%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYP007^1 : 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 : n024.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 09:56:36 AM UTC 2026
% Result : Theorem 1.01s 0.92s
% Output : Refutation 1.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 106 ( 31 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 210 ( 18 ~; 5 |; 16 &; 164 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 41 ( 0 ^; 24 !; 17 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
nat: $tType ).
thf(type_def_7,type,
fin: $tType ).
thf(func_def_0,type,
isPer:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > $o ) ).
thf(func_def_2,type,
nat: $tType ).
thf(func_def_3,type,
natStar: nat > nat > $o ).
thf(func_def_4,type,
fin: $tType ).
thf(func_def_5,type,
finStar: nat > fin > fin > $o ).
thf(func_def_6,type,
p: nat > fin > $o ).
thf(func_def_9,type,
sK0: ( nat > fin ) > nat ).
thf(func_def_10,type,
sK1: ( nat > fin ) > nat ).
thf(func_def_11,type,
sK2: nat > fin ).
thf(func_def_13,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f37,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f36,f26]) ).
thf(f26,plain,
! [X3: nat] :
( $true
= ( p @ X3 @ ( sK2 @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( ! [X0: nat > fin] :
( ( $true
!= ( p @ ( sK0 @ X0 ) @ ( X0 @ ( sK0 @ X0 ) ) ) )
| ( $true
!= ( finStar @ ( sK1 @ X0 ) @ ( X0 @ ( sK1 @ X0 ) ) @ ( X0 @ ( sK1 @ X0 ) ) ) ) )
& ! [X3: nat] :
( ( $true
= ( p @ X3 @ ( sK2 @ X3 ) ) )
& ( $true
= ( finStar @ X3 @ ( sK2 @ X3 ) @ ( sK2 @ X3 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f20,f23,f22,f21]) ).
thf(f21,plain,
! [X0: nat > fin] :
( ? [X1: nat] :
( $true
!= ( p @ X1 @ ( X0 @ X1 ) ) )
=> ( $true
!= ( p @ ( sK0 @ X0 ) @ ( X0 @ ( sK0 @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f22,plain,
! [X0: nat > fin] :
( ? [X2: nat] :
( $true
!= ( finStar @ X2 @ ( X0 @ X2 ) @ ( X0 @ X2 ) ) )
=> ( $true
!= ( finStar @ ( sK1 @ X0 ) @ ( X0 @ ( sK1 @ X0 ) ) @ ( X0 @ ( sK1 @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f23,plain,
! [X3: nat] :
( ? [X4: fin] :
( ( $true
= ( p @ X3 @ X4 ) )
& ( $true
= ( finStar @ X3 @ X4 @ X4 ) ) )
=> ( ( $true
= ( p @ X3 @ ( sK2 @ X3 ) ) )
& ( $true
= ( finStar @ X3 @ ( sK2 @ X3 ) @ ( sK2 @ X3 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f20,plain,
( ! [X0: nat > fin] :
( ? [X1: nat] :
( $true
!= ( p @ X1 @ ( X0 @ X1 ) ) )
| ? [X2: nat] :
( $true
!= ( finStar @ X2 @ ( X0 @ X2 ) @ ( X0 @ X2 ) ) ) )
& ! [X3: nat] :
? [X4: fin] :
( ( $true
= ( p @ X3 @ X4 ) )
& ( $true
= ( finStar @ X3 @ X4 @ X4 ) ) ) ),
inference(rectify,[status(thm)],[f18]) ).
