%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYP003^1 : TPTP v9.2.1. Released v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n009.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 09:56:35 AM UTC 2026
% Result : Theorem 1.67s 1.32s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 97 ( 28 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 193 ( 17 ~; 4 |; 14 &; 151 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 2 con; 0-3 aty)
% Number of variables : 36 ( 0 ^; 22 !; 14 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
a: $tType ).
thf(type_def_7,type,
b: $tType ).
thf(func_def_0,type,
isPer:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > $o ) ).
thf(func_def_2,type,
a: $tType ).
thf(func_def_3,type,
aStar: a > a > $o ).
thf(func_def_4,type,
b: $tType ).
thf(func_def_5,type,
bStar: a > b > b > $o ).
thf(func_def_6,type,
p: a > b > $o ).
thf(func_def_7,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_10,type,
sK0: a > b ).
thf(func_def_11,type,
sK1: ( a > b ) > a ).
thf(func_def_12,type,
sK2: ( a > b ) > a ).
thf(func_def_13,type,
sK3:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_14,type,
sK4:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_15,type,
sK5:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_16,type,
sK6:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_17,type,
sK7:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_19,type,
ph9:
!>[X0: $tType] : X0 ).
thf(f107,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f106]) ).
thf(f106,plain,
$true != $true,
inference(superposition,[status(thm)],[f105,f35]) ).
thf(f35,plain,
! [X0: a] :
( ( p @ X0 @ ( sK0 @ X0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
( ! [X0: a] :
( ( ( bStar @ X0 @ ( sK0 @ X0 ) @ ( sK0 @ X0 ) )
= $true )
& ( ( p @ X0 @ ( sK0 @ X0 ) )
= $true ) )
& ! [X2: a > b] :
( ( ( p @ ( sK1 @ X2 ) @ ( X2 @ ( sK1 @ X2 ) ) )
!= $true )
| ( $true
!= ( bStar @ ( sK2 @ X2 ) @ ( X2 @ ( sK2 @ X2 ) ) @ ( X2 @ ( sK2 @ X2 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f21,f24,f23,f22]) ).
thf(f22,plain,
! [X0: a] :
( ? [X1: b] :
( ( $true
= ( bStar @ X0 @ X1 @ X1 ) )
& ( ( p @ X0 @ X1 )
= $true ) )
=> ( ( ( bStar @ X0 @ ( sK0 @ X0 ) @ ( sK0 @ X0 ) )
= $true )
& ( ( p @ X0 @ ( sK0 @ X0 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f23,plain,
! [X2: a > b] :
( ? [X3: a] :
( ( p @ X3 @ ( X2 @ X3 ) )
!= $true )
=> ( ( p @ ( sK1 @ X2 ) @ ( X2 @ ( sK1 @ X2 ) ) )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f24,plain,
! [X2: a > b] :
( ? [X4: a] :
( $true
!= ( bStar @ X4 @ ( X2 @ X4 ) @ ( X2 @ X4 ) ) )
=> ( $true
!= ( bStar @ ( sK2 @ X2 ) @ ( X2 @ ( sK2 @ X2 ) ) @ ( X2 @ ( sK2 @ X2 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
( ! [X0: a] :
? [X1: b] :
( ( $true
= ( bStar @ X0 @ X1 @ X1 ) )
& ( ( p @ X0 @ X1 )
= $true ) )
& ! [X2: a > b] :
( ? [X3: a] :
( ( p @ X3 @ ( X2 @ X3 ) )
!= $true )
| ? [X4: a] :
( $true
!= ( bStar @ X4 @ ( X2 @ X4 ) @ ( X2 @ X4 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
~ ( ! [X0: a] :
? [X1: b] :
( ( $true
= ( bStar @ X0 @ X1 @ X1 ) )
& ( ( p @ X0 @ X1 )
= $true ) )
=> ? [X2: a > b] :
( ! [X4: a] :
( $true
= ( bStar @ X4 @ ( X2 @ X4 ) @ ( X2 @ X4 ) ) )
& ! [X3: a] :
