%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO001^1 : 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 09:53:06 AM UTC 2026
% Result : Theorem 1.65s 1.41s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of formulae : 37 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 203 ( 50 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 185 ( 11 ~; 4 |; 14 &; 127 @)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 7 usr; 6 con; 0-2 aty)
% ( 8 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 54 ( 25 ^; 20 !; 9 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
leibeq: $i > $i > $o ).
thf(func_def_2,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_15,type,
sK4: $i > $o ).
thf(func_def_16,type,
ph5:
!>[X0: $tType] : X0 ).
thf(f42,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f41]) ).
thf(f41,plain,
$false = $true,
inference(backward_demodulation,[status(thm)],[f32,f39]) ).
thf(f39,plain,
( $false
= ( sK4 @ sK0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f38]) ).
thf(f38,plain,
( ( $false = $true )
| ( $false
= ( sK4 @ sK0 ) ) ),
inference(superposition,[status(thm)],[f35,f27]) ).
thf(f27,plain,
! [X1: $i > $o] :
( ( $true
= ( X1 @ sK2 ) )
| ( $false
= ( X1 @ sK0 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
! [X1: $i > $o] :
( ( ( X1 @ sK0 )
=> ( X1 @ sK2 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f25]) ).
thf(f25,plain,
! [X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( ( Y0 @ sK0 )
=> ( Y0 @ sK2 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0 @ sK0 )
=> ( Y0 @ sK2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f17]) ).
thf(f17,plain,
( $true
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) )
@ sK0
@ sK2 ) ),
inference(definition_unfolding,[status(thm)],[f15,f16]) ).
thf(f16,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/sandbox2/tmp/tmp.yWYoV4vXaL/DTF2THF_10602.p',leibeq) ).
thf(f15,plain,
( $true
= ( leibeq @ sK0 @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( $true
= ( leibeq @ sK0 @ sK2 ) )
& ( ( leibeq @ sK0 @ sK1 )
!= $true )
& ( $true
= ( leibeq @ sK2 @ sK1 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f10,f11]) ).
thf(f11,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( leibeq @ X0 @ X2 ) )
& ( ( leibeq @ X0 @ X1 )
!= $true )
& ( $true
= ( leibeq @ X2 @ X1 ) ) )
=> ( ( $true
= ( leibeq @ sK0 @ sK2 ) )
& ( ( leibeq @ sK0 @ sK1 )
!= $true )
& ( $true
= ( leibeq @ sK2 @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( leibeq @ X0 @ X2 ) )
& ( ( leibeq @ X0 @ X1 )
!= $true )
& ( $true
= ( leibeq @ X2 @ X1 ) ) ),
inference(flattening,[status(thm)],[f9]) ).
thf(f9,plain,
? [X0: $i,X1: $i,X2: $i] :
( ( ( leibeq @ X0 @ X1 )
!= $true )
& ( $true
= ( leibeq @ X2 @ X1 ) )
& ( $true
= ( leibeq @ X0 @ X2 ) ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ! [X0: $i,X1: $i,X2: $i] :
( ( ( $true
= ( leibeq @ X2 @ X1 ) )
& ( $true
= ( leibeq @ X0 @ X2 ) ) )
=> ( ( leibeq @ X0 @ X1 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ! [X0: $i,X1: $i,X2: $i] :
( ( ( leibeq @ X2 @ X1 )
& ( leibeq @ X0 @ X2 ) )
=> ( leibeq @ X0 @ X1 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ! [X0: $i,X3: $i,X1: $i] :
( ( ( leibeq @ X1 @ X3 )
& ( leibeq @ X0 @ X1 ) )
=> ( leibeq @ X0 @ X3 ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
! [X0: $i,X3: $i,X1: $i] :
( ( ( leibeq @ X1 @ X3 )
& ( leibeq @ X0 @ X1 ) )
=> ( leibeq @ X0 @ X3 ) ),
file('/export/starexec/sandbox2/tmp/tmp.yWYoV4vXaL/DTF2THF_10602.p',conj) ).
thf(f35,plain,
( $false
= ( sK4 @ sK2 ) ),
inference(trivial_inequality_removal,[status(thm)],[f34]) ).
