%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO010^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n010.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 09:53:07 AM UTC 2026
% Result : Theorem 1.45s 1.28s
% Output : Refutation 1.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 2
% Syntax : Number of formulae : 27 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 97 ( 33 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 129 ( 14 ~; 2 |; 9 &; 87 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 5 usr; 4 con; 0-2 aty)
% ( 4 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 53 ( 34 ^; 19 !; 0 ?; 53 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
leibeq: $i > $i > $o ).
thf(func_def_2,type,
p: ( $i > $i ) > $o ).
thf(func_def_3,type,
f: $i > $i ).
thf(func_def_14,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f55,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f53]) ).
thf(f53,plain,
sK2 != sK2,
inference(superposition,[status(thm)],[f25,f27]) ).
thf(f27,plain,
! [X0: $i] :
( ( f @ X0 )
= X0 ),
inference(leibniz_equality_elimination,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: $i,X1: $i > $o] :
( ( ( X1 @ ( f @ X0 ) )
= $false )
| ( $true
= ( X1 @ X0 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: $i,X1: $i > $o] :
( ( ( X1 @ ( f @ X0 ) )
=> ( X1 @ X0 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: $i,X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( ( Y0 @ ( f @ X0 ) )
=> ( Y0 @ X0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: $i] :
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0 @ ( f @ X0 ) )
=> ( Y0 @ X0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: $i] :
( $true
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) )
@ ( f @ X0 )
@ X0 ) ),
inference(definition_unfolding,[status(thm)],[f12,f15]) ).
thf(f15,plain,
( leibeq
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( leibeq
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ^ [X0: $i,X1: $i] :
! [X2: $i > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) )
= leibeq ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: $i,X1: $i] :
! [X2: $i > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) )
= leibeq ),
file('/export/starexec/sandbox2/tmp/tmp.YR0tdaJfiN/DTF2THF_4429.p',leibeq) ).
thf(f12,plain,
! [X0: $i] :
( ( leibeq @ ( f @ X0 ) @ X0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( p
@ ^ [Y0: $i] : ( f @ Y0 ) )
!= $true )
& ( ( p
@ ^ [Y0: $i] : Y0 )
= $true )
& ! [X0: $i] :
( ( leibeq @ ( f @ X0 ) @ X0 )
= $true ) ),
inference(flattening,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ( p
@ ^ [Y0: $i] : ( f @ Y0 ) )
!= $true )
& ( ( p
@ ^ [Y0: $i] : Y0 )
= $true )
& ! [X0: $i] :
( ( leibeq @ ( f @ X0 ) @ X0 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( ( ( ( p
@ ^ [Y0: $i] : Y0 )
= $true )
& ! [X0: $i] :
( ( leibeq @ ( f @ X0 ) @ X0 )
= $true ) )
=> ( ( p
@ ^ [Y0: $i] : ( f @ Y0 ) )
= $true ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ( ( ( p
@ ^ [Y0: $i] : Y0 )
= $true )
& ! [X1: $i] :
( $true
= ( leibeq @ ( f @ X1 ) @ X1 ) ) )
=> ( ( p
@ ^ [Y0: $i] : ( f @ Y0 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ( p
@ ^ [X0: $i] : X0 )
& ! [X1: $i] : ( leibeq @ ( f @ X1 ) @ X1 ) )
=> ( p
@ ^ [X2: $i] : ( f @ X2 ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ( ( ( p
@ ^ [X3: $i] : X3 )
& ! [X3: $i] : ( leibeq @ ( f @ X3 ) @ X3 ) )
=> ( p
@ ^ [X3: $i] : ( f @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( ( ( p
@ ^ [X3: $i] : X3 )
& ! [X3: $i] : ( leibeq @ ( f @ X3 ) @ X3 ) )
=> ( p
@ ^ [X3: $i] : ( f @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.YR0tdaJfiN/DTF2THF_4429.p',conj) ).
thf(f25,plain,
( sK2
!= ( f @ sK2 ) ),
inference(beta_eta_normalization,[status(thm)],[f24]) ).
thf(f24,plain,
( ( f @ sK2 )
!= ( ^ [Y0: $i] : Y0
@ sK2 ) ),
inference(negative_extensionality,[status(thm)],[f23]) ).
thf(f23,plain,
( f
!= ( ^ [Y0: $i] : Y0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f22]) ).
thf(f22,plain,
( ( $true != $true )
| ( f
!= ( ^ [Y0: $i] : Y0 ) ) ),
inference(constrained_superposition,[status(thm)],[f17,f13]) ).
thf(f13,plain,
( ( p
@ ^ [Y0: $i] : Y0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f17,plain,
( ( p @ f )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
( ( p
@ ^ [Y0: $i] : ( f @ Y0 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO010^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n010.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 14:21:03 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.25/0.46 ---- Original DTF file ---
% 0.25/0.46 thf(spec,logic,$$dhol).