( ( p @ X3 @ ( X2 @ X3 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
~ ( ! [X0: a] :
? [X1: b] :
( ( bStar @ X0 @ X1 @ X1 )
& ( p @ X0 @ X1 ) )
=> ? [X2: a > b] :
( ! [X3: a] : ( p @ X3 @ ( X2 @ X3 ) )
& ! [X4: a] : ( bStar @ X4 @ ( X2 @ X4 ) @ ( X2 @ X4 ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( ! [X2: a] :
? [X3: b] :
( ( bStar @ X2 @ X3 @ X3 )
& ( p @ X2 @ X3 ) )
=> ? [X8: a > b] :
( ! [X2: a] : ( p @ X2 @ ( X8 @ X2 ) )
& ! [X9: a] : ( bStar @ X9 @ ( X8 @ X9 ) @ ( X8 @ X9 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( ! [X2: a] :
? [X3: b] :
( ( bStar @ X2 @ X3 @ X3 )
& ( p @ X2 @ X3 ) )
=> ? [X8: a > b] :
( ! [X2: a] : ( p @ X2 @ ( X8 @ X2 ) )
& ! [X9: a] : ( bStar @ X9 @ ( X8 @ X9 ) @ ( X8 @ X9 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XV6m3CeOMf/DTF2THF_26796.p',dskolem1) ).
thf(f105,plain,
( ( p @ ( sK1 @ sK0 ) @ ( sK0 @ ( sK1 @ sK0 ) ) )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f104]) ).
thf(f104,plain,
( ( ( p @ ( sK1 @ sK0 ) @ ( sK0 @ ( sK1 @ sK0 ) ) )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f34,f36]) ).
thf(f36,plain,
! [X0: a] :
( ( bStar @ X0 @ ( sK0 @ X0 ) @ ( sK0 @ X0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f34,plain,
! [X2: a > b] :
( ( $true
!= ( bStar @ ( sK2 @ X2 ) @ ( X2 @ ( sK2 @ X2 ) ) @ ( X2 @ ( sK2 @ X2 ) ) ) )
| ( ( p @ ( sK1 @ X2 ) @ ( X2 @ ( sK1 @ X2 ) ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYP003^1 : TPTP v9.2.1. Released v9.2.0.
% 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n009.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 14:56:40 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.46 thf(spec,logic,$$dhol).
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % File : SYP003^1 : TPTP v9.2.1. Released v9.2.0.
% 0.31/0.46 % Domain : Syntactic
% 0.31/0.46 % Problem : Axiom of (higher-order) choice for arbitrary types.
% 0.31/0.46 % Version : Especial.
% 0.31/0.46 % English :
% 0.31/0.46
% 0.31/0.46 % Refs : [RRB23] Rothgang et al. (2023), Theorem Proving in Dependently
% 0.31/0.46 % : [Rot25] Rothgang (2025), Email to Geoff Sutcliffe
% 0.31/0.46 % : [RK+25] Ranalter et al. (2025), The Dependently Typed Higher-O
% 0.31/0.46 % Source : [Rot25]
% 0.31/0.46 % Names : ChoiceBasic/dskolem1.p [Rot25]
% 0.31/0.46
% 0.31/0.46 % Status : Theorem
% 0.31/0.46 % Rating : ? v9.2.0
% 0.31/0.46 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.31/0.46 % Number of atoms : 2 ( 0 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 2 ( 2 avg)
% 0.31/0.46 % Number of connectives : 9 ( 0 ~; 0 |; 0 &; 8 @)
% 0.31/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.31/0.46 % Maximal formula depth : 6 ( 6 avg)
% 0.31/0.46 % Number of types : 2 ( 1 usr)
% 0.31/0.46 % Number of type decls : 3 ( 0 !>P; 2 !>D)
% 0.31/0.46 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 2 ( 2 usr; 0 con; 1-2 aty)
% 0.31/0.46 % Number of variables : 6 ( 0 ^; 2 !; 2 ?; 6 :)
% 0.31/0.46 % ( 2 !>; 0 ?*; 0 @-; 0 @+)
% 0.31/0.46 % SPC : DH0_THM_NEQ_NAR
% 0.31/0.46
% 0.31/0.46 % Comments :
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 thf(a_type,type,
% 0.31/0.46 a: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(b_type,type,
% 0.31/0.46 b: a > $tType ).
