%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO024^1 : 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 : n007.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 09:53:10 AM UTC 2026
% Result : Theorem 1.51s 1.39s
% Output : Refutation 1.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 6
% Syntax : Number of formulae : 58 ( 23 unt; 0 typ; 4 def)
% Number of atoms : 270 ( 71 equ; 15 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 245 ( 98 ~; 61 |; 25 &; 45 @)
% ( 4 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 53 ( 53 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 9 usr; 10 con; 0-2 aty)
% ( 4 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 47 ( 45 ^; 2 !; 0 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
leibeq: ( $o > $o > $o ) > ( $o > $o > $o ) > $o ).
thf(func_def_14,type,
sK1: ( $o > $o > $o ) > $o ).
thf(func_def_15,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f80,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f55,f56,f66,f72,f79]) ).
thf(f79,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f78]) ).
thf(f78,plain,
( $false
| ~ spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f74]) ).
thf(f74,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f53,f61]) ).
thf(f61,plain,
( ( sK3 = $false )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f59]) ).
thf(f59,definition,
( spl0_3
<=> ( sK3 = $false ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f53,plain,
( ( sK3 = $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f51]) ).
thf(f51,definition,
( spl0_2
<=> ( sK3 = $true ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f72,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f71]) ).
thf(f71,plain,
( $false
| ~ spl0_1
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f67]) ).
thf(f67,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f49,f65]) ).
thf(f65,plain,
( ( $false = sK4 )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f63]) ).
thf(f63,definition,
( spl0_4
<=> ( $false = sK4 ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f49,plain,
( ( $true = sK4 )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f47]) ).
thf(f47,definition,
( spl0_1
<=> ( $true = sK4 ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f66,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f34,f63,f59]) ).
thf(f34,plain,
( ( sK3 = $false )
| ( $false = sK4 ) ),
inference(duplicate_literal_removal,[status(thm)],[f33]) ).
thf(f33,plain,
( ( sK3 = $false )
| ( $false = sK4 )
| ( $false = sK4 ) ),
inference(not_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
( ( $false = sK4 )
| ( sK3 = $false )
| ( $true = ( ~ sK4 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f31]) ).
thf(f31,plain,
( ( $false = sK4 )
| ( sK3 = $false )
| ( sK3 = $false )
| ( $true = ( ~ sK4 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( ( sK3 = $false )
| ( $false = sK4 )
| ( $true = ( ~ sK3 ) )
| ( $true = ( ~ sK4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
( ( sK3 = $false )
| ( $true
= ( ~ sK4
| ~ sK3 ) )
| ( $false = sK4 ) ),
inference(binary_proxy_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( ( $false
= ( sK3
& sK4 ) )
| ( $true
= ( ~ sK4
| ~ sK3 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( ( $false
= ( ~ ( ~ sK4
| ~ sK3 ) ) )
| ( $false
= ( sK3
& sK4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( ( sK3
& sK4 )
!= ( ~ ( ~ sK4
| ~ sK3 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ^ [Y0: $o] :
~ ( ~ Y0
| ~ sK3 )
@ sK4 )
!= ( sK3
& sK4 ) ),
inference(negative_extensionality,[status(thm)],[f23]) ).
thf(f23,plain,
( ( (&) @ sK3 )
!= ( ^ [Y0: $o] :
~ ( ~ Y0
| ~ sK3 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f22]) ).
thf(f22,plain,
( ( (&) @ sK3 )
!= ( ^ [Y0: $o,Y1: $o] :
~ ( ~ Y1
| ~ Y0 )
@ sK3 ) ),
inference(negative_extensionality,[status(thm)],[f21]) ).
thf(f21,plain,
( (&)
!= ( ^ [Y0: $o,Y1: $o] :
~ ( ~ Y1
| ~ Y0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f18]) ).
thf(f18,plain,
( ( $true = $false )
| ( (&)
!= ( ^ [Y0: $o,Y1: $o] :
~ ( ~ Y1
| ~ Y0 ) ) ) ),
inference(constrained_superposition,[status(thm)],[f16,f17]) ).