thf(f34,plain,
( ( $false = $true )
| ( $false
= ( sK4 @ sK2 ) ) ),
inference(superposition,[status(thm)],[f31,f23]) ).
thf(f23,plain,
! [X1: $i > $o] :
( ( $true
= ( X1 @ sK1 ) )
| ( $false
= ( X1 @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
! [X1: $i > $o] :
( $true
= ( ( X1 @ sK2 )
=> ( X1 @ sK1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f21]) ).
thf(f21,plain,
! [X1: $i > $o] :
( ( ^ [Y0: $i > $o] :
( ( Y0 @ sK2 )
=> ( Y0 @ sK1 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0 @ sK2 )
=> ( Y0 @ sK1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f19]) ).
thf(f19,plain,
( $true
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) )
@ sK2
@ sK1 ) ),
inference(definition_unfolding,[status(thm)],[f13,f16]) ).
thf(f13,plain,
( $true
= ( leibeq @ sK2 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f31,plain,
( $false
= ( sK4 @ sK1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( $false
= ( ( sK4 @ sK0 )
=> ( sK4 @ sK1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f29]) ).
thf(f29,plain,
( $false
= ( ^ [Y0: $i > $o] :
( ( Y0 @ sK0 )
=> ( Y0 @ sK1 ) )
@ sK4 ) ),
inference(sigma_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( $true
!= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0 @ sK0 )
=> ( Y0 @ sK1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f18]) ).
thf(f18,plain,
( $true
!= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) )
@ sK0
@ sK1 ) ),
inference(definition_unfolding,[status(thm)],[f14,f16]) ).
thf(f14,plain,
( ( leibeq @ sK0 @ sK1 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f32,plain,
( $true
= ( sK4 @ sK0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO001^1 : 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
% 0.19/0.36 % Computer : n005.cluster.edu
% 0.19/0.36 % Model : x86_64 x86_64
% 0.19/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.36 % Memory : 8042.1875MB
% 0.19/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.36 % CPULimit : 300
% 0.19/0.36 % WCLimit : 300
% 0.19/0.36 % DateTime : Tue Feb 24 14:21:45 EST 2026
% 0.19/0.37 % CPUTime :
% 0.19/0.37 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.47 ---- Original DTF file ---
% 0.30/0.47 thf(spec,logic,$$dhol).
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 % File : SYO001^1 : TPTP v9.2.1. Released v3.7.0.
% 0.30/0.47 % Domain : Syntactic
% 0.30/0.47 % Problem : Leibniz equality is transitive
% 0.30/0.47 % Version : Especial.
% 0.30/0.47 % English :
% 0.30/0.47
% 0.30/0.47 % Refs : [BB05] Benzmueller & Brown (2005), A Structured Set of Higher
% 0.30/0.47 % : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% 0.30/0.47 % Source : [Ben09]
% 0.30/0.47 % Names : Example 6c [BB05]
% 0.30/0.47
% 0.30/0.47 % Status : Theorem
% 0.30/0.47 % Rating : 0.00 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 0.00 v6.2.0, 0.14 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
% 0.30/0.47 % Syntax : Number of formulae : 3 ( 1 unt; 1 typ; 1 def)
% 0.30/0.47 % Number of atoms : 5 ( 1 equ; 0 cnn)
% 0.30/0.47 % Maximal formula atoms : 3 ( 2 avg)
% 0.30/0.47 % Number of connectives : 11 ( 0 ~; 0 |; 1 &; 8 @)
% 0.30/0.47 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.30/0.47 % Maximal formula depth : 8 ( 5 avg)
% 0.30/0.47 % Number of types : 2 ( 0 usr)
% 0.30/0.47 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.30/0.47 % Number of symbols : 2 ( 1 usr; 0 con; 2-2 aty)
% 0.30/0.47 % Number of variables : 6 ( 2 ^; 4 !; 0 ?; 6 :)
% 0.30/0.47 % SPC : TH0_THM_EQU_NAR
% 0.30/0.47
% 0.30/0.47 % Comments :
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 thf(leibeq_decl,type,
% 0.30/0.47 leibeq: $i > $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(leibeq,definition,
% 0.30/0.47 ( leibeq
% 0.30/0.47 = ( ^ [X: $i,Y: $i] :
% 0.30/0.47 ! [P: $i > $o] :
% 0.30/0.47 ( ( P @ X )
% 0.30/0.47 => ( P @ Y ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(conj,conjecture,
% 0.30/0.47 ! [X: $i,Y: $i,Z: $i] :
% 0.30/0.47 ( ( ( leibeq @ X @ Y )
% 0.30/0.47 & ( leibeq @ Y @ Z ) )
% 0.30/0.47 => ( leibeq @ X @ Z ) ) ).
