%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO005^1 : 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 : 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 09:53:07 AM UTC 2026
% Result : Theorem 1.57s 1.33s
% Output : Refutation 1.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 127 ( 38 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 181 ( 12 ~; 1 |; 4 &; 134 @)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 61 ( 61 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 7 usr; 4 con; 0-2 aty)
% ( 8 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 58 ( 30 ^; 20 !; 8 ?; 58 :)
% 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_15,type,
sK4: $i > $o ).
thf(func_def_17,type,
ph5:
!>[X0: $tType] : X0 ).
thf(f50,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f49]) ).
thf(f49,plain,
$true = $false,
inference(backward_demodulation,[status(thm)],[f30,f48]) ).
thf(f48,plain,
( $false
= ( sK4 @ ( sK0 @ sK2 ) ) ),
inference(backward_demodulation,[status(thm)],[f29,f47]) ).
thf(f47,plain,
! [X1: $i] :
( ( sK1 @ X1 )
= ( sK0 @ X1 ) ),
inference(argument_congruence,[status(thm)],[f33]) ).
thf(f33,plain,
sK0 = sK1,
inference(leibniz_equality_elimination,[status(thm)],[f26]) ).
thf(f26,plain,
! [X1: ( $i > $i ) > $o] :
( ( $true
= ( X1 @ sK1 ) )
| ( $false
= ( X1 @ sK0 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
! [X1: ( $i > $i ) > $o] :
( $true
= ( ( X1 @ sK0 )
=> ( X1 @ sK1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f24]) ).
thf(f24,plain,
! [X1: ( $i > $i ) > $o] :
( $true
= ( ^ [Y0: ( $i > $i ) > $o] :
( ( Y0 @ sK0 )
=> ( Y0 @ sK1 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( $true
= ( !! @ ( ( $i > $i ) > $o )
@ ^ [Y0: ( $i > $i ) > $o] :
( ( Y0 @ sK0 )
=> ( Y0 @ sK1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f21]) ).
thf(f21,plain,
( $true
= ( ^ [Y0: $i > $i,Y1: $i > $i] :
( !! @ ( ( $i > $i ) > $o )
@ ^ [Y2: ( $i > $i ) > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) )
@ sK0
@ sK1 ) ),
inference(definition_unfolding,[status(thm)],[f17,f16]) ).
thf(f16,plain,
( leibeq2
= ( ^ [Y0: $i > $i,Y1: $i > $i] :
( !! @ ( ( $i > $i ) > $o )
@ ^ [Y2: ( $i > $i ) > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( leibeq2
= ( ^ [Y0: $i > $i,Y1: $i > $i] :
( !! @ ( ( $i > $i ) > $o )
@ ^ [Y2: ( $i > $i ) > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
( leibeq2
= ( ^ [X0: $i > $i,X1: $i > $i] :
! [X2: ( $i > $i ) > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( leibeq2
= ( ^ [X3: $i > $i,X4: $i > $i] :
! [X5: ( $i > $i ) > $o] :
( ( X5 @ X3 )
=> ( X5 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.RhjGW7INe5/DTF2THF_11332.p',leibeq2) ).
thf(f17,plain,
( $true
= ( leibeq2 @ sK0 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( $true
!= ( leibeq1 @ ( sK0 @ sK2 ) @ ( sK1 @ sK2 ) ) )
& ( $true
= ( leibeq2 @ sK0 @ sK1 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f12,f14,f13]) ).
