%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO002^1 : 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 : n021.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 09:53:06 AM UTC 2026
% Result : Theorem 1.11s 1.11s
% Output : Refutation 1.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 28 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 128 ( 31 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 150 ( 10 ~; 1 |; 4 &; 112 @)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 25 ( 25 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 6 usr; 5 con; 0-2 aty)
% ( 6 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 43 ( 20 ^; 17 !; 6 ?; 43 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
leibeq: $i > $i > $o ).
thf(func_def_11,type,
sK1: $i > $i ).
thf(func_def_14,type,
sK4: $i > $o ).
thf(func_def_16,type,
ph5:
!>[X0: $tType] : X0 ).
thf(f46,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f45]) ).
thf(f45,plain,
$true = $false,
inference(backward_demodulation,[status(thm)],[f21,f43]) ).
thf(f43,plain,
( ( sK4 @ ( sK1 @ sK0 ) )
= $false ),
inference(backward_demodulation,[status(thm)],[f20,f27]) ).
thf(f27,plain,
sK2 = sK0,
inference(leibniz_equality_elimination,[status(thm)],[f25]) ).
thf(f25,plain,
! [X1: $i > $o] :
( ( $true
= ( X1 @ sK2 ) )
| ( $false
= ( X1 @ sK0 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
! [X1: $i > $o] :
( ( ( X1 @ sK0 )
=> ( X1 @ sK2 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f23]) ).
thf(f23,plain,
! [X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( ( Y0 @ sK0 )
=> ( Y0 @ sK2 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0 @ sK0 )
=> ( Y0 @ sK2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) )
@ sK0
@ sK2 )
= $true ),
inference(definition_unfolding,[status(thm)],[f14,f12]) ).
thf(f12,plain,
( leibeq
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( leibeq
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,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/sandbox/tmp/tmp.FhFeFTdbl7/DTF2THF_18550.p',leibeq) ).
thf(f14,plain,
( $true
= ( leibeq @ sK0 @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( $true
= ( leibeq @ sK0 @ sK2 ) )
& ( ( leibeq @ ( sK1 @ sK0 ) @ ( sK1 @ sK2 ) )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f9,f10]) ).
thf(f10,plain,
( ? [X0: $i,X1: $i > $i,X2: $i] :
( ( $true
= ( leibeq @ X0 @ X2 ) )
& ( ( leibeq @ ( X1 @ X0 ) @ ( X1 @ X2 ) )
!= $true ) )
=> ( ( $true
= ( leibeq @ sK0 @ sK2 ) )
& ( ( leibeq @ ( sK1 @ sK0 ) @ ( sK1 @ sK2 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
? [X0: $i,X1: $i > $i,X2: $i] :
( ( $true
= ( leibeq @ X0 @ X2 ) )
& ( ( leibeq @ ( X1 @ X0 ) @ ( X1 @ X2 ) )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ! [X0: $i,X1: $i > $i,X2: $i] :
( ( $true
= ( leibeq @ X0 @ X2 ) )
=> ( ( leibeq @ ( X1 @ X0 ) @ ( X1 @ X2 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ! [X0: $i,X1: $i > $i,X2: $i] :
( ( leibeq @ X0 @ X2 )
=> ( leibeq @ ( X1 @ X0 ) @ ( X1 @ X2 ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ! [X0: $i,X3: $i > $i,X1: $i] :
( ( leibeq @ X0 @ X1 )
=> ( leibeq @ ( X3 @ X0 ) @ ( X3 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
! [X0: $i,X3: $i > $i,X1: $i] :
( ( leibeq @ X0 @ X1 )
=> ( leibeq @ ( X3 @ X0 ) @ ( X3 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.FhFeFTdbl7/DTF2THF_18550.p',conj) ).
thf(f20,plain,
( ( sK4 @ ( sK1 @ sK2 ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ( sK4 @ ( sK1 @ sK0 ) )
=> ( sK4 @ ( sK1 @ sK2 ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f18]) ).
thf(f18,plain,
( $false
= ( ^ [Y0: $i > $o] :
( ( Y0 @ ( sK1 @ sK0 ) )
=> ( Y0 @ ( sK1 @ sK2 ) ) )
@ sK4 ) ),
inference(sigma_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( $true
!= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0 @ ( sK1 @ sK0 ) )
=> ( Y0 @ ( sK1 @ sK2 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) )
@ ( sK1 @ sK0 )
@ ( sK1 @ sK2 ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f13,f12]) ).
thf(f13,plain,
( ( leibeq @ ( sK1 @ sK0 ) @ ( sK1 @ sK2 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f21,plain,
( ( sK4 @ ( sK1 @ sK0 ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SYO002^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.31 % Computer : n021.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Tue Feb 24 14:21:53 EST 2026
% 0.12/0.31 % CPUTime :
% 0.12/0.31 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.42 ---- Original DTF file ---
% 0.15/0.42 thf(spec,logic,$$dhol).