thf(f17,plain,
( $true
= ( sK1 @ (&) ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( $false
= ( ( sK1 @ (&) )
=> ( sK1
@ ^ [Y0: $o,Y1: $o] :
~ ( ~ Y1
| ~ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
( $false
= ( ^ [Y0: ( $o > $o > $o ) > $o] :
( ( Y0 @ (&) )
=> ( Y0
@ ^ [Y1: $o,Y2: $o] :
~ ( ~ Y2
| ~ Y1 ) ) )
@ sK1 ) ),
inference(sigma_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( $true
!= ( !! @ ( ( $o > $o > $o ) > $o )
@ ^ [Y0: ( $o > $o > $o ) > $o] :
( ( Y0 @ (&) )
=> ( Y0
@ ^ [Y1: $o,Y2: $o] :
~ ( ~ Y2
| ~ Y1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
( $true
!= ( ^ [Y0: $o > $o > $o,Y1: $o > $o > $o] :
( !! @ ( ( $o > $o > $o ) > $o )
@ ^ [Y2: ( $o > $o > $o ) > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) )
@ (&)
@ ^ [Y0: $o,Y1: $o] :
~ ( ~ Y1
| ~ Y0 ) ) ),
inference(definition_unfolding,[status(thm)],[f10,f11]) ).
thf(f11,plain,
( leibeq
= ( ^ [Y0: $o > $o > $o,Y1: $o > $o > $o] :
( !! @ ( ( $o > $o > $o ) > $o )
@ ^ [Y2: ( $o > $o > $o ) > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( leibeq
= ( ^ [Y0: $o > $o > $o,Y1: $o > $o > $o] :
( !! @ ( ( $o > $o > $o ) > $o )
@ ^ [Y2: ( $o > $o > $o ) > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( leibeq
= ( ^ [X0: $o > $o > $o,X1: $o > $o > $o] :
! [X2: ( $o > $o > $o ) > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( leibeq
= ( ^ [X0: $o > $o > $o,X1: $o > $o > $o] :
! [X2: ( $o > $o > $o ) > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.oXfmwGv9ye/DTF2THF_31003.p',leibeq) ).
thf(f10,plain,
( $true
!= ( leibeq @ (&)
@ ^ [Y0: $o,Y1: $o] :
~ ( ~ Y1
| ~ Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( $true
!= ( leibeq @ (&)
@ ^ [Y0: $o,Y1: $o] :
~ ( ~ Y1
| ~ Y0 ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( $true
!= ( leibeq @ (&)
@ ^ [Y0: $o,Y1: $o] :
~ ( ~ Y1
| ~ Y0 ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( leibeq @ (&)
@ ^ [X0: $o,X1: $o] :
~ ( ~ X0
| ~ X1 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ( leibeq @ (&)
@ ^ [X0: $o,X1: $o] :
~ ( ~ X0
| ~ X1 ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( leibeq @ (&)
@ ^ [X0: $o,X1: $o] :
~ ( ~ X0
| ~ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.oXfmwGv9ye/DTF2THF_31003.p',conj) ).
thf(f16,plain,
( $false
= ( sK1
@ ^ [Y0: $o,Y1: $o] :
~ ( ~ Y1
| ~ Y0 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f56,plain,
spl0_1,
inference(avatar_split_clause,[status(thm)],[f41,f47]) ).
thf(f41,plain,
$true = sK4,
inference(duplicate_literal_removal,[status(thm)],[f39]) ).
thf(f39,plain,
( ( $true = sK4 )
| ( $true = sK4 ) ),
inference(binary_proxy_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
( ( $true
= ( sK3
& sK4 ) )
| ( $true = sK4 ) ),
inference(not_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
( ( $false = ( ~ sK4 ) )
| ( $true
= ( sK3
& sK4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
( ( $false
= ( ~ sK4
| ~ sK3 ) )
| ( $true
= ( sK3
& sK4 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
( ( $true
= ( ~ ( ~ sK4
| ~ sK3 ) ) )
| ( $true
= ( sK3
& sK4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f55,plain,
spl0_2,
inference(avatar_split_clause,[status(thm)],[f45,f51]) ).
thf(f45,plain,
sK3 = $true,
inference(duplicate_literal_removal,[status(thm)],[f44]) ).
thf(f44,plain,
( ( sK3 = $true )
| ( sK3 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
( ( sK3 = $true )
| ( $true
= ( sK3
& sK4 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
( ( $false = ( ~ sK3 ) )
| ( $true
= ( sK3
& sK4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYO024^1 : 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
% 0.11/0.30 % Computer : n007.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Tue Feb 24 14:20:53 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
% 0.18/0.40 ---- Original DTF file ---
% 0.18/0.40 thf(spec,logic,$$dhol).
