%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO016^1 : 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 : n029.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 09:53:08 AM UTC 2026
% Result : Theorem 1.29s 1.17s
% Output : Refutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 12
% Syntax : Number of formulae : 108 ( 15 unt; 0 typ; 10 def)
% Number of atoms : 775 ( 118 equ; 0 cnn)
% Maximal formula atoms : 9 ( 7 avg)
% Number of connectives : 690 ( 124 ~; 162 |; 0 &; 340 @)
% ( 10 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 62 ( 62 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 21 usr; 13 con; 0-2 aty)
% ( 21 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 54 ( 39 ^; 15 !; 0 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
leibeq: $o > $o > $o ).
thf(func_def_2,type,
h: $o > $o ).
thf(func_def_12,type,
sK1: $o > $o ).
thf(func_def_14,type,
ph2:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
sK3: $o > $o ).
thf(func_def_17,type,
sK4: $o > $o ).
thf(func_def_18,type,
sK5: $o > $o ).
thf(func_def_19,type,
sK6: $o > $o ).
thf(func_def_20,type,
sK7: $o > $o ).
thf(func_def_21,type,
sK8: $o > $o ).
thf(func_def_22,type,
sK9: $o > $o ).
thf(f533,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f44,f78,f142,f145,f160,f200,f303,f392,f397,f433,f457,f459,f477,f532]) ).
thf(f532,plain,
( spl0_6
| spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f500,f31,f27,f56]) ).
thf(f56,definition,
( spl0_6
<=> ! [X1: $o > $o] :
( ( ( X1 @ ( h @ $true ) )
= $false )
| ( ( X1 @ ( h @ $false ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f27,definition,
( spl0_1
<=> ( ( h @ $false )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f31,definition,
( spl0_2
<=> ( ( h
@ ( !! @ ( $o > $o )
@ ^ [Y0: $o > $o] :
( ( Y0 @ ( h @ $true ) )
=> ( Y0 @ ( h @ $false ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f500,plain,
( ! [X1: $o > $o] :
( ( ( X1 @ ( h @ $true ) )
= $false )
| ( ( X1 @ ( h @ $false ) )
= $true ) )
| spl0_1
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f499]) ).
thf(f499,plain,
( ! [X1: $o > $o] :
( ( ( X1 @ ( h @ $true ) )
=> ( X1 @ ( h @ $false ) ) )
= $true )
| spl0_1
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f498]) ).
thf(f498,plain,
( ! [X1: $o > $o] :
( ( ^ [Y0: $o > $o] :
( ( Y0 @ ( h @ $true ) )
=> ( Y0 @ ( h @ $false ) ) )
@ X1 )
= $true )
| spl0_1
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f497]) ).
thf(f497,plain,
( ( $false
!= ( !! @ ( $o > $o )
@ ^ [Y0: $o > $o] :
( ( Y0 @ ( h @ $true ) )
=> ( Y0 @ ( h @ $false ) ) ) ) )
| spl0_1
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f485]) ).
thf(f485,plain,
( ( $true != $true )
| ( $false
!= ( !! @ ( $o > $o )
@ ^ [Y0: $o > $o] :
( ( Y0 @ ( h @ $true ) )
=> ( Y0 @ ( h @ $false ) ) ) ) )
| spl0_1
| ~ spl0_2 ),
inference(constrained_superposition,[status(thm)],[f28,f33]) ).
thf(f33,plain,
( ( ( h
@ ( !! @ ( $o > $o )
@ ^ [Y0: $o > $o] :
( ( Y0 @ ( h @ $true ) )
=> ( Y0 @ ( h @ $false ) ) ) ) )
= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f31]) ).
thf(f28,plain,
( ( ( h @ $false )
!= $true )
| spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f27]) ).
thf(f477,plain,
( ~ spl0_2
| spl0_10 ),
inference(avatar_contradiction_clause,[status(thm)],[f476]) ).
thf(f476,plain,
( $false
| ~ spl0_2
| spl0_10 ),
inference(subsumption_resolution,[status(thm)],[f475,f33]) ).
thf(f475,plain,
( ( ( h
@ ( !! @ ( $o > $o )
@ ^ [Y0: $o > $o] :
( ( Y0 @ ( h @ $true ) )
=> ( Y0 @ ( h @ $false ) ) ) ) )
!= $true )
| spl0_10 ),
inference(trivial_inequality_removal,[status(thm)],[f472]) ).
thf(f472,plain,
( ( ( h
@ ( !! @ ( $o > $o )
@ ^ [Y0: $o > $o] :
( ( Y0 @ ( h @ $true ) )
=> ( Y0 @ ( h @ $false ) ) ) ) )
!= $true )
| ( $true != $true )
| spl0_10 ),
inference(constrained_superposition,[status(thm)],[f283,f17]) ).
thf(f17,plain,
( ( sK1
@ ( h
@ ( !! @ ( $o > $o )
@ ^ [Y0: $o > $o] :
( ( Y0 @ ( h @ $true ) )
=> ( Y0 @ ( h @ $false ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( $false
= ( ( sK1
@ ( h
@ ( !! @ ( $o > $o )
@ ^ [Y0: $o > $o] :
( ( Y0 @ ( h @ $true ) )
=> ( Y0 @ ( h @ $false ) ) ) ) ) )
=> ( sK1 @ ( h @ $false ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ^ [Y0: $o > $o] :
( ( Y0
@ ( h
@ ( !! @ ( $o > $o )
@ ^ [Y1: $o > $o] :
( ( Y1 @ ( h @ $true ) )
=> ( Y1 @ ( h @ $false ) ) ) ) ) )
=> ( Y0 @ ( h @ $false ) ) )
@ sK1 )
= $false ),
inference(sigma_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( !! @ ( $o > $o )
@ ^ [Y0: $o > $o] :
( ( Y0
@ ( h
@ ( !! @ ( $o > $o )
@ ^ [Y1: $o > $o] :
( ( Y1 @ ( h @ $true ) )
=> ( Y1 @ ( h @ $false ) ) ) ) ) )
=> ( Y0 @ ( h @ $false ) ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
( $true
!= ( ^ [Y0: $o,Y1: $o] :
( !! @ ( $o > $o )
@ ^ [Y2: $o > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) )
@ ( h
@ ( ^ [Y0: $o,Y1: $o] :
( !! @ ( $o > $o )
@ ^ [Y2: $o > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) )
@ ( h @ $true )
@ ( h @ $false ) ) )
@ ( h @ $false ) ) ),
inference(definition_unfolding,[status(thm)],[f11,f10,f10]) ).
thf(f10,plain,
( leibeq
= ( ^ [Y0: $o,Y1: $o] :
( !! @ ( $o > $o )
@ ^ [Y2: $o > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( leibeq
= ( ^ [Y0: $o,Y1: $o] :
( !! @ ( $o > $o )
@ ^ [Y2: $o > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ^ [X0: $o,X1: $o] :
! [X2: $o > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) )
= leibeq ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: $o,X1: $o] :
! [X2: $o > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) )
= leibeq ),
file('/export/starexec/sandbox2/tmp/tmp.Ef6o0l781v/DTF2THF_14039.p',leibeq) ).
thf(f11,plain,
( ( leibeq @ ( h @ ( leibeq @ ( h @ $true ) @ ( h @ $false ) ) ) @ ( h @ $false ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ( leibeq @ ( h @ ( leibeq @ ( h @ $true ) @ ( h @ $false ) ) ) @ ( h @ $false ) )
!= $true ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ( leibeq @ ( h @ ( leibeq @ ( h @ $true ) @ ( h @ $false ) ) ) @ ( h @ $false ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( leibeq @ ( h @ ( leibeq @ ( h @ $true ) @ ( h @ $false ) ) ) @ ( h @ $false ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ( leibeq @ ( h @ ( leibeq @ ( h @ $true ) @ ( h @ $false ) ) ) @ ( h @ $false ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
leibeq @ ( h @ ( leibeq @ ( h @ $true ) @ ( h @ $false ) ) ) @ ( h @ $false ),
file('/export/starexec/sandbox2/tmp/tmp.Ef6o0l781v/DTF2THF_14039.p',conj) ).