% 0.30/0.47
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 ------------------------
% 1.46/1.38 ---- Embedded in THF ---
% 1.46/1.38 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.38 %%% Generated on Tue Feb 24 14:21:45 EST 2026
% 1.46/1.38 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.38 %%% Logic specification used:
% 1.46/1.38 %%% thf(spec, logic, $$dhol).
% 1.46/1.38
% 1.46/1.38 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.yWYoV4vXaL/DTF2DTF10602.p
% See solution above
% 1.46/1.38 ------------------------
% 1.46/1.39 ---- Cleaned THF ---
% 1.46/1.39 thf(leibeq_decl,type,
% 1.46/1.39 leibeq: $i > $i > $o ).
% 1.46/1.39
% 1.46/1.39 thf(leibeq,definition,
% 1.46/1.39 ( leibeq
% 1.46/1.39 = ( ^ [X: $i,Y: $i] :
% 1.46/1.39 ! [P: $i > $o] :
% 1.46/1.39 ( ( P @ X )
% 1.46/1.39 => ( P @ Y ) ) ) ) ).
% 1.46/1.39
% 1.46/1.39 thf(conj,conjecture,
% 1.46/1.39 ! [X: $i,Y: $i,Z: $i] :
% 1.46/1.39 ( ( ( leibeq @ X @ Y )
% 1.46/1.39 & ( leibeq @ Y @ Z ) )
% 1.46/1.39 => ( leibeq @ X @ Z ) ) ).
% 1.46/1.39 ------------------------
% 1.65/1.41 % (10699)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10602 for (2999ds/183Mi)
% 1.65/1.41 % (10704)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_10602 for (2999ds/275Mi)
% 1.65/1.41 % (10701)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_10602 for (2999ds/27Mi)
% 1.65/1.41 % (10705)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_10602 for (2999ds/18Mi)
% 1.65/1.41 % (10702)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_10602 for (2999ds/2Mi)
% 1.65/1.41 % (10703)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_10602 for (2999ds/2Mi)
% 1.65/1.41 % (10700)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_10602 for (2999ds/4Mi)
% 1.65/1.41 % (10702)Instruction limit reached!
% 1.65/1.41 % (10702)------------------------------
% 1.65/1.41 % (10702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.41 % (10702)Termination reason: Unknown
% 1.65/1.41 % (10702)Termination phase: Saturation
% 1.65/1.41 % (10703)Instruction limit reached!
% 1.65/1.41 % (10703)------------------------------
% 1.65/1.41 % (10703)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.41
% 1.65/1.41 % (10702)Memory used [KB]: 5373
% 1.65/1.41 % (10702)Time elapsed: 0.003 s
% 1.65/1.41 % (10702)Instructions burned: 2 (million)
% 1.65/1.41 % (10702)------------------------------
% 1.65/1.41 % (10702)------------------------------
% 1.65/1.41 % (10703)Termination reason: Unknown
% 1.65/1.41 % (10703)Termination phase: Saturation
% 1.65/1.41
% 1.65/1.41 % (10703)Memory used [KB]: 895
% 1.65/1.41 % (10703)Time elapsed: 0.003 s
% 1.65/1.41 % (10703)Instructions burned: 2 (million)
% 1.65/1.41 % (10703)------------------------------
% 1.65/1.41 % (10703)------------------------------
% 1.65/1.41 % (10704)Refutation not found, incomplete strategy
% 1.65/1.41 % (10704)------------------------------
% 1.65/1.41 % (10704)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.41 % (10704)Termination reason: Refutation not found, incomplete strategy
% 1.65/1.41
% 1.65/1.41
% 1.65/1.41 % (10704)Memory used [KB]: 5500
% 1.65/1.41 % (10704)Time elapsed: 0.003 s
% 1.65/1.41 % (10704)Instructions burned: 2 (million)
% 1.65/1.41 % (10704)------------------------------
% 1.65/1.41 % (10704)------------------------------
% 1.65/1.41 % (10701)First to succeed.
