%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYN999^1 : 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 : n008.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 09:51:42 AM UTC 2026
% Result : Theorem 1.48s 1.25s
% Output : Refutation 1.48s
% 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 : 121 ( 10 ~; 1 |; 4 &; 83 @)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 5 usr; 5 con; 0-2 aty)
% ( 6 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 37 ( 20 ^; 13 !; 4 ?; 37 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
leibeq: $i > $i > $o ).
thf(func_def_13,type,
sK3: $i > $o ).
thf(func_def_15,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f45,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f44]) ).
thf(f44,plain,
$true = $false,
inference(backward_demodulation,[status(thm)],[f22,f43]) ).
thf(f43,plain,
( ( sK3 @ sK0 )
= $false ),
inference(backward_demodulation,[status(thm)],[f21,f28]) ).
thf(f28,plain,
sK0 = sK1,
inference(leibniz_equality_elimination,[status(thm)],[f25]) ).
thf(f25,plain,
! [X1: $i > $o] :
( ( $false
= ( X1 @ sK1 ) )
| ( $true
= ( X1 @ sK0 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
! [X1: $i > $o] :
( $true
= ( ( X1 @ sK1 )
=> ( X1 @ sK0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f23]) ).
thf(f23,plain,
! [X1: $i > $o] :
( ( ^ [Y0: $i > $o] :
( ( Y0 @ sK1 )
=> ( Y0 @ sK0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0 @ sK1 )
=> ( Y0 @ sK0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
( $true
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) )
@ sK1
@ sK0 ) ),
inference(definition_unfolding,[status(thm)],[f13,f12]) ).
thf(f12,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,
( leibeq
= ( ^ [X0: $i,X1: $i] :
! [X2: $i > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( leibeq
= ( ^ [X0: $i,X1: $i] :
! [X2: $i > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tDlPxvbSWo/DTF2THF_12017.p',leibeq) ).
thf(f13,plain,
( ( leibeq @ sK1 @ sK0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( $true
!= ( leibeq @ sK0 @ sK1 ) )
& ( ( leibeq @ sK1 @ sK0 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f10]) ).
thf(f10,plain,
( ? [X0: $i,X1: $i] :
( ( ( leibeq @ X0 @ X1 )
!= $true )
& ( ( leibeq @ X1 @ X0 )
= $true ) )
=> ( ( $true
!= ( leibeq @ sK0 @ sK1 ) )
& ( ( leibeq @ sK1 @ sK0 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
? [X0: $i,X1: $i] :
( ( ( leibeq @ X0 @ X1 )
!= $true )
& ( ( leibeq @ X1 @ X0 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: $i,X1: $i] :
( ( ( leibeq @ X1 @ X0 )
= $true )
=> ( ( leibeq @ X0 @ X1 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: $i,X1: $i] :
( ( leibeq @ X1 @ X0 )
=> ( leibeq @ X0 @ X1 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ! [X1: $i,X0: $i] :
( ( leibeq @ X0 @ X1 )
=> ( leibeq @ X1 @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
! [X1: $i,X0: $i] :
( ( leibeq @ X0 @ X1 )
=> ( leibeq @ X1 @ X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.tDlPxvbSWo/DTF2THF_12017.p',conj) ).
thf(f21,plain,
( ( sK3 @ sK1 )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
( $false
= ( ( sK3 @ sK0 )
=> ( sK3 @ sK1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ^ [Y0: $i > $o] :
( ( Y0 @ sK0 )
=> ( Y0 @ sK1 ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
( $true
!= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0 @ sK0 )
=> ( Y0 @ sK1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f15]) ).
thf(f15,plain,
( $true
!= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) )
@ sK0
@ sK1 ) ),
inference(definition_unfolding,[status(thm)],[f14,f12]) ).
thf(f14,plain,
( $true
!= ( leibeq @ sK0 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f22,plain,
( ( sK3 @ sK0 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYN999^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n008.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 14:21:54 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.45 ---- Original DTF file ---
% 0.29/0.45 thf(spec,logic,$$dhol).