% 0.18/0.40 %------------------------------------------------------------------------------
% 0.18/0.40 % File : SYO024^1 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.40 % Domain : Syntactic
% 0.18/0.40 % Problem : De Morgan by connectives and Leibnitz
% 0.18/0.40 % Version : Especial.
% 0.18/0.40 % English :
% 0.18/0.40
% 0.18/0.40 % Refs : [BB05] Benzmueller & Brown (2005), A Structured Set of Higher
% 0.18/0.40 % : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% 0.18/0.40 % Source : [Ben09]
% 0.18/0.40 % Names : Example 20d [BB05]
% 0.18/0.40
% 0.18/0.40 % Status : Theorem
% 0.18/0.40 % : Without Boolean extensionality : CounterSatisfiable
% 0.18/0.40 % : Without functional extensionality : CounterSatisfiable
% 0.18/0.40 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.54 v8.1.0, 0.36 v7.5.0, 0.29 v7.4.0, 0.33 v7.2.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0, 0.33 v3.7.0
% 0.18/0.40 % Syntax : Number of formulae : 3 ( 1 unt; 1 typ; 1 def)
% 0.18/0.40 % Number of atoms : 4 ( 1 equ; 1 cnn)
% 0.18/0.40 % Maximal formula atoms : 2 ( 2 avg)
% 0.18/0.40 % Number of connectives : 10 ( 3 ~; 1 |; 1 &; 4 @)
% 0.18/0.40 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.18/0.40 % Maximal formula depth : 7 ( 4 avg)
% 0.18/0.40 % Number of types : 1 ( 0 usr)
% 0.18/0.40 % Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% 0.18/0.40 % Number of symbols : 3 ( 1 usr; 1 con; 0-2 aty)
% 0.18/0.40 % Number of variables : 5 ( 4 ^; 1 !; 0 ?; 5 :)
% 0.18/0.40 % SPC : TH0_THM_EQU_NAR
% 0.18/0.40
% 0.18/0.40 % Comments :
% 0.18/0.40 %------------------------------------------------------------------------------
% 0.18/0.40 thf(leibeq_decl,type,
% 0.18/0.40 leibeq: ( $o > $o > $o ) > ( $o > $o > $o ) > $o ).
% 0.18/0.40
% 0.18/0.40 thf(leibeq,definition,
% 0.18/0.40 ( leibeq
% 0.18/0.40 = ( ^ [X: $o > $o > $o,Y: $o > $o > $o] :
% 0.18/0.40 ! [P: ( $o > $o > $o ) > $o] :
% 0.18/0.40 ( ( P @ X )
% 0.18/0.40 => ( P @ Y ) ) ) ) ).
% 0.18/0.40
% 0.18/0.40 thf(conj,conjecture,
% 0.18/0.40 ( leibeq @ (&)
% 0.18/0.40 @ ^ [X: $o,Y: $o] :
% 0.18/0.40 ~ ( ~ X
% 0.18/0.40 | ~ Y ) ) ).
% 0.18/0.40
% 0.18/0.40 %------------------------------------------------------------------------------
% 0.18/0.40 ------------------------
% 1.51/1.35 ---- Embedded in THF ---
% 1.51/1.35 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.51/1.35 %%% Generated on Tue Feb 24 14:20:54 EST 2026
% 1.51/1.35 %%% using '$$dhol' embedding, version 1.3.0.
% 1.51/1.35 %%% Logic specification used:
% 1.51/1.35 %%% thf(spec, logic, $$dhol).
% 1.51/1.35
% 1.51/1.35 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.oXfmwGv9ye/DTF2DTF31003.p
% See solution above
% 1.51/1.35 ------------------------
% 1.51/1.36 ---- Cleaned THF ---
% 1.51/1.36 thf(leibeq_decl,type,
% 1.51/1.36 leibeq: ( $o > $o > $o ) > ( $o > $o > $o ) > $o ).