% 0.15/0.42 %------------------------------------------------------------------------------
% 0.15/0.42 % File : SYO002^1 : TPTP v9.2.1. Released v3.7.0.
% 0.15/0.42 % Domain : Syntactic
% 0.15/0.42 % Problem : Leibniz equality obeys the congruence property under functions
% 0.15/0.42 % Version : Especial.
% 0.15/0.42 % English :
% 0.15/0.42
% 0.15/0.42 % Refs : [BB05] Benzmueller & Brown (2005), A Structured Set of Higher
% 0.15/0.42 % : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% 0.15/0.42 % Source : [Ben09]
% 0.15/0.42 % Names : Example 7a [BB05]
% 0.15/0.42
% 0.15/0.42 % Status : Theorem
% 0.15/0.42 % 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
% 0.15/0.42 % Syntax : Number of formulae : 3 ( 1 unt; 1 typ; 1 def)
% 0.15/0.42 % Number of atoms : 4 ( 1 equ; 0 cnn)
% 0.15/0.42 % Maximal formula atoms : 2 ( 2 avg)
% 0.15/0.42 % Number of connectives : 10 ( 0 ~; 0 |; 0 &; 8 @)
% 0.15/0.42 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.15/0.42 % Maximal formula depth : 8 ( 5 avg)
% 0.15/0.42 % Number of types : 2 ( 0 usr)
% 0.15/0.42 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.15/0.42 % Number of symbols : 2 ( 1 usr; 0 con; 2-2 aty)
% 0.15/0.42 % Number of variables : 6 ( 2 ^; 4 !; 0 ?; 6 :)
% 0.15/0.42 % SPC : TH0_THM_EQU_NAR
% 0.15/0.42
% 0.15/0.42 % Comments :
% 0.15/0.42 %------------------------------------------------------------------------------
% 0.15/0.42 thf(leibeq_decl,type,
% 0.15/0.42 leibeq: $i > $i > $o ).
% 0.15/0.42
% 0.15/0.42 thf(leibeq,definition,
% 0.15/0.42 ( leibeq
% 0.15/0.42 = ( ^ [X: $i,Y: $i] :
% 0.15/0.42 ! [P: $i > $o] :
% 0.15/0.42 ( ( P @ X )
% 0.15/0.42 => ( P @ Y ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(conj,conjecture,
% 0.15/0.42 ! [X: $i,Y: $i,F: $i > $i] :
% 0.15/0.42 ( ( leibeq @ X @ Y )
% 0.15/0.42 => ( leibeq @ ( F @ X ) @ ( F @ Y ) ) ) ).
% 0.15/0.42
% 0.15/0.42 %------------------------------------------------------------------------------
% 0.15/0.42 ------------------------
% 1.11/1.08 ---- Embedded in THF ---
% 1.11/1.08 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.11/1.08 %%% Generated on Tue Feb 24 14:21:54 EST 2026
% 1.11/1.08 %%% using '$$dhol' embedding, version 1.3.0.
% 1.11/1.08 %%% Logic specification used:
% 1.11/1.08 %%% thf(spec, logic, $$dhol).
% 1.11/1.08
% 1.11/1.08 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.FhFeFTdbl7/DTF2DTF18550.p
% See solution above
% 1.11/1.08 ------------------------
% 1.11/1.09 ---- Cleaned THF ---
% 1.11/1.09 thf(leibeq_decl,type,
% 1.11/1.09 leibeq: $i > $i > $o ).
% 1.11/1.09
% 1.11/1.09 thf(leibeq,definition,
% 1.11/1.09 ( leibeq
% 1.11/1.09 = ( ^ [X: $i,Y: $i] :
% 1.11/1.09 ! [P: $i > $o] :
% 1.11/1.09 ( ( P @ X )
% 1.11/1.09 => ( P @ Y ) ) ) ) ).