thf(f283,plain,
( ( ( sK1 @ $true )
!= $true )
| spl0_10 ),
inference(avatar_component_clause,[status(thm)],[f282]) ).
thf(f282,definition,
( spl0_10
<=> ( ( sK1 @ $true )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition]) ).
thf(f459,plain,
( spl0_6
| ~ spl0_1
| spl0_10 ),
inference(avatar_split_clause,[status(thm)],[f458,f282,f27,f56]) ).
thf(f458,plain,
( ! [X1: $o > $o] :
( ( ( X1 @ ( h @ $true ) )
= $false )
| ( ( X1 @ ( h @ $false ) )
= $true ) )
| ~ spl0_1
| spl0_10 ),
inference(subsumption_resolution,[status(thm)],[f205,f283]) ).
thf(f205,plain,
( ! [X1: $o > $o] :
( ( ( X1 @ ( h @ $true ) )
= $false )
| ( ( sK1 @ $true )
= $true )
| ( ( X1 @ ( h @ $false ) )
= $true ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f204]) ).
thf(f204,plain,
( ! [X1: $o > $o] :
( ( ( sK1 @ $true )
= $true )
| ( ( ( X1 @ ( h @ $true ) )
=> ( X1 @ ( h @ $false ) ) )
= $true ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f203]) ).
thf(f203,plain,
( ! [X1: $o > $o] :
( ( ( sK1 @ $true )
= $true )
| ( ( ^ [Y0: $o > $o] :
( ( Y0 @ ( h @ $true ) )
=> ( Y0 @ ( h @ $false ) ) )
@ X1 )
= $true ) )
| ~ spl0_1 ),
inference(pi_clausification,[status(thm)],[f202]) ).
thf(f202,plain,
( ( ( sK1 @ $true )
= $true )
| ( $false
!= ( !! @ ( $o > $o )
@ ^ [Y0: $o > $o] :
( ( Y0 @ ( h @ $true ) )
=> ( Y0 @ ( h @ $false ) ) ) ) )
| ~ spl0_1 ),
inference(constrained_superposition,[status(thm)],[f17,f29]) ).
thf(f29,plain,
( ( ( h @ $false )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f27]) ).
thf(f457,plain,
( ~ spl0_1
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[status(thm)],[f456]) ).
thf(f456,plain,
( $false
| ~ spl0_1
| ~ spl0_10 ),
inference(subsumption_resolution,[status(thm)],[f448,f29]) ).
thf(f448,plain,
( ( ( h @ $false )
!= $true )
| ~ spl0_10 ),
inference(trivial_inequality_removal,[status(thm)],[f438]) ).
thf(f438,plain,
( ( ( h @ $false )
!= $true )
| ( $true = $false )
| ~ spl0_10 ),
inference(constrained_superposition,[status(thm)],[f284,f16]) ).
thf(f16,plain,
( $false
= ( sK1 @ ( h @ $false ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f284,plain,
( ( ( sK1 @ $true )
= $true )
| ~ spl0_10 ),
inference(avatar_component_clause,[status(thm)],[f282]) ).
thf(f433,plain,
( ~ spl0_1
| spl0_3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[status(thm)],[f432]) ).
thf(f432,plain,
( $false
| ~ spl0_1
| spl0_3
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15 ),
inference(subsumption_resolution,[status(thm)],[f422,f370]) ).
thf(f370,plain,
( ( ( h @ $true )
= $true )
| spl0_3
| ~ spl0_6 ),
inference(subsumption_resolution,[status(thm)],[f363,f37]) ).
thf(f37,plain,
( ( ( h @ $false )
!= $false )
| spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f36]) ).
thf(f36,definition,
( spl0_3
<=> ( ( h @ $false )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f363,plain,
( ( ( h @ $false )
= $false )
| ( ( h @ $true )
= $true )
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f304]) ).
thf(f304,plain,
( ( ( h @ $false )
= ( h @ $true ) )
| ~ spl0_6 ),
inference(leibniz_equality_elimination,[status(thm)],[f57]) ).
thf(f57,plain,
( ! [X1: $o > $o] :
( ( ( X1 @ ( h @ $true ) )
= $false )
| ( ( X1 @ ( h @ $false ) )
= $true ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f56]) ).
thf(f422,plain,
( ( ( h @ $true )
!= $true )
| ~ spl0_1
| ~ spl0_14
| ~ spl0_15 ),
inference(trivial_inequality_removal,[status(thm)],[f408]) ).
thf(f408,plain,
( ( ( h @ $true )
!= $true )
| ( $true = $false )
| ~ spl0_1
| ~ spl0_14
| ~ spl0_15 ),
inference(constrained_superposition,[status(thm)],[f396,f399]) ).
thf(f399,plain,
( ( ( sK5 @ $true )
= $false )
| ~ spl0_1
| ~ spl0_14 ),
inference(superposition,[status(thm)],[f391,f29]) ).
thf(f391,plain,
( ( $false
= ( sK5 @ ( h @ $false ) ) )
| ~ spl0_14 ),
inference(avatar_component_clause,[status(thm)],[f389]) ).
thf(f389,definition,
( spl0_14
<=> ( $false
= ( sK5 @ ( h @ $false ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_14])],[avatar_definition]) ).
thf(f396,plain,
( ( ( sK5 @ ( h @ $true ) )
= $true )
| ~ spl0_15 ),
inference(avatar_component_clause,[status(thm)],[f394]) ).
thf(f394,definition,
( spl0_15
<=> ( ( sK5 @ ( h @ $true ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_15])],[avatar_definition]) ).
thf(f397,plain,
( spl0_15
| spl0_10
| spl0_3
| ~ spl0_6 ),
inference(avatar_split_clause,[status(thm)],[f387,f56,f36,f282,f394]) ).
thf(f387,plain,
( ( ( sK1 @ $true )
= $true )
| ( ( sK5 @ ( h @ $true ) )
= $true )
| spl0_3
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f385]) ).
thf(f385,plain,
( ( ( sK1 @ $true )
= $true )
| ( ( ( sK5 @ ( h @ $true ) )
=> ( sK5 @ ( h @ $false ) ) )
= $false )
| spl0_3
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f384]) ).
thf(f384,plain,
( ( ( sK1 @ $true )
= $true )
| ( ( ^ [Y0: $o > $o] :
( ( Y0 @ ( h @ $true ) )
=> ( Y0 @ ( h @ $false ) ) )
@ sK5 )
= $false )
| spl0_3
| ~ spl0_6 ),
inference(sigma_clausification,[status(thm)],[f374]) ).
thf(f374,plain,
( ( ( sK1 @ $true )
= $true )
| ( $true
!= ( !! @ ( $o > $o )
@ ^ [Y0: $o > $o] :
( ( Y0 @ ( h @ $true ) )
=> ( Y0 @ ( h @ $false ) ) ) ) )
| spl0_3
| ~ spl0_6 ),
inference(constrained_superposition,[status(thm)],[f17,f370]) ).
thf(f392,plain,
( spl0_10
| spl0_14
| spl0_3
| ~ spl0_6 ),
inference(avatar_split_clause,[status(thm)],[f386,f56,f36,f389,f282]) ).
thf(f386,plain,
( ( $false
= ( sK5 @ ( h @ $false ) ) )
| ( ( sK1 @ $true )
= $true )
| spl0_3
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f385]) ).