% 1.51/1.36
% 1.51/1.36 thf(leibeq,definition,
% 1.51/1.36 ( leibeq
% 1.51/1.36 = ( ^ [X: $o > $o > $o,Y: $o > $o > $o] :
% 1.51/1.36 ! [P: ( $o > $o > $o ) > $o] :
% 1.51/1.36 ( ( P @ X )
% 1.51/1.36 => ( P @ Y ) ) ) ) ).
% 1.51/1.36
% 1.51/1.36 thf(conj,conjecture,
% 1.51/1.36 ( leibeq @ (&)
% 1.51/1.36 @ ^ [X: $o,Y: $o] :
% 1.51/1.36 ~ ( ~ X
% 1.51/1.36 | ~ Y ) ) ).
% 1.51/1.36 ------------------------
% 1.51/1.38 % (31103)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_31003 for (2999ds/27Mi)
% 1.51/1.38 % (31106)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_31003 for (2999ds/275Mi)
% 1.51/1.38 % (31105)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_31003 for (2999ds/2Mi)
% 1.51/1.38 % (31107)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_31003 for (2999ds/18Mi)
% 1.51/1.38 % (31104)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_31003 for (2999ds/2Mi)
% 1.51/1.38 % (31101)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_31003 for (2999ds/183Mi)
% 1.51/1.39 % (31102)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_31003 for (2999ds/4Mi)
% 1.51/1.39 % (31106)Refutation not found, incomplete strategy
% 1.51/1.39 % (31106)------------------------------
% 1.51/1.39 % (31106)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.39 % (31106)Termination reason: Refutation not found, incomplete strategy
% 1.51/1.39
% 1.51/1.39
% 1.51/1.39 % (31106)Memory used [KB]: 5373
% 1.51/1.39 % (31106)Time elapsed: 0.003 s
% 1.51/1.39 % (31106)Instructions burned: 1 (million)
% 1.51/1.39 % (31106)------------------------------
% 1.51/1.39 % (31106)------------------------------
% 1.51/1.39 % (31104)Instruction limit reached!
% 1.51/1.39 % (31104)------------------------------
% 1.51/1.39 % (31104)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.39 % (31104)Termination reason: Unknown
% 1.51/1.39 % (31104)Termination phase: Saturation
% 1.51/1.39
% 1.51/1.39 % (31105)Instruction limit reached!
% 1.51/1.39 % (31105)------------------------------
% 1.51/1.39 % (31105)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.39 % (31105)Termination reason: Unknown
% 1.51/1.39 % (31105)Termination phase: Saturation
% 1.51/1.39
% 1.51/1.39 % (31105)Memory used [KB]: 5500
% 1.51/1.39 % (31105)Time elapsed: 0.004 s
% 1.51/1.39 % (31105)Instructions burned: 2 (million)
% 1.51/1.39 % (31105)------------------------------
% 1.51/1.39 % (31105)------------------------------
% 1.51/1.39 % (31104)Memory used [KB]: 5500
% 1.51/1.39 % (31104)Time elapsed: 0.003 s
% 1.51/1.39 % (31104)Instructions burned: 2 (million)
% 1.51/1.39 % (31104)------------------------------
% 1.51/1.39 % (31104)------------------------------
% 1.51/1.39 % (31103)Refutation not found, incomplete strategy
% 1.51/1.39 % (31103)------------------------------
% 1.51/1.39 % (31103)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.39 % (31103)Termination reason: Refutation not found, incomplete strategy
% 1.51/1.39
% 1.51/1.39
% 1.51/1.39 % (31103)Memory used [KB]: 5500
% 1.51/1.39 % (31103)Time elapsed: 0.003 s
% 1.51/1.39 % (31103)Instructions burned: 2 (million)
% 1.51/1.39 % (31103)------------------------------
% 1.51/1.39 % (31103)------------------------------
% 1.51/1.39 % (31102)Refutation not found, incomplete strategy
% 1.51/1.39 % (31102)------------------------------
% 1.51/1.39 % (31102)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.39 % (31102)Termination reason: Refutation not found, incomplete strategy
% 1.51/1.39
% 1.51/1.39
% 1.51/1.39 % (31102)Memory used [KB]: 5500
% 1.51/1.39 % (31102)Time elapsed: 0.002 s
% 1.51/1.39 % (31102)Instructions burned: 2 (million)
% 1.51/1.39 % (31102)------------------------------
% 1.51/1.39 % (31102)------------------------------
% 1.51/1.39 % (31101)First to succeed.