thf(f18,plain,
( ! [X2: nat > fin] :
( ? [X4: nat] :
( $true
!= ( p @ X4 @ ( X2 @ X4 ) ) )
| ? [X3: nat] :
( $true
!= ( finStar @ X3 @ ( X2 @ X3 ) @ ( X2 @ X3 ) ) ) )
& ! [X0: nat] :
? [X1: fin] :
( ( $true
= ( p @ X0 @ X1 ) )
& ( $true
= ( finStar @ X0 @ X1 @ X1 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( ! [X0: nat] :
? [X1: fin] :
( ( $true
= ( p @ X0 @ X1 ) )
& ( $true
= ( finStar @ X0 @ X1 @ X1 ) ) )
=> ? [X2: nat > fin] :
( ! [X3: nat] :
( $true
= ( finStar @ X3 @ ( X2 @ X3 ) @ ( X2 @ X3 ) ) )
& ! [X4: nat] :
( $true
= ( p @ X4 @ ( X2 @ X4 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( ! [X0: nat] :
? [X1: fin] :
( ( p @ X0 @ X1 )
& ( finStar @ X0 @ X1 @ X1 ) )
=> ? [X2: nat > fin] :
( ! [X3: nat] : ( finStar @ X3 @ ( X2 @ X3 ) @ ( X2 @ X3 ) )
& ! [X4: nat] : ( p @ X4 @ ( X2 @ X4 ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( ! [X8: nat] :
? [X3: fin] :
( ( p @ X8 @ X3 )
& ( finStar @ X8 @ X3 @ X3 ) )
=> ? [X9: nat > fin] :
( ! [X10: nat] : ( finStar @ X10 @ ( X9 @ X10 ) @ ( X9 @ X10 ) )
& ! [X4: nat] : ( p @ X4 @ ( X9 @ X4 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( ! [X8: nat] :
? [X3: fin] :
( ( p @ X8 @ X3 )
& ( finStar @ X8 @ X3 @ X3 ) )
=> ? [X9: nat > fin] :
( ! [X10: nat] : ( finStar @ X10 @ ( X9 @ X10 ) @ ( X9 @ X10 ) )
& ! [X4: nat] : ( p @ X4 @ ( X9 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XeR12iRrKN/DTF2THF_32741.p',ho_choice) ).
thf(f36,plain,
( ( p @ ( sK0 @ sK2 ) @ ( sK2 @ ( sK0 @ sK2 ) ) )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f35]) ).
thf(f35,plain,
( ( $true != $true )
| ( ( p @ ( sK0 @ sK2 ) @ ( sK2 @ ( sK0 @ sK2 ) ) )
!= $true ) ),
inference(superposition,[status(thm)],[f27,f25]) ).
thf(f25,plain,
! [X3: nat] :
( $true
= ( finStar @ X3 @ ( sK2 @ X3 ) @ ( sK2 @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f27,plain,
! [X0: nat > fin] :
( ( $true
!= ( finStar @ ( sK1 @ X0 ) @ ( X0 @ ( sK1 @ X0 ) ) @ ( X0 @ ( sK1 @ X0 ) ) ) )
| ( $true
!= ( p @ ( sK0 @ X0 ) @ ( X0 @ ( sK0 @ X0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SYP007^1 : TPTP v9.2.1. Released v9.2.0.
% 0.00/0.06 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.24 % Computer : n024.cluster.edu
% 0.08/0.24 % Model : x86_64 x86_64
% 0.08/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.24 % Memory : 8042.1875MB
% 0.08/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.24 % CPULimit : 300
% 0.08/0.24 % WCLimit : 300
% 0.08/0.24 % DateTime : Tue Feb 24 09:56:40 EST 2026
% 0.08/0.25 % CPUTime :
% 0.08/0.25 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.31 ---- Original DTF file ---
% 0.08/0.31 thf(spec,logic,$$dhol).
% 0.08/0.31 %------------------------------------------------------------------------------
% 0.08/0.31 % File : SYP007^1 : TPTP v9.2.1. Released v9.2.0.
% 0.08/0.31 % Domain : Syntactic
% 0.08/0.31 % Problem : Axiom of higher-order choice for natural numbers and finite sets
% 0.08/0.31 % Version : Especial.