% 0.31/0.46
% 0.31/0.46 thf(p_type,type,
% 0.31/0.46 p:
% 0.31/0.46 !>[X: a] : ( ( b @ X ) > $o ) ).
% 0.31/0.46
% 0.31/0.46 thf(dskolem1,conjecture,
% 0.31/0.46 ( ! [X: a] :
% 0.31/0.46 ? [Y: b @ X] : ( p @ X @ Y )
% 0.31/0.46 => ? [F: !>[N: a] : ( b @ N )] :
% 0.31/0.46 ! [X: a] : ( p @ X @ ( F @ X ) ) ) ).
% 0.31/0.46
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 ------------------------
% 1.48/1.28 ---- Embedded in THF ---
% 1.48/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.28 %%% Generated on Tue Feb 24 14:56:41 EST 2026
% 1.48/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.28 %%% Logic specification used:
% 1.48/1.28 %%% thf(spec, logic, $$dhol).
% 1.48/1.28
% 1.48/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.XV6m3CeOMf/DTF2DTF26796.p
% See solution above
% 1.48/1.28 ------------------------
% 1.48/1.29 ---- Cleaned THF ---
% 1.48/1.29 thf(is_per_type,type,
% 1.48/1.29 isPer:
% 1.48/1.29 !>[A: $tType] : ( ( A > A > $o ) > $o ) ).
% 1.48/1.29
% 1.48/1.29 thf(is_per,definition,
% 1.48/1.29 ! [A: $tType,AStar: A > A > $o] :
% 1.48/1.29 ( ( isPer @ A @ AStar )
% 1.48/1.29 <=> ( ! [X: A,Y: A] :
% 1.48/1.29 ( ( AStar @ X @ Y )
% 1.48/1.29 => ( AStar @ Y @ X ) )
% 1.48/1.29 & ! [X: A,Y: A,Z: A] :
% 1.48/1.29 ( ( AStar @ X @ Y )
% 1.48/1.29 => ( ( AStar @ Y @ Z )
% 1.48/1.29 => ( AStar @ X @ Z ) ) ) ) ) ).
% 1.48/1.29
% 1.48/1.29 thf(a_type,type,
% 1.48/1.29 a: $tType ).
% 1.48/1.29
% 1.48/1.29 thf(aStar,type,
% 1.48/1.29 aStar: a > a > $o ).
% 1.48/1.29
% 1.48/1.29 thf(aStar_is_eq,axiom,
% 1.48/1.29 ! [X: a,Y: a] :
% 1.48/1.29 ( ( aStar @ X @ Y )
% 1.48/1.29 <=> ( X = Y ) ) ).
% 1.48/1.29
% 1.48/1.29 thf(b_type,type,
% 1.48/1.29 b: $tType ).
% 1.48/1.29
% 1.48/1.29 thf(bStar,type,
% 1.48/1.29 bStar: a > b > b > $o ).
% 1.48/1.29
% 1.48/1.29 thf('\'bStar\'_is_per',axiom,
% 1.48/1.29 ! [C: a] : ( isPer @ b @ ( bStar @ C ) ) ).
% 1.48/1.29
% 1.48/1.29 thf(p_type,type,
% 1.48/1.29 p: a > b > $o ).