% 0.25/0.46 %------------------------------------------------------------------------------
% 0.25/0.46 % File : SYO010^1 : TPTP v9.2.1. Released v3.7.0.
% 0.25/0.46 % Domain : Syntactic
% 0.25/0.46 % Problem : Something requiring Xi but not Eta
% 0.25/0.46 % Version : Especial.
% 0.25/0.46 % English :
% 0.25/0.46
% 0.25/0.46 % Refs : [BB05] Benzmueller & Brown (2005), A Structured Set of Higher
% 0.25/0.46 % : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% 0.25/0.46 % Source : [Ben09]
% 0.25/0.46 % Names : Example 13 [BB05]
% 0.25/0.46
% 0.25/0.46 % Status : Theorem
% 0.25/0.46 % : Without xi extensionality : CounterSatisfiable
% 0.25/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0, 0.29 v7.4.0, 0.11 v7.2.0, 0.12 v7.1.0, 0.00 v6.2.0, 0.29 v6.1.0, 0.43 v6.0.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.3.0, 0.60 v4.1.0, 0.67 v4.0.1, 1.00 v3.7.0
% 0.25/0.46 % Syntax : Number of formulae : 5 ( 1 unt; 3 typ; 1 def)
% 0.25/0.46 % Number of atoms : 5 ( 1 equ; 0 cnn)
% 0.25/0.46 % Maximal formula atoms : 3 ( 2 avg)
% 0.25/0.46 % Number of connectives : 11 ( 0 ~; 0 |; 1 &; 8 @)
% 0.25/0.46 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.25/0.46 % Maximal formula depth : 7 ( 4 avg)
% 0.25/0.46 % Number of types : 2 ( 0 usr)
% 0.25/0.46 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.25/0.46 % Number of symbols : 4 ( 3 usr; 0 con; 1-2 aty)
% 0.25/0.46 % Number of variables : 6 ( 4 ^; 2 !; 0 ?; 6 :)
% 0.25/0.46 % SPC : TH0_THM_EQU_NAR
% 0.25/0.46
% 0.25/0.46 % Comments :
% 0.25/0.46 %------------------------------------------------------------------------------
% 0.25/0.46 thf(leibeq_type,type,
% 0.25/0.46 leibeq: $i > $i > $o ).
% 0.25/0.46
% 0.25/0.46 thf(leibeq,definition,
% 0.25/0.46 ( leibeq
% 0.25/0.46 = ( ^ [U: $i,V: $i] :
% 0.25/0.46 ! [Q: $i > $o] :
% 0.25/0.46 ( ( Q @ U )
% 0.25/0.46 => ( Q @ V ) ) ) ) ).
% 0.25/0.46
% 0.25/0.46 thf(p_type,type,
% 0.25/0.46 p: ( $i > $i ) > $o ).
% 0.25/0.46
% 0.25/0.46 thf(f_type,type,
% 0.25/0.46 f: $i > $i ).
% 0.25/0.46
% 0.25/0.46 thf(conj,conjecture,
% 0.25/0.46 ( ( ! [X: $i] : ( leibeq @ ( f @ X ) @ X )
% 0.25/0.46 & ( p
% 0.25/0.46 @ ^ [X: $i] : X ) )
% 0.25/0.46 => ( p
% 0.25/0.46 @ ^ [X: $i] : ( f @ X ) ) ) ).
% 0.25/0.46
% 0.25/0.46 %------------------------------------------------------------------------------
% 0.25/0.46 ------------------------
% 1.45/1.24 ---- Embedded in THF ---
% 1.45/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.45/1.24 %%% Generated on Tue Feb 24 14:21:04 EST 2026
% 1.45/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.45/1.24 %%% Logic specification used:
% 1.45/1.24 %%% thf(spec, logic, $$dhol).
% 1.45/1.24
% 1.45/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.YR0tdaJfiN/DTF2DTF4429.p
% See solution above
% 1.45/1.24 ------------------------
% 1.45/1.25 ---- Cleaned THF ---
% 1.45/1.25 thf(leibeq_type,type,
% 1.45/1.25 leibeq: $i > $i > $o ).
% 1.45/1.25
% 1.45/1.25 thf(leibeq,definition,
% 1.45/1.25 ( leibeq
% 1.45/1.25 = ( ^ [U: $i,V: $i] :
% 1.45/1.25 ! [Q: $i > $o] :
% 1.45/1.25 ( ( Q @ U )
% 1.45/1.25 => ( Q @ V ) ) ) ) ).
