%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO008^1 : 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 : n023.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 1.63s 1.45s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 33 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 105 ( 37 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 174 ( 13 ~; 2 |; 4 &; 126 @)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 58 ( 58 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 7 usr; 4 con; 0-2 aty)
% ( 8 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 64 ( 30 ^; 30 !; 4 ?; 64 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
leibeq1: $i > $i > $o ).
thf(func_def_2,type,
leibeq2: ( $i > $i ) > ( $i > $i ) > $o ).
thf(func_def_11,type,
sK0: $i > $i ).
thf(func_def_12,type,
sK1: $i > $i ).
thf(func_def_14,type,
sK3: ( $i > $i ) > $o ).
thf(func_def_16,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f56,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f55,f30]) ).
thf(f30,plain,
! [X0: $i] :
( ( sK0 @ X0 )
= ( sK1 @ X0 ) ),
inference(leibniz_equality_elimination,[status(thm)],[f29]) ).
thf(f29,plain,
! [X2: $i,X3: $i > $o] :
( ( ( X3 @ ( sK1 @ X2 ) )
= $false )
| ( ( X3 @ ( sK0 @ X2 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
! [X2: $i,X3: $i > $o] :
( ( ( X3 @ ( sK1 @ X2 ) )
=> ( X3 @ ( sK0 @ X2 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f27]) ).
thf(f27,plain,
! [X2: $i,X3: $i > $o] :
( ( ^ [Y0: $i > $o] :
( ( Y0 @ ( sK1 @ X2 ) )
=> ( Y0 @ ( sK0 @ X2 ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
! [X2: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0 @ ( sK1 @ X2 ) )
=> ( Y0 @ ( sK0 @ X2 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f19]) ).
thf(f19,plain,
! [X2: $i] :
( $true
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) )
@ ( sK1 @ X2 )
@ ( sK0 @ X2 ) ) ),
inference(definition_unfolding,[status(thm)],[f17,f18]) ).
thf(f18,plain,
( leibeq1
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( leibeq1
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( leibeq1
= ( ^ [X0: $i,X1: $i] :
! [X2: $i > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( leibeq1
= ( ^ [X0: $i,X1: $i] :
! [X2: $i > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.LnJjUz9sZP/DTF2THF_10806.p',leibeq1) ).
thf(f17,plain,
! [X2: $i] :
( $true
= ( leibeq1 @ ( sK1 @ X2 ) @ ( sK0 @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ! [X2: $i] :
( $true
= ( leibeq1 @ ( sK1 @ X2 ) @ ( sK0 @ X2 ) ) )
& ( ( leibeq2 @ sK1 @ sK0 )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f12,f13]) ).
thf(f13,plain,
( ? [X0: $i > $i,X1: $i > $i] :
( ! [X2: $i] :
( $true
= ( leibeq1 @ ( X1 @ X2 ) @ ( X0 @ X2 ) ) )
& ( ( leibeq2 @ X1 @ X0 )
!= $true ) )
=> ( ! [X2: $i] :
( $true
= ( leibeq1 @ ( sK1 @ X2 ) @ ( sK0 @ X2 ) ) )
& ( ( leibeq2 @ sK1 @ sK0 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
? [X0: $i > $i,X1: $i > $i] :
( ! [X2: $i] :
( $true
= ( leibeq1 @ ( X1 @ X2 ) @ ( X0 @ X2 ) ) )
& ( ( leibeq2 @ X1 @ X0 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
~ ! [X0: $i > $i,X1: $i > $i] :
( ! [X2: $i] :
( $true
= ( leibeq1 @ ( X1 @ X2 ) @ ( X0 @ X2 ) ) )
=> ( ( leibeq2 @ X1 @ X0 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: $i > $i,X1: $i > $i] :
( ! [X2: $i] : ( leibeq1 @ ( X1 @ X2 ) @ ( X0 @ X2 ) )
=> ( leibeq2 @ X1 @ X0 ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X7: $i > $i,X6: $i > $i] :
( ! [X3: $i] : ( leibeq1 @ ( X6 @ X3 ) @ ( X7 @ X3 ) )
=> ( leibeq2 @ X6 @ X7 ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
! [X7: $i > $i,X6: $i > $i] :
( ! [X3: $i] : ( leibeq1 @ ( X6 @ X3 ) @ ( X7 @ X3 ) )
=> ( leibeq2 @ X6 @ X7 ) ),
file('/export/starexec/sandbox/tmp/tmp.LnJjUz9sZP/DTF2THF_10806.p',conj) ).
