%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU697^2 : 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 : n002.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 09:36:29 AM UTC 2026
% Result : Theorem 1.52s 1.30s
% Output : Refutation 1.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 9 ( 2 unt; 0 typ; 0 def)
% Number of atoms : 62 ( 19 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 141 ( 12 ~; 4 |; 4 &; 112 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-3 aty)
% Number of variables : 44 ( 18 ^; 20 !; 6 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_2,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(func_def_13,type,
sK2: $i > $i ).
thf(f13,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f12]) ).
thf(f12,plain,
( ( lam @ sK1 @ sK0
@ ^ [Y0: $i] : ( sK2 @ Y0 ) )
!= ( lam @ sK1 @ sK0
@ ^ [Y0: $i] : ( sK2 @ Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ( lam @ sK1 @ sK0
@ ^ [Y0: $i] : ( sK2 @ Y0 ) )
!= ( lam @ sK1 @ sK0
@ ^ [Y0: $i] : ( sK2 @ Y0 ) ) )
& ! [X3: $i] :
( ( $true
= ( in @ ( sK2 @ X3 ) @ sK0 ) )
| ( $true
!= ( in @ X3 @ sK1 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f9]) ).
thf(f9,plain,
( ? [X0: $i,X1: $i,X2: $i > $i] :
( ( ( lam @ X1 @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) )
!= ( lam @ X1 @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
& ! [X3: $i] :
( ( $true
= ( in @ ( X2 @ X3 ) @ X0 ) )
| ( ( in @ X3 @ X1 )
!= $true ) ) )
=> ( ( ( lam @ sK1 @ sK0
@ ^ [Y0: $i] : ( sK2 @ Y0 ) )
!= ( lam @ sK1 @ sK0
@ ^ [Y0: $i] : ( sK2 @ Y0 ) ) )
& ! [X3: $i] :
( ( $true
= ( in @ ( sK2 @ X3 ) @ sK0 ) )
| ( $true
!= ( in @ X3 @ sK1 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: $i,X1: $i,X2: $i > $i] :
( ( ( lam @ X1 @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) )
!= ( lam @ X1 @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
& ! [X3: $i] :
( ( $true
= ( in @ ( X2 @ X3 ) @ X0 ) )
| ( ( in @ X3 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
~ ! [X0: $i,X1: $i,X2: $i > $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( $true
= ( in @ ( X2 @ X3 ) @ X0 ) ) )
=> ( ( lam @ X1 @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) )
= ( lam @ X1 @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: $i,X1: $i,X2: $i > $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ ( X2 @ X3 ) @ X0 ) )
=> ( ( lam @ X1 @ X0
@ ^ [X4: $i] : ( X2 @ X4 ) )
= ( lam @ X1 @ X0
@ ^ [X5: $i] : ( X2 @ X5 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ! [X1: $i,X0: $i,X2: $i > $i] :
( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( X2 @ X3 ) @ X1 ) )
=> ( ( lam @ X0 @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) )
= ( lam @ X0 @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
! [X1: $i,X0: $i,X2: $i > $i] :
( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( X2 @ X3 ) @ X1 ) )
=> ( ( lam @ X0 @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) )
= ( lam @ X0 @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.LpA2BnLise/DTF2THF_6945.p',lam2lamEq) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU697^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.09 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n002.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 12:31:33 EST 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.38 ---- Original DTF file ---
% 0.17/0.38 thf(spec,logic,$$dhol).
% 0.17/0.38 %------------------------------------------------------------------------------
% 0.17/0.38 % File : SEU697^2 : TPTP v9.2.1. Released v3.7.0.
% 0.17/0.38 % Domain : Set Theory
% 0.17/0.38 % Problem : Functions - Extensionality and Beta Reduction
% 0.17/0.38 % Version : Especial > Reduced > Especial.