% 1.45/1.25
% 1.45/1.25 thf(p_type,type,
% 1.45/1.25 p: ( $i > $i ) > $o ).
% 1.45/1.25
% 1.45/1.25 thf(f_type,type,
% 1.45/1.25 f: $i > $i ).
% 1.45/1.25
% 1.45/1.25 thf(conj,conjecture,
% 1.45/1.25 ( ( ! [X: $i] : ( leibeq @ ( f @ X ) @ X )
% 1.45/1.25 & ( p
% 1.45/1.25 @ ^ [X: $i] : X ) )
% 1.45/1.25 => ( p
% 1.45/1.25 @ ^ [X: $i] : ( f @ X ) ) ) ).
% 1.45/1.25 ------------------------
% 1.45/1.27 % (4702)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_4429 for (2999ds/2Mi)
% 1.45/1.27 % (4701)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_4429 for (2999ds/27Mi)
% 1.45/1.27 % (4702)Instruction limit reached!
% 1.45/1.27 % (4702)------------------------------
% 1.45/1.27 % (4702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.27 % (4702)Termination reason: Unknown
% 1.45/1.27 % (4702)Termination phase: Saturation
% 1.45/1.27
% 1.45/1.27 % (4702)Memory used [KB]: 5500
% 1.45/1.27 % (4702)Time elapsed: 0.003 s
% 1.45/1.27 % (4702)Instructions burned: 3 (million)
% 1.45/1.27 % (4702)------------------------------
% 1.45/1.27 % (4702)------------------------------
% 1.45/1.27 % (4701)Refutation not found, incomplete strategy
% 1.45/1.27 % (4701)------------------------------
% 1.45/1.27 % (4701)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.27 % (4701)Termination reason: Refutation not found, incomplete strategy
% 1.45/1.27
% 1.45/1.27
% 1.45/1.27 % (4701)Memory used [KB]: 5500
% 1.45/1.27 % (4701)Time elapsed: 0.002 s
% 1.45/1.27 % (4701)Instructions burned: 2 (million)
% 1.45/1.27 % (4701)------------------------------
% 1.45/1.27 % (4701)------------------------------
% 1.45/1.27 % (4699)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_4429 for (2999ds/183Mi)
% 1.45/1.27 % (4700)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_4429 for (2999ds/4Mi)
% 1.45/1.27 % (4703)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_4429 for (2999ds/2Mi)
% 1.45/1.27 % (4704)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_4429 for (2999ds/275Mi)
% 1.45/1.27 % (4705)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_4429 for (2999ds/18Mi)
% 1.45/1.27 % (4703)Instruction limit reached!
% 1.45/1.27 % (4703)------------------------------
% 1.45/1.27 % (4703)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.27 % (4703)Termination reason: Unknown
% 1.45/1.27 % (4703)Termination phase: Property scanning
% 1.45/1.27
% 1.45/1.27 % (4703)Memory used [KB]: 895
% 1.45/1.27 % (4703)Time elapsed: 0.003 s
% 1.45/1.27 % (4703)Instructions burned: 2 (million)
% 1.45/1.27 % (4703)------------------------------
% 1.45/1.27 % (4703)------------------------------
% 1.45/1.28 % (4704)Refutation not found, incomplete strategy
% 1.45/1.28 % (4704)------------------------------
% 1.45/1.28 % (4704)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.28 % (4704)Termination reason: Refutation not found, incomplete strategy
% 1.45/1.28
% 1.45/1.28
% 1.45/1.28 % (4704)Memory used [KB]: 5500
% 1.45/1.28 % (4704)Time elapsed: 0.003 s
% 1.45/1.28 % (4704)Instructions burned: 1 (million)
% 1.45/1.28 % (4704)------------------------------
% 1.45/1.28 % (4704)------------------------------
% 1.45/1.28 % (4700)Instruction limit reached!
% 1.45/1.28 % (4700)------------------------------
% 1.45/1.28 % (4700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.28 % (4700)Termination reason: Unknown
% 1.45/1.28 % (4700)Termination phase: Saturation
% 1.45/1.28
% 1.45/1.28 % (4700)Memory used [KB]: 5500
% 1.45/1.28 % (4700)Time elapsed: 0.005 s
% 1.45/1.28 % (4700)Instructions burned: 4 (million)
% 1.45/1.28 % (4700)------------------------------
% 1.45/1.28 % (4700)------------------------------
% 1.45/1.28 % (4699)First to succeed.