thf(f13,plain,
( ? [X0: $i > $i,X1: $i > $i] :
( ? [X2: $i] :
( ( leibeq1 @ ( X0 @ X2 ) @ ( X1 @ X2 ) )
!= $true )
& ( $true
= ( leibeq2 @ X0 @ X1 ) ) )
=> ( ? [X2: $i] :
( $true
!= ( leibeq1 @ ( sK0 @ X2 ) @ ( sK1 @ X2 ) ) )
& ( $true
= ( leibeq2 @ sK0 @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
( ? [X2: $i] :
( $true
!= ( leibeq1 @ ( sK0 @ X2 ) @ ( sK1 @ X2 ) ) )
=> ( $true
!= ( leibeq1 @ ( sK0 @ sK2 ) @ ( sK1 @ sK2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
? [X0: $i > $i,X1: $i > $i] :
( ? [X2: $i] :
( ( leibeq1 @ ( X0 @ X2 ) @ ( X1 @ X2 ) )
!= $true )
& ( $true
= ( leibeq2 @ X0 @ X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
~ ! [X0: $i > $i,X1: $i > $i] :
( ( $true
= ( leibeq2 @ X0 @ X1 ) )
=> ! [X2: $i] :
( ( leibeq1 @ ( X0 @ X2 ) @ ( X1 @ X2 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ! [X0: $i > $i,X1: $i > $i] :
( ( leibeq2 @ X0 @ X1 )
=> ! [X2: $i] : ( leibeq1 @ ( X0 @ X2 ) @ ( X1 @ X2 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X6: $i > $i,X7: $i > $i] :
( ( leibeq2 @ X6 @ X7 )
=> ! [X3: $i] : ( leibeq1 @ ( X6 @ X3 ) @ ( X7 @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
! [X6: $i > $i,X7: $i > $i] :
( ( leibeq2 @ X6 @ X7 )
=> ! [X3: $i] : ( leibeq1 @ ( X6 @ X3 ) @ ( X7 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.RhjGW7INe5/DTF2THF_11332.p',conj) ).
thf(f29,plain,
( ( sK4 @ ( sK1 @ sK2 ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( $false
= ( ( sK4 @ ( sK0 @ sK2 ) )
=> ( sK4 @ ( sK1 @ sK2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f27]) ).
thf(f27,plain,
( $false
= ( ^ [Y0: $i > $o] :
( ( Y0 @ ( sK0 @ sK2 ) )
=> ( Y0 @ ( sK1 @ sK2 ) ) )
@ sK4 ) ),
inference(sigma_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0 @ ( sK0 @ sK2 ) )
=> ( Y0 @ ( sK1 @ sK2 ) ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
( $true
!= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) )
@ ( sK0 @ sK2 )
@ ( sK1 @ sK2 ) ) ),
inference(definition_unfolding,[status(thm)],[f18,f19]) ).
thf(f19,plain,
( leibeq1
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( leibeq1
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,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/sandbox2/tmp/tmp.RhjGW7INe5/DTF2THF_11332.p',leibeq1) ).
thf(f18,plain,
( $true
!= ( leibeq1 @ ( sK0 @ sK2 ) @ ( sK1 @ sK2 ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f30,plain,
( $true
= ( sK4 @ ( sK0 @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYO005^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.10 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n005.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 14:21:59 EST 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.39 ---- Original DTF file ---
% 0.17/0.39 thf(spec,logic,$$dhol).
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 % File : SYO005^1 : TPTP v9.2.1. Released v3.7.0.
% 0.17/0.39 % Domain : Syntactic
% 0.17/0.39 % Problem : The trivial direction of functional extensionality
% 0.17/0.39 % Version : Especial.
% 0.17/0.39 % English :
% 0.17/0.39
% 0.17/0.39 % Refs : [BB05] Benzmueller & Brown (2005), A Structured Set of Higher
% 0.17/0.39 % : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% 0.17/0.39 % Source : [Ben09]
% 0.17/0.39 % Names : Example 9a [BB05]
% 0.17/0.39
% 0.17/0.39 % Status : Theorem
% 0.17/0.39 % 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, 0.14 v7.4.0, 0.00 v6.2.0, 0.29 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0, 0.00 v3.7.0
% 0.17/0.39 % Syntax : Number of formulae : 5 ( 2 unt; 2 typ; 2 def)
% 0.17/0.39 % Number of atoms : 6 ( 2 equ; 0 cnn)
% 0.17/0.39 % Maximal formula atoms : 2 ( 2 avg)
% 0.17/0.39 % Number of connectives : 13 ( 0 ~; 0 |; 0 &; 10 @)
% 0.17/0.39 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.17/0.39 % Maximal formula depth : 8 ( 3 avg)
% 0.17/0.39 % Number of types : 2 ( 0 usr)
% 0.17/0.39 % Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% 0.17/0.39 % Number of symbols : 3 ( 2 usr; 0 con; 2-2 aty)
% 0.17/0.39 % Number of variables : 9 ( 4 ^; 5 !; 0 ?; 9 :)
% 0.17/0.39 % SPC : TH0_THM_EQU_NAR
% 0.17/0.39
% 0.17/0.39 % Comments :
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 thf(leibeq1_type,type,
% 0.17/0.39 leibeq1: $i > $i > $o ).