% 1.65/1.41 % (10700)Instruction limit reached!
% 1.65/1.41 % (10700)------------------------------
% 1.65/1.41 % (10700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.41 % (10700)Termination reason: Unknown
% 1.65/1.41 % (10700)Termination phase: Saturation
% 1.65/1.41
% 1.65/1.41 % (10700)Memory used [KB]: 5500
% 1.65/1.41 % (10700)Time elapsed: 0.004 s
% 1.65/1.41 % (10700)Instructions burned: 4 (million)
% 1.65/1.41 % (10700)------------------------------
% 1.65/1.41 % (10700)------------------------------
% 1.65/1.41 % (10705)Also succeeded, but the first one will report.
% 1.65/1.41 % (10701)Refutation found. Thanks to Tanya!
% 1.65/1.41 % SZS status Theorem for DTF2THF_10602
% 1.65/1.41 % SZS output start Proof for DTF2THF_10602
% 1.65/1.41 thf(func_def_0, type, leibeq: $i > $i > $o).
% 1.65/1.41 thf(func_def_2, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.65/1.41 thf(func_def_15, type, sK4: $i > $o).
% 1.65/1.41 thf(func_def_16, type, ph5: !>[X0: $tType]:(X0)).
% 1.65/1.41 thf(f42,plain,(
% 1.65/1.41 $false),
% 1.65/1.41 inference(trivial_inequality_removal,[status(thm)],[f41])).
% 1.65/1.41 thf(f41,plain,(
% 1.65/1.41 ($false = $true)),
% 1.65/1.41 inference(backward_demodulation,[status(thm)],[f32,f39])).
% 1.65/1.41 thf(f39,plain,(
% 1.65/1.41 ($false = (sK4 @ sK0))),
% 1.65/1.41 inference(trivial_inequality_removal,[status(thm)],[f38])).
% 1.65/1.41 thf(f38,plain,(
% 1.65/1.41 ($false = $true) | ($false = (sK4 @ sK0))),
% 1.65/1.41 inference(superposition,[status(thm)],[f35,f27])).
% 1.65/1.41 thf(f27,plain,(
% 1.65/1.41 ( ! [X1 : $i > $o] : (($true = (X1 @ sK2)) | ($false = (X1 @ sK0))) )),
% 1.65/1.41 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 1.65/1.41 thf(f26,plain,(
% 1.65/1.41 ( ! [X1 : $i > $o] : ((((X1 @ sK0) => (X1 @ sK2)) = $true)) )),
% 1.65/1.41 inference(beta_eta_normalization,[status(thm)],[f25])).
% 1.65/1.41 thf(f25,plain,(
% 1.65/1.41 ( ! [X1 : $i > $o] : (($true = ((^[Y0 : $i > $o]: ((Y0 @ sK0) => (Y0 @ sK2))) @ X1))) )),
% 1.65/1.41 inference(pi_clausification,[status(thm)],[f24])).
% 1.65/1.41 thf(f24,plain,(
% 1.65/1.41 ($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((Y0 @ sK0) => (Y0 @ sK2)))))),
% 1.65/1.41 inference(beta_eta_normalization,[status(thm)],[f17])).
% 1.65/1.41 thf(f17,plain,(
% 1.65/1.41 ($true = ((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))) @ sK0 @ sK2))),
% 1.65/1.41 inference(definition_unfolding,[status(thm)],[f15,f16])).
% 1.65/1.41 thf(f16,plain,(
% 1.65/1.41 (leibeq = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 1.65/1.41 inference(cnf_transformation,[status(thm)],[f6])).