% 1.45/1.28 % (4706)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_4429 for (2999ds/3Mi)
% 1.45/1.28 % (4705)Also succeeded, but the first one will report.
% 1.45/1.28 % (4699)Refutation found. Thanks to Tanya!
% 1.45/1.28 % SZS status Theorem for DTF2THF_4429
% 1.45/1.28 % SZS output start Proof for DTF2THF_4429
% 1.45/1.28 thf(func_def_0, type, leibeq: $i > $i > $o).
% 1.45/1.28 thf(func_def_2, type, p: ($i > $i) > $o).
% 1.45/1.28 thf(func_def_3, type, f: $i > $i).
% 1.45/1.28 thf(func_def_14, type, ph1: !>[X0: $tType]:(X0)).
% 1.45/1.28 thf(f55,plain,(
% 1.45/1.28 $false),
% 1.45/1.28 inference(trivial_inequality_removal,[status(thm)],[f53])).
% 1.45/1.28 thf(f53,plain,(
% 1.45/1.28 (sK2 != sK2)),
% 1.45/1.28 inference(superposition,[status(thm)],[f25,f27])).
% 1.45/1.28 thf(f27,plain,(
% 1.45/1.28 ( ! [X0 : $i] : (((f @ X0) = X0)) )),
% 1.45/1.28 inference(leibniz_equality_elimination,[status(thm)],[f21])).
% 1.45/1.28 thf(f21,plain,(
% 1.45/1.28 ( ! [X0 : $i,X1 : $i > $o] : (((X1 @ (f @ X0)) = $false) | ($true = (X1 @ X0))) )),
% 1.45/1.28 inference(binary_proxy_clausification,[status(thm)],[f20])).
% 1.45/1.28 thf(f20,plain,(
% 1.45/1.28 ( ! [X0 : $i,X1 : $i > $o] : ((((X1 @ (f @ X0)) => (X1 @ X0)) = $true)) )),
% 1.45/1.28 inference(beta_eta_normalization,[status(thm)],[f19])).
% 1.45/1.28 thf(f19,plain,(
% 1.45/1.28 ( ! [X0 : $i,X1 : $i > $o] : (($true = ((^[Y0 : $i > $o]: ((Y0 @ (f @ X0)) => (Y0 @ X0))) @ X1))) )),
% 1.45/1.28 inference(pi_clausification,[status(thm)],[f18])).
% 1.45/1.28 thf(f18,plain,(
% 1.45/1.28 ( ! [X0 : $i] : (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((Y0 @ (f @ X0)) => (Y0 @ X0)))) = $true)) )),
% 1.45/1.28 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.45/1.28 thf(f16,plain,(
% 1.45/1.28 ( ! [X0 : $i] : (($true = ((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))) @ (f @ X0) @ X0))) )),
% 1.45/1.28 inference(definition_unfolding,[status(thm)],[f12,f15])).
% 1.45/1.28 thf(f15,plain,(
% 1.45/1.28 (leibeq = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 1.45/1.28 inference(cnf_transformation,[status(thm)],[f8])).
% 1.45/1.28 thf(f8,plain,(
% 1.45/1.28 (leibeq = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 1.45/1.28 inference(fool_elimination,[status(thm)],[f7])).
% 1.45/1.28 thf(f7,plain,(
% 1.45/1.28 ((^[X0 : $i, X1 : $i] : (! [X2 : $i > $o] : ((X2 @ X0) => (X2 @ X1)))) = leibeq)),
% 1.45/1.28 inference(rectify,[status(thm)],[f1])).
% 1.45/1.28 thf(f1,axiom,(
% 1.45/1.28 ((^[X0 : $i, X1 : $i] : (! [X2 : $i > $o] : ((X2 @ X0) => (X2 @ X1)))) = leibeq)),
% 1.45/1.28 file('/export/starexec/sandbox2/tmp/tmp.YR0tdaJfiN/DTF2THF_4429.p',leibeq)).
% 1.45/1.28 thf(f12,plain,(
% 1.45/1.28 ( ! [X0 : $i] : (((leibeq @ (f @ X0) @ X0) = $true)) )),
% 1.45/1.28 inference(cnf_transformation,[status(thm)],[f11])).
% 1.45/1.28 thf(f11,plain,(
% 1.45/1.28 ((p @ (^[Y0 : $i]: (f @ Y0))) != $true) & ((p @ (^[Y0 : $i]: (Y0))) = $true) & ! [X0 : $i] : ((leibeq @ (f @ X0) @ X0) = $true)),
% 1.45/1.28 inference(flattening,[status(thm)],[f10])).