% 1.11/1.09
% 1.11/1.09 thf(conj,conjecture,
% 1.11/1.09 ! [X: $i,Y: $i,F: $i > $i] :
% 1.11/1.09 ( ( leibeq @ X @ Y )
% 1.11/1.09 => ( leibeq @ ( F @ X ) @ ( F @ Y ) ) ) ).
% 1.11/1.09 ------------------------
% 1.11/1.10 % (18677)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_18550 for (3000ds/183Mi)
% 1.11/1.10 % (18683)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_18550 for (3000ds/275Mi)
% 1.11/1.10 % (18679)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_18550 for (3000ds/27Mi)
% 1.11/1.10 % (18684)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_18550 for (3000ds/18Mi)
% 1.11/1.10 % (18680)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_18550 for (3000ds/2Mi)
% 1.11/1.10 % (18678)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_18550 for (3000ds/4Mi)
% 1.11/1.10 % (18681)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_18550 for (3000ds/2Mi)
% 1.11/1.10 % (18680)Instruction limit reached!
% 1.11/1.10 % (18680)------------------------------
% 1.11/1.10 % (18680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.11/1.10 % (18680)Termination reason: Unknown
% 1.11/1.10 % (18680)Termination phase: Saturation
% 1.11/1.10
% 1.11/1.10 % (18680)Memory used [KB]: 895
% 1.11/1.10 % (18680)Time elapsed: 0.002 s
% 1.11/1.10 % (18680)Instructions burned: 2 (million)
% 1.11/1.10 % (18680)------------------------------
% 1.11/1.10 % (18680)------------------------------
% 1.11/1.10 % (18681)Instruction limit reached!
% 1.11/1.10 % (18681)------------------------------
% 1.11/1.10 % (18681)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.11/1.10 % (18681)Termination reason: Unknown
% 1.11/1.10 % (18681)Termination phase: Saturation
% 1.11/1.10
% 1.11/1.10 % (18681)Memory used [KB]: 895
% 1.11/1.10 % (18681)Time elapsed: 0.002 s
% 1.11/1.10 % (18681)Instructions burned: 2 (million)
% 1.11/1.10 % (18681)------------------------------
% 1.11/1.10 % (18681)------------------------------
% 1.11/1.10 % (18683)Refutation not found, incomplete strategy
% 1.11/1.10 % (18683)------------------------------
% 1.11/1.10 % (18683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.11/1.10 % (18683)Termination reason: Refutation not found, incomplete strategy
% 1.11/1.10
% 1.11/1.10
% 1.11/1.10 % (18683)Memory used [KB]: 5500
% 1.11/1.10 % (18683)Time elapsed: 0.002 s
% 1.11/1.10 % (18683)Instructions burned: 1 (million)
% 1.11/1.10 % (18683)------------------------------
% 1.11/1.10 % (18683)------------------------------
% 1.11/1.10 % (18679)Refutation not found, incomplete strategy
% 1.11/1.10 % (18679)------------------------------
% 1.11/1.10 % (18679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.11/1.10 % (18679)Termination reason: Refutation not found, incomplete strategy
% 1.11/1.10
% 1.11/1.10
% 1.11/1.10 % (18679)Memory used [KB]: 5500
% 1.11/1.10 % (18679)Time elapsed: 0.002 s
% 1.11/1.10 % (18679)Instructions burned: 2 (million)
% 1.11/1.10 % (18679)------------------------------
% 1.11/1.10 % (18679)------------------------------
% 1.11/1.10 % (18684)First to succeed.
% 1.11/1.11 % (18677)Also succeeded, but the first one will report.
% 1.11/1.11 % (18684)Refutation found. Thanks to Tanya!
% 1.11/1.11 % SZS status Theorem for DTF2THF_18550
% 1.11/1.11 % SZS output start Proof for DTF2THF_18550
% 1.11/1.11 thf(func_def_0, type, leibeq: $i > $i > $o).
% 1.11/1.11 thf(func_def_11, type, sK1: $i > $i).
% 1.11/1.11 thf(func_def_14, type, sK4: $i > $o).
% 1.11/1.11 thf(func_def_16, type, ph5: !>[X0: $tType]:(X0)).
