%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYN997^1 : 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 : 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 09:51:42 AM UTC 2026
% Result : Theorem 1.61s 1.32s
% Output : Refutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 62 ( 20 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 80 ( 9 ~; 2 |; 4 &; 56 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 4 usr; 3 con; 0-2 aty)
% ( 0 !!; 0 ??; 3 @@+; 0 @@-)
% Number of variables : 28 ( 0 ^; 14 !; 14 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_4,type,
sK0: ( ( $i > $o ) > $i ) > $i > $o ).
thf(func_def_5,type,
sK1: ( ( $i > $o ) > $i ) > $i ).
thf(func_def_7,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f23,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f17]) ).
thf(f17,plain,
$true = $false,
inference(superposition,[status(thm)],[f16,f10]) ).
thf(f10,plain,
! [X0: ( $i > $o ) > $i] :
( ( sK0 @ X0 @ ( sK1 @ X0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: ( $i > $o ) > $i] :
( ( ( sK0 @ X0 @ ( X0 @ ( sK0 @ X0 ) ) )
!= $true )
& ( ( sK0 @ X0 @ ( sK1 @ X0 ) )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f8,f7]) ).
thf(f7,plain,
! [X0: ( $i > $o ) > $i] :
( ? [X1: $i > $o] :
( ( ( X1 @ ( X0 @ X1 ) )
!= $true )
& ? [X2: $i] :
( ( X1 @ X2 )
= $true ) )
=> ( ( ( sK0 @ X0 @ ( X0 @ ( sK0 @ X0 ) ) )
!= $true )
& ? [X2: $i] :
( $true
= ( sK0 @ X0 @ X2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
! [X0: ( $i > $o ) > $i] :
( ? [X2: $i] :
( $true
= ( sK0 @ X0 @ X2 ) )
=> ( ( sK0 @ X0 @ ( sK1 @ X0 ) )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
! [X0: ( $i > $o ) > $i] :
? [X1: $i > $o] :
( ( ( X1 @ ( X0 @ X1 ) )
!= $true )
& ? [X2: $i] :
( ( X1 @ X2 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ? [X0: ( $i > $o ) > $i] :
! [X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
= $true )
=> ( ( X1 @ ( X0 @ X1 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: ( $i > $o ) > $i] :
! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( X1 @ ( X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X0: ( $i > $o ) > $i] :
! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( X1 @ ( X0 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X0: ( $i > $o ) > $i] :
! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( X1 @ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qJ5bK45LbH/DTF2THF_8012.p',conj) ).
thf(f16,plain,
! [X0: $i] :
( ( sK0 @ @@+ @ $i @ X0 )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: $i] :
( ( ( sK0 @ @@+ @ $i @ X0 )
= $false )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f11,f12]) ).
thf(f12,plain,
! [X0: ( $i > $o ) > $i,X1: $i] :
( ( ( sK0 @ X0 @ ( @@+ @ $i @ ( sK0 @ X0 ) ) )
= $true )
| ( ( sK0 @ X0 @ X1 )
= $false ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X0: ( $i > $o ) > $i] :
( ( sK0 @ X0 @ ( X0 @ ( sK0 @ X0 ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYN997^1 : 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 : n005.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 14:21:14 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
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : SYN997^1 : TPTP v9.2.1. Released v3.7.0.
% 0.29/0.46 % Domain : Syntactic
% 0.29/0.46 % Problem : Test for validity of axiom of choice
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English :
% 0.29/0.46
% 0.29/0.46 % Refs : [BB05] Benzmueller & Brown (2005), A Structured Set of Higher
% 0.29/0.46 % : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% 0.29/0.46 % : [Hoe09] Hoeschele (2009), Towards a Semi-Automatic Higher-Orde
% 0.29/0.46 % Source : [Ben09]
% 0.29/0.46 % Names : Example 5 [BB05]
% 0.29/0.46 % : choicei [Bro09]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % : Without choice : CounterSatisfiable
% 0.29/0.46 % Rating : 0.17 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, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.2.0, 0.50 v6.1.0, 0.17 v6.0.0, 0.50 v5.5.0, 0.80 v5.4.0, 0.75 v4.1.0, 1.00 v3.7.0
% 0.29/0.46 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.29/0.46 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 0 ( 0 avg)
% 0.29/0.46 % Number of connectives : 4 ( 0 ~; 0 |; 0 &; 3 @)
% 0.29/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 6 ( 6 avg)
% 0.29/0.46 % Number of types : 2 ( 0 usr)
% 0.29/0.46 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.29/0.46 % Number of variables : 3 ( 0 ^; 1 !; 2 ?; 3 :)
% 0.29/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.29/0.46
% 0.29/0.46 % Comments : Even with naive Skolemization this statement should not be
% 0.29/0.46 % provable.
% 0.29/0.46 % :
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf(conj,conjecture,
% 0.29/0.46 ? [E: ( $i > $o ) > $i] :
% 0.29/0.46 ! [P: $i > $o] :
% 0.29/0.46 ( ? [Y: $i] : ( P @ Y )
% 0.29/0.46 => ( P @ ( E @ P ) ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 1.46/1.28 ---- Embedded in THF ---
% 1.46/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.28 %%% Generated on Tue Feb 24 14:21:15 EST 2026
% 1.46/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.28 %%% Logic specification used:
% 1.46/1.28 %%% thf(spec, logic, $$dhol).