% 0.08/0.31 % English :
% 0.08/0.31
% 0.08/0.31 % Refs : [RRB23] Rothgang et al. (2023), Theorem Proving in Dependently
% 0.08/0.31 % : [Rot25] Rothgang (2025), Email to Geoff Sutcliffe
% 0.08/0.31 % : [RK+25] Ranalter et al. (2025), The Dependently Typed Higher-O
% 0.08/0.31 % Source : [Rot25]
% 0.08/0.31 % Names : ChoiceBasic/choice1.p [Rot25]
% 0.08/0.31
% 0.08/0.31 % Status : Theorem
% 0.08/0.31 % Rating : ? v9.2.0
% 0.08/0.31 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.08/0.31 % Number of atoms : 2 ( 0 equ; 0 cnn)
% 0.08/0.31 % Maximal formula atoms : 2 ( 2 avg)
% 0.08/0.31 % Number of connectives : 9 ( 0 ~; 0 |; 0 &; 8 @)
% 0.08/0.31 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.08/0.31 % Maximal formula depth : 6 ( 6 avg)
% 0.08/0.31 % Number of types : 2 ( 1 usr)
% 0.08/0.31 % Number of type decls : 3 ( 0 !>P; 2 !>D)
% 0.08/0.31 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.08/0.31 % Number of symbols : 2 ( 2 usr; 0 con; 1-2 aty)
% 0.08/0.31 % Number of variables : 6 ( 0 ^; 2 !; 2 ?; 6 :)
% 0.08/0.31 % ( 2 !>; 0 ?*; 0 @-; 0 @+)
% 0.08/0.31 % SPC : DH0_THM_NEQ_NAR
% 0.08/0.31
% 0.08/0.31 % Comments :
% 0.08/0.31 %------------------------------------------------------------------------------
% 0.08/0.31 thf(nat_type,type,
% 0.08/0.31 nat: $tType ).
% 0.08/0.31
% 0.08/0.31 thf(fin_type,type,
% 0.08/0.31 fin: nat > $tType ).
% 0.08/0.31
% 0.08/0.31 thf(p_type,type,
% 0.08/0.31 p:
% 0.08/0.31 !>[Y: nat] : ( ( fin @ Y ) > $o ) ).
% 0.08/0.31
% 0.08/0.31 thf(ho_choice,conjecture,
% 0.08/0.31 ( ! [W: nat] :
% 0.08/0.31 ? [Y: fin @ W] : ( p @ W @ Y )
% 0.08/0.31 => ? [F: !>[N: nat] : ( fin @ N )] :
% 0.08/0.31 ! [Z: nat] : ( p @ Z @ ( F @ Z ) ) ) ).
% 0.08/0.31
% 0.08/0.31 %------------------------------------------------------------------------------
% 0.08/0.31 ------------------------
% 1.01/0.90 ---- Embedded in THF ---
% 1.01/0.90 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.01/0.90 %%% Generated on Tue Feb 24 09:56:41 EST 2026
% 1.01/0.90 %%% using '$$dhol' embedding, version 1.3.0.
% 1.01/0.90 %%% Logic specification used:
% 1.01/0.90 %%% thf(spec, logic, $$dhol).
% 1.01/0.90
% 1.01/0.90 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.XeR12iRrKN/DTF2DTF32741.p
% See solution above
% 1.01/0.90 ------------------------
% 1.01/0.91 ---- Cleaned THF ---
% 1.01/0.91 thf(is_per_type,type,
% 1.01/0.91 isPer:
% 1.01/0.91 !>[A: $tType] : ( ( A > A > $o ) > $o ) ).
% 1.01/0.91
% 1.01/0.91 thf(is_per,definition,
% 1.01/0.91 ! [A: $tType,AStar: A > A > $o] :
% 1.01/0.91 ( ( isPer @ A @ AStar )
% 1.01/0.91 <=> ( ! [X: A,Y: A] :
% 1.01/0.91 ( ( AStar @ X @ Y )
% 1.01/0.91 => ( AStar @ Y @ X ) )
% 1.01/0.91 & ! [X: A,Y: A,Z: A] :
% 1.01/0.91 ( ( AStar @ X @ Y )
% 1.01/0.91 => ( ( AStar @ Y @ Z )
% 1.01/0.91 => ( AStar @ X @ Z ) ) ) ) ) ).
% 1.01/0.91
% 1.01/0.91 thf(nat_type,type,
% 1.01/0.91 nat: $tType ).
% 1.01/0.91
% 1.01/0.91 thf(natStar,type,
% 1.01/0.91 natStar: nat > nat > $o ).
% 1.01/0.91
% 1.01/0.91 thf(natStar_is_eq,axiom,
% 1.01/0.91 ! [X: nat,Y: nat] :
% 1.01/0.91 ( ( natStar @ X @ Y )
% 1.01/0.91 <=> ( X = Y ) ) ).
% 1.01/0.91
% 1.01/0.91 thf(fin_type,type,
% 1.01/0.91 fin: $tType ).
% 1.01/0.91
% 1.01/0.91 thf(finStar,type,
% 1.01/0.91 finStar: nat > fin > fin > $o ).