% 1.51/1.39 % (31107)Also succeeded, but the first one will report.
% 1.51/1.39 % (31101)Refutation found. Thanks to Tanya!
% 1.51/1.39 % SZS status Theorem for DTF2THF_31003
% 1.51/1.39 % SZS output start Proof for DTF2THF_31003
% 1.51/1.39 thf(func_def_0, type, leibeq: ($o > $o > $o) > ($o > $o > $o) > $o).
% 1.51/1.39 thf(func_def_14, type, sK1: ($o > $o > $o) > $o).
% 1.51/1.39 thf(func_def_15, type, ph2: !>[X0: $tType]:(X0)).
% 1.51/1.39 thf(f80,plain,(
% 1.51/1.39 $false),
% 1.51/1.39 inference(avatar_sat_refutation,[status(thm)],[f55,f56,f66,f72,f79])).
% 1.51/1.39 thf(f79,plain,(
% 1.51/1.39 ~spl0_2 | ~spl0_3),
% 1.51/1.39 inference(avatar_contradiction_clause,[status(thm)],[f78])).
% 1.51/1.39 thf(f78,plain,(
% 1.51/1.39 $false | (~spl0_2 | ~spl0_3)),
% 1.51/1.39 inference(trivial_inequality_removal,[status(thm)],[f74])).
% 1.51/1.39 thf(f74,plain,(
% 1.51/1.39 ($true = $false) | (~spl0_2 | ~spl0_3)),
% 1.51/1.39 inference(superposition,[status(thm)],[f53,f61])).
% 1.51/1.39 thf(f61,plain,(
% 1.51/1.39 (sK3 = $false) | ~spl0_3),
% 1.51/1.39 inference(avatar_component_clause,[status(thm)],[f59])).
% 1.51/1.39 thf(f59,definition,(
% 1.51/1.39 spl0_3 <=> (sK3 = $false)),
% 1.51/1.39 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.51/1.39 thf(f53,plain,(
% 1.51/1.39 (sK3 = $true) | ~spl0_2),
% 1.51/1.39 inference(avatar_component_clause,[status(thm)],[f51])).
% 1.51/1.39 thf(f51,definition,(
% 1.51/1.39 spl0_2 <=> (sK3 = $true)),
% 1.51/1.39 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.51/1.39 thf(f72,plain,(
% 1.51/1.39 ~spl0_1 | ~spl0_4),
% 1.51/1.39 inference(avatar_contradiction_clause,[status(thm)],[f71])).
% 1.51/1.39 thf(f71,plain,(
% 1.51/1.39 $false | (~spl0_1 | ~spl0_4)),
% 1.51/1.39 inference(trivial_inequality_removal,[status(thm)],[f67])).
% 1.51/1.39 thf(f67,plain,(
% 1.51/1.39 ($true = $false) | (~spl0_1 | ~spl0_4)),
% 1.51/1.39 inference(superposition,[status(thm)],[f49,f65])).
% 1.51/1.39 thf(f65,plain,(
% 1.51/1.39 ($false = sK4) | ~spl0_4),
% 1.51/1.39 inference(avatar_component_clause,[status(thm)],[f63])).
% 1.51/1.39 thf(f63,definition,(
% 1.51/1.39 spl0_4 <=> ($false = sK4)),
% 1.51/1.39 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.51/1.39 thf(f49,plain,(
% 1.51/1.39 ($true = sK4) | ~spl0_1),
% 1.51/1.39 inference(avatar_component_clause,[status(thm)],[f47])).
% 1.51/1.39 thf(f47,definition,(
% 1.51/1.39 spl0_1 <=> ($true = sK4)),
% 1.51/1.39 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.51/1.39 thf(f66,plain,(
% 1.51/1.39 spl0_3 | spl0_4),
% 1.51/1.39 inference(avatar_split_clause,[status(thm)],[f34,f63,f59])).