% 1.46/1.28
% 1.46/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.qJ5bK45LbH/DTF2DTF8012.p
% See solution above
% 1.46/1.28 ------------------------
% 1.46/1.29 ---- Cleaned THF ---
% 1.46/1.29 thf(conj,conjecture,
% 1.46/1.29 ? [E: ( $i > $o ) > $i] :
% 1.46/1.29 ! [P: $i > $o] :
% 1.46/1.29 ( ? [Y: $i] : ( P @ Y )
% 1.46/1.29 => ( P @ ( E @ P ) ) ) ).
% 1.46/1.29 ------------------------
% 1.61/1.30 % (8295)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_8012 for (2999ds/183Mi)
% 1.61/1.31 % (8296)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_8012 for (2999ds/4Mi)
% 1.61/1.31 % (8296)Instruction limit reached!
% 1.61/1.31 % (8296)------------------------------
% 1.61/1.31 % (8296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.31 % (8296)Termination reason: Unknown
% 1.61/1.31 % (8296)Termination phase: Saturation
% 1.61/1.31
% 1.61/1.31 % (8296)Memory used [KB]: 5500
% 1.61/1.31 % (8296)Time elapsed: 0.003 s
% 1.61/1.31 % (8296)Instructions burned: 5 (million)
% 1.61/1.31 % (8296)------------------------------
% 1.61/1.31 % (8296)------------------------------
% 1.61/1.31 % (8297)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_8012 for (2999ds/27Mi)
% 1.61/1.31 % (8298)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_8012 for (2999ds/2Mi)
% 1.61/1.31 % (8299)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_8012 for (2999ds/2Mi)
% 1.61/1.31 % (8300)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_8012 for (2999ds/275Mi)
% 1.61/1.31 % (8301)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_8012 for (2999ds/18Mi)
% 1.61/1.31 % (8298)Refutation not found, incomplete strategy
% 1.61/1.31 % (8298)------------------------------
% 1.61/1.31 % (8298)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.31 % (8298)Termination reason: Refutation not found, incomplete strategy
% 1.61/1.31
% 1.61/1.31
% 1.61/1.31 % (8298)Memory used [KB]: 5500
% 1.61/1.31 % (8300)Refutation not found, incomplete strategy
% 1.61/1.31 % (8300)------------------------------
% 1.61/1.31 % (8300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.31 % (8298)Time elapsed: 0.003 s
% 1.61/1.31 % (8300)Termination reason: Refutation not found, incomplete strategy
% 1.61/1.31
% 1.61/1.31
% 1.61/1.31 % (8298)Instructions burned: 1 (million)
% 1.61/1.31 % (8298)------------------------------
% 1.61/1.31 % (8298)------------------------------
% 1.61/1.31 % (8300)Memory used [KB]: 5500
% 1.61/1.31 % (8300)Time elapsed: 0.003 s
% 1.61/1.31 % (8300)Instructions burned: 1 (million)
% 1.61/1.31 % (8300)------------------------------
% 1.61/1.31 % (8300)------------------------------
% 1.61/1.31 % (8299)Instruction limit reached!
% 1.61/1.31 % (8299)------------------------------
% 1.61/1.31 % (8299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.31 % (8299)Termination reason: Unknown
% 1.61/1.31 % (8299)Termination phase: Saturation
% 1.61/1.31
% 1.61/1.31 % (8299)Memory used [KB]: 5500
% 1.61/1.31 % (8299)Time elapsed: 0.004 s
% 1.61/1.31 % (8299)Instructions burned: 2 (million)
% 1.61/1.31 % (8299)------------------------------
% 1.61/1.31 % (8299)------------------------------
% 1.61/1.32 % (8297)First to succeed.
% 1.61/1.32 % (8297)Refutation found. Thanks to Tanya!
% 1.61/1.32 % SZS status Theorem for DTF2THF_8012
% 1.61/1.32 % SZS output start Proof for DTF2THF_8012
% 1.61/1.32 thf(func_def_1, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.61/1.32 thf(func_def_4, type, sK0: (($i > $o) > $i) > $i > $o).
% 1.61/1.32 thf(func_def_5, type, sK1: (($i > $o) > $i) > $i).
% 1.61/1.32 thf(func_def_7, type, ph3: !>[X0: $tType]:(X0)).
% 1.61/1.32 thf(f23,plain,(
% 1.61/1.32 $false),
% 1.61/1.32 inference(trivial_inequality_removal,[status(thm)],[f17])).
% 1.61/1.32 thf(f17,plain,(
% 1.61/1.32 ($true = $false)),
% 1.61/1.32 inference(superposition,[status(thm)],[f16,f10])).
% 1.61/1.32 thf(f10,plain,(
% 1.61/1.32 ( ! [X0 : ($i > $o) > $i] : (((sK0 @ X0 @ (sK1 @ X0)) = $true)) )),
% 1.61/1.32 inference(cnf_transformation,[status(thm)],[f9])).