thf(f55,plain,
( ( sK0 @ sK5 )
!= ( sK1 @ sK5 ) ),
inference(negative_extensionality,[status(thm)],[f54]) ).
thf(f54,plain,
sK1 != sK0,
inference(trivial_inequality_removal,[status(thm)],[f52]) ).
thf(f52,plain,
( ( $false = $true )
| ( sK1 != sK0 ) ),
inference(constrained_superposition,[status(thm)],[f24,f25]) ).
thf(f25,plain,
( ( sK3 @ sK1 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( $false
= ( ( sK3 @ sK1 )
=> ( sK3 @ sK0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f22]) ).
thf(f22,plain,
( $false
= ( ^ [Y0: ( $i > $i ) > $o] :
( ( Y0 @ sK1 )
=> ( Y0 @ sK0 ) )
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( $true
!= ( !! @ ( ( $i > $i ) > $o )
@ ^ [Y0: ( $i > $i ) > $o] :
( ( Y0 @ sK1 )
=> ( Y0 @ sK0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
( $true
!= ( ^ [Y0: $i > $i,Y1: $i > $i] :
( !! @ ( ( $i > $i ) > $o )
@ ^ [Y2: ( $i > $i ) > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) )
@ sK1
@ sK0 ) ),
inference(definition_unfolding,[status(thm)],[f16,f15]) ).
thf(f15,plain,
( leibeq2
= ( ^ [Y0: $i > $i,Y1: $i > $i] :
( !! @ ( ( $i > $i ) > $o )
@ ^ [Y2: ( $i > $i ) > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( leibeq2
= ( ^ [Y0: $i > $i,Y1: $i > $i] :
( !! @ ( ( $i > $i ) > $o )
@ ^ [Y2: ( $i > $i ) > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [X0: $i > $i,X1: $i > $i] :
! [X2: ( $i > $i ) > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) )
= leibeq2 ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( ( ^ [X3: $i > $i,X4: $i > $i] :
! [X5: ( $i > $i ) > $o] :
( ( X5 @ X3 )
=> ( X5 @ X4 ) ) )
= leibeq2 ),
file('/export/starexec/sandbox/tmp/tmp.LnJjUz9sZP/DTF2THF_10806.p',leibeq2) ).
thf(f16,plain,
( ( leibeq2 @ sK1 @ sK0 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f24,plain,
( $false
= ( sK3 @ sK0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO008^1 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n023.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 14:28:04 EST 2026
% 0.19/0.35 % CPUTime :
% 0.19/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.27/0.50 ---- Original DTF file ---
% 0.27/0.50 thf(spec,logic,$$dhol).
% 0.27/0.50 %------------------------------------------------------------------------------
% 0.27/0.50 % File : SYO008^1 : TPTP v9.2.1. Released v3.7.0.
% 0.27/0.50 % Domain : Syntactic
% 0.27/0.50 % Problem : The non-trivial direction of functional extensionality
% 0.27/0.50 % Version : Especial.