% 1.51/1.39 thf(f34,plain,(
% 1.51/1.39 (sK3 = $false) | ($false = sK4)),
% 1.51/1.39 inference(duplicate_literal_removal,[status(thm)],[f33])).
% 1.51/1.39 thf(f33,plain,(
% 1.51/1.39 (sK3 = $false) | ($false = sK4) | ($false = sK4)),
% 1.51/1.39 inference(not_proxy_clausification,[status(thm)],[f32])).
% 1.51/1.39 thf(f32,plain,(
% 1.51/1.39 ($false = sK4) | (sK3 = $false) | ($true = (~ sK4))),
% 1.51/1.39 inference(duplicate_literal_removal,[status(thm)],[f31])).
% 1.51/1.39 thf(f31,plain,(
% 1.51/1.39 ($false = sK4) | (sK3 = $false) | (sK3 = $false) | ($true = (~ sK4))),
% 1.51/1.39 inference(not_proxy_clausification,[status(thm)],[f30])).
% 1.51/1.39 thf(f30,plain,(
% 1.51/1.39 (sK3 = $false) | ($false = sK4) | ($true = (~ sK3)) | ($true = (~ sK4))),
% 1.51/1.39 inference(binary_proxy_clausification,[status(thm)],[f29])).
% 1.51/1.39 thf(f29,plain,(
% 1.51/1.39 (sK3 = $false) | ($true = ((~ sK4) | (~ sK3))) | ($false = sK4)),
% 1.51/1.39 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 1.51/1.39 thf(f28,plain,(
% 1.51/1.39 ($false = (sK3 & sK4)) | ($true = ((~ sK4) | (~ sK3)))),
% 1.51/1.39 inference(not_proxy_clausification,[status(thm)],[f27])).
% 1.51/1.39 thf(f27,plain,(
% 1.51/1.39 ($false = (~ ((~ sK4) | (~ sK3)))) | ($false = (sK3 & sK4))),
% 1.51/1.39 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.51/1.39 thf(f25,plain,(
% 1.51/1.39 ((sK3 & sK4) != (~ ((~ sK4) | (~ sK3))))),
% 1.51/1.39 inference(beta_eta_normalization,[status(thm)],[f24])).
% 1.51/1.39 thf(f24,plain,(
% 1.51/1.39 (((^[Y0 : $o]: (~ ((~ Y0) | (~ sK3)))) @ sK4) != (sK3 & sK4))),
% 1.51/1.39 inference(negative_extensionality,[status(thm)],[f23])).
% 1.51/1.39 thf(f23,plain,(
% 1.51/1.39 ((& @ sK3) != (^[Y0 : $o]: (~ ((~ Y0) | (~ sK3)))))),
% 1.51/1.39 inference(beta_eta_normalization,[status(thm)],[f22])).
% 1.51/1.39 thf(f22,plain,(
% 1.51/1.39 ((& @ sK3) != ((^[Y0 : $o]: ((^[Y1 : $o]: (~ ((~ Y1) | (~ Y0)))))) @ sK3))),
% 1.51/1.39 inference(negative_extensionality,[status(thm)],[f21])).
% 1.51/1.39 thf(f21,plain,(
% 1.51/1.39 (& != (^[Y0 : $o]: ((^[Y1 : $o]: (~ ((~ Y1) | (~ Y0)))))))),
% 1.51/1.39 inference(trivial_inequality_removal,[status(thm)],[f18])).
% 1.51/1.39 thf(f18,plain,(
% 1.51/1.39 ($true = $false) | (& != (^[Y0 : $o]: ((^[Y1 : $o]: (~ ((~ Y1) | (~ Y0)))))))),
% 1.51/1.39 inference(constrained_superposition,[status(thm)],[f16,f17])).
% 1.51/1.39 thf(f17,plain,(
% 1.51/1.39 ($true = (sK1 @ &))),
% 1.51/1.39 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.51/1.39 thf(f15,plain,(
% 1.51/1.39 ($false = ((sK1 @ &) => (sK1 @ (^[Y0 : $o]: ((^[Y1 : $o]: (~ ((~ Y1) | (~ Y0)))))))))),
% 1.51/1.39 inference(beta_eta_normalization,[status(thm)],[f14])).
