cnn)
% 0.33/0.49 % Maximal formula atoms : 3 ( 3 avg)
% 0.33/0.49 % Number of connectives : 16 ( 0 ~; 0 |; 0 &; 14 @)
% 0.33/0.49 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.33/0.49 % Maximal formula depth : 9 ( 9 avg)
% 0.33/0.49 % Number of types : 2 ( 0 usr)
% 0.33/0.49 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.33/0.49 % Number of symbols : 4 ( 3 usr; 0 con; 2-4 aty)
% 0.33/0.49 % Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% 0.33/0.49 % SPC : TH0_THM_EQU_NAR
% 0.33/0.49
% 0.33/0.49 % Comments : http://mathgate.info/detsetitem.php?id=247
% 0.33/0.49 %------------------------------------------------------------------------------
% 0.33/0.49 thf(in,type,
% 0.33/0.49 in: $i > $i > $o ).
% 0.33/0.49
% 0.33/0.49 thf(funcSet,type,
% 0.33/0.49 funcSet: $i > $i > $i ).
% 0.33/0.49
% 0.33/0.49 thf(ap,type,
% 0.33/0.49 ap: $i > $i > $i > $i > $i ).
% 0.33/0.49
% 0.33/0.49 thf(ap2apEq1,conjecture,
% 0.33/0.49 ! [A: $i,B: $i,Xf: $i] :
% 0.33/0.49 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.33/0.49 => ! [Xx: $i] :
% 0.33/0.49 ( ( in @ Xx @ A )
% 0.33/0.49 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.33/0.49 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ).
% 0.33/0.49
% 0.33/0.49 %------------------------------------------------------------------------------
% 0.33/0.49 ------------------------
% 1.51/1.39 ---- Embedded in THF ---
% 1.51/1.39 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.51/1.39 %%% Generated on Tue Feb 24 12:29:42 EST 2026
% 1.51/1.39 %%% using '$$dhol' embedding, version 1.3.0.
% 1.51/1.39 %%% Logic specification used:
% 1.51/1.39 %%% thf(spec, logic, $$dhol).
% 1.51/1.39
% 1.51/1.39 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.ATyxB2qjju/DTF2DTF24395.p
% See solution above
% 1.51/1.39 ------------------------
% 1.71/1.40 ---- Cleaned THF ---
% 1.71/1.40 thf(in,type,
% 1.71/1.40 in: $i > $i > $o ).
% 1.71/1.40
% 1.71/1.40 thf(funcSet,type,
% 1.71/1.40 funcSet: $i > $i > $i ).
% 1.71/1.40
% 1.71/1.40 thf(ap,type,
% 1.71/1.40 ap: $i > $i > $i > $i > $i ).
% 1.71/1.40
% 1.71/1.40 thf(ap2apEq1,conjecture,
% 1.71/1.40 ! [A: $i,B: $i,Xf: $i] :
% 1.71/1.40 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 1.71/1.40 => ! [Xx: $i] :
% 1.71/1.40 ( ( in @ Xx @ A )
% 1.71/1.40 => ( ( ap @ A @ B @ Xf @ Xx )
% 1.71/1.40 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ).
% 1.71/1.40 ------------------------
% 1.71/1.42 % (24518)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_24395 for (2999ds/2Mi)
% 1.71/1.42 % (24514)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_24395 for (2999ds/183Mi)
% 1.71/1.42 % (24515)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_24395 for (2999ds/4Mi)
% 1.71/1.42 % (24520)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_24395 for (2999ds/18Mi)
% 1.71/1.42 % (24519)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_24395 for (2999ds/275Mi)
% 1.71/1.42 % (24517)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_24395 for (2999ds/2Mi)
% 1.71/1.42 % (24516)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_24395 for (2999ds/27Mi)
% 1.71/1.42 % (24517)Instruction limit reached!
% 1.71/1.42 % (24517)------------------------------
% 1.71/1.42 % (24517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.42 % (24517)Termination reason: Unknown
% 1.71/1.42 % (24517)Termination phase: Saturation
% 1.71/1.42
% 1.71/1.42 % (24517)Memory used [KB]: 895
% 1.71/1.42 % (24517)Time elapsed: 0.003 s
% 1.71/1.42 % (24517)Instructions burned: 2 (million)
% 1.71/1.42 % (24517)------------------------------
% 1.71/1.42 % (24517)------------------------------
% 1.71/1.42 % (24518)Instruction limit reached!
% 1.71/1.42 % (24518)------------------------------
% 1.71/1.42 % (24518)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.42 % (24518)Termination reason: Unknown
% 1.71/1.42 % (24518)Termination phase: Saturation
% 1.71/1.42
% 1.71/1.42 % (24518)Memory used [KB]: 895
% 1.71/1.42 % (24518)Time elapsed: 0.003 s
% 1.71/1.42 % (24518)Instructions burned: 2 (million)
% 1.71/1.42 % (24518)------------------------------
% 1.71/1.42 % (24518)------------------------------
% 1.71/1.42 % (24514)First to succeed.
% 1.71/1.42 % (24519)Also succeeded, but the first one will report.
% 1.71/1.42 % (24515)Also succeeded, but the first one will report.
% 1.71/1.42 % (24514)Refutation found. Thanks to Tanya!
% 1.71/1.42 % SZS status Theorem for DTF2THF_24395
% 1.71/1.42 % SZS output start Proof for DTF2THF_24395
% 1.71/1.42 thf(func_def_0, type, in: $i > $i > $o).
% 1.71/1.42 thf(func_def_1, type, funcSet: $i > $i > $i).