% 0.27/0.50 % English :
% 0.27/0.50
% 0.27/0.50 % Refs : [BB05] Benzmueller & Brown (2005), A Structured Set of Higher
% 0.27/0.50 % : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% 0.27/0.50 % Source : [Ben09]
% 0.27/0.50 % Names : Example 11 [BB05]
% 0.27/0.50
% 0.27/0.50 % Status : Theorem
% 0.27/0.50 % : Without functional extensionality : CounterSatisfiable
% 0.27/0.50 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.38 v8.1.0, 0.45 v7.5.0, 0.29 v7.4.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.2.0, 0.29 v6.0.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.40 v5.3.0, 0.60 v4.1.0, 0.67 v4.0.1, 1.00 v3.7.0
% 0.27/0.50 % Syntax : Number of formulae : 5 ( 2 unt; 2 typ; 2 def)
% 0.27/0.50 % Number of atoms : 6 ( 2 equ; 0 cnn)
% 0.27/0.50 % Maximal formula atoms : 2 ( 2 avg)
% 0.27/0.50 % Number of connectives : 13 ( 0 ~; 0 |; 0 &; 10 @)
% 0.27/0.50 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.27/0.50 % Maximal formula depth : 8 ( 3 avg)
% 0.27/0.50 % Number of types : 2 ( 0 usr)
% 0.27/0.50 % Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% 0.27/0.50 % Number of symbols : 3 ( 2 usr; 0 con; 2-2 aty)
% 0.27/0.50 % Number of variables : 9 ( 4 ^; 5 !; 0 ?; 9 :)
% 0.27/0.50 % SPC : TH0_THM_EQU_NAR
% 0.27/0.50
% 0.27/0.50 % Comments :
% 0.27/0.50 %------------------------------------------------------------------------------
% 0.27/0.50 thf(leibeq1_type,type,
% 0.27/0.50 leibeq1: $i > $i > $o ).
% 0.27/0.50
% 0.27/0.50 thf(leibeq1,definition,
% 0.27/0.50 ( leibeq1
% 0.27/0.50 = ( ^ [U: $i,V: $i] :
% 0.27/0.50 ! [Q: $i > $o] :
% 0.27/0.50 ( ( Q @ U )
% 0.27/0.50 => ( Q @ V ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(leibeq2_type,type,
% 0.27/0.50 leibeq2: ( $i > $i ) > ( $i > $i ) > $o ).
% 0.27/0.50
% 0.27/0.50 thf(leibeq2,definition,
% 0.27/0.50 ( leibeq2
% 0.27/0.50 = ( ^ [X: $i > $i,Y: $i > $i] :
% 0.27/0.50 ! [P: ( $i > $i ) > $o] :
% 0.27/0.50 ( ( P @ X )
% 0.27/0.50 => ( P @ Y ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(conj,conjecture,
% 0.27/0.50 ! [F: $i > $i,G: $i > $i] :
% 0.27/0.50 ( ! [X: $i] : ( leibeq1 @ ( F @ X ) @ ( G @ X ) )
% 0.27/0.50 => ( leibeq2 @ F @ G ) ) ).
% 0.27/0.50
% 0.27/0.50 %------------------------------------------------------------------------------
% 0.27/0.50 ------------------------
% 1.63/1.41 ---- Embedded in THF ---
% 1.63/1.41 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.63/1.41 %%% Generated on Tue Feb 24 14:28:05 EST 2026
% 1.63/1.41 %%% using '$$dhol' embedding, version 1.3.0.
% 1.63/1.41 %%% Logic specification used:
% 1.63/1.41 %%% thf(spec, logic, $$dhol).
% 1.63/1.41
% 1.63/1.41 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.LnJjUz9sZP/DTF2DTF10806.p
% See solution above
% 1.63/1.41 ------------------------
% 1.63/1.42 ---- Cleaned THF ---
% 1.63/1.42 thf(leibeq1_type,type,
% 1.63/1.42 leibeq1: $i > $i > $o ).
% 1.63/1.42
% 1.63/1.42 thf(leibeq1,definition,
% 1.63/1.42 ( leibeq1
% 1.63/1.42 = ( ^ [U: $i,V: $i] :
% 1.63/1.42 ! [Q: $i > $o] :
% 1.63/1.42 ( ( Q @ U )
% 1.63/1.42 => ( Q @ V ) ) ) ) ).
% 1.63/1.42
% 1.63/1.42 thf(leibeq2_type,type,
% 1.63/1.42 leibeq2: ( $i > $i ) > ( $i > $i ) > $o ).