thf(f303,plain,
( spl0_3
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f302]) ).
thf(f302,plain,
( $false
| spl0_3
| ~ spl0_8 ),
inference(subsumption_resolution,[status(thm)],[f233,f37]) ).
thf(f233,plain,
( ( ( h @ $false )
= $false )
| ~ spl0_8 ),
inference(leibniz_equality_elimination,[status(thm)],[f141]) ).
thf(f141,plain,
( ! [X0: $o > $o] :
( ( ( X0 @ ( h @ $false ) )
= $true )
| ( ( X0 @ $false )
= $false ) )
| ~ spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f140]) ).
thf(f140,definition,
( spl0_8
<=> ! [X0: $o > $o] :
( ( ( X0 @ $false )
= $false )
| ( ( X0 @ ( h @ $false ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition]) ).
thf(f200,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f199]) ).
thf(f199,plain,
( $false
| ~ spl0_3
| spl0_5
| ~ spl0_7 ),
inference(subsumption_resolution,[status(thm)],[f188,f137]) ).
thf(f137,plain,
( ( ( h @ $true )
= $false )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f135]) ).
thf(f135,definition,
( spl0_7
<=> ( ( h @ $true )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f188,plain,
( ( ( h @ $true )
!= $false )
| ~ spl0_3
| spl0_5
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f184]) ).
thf(f184,plain,
( ( $true = $false )
| ( ( h @ $true )
!= $false )
| ~ spl0_3
| spl0_5
| ~ spl0_7 ),
inference(constrained_superposition,[status(thm)],[f179,f181]) ).
thf(f181,plain,
( ( ( sK3 @ $false )
= $false )
| ~ spl0_3
| spl0_5
| ~ spl0_7 ),
inference(superposition,[status(thm)],[f178,f38]) ).
thf(f38,plain,
( ( ( h @ $false )
= $false )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f36]) ).
thf(f178,plain,
( ( ( sK3 @ ( h @ $false ) )
= $false )
| spl0_5
| ~ spl0_7 ),
inference(subsumption_resolution,[status(thm)],[f176,f53]) ).
thf(f53,plain,
( ( ( sK1 @ $false )
!= $true )
| spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f52]) ).
thf(f52,definition,
( spl0_5
<=> ( ( sK1 @ $false )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f176,plain,
( ( ( sK1 @ $false )
= $true )
| ( ( sK3 @ ( h @ $false ) )
= $false )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[status(thm)],[f175]) ).
thf(f175,plain,
( ( ( sK1 @ $false )
= $true )
| ( $false
= ( ( sK3 @ ( h @ $true ) )
=> ( sK3 @ ( h @ $false ) ) ) )
| ~ spl0_7 ),
inference(beta_eta_normalization,[status(thm)],[f174]) ).
thf(f174,plain,
( ( ( ^ [Y0: $o > $o] :
( ( Y0 @ ( h @ $true ) )
=> ( Y0 @ ( h @ $false ) ) )
@ sK3 )
= $false )
| ( ( sK1 @ $false )
= $true )
| ~ spl0_7 ),
inference(sigma_clausification,[status(thm)],[f171]) ).
thf(f171,plain,
( ( $true
!= ( !! @ ( $o > $o )
@ ^ [Y0: $o > $o] :
( ( Y0 @ ( h @ $true ) )
=> ( Y0 @ ( h @ $false ) ) ) ) )
| ( ( sK1 @ $false )
= $true )
| ~ spl0_7 ),
inference(constrained_superposition,[status(thm)],[f17,f137]) ).
thf(f179,plain,
( ( $true
= ( sK3 @ ( h @ $true ) ) )
| spl0_5
| ~ spl0_7 ),
inference(subsumption_resolution,[status(thm)],[f177,f53]) ).
thf(f177,plain,
( ( $true
= ( sK3 @ ( h @ $true ) ) )
| ( ( sK1 @ $false )
= $true )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[status(thm)],[f175]) ).
thf(f160,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f159]) ).
thf(f159,plain,
( $false
| ~ spl0_1
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f153]) ).
thf(f153,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f38,f29]) ).
thf(f145,plain,
( spl0_7
| spl0_1
| ~ spl0_6 ),
inference(avatar_split_clause,[status(thm)],[f110,f56,f27,f135]) ).
thf(f110,plain,
( ( ( h @ $true )
= $false )
| ( ( h @ $false )
= $true )
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f83]) ).
thf(f83,plain,
( ( ( h @ $false )
= ( h @ $true ) )
| ~ spl0_6 ),
inference(leibniz_equality_elimination,[status(thm)],[f57]) ).
thf(f142,plain,
( spl0_1
| spl0_8
| ~ spl0_6 ),
inference(avatar_split_clause,[status(thm)],[f129,f56,f140,f27]) ).
thf(f129,plain,
( ! [X0: $o > $o] :
( ( ( h @ $false )
= $true )
| ( ( X0 @ $false )
= $false )
| ( ( X0 @ ( h @ $false ) )
= $true ) )
| ~ spl0_6 ),
inference(beta_eta_normalization,[status(thm)],[f91]) ).
thf(f91,plain,
( ! [X0: $o > $o] :
( ( $true
= ( ^ [Y0: $o] : Y0
@ ( h @ $false ) ) )
| ( ( X0 @ ( h @ $false ) )
= $true )
| ( ( X0 @ $false )
= $false ) )
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f57,f57]) ).
thf(f78,plain,
( ~ spl0_3
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f77]) ).
thf(f77,plain,
( $false
| ~ spl0_3
| ~ spl0_5 ),
inference(subsumption_resolution,[status(thm)],[f71,f38]) ).
thf(f71,plain,
( ( ( h @ $false )
!= $false )
| ~ spl0_5 ),
inference(trivial_inequality_removal,[status(thm)],[f68]) ).
thf(f68,plain,
( ( $true = $false )
| ( ( h @ $false )
!= $false )
| ~ spl0_5 ),
inference(constrained_superposition,[status(thm)],[f16,f54]) ).
thf(f54,plain,
( ( ( sK1 @ $false )
= $true )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f52]) ).
thf(f44,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f21,f31,f27]) ).
thf(f21,plain,
( ( ( h @ $false )
= $true )
| ( ( h
@ ( !! @ ( $o > $o )
@ ^ [Y0: $o > $o] :
( ( Y0 @ ( h @ $true ) )
=> ( Y0 @ ( h @ $false ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
( ( h
@ ( !! @ ( $o > $o )
@ ^ [Y0: $o > $o] :
( ( Y0 @ ( h @ $true ) )
=> ( Y0 @ ( h @ $false ) ) ) ) )
!= ( h @ $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f18]) ).
thf(f18,plain,
( ( $true = $false )
| ( ( h
@ ( !! @ ( $o > $o )
@ ^ [Y0: $o > $o] :
( ( Y0 @ ( h @ $true ) )
=> ( Y0 @ ( h @ $false ) ) ) ) )
!= ( h @ $false ) ) ),
inference(constrained_superposition,[status(thm)],[f17,f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO016^1 : TPTP v9.2.1. Released v3.7.0.
% 0.10/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.32 % Computer : n029.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Tue Feb 24 14:21:29 EST 2026
% 0.11/0.32 % CPUTime :
% 0.11/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.14/0.41 ---- Original DTF file ---
% 0.14/0.41 thf(spec,logic,$$dhol).
% 0.14/0.41 %------------------------------------------------------------------------------
% 0.14/0.41 % File : SYO016^1 : TPTP v9.2.1. Released v3.7.0.
% 0.14/0.41 % Domain : Syntactic
% 0.14/0.41 % Problem : Formula valid in MBb, but not in model classes not requiring b
% 0.14/0.41 % Version : Especial.