% 1.65/1.41 thf(f6,plain,(
% 1.65/1.41 (leibeq = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 1.65/1.41 inference(fool_elimination,[status(thm)],[f5])).
% 1.65/1.41 thf(f5,plain,(
% 1.65/1.41 ((^[X0 : $i, X1 : $i] : (! [X2 : $i > $o] : ((X2 @ X0) => (X2 @ X1)))) = leibeq)),
% 1.65/1.41 inference(rectify,[status(thm)],[f1])).
% 1.65/1.41 thf(f1,axiom,(
% 1.65/1.41 ((^[X0 : $i, X1 : $i] : (! [X2 : $i > $o] : ((X2 @ X0) => (X2 @ X1)))) = leibeq)),
% 1.65/1.41 file('/export/starexec/sandbox2/tmp/tmp.yWYoV4vXaL/DTF2THF_10602.p',leibeq)).
% 1.65/1.41 thf(f15,plain,(
% 1.65/1.41 ($true = (leibeq @ sK0 @ sK2))),
% 1.65/1.41 inference(cnf_transformation,[status(thm)],[f12])).
% 1.65/1.41 thf(f12,plain,(
% 1.65/1.41 ($true = (leibeq @ sK0 @ sK2)) & ((leibeq @ sK0 @ sK1) != $true) & ($true = (leibeq @ sK2 @ sK1))),
% 1.65/1.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f10,f11])).
% 1.65/1.41 thf(f11,plain,(
% 1.65/1.41 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (leibeq @ X0 @ X2)) & ((leibeq @ X0 @ X1) != $true) & ($true = (leibeq @ X2 @ X1))) => (($true = (leibeq @ sK0 @ sK2)) & ((leibeq @ sK0 @ sK1) != $true) & ($true = (leibeq @ sK2 @ sK1)))),
% 1.65/1.41 introduced(definition,[],[choice_axiom])).
% 1.65/1.41 thf(f10,plain,(
% 1.65/1.41 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (leibeq @ X0 @ X2)) & ((leibeq @ X0 @ X1) != $true) & ($true = (leibeq @ X2 @ X1)))),
% 1.65/1.41 inference(flattening,[status(thm)],[f9])).
% 1.65/1.41 thf(f9,plain,(
% 1.65/1.41 ? [X0 : $i,X1 : $i,X2 : $i] : (((leibeq @ X0 @ X1) != $true) & (($true = (leibeq @ X2 @ X1)) & ($true = (leibeq @ X0 @ X2))))),
% 1.65/1.41 inference(ennf_transformation,[status(thm)],[f8])).
% 1.65/1.41 thf(f8,plain,(
% 1.65/1.41 ~! [X0 : $i,X1 : $i,X2 : $i] : ((($true = (leibeq @ X2 @ X1)) & ($true = (leibeq @ X0 @ X2))) => ((leibeq @ X0 @ X1) = $true))),
% 1.65/1.41 inference(fool_elimination,[status(thm)],[f7])).
% 1.65/1.41 thf(f7,plain,(
% 1.65/1.41 ~! [X0 : $i,X1 : $i,X2 : $i] : (((leibeq @ X2 @ X1) & (leibeq @ X0 @ X2)) => (leibeq @ X0 @ X1))),
% 1.65/1.41 inference(rectify,[status(thm)],[f3])).
% 1.65/1.41 thf(f3,negated_conjecture,(
% 1.65/1.41 ~! [X0 : $i,X3 : $i,X1 : $i] : (((leibeq @ X1 @ X3) & (leibeq @ X0 @ X1)) => (leibeq @ X0 @ X3))),
% 1.65/1.41 inference(negated_conjecture,[status(cth)],[f2])).
% 1.65/1.41 thf(f2,conjecture,(
% 1.65/1.41 ! [X0 : $i,X3 : $i,X1 : $i] : (((leibeq @ X1 @ X3) & (leibeq @ X0 @ X1)) => (leibeq @ X0 @ X3))),
% 1.65/1.41 file('/export/starexec/sandbox2/tmp/tmp.yWYoV4vXaL/DTF2THF_10602.p',conj)).