% 1.48/1.29
% 1.48/1.29 thf(p_tp_ax,axiom,
% 1.48/1.29 ! [X: a,D: b,D_prime: b] :
% 1.48/1.29 ( ( bStar @ X @ D @ D_prime )
% 1.48/1.29 => ( ( p @ X @ D )
% 1.48/1.29 = ( p @ X @ D_prime ) ) ) ).
% 1.48/1.29
% 1.48/1.29 thf(dskolem1,conjecture,
% 1.48/1.29 ( ! [X: a] :
% 1.48/1.29 ? [Y: b] :
% 1.48/1.29 ( ( bStar @ X @ Y @ Y )
% 1.48/1.29 & ( p @ X @ Y ) )
% 1.48/1.29 => ? [F: a > b] :
% 1.48/1.29 ( ! [N: a] : ( bStar @ N @ ( F @ N ) @ ( F @ N ) )
% 1.48/1.29 & ! [X: a] : ( p @ X @ ( F @ X ) ) ) ) ).
% 1.48/1.29 ------------------------
% 1.67/1.31 % (27069)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_26796 for (2999ds/2Mi)
% 1.67/1.31 % (27069)Instruction limit reached!
% 1.67/1.31 % (27069)------------------------------
% 1.67/1.31 % (27069)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.31 % (27069)Termination reason: Unknown
% 1.67/1.31 % (27069)Termination phase: Preprocessing 1
% 1.67/1.31
% 1.67/1.31 % (27069)Memory used [KB]: 895
% 1.67/1.31 % (27069)Time elapsed: 0.002 s
% 1.67/1.31 % (27069)Instructions burned: 2 (million)
% 1.67/1.31 % (27069)------------------------------
% 1.67/1.31 % (27069)------------------------------
% 1.67/1.31 % (27068)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_26796 for (2999ds/27Mi)
% 1.67/1.32 % (27066)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_26796 for (2999ds/183Mi)
% 1.67/1.32 % (27067)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_26796 for (2999ds/4Mi)
% 1.67/1.32 % (27068)First to succeed.
% 1.67/1.32 % (27070)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_26796 for (2999ds/2Mi)
% 1.67/1.32 % (27071)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_26796 for (2999ds/275Mi)
% 1.67/1.32 % (27072)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_26796 for (2999ds/18Mi)
% 1.67/1.32 % (27070)Instruction limit reached!
% 1.67/1.32 % (27070)------------------------------
% 1.67/1.32 % (27070)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.32 % (27070)Termination reason: Unknown
% 1.67/1.32 % (27070)Termination phase: shuffling
% 1.67/1.32
% 1.67/1.32 % (27070)Memory used [KB]: 1023
% 1.67/1.32 % (27070)Time elapsed: 0.003 s
% 1.67/1.32 % (27070)Instructions burned: 2 (million)
% 1.67/1.32 % (27070)------------------------------
% 1.67/1.32 % (27070)------------------------------
% 1.67/1.32 % (27068)Refutation found. Thanks to Tanya!
% 1.67/1.32 % SZS status Theorem for DTF2THF_26796
% 1.67/1.32 % SZS output start Proof for DTF2THF_26796
% 1.67/1.32 thf(type_def_6, type, a: $tType).
% 1.67/1.32 thf(type_def_7, type, b: $tType).
% 1.67/1.32 thf(func_def_0, type, isPer: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 1.67/1.32 thf(func_def_2, type, a: $tType).
% 1.67/1.32 thf(func_def_3, type, aStar: a > a > $o).
% 1.67/1.32 thf(func_def_4, type, b: $tType).
% 1.67/1.32 thf(func_def_5, type, bStar: a > b > b > $o).
% 1.67/1.32 thf(func_def_6, type, p: a > b > $o).
% 1.67/1.32 thf(func_def_7, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.67/1.32 thf(func_def_10, type, sK0: a > b).
% 1.67/1.32 thf(func_def_11, type, sK1: (a > b) > a).