% 0.14/0.41 % English :
% 0.14/0.41
% 0.14/0.41 % Refs : [BB05] Benzmueller & Brown (2005), A Structured Set of Higher
% 0.14/0.41 % : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% 0.14/0.41 % Source : [Ben09]
% 0.14/0.41 % Names : Example 18a [BB05]
% 0.14/0.41
% 0.14/0.41 % Status : Theorem
% 0.14/0.41 % : Without Boolean extensionality : CounterSatisfiable
% 0.14/0.41 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v6.1.0, 0.43 v5.5.0, 0.33 v5.4.0, 0.60 v5.1.0, 0.80 v4.1.0, 1.00 v4.0.1, 0.67 v3.7.0
% 0.14/0.41 % Syntax : Number of formulae : 4 ( 1 unt; 2 typ; 1 def)
% 0.14/0.41 % Number of atoms : 11 ( 1 equ; 0 cnn)
% 0.14/0.41 % Maximal formula atoms : 9 ( 5 avg)
% 0.14/0.41 % Number of connectives : 11 ( 0 ~; 0 |; 0 &; 10 @)
% 0.14/0.41 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.14/0.41 % Maximal formula depth : 7 ( 4 avg)
% 0.14/0.41 % Number of types : 1 ( 0 usr)
% 0.14/0.41 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.14/0.41 % Number of symbols : 5 ( 2 usr; 2 con; 0-2 aty)
% 0.14/0.41 % Number of variables : 3 ( 2 ^; 1 !; 0 ?; 3 :)
% 0.14/0.41 % SPC : TH0_THM_EQU_NAR
% 0.14/0.41
% 0.14/0.41 % Comments :
% 0.14/0.41 %------------------------------------------------------------------------------
% 0.14/0.41 thf(leibeq_decl,type,
% 0.14/0.41 leibeq: $o > $o > $o ).
% 0.14/0.41
% 0.14/0.41 thf(leibeq,definition,
% 0.14/0.41 ( leibeq
% 0.14/0.41 = ( ^ [X: $o,Y: $o] :
% 0.14/0.41 ! [P: $o > $o] :
% 0.14/0.41 ( ( P @ X )
% 0.14/0.41 => ( P @ Y ) ) ) ) ).
% 0.14/0.41
% 0.14/0.41 thf(h,type,
% 0.14/0.41 h: $o > $o ).
% 0.14/0.41
% 0.14/0.41 thf(conj,conjecture,
% 0.14/0.41 leibeq @ ( h @ ( leibeq @ ( h @ $true ) @ ( h @ $false ) ) ) @ ( h @ $false ) ).
% 0.14/0.41
% 0.14/0.41 %------------------------------------------------------------------------------
% 0.14/0.41 ------------------------
% 1.29/1.13 ---- Embedded in THF ---
% 1.29/1.13 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.29/1.13 %%% Generated on Tue Feb 24 14:21:30 EST 2026
% 1.29/1.13 %%% using '$$dhol' embedding, version 1.3.0.
% 1.29/1.13 %%% Logic specification used:
% 1.29/1.13 %%% thf(spec, logic, $$dhol).
% 1.29/1.13
% 1.29/1.13 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.Ef6o0l781v/DTF2DTF14039.p
% See solution above
% 1.29/1.13 ------------------------
% 1.29/1.14 ---- Cleaned THF ---
% 1.29/1.14 thf(leibeq_decl,type,
% 1.29/1.14 leibeq: $o > $o > $o ).
% 1.29/1.14
% 1.29/1.14 thf(leibeq,definition,
% 1.29/1.14 ( leibeq
% 1.29/1.14 = ( ^ [X: $o,Y: $o] :
% 1.29/1.14 ! [P: $o > $o] :
% 1.29/1.14 ( ( P @ X )
% 1.29/1.14 => ( P @ Y ) ) ) ) ).
% 1.29/1.14
% 1.29/1.14 thf(h,type,
% 1.29/1.14 h: $o > $o ).
% 1.29/1.14
% 1.29/1.14 thf(conj,conjecture,
% 1.29/1.14 leibeq @ ( h @ ( leibeq @ ( h @ $true ) @ ( h @ $false ) ) ) @ ( h @ $false ) ).
% 1.29/1.14 ------------------------
% 1.29/1.15 % (14138)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_14039 for (3000ds/183Mi)
% 1.29/1.16 % (14141)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_14039 for (3000ds/2Mi)
% 1.29/1.16 % (14140)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_14039 for (3000ds/27Mi)
% 1.29/1.16 % (14142)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_14039 for (3000ds/2Mi)
% 1.29/1.16 % (14143)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_14039 for (3000ds/275Mi)
% 1.29/1.16 % (14139)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_14039 for (3000ds/4Mi)
% 1.29/1.16 % (14144)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_14039 for (3000ds/18Mi)
% 1.29/1.16 % (14143)Refutation not found, incomplete strategy
% 1.29/1.16 % (14143)------------------------------
% 1.29/1.16 % (14143)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.29/1.16 % (14143)Termination reason: Refutation not found, incomplete strategy
% 1.29/1.16
% 1.29/1.16
% 1.29/1.16 % (14143)Memory used [KB]: 5373
% 1.29/1.16 % (14143)Time elapsed: 0.002 s
% 1.29/1.16 % (14143)Instructions burned: 1 (million)
% 1.29/1.16 % (14143)------------------------------
% 1.29/1.16 % (14143)------------------------------
% 1.29/1.16 % (14141)Refutation not found, incomplete strategy
% 1.29/1.16 % (14141)------------------------------
% 1.29/1.16 % (14141)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.29/1.16 % (14141)Termination reason: Refutation not found, incomplete strategy
% 1.29/1.16
% 1.29/1.16 % (14142)Instruction limit reached!
% 1.29/1.16 % (14142)------------------------------
% 1.29/1.16 % (14142)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.29/1.16 % (14142)Termination reason: Unknown
% 1.29/1.16 % (14142)Termination phase: Saturation
% 1.29/1.16
% 1.29/1.16 % (14142)Memory used [KB]: 5500
% 1.29/1.16 % (14142)Time elapsed: 0.003 s
% 1.29/1.16 % (14142)Instructions burned: 2 (million)
% 1.29/1.16 % (14142)------------------------------
% 1.29/1.16 % (14142)------------------------------
% 1.29/1.16
% 1.29/1.16 % (14140)Refutation not found, incomplete strategy
% 1.29/1.16 % (14140)------------------------------
% 1.29/1.16 % (14140)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.29/1.16 % (14140)Termination reason: Refutation not found, incomplete strategy
% 1.29/1.16
% 1.29/1.16
% 1.29/1.16 % (14140)Memory used [KB]: 5500
% 1.29/1.16 % (14140)Time elapsed: 0.003 s
% 1.29/1.16 % (14140)Instructions burned: 2 (million)
% 1.29/1.16 % (14140)------------------------------
% 1.29/1.16 % (14140)------------------------------
% 1.29/1.16 % (14141)Memory used [KB]: 5500
% 1.29/1.16 % (14141)Time elapsed: 0.003 s
% 1.29/1.16 % (14141)Instructions burned: 1 (million)
% 1.29/1.16 % (14141)------------------------------
% 1.29/1.16 % (14141)------------------------------
% 1.29/1.16 % (14139)Instruction limit reached!
% 1.29/1.16 % (14139)------------------------------
% 1.29/1.16 % (14139)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.29/1.16 % (14139)Termination reason: Unknown
% 1.29/1.16 % (14139)Termination phase: Saturation
% 1.29/1.16
% 1.29/1.16 % (14139)Memory used [KB]: 5500
% 1.29/1.16 % (14139)Time elapsed: 0.004 s
% 1.29/1.16 % (14139)Instructions burned: 4 (million)
% 1.29/1.16 % (14139)------------------------------
% 1.29/1.16 % (14139)------------------------------
% 1.29/1.16 % (14138)First to succeed.