% 0.17/0.38 % English : (! A:i.! B:i.! f:i>i.(! x:i.in x A -> in (f x) B) ->
% 0.17/0.38 % lam A B (^ x:i.f x) = lam A B (^ x:i.f x))
% 0.17/0.38
% 0.17/0.38 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.17/0.38 % Source : [Bro08]
% 0.17/0.38 % Names : ZFC199l [Bro08]
% 0.17/0.38
% 0.17/0.38 % Status : Theorem
% 0.17/0.38 % 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
% 0.17/0.38 % Syntax : Number of formulae : 5 ( 1 unt; 3 typ; 1 def)
% 0.17/0.38 % Number of atoms : 5 ( 3 equ; 0 cnn)
% 0.17/0.38 % Maximal formula atoms : 3 ( 2 avg)
% 0.17/0.38 % Number of connectives : 19 ( 0 ~; 0 |; 0 &; 17 @)
% 0.17/0.38 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.17/0.38 % Maximal formula depth : 10 ( 6 avg)
% 0.17/0.38 % Number of types : 2 ( 0 usr)
% 0.17/0.38 % Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% 0.17/0.38 % Number of symbols : 4 ( 3 usr; 0 con; 2-3 aty)
% 0.17/0.38 % Number of variables : 11 ( 7 ^; 4 !; 0 ?; 11 :)
% 0.17/0.38 % SPC : TH0_THM_EQU_NAR
% 0.17/0.38
% 0.17/0.38 % Comments : http://mathgate.info/detsetitem.php?id=249
% 0.17/0.38 %------------------------------------------------------------------------------
% 0.17/0.38 thf(in_type,type,
% 0.17/0.38 in: $i > $i > $o ).
% 0.17/0.38
% 0.17/0.38 thf(dpsetconstr_type,type,
% 0.17/0.38 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.17/0.38
% 0.17/0.38 thf(lam_type,type,
% 0.17/0.38 lam: $i > $i > ( $i > $i ) > $i ).
% 0.17/0.38
% 0.17/0.38 thf(lam,definition,
% 0.17/0.38 ( lam
% 0.17/0.38 = ( ^ [A: $i,B: $i,Xf: $i > $i] :
% 0.17/0.38 ( dpsetconstr @ A @ B
% 0.17/0.38 @ ^ [Xx: $i,Xy: $i] :
% 0.17/0.38 ( ( Xf @ Xx )
% 0.17/0.38 = Xy ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(lam2lamEq,conjecture,
% 0.17/0.38 ! [A: $i,B: $i,Xf: $i > $i] :
% 0.17/0.38 ( ! [Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ A )
% 0.17/0.38 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.17/0.38 => ( ( lam @ A @ B
% 0.17/0.38 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.17/0.38 = ( lam @ A @ B
% 0.17/0.38 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 %------------------------------------------------------------------------------
% 0.17/0.38 ------------------------
% 1.39/1.27 ---- Embedded in THF ---
% 1.39/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.39/1.27 %%% Generated on Tue Feb 24 12:31:34 EST 2026
% 1.39/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.39/1.27 %%% Logic specification used:
% 1.39/1.27 %%% thf(spec, logic, $$dhol).
% 1.39/1.27
% 1.39/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.LpA2BnLise/DTF2DTF6945.p
% See solution above
% 1.39/1.27 ------------------------
% 1.39/1.28 ---- Cleaned THF ---
% 1.39/1.28 thf(in_type,type,
% 1.39/1.28 in: $i > $i > $o ).
% 1.39/1.28
% 1.39/1.28 thf(dpsetconstr_type,type,
% 1.39/1.28 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 1.39/1.28
% 1.39/1.28 thf(lam_type,type,
% 1.39/1.28 lam: $i > $i > ( $i > $i ) > $i ).
% 1.39/1.28
% 1.39/1.28 thf(lam,definition,
% 1.39/1.28 ( lam
% 1.39/1.28 = ( ^ [A: $i,B: $i,Xf: $i > $i] :
% 1.39/1.28 ( dpsetconstr @ A @ B
% 1.39/1.28 @ ^ [Xx: $i,Xy: $i] :
% 1.39/1.28 ( ( Xf @ Xx )
% 1.39/1.28 = Xy ) ) ) ) ).