% 1.51/1.39 thf(f14,plain,(
% 1.51/1.39 ($false = ((^[Y0 : ($o > $o > $o) > $o]: ((Y0 @ &) => (Y0 @ (^[Y1 : $o]: ((^[Y2 : $o]: (~ ((~ Y2) | (~ Y1))))))))) @ sK1))),
% 1.51/1.39 inference(sigma_clausification,[status(thm)],[f13])).
% 1.51/1.39 thf(f13,plain,(
% 1.51/1.39 ($true != (!! @ (($o > $o > $o) > $o) @ (^[Y0 : ($o > $o > $o) > $o]: ((Y0 @ &) => (Y0 @ (^[Y1 : $o]: ((^[Y2 : $o]: (~ ((~ Y2) | (~ Y1)))))))))))),
% 1.51/1.39 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.51/1.39 thf(f12,plain,(
% 1.51/1.39 ($true != ((^[Y0 : $o > $o > $o]: ((^[Y1 : $o > $o > $o]: (!! @ (($o > $o > $o) > $o) @ (^[Y2 : ($o > $o > $o) > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))) @ & @ (^[Y0 : $o]: ((^[Y1 : $o]: (~ ((~ Y1) | (~ Y0))))))))),
% 1.51/1.39 inference(definition_unfolding,[status(thm)],[f10,f11])).
% 1.51/1.39 thf(f11,plain,(
% 1.51/1.39 (leibeq = (^[Y0 : $o > $o > $o]: ((^[Y1 : $o > $o > $o]: (!! @ (($o > $o > $o) > $o) @ (^[Y2 : ($o > $o > $o) > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 1.51/1.39 inference(cnf_transformation,[status(thm)],[f8])).
% 1.51/1.39 thf(f8,plain,(
% 1.51/1.39 (leibeq = (^[Y0 : $o > $o > $o]: ((^[Y1 : $o > $o > $o]: (!! @ (($o > $o > $o) > $o) @ (^[Y2 : ($o > $o > $o) > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 1.51/1.39 inference(fool_elimination,[status(thm)],[f7])).
% 1.51/1.39 thf(f7,plain,(
% 1.51/1.39 (leibeq = (^[X0 : $o > $o > $o, X1 : $o > $o > $o] : (! [X2 : ($o > $o > $o) > $o] : ((X2 @ X0) => (X2 @ X1)))))),
% 1.51/1.39 inference(rectify,[status(thm)],[f1])).
% 1.51/1.39 thf(f1,axiom,(
% 1.51/1.39 (leibeq = (^[X0 : $o > $o > $o, X1 : $o > $o > $o] : (! [X2 : ($o > $o > $o) > $o] : ((X2 @ X0) => (X2 @ X1)))))),
% 1.51/1.39 file('/export/starexec/sandbox2/tmp/tmp.oXfmwGv9ye/DTF2THF_31003.p',leibeq)).
% 1.51/1.39 thf(f10,plain,(
% 1.51/1.39 ($true != (leibeq @ & @ (^[Y0 : $o]: ((^[Y1 : $o]: (~ ((~ Y1) | (~ Y0))))))))),
% 1.51/1.39 inference(cnf_transformation,[status(thm)],[f9])).
% 1.51/1.39 thf(f9,plain,(
% 1.51/1.39 ($true != (leibeq @ & @ (^[Y0 : $o]: ((^[Y1 : $o]: (~ ((~ Y1) | (~ Y0))))))))),
% 1.51/1.39 inference(flattening,[status(thm)],[f6])).
% 1.51/1.39 thf(f6,plain,(
% 1.51/1.39 ~($true = (leibeq @ & @ (^[Y0 : $o]: ((^[Y1 : $o]: (~ ((~ Y1) | (~ Y0))))))))),
% 1.51/1.39 inference(fool_elimination,[status(thm)],[f5])).
% 1.51/1.39 thf(f5,plain,(
% 1.51/1.39 ~(leibeq @ & @ (^[X0 : $o, X1 : $o] : (~(~X0 | ~X1))))),
% 1.51/1.39 inference(rectify,[status(thm)],[f3])).