% 1.45/1.28 thf(f10,plain,(
% 1.45/1.28 ((p @ (^[Y0 : $i]: (f @ Y0))) != $true) & (((p @ (^[Y0 : $i]: (Y0))) = $true) & ! [X0 : $i] : ((leibeq @ (f @ X0) @ X0) = $true))),
% 1.45/1.28 inference(ennf_transformation,[status(thm)],[f9])).
% 1.45/1.28 thf(f9,plain,(
% 1.45/1.28 ~((((p @ (^[Y0 : $i]: (Y0))) = $true) & ! [X0 : $i] : ((leibeq @ (f @ X0) @ X0) = $true)) => ((p @ (^[Y0 : $i]: (f @ Y0))) = $true))),
% 1.45/1.28 inference(rectify,[status(thm)],[f6])).
% 1.45/1.28 thf(f6,plain,(
% 1.45/1.28 ~((((p @ (^[Y0 : $i]: (Y0))) = $true) & ! [X1 : $i] : ($true = (leibeq @ (f @ X1) @ X1))) => ((p @ (^[Y0 : $i]: (f @ Y0))) = $true))),
% 1.45/1.28 inference(fool_elimination,[status(thm)],[f5])).
% 1.45/1.28 thf(f5,plain,(
% 1.45/1.28 ~(((p @ (^[X0 : $i] : (X0))) & ! [X1 : $i] : (leibeq @ (f @ X1) @ X1)) => (p @ (^[X2 : $i] : (f @ X2))))),
% 1.45/1.28 inference(rectify,[status(thm)],[f3])).
% 1.45/1.28 thf(f3,negated_conjecture,(
% 1.45/1.28 ~(((p @ (^[X3 : $i] : (X3))) & ! [X3 : $i] : (leibeq @ (f @ X3) @ X3)) => (p @ (^[X3 : $i] : (f @ X3))))),
% 1.45/1.28 inference(negated_conjecture,[status(cth)],[f2])).
% 1.45/1.28 thf(f2,conjecture,(
% 1.45/1.28 ((p @ (^[X3 : $i] : (X3))) & ! [X3 : $i] : (leibeq @ (f @ X3) @ X3)) => (p @ (^[X3 : $i] : (f @ X3)))),
% 1.45/1.28 file('/export/starexec/sandbox2/tmp/tmp.YR0tdaJfiN/DTF2THF_4429.p',conj)).
% 1.45/1.28 thf(f25,plain,(
% 1.45/1.28 (sK2 != (f @ sK2))),
% 1.45/1.28 inference(beta_eta_normalization,[status(thm)],[f24])).
% 1.45/1.28 thf(f24,plain,(
% 1.45/1.28 ((f @ sK2) != ((^[Y0 : $i]: (Y0)) @ sK2))),
% 1.45/1.28 inference(negative_extensionality,[status(thm)],[f23])).
% 1.45/1.28 thf(f23,plain,(
% 1.45/1.28 (f != (^[Y0 : $i]: (Y0)))),
% 1.45/1.28 inference(trivial_inequality_removal,[status(thm)],[f22])).
% 1.45/1.28 thf(f22,plain,(
% 1.45/1.28 ($true != $true) | (f != (^[Y0 : $i]: (Y0)))),
% 1.45/1.28 inference(constrained_superposition,[status(thm)],[f17,f13])).
% 1.45/1.28 thf(f13,plain,(
% 1.45/1.28 ((p @ (^[Y0 : $i]: (Y0))) = $true)),
% 1.45/1.28 inference(cnf_transformation,[status(thm)],[f11])).
% 1.45/1.28 thf(f17,plain,(
% 1.45/1.28 ((p @ f) != $true)),
% 1.45/1.28 inference(beta_eta_normalization,[status(thm)],[f14])).
% 1.45/1.28 thf(f14,plain,(
% 1.45/1.28 ((p @ (^[Y0 : $i]: (f @ Y0))) != $true)),
% 1.45/1.28 inference(cnf_transformation,[status(thm)],[f11])).
% 1.45/1.28 % SZS output end Proof for DTF2THF_4429
% 1.45/1.28 % (4699)------------------------------
% 1.45/1.28 % (4699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.28 % (4699)Termination reason: Refutation
% 1.45/1.28
% 1.45/1.28 % (4699)Memory used [KB]: 5500
% 1.45/1.28 % (4699)Time elapsed: 0.006 s
% 1.45/1.28 % (4699)Instructions burned: 4 (million)
% 1.45/1.28 % (4699)------------------------------
% 1.45/1.28 % (4699)------------------------------
% 1.45/1.28 % (4698)Success in time 0.02 s
%------------------------------------------------------------------------------