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 % File : SYN999^1 : TPTP v9.2.1. Released v3.7.0.
% 0.29/0.45 % Domain : Syntactic
% 0.29/0.45 % Problem : Leibniz equality is symmetric
% 0.29/0.45 % Version : Especial.
% 0.29/0.45 % English :
% 0.29/0.45
% 0.29/0.45 % Refs : [BB05] Benzmueller & Brown (2005), A Structured Set of Higher
% 0.29/0.45 % : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% 0.29/0.45 % Source : [Ben09]
% 0.29/0.45 % Names : Example 6b [BB05]
% 0.29/0.45
% 0.29/0.45 % Status : Theorem
% 0.29/0.45 % 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, 0.00 v6.2.0, 0.29 v6.1.0, 0.14 v6.0.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.3.0, 0.60 v5.2.0, 0.40 v4.1.0, 0.33 v3.7.0
% 0.29/0.45 % Syntax : Number of formulae : 3 ( 1 unt; 1 typ; 1 def)
% 0.29/0.45 % Number of atoms : 4 ( 1 equ; 0 cnn)
% 0.29/0.45 % Maximal formula atoms : 2 ( 2 avg)
% 0.29/0.45 % Number of connectives : 8 ( 0 ~; 0 |; 0 &; 6 @)
% 0.29/0.45 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.29/0.45 % Maximal formula depth : 6 ( 4 avg)
% 0.29/0.45 % Number of types : 2 ( 0 usr)
% 0.29/0.45 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.29/0.45 % Number of symbols : 2 ( 1 usr; 0 con; 2-2 aty)
% 0.29/0.45 % Number of variables : 5 ( 2 ^; 3 !; 0 ?; 5 :)
% 0.29/0.45 % SPC : TH0_THM_EQU_NAR
% 0.29/0.45
% 0.29/0.45 % Comments :
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 thf(leibeq_decl,type,
% 0.29/0.45 leibeq: $i > $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(leibeq,definition,
% 0.29/0.45 ( leibeq
% 0.29/0.45 = ( ^ [X: $i,Y: $i] :
% 0.29/0.45 ! [P: $i > $o] :
% 0.29/0.45 ( ( P @ X )
% 0.29/0.45 => ( P @ Y ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(conj,conjecture,
% 0.29/0.45 ! [X: $i,Y: $i] :
% 0.29/0.45 ( ( leibeq @ X @ Y )
% 0.29/0.45 => ( leibeq @ Y @ X ) ) ).
% 0.29/0.45
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 ------------------------
% 1.48/1.21 ---- Embedded in THF ---
% 1.48/1.21 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.21 %%% Generated on Tue Feb 24 14:21:55 EST 2026
% 1.48/1.21 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.21 %%% Logic specification used:
% 1.48/1.21 %%% thf(spec, logic, $$dhol).
% 1.48/1.21
% 1.48/1.21 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.tDlPxvbSWo/DTF2DTF12017.p
% See solution above
% 1.48/1.21 ------------------------
% 1.48/1.22 ---- Cleaned THF ---
% 1.48/1.22 thf(leibeq_decl,type,
% 1.48/1.22 leibeq: $i > $i > $o ).
% 1.48/1.22
% 1.48/1.22 thf(leibeq,definition,
% 1.48/1.22 ( leibeq
% 1.48/1.22 = ( ^ [X: $i,Y: $i] :
% 1.48/1.22 ! [P: $i > $o] :
% 1.48/1.22 ( ( P @ X )
% 1.48/1.22 => ( P @ Y ) ) ) ) ).
% 1.48/1.22
% 1.48/1.22 thf(conj,conjecture,
% 1.48/1.22 ! [X: $i,Y: $i] :
% 1.48/1.22 ( ( leibeq @ X @ Y )
% 1.48/1.22 => ( leibeq @ Y @ X ) ) ).