% 1.71/1.42 thf(func_def_2, type, ap: $i > $i > $i > $i > $i).
% 1.71/1.42 thf(f14,plain,(
% 1.71/1.42 $false),
% 1.71/1.42 inference(trivial_inequality_removal,[status(thm)],[f13])).
% 1.71/1.42 thf(f13,plain,(
% 1.71/1.42 ((ap @ sK0 @ sK2 @ sK1 @ sK3) != (ap @ sK0 @ sK2 @ sK1 @ sK3))),
% 1.71/1.42 inference(cnf_transformation,[status(thm)],[f10])).
% 1.71/1.42 thf(f10,plain,(
% 1.71/1.42 (((ap @ sK0 @ sK2 @ sK1 @ sK3) != (ap @ sK0 @ sK2 @ sK1 @ sK3)) & ((in @ sK3 @ sK0) = $true)) & ($true = (in @ sK1 @ (funcSet @ sK0 @ sK2)))),
% 1.71/1.42 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f7,f9,f8])).
% 1.71/1.42 thf(f8,plain,(
% 1.71/1.42 ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : (((ap @ X0 @ X2 @ X1 @ X3) != (ap @ X0 @ X2 @ X1 @ X3)) & ((in @ X3 @ X0) = $true)) & ((in @ X1 @ (funcSet @ X0 @ X2)) = $true)) => (? [X3 : $i] : (((ap @ sK0 @ sK2 @ sK1 @ X3) != (ap @ sK0 @ sK2 @ sK1 @ X3)) & ((in @ X3 @ sK0) = $true)) & ($true = (in @ sK1 @ (funcSet @ sK0 @ sK2))))),
% 1.71/1.42 introduced(definition,[],[choice_axiom])).
% 1.71/1.42 thf(f9,plain,(
% 1.71/1.42 ? [X3 : $i] : (((ap @ sK0 @ sK2 @ sK1 @ X3) != (ap @ sK0 @ sK2 @ sK1 @ X3)) & ((in @ X3 @ sK0) = $true)) => (((ap @ sK0 @ sK2 @ sK1 @ sK3) != (ap @ sK0 @ sK2 @ sK1 @ sK3)) & ((in @ sK3 @ sK0) = $true))),
% 1.71/1.42 introduced(definition,[],[choice_axiom])).
% 1.71/1.42 thf(f7,plain,(
% 1.71/1.42 ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : (((ap @ X0 @ X2 @ X1 @ X3) != (ap @ X0 @ X2 @ X1 @ X3)) & ((in @ X3 @ X0) = $true)) & ((in @ X1 @ (funcSet @ X0 @ X2)) = $true))),
% 1.71/1.42 inference(rectify,[status(thm)],[f6])).
% 1.71/1.42 thf(f6,plain,(
% 1.71/1.42 ? [X1 : $i,X0 : $i,X2 : $i] : (? [X3 : $i] : (((ap @ X1 @ X2 @ X0 @ X3) != (ap @ X1 @ X2 @ X0 @ X3)) & ((in @ X3 @ X1) = $true)) & ((in @ X0 @ (funcSet @ X1 @ X2)) = $true))),
% 1.71/1.42 inference(ennf_transformation,[status(thm)],[f5])).
% 1.71/1.42 thf(f5,plain,(
% 1.71/1.42 ~! [X1 : $i,X2 : $i,X0 : $i] : (((in @ X0 @ (funcSet @ X1 @ X2)) = $true) => ! [X3 : $i] : (((in @ X3 @ X1) = $true) => ((ap @ X1 @ X2 @ X0 @ X3) = (ap @ X1 @ X2 @ X0 @ X3))))),
% 1.71/1.42 inference(fool_elimination,[status(thm)],[f4])).
% 1.71/1.42 thf(f4,plain,(
% 1.71/1.42 ~! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (funcSet @ X1 @ X2)) => ! [X3 : $i] : ((in @ X3 @ X1) => ((ap @ X1 @ X2 @ X0 @ X3) = (ap @ X1 @ X2 @ X0 @ X3))))),
% 1.71/1.42 inference(rectify,[status(thm)],[f2])).
% 1.71/1.42 thf(f2,negated_conjecture,(
% 1.71/1.42 ~! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X2 @ (funcSet @ X0 @ X1)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((ap @ X0 @ X1 @ X2 @ X3) = (ap @ X0 @ X1 @ X2 @ X3))))),
% 1.71/1.42 inference(negated_conjecture,[status(cth)],[f1])).
% 1.71/1.42 thf(f1,conjecture,(
% 1.71/1.42 ! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X2 @ (funcSet @ X0 @ X1)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((ap @ X0 @ X1 @ X2 @ X3) = (ap @ X0 @ X1 @ X2 @ X3))))),
% 1.71/1.42 file('/export/starexec/sandbox/tmp/tmp.ATyxB2qjju/DTF2THF_24395.p',ap2apEq1)).
% 1.71/1.42 % SZS output end Proof for DTF2THF_24395
% 1.71/1.42 % (24514)------------------------------
% 1.71/1.42 % (24514)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.42 % (24514)Termination reason: Refutation
% 1.71/1.42
% 1.71/1.42 % (24514)Memory used [KB]: 5373
% 1.71/1.42 % (24514)Time elapsed: 0.003 s
% 1.71/1.42 % (24514)Instructions burned: 1 (million)
% 1.71/1.42 % (24514)------------------------------
% 1.71/1.42 % (24514)------------------------------
% 1.71/1.42 % (24513)Success in time 0.019 s
%------------------------------------------------------------------------------