% 1.63/1.42
% 1.63/1.42 thf(leibeq2,definition,
% 1.63/1.42 ( leibeq2
% 1.63/1.42 = ( ^ [X: $i > $i,Y: $i > $i] :
% 1.63/1.42 ! [P: ( $i > $i ) > $o] :
% 1.63/1.42 ( ( P @ X )
% 1.63/1.42 => ( P @ Y ) ) ) ) ).
% 1.63/1.42
% 1.63/1.42 thf(conj,conjecture,
% 1.63/1.42 ! [F: $i > $i,G: $i > $i] :
% 1.63/1.42 ( ! [X: $i] : ( leibeq1 @ ( F @ X ) @ ( G @ X ) )
% 1.63/1.42 => ( leibeq2 @ F @ G ) ) ).
% 1.63/1.42 ------------------------
% 1.63/1.44 % (10903)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10806 for (3000ds/183Mi)
% 1.63/1.44 % (10904)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_10806 for (3000ds/4Mi)
% 1.63/1.44 % (10905)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_10806 for (3000ds/27Mi)
% 1.63/1.44 % (10906)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_10806 for (3000ds/2Mi)
% 1.63/1.44 % (10907)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_10806 for (3000ds/2Mi)
% 1.63/1.44 % (10908)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_10806 for (3000ds/275Mi)
% 1.63/1.44 % (10909)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_10806 for (3000ds/18Mi)
% 1.63/1.44 % (10906)Instruction limit reached!
% 1.63/1.44 % (10906)------------------------------
% 1.63/1.44 % (10906)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.44 % (10906)Termination reason: Unknown
% 1.63/1.44 % (10906)Termination phase: Saturation
% 1.63/1.44
% 1.63/1.44 % (10906)Memory used [KB]: 5500
% 1.63/1.44 % (10906)Time elapsed: 0.003 s
% 1.63/1.44 % (10906)Instructions burned: 2 (million)
% 1.63/1.44 % (10906)------------------------------
% 1.63/1.44 % (10906)------------------------------
% 1.63/1.44 % (10907)Instruction limit reached!
% 1.63/1.44 % (10907)------------------------------
% 1.63/1.44 % (10907)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.44 % (10907)Termination reason: Unknown
% 1.63/1.44 % (10907)Termination phase: Saturation
% 1.63/1.44
% 1.63/1.44 % (10907)Memory used [KB]: 5500
% 1.63/1.44 % (10907)Time elapsed: 0.003 s
% 1.63/1.44 % (10907)Instructions burned: 3 (million)
% 1.63/1.44 % (10907)------------------------------
% 1.63/1.44 % (10907)------------------------------
% 1.63/1.44 % (10905)Refutation not found, incomplete strategy
% 1.63/1.44 % (10905)------------------------------
% 1.63/1.44 % (10905)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.44 % (10905)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.44
% 1.63/1.44
% 1.63/1.44 % (10905)Memory used [KB]: 5500
% 1.63/1.44 % (10905)Time elapsed: 0.003 s
% 1.63/1.44 % (10905)Instructions burned: 2 (million)
% 1.63/1.44 % (10905)------------------------------
% 1.63/1.44 % (10905)------------------------------
% 1.63/1.44 % (10904)Instruction limit reached!
% 1.63/1.44 % (10904)------------------------------
% 1.63/1.44 % (10904)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.44 % (10904)Termination reason: Unknown
% 1.63/1.44 % (10904)Termination phase: Saturation
% 1.63/1.44
% 1.63/1.44 % (10904)Memory used [KB]: 5500
% 1.63/1.44 % (10904)Time elapsed: 0.004 s
% 1.63/1.44 % (10904)Instructions burned: 4 (million)
% 1.63/1.44 % (10904)------------------------------
% 1.63/1.44 % (10904)------------------------------
% 1.63/1.45 % (10909)First to succeed.