% 0.17/0.39
% 0.17/0.39 thf(leibeq1,definition,
% 0.17/0.39 ( leibeq1
% 0.17/0.39 = ( ^ [U: $i,V: $i] :
% 0.17/0.39 ! [Q: $i > $o] :
% 0.17/0.39 ( ( Q @ U )
% 0.17/0.39 => ( Q @ V ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(leibeq2_type,type,
% 0.17/0.39 leibeq2: ( $i > $i ) > ( $i > $i ) > $o ).
% 0.17/0.39
% 0.17/0.39 thf(leibeq2,definition,
% 0.17/0.39 ( leibeq2
% 0.17/0.39 = ( ^ [X: $i > $i,Y: $i > $i] :
% 0.17/0.39 ! [P: ( $i > $i ) > $o] :
% 0.17/0.39 ( ( P @ X )
% 0.17/0.39 => ( P @ Y ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(conj,conjecture,
% 0.17/0.39 ! [F: $i > $i,G: $i > $i] :
% 0.17/0.39 ( ( leibeq2 @ F @ G )
% 0.17/0.39 => ! [X: $i] : ( leibeq1 @ ( F @ X ) @ ( G @ X ) ) ) ).
% 0.17/0.39
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 ------------------------
% 1.36/1.29 ---- Embedded in THF ---
% 1.36/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.36/1.29 %%% Generated on Tue Feb 24 14:22:00 EST 2026
% 1.36/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.36/1.29 %%% Logic specification used:
% 1.36/1.29 %%% thf(spec, logic, $$dhol).
% 1.36/1.29
% 1.36/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.RhjGW7INe5/DTF2DTF11332.p
% See solution above
% 1.36/1.29 ------------------------
% 1.57/1.30 ---- Cleaned THF ---
% 1.57/1.30 thf(leibeq1_type,type,
% 1.57/1.30 leibeq1: $i > $i > $o ).
% 1.57/1.30
% 1.57/1.30 thf(leibeq1,definition,
% 1.57/1.30 ( leibeq1
% 1.57/1.30 = ( ^ [U: $i,V: $i] :
% 1.57/1.30 ! [Q: $i > $o] :
% 1.57/1.30 ( ( Q @ U )
% 1.57/1.30 => ( Q @ V ) ) ) ) ).
% 1.57/1.30
% 1.57/1.30 thf(leibeq2_type,type,
% 1.57/1.30 leibeq2: ( $i > $i ) > ( $i > $i ) > $o ).
% 1.57/1.30
% 1.57/1.30 thf(leibeq2,definition,
% 1.57/1.30 ( leibeq2
% 1.57/1.30 = ( ^ [X: $i > $i,Y: $i > $i] :
% 1.57/1.30 ! [P: ( $i > $i ) > $o] :
% 1.57/1.30 ( ( P @ X )
% 1.57/1.30 => ( P @ Y ) ) ) ) ).
% 1.57/1.30
% 1.57/1.30 thf(conj,conjecture,
% 1.57/1.30 ! [F: $i > $i,G: $i > $i] :
% 1.57/1.30 ( ( leibeq2 @ F @ G )
% 1.57/1.30 => ! [X: $i] : ( leibeq1 @ ( F @ X ) @ ( G @ X ) ) ) ).
% 1.57/1.30 ------------------------
% 1.57/1.32 % (11432)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_11332 for (2999ds/2Mi)
% 1.57/1.32 % (11434)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_11332 for (2999ds/275Mi)
% 1.57/1.32 % (11431)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_11332 for (2999ds/27Mi)
% 1.57/1.32 % (11433)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_11332 for (2999ds/2Mi)
% 1.57/1.32 % (11429)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_11332 for (2999ds/183Mi)
% 1.57/1.32 % (11435)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_11332 for (2999ds/18Mi)
% 1.57/1.32 % (11430)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_11332 for (2999ds/4Mi)
% 1.57/1.32 % (11432)Instruction limit reached!
% 1.57/1.32 % (11432)------------------------------
% 1.57/1.32 % (11432)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.32 % (11432)Termination reason: Unknown
% 1.57/1.32 % (11432)Termination phase: Saturation
% 1.57/1.32
% 1.57/1.32 % (11433)Instruction limit reached!