% 1.29/1.17 % (14138)Refutation found. Thanks to Tanya!
% 1.29/1.17 % SZS status Theorem for DTF2THF_14039
% 1.29/1.17 % SZS output start Proof for DTF2THF_14039
% 1.29/1.17 thf(func_def_0, type, leibeq: $o > $o > $o).
% 1.29/1.17 thf(func_def_2, type, h: $o > $o).
% 1.29/1.17 thf(func_def_12, type, sK1: $o > $o).
% 1.29/1.17 thf(func_def_14, type, ph2: !>[X0: $tType]:(X0)).
% 1.29/1.17 thf(func_def_16, type, sK3: $o > $o).
% 1.29/1.17 thf(func_def_17, type, sK4: $o > $o).
% 1.29/1.17 thf(func_def_18, type, sK5: $o > $o).
% 1.29/1.17 thf(func_def_19, type, sK6: $o > $o).
% 1.29/1.17 thf(func_def_20, type, sK7: $o > $o).
% 1.29/1.17 thf(func_def_21, type, sK8: $o > $o).
% 1.29/1.17 thf(func_def_22, type, sK9: $o > $o).
% 1.29/1.17 thf(f533,plain,(
% 1.29/1.17 $false),
% 1.29/1.17 inference(avatar_sat_refutation,[status(thm)],[f44,f78,f142,f145,f160,f200,f303,f392,f397,f433,f457,f459,f477,f532])).
% 1.29/1.17 thf(f532,plain,(
% 1.29/1.17 spl0_6 | spl0_1 | ~spl0_2),
% 1.29/1.17 inference(avatar_split_clause,[status(thm)],[f500,f31,f27,f56])).
% 1.29/1.17 thf(f56,definition,(
% 1.29/1.17 spl0_6 <=> ! [X1 : $o > $o] : (((X1 @ (h @ $true)) = $false) | ((X1 @ (h @ $false)) = $true))),
% 1.29/1.17 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.29/1.17 thf(f27,definition,(
% 1.29/1.17 spl0_1 <=> ((h @ $false) = $true)),
% 1.29/1.17 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.29/1.17 thf(f31,definition,(
% 1.29/1.17 spl0_2 <=> ((h @ (!! @ ($o > $o) @ (^[Y0 : $o > $o]: ((Y0 @ (h @ $true)) => (Y0 @ (h @ $false)))))) = $true)),
% 1.29/1.17 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.29/1.17 thf(f500,plain,(
% 1.29/1.17 ( ! [X1 : $o > $o] : (((X1 @ (h @ $true)) = $false) | ((X1 @ (h @ $false)) = $true)) ) | (spl0_1 | ~spl0_2)),
% 1.29/1.17 inference(binary_proxy_clausification,[status(thm)],[f499])).
% 1.29/1.17 thf(f499,plain,(
% 1.29/1.17 ( ! [X1 : $o > $o] : ((((X1 @ (h @ $true)) => (X1 @ (h @ $false))) = $true)) ) | (spl0_1 | ~spl0_2)),
% 1.29/1.17 inference(beta_eta_normalization,[status(thm)],[f498])).
% 1.29/1.17 thf(f498,plain,(
% 1.29/1.17 ( ! [X1 : $o > $o] : ((((^[Y0 : $o > $o]: ((Y0 @ (h @ $true)) => (Y0 @ (h @ $false)))) @ X1) = $true)) ) | (spl0_1 | ~spl0_2)),
% 1.29/1.17 inference(pi_clausification,[status(thm)],[f497])).
% 1.29/1.17 thf(f497,plain,(
% 1.29/1.17 ($false != (!! @ ($o > $o) @ (^[Y0 : $o > $o]: ((Y0 @ (h @ $true)) => (Y0 @ (h @ $false)))))) | (spl0_1 | ~spl0_2)),
% 1.29/1.17 inference(trivial_inequality_removal,[status(thm)],[f485])).
% 1.29/1.17 thf(f485,plain,(
% 1.29/1.17 ($true != $true) | ($false != (!! @ ($o > $o) @ (^[Y0 : $o > $o]: ((Y0 @ (h @ $true)) => (Y0 @ (h @ $false)))))) | (spl0_1 | ~spl0_2)),
% 1.29/1.17 inference(constrained_superposition,[status(thm)],[f28,f33])).
% 1.29/1.17 thf(f33,plain,(
% 1.29/1.17 ((h @ (!! @ ($o > $o) @ (^[Y0 : $o > $o]: ((Y0 @ (h @ $true)) => (Y0 @ (h @ $false)))))) = $true) | ~spl0_2),
% 1.29/1.17 inference(avatar_component_clause,[status(thm)],[f31])).
% 1.29/1.17 thf(f28,plain,(
% 1.29/1.17 ((h @ $false) != $true) | spl0_1),
% 1.29/1.17 inference(avatar_component_clause,[status(thm)],[f27])).
% 1.29/1.17 thf(f477,plain,(
% 1.29/1.17 ~spl0_2 | spl0_10),
% 1.29/1.17 inference(avatar_contradiction_clause,[status(thm)],[f476])).
% 1.29/1.17 thf(f476,plain,(
% 1.29/1.17 $false | (~spl0_2 | spl0_10)),
% 1.29/1.17 inference(subsumption_resolution,[status(thm)],[f475,f33])).
% 1.29/1.17 thf(f475,plain,(
% 1.29/1.17 ((h @ (!! @ ($o > $o) @ (^[Y0 : $o > $o]: ((Y0 @ (h @ $true)) => (Y0 @ (h @ $false)))))) != $true) | spl0_10),
% 1.29/1.17 inference(trivial_inequality_removal,[status(thm)],[f472])).
% 1.29/1.17 thf(f472,plain,(
% 1.29/1.17 ((h @ (!! @ ($o > $o) @ (^[Y0 : $o > $o]: ((Y0 @ (h @ $true)) => (Y0 @ (h @ $false)))))) != $true) | ($true != $true) | spl0_10),
% 1.29/1.17 inference(constrained_superposition,[status(thm)],[f283,f17])).
% 1.29/1.17 thf(f17,plain,(
% 1.29/1.17 ((sK1 @ (h @ (!! @ ($o > $o) @ (^[Y0 : $o > $o]: ((Y0 @ (h @ $true)) => (Y0 @ (h @ $false))))))) = $true)),
% 1.29/1.17 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.29/1.17 thf(f15,plain,(
% 1.29/1.17 ($false = ((sK1 @ (h @ (!! @ ($o > $o) @ (^[Y0 : $o > $o]: ((Y0 @ (h @ $true)) => (Y0 @ (h @ $false))))))) => (sK1 @ (h @ $false))))),
% 1.29/1.17 inference(beta_eta_normalization,[status(thm)],[f14])).
% 1.29/1.17 thf(f14,plain,(
% 1.29/1.17 (((^[Y0 : $o > $o]: ((Y0 @ (h @ (!! @ ($o > $o) @ (^[Y1 : $o > $o]: ((Y1 @ (h @ $true)) => (Y1 @ (h @ $false))))))) => (Y0 @ (h @ $false)))) @ sK1) = $false)),
% 1.29/1.17 inference(sigma_clausification,[status(thm)],[f13])).