% 1.11/1.11 thf(f46,plain,(
% 1.11/1.11 $false),
% 1.11/1.11 inference(trivial_inequality_removal,[status(thm)],[f45])).
% 1.11/1.11 thf(f45,plain,(
% 1.11/1.11 ($true = $false)),
% 1.11/1.11 inference(backward_demodulation,[status(thm)],[f21,f43])).
% 1.11/1.11 thf(f43,plain,(
% 1.11/1.11 ((sK4 @ (sK1 @ sK0)) = $false)),
% 1.11/1.11 inference(backward_demodulation,[status(thm)],[f20,f27])).
% 1.11/1.11 thf(f27,plain,(
% 1.11/1.11 (sK2 = sK0)),
% 1.11/1.11 inference(leibniz_equality_elimination,[status(thm)],[f25])).
% 1.11/1.11 thf(f25,plain,(
% 1.11/1.11 ( ! [X1 : $i > $o] : (($true = (X1 @ sK2)) | ($false = (X1 @ sK0))) )),
% 1.11/1.11 inference(binary_proxy_clausification,[status(thm)],[f24])).
% 1.11/1.11 thf(f24,plain,(
% 1.11/1.11 ( ! [X1 : $i > $o] : ((((X1 @ sK0) => (X1 @ sK2)) = $true)) )),
% 1.11/1.11 inference(beta_eta_normalization,[status(thm)],[f23])).
% 1.11/1.11 thf(f23,plain,(
% 1.11/1.11 ( ! [X1 : $i > $o] : (($true = ((^[Y0 : $i > $o]: ((Y0 @ sK0) => (Y0 @ sK2))) @ X1))) )),
% 1.11/1.11 inference(pi_clausification,[status(thm)],[f22])).
% 1.11/1.11 thf(f22,plain,(
% 1.11/1.11 ($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((Y0 @ sK0) => (Y0 @ sK2)))))),
% 1.11/1.11 inference(beta_eta_normalization,[status(thm)],[f15])).
% 1.11/1.11 thf(f15,plain,(
% 1.11/1.11 (((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))) @ sK0 @ sK2) = $true)),
% 1.11/1.11 inference(definition_unfolding,[status(thm)],[f14,f12])).
% 1.11/1.11 thf(f12,plain,(
% 1.11/1.11 (leibeq = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 1.11/1.11 inference(cnf_transformation,[status(thm)],[f6])).
% 1.11/1.11 thf(f6,plain,(
% 1.11/1.11 (leibeq = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 1.11/1.11 inference(fool_elimination,[status(thm)],[f5])).
% 1.11/1.11 thf(f5,plain,(
% 1.11/1.11 ((^[X0 : $i, X1 : $i] : (! [X2 : $i > $o] : ((X2 @ X0) => (X2 @ X1)))) = leibeq)),
% 1.11/1.11 inference(rectify,[status(thm)],[f1])).
% 1.11/1.11 thf(f1,axiom,(
% 1.11/1.11 ((^[X0 : $i, X1 : $i] : (! [X2 : $i > $o] : ((X2 @ X0) => (X2 @ X1)))) = leibeq)),
% 1.11/1.11 file('/export/starexec/sandbox/tmp/tmp.FhFeFTdbl7/DTF2THF_18550.p',leibeq)).
% 1.11/1.11 thf(f14,plain,(
% 1.11/1.11 ($true = (leibeq @ sK0 @ sK2))),
% 1.11/1.11 inference(cnf_transformation,[status(thm)],[f11])).
% 1.11/1.11 thf(f11,plain,(
% 1.11/1.11 ($true = (leibeq @ sK0 @ sK2)) & ((leibeq @ (sK1 @ sK0) @ (sK1 @ sK2)) != $true)),
% 1.11/1.11 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f9,f10])).
% 1.11/1.11 thf(f10,plain,(
% 1.11/1.11 ? [X0 : $i,X1 : $i > $i,X2 : $i] : (($true = (leibeq @ X0 @ X2)) & ((leibeq @ (X1 @ X0) @ (X1 @ X2)) != $true)) => (($true = (leibeq @ sK0 @ sK2)) & ((leibeq @ (sK1 @ sK0) @ (sK1 @ sK2)) != $true))),
% 1.11/1.11 introduced(definition,[],[choice_axiom])).