% 1.57/1.32 % (11433)------------------------------
% 1.57/1.32 % (11433)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.32 % (11433)Termination reason: Unknown
% 1.57/1.32 % (11433)Termination phase: Saturation
% 1.57/1.32
% 1.57/1.32 % (11433)Memory used [KB]: 5373
% 1.57/1.32 % (11433)Time elapsed: 0.003 s
% 1.57/1.32 % (11433)Instructions burned: 2 (million)
% 1.57/1.32 % (11433)------------------------------
% 1.57/1.32 % (11433)------------------------------
% 1.57/1.32 % (11432)Memory used [KB]: 5373
% 1.57/1.32 % (11432)Time elapsed: 0.003 s
% 1.57/1.32 % (11432)Instructions burned: 2 (million)
% 1.57/1.32 % (11432)------------------------------
% 1.57/1.32 % (11432)------------------------------
% 1.57/1.32 % (11431)Refutation not found, incomplete strategy
% 1.57/1.32 % (11431)------------------------------
% 1.57/1.32 % (11431)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.32 % (11431)Termination reason: Refutation not found, incomplete strategy
% 1.57/1.32
% 1.57/1.32
% 1.57/1.32 % (11431)Memory used [KB]: 5500
% 1.57/1.32 % (11431)Time elapsed: 0.004 s
% 1.57/1.32 % (11431)Instructions burned: 2 (million)
% 1.57/1.32 % (11431)------------------------------
% 1.57/1.32 % (11431)------------------------------
% 1.57/1.32 % (11430)First to succeed.
% 1.57/1.33 % (11434)Also succeeded, but the first one will report.
% 1.57/1.33 % (11430)Refutation found. Thanks to Tanya!
% 1.57/1.33 % SZS status Theorem for DTF2THF_11332
% 1.57/1.33 % SZS output start Proof for DTF2THF_11332
% 1.57/1.33 thf(func_def_0, type, leibeq1: $i > $i > $o).
% 1.57/1.33 thf(func_def_2, type, leibeq2: ($i > $i) > ($i > $i) > $o).
% 1.57/1.33 thf(func_def_11, type, sK0: $i > $i).
% 1.57/1.33 thf(func_def_12, type, sK1: $i > $i).
% 1.57/1.33 thf(func_def_15, type, sK4: $i > $o).
% 1.57/1.33 thf(func_def_17, type, ph5: !>[X0: $tType]:(X0)).
% 1.57/1.33 thf(f50,plain,(
% 1.57/1.33 $false),
% 1.57/1.33 inference(trivial_inequality_removal,[status(thm)],[f49])).
% 1.57/1.33 thf(f49,plain,(
% 1.57/1.33 ($true = $false)),
% 1.57/1.33 inference(backward_demodulation,[status(thm)],[f30,f48])).
% 1.57/1.33 thf(f48,plain,(
% 1.57/1.33 ($false = (sK4 @ (sK0 @ sK2)))),
% 1.57/1.33 inference(backward_demodulation,[status(thm)],[f29,f47])).
% 1.57/1.33 thf(f47,plain,(
% 1.57/1.33 ( ! [X1 : $i] : (((sK1 @ X1) = (sK0 @ X1))) )),
% 1.57/1.33 inference(argument_congruence,[status(thm)],[f33])).
% 1.57/1.33 thf(f33,plain,(
% 1.57/1.33 (sK0 = sK1)),
% 1.57/1.33 inference(leibniz_equality_elimination,[status(thm)],[f26])).
% 1.57/1.33 thf(f26,plain,(
% 1.57/1.33 ( ! [X1 : ($i > $i) > $o] : (($true = (X1 @ sK1)) | ($false = (X1 @ sK0))) )),
% 1.57/1.33 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.57/1.33 thf(f25,plain,(
% 1.57/1.33 ( ! [X1 : ($i > $i) > $o] : (($true = ((X1 @ sK0) => (X1 @ sK1)))) )),
% 1.57/1.33 inference(beta_eta_normalization,[status(thm)],[f24])).
% 1.57/1.33 thf(f24,plain,(
% 1.57/1.33 ( ! [X1 : ($i > $i) > $o] : (($true = ((^[Y0 : ($i > $i) > $o]: ((Y0 @ sK0) => (Y0 @ sK1))) @ X1))) )),
% 1.57/1.33 inference(pi_clausification,[status(thm)],[f23])).
% 1.57/1.33 thf(f23,plain,(
% 1.57/1.33 ($true = (!! @ (($i > $i) > $o) @ (^[Y0 : ($i > $i) > $o]: ((Y0 @ sK0) => (Y0 @ sK1)))))),
% 1.57/1.33 inference(beta_eta_normalization,[status(thm)],[f21])).