% 1.29/1.17 thf(f13,plain,(
% 1.29/1.17 ((!! @ ($o > $o) @ (^[Y0 : $o > $o]: ((Y0 @ (h @ (!! @ ($o > $o) @ (^[Y1 : $o > $o]: ((Y1 @ (h @ $true)) => (Y1 @ (h @ $false))))))) => (Y0 @ (h @ $false))))) != $true)),
% 1.29/1.17 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.29/1.17 thf(f12,plain,(
% 1.29/1.17 ($true != ((^[Y0 : $o]: ((^[Y1 : $o]: (!! @ ($o > $o) @ (^[Y2 : $o > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))) @ (h @ ((^[Y0 : $o]: ((^[Y1 : $o]: (!! @ ($o > $o) @ (^[Y2 : $o > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))) @ (h @ $true) @ (h @ $false))) @ (h @ $false)))),
% 1.29/1.17 inference(definition_unfolding,[status(thm)],[f11,f10,f10])).
% 1.29/1.17 thf(f10,plain,(
% 1.29/1.17 (leibeq = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ ($o > $o) @ (^[Y2 : $o > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 1.29/1.17 inference(cnf_transformation,[status(thm)],[f8])).
% 1.29/1.17 thf(f8,plain,(
% 1.29/1.17 (leibeq = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ ($o > $o) @ (^[Y2 : $o > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 1.29/1.17 inference(fool_elimination,[status(thm)],[f7])).
% 1.29/1.17 thf(f7,plain,(
% 1.29/1.17 ((^[X0 : $o, X1 : $o] : (! [X2 : $o > $o] : ((X2 @ X0) => (X2 @ X1)))) = leibeq)),
% 1.29/1.17 inference(rectify,[status(thm)],[f1])).
% 1.29/1.17 thf(f1,axiom,(
% 1.29/1.17 ((^[X0 : $o, X1 : $o] : (! [X2 : $o > $o] : ((X2 @ X0) => (X2 @ X1)))) = leibeq)),
% 1.29/1.17 file('/export/starexec/sandbox2/tmp/tmp.Ef6o0l781v/DTF2THF_14039.p',leibeq)).
% 1.29/1.17 thf(f11,plain,(
% 1.29/1.17 ((leibeq @ (h @ (leibeq @ (h @ $true) @ (h @ $false))) @ (h @ $false)) != $true)),
% 1.29/1.17 inference(cnf_transformation,[status(thm)],[f9])).
% 1.29/1.17 thf(f9,plain,(
% 1.29/1.17 ((leibeq @ (h @ (leibeq @ (h @ $true) @ (h @ $false))) @ (h @ $false)) != $true)),
% 1.29/1.17 inference(flattening,[status(thm)],[f6])).
% 1.29/1.17 thf(f6,plain,(
% 1.29/1.17 ~((leibeq @ (h @ (leibeq @ (h @ $true) @ (h @ $false))) @ (h @ $false)) = $true)),
% 1.29/1.17 inference(fool_elimination,[status(thm)],[f5])).
% 1.29/1.17 thf(f5,plain,(
% 1.29/1.17 ~(leibeq @ (h @ (leibeq @ (h @ $true) @ (h @ $false))) @ (h @ $false))),
% 1.29/1.17 inference(rectify,[status(thm)],[f3])).
% 1.29/1.17 thf(f3,negated_conjecture,(
% 1.29/1.17 ~(leibeq @ (h @ (leibeq @ (h @ $true) @ (h @ $false))) @ (h @ $false))),
% 1.29/1.17 inference(negated_conjecture,[status(cth)],[f2])).
% 1.29/1.17 thf(f2,conjecture,(
% 1.29/1.17 (leibeq @ (h @ (leibeq @ (h @ $true) @ (h @ $false))) @ (h @ $false))),
% 1.29/1.17 file('/export/starexec/sandbox2/tmp/tmp.Ef6o0l781v/DTF2THF_14039.p',conj)).
% 1.29/1.17 thf(f283,plain,(
% 1.29/1.17 ((sK1 @ $true) != $true) | spl0_10),
% 1.29/1.17 inference(avatar_component_clause,[status(thm)],[f282])).
% 1.29/1.17 thf(f282,definition,(
% 1.29/1.17 spl0_10 <=> ((sK1 @ $true) = $true)),
% 1.29/1.17 introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition])).
% 1.29/1.17 thf(f459,plain,(
% 1.29/1.17 spl0_6 | ~spl0_1 | spl0_10),
% 1.29/1.17 inference(avatar_split_clause,[status(thm)],[f458,f282,f27,f56])).
% 1.29/1.17 thf(f458,plain,(
% 1.29/1.17 ( ! [X1 : $o > $o] : (((X1 @ (h @ $true)) = $false) | ((X1 @ (h @ $false)) = $true)) ) | (~spl0_1 | spl0_10)),
% 1.29/1.17 inference(subsumption_resolution,[status(thm)],[f205,f283])).
% 1.29/1.17 thf(f205,plain,(
% 1.29/1.17 ( ! [X1 : $o > $o] : (((X1 @ (h @ $true)) = $false) | ((sK1 @ $true) = $true) | ((X1 @ (h @ $false)) = $true)) ) | ~spl0_1),
% 1.29/1.17 inference(binary_proxy_clausification,[status(thm)],[f204])).
% 1.29/1.17 thf(f204,plain,(
% 1.29/1.17 ( ! [X1 : $o > $o] : (((sK1 @ $true) = $true) | (((X1 @ (h @ $true)) => (X1 @ (h @ $false))) = $true)) ) | ~spl0_1),
% 1.29/1.17 inference(beta_eta_normalization,[status(thm)],[f203])).
% 1.29/1.17 thf(f203,plain,(
% 1.29/1.17 ( ! [X1 : $o > $o] : (((sK1 @ $true) = $true) | (((^[Y0 : $o > $o]: ((Y0 @ (h @ $true)) => (Y0 @ (h @ $false)))) @ X1) = $true)) ) | ~spl0_1),
% 1.29/1.17 inference(pi_clausification,[status(thm)],[f202])).
% 1.29/1.17 thf(f202,plain,(
% 1.29/1.17 ((sK1 @ $true) = $true) | ($false != (!! @ ($o > $o) @ (^[Y0 : $o > $o]: ((Y0 @ (h @ $true)) => (Y0 @ (h @ $false)))))) | ~spl0_1),
% 1.29/1.17 inference(constrained_superposition,[status(thm)],[f17,f29])).
% 1.29/1.17 thf(f29,plain,(
% 1.29/1.17 ((h @ $false) = $true) | ~spl0_1),
% 1.29/1.17 inference(avatar_component_clause,[status(thm)],[f27])).
% 1.29/1.17 thf(f457,plain,(
% 1.29/1.17 ~spl0_1 | ~spl0_10),
% 1.29/1.17 inference(avatar_contradiction_clause,[status(thm)],[f456])).
% 1.29/1.17 thf(f456,plain,(
% 1.29/1.17 $false | (~spl0_1 | ~spl0_10)),
% 1.29/1.17 inference(subsumption_resolution,[status(thm)],[f448,f29])).
% 1.29/1.17 thf(f448,plain,(
% 1.29/1.17 ((h @ $false) != $true) | ~spl0_10),
% 1.29/1.17 inference(trivial_inequality_removal,[status(thm)],[f438])).
% 1.29/1.17 thf(f438,plain,(
% 1.29/1.17 ((h @ $false) != $true) | ($true = $false) | ~spl0_10),
% 1.29/1.17 inference(constrained_superposition,[status(thm)],[f284,f16])).
% 1.29/1.17 thf(f16,plain,(
% 1.29/1.17 ($false = (sK1 @ (h @ $false)))),
% 1.29/1.17 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.29/1.17 thf(f284,plain,(
% 1.29/1.17 ((sK1 @ $true) = $true) | ~spl0_10),
% 1.29/1.17 inference(avatar_component_clause,[status(thm)],[f282])).