% 1.63/1.45 % (10908)Refutation not found, incomplete strategy
% 1.63/1.45 % (10908)------------------------------
% 1.63/1.45 % (10908)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.45 % (10908)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.45
% 1.63/1.45
% 1.63/1.45 % (10908)Memory used [KB]: 5500
% 1.63/1.45 % (10908)Time elapsed: 0.004 s
% 1.63/1.45 % (10908)Instructions burned: 4 (million)
% 1.63/1.45 % (10908)------------------------------
% 1.63/1.45 % (10908)------------------------------
% 1.63/1.45 % (10903)Also succeeded, but the first one will report.
% 1.63/1.45 % (10909)Refutation found. Thanks to Tanya!
% 1.63/1.45 % SZS status Theorem for DTF2THF_10806
% 1.63/1.45 % SZS output start Proof for DTF2THF_10806
% 1.63/1.45 thf(func_def_0, type, leibeq1: $i > $i > $o).
% 1.63/1.45 thf(func_def_2, type, leibeq2: ($i > $i) > ($i > $i) > $o).
% 1.63/1.45 thf(func_def_11, type, sK0: $i > $i).
% 1.63/1.45 thf(func_def_12, type, sK1: $i > $i).
% 1.63/1.45 thf(func_def_14, type, sK3: ($i > $i) > $o).
% 1.63/1.45 thf(func_def_16, type, ph4: !>[X0: $tType]:(X0)).
% 1.63/1.45 thf(f56,plain,(
% 1.63/1.45 $false),
% 1.63/1.45 inference(subsumption_resolution,[status(thm)],[f55,f30])).
% 1.63/1.45 thf(f30,plain,(
% 1.63/1.45 ( ! [X0 : $i] : (((sK0 @ X0) = (sK1 @ X0))) )),
% 1.63/1.45 inference(leibniz_equality_elimination,[status(thm)],[f29])).
% 1.63/1.45 thf(f29,plain,(
% 1.63/1.45 ( ! [X2 : $i,X3 : $i > $o] : (((X3 @ (sK1 @ X2)) = $false) | ((X3 @ (sK0 @ X2)) = $true)) )),
% 1.63/1.45 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 1.63/1.45 thf(f28,plain,(
% 1.63/1.45 ( ! [X2 : $i,X3 : $i > $o] : ((((X3 @ (sK1 @ X2)) => (X3 @ (sK0 @ X2))) = $true)) )),
% 1.63/1.45 inference(beta_eta_normalization,[status(thm)],[f27])).
% 1.63/1.45 thf(f27,plain,(
% 1.63/1.45 ( ! [X2 : $i,X3 : $i > $o] : ((((^[Y0 : $i > $o]: ((Y0 @ (sK1 @ X2)) => (Y0 @ (sK0 @ X2)))) @ X3) = $true)) )),
% 1.63/1.45 inference(pi_clausification,[status(thm)],[f26])).
% 1.63/1.45 thf(f26,plain,(
% 1.63/1.45 ( ! [X2 : $i] : (($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((Y0 @ (sK1 @ X2)) => (Y0 @ (sK0 @ X2))))))) )),
% 1.63/1.45 inference(beta_eta_normalization,[status(thm)],[f19])).
% 1.63/1.45 thf(f19,plain,(
% 1.63/1.45 ( ! [X2 : $i] : (($true = ((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))) @ (sK1 @ X2) @ (sK0 @ X2)))) )),
% 1.63/1.45 inference(definition_unfolding,[status(thm)],[f17,f18])).
% 1.63/1.45 thf(f18,plain,(
% 1.63/1.45 (leibeq1 = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 1.63/1.45 inference(cnf_transformation,[status(thm)],[f11])).
% 1.63/1.45 thf(f11,plain,(
% 1.63/1.45 (leibeq1 = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 1.63/1.45 inference(fool_elimination,[status(thm)],[f10])).
% 1.63/1.45 thf(f10,plain,(
% 1.63/1.45 (leibeq1 = (^[X0 : $i, X1 : $i] : (! [X2 : $i > $o] : ((X2 @ X0) => (X2 @ X1)))))),
% 1.63/1.45 inference(rectify,[status(thm)],[f1])).