% 1.11/1.11 thf(f9,plain,(
% 1.11/1.11 ? [X0 : $i,X1 : $i > $i,X2 : $i] : (($true = (leibeq @ X0 @ X2)) & ((leibeq @ (X1 @ X0) @ (X1 @ X2)) != $true))),
% 1.11/1.11 inference(ennf_transformation,[status(thm)],[f8])).
% 1.11/1.11 thf(f8,plain,(
% 1.11/1.11 ~! [X0 : $i,X1 : $i > $i,X2 : $i] : (($true = (leibeq @ X0 @ X2)) => ((leibeq @ (X1 @ X0) @ (X1 @ X2)) = $true))),
% 1.11/1.11 inference(fool_elimination,[status(thm)],[f7])).
% 1.11/1.11 thf(f7,plain,(
% 1.11/1.11 ~! [X0 : $i,X1 : $i > $i,X2 : $i] : ((leibeq @ X0 @ X2) => (leibeq @ (X1 @ X0) @ (X1 @ X2)))),
% 1.11/1.11 inference(rectify,[status(thm)],[f3])).
% 1.11/1.11 thf(f3,negated_conjecture,(
% 1.11/1.11 ~! [X0 : $i,X3 : $i > $i,X1 : $i] : ((leibeq @ X0 @ X1) => (leibeq @ (X3 @ X0) @ (X3 @ X1)))),
% 1.11/1.11 inference(negated_conjecture,[status(cth)],[f2])).
% 1.11/1.11 thf(f2,conjecture,(
% 1.11/1.11 ! [X0 : $i,X3 : $i > $i,X1 : $i] : ((leibeq @ X0 @ X1) => (leibeq @ (X3 @ X0) @ (X3 @ X1)))),
% 1.11/1.11 file('/export/starexec/sandbox/tmp/tmp.FhFeFTdbl7/DTF2THF_18550.p',conj)).
% 1.11/1.11 thf(f20,plain,(
% 1.11/1.11 ((sK4 @ (sK1 @ sK2)) = $false)),
% 1.11/1.11 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.11/1.11 thf(f19,plain,(
% 1.11/1.11 (((sK4 @ (sK1 @ sK0)) => (sK4 @ (sK1 @ sK2))) = $false)),
% 1.11/1.11 inference(beta_eta_normalization,[status(thm)],[f18])).
% 1.11/1.11 thf(f18,plain,(
% 1.11/1.11 ($false = ((^[Y0 : $i > $o]: ((Y0 @ (sK1 @ sK0)) => (Y0 @ (sK1 @ sK2)))) @ sK4))),
% 1.11/1.11 inference(sigma_clausification,[status(thm)],[f17])).
% 1.11/1.11 thf(f17,plain,(
% 1.11/1.11 ($true != (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((Y0 @ (sK1 @ sK0)) => (Y0 @ (sK1 @ sK2))))))),
% 1.11/1.11 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.11/1.11 thf(f16,plain,(
% 1.11/1.11 (((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))) @ (sK1 @ sK0) @ (sK1 @ sK2)) != $true)),
% 1.11/1.11 inference(definition_unfolding,[status(thm)],[f13,f12])).
% 1.11/1.11 thf(f13,plain,(
% 1.11/1.11 ((leibeq @ (sK1 @ sK0) @ (sK1 @ sK2)) != $true)),
% 1.11/1.11 inference(cnf_transformation,[status(thm)],[f11])).
% 1.11/1.11 thf(f21,plain,(
% 1.11/1.11 ((sK4 @ (sK1 @ sK0)) = $true)),
% 1.11/1.11 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.11/1.11 % SZS output end Proof for DTF2THF_18550
% 1.11/1.11 % (18684)------------------------------
% 1.11/1.11 % (18684)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.11/1.11 % (18684)Termination reason: Refutation
% 1.11/1.11
% 1.11/1.11 % (18684)Memory used [KB]: 5500
% 1.11/1.11 % (18684)Time elapsed: 0.003 s
% 1.11/1.11 % (18684)Instructions burned: 2 (million)
% 1.11/1.11 % (18684)------------------------------
% 1.11/1.11 % (18684)------------------------------
% 1.11/1.11 % (18675)Success in time 0.011 s
%------------------------------------------------------------------------------