% 1.29/1.17 thf(f433,plain,(
% 1.29/1.17 ~spl0_1 | spl0_3 | ~spl0_6 | ~spl0_14 | ~spl0_15),
% 1.29/1.17 inference(avatar_contradiction_clause,[status(thm)],[f432])).
% 1.29/1.17 thf(f432,plain,(
% 1.29/1.17 $false | (~spl0_1 | spl0_3 | ~spl0_6 | ~spl0_14 | ~spl0_15)),
% 1.29/1.17 inference(subsumption_resolution,[status(thm)],[f422,f370])).
% 1.29/1.17 thf(f370,plain,(
% 1.29/1.17 ((h @ $true) = $true) | (spl0_3 | ~spl0_6)),
% 1.29/1.17 inference(subsumption_resolution,[status(thm)],[f363,f37])).
% 1.29/1.17 thf(f37,plain,(
% 1.29/1.17 ((h @ $false) != $false) | spl0_3),
% 1.29/1.17 inference(avatar_component_clause,[status(thm)],[f36])).
% 1.29/1.17 thf(f36,definition,(
% 1.29/1.17 spl0_3 <=> ((h @ $false) = $false)),
% 1.29/1.17 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.29/1.17 thf(f363,plain,(
% 1.29/1.17 ((h @ $false) = $false) | ((h @ $true) = $true) | ~spl0_6),
% 1.29/1.17 inference(binary_proxy_clausification,[status(thm)],[f304])).
% 1.29/1.17 thf(f304,plain,(
% 1.29/1.17 ((h @ $false) = (h @ $true)) | ~spl0_6),
% 1.29/1.17 inference(leibniz_equality_elimination,[status(thm)],[f57])).
% 1.29/1.17 thf(f57,plain,(
% 1.29/1.17 ( ! [X1 : $o > $o] : (((X1 @ (h @ $true)) = $false) | ((X1 @ (h @ $false)) = $true)) ) | ~spl0_6),
% 1.29/1.17 inference(avatar_component_clause,[status(thm)],[f56])).
% 1.29/1.17 thf(f422,plain,(
% 1.29/1.17 ((h @ $true) != $true) | (~spl0_1 | ~spl0_14 | ~spl0_15)),
% 1.29/1.17 inference(trivial_inequality_removal,[status(thm)],[f408])).
% 1.29/1.17 thf(f408,plain,(
% 1.29/1.17 ((h @ $true) != $true) | ($true = $false) | (~spl0_1 | ~spl0_14 | ~spl0_15)),
% 1.29/1.17 inference(constrained_superposition,[status(thm)],[f396,f399])).
% 1.29/1.17 thf(f399,plain,(
% 1.29/1.17 ((sK5 @ $true) = $false) | (~spl0_1 | ~spl0_14)),
% 1.29/1.17 inference(superposition,[status(thm)],[f391,f29])).
% 1.29/1.17 thf(f391,plain,(
% 1.29/1.17 ($false = (sK5 @ (h @ $false))) | ~spl0_14),
% 1.29/1.17 inference(avatar_component_clause,[status(thm)],[f389])).
% 1.29/1.17 thf(f389,definition,(
% 1.29/1.17 spl0_14 <=> ($false = (sK5 @ (h @ $false)))),
% 1.29/1.17 introduced(definition,[new_symbols(naming,[spl0_14])],[avatar_definition])).
% 1.29/1.17 thf(f396,plain,(
% 1.29/1.17 ((sK5 @ (h @ $true)) = $true) | ~spl0_15),
% 1.29/1.17 inference(avatar_component_clause,[status(thm)],[f394])).
% 1.29/1.17 thf(f394,definition,(
% 1.29/1.17 spl0_15 <=> ((sK5 @ (h @ $true)) = $true)),
% 1.29/1.17 introduced(definition,[new_symbols(naming,[spl0_15])],[avatar_definition])).
% 1.29/1.17 thf(f397,plain,(
% 1.29/1.17 spl0_15 | spl0_10 | spl0_3 | ~spl0_6),
% 1.29/1.17 inference(avatar_split_clause,[status(thm)],[f387,f56,f36,f282,f394])).
% 1.29/1.17 thf(f387,plain,(
% 1.29/1.17 ((sK1 @ $true) = $true) | ((sK5 @ (h @ $true)) = $true) | (spl0_3 | ~spl0_6)),
% 1.29/1.17 inference(binary_proxy_clausification,[status(thm)],[f385])).
% 1.29/1.17 thf(f385,plain,(
% 1.29/1.17 ((sK1 @ $true) = $true) | (((sK5 @ (h @ $true)) => (sK5 @ (h @ $false))) = $false) | (spl0_3 | ~spl0_6)),
% 1.29/1.17 inference(beta_eta_normalization,[status(thm)],[f384])).
% 1.29/1.17 thf(f384,plain,(
% 1.29/1.17 ((sK1 @ $true) = $true) | (((^[Y0 : $o > $o]: ((Y0 @ (h @ $true)) => (Y0 @ (h @ $false)))) @ sK5) = $false) | (spl0_3 | ~spl0_6)),
% 1.29/1.17 inference(sigma_clausification,[status(thm)],[f374])).
% 1.29/1.17 thf(f374,plain,(
% 1.29/1.17 ((sK1 @ $true) = $true) | ($true != (!! @ ($o > $o) @ (^[Y0 : $o > $o]: ((Y0 @ (h @ $true)) => (Y0 @ (h @ $false)))))) | (spl0_3 | ~spl0_6)),
% 1.29/1.17 inference(constrained_superposition,[status(thm)],[f17,f370])).
% 1.29/1.17 thf(f392,plain,(
% 1.29/1.17 spl0_10 | spl0_14 | spl0_3 | ~spl0_6),
% 1.29/1.17 inference(avatar_split_clause,[status(thm)],[f386,f56,f36,f389,f282])).
% 1.29/1.17 thf(f386,plain,(
% 1.29/1.17 ($false = (sK5 @ (h @ $false))) | ((sK1 @ $true) = $true) | (spl0_3 | ~spl0_6)),
% 1.29/1.17 inference(binary_proxy_clausification,[status(thm)],[f385])).
% 1.29/1.17 thf(f303,plain,(
% 1.29/1.17 spl0_3 | ~spl0_8),
% 1.29/1.17 inference(avatar_contradiction_clause,[status(thm)],[f302])).
% 1.29/1.17 thf(f302,plain,(
% 1.29/1.17 $false | (spl0_3 | ~spl0_8)),
% 1.29/1.17 inference(subsumption_resolution,[status(thm)],[f233,f37])).
% 1.29/1.17 thf(f233,plain,(
% 1.29/1.17 ((h @ $false) = $false) | ~spl0_8),
% 1.29/1.17 inference(leibniz_equality_elimination,[status(thm)],[f141])).
% 1.29/1.17 thf(f141,plain,(
% 1.29/1.17 ( ! [X0 : $o > $o] : (((X0 @ (h @ $false)) = $true) | ((X0 @ $false) = $false)) ) | ~spl0_8),
% 1.29/1.17 inference(avatar_component_clause,[status(thm)],[f140])).
% 1.29/1.17 thf(f140,definition,(
% 1.29/1.17 spl0_8 <=> ! [X0 : $o > $o] : (((X0 @ $false) = $false) | ((X0 @ (h @ $false)) = $true))),
% 1.29/1.17 introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition])).
% 1.29/1.17 thf(f200,plain,(
% 1.29/1.17 ~spl0_3 | spl0_5 | ~spl0_7),
% 1.29/1.17 inference(avatar_contradiction_clause,[status(thm)],[f199])).