% 1.48/1.22 ------------------------
% 1.48/1.24 % (12137)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_12017 for (2999ds/275Mi)
% 1.48/1.24 % (12134)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_12017 for (2999ds/27Mi)
% 1.48/1.24 % (12137)Refutation not found, incomplete strategy
% 1.48/1.24 % (12137)------------------------------
% 1.48/1.24 % (12137)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.24 % (12137)Termination reason: Refutation not found, incomplete strategy
% 1.48/1.24
% 1.48/1.24
% 1.48/1.24 % (12137)Memory used [KB]: 5500
% 1.48/1.24 % (12137)Time elapsed: 0.002 s
% 1.48/1.24 % (12137)Instructions burned: 1 (million)
% 1.48/1.24 % (12137)------------------------------
% 1.48/1.24 % (12137)------------------------------
% 1.48/1.24 % (12134)Refutation not found, incomplete strategy
% 1.48/1.24 % (12134)------------------------------
% 1.48/1.24 % (12134)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.24 % (12134)Termination reason: Refutation not found, incomplete strategy
% 1.48/1.24
% 1.48/1.24
% 1.48/1.24 % (12134)Memory used [KB]: 5500
% 1.48/1.24 % (12134)Time elapsed: 0.002 s
% 1.48/1.24 % (12134)Instructions burned: 2 (million)
% 1.48/1.24 % (12134)------------------------------
% 1.48/1.24 % (12134)------------------------------
% 1.48/1.25 % (12132)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_12017 for (2999ds/183Mi)
% 1.48/1.25 % (12133)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_12017 for (2999ds/4Mi)
% 1.48/1.25 % (12135)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_12017 for (2999ds/2Mi)
% 1.48/1.25 % (12136)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_12017 for (2999ds/2Mi)
% 1.48/1.25 % (12138)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_12017 for (2999ds/18Mi)
% 1.48/1.25 % (12135)Instruction limit reached!
% 1.48/1.25 % (12135)------------------------------
% 1.48/1.25 % (12135)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.25 % (12135)Termination reason: Unknown
% 1.48/1.25 % (12135)Termination phase: Saturation
% 1.48/1.25
% 1.48/1.25 % (12135)Memory used [KB]: 895
% 1.48/1.25 % (12135)Time elapsed: 0.003 s
% 1.48/1.25 % (12135)Instructions burned: 2 (million)
% 1.48/1.25 % (12135)------------------------------
% 1.48/1.25 % (12135)------------------------------
% 1.48/1.25 % (12136)Instruction limit reached!
% 1.48/1.25 % (12136)------------------------------
% 1.48/1.25 % (12136)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.25 % (12136)Termination reason: Unknown
% 1.48/1.25 % (12136)Termination phase: Saturation
% 1.48/1.25
% 1.48/1.25 % (12136)Memory used [KB]: 5500
% 1.48/1.25 % (12136)Time elapsed: 0.004 s
% 1.48/1.25 % (12136)Instructions burned: 2 (million)
% 1.48/1.25 % (12136)------------------------------
% 1.48/1.25 % (12136)------------------------------
% 1.48/1.25 % (12133)First to succeed.
% 1.48/1.25 % (12138)Also succeeded, but the first one will report.
% 1.48/1.25 % (12133)Refutation found. Thanks to Tanya!
% 1.48/1.25 % SZS status Theorem for DTF2THF_12017
% 1.48/1.25 % SZS output start Proof for DTF2THF_12017
% 1.48/1.25 thf(func_def_0, type, leibeq: $i > $i > $o).
% 1.48/1.25 thf(func_def_13, type, sK3: $i > $o).
% 1.48/1.25 thf(func_def_15, type, ph4: !>[X0: $tType]:(X0)).
% 1.48/1.25 thf(f45,plain,(
% 1.48/1.25 $false),
% 1.48/1.25 inference(trivial_inequality_removal,[status(thm)],[f44])).