% 1.63/1.45 thf(f1,axiom,(
% 1.63/1.45 (leibeq1 = (^[X0 : $i, X1 : $i] : (! [X2 : $i > $o] : ((X2 @ X0) => (X2 @ X1)))))),
% 1.63/1.45 file('/export/starexec/sandbox/tmp/tmp.LnJjUz9sZP/DTF2THF_10806.p',leibeq1)).
% 1.63/1.45 thf(f17,plain,(
% 1.63/1.45 ( ! [X2 : $i] : (($true = (leibeq1 @ (sK1 @ X2) @ (sK0 @ X2)))) )),
% 1.63/1.45 inference(cnf_transformation,[status(thm)],[f14])).
% 1.63/1.45 thf(f14,plain,(
% 1.63/1.45 ! [X2 : $i] : ($true = (leibeq1 @ (sK1 @ X2) @ (sK0 @ X2))) & ((leibeq2 @ sK1 @ sK0) != $true)),
% 1.63/1.45 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f12,f13])).
% 1.63/1.45 thf(f13,plain,(
% 1.63/1.45 ? [X0 : $i > $i,X1 : $i > $i] : (! [X2 : $i] : ($true = (leibeq1 @ (X1 @ X2) @ (X0 @ X2))) & ((leibeq2 @ X1 @ X0) != $true)) => (! [X2 : $i] : ($true = (leibeq1 @ (sK1 @ X2) @ (sK0 @ X2))) & ((leibeq2 @ sK1 @ sK0) != $true))),
% 1.63/1.45 introduced(definition,[],[choice_axiom])).
% 1.63/1.45 thf(f12,plain,(
% 1.63/1.45 ? [X0 : $i > $i,X1 : $i > $i] : (! [X2 : $i] : ($true = (leibeq1 @ (X1 @ X2) @ (X0 @ X2))) & ((leibeq2 @ X1 @ X0) != $true))),
% 1.63/1.45 inference(ennf_transformation,[status(thm)],[f7])).
% 1.63/1.45 thf(f7,plain,(
% 1.63/1.45 ~! [X0 : $i > $i,X1 : $i > $i] : (! [X2 : $i] : ($true = (leibeq1 @ (X1 @ X2) @ (X0 @ X2))) => ((leibeq2 @ X1 @ X0) = $true))),
% 1.63/1.45 inference(fool_elimination,[status(thm)],[f6])).
% 1.63/1.45 thf(f6,plain,(
% 1.63/1.45 ~! [X0 : $i > $i,X1 : $i > $i] : (! [X2 : $i] : (leibeq1 @ (X1 @ X2) @ (X0 @ X2)) => (leibeq2 @ X1 @ X0))),
% 1.63/1.45 inference(rectify,[status(thm)],[f4])).
% 1.63/1.45 thf(f4,negated_conjecture,(
% 1.63/1.45 ~! [X7 : $i > $i,X6 : $i > $i] : (! [X3 : $i] : (leibeq1 @ (X6 @ X3) @ (X7 @ X3)) => (leibeq2 @ X6 @ X7))),
% 1.63/1.45 inference(negated_conjecture,[status(cth)],[f3])).
% 1.63/1.45 thf(f3,conjecture,(
% 1.63/1.45 ! [X7 : $i > $i,X6 : $i > $i] : (! [X3 : $i] : (leibeq1 @ (X6 @ X3) @ (X7 @ X3)) => (leibeq2 @ X6 @ X7))),
% 1.63/1.45 file('/export/starexec/sandbox/tmp/tmp.LnJjUz9sZP/DTF2THF_10806.p',conj)).
% 1.63/1.45 thf(f55,plain,(
% 1.63/1.45 ((sK0 @ sK5) != (sK1 @ sK5))),
% 1.63/1.45 inference(negative_extensionality,[status(thm)],[f54])).
% 1.63/1.45 thf(f54,plain,(
% 1.63/1.45 (sK1 != sK0)),
% 1.63/1.45 inference(trivial_inequality_removal,[status(thm)],[f52])).