% 1.65/1.41 thf(f35,plain,(
% 1.65/1.41 ($false = (sK4 @ sK2))),
% 1.65/1.41 inference(trivial_inequality_removal,[status(thm)],[f34])).
% 1.65/1.41 thf(f34,plain,(
% 1.65/1.41 ($false = $true) | ($false = (sK4 @ sK2))),
% 1.65/1.41 inference(superposition,[status(thm)],[f31,f23])).
% 1.65/1.41 thf(f23,plain,(
% 1.65/1.41 ( ! [X1 : $i > $o] : (($true = (X1 @ sK1)) | ($false = (X1 @ sK2))) )),
% 1.65/1.41 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 1.65/1.41 thf(f22,plain,(
% 1.65/1.41 ( ! [X1 : $i > $o] : (($true = ((X1 @ sK2) => (X1 @ sK1)))) )),
% 1.65/1.41 inference(beta_eta_normalization,[status(thm)],[f21])).
% 1.65/1.41 thf(f21,plain,(
% 1.65/1.41 ( ! [X1 : $i > $o] : ((((^[Y0 : $i > $o]: ((Y0 @ sK2) => (Y0 @ sK1))) @ X1) = $true)) )),
% 1.65/1.41 inference(pi_clausification,[status(thm)],[f20])).
% 1.65/1.41 thf(f20,plain,(
% 1.65/1.41 ($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((Y0 @ sK2) => (Y0 @ sK1)))))),
% 1.65/1.41 inference(beta_eta_normalization,[status(thm)],[f19])).
% 1.65/1.41 thf(f19,plain,(
% 1.65/1.41 ($true = ((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))) @ sK2 @ sK1))),
% 1.65/1.41 inference(definition_unfolding,[status(thm)],[f13,f16])).
% 1.65/1.41 thf(f13,plain,(
% 1.65/1.41 ($true = (leibeq @ sK2 @ sK1))),
% 1.65/1.41 inference(cnf_transformation,[status(thm)],[f12])).
% 1.65/1.41 thf(f31,plain,(
% 1.65/1.41 ($false = (sK4 @ sK1))),
% 1.65/1.41 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.65/1.41 thf(f30,plain,(
% 1.65/1.41 ($false = ((sK4 @ sK0) => (sK4 @ sK1)))),
% 1.65/1.41 inference(beta_eta_normalization,[status(thm)],[f29])).
% 1.65/1.41 thf(f29,plain,(
% 1.65/1.41 ($false = ((^[Y0 : $i > $o]: ((Y0 @ sK0) => (Y0 @ sK1))) @ sK4))),
% 1.65/1.41 inference(sigma_clausification,[status(thm)],[f28])).
% 1.65/1.41 thf(f28,plain,(
% 1.65/1.41 ($true != (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((Y0 @ sK0) => (Y0 @ sK1)))))),
% 1.65/1.41 inference(beta_eta_normalization,[status(thm)],[f18])).
% 1.65/1.41 thf(f18,plain,(
% 1.65/1.41 ($true != ((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))) @ sK0 @ sK1))),
% 1.65/1.41 inference(definition_unfolding,[status(thm)],[f14,f16])).
% 1.65/1.41 thf(f14,plain,(
% 1.65/1.41 ((leibeq @ sK0 @ sK1) != $true)),
% 1.65/1.41 inference(cnf_transformation,[status(thm)],[f12])).
% 1.65/1.41 thf(f32,plain,(
% 1.65/1.41 ($true = (sK4 @ sK0))),
% 1.65/1.41 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.65/1.41 % SZS output end Proof for DTF2THF_10602
% 1.65/1.41 % (10701)------------------------------
% 1.65/1.41 % (10701)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.41 % (10701)Termination reason: Refutation
% 1.65/1.41
% 1.65/1.41 % (10701)Memory used [KB]: 5500
% 1.65/1.41 % (10701)Time elapsed: 0.005 s
% 1.65/1.41 % (10701)Instructions burned: 3 (million)
% 1.65/1.41 % (10701)------------------------------
% 1.65/1.41 % (10701)------------------------------
% 1.65/1.41 % (10698)Success in time 0.019 s
%------------------------------------------------------------------------------