% 1.48/1.25 thf(f44,plain,(
% 1.48/1.25 ($true = $false)),
% 1.48/1.25 inference(backward_demodulation,[status(thm)],[f22,f43])).
% 1.48/1.25 thf(f43,plain,(
% 1.48/1.25 ((sK3 @ sK0) = $false)),
% 1.48/1.25 inference(backward_demodulation,[status(thm)],[f21,f28])).
% 1.48/1.25 thf(f28,plain,(
% 1.48/1.25 (sK0 = sK1)),
% 1.48/1.25 inference(leibniz_equality_elimination,[status(thm)],[f25])).
% 1.48/1.25 thf(f25,plain,(
% 1.48/1.25 ( ! [X1 : $i > $o] : (($false = (X1 @ sK1)) | ($true = (X1 @ sK0))) )),
% 1.48/1.25 inference(binary_proxy_clausification,[status(thm)],[f24])).
% 1.48/1.25 thf(f24,plain,(
% 1.48/1.25 ( ! [X1 : $i > $o] : (($true = ((X1 @ sK1) => (X1 @ sK0)))) )),
% 1.48/1.25 inference(beta_eta_normalization,[status(thm)],[f23])).
% 1.48/1.25 thf(f23,plain,(
% 1.48/1.25 ( ! [X1 : $i > $o] : ((((^[Y0 : $i > $o]: ((Y0 @ sK1) => (Y0 @ sK0))) @ X1) = $true)) )),
% 1.48/1.25 inference(pi_clausification,[status(thm)],[f17])).
% 1.48/1.25 thf(f17,plain,(
% 1.48/1.25 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((Y0 @ sK1) => (Y0 @ sK0)))) = $true)),
% 1.48/1.25 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.48/1.25 thf(f16,plain,(
% 1.48/1.25 ($true = ((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))) @ sK1 @ sK0))),
% 1.48/1.25 inference(definition_unfolding,[status(thm)],[f13,f12])).
% 1.48/1.25 thf(f12,plain,(
% 1.48/1.25 (leibeq = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 1.48/1.25 inference(cnf_transformation,[status(thm)],[f8])).
% 1.48/1.25 thf(f8,plain,(
% 1.48/1.25 (leibeq = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 1.48/1.25 inference(fool_elimination,[status(thm)],[f7])).
% 1.48/1.25 thf(f7,plain,(
% 1.48/1.25 (leibeq = (^[X0 : $i, X1 : $i] : (! [X2 : $i > $o] : ((X2 @ X0) => (X2 @ X1)))))),
% 1.48/1.25 inference(rectify,[status(thm)],[f1])).
% 1.48/1.25 thf(f1,axiom,(
% 1.48/1.25 (leibeq = (^[X0 : $i, X1 : $i] : (! [X2 : $i > $o] : ((X2 @ X0) => (X2 @ X1)))))),
% 1.48/1.25 file('/export/starexec/sandbox/tmp/tmp.tDlPxvbSWo/DTF2THF_12017.p',leibeq)).
% 1.48/1.25 thf(f13,plain,(
% 1.48/1.25 ((leibeq @ sK1 @ sK0) = $true)),
% 1.48/1.25 inference(cnf_transformation,[status(thm)],[f11])).
% 1.48/1.25 thf(f11,plain,(
% 1.48/1.25 ($true != (leibeq @ sK0 @ sK1)) & ((leibeq @ sK1 @ sK0) = $true)),
% 1.48/1.25 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f10])).
% 1.48/1.25 thf(f10,plain,(
% 1.48/1.25 ? [X0 : $i,X1 : $i] : (((leibeq @ X0 @ X1) != $true) & ((leibeq @ X1 @ X0) = $true)) => (($true != (leibeq @ sK0 @ sK1)) & ((leibeq @ sK1 @ sK0) = $true))),
% 1.48/1.25 introduced(definition,[],[choice_axiom])).