% 1.63/1.45 thf(f52,plain,(
% 1.63/1.45 ($false = $true) | (sK1 != sK0)),
% 1.63/1.45 inference(constrained_superposition,[status(thm)],[f24,f25])).
% 1.63/1.45 thf(f25,plain,(
% 1.63/1.45 ((sK3 @ sK1) = $true)),
% 1.63/1.45 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 1.63/1.45 thf(f23,plain,(
% 1.63/1.45 ($false = ((sK3 @ sK1) => (sK3 @ sK0)))),
% 1.63/1.45 inference(beta_eta_normalization,[status(thm)],[f22])).
% 1.63/1.45 thf(f22,plain,(
% 1.63/1.45 ($false = ((^[Y0 : ($i > $i) > $o]: ((Y0 @ sK1) => (Y0 @ sK0))) @ sK3))),
% 1.63/1.45 inference(sigma_clausification,[status(thm)],[f21])).
% 1.63/1.45 thf(f21,plain,(
% 1.63/1.45 ($true != (!! @ (($i > $i) > $o) @ (^[Y0 : ($i > $i) > $o]: ((Y0 @ sK1) => (Y0 @ sK0)))))),
% 1.63/1.45 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.63/1.45 thf(f20,plain,(
% 1.63/1.45 ($true != ((^[Y0 : $i > $i]: ((^[Y1 : $i > $i]: (!! @ (($i > $i) > $o) @ (^[Y2 : ($i > $i) > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))) @ sK1 @ sK0))),
% 1.63/1.45 inference(definition_unfolding,[status(thm)],[f16,f15])).
% 1.63/1.45 thf(f15,plain,(
% 1.63/1.45 (leibeq2 = (^[Y0 : $i > $i]: ((^[Y1 : $i > $i]: (!! @ (($i > $i) > $o) @ (^[Y2 : ($i > $i) > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 1.63/1.45 inference(cnf_transformation,[status(thm)],[f9])).
% 1.63/1.45 thf(f9,plain,(
% 1.63/1.45 (leibeq2 = (^[Y0 : $i > $i]: ((^[Y1 : $i > $i]: (!! @ (($i > $i) > $o) @ (^[Y2 : ($i > $i) > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 1.63/1.45 inference(fool_elimination,[status(thm)],[f8])).
% 1.63/1.45 thf(f8,plain,(
% 1.63/1.45 ((^[X0 : $i > $i, X1 : $i > $i] : (! [X2 : ($i > $i) > $o] : ((X2 @ X0) => (X2 @ X1)))) = leibeq2)),
% 1.63/1.45 inference(rectify,[status(thm)],[f2])).
% 1.63/1.45 thf(f2,axiom,(
% 1.63/1.45 ((^[X3 : $i > $i, X4 : $i > $i] : (! [X5 : ($i > $i) > $o] : ((X5 @ X3) => (X5 @ X4)))) = leibeq2)),
% 1.63/1.45 file('/export/starexec/sandbox/tmp/tmp.LnJjUz9sZP/DTF2THF_10806.p',leibeq2)).
% 1.63/1.45 thf(f16,plain,(
% 1.63/1.45 ((leibeq2 @ sK1 @ sK0) != $true)),
% 1.63/1.45 inference(cnf_transformation,[status(thm)],[f14])).
% 1.63/1.45 thf(f24,plain,(
% 1.63/1.45 ($false = (sK3 @ sK0))),
% 1.63/1.45 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 1.63/1.45 % SZS output end Proof for DTF2THF_10806
% 1.63/1.45 % (10909)------------------------------
% 1.63/1.45 % (10909)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.45 % (10909)Termination reason: Refutation
% 1.63/1.45
% 1.63/1.45 % (10909)Memory used [KB]: 5500
% 1.63/1.45 % (10909)Time elapsed: 0.004 s
% 1.63/1.45 % (10909)Instructions burned: 4 (million)
% 1.63/1.45 % (10909)------------------------------
% 1.63/1.45 % (10909)------------------------------
% 1.63/1.45 % (10902)Success in time 0.018 s
%------------------------------------------------------------------------------