% 1.67/1.32 thf(func_def_12, type, sK2: (a > b) > a).
% 1.67/1.32 thf(func_def_13, type, sK3: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.67/1.32 thf(func_def_14, type, sK4: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.67/1.32 thf(func_def_15, type, sK5: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.67/1.32 thf(func_def_16, type, sK6: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.67/1.32 thf(func_def_17, type, sK7: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.67/1.32 thf(func_def_19, type, ph9: !>[X0: $tType]:(X0)).
% 1.67/1.32 thf(f107,plain,(
% 1.67/1.32 $false),
% 1.67/1.32 inference(trivial_inequality_removal,[status(thm)],[f106])).
% 1.67/1.32 thf(f106,plain,(
% 1.67/1.32 ($true != $true)),
% 1.67/1.32 inference(superposition,[status(thm)],[f105,f35])).
% 1.67/1.32 thf(f35,plain,(
% 1.67/1.32 ( ! [X0 : a] : (((p @ X0 @ (sK0 @ X0)) = $true)) )),
% 1.67/1.32 inference(cnf_transformation,[status(thm)],[f25])).
% 1.67/1.32 thf(f25,plain,(
% 1.67/1.32 ! [X0 : a] : (((bStar @ X0 @ (sK0 @ X0) @ (sK0 @ X0)) = $true) & ((p @ X0 @ (sK0 @ X0)) = $true)) & ! [X2 : a > b] : (((p @ (sK1 @ X2) @ (X2 @ (sK1 @ X2))) != $true) | ($true != (bStar @ (sK2 @ X2) @ (X2 @ (sK2 @ X2)) @ (X2 @ (sK2 @ X2)))))),
% 1.67/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f21,f24,f23,f22])).
% 1.67/1.32 thf(f22,plain,(
% 1.67/1.32 ! [X0 : a] : (? [X1 : b] : (($true = (bStar @ X0 @ X1 @ X1)) & ((p @ X0 @ X1) = $true)) => (((bStar @ X0 @ (sK0 @ X0) @ (sK0 @ X0)) = $true) & ((p @ X0 @ (sK0 @ X0)) = $true)))),
% 1.67/1.32 introduced(definition,[],[choice_axiom])).
% 1.67/1.32 thf(f23,plain,(
% 1.67/1.32 ! [X2 : a > b] : (? [X3 : a] : ((p @ X3 @ (X2 @ X3)) != $true) => ((p @ (sK1 @ X2) @ (X2 @ (sK1 @ X2))) != $true))),
% 1.67/1.32 introduced(definition,[],[choice_axiom])).
% 1.67/1.32 thf(f24,plain,(
% 1.67/1.32 ! [X2 : a > b] : (? [X4 : a] : ($true != (bStar @ X4 @ (X2 @ X4) @ (X2 @ X4))) => ($true != (bStar @ (sK2 @ X2) @ (X2 @ (sK2 @ X2)) @ (X2 @ (sK2 @ X2)))))),
% 1.67/1.32 introduced(definition,[],[choice_axiom])).
% 1.67/1.32 thf(f21,plain,(
% 1.67/1.32 ! [X0 : a] : ? [X1 : b] : (($true = (bStar @ X0 @ X1 @ X1)) & ((p @ X0 @ X1) = $true)) & ! [X2 : a > b] : (? [X3 : a] : ((p @ X3 @ (X2 @ X3)) != $true) | ? [X4 : a] : ($true != (bStar @ X4 @ (X2 @ X4) @ (X2 @ X4))))),
% 1.67/1.32 inference(ennf_transformation,[status(thm)],[f17])).
% 1.67/1.32 thf(f17,plain,(
% 1.67/1.32 ~(! [X0 : a] : ? [X1 : b] : (($true = (bStar @ X0 @ X1 @ X1)) & ((p @ X0 @ X1) = $true)) => ? [X2 : a > b] : (! [X4 : a] : ($true = (bStar @ X4 @ (X2 @ X4) @ (X2 @ X4))) & ! [X3 : a] : ((p @ X3 @ (X2 @ X3)) = $true)))),
% 1.67/1.32 inference(fool_elimination,[status(thm)],[f16])).