% 1.01/0.91
% 1.01/0.91 thf('\'finStar\'_is_per',axiom,
% 1.01/0.91 ! [C: nat] : ( isPer @ fin @ ( finStar @ C ) ) ).
% 1.01/0.91
% 1.01/0.91 thf(p_type,type,
% 1.01/0.91 p: nat > fin > $o ).
% 1.01/0.91
% 1.01/0.91 thf(p_tp_ax,axiom,
% 1.01/0.91 ! [Y: nat,D: fin,D_prime: fin] :
% 1.01/0.91 ( ( finStar @ Y @ D @ D_prime )
% 1.01/0.91 => ( ( p @ Y @ D )
% 1.01/0.91 = ( p @ Y @ D_prime ) ) ) ).
% 1.01/0.91
% 1.01/0.91 thf(ho_choice,conjecture,
% 1.01/0.91 ( ! [W: nat] :
% 1.01/0.91 ? [Y: fin] :
% 1.01/0.91 ( ( finStar @ W @ Y @ Y )
% 1.01/0.91 & ( p @ W @ Y ) )
% 1.01/0.91 => ? [F: nat > fin] :
% 1.01/0.91 ( ! [N: nat] : ( finStar @ N @ ( F @ N ) @ ( F @ N ) )
% 1.01/0.91 & ! [Z: nat] : ( p @ Z @ ( F @ Z ) ) ) ) ).
% 1.01/0.91 ------------------------
% 1.01/0.92 % (493)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_32741 for (3000ds/183Mi)
% 1.01/0.92 % (501)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_32741 for (3000ds/18Mi)
% 1.01/0.92 % (498)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_32741 for (3000ds/2Mi)
% 1.01/0.92 % (495)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_32741 for (3000ds/27Mi)
% 1.01/0.92 % (499)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_32741 for (3000ds/275Mi)
% 1.01/0.92 % (494)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_32741 for (3000ds/4Mi)
% 1.01/0.92 % (496)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_32741 for (3000ds/2Mi)
% 1.01/0.92 % (496)Instruction limit reached!
% 1.01/0.92 % (496)------------------------------
% 1.01/0.92 % (496)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.01/0.92 % (496)Termination reason: Unknown
% 1.01/0.92 % (496)Termination phase: Property scanning
% 1.01/0.92
% 1.01/0.92 % (496)Memory used [KB]: 1023
% 1.01/0.92 % (496)Time elapsed: 0.002 s
% 1.01/0.92 % (496)Instructions burned: 3 (million)
% 1.01/0.92 % (496)------------------------------
% 1.01/0.92 % (496)------------------------------
% 1.01/0.92 % (498)Instruction limit reached!
% 1.01/0.92 % (498)------------------------------
% 1.01/0.92 % (498)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.01/0.92 % (498)Termination reason: Unknown
% 1.01/0.92 % (498)Termination phase: Saturation
% 1.01/0.92
% 1.01/0.92 % (498)Memory used [KB]: 1023
% 1.01/0.92 % (498)Time elapsed: 0.002 s
% 1.01/0.92 % (498)Instructions burned: 3 (million)
% 1.01/0.92 % (498)------------------------------
% 1.01/0.92 % (498)------------------------------
% 1.01/0.92 % (494)Instruction limit reached!
% 1.01/0.92 % (494)------------------------------
% 1.01/0.92 % (494)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.01/0.92 % (494)Termination reason: Unknown
% 1.01/0.92 % (494)Termination phase: Saturation
% 1.01/0.92
% 1.01/0.92 % (494)Memory used [KB]: 5500
% 1.01/0.92 % (494)Time elapsed: 0.003 s
% 1.01/0.92 % (494)Instructions burned: 5 (million)
% 1.01/0.92 % (494)------------------------------
% 1.01/0.92 % (494)------------------------------
% 1.01/0.92 % (499)First to succeed.
% 1.01/0.92 % (499)Refutation found. Thanks to Tanya!
% 1.01/0.92 % SZS status Theorem for DTF2THF_32741
% 1.01/0.92 % SZS output start Proof for DTF2THF_32741
% 1.01/0.92 thf(type_def_6, type, nat: $tType).
% 1.01/0.92 thf(type_def_7, type, fin: $tType).