% 1.39/1.28
% 1.39/1.28 thf(lam2lamEq,conjecture,
% 1.39/1.28 ! [A: $i,B: $i,Xf: $i > $i] :
% 1.39/1.28 ( ! [Xx: $i] :
% 1.39/1.28 ( ( in @ Xx @ A )
% 1.39/1.28 => ( in @ ( Xf @ Xx ) @ B ) )
% 1.39/1.28 => ( ( lam @ A @ B
% 1.39/1.28 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 1.39/1.28 = ( lam @ A @ B
% 1.39/1.28 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ).
% 1.39/1.28 ------------------------
% 1.39/1.30 % (7046)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6945 for (2999ds/2Mi)
% 1.39/1.30 % (7044)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_6945 for (2999ds/4Mi)
% 1.39/1.30 % (7043)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6945 for (2999ds/183Mi)
% 1.39/1.30 % (7045)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_6945 for (2999ds/27Mi)
% 1.39/1.30 % (7048)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_6945 for (2999ds/275Mi)
% 1.39/1.30 % (7047)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_6945 for (2999ds/2Mi)
% 1.52/1.30 % (7049)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6945 for (2999ds/18Mi)
% 1.52/1.30 % (7048)First to succeed.
% 1.52/1.30 % (7047)Instruction limit reached!
% 1.52/1.30 % (7047)------------------------------
% 1.52/1.30 % (7047)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.30 % (7047)Termination reason: Unknown
% 1.52/1.30 % (7047)Termination phase: Saturation
% 1.52/1.30
% 1.52/1.30 % (7047)Memory used [KB]: 5500
% 1.52/1.30 % (7047)Time elapsed: 0.003 s
% 1.52/1.30 % (7047)Instructions burned: 3 (million)
% 1.52/1.30 % (7047)------------------------------
% 1.52/1.30 % (7047)------------------------------
% 1.52/1.30 % (7043)Also succeeded, but the first one will report.
% 1.52/1.30 % (7049)Also succeeded, but the first one will report.
% 1.52/1.30 % (7048)Refutation found. Thanks to Tanya!
% 1.52/1.30 % SZS status Theorem for DTF2THF_6945
% 1.52/1.30 % SZS output start Proof for DTF2THF_6945
% 1.52/1.30 thf(func_def_0, type, in: $i > $i > $o).
% 1.52/1.30 thf(func_def_1, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 1.52/1.30 thf(func_def_2, type, lam: $i > $i > ($i > $i) > $i).
% 1.52/1.30 thf(func_def_13, type, sK2: $i > $i).
% 1.52/1.30 thf(f13,plain,(
% 1.52/1.30 $false),
% 1.52/1.30 inference(trivial_inequality_removal,[status(thm)],[f12])).
% 1.52/1.30 thf(f12,plain,(
% 1.52/1.30 ((lam @ sK1 @ sK0 @ (^[Y0 : $i]: (sK2 @ Y0))) != (lam @ sK1 @ sK0 @ (^[Y0 : $i]: (sK2 @ Y0))))),
% 1.52/1.30 inference(cnf_transformation,[status(thm)],[f10])).
% 1.52/1.30 thf(f10,plain,(
% 1.52/1.30 ((lam @ sK1 @ sK0 @ (^[Y0 : $i]: (sK2 @ Y0))) != (lam @ sK1 @ sK0 @ (^[Y0 : $i]: (sK2 @ Y0)))) & ! [X3 : $i] : (($true = (in @ (sK2 @ X3) @ sK0)) | ($true != (in @ X3 @ sK1)))),
% 1.52/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f9])).