% 1.61/1.32 thf(f9,plain,(
% 1.61/1.32 ! [X0 : ($i > $o) > $i] : (((sK0 @ X0 @ (X0 @ (sK0 @ X0))) != $true) & ((sK0 @ X0 @ (sK1 @ X0)) = $true))),
% 1.61/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f8,f7])).
% 1.61/1.32 thf(f7,plain,(
% 1.61/1.32 ! [X0 : ($i > $o) > $i] : (? [X1 : $i > $o] : (((X1 @ (X0 @ X1)) != $true) & ? [X2 : $i] : ((X1 @ X2) = $true)) => (((sK0 @ X0 @ (X0 @ (sK0 @ X0))) != $true) & ? [X2 : $i] : ($true = (sK0 @ X0 @ X2))))),
% 1.61/1.32 introduced(definition,[],[choice_axiom])).
% 1.61/1.32 thf(f8,plain,(
% 1.61/1.32 ! [X0 : ($i > $o) > $i] : (? [X2 : $i] : ($true = (sK0 @ X0 @ X2)) => ((sK0 @ X0 @ (sK1 @ X0)) = $true))),
% 1.61/1.32 introduced(definition,[],[choice_axiom])).
% 1.61/1.32 thf(f6,plain,(
% 1.61/1.32 ! [X0 : ($i > $o) > $i] : ? [X1 : $i > $o] : (((X1 @ (X0 @ X1)) != $true) & ? [X2 : $i] : ((X1 @ X2) = $true))),
% 1.61/1.32 inference(ennf_transformation,[status(thm)],[f5])).
% 1.61/1.32 thf(f5,plain,(
% 1.61/1.32 ~? [X0 : ($i > $o) > $i] : ! [X1 : $i > $o] : (? [X2 : $i] : ((X1 @ X2) = $true) => ((X1 @ (X0 @ X1)) = $true))),
% 1.61/1.32 inference(fool_elimination,[status(thm)],[f4])).
% 1.61/1.32 thf(f4,plain,(
% 1.61/1.32 ~? [X0 : ($i > $o) > $i] : ! [X1 : $i > $o] : (? [X2 : $i] : (X1 @ X2) => (X1 @ (X0 @ X1)))),
% 1.61/1.32 inference(rectify,[status(thm)],[f2])).
% 1.61/1.32 thf(f2,negated_conjecture,(
% 1.61/1.32 ~? [X0 : ($i > $o) > $i] : ! [X1 : $i > $o] : (? [X2 : $i] : (X1 @ X2) => (X1 @ (X0 @ X1)))),
% 1.61/1.32 inference(negated_conjecture,[status(cth)],[f1])).
% 1.61/1.32 thf(f1,conjecture,(
% 1.61/1.32 ? [X0 : ($i > $o) > $i] : ! [X1 : $i > $o] : (? [X2 : $i] : (X1 @ X2) => (X1 @ (X0 @ X1)))),
% 1.61/1.32 file('/export/starexec/sandbox/tmp/tmp.qJ5bK45LbH/DTF2THF_8012.p',conj)).
% 1.61/1.32 thf(f16,plain,(
% 1.61/1.32 ( ! [X0 : $i] : (((sK0 @ @@+ @ $i @ X0) = $false)) )),
% 1.61/1.32 inference(trivial_inequality_removal,[status(thm)],[f14])).
% 1.61/1.32 thf(f14,plain,(
% 1.61/1.32 ( ! [X0 : $i] : (((sK0 @ @@+ @ $i @ X0) = $false) | ($true != $true)) )),
% 1.61/1.32 inference(superposition,[status(thm)],[f11,f12])).
% 1.61/1.32 thf(f12,plain,(
% 1.61/1.32 ( ! [X0 : ($i > $o) > $i,X1 : $i] : (((sK0 @ X0 @ (@@+ @ $i @ (sK0 @ X0))) = $true) | ((sK0 @ X0 @ X1) = $false)) )),
% 1.61/1.32 introduced(definition,[],[choice_axiom])).
% 1.61/1.32 thf(f11,plain,(
% 1.61/1.32 ( ! [X0 : ($i > $o) > $i] : (((sK0 @ X0 @ (X0 @ (sK0 @ X0))) != $true)) )),
% 1.61/1.32 inference(cnf_transformation,[status(thm)],[f9])).
% 1.61/1.32 % SZS output end Proof for DTF2THF_8012
% 1.61/1.32 % (8297)------------------------------
% 1.61/1.32 % (8297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.32 % (8297)Termination reason: Refutation
% 1.61/1.32
% 1.61/1.32 % (8297)Memory used [KB]: 5500
% 1.61/1.32 % (8297)Time elapsed: 0.005 s
% 1.61/1.32 % (8297)Instructions burned: 2 (million)
% 1.61/1.32 % (8297)------------------------------
% 1.61/1.32 % (8297)------------------------------
% 1.61/1.32 % (8294)Success in time 0.021 s
%------------------------------------------------------------------------------