% 1.57/1.33 thf(f21,plain,(
% 1.57/1.33 ($true = ((^[Y0 : $i > $i]: ((^[Y1 : $i > $i]: (!! @ (($i > $i) > $o) @ (^[Y2 : ($i > $i) > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))) @ sK0 @ sK1))),
% 1.57/1.33 inference(definition_unfolding,[status(thm)],[f17,f16])).
% 1.57/1.33 thf(f16,plain,(
% 1.57/1.33 (leibeq2 = (^[Y0 : $i > $i]: ((^[Y1 : $i > $i]: (!! @ (($i > $i) > $o) @ (^[Y2 : ($i > $i) > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 1.57/1.33 inference(cnf_transformation,[status(thm)],[f7])).
% 1.57/1.33 thf(f7,plain,(
% 1.57/1.33 (leibeq2 = (^[Y0 : $i > $i]: ((^[Y1 : $i > $i]: (!! @ (($i > $i) > $o) @ (^[Y2 : ($i > $i) > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 1.57/1.33 inference(fool_elimination,[status(thm)],[f6])).
% 1.57/1.33 thf(f6,plain,(
% 1.57/1.33 (leibeq2 = (^[X0 : $i > $i, X1 : $i > $i] : (! [X2 : ($i > $i) > $o] : ((X2 @ X0) => (X2 @ X1)))))),
% 1.57/1.33 inference(rectify,[status(thm)],[f2])).
% 1.57/1.33 thf(f2,axiom,(
% 1.57/1.33 (leibeq2 = (^[X3 : $i > $i, X4 : $i > $i] : (! [X5 : ($i > $i) > $o] : ((X5 @ X3) => (X5 @ X4)))))),
% 1.57/1.33 file('/export/starexec/sandbox2/tmp/tmp.RhjGW7INe5/DTF2THF_11332.p',leibeq2)).
% 1.57/1.33 thf(f17,plain,(
% 1.57/1.33 ($true = (leibeq2 @ sK0 @ sK1))),
% 1.57/1.33 inference(cnf_transformation,[status(thm)],[f15])).
% 1.57/1.33 thf(f15,plain,(
% 1.57/1.33 ($true != (leibeq1 @ (sK0 @ sK2) @ (sK1 @ sK2))) & ($true = (leibeq2 @ sK0 @ sK1))),
% 1.57/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f12,f14,f13])).
% 1.57/1.33 thf(f13,plain,(
% 1.57/1.33 ? [X0 : $i > $i,X1 : $i > $i] : (? [X2 : $i] : ((leibeq1 @ (X0 @ X2) @ (X1 @ X2)) != $true) & ($true = (leibeq2 @ X0 @ X1))) => (? [X2 : $i] : ($true != (leibeq1 @ (sK0 @ X2) @ (sK1 @ X2))) & ($true = (leibeq2 @ sK0 @ sK1)))),
% 1.57/1.33 introduced(definition,[],[choice_axiom])).
% 1.57/1.33 thf(f14,plain,(
% 1.57/1.33 ? [X2 : $i] : ($true != (leibeq1 @ (sK0 @ X2) @ (sK1 @ X2))) => ($true != (leibeq1 @ (sK0 @ sK2) @ (sK1 @ sK2)))),
% 1.57/1.33 introduced(definition,[],[choice_axiom])).
% 1.57/1.33 thf(f12,plain,(
% 1.57/1.33 ? [X0 : $i > $i,X1 : $i > $i] : (? [X2 : $i] : ((leibeq1 @ (X0 @ X2) @ (X1 @ X2)) != $true) & ($true = (leibeq2 @ X0 @ X1)))),
% 1.57/1.33 inference(ennf_transformation,[status(thm)],[f11])).
% 1.57/1.33 thf(f11,plain,(
% 1.57/1.33 ~! [X0 : $i > $i,X1 : $i > $i] : (($true = (leibeq2 @ X0 @ X1)) => ! [X2 : $i] : ((leibeq1 @ (X0 @ X2) @ (X1 @ X2)) = $true))),
% 1.57/1.33 inference(fool_elimination,[status(thm)],[f10])).
% 1.57/1.33 thf(f10,plain,(
% 1.57/1.33 ~! [X0 : $i > $i,X1 : $i > $i] : ((leibeq2 @ X0 @ X1) => ! [X2 : $i] : (leibeq1 @ (X0 @ X2) @ (X1 @ X2)))),
% 1.57/1.33 inference(rectify,[status(thm)],[f4])).