% 1.51/1.39 thf(f3,negated_conjecture,(
% 1.51/1.39 ~(leibeq @ & @ (^[X0 : $o, X1 : $o] : (~(~X0 | ~X1))))),
% 1.51/1.39 inference(negated_conjecture,[status(cth)],[f2])).
% 1.51/1.39 thf(f2,conjecture,(
% 1.51/1.39 (leibeq @ & @ (^[X0 : $o, X1 : $o] : (~(~X0 | ~X1))))),
% 1.51/1.39 file('/export/starexec/sandbox2/tmp/tmp.oXfmwGv9ye/DTF2THF_31003.p',conj)).
% 1.51/1.39 thf(f16,plain,(
% 1.51/1.39 ($false = (sK1 @ (^[Y0 : $o]: ((^[Y1 : $o]: (~ ((~ Y1) | (~ Y0))))))))),
% 1.51/1.39 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.51/1.39 thf(f56,plain,(
% 1.51/1.39 spl0_1),
% 1.51/1.39 inference(avatar_split_clause,[status(thm)],[f41,f47])).
% 1.51/1.39 thf(f41,plain,(
% 1.51/1.39 ($true = sK4)),
% 1.51/1.39 inference(duplicate_literal_removal,[status(thm)],[f39])).
% 1.51/1.39 thf(f39,plain,(
% 1.51/1.39 ($true = sK4) | ($true = sK4)),
% 1.51/1.39 inference(binary_proxy_clausification,[status(thm)],[f38])).
% 1.51/1.39 thf(f38,plain,(
% 1.51/1.39 ($true = (sK3 & sK4)) | ($true = sK4)),
% 1.51/1.39 inference(not_proxy_clausification,[status(thm)],[f37])).
% 1.51/1.39 thf(f37,plain,(
% 1.51/1.39 ($false = (~ sK4)) | ($true = (sK3 & sK4))),
% 1.51/1.39 inference(binary_proxy_clausification,[status(thm)],[f35])).
% 1.51/1.39 thf(f35,plain,(
% 1.51/1.39 ($false = ((~ sK4) | (~ sK3))) | ($true = (sK3 & sK4))),
% 1.51/1.39 inference(not_proxy_clausification,[status(thm)],[f26])).
% 1.51/1.39 thf(f26,plain,(
% 1.51/1.39 ($true = (~ ((~ sK4) | (~ sK3)))) | ($true = (sK3 & sK4))),
% 1.51/1.39 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.51/1.39 thf(f55,plain,(
% 1.51/1.39 spl0_2),
% 1.51/1.39 inference(avatar_split_clause,[status(thm)],[f45,f51])).
% 1.51/1.39 thf(f45,plain,(
% 1.51/1.39 (sK3 = $true)),
% 1.51/1.39 inference(duplicate_literal_removal,[status(thm)],[f44])).
% 1.51/1.39 thf(f44,plain,(
% 1.51/1.39 (sK3 = $true) | (sK3 = $true)),
% 1.51/1.39 inference(binary_proxy_clausification,[status(thm)],[f42])).
% 1.51/1.39 thf(f42,plain,(
% 1.51/1.39 (sK3 = $true) | ($true = (sK3 & sK4))),
% 1.51/1.39 inference(not_proxy_clausification,[status(thm)],[f36])).
% 1.51/1.39 thf(f36,plain,(
% 1.51/1.39 ($false = (~ sK3)) | ($true = (sK3 & sK4))),
% 1.51/1.39 inference(binary_proxy_clausification,[status(thm)],[f35])).
% 1.51/1.39 % SZS output end Proof for DTF2THF_31003
% 1.51/1.39 % (31101)------------------------------
% 1.51/1.39 % (31101)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.39 % (31101)Termination reason: Refutation
% 1.51/1.39
% 1.51/1.39 % (31101)Memory used [KB]: 5500
% 1.51/1.39 % (31101)Time elapsed: 0.005 s
% 1.51/1.39 % (31101)Instructions burned: 3 (million)
% 1.51/1.39 % (31101)------------------------------
% 1.51/1.39 % (31101)------------------------------
% 1.51/1.39 % (31100)Success in time 0.021 s
%------------------------------------------------------------------------------