% 1.48/1.25 thf(f9,plain,(
% 1.48/1.25 ? [X0 : $i,X1 : $i] : (((leibeq @ X0 @ X1) != $true) & ((leibeq @ X1 @ X0) = $true))),
% 1.48/1.25 inference(ennf_transformation,[status(thm)],[f6])).
% 1.48/1.25 thf(f6,plain,(
% 1.48/1.25 ~! [X0 : $i,X1 : $i] : (((leibeq @ X1 @ X0) = $true) => ((leibeq @ X0 @ X1) = $true))),
% 1.48/1.25 inference(fool_elimination,[status(thm)],[f5])).
% 1.48/1.25 thf(f5,plain,(
% 1.48/1.25 ~! [X0 : $i,X1 : $i] : ((leibeq @ X1 @ X0) => (leibeq @ X0 @ X1))),
% 1.48/1.25 inference(rectify,[status(thm)],[f3])).
% 1.48/1.25 thf(f3,negated_conjecture,(
% 1.48/1.25 ~! [X1 : $i,X0 : $i] : ((leibeq @ X0 @ X1) => (leibeq @ X1 @ X0))),
% 1.48/1.25 inference(negated_conjecture,[status(cth)],[f2])).
% 1.48/1.25 thf(f2,conjecture,(
% 1.48/1.25 ! [X1 : $i,X0 : $i] : ((leibeq @ X0 @ X1) => (leibeq @ X1 @ X0))),
% 1.48/1.25 file('/export/starexec/sandbox/tmp/tmp.tDlPxvbSWo/DTF2THF_12017.p',conj)).
% 1.48/1.25 thf(f21,plain,(
% 1.48/1.25 ((sK3 @ sK1) = $false)),
% 1.48/1.25 inference(binary_proxy_clausification,[status(thm)],[f20])).
% 1.48/1.25 thf(f20,plain,(
% 1.48/1.25 ($false = ((sK3 @ sK0) => (sK3 @ sK1)))),
% 1.48/1.25 inference(beta_eta_normalization,[status(thm)],[f19])).
% 1.48/1.25 thf(f19,plain,(
% 1.48/1.25 (((^[Y0 : $i > $o]: ((Y0 @ sK0) => (Y0 @ sK1))) @ sK3) = $false)),
% 1.48/1.25 inference(sigma_clausification,[status(thm)],[f18])).
% 1.48/1.25 thf(f18,plain,(
% 1.48/1.25 ($true != (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((Y0 @ sK0) => (Y0 @ sK1)))))),
% 1.48/1.25 inference(beta_eta_normalization,[status(thm)],[f15])).
% 1.48/1.25 thf(f15,plain,(
% 1.48/1.25 ($true != ((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))) @ sK0 @ sK1))),
% 1.48/1.25 inference(definition_unfolding,[status(thm)],[f14,f12])).
% 1.48/1.25 thf(f14,plain,(
% 1.48/1.25 ($true != (leibeq @ sK0 @ sK1))),
% 1.48/1.25 inference(cnf_transformation,[status(thm)],[f11])).
% 1.48/1.25 thf(f22,plain,(
% 1.48/1.25 ((sK3 @ sK0) = $true)),
% 1.48/1.25 inference(binary_proxy_clausification,[status(thm)],[f20])).
% 1.48/1.25 % SZS output end Proof for DTF2THF_12017
% 1.48/1.25 % (12133)------------------------------
% 1.48/1.25 % (12133)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.25 % (12133)Termination reason: Refutation
% 1.48/1.25
% 1.48/1.25 % (12133)Memory used [KB]: 5500
% 1.48/1.25 % (12133)Time elapsed: 0.005 s
% 1.48/1.25 % (12133)Instructions burned: 2 (million)
% 1.48/1.25 % (12133)------------------------------
% 1.48/1.25 % (12133)------------------------------
% 1.48/1.25 % (12131)Success in time 0.01 s
%------------------------------------------------------------------------------