% 1.57/1.33 thf(f4,negated_conjecture,(
% 1.57/1.33 ~! [X6 : $i > $i,X7 : $i > $i] : ((leibeq2 @ X6 @ X7) => ! [X3 : $i] : (leibeq1 @ (X6 @ X3) @ (X7 @ X3)))),
% 1.57/1.33 inference(negated_conjecture,[status(cth)],[f3])).
% 1.57/1.33 thf(f3,conjecture,(
% 1.57/1.33 ! [X6 : $i > $i,X7 : $i > $i] : ((leibeq2 @ X6 @ X7) => ! [X3 : $i] : (leibeq1 @ (X6 @ X3) @ (X7 @ X3)))),
% 1.57/1.33 file('/export/starexec/sandbox2/tmp/tmp.RhjGW7INe5/DTF2THF_11332.p',conj)).
% 1.57/1.33 thf(f29,plain,(
% 1.57/1.33 ((sK4 @ (sK1 @ sK2)) = $false)),
% 1.57/1.33 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 1.57/1.33 thf(f28,plain,(
% 1.57/1.33 ($false = ((sK4 @ (sK0 @ sK2)) => (sK4 @ (sK1 @ sK2))))),
% 1.57/1.33 inference(beta_eta_normalization,[status(thm)],[f27])).
% 1.57/1.33 thf(f27,plain,(
% 1.57/1.33 ($false = ((^[Y0 : $i > $o]: ((Y0 @ (sK0 @ sK2)) => (Y0 @ (sK1 @ sK2)))) @ sK4))),
% 1.57/1.33 inference(sigma_clausification,[status(thm)],[f22])).
% 1.57/1.33 thf(f22,plain,(
% 1.57/1.33 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((Y0 @ (sK0 @ sK2)) => (Y0 @ (sK1 @ sK2))))) != $true)),
% 1.57/1.33 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.57/1.33 thf(f20,plain,(
% 1.57/1.33 ($true != ((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))) @ (sK0 @ sK2) @ (sK1 @ sK2)))),
% 1.57/1.33 inference(definition_unfolding,[status(thm)],[f18,f19])).
% 1.57/1.33 thf(f19,plain,(
% 1.57/1.33 (leibeq1 = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 1.57/1.33 inference(cnf_transformation,[status(thm)],[f9])).
% 1.57/1.33 thf(f9,plain,(
% 1.57/1.33 (leibeq1 = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 1.57/1.33 inference(fool_elimination,[status(thm)],[f8])).
% 1.57/1.33 thf(f8,plain,(
% 1.57/1.33 (leibeq1 = (^[X0 : $i, X1 : $i] : (! [X2 : $i > $o] : ((X2 @ X0) => (X2 @ X1)))))),
% 1.57/1.33 inference(rectify,[status(thm)],[f1])).
% 1.57/1.33 thf(f1,axiom,(
% 1.57/1.33 (leibeq1 = (^[X0 : $i, X1 : $i] : (! [X2 : $i > $o] : ((X2 @ X0) => (X2 @ X1)))))),
% 1.57/1.33 file('/export/starexec/sandbox2/tmp/tmp.RhjGW7INe5/DTF2THF_11332.p',leibeq1)).
% 1.57/1.33 thf(f18,plain,(
% 1.57/1.33 ($true != (leibeq1 @ (sK0 @ sK2) @ (sK1 @ sK2)))),
% 1.57/1.33 inference(cnf_transformation,[status(thm)],[f15])).
% 1.57/1.33 thf(f30,plain,(
% 1.57/1.33 ($true = (sK4 @ (sK0 @ sK2)))),
% 1.57/1.33 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 1.57/1.33 % SZS output end Proof for DTF2THF_11332
% 1.57/1.33 % (11430)------------------------------
% 1.57/1.33 % (11430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.33 % (11430)Termination reason: Refutation
% 1.57/1.33
% 1.57/1.33 % (11430)Memory used [KB]: 5500
% 1.57/1.33 % (11430)Time elapsed: 0.005 s
% 1.57/1.33 % (11430)Instructions burned: 3 (million)
% 1.57/1.33 % (11430)------------------------------
% 1.57/1.33 % (11430)------------------------------
% 1.57/1.33 % (11428)Success in time 0.019 s
%------------------------------------------------------------------------------