% 1.01/0.92 thf(func_def_0, type, isPer: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 1.01/0.92 thf(func_def_2, type, nat: $tType).
% 1.01/0.92 thf(func_def_3, type, natStar: nat > nat > $o).
% 1.01/0.92 thf(func_def_4, type, fin: $tType).
% 1.01/0.92 thf(func_def_5, type, finStar: nat > fin > fin > $o).
% 1.01/0.92 thf(func_def_6, type, p: nat > fin > $o).
% 1.01/0.92 thf(func_def_9, type, sK0: (nat > fin) > nat).
% 1.01/0.92 thf(func_def_10, type, sK1: (nat > fin) > nat).
% 1.01/0.92 thf(func_def_11, type, sK2: nat > fin).
% 1.01/0.92 thf(func_def_13, type, ph4: !>[X0: $tType]:(X0)).
% 1.01/0.92 thf(f37,plain,(
% 1.01/0.92 $false),
% 1.01/0.92 inference(subsumption_resolution,[status(thm)],[f36,f26])).
% 1.01/0.92 thf(f26,plain,(
% 1.01/0.92 ( ! [X3 : nat] : (($true = (p @ X3 @ (sK2 @ X3)))) )),
% 1.01/0.92 inference(cnf_transformation,[status(thm)],[f24])).
% 1.01/0.92 thf(f24,plain,(
% 1.01/0.92 ! [X0 : nat > fin] : (($true != (p @ (sK0 @ X0) @ (X0 @ (sK0 @ X0)))) | ($true != (finStar @ (sK1 @ X0) @ (X0 @ (sK1 @ X0)) @ (X0 @ (sK1 @ X0))))) & ! [X3 : nat] : (($true = (p @ X3 @ (sK2 @ X3))) & ($true = (finStar @ X3 @ (sK2 @ X3) @ (sK2 @ X3))))),
% 1.01/0.92 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f20,f23,f22,f21])).
% 1.01/0.92 thf(f21,plain,(
% 1.01/0.92 ! [X0 : nat > fin] : (? [X1 : nat] : ($true != (p @ X1 @ (X0 @ X1))) => ($true != (p @ (sK0 @ X0) @ (X0 @ (sK0 @ X0)))))),
% 1.01/0.92 introduced(definition,[],[choice_axiom])).
% 1.01/0.92 thf(f22,plain,(
% 1.01/0.92 ! [X0 : nat > fin] : (? [X2 : nat] : ($true != (finStar @ X2 @ (X0 @ X2) @ (X0 @ X2))) => ($true != (finStar @ (sK1 @ X0) @ (X0 @ (sK1 @ X0)) @ (X0 @ (sK1 @ X0)))))),
% 1.01/0.92 introduced(definition,[],[choice_axiom])).
% 1.01/0.92 thf(f23,plain,(
% 1.01/0.92 ! [X3 : nat] : (? [X4 : fin] : (($true = (p @ X3 @ X4)) & ($true = (finStar @ X3 @ X4 @ X4))) => (($true = (p @ X3 @ (sK2 @ X3))) & ($true = (finStar @ X3 @ (sK2 @ X3) @ (sK2 @ X3)))))),
% 1.01/0.92 introduced(definition,[],[choice_axiom])).
% 1.01/0.92 thf(f20,plain,(
% 1.01/0.92 ! [X0 : nat > fin] : (? [X1 : nat] : ($true != (p @ X1 @ (X0 @ X1))) | ? [X2 : nat] : ($true != (finStar @ X2 @ (X0 @ X2) @ (X0 @ X2)))) & ! [X3 : nat] : ? [X4 : fin] : (($true = (p @ X3 @ X4)) & ($true = (finStar @ X3 @ X4 @ X4)))),
% 1.01/0.92 inference(rectify,[status(thm)],[f18])).
% 1.01/0.92 thf(f18,plain,(
% 1.01/0.92 ! [X2 : nat > fin] : (? [X4 : nat] : ($true != (p @ X4 @ (X2 @ X4))) | ? [X3 : nat] : ($true != (finStar @ X3 @ (X2 @ X3) @ (X2 @ X3)))) & ! [X0 : nat] : ? [X1 : fin] : (($true = (p @ X0 @ X1)) & ($true = (finStar @ X0 @ X1 @ X1)))),
% 1.01/0.92 inference(ennf_transformation,[status(thm)],[f9])).