% 1.52/1.30 thf(f9,plain,(
% 1.52/1.30 ? [X0 : $i,X1 : $i,X2 : $i > $i] : (((lam @ X1 @ X0 @ (^[Y0 : $i]: (X2 @ Y0))) != (lam @ X1 @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))) & ! [X3 : $i] : (($true = (in @ (X2 @ X3) @ X0)) | ((in @ X3 @ X1) != $true))) => (((lam @ sK1 @ sK0 @ (^[Y0 : $i]: (sK2 @ Y0))) != (lam @ sK1 @ sK0 @ (^[Y0 : $i]: (sK2 @ Y0)))) & ! [X3 : $i] : (($true = (in @ (sK2 @ X3) @ sK0)) | ($true != (in @ X3 @ sK1))))),
% 1.52/1.30 introduced(definition,[],[choice_axiom])).
% 1.52/1.30 thf(f8,plain,(
% 1.52/1.30 ? [X0 : $i,X1 : $i,X2 : $i > $i] : (((lam @ X1 @ X0 @ (^[Y0 : $i]: (X2 @ Y0))) != (lam @ X1 @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))) & ! [X3 : $i] : (($true = (in @ (X2 @ X3) @ X0)) | ((in @ X3 @ X1) != $true)))),
% 1.52/1.30 inference(ennf_transformation,[status(thm)],[f7])).
% 1.52/1.30 thf(f7,plain,(
% 1.52/1.30 ~! [X0 : $i,X1 : $i,X2 : $i > $i] : (! [X3 : $i] : (((in @ X3 @ X1) = $true) => ($true = (in @ (X2 @ X3) @ X0))) => ((lam @ X1 @ X0 @ (^[Y0 : $i]: (X2 @ Y0))) = (lam @ X1 @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))))),
% 1.52/1.30 inference(fool_elimination,[status(thm)],[f6])).
% 1.52/1.30 thf(f6,plain,(
% 1.52/1.30 ~! [X0 : $i,X1 : $i,X2 : $i > $i] : (! [X3 : $i] : ((in @ X3 @ X1) => (in @ (X2 @ X3) @ X0)) => ((lam @ X1 @ X0 @ (^[X4 : $i] : (X2 @ X4))) = (lam @ X1 @ X0 @ (^[X5 : $i] : (X2 @ X5)))))),
% 1.52/1.30 inference(rectify,[status(thm)],[f3])).
% 1.52/1.30 thf(f3,negated_conjecture,(
% 1.52/1.30 ~! [X1 : $i,X0 : $i,X2 : $i > $i] : (! [X3 : $i] : ((in @ X3 @ X0) => (in @ (X2 @ X3) @ X1)) => ((lam @ X0 @ X1 @ (^[X3 : $i] : (X2 @ X3))) = (lam @ X0 @ X1 @ (^[X3 : $i] : (X2 @ X3)))))),
% 1.52/1.30 inference(negated_conjecture,[status(cth)],[f2])).
% 1.52/1.30 thf(f2,conjecture,(
% 1.52/1.30 ! [X1 : $i,X0 : $i,X2 : $i > $i] : (! [X3 : $i] : ((in @ X3 @ X0) => (in @ (X2 @ X3) @ X1)) => ((lam @ X0 @ X1 @ (^[X3 : $i] : (X2 @ X3))) = (lam @ X0 @ X1 @ (^[X3 : $i] : (X2 @ X3)))))),
% 1.52/1.30 file('/export/starexec/sandbox/tmp/tmp.LpA2BnLise/DTF2THF_6945.p',lam2lamEq)).
% 1.52/1.30 % SZS output end Proof for DTF2THF_6945
% 1.52/1.30 % (7048)------------------------------
% 1.52/1.30 % (7048)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.30 % (7048)Termination reason: Refutation
% 1.52/1.30
% 1.52/1.30 % (7048)Memory used [KB]: 5500
% 1.52/1.30 % (7048)Time elapsed: 0.003 s
% 1.52/1.30 % (7048)Instructions burned: 1 (million)
% 1.52/1.30 % (7048)------------------------------
% 1.52/1.30 % (7048)------------------------------
% 1.52/1.30 % (7042)Success in time 0.016 s
%------------------------------------------------------------------------------