% 1.67/1.32 thf(f16,plain,(
% 1.67/1.32 ~(! [X0 : a] : ? [X1 : b] : ((bStar @ X0 @ X1 @ X1) & (p @ X0 @ X1)) => ? [X2 : a > b] : (! [X3 : a] : (p @ X3 @ (X2 @ X3)) & ! [X4 : a] : (bStar @ X4 @ (X2 @ X4) @ (X2 @ X4))))),
% 1.67/1.32 inference(rectify,[status(thm)],[f6])).
% 1.67/1.32 thf(f6,negated_conjecture,(
% 1.67/1.32 ~(! [X2 : a] : ? [X3 : b] : ((bStar @ X2 @ X3 @ X3) & (p @ X2 @ X3)) => ? [X8 : a > b] : (! [X2 : a] : (p @ X2 @ (X8 @ X2)) & ! [X9 : a] : (bStar @ X9 @ (X8 @ X9) @ (X8 @ X9))))),
% 1.67/1.32 inference(negated_conjecture,[status(cth)],[f5])).
% 1.67/1.32 thf(f5,conjecture,(
% 1.67/1.32 ! [X2 : a] : ? [X3 : b] : ((bStar @ X2 @ X3 @ X3) & (p @ X2 @ X3)) => ? [X8 : a > b] : (! [X2 : a] : (p @ X2 @ (X8 @ X2)) & ! [X9 : a] : (bStar @ X9 @ (X8 @ X9) @ (X8 @ X9)))),
% 1.67/1.32 file('/export/starexec/sandbox2/tmp/tmp.XV6m3CeOMf/DTF2THF_26796.p',dskolem1)).
% 1.67/1.32 thf(f105,plain,(
% 1.67/1.32 ((p @ (sK1 @ sK0) @ (sK0 @ (sK1 @ sK0))) != $true)),
% 1.67/1.32 inference(trivial_inequality_removal,[status(thm)],[f104])).
% 1.67/1.32 thf(f104,plain,(
% 1.67/1.32 ((p @ (sK1 @ sK0) @ (sK0 @ (sK1 @ sK0))) != $true) | ($true != $true)),
% 1.67/1.32 inference(superposition,[status(thm)],[f34,f36])).
% 1.67/1.32 thf(f36,plain,(
% 1.67/1.32 ( ! [X0 : a] : (((bStar @ X0 @ (sK0 @ X0) @ (sK0 @ X0)) = $true)) )),
% 1.67/1.32 inference(cnf_transformation,[status(thm)],[f25])).
% 1.67/1.32 thf(f34,plain,(
% 1.67/1.32 ( ! [X2 : a > b] : (($true != (bStar @ (sK2 @ X2) @ (X2 @ (sK2 @ X2)) @ (X2 @ (sK2 @ X2)))) | ((p @ (sK1 @ X2) @ (X2 @ (sK1 @ X2))) != $true)) )),
% 1.67/1.32 inference(cnf_transformation,[status(thm)],[f25])).
% 1.67/1.32 % SZS output end Proof for DTF2THF_26796
% 1.67/1.32 % (27068)------------------------------
% 1.67/1.32 % (27068)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.32 % (27068)Termination reason: Refutation
% 1.67/1.32
% 1.67/1.32 % (27068)Memory used [KB]: 5628
% 1.67/1.32 % (27068)Time elapsed: 0.008 s
% 1.67/1.32 % (27068)Instructions burned: 17 (million)
% 1.67/1.32 % (27068)------------------------------
% 1.67/1.32 % (27068)------------------------------
% 1.67/1.32 % (27065)Success in time 0.019 s
%------------------------------------------------------------------------------