% 1.01/0.92 thf(f9,plain,(
% 1.01/0.92 ~(! [X0 : nat] : ? [X1 : fin] : (($true = (p @ X0 @ X1)) & ($true = (finStar @ X0 @ X1 @ X1))) => ? [X2 : nat > fin] : (! [X3 : nat] : ($true = (finStar @ X3 @ (X2 @ X3) @ (X2 @ X3))) & ! [X4 : nat] : ($true = (p @ X4 @ (X2 @ X4)))))),
% 1.01/0.92 inference(fool_elimination,[status(thm)],[f8])).
% 1.01/0.92 thf(f8,plain,(
% 1.01/0.92 ~(! [X0 : nat] : ? [X1 : fin] : ((p @ X0 @ X1) & (finStar @ X0 @ X1 @ X1)) => ? [X2 : nat > fin] : (! [X3 : nat] : (finStar @ X3 @ (X2 @ X3) @ (X2 @ X3)) & ! [X4 : nat] : (p @ X4 @ (X2 @ X4))))),
% 1.01/0.92 inference(rectify,[status(thm)],[f6])).
% 1.01/0.92 thf(f6,negated_conjecture,(
% 1.01/0.92 ~(! [X8 : nat] : ? [X3 : fin] : ((p @ X8 @ X3) & (finStar @ X8 @ X3 @ X3)) => ? [X9 : nat > fin] : (! [X10 : nat] : (finStar @ X10 @ (X9 @ X10) @ (X9 @ X10)) & ! [X4 : nat] : (p @ X4 @ (X9 @ X4))))),
% 1.01/0.92 inference(negated_conjecture,[status(cth)],[f5])).
% 1.01/0.92 thf(f5,conjecture,(
% 1.01/0.92 ! [X8 : nat] : ? [X3 : fin] : ((p @ X8 @ X3) & (finStar @ X8 @ X3 @ X3)) => ? [X9 : nat > fin] : (! [X10 : nat] : (finStar @ X10 @ (X9 @ X10) @ (X9 @ X10)) & ! [X4 : nat] : (p @ X4 @ (X9 @ X4)))),
% 1.01/0.92 file('/export/starexec/sandbox2/tmp/tmp.XeR12iRrKN/DTF2THF_32741.p',ho_choice)).
% 1.01/0.92 thf(f36,plain,(
% 1.01/0.92 ((p @ (sK0 @ sK2) @ (sK2 @ (sK0 @ sK2))) != $true)),
% 1.01/0.92 inference(trivial_inequality_removal,[status(thm)],[f35])).
% 1.01/0.92 thf(f35,plain,(
% 1.01/0.92 ($true != $true) | ((p @ (sK0 @ sK2) @ (sK2 @ (sK0 @ sK2))) != $true)),
% 1.01/0.92 inference(superposition,[status(thm)],[f27,f25])).
% 1.01/0.92 thf(f25,plain,(
% 1.01/0.92 ( ! [X3 : nat] : (($true = (finStar @ X3 @ (sK2 @ X3) @ (sK2 @ X3)))) )),
% 1.01/0.92 inference(cnf_transformation,[status(thm)],[f24])).
% 1.01/0.92 thf(f27,plain,(
% 1.01/0.92 ( ! [X0 : nat > fin] : (($true != (finStar @ (sK1 @ X0) @ (X0 @ (sK1 @ X0)) @ (X0 @ (sK1 @ X0)))) | ($true != (p @ (sK0 @ X0) @ (X0 @ (sK0 @ X0))))) )),
% 1.01/0.92 inference(cnf_transformation,[status(thm)],[f24])).
% 1.01/0.92 % SZS output end Proof for DTF2THF_32741
% 1.01/0.92 % (499)------------------------------
% 1.01/0.92 % (499)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.01/0.92 % (499)Termination reason: Refutation
% 1.01/0.92
% 1.01/0.92 % (499)Memory used [KB]: 5500
% 1.01/0.92 % (499)Time elapsed: 0.003 s
% 1.01/0.92 % (499)Instructions burned: 2 (million)
% 1.01/0.92 % (499)------------------------------
% 1.01/0.92 % (499)------------------------------
% 1.01/0.92 % (489)Success in time 0.01 s
%------------------------------------------------------------------------------