% 1.29/1.17 thf(f199,plain,(
% 1.29/1.17 $false | (~spl0_3 | spl0_5 | ~spl0_7)),
% 1.29/1.17 inference(subsumption_resolution,[status(thm)],[f188,f137])).
% 1.29/1.17 thf(f137,plain,(
% 1.29/1.17 ((h @ $true) = $false) | ~spl0_7),
% 1.29/1.17 inference(avatar_component_clause,[status(thm)],[f135])).
% 1.29/1.17 thf(f135,definition,(
% 1.29/1.17 spl0_7 <=> ((h @ $true) = $false)),
% 1.29/1.17 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 1.29/1.17 thf(f188,plain,(
% 1.29/1.17 ((h @ $true) != $false) | (~spl0_3 | spl0_5 | ~spl0_7)),
% 1.29/1.17 inference(trivial_inequality_removal,[status(thm)],[f184])).
% 1.29/1.17 thf(f184,plain,(
% 1.29/1.17 ($true = $false) | ((h @ $true) != $false) | (~spl0_3 | spl0_5 | ~spl0_7)),
% 1.29/1.17 inference(constrained_superposition,[status(thm)],[f179,f181])).
% 1.29/1.17 thf(f181,plain,(
% 1.29/1.17 ((sK3 @ $false) = $false) | (~spl0_3 | spl0_5 | ~spl0_7)),
% 1.29/1.17 inference(superposition,[status(thm)],[f178,f38])).
% 1.29/1.17 thf(f38,plain,(
% 1.29/1.17 ((h @ $false) = $false) | ~spl0_3),
% 1.29/1.17 inference(avatar_component_clause,[status(thm)],[f36])).
% 1.29/1.17 thf(f178,plain,(
% 1.29/1.17 ((sK3 @ (h @ $false)) = $false) | (spl0_5 | ~spl0_7)),
% 1.29/1.17 inference(subsumption_resolution,[status(thm)],[f176,f53])).
% 1.29/1.17 thf(f53,plain,(
% 1.29/1.17 ((sK1 @ $false) != $true) | spl0_5),
% 1.29/1.17 inference(avatar_component_clause,[status(thm)],[f52])).
% 1.29/1.17 thf(f52,definition,(
% 1.29/1.17 spl0_5 <=> ((sK1 @ $false) = $true)),
% 1.29/1.17 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.29/1.17 thf(f176,plain,(
% 1.29/1.17 ((sK1 @ $false) = $true) | ((sK3 @ (h @ $false)) = $false) | ~spl0_7),
% 1.29/1.17 inference(binary_proxy_clausification,[status(thm)],[f175])).
% 1.29/1.17 thf(f175,plain,(
% 1.29/1.17 ((sK1 @ $false) = $true) | ($false = ((sK3 @ (h @ $true)) => (sK3 @ (h @ $false)))) | ~spl0_7),
% 1.29/1.17 inference(beta_eta_normalization,[status(thm)],[f174])).
% 1.29/1.17 thf(f174,plain,(
% 1.29/1.17 (((^[Y0 : $o > $o]: ((Y0 @ (h @ $true)) => (Y0 @ (h @ $false)))) @ sK3) = $false) | ((sK1 @ $false) = $true) | ~spl0_7),
% 1.29/1.17 inference(sigma_clausification,[status(thm)],[f171])).
% 1.29/1.17 thf(f171,plain,(
% 1.29/1.17 ($true != (!! @ ($o > $o) @ (^[Y0 : $o > $o]: ((Y0 @ (h @ $true)) => (Y0 @ (h @ $false)))))) | ((sK1 @ $false) = $true) | ~spl0_7),
% 1.29/1.17 inference(constrained_superposition,[status(thm)],[f17,f137])).
% 1.29/1.17 thf(f179,plain,(
% 1.29/1.17 ($true = (sK3 @ (h @ $true))) | (spl0_5 | ~spl0_7)),
% 1.29/1.17 inference(subsumption_resolution,[status(thm)],[f177,f53])).
% 1.29/1.17 thf(f177,plain,(
% 1.29/1.17 ($true = (sK3 @ (h @ $true))) | ((sK1 @ $false) = $true) | ~spl0_7),
% 1.29/1.17 inference(binary_proxy_clausification,[status(thm)],[f175])).
% 1.29/1.17 thf(f160,plain,(
% 1.29/1.17 ~spl0_1 | ~spl0_3),
% 1.29/1.17 inference(avatar_contradiction_clause,[status(thm)],[f159])).
% 1.29/1.17 thf(f159,plain,(
% 1.29/1.17 $false | (~spl0_1 | ~spl0_3)),
% 1.29/1.17 inference(trivial_inequality_removal,[status(thm)],[f153])).
% 1.29/1.17 thf(f153,plain,(
% 1.29/1.17 ($true = $false) | (~spl0_1 | ~spl0_3)),
% 1.29/1.17 inference(superposition,[status(thm)],[f38,f29])).
% 1.29/1.17 thf(f145,plain,(
% 1.29/1.17 spl0_7 | spl0_1 | ~spl0_6),
% 1.29/1.17 inference(avatar_split_clause,[status(thm)],[f110,f56,f27,f135])).
% 1.29/1.17 thf(f110,plain,(
% 1.29/1.17 ((h @ $true) = $false) | ((h @ $false) = $true) | ~spl0_6),
% 1.29/1.17 inference(binary_proxy_clausification,[status(thm)],[f83])).
% 1.29/1.17 thf(f83,plain,(
% 1.29/1.17 ((h @ $false) = (h @ $true)) | ~spl0_6),
% 1.29/1.17 inference(leibniz_equality_elimination,[status(thm)],[f57])).
% 1.29/1.17 thf(f142,plain,(
% 1.29/1.17 spl0_1 | spl0_8 | ~spl0_6),
% 1.29/1.17 inference(avatar_split_clause,[status(thm)],[f129,f56,f140,f27])).
% 1.29/1.17 thf(f129,plain,(
% 1.29/1.17 ( ! [X0 : $o > $o] : (((h @ $false) = $true) | ((X0 @ $false) = $false) | ((X0 @ (h @ $false)) = $true)) ) | ~spl0_6),
% 1.29/1.17 inference(beta_eta_normalization,[status(thm)],[f91])).
% 1.29/1.17 thf(f91,plain,(
% 1.29/1.17 ( ! [X0 : $o > $o] : (($true = ((^[Y0 : $o]: (Y0)) @ (h @ $false))) | ((X0 @ (h @ $false)) = $true) | ((X0 @ $false) = $false)) ) | ~spl0_6),
% 1.29/1.17 inference(superposition,[status(thm)],[f57,f57])).
% 1.29/1.17 thf(f78,plain,(
% 1.29/1.17 ~spl0_3 | ~spl0_5),
% 1.29/1.17 inference(avatar_contradiction_clause,[status(thm)],[f77])).
% 1.29/1.17 thf(f77,plain,(
% 1.29/1.17 $false | (~spl0_3 | ~spl0_5)),
% 1.29/1.17 inference(subsumption_resolution,[status(thm)],[f71,f38])).
% 1.29/1.17 thf(f71,plain,(
% 1.29/1.17 ((h @ $false) != $false) | ~spl0_5),
% 1.29/1.17 inference(trivial_inequality_removal,[status(thm)],[f68])).
% 1.29/1.17 thf(f68,plain,(
% 1.29/1.17 ($true = $false) | ((h @ $false) != $false) | ~spl0_5),
% 1.29/1.17 inference(constrained_superposition,[status(thm)],[f16,f54])).
% 1.29/1.17 thf(f54,plain,(
% 1.29/1.17 ((sK1 @ $false) = $true) | ~spl0_5),
% 1.29/1.17 inference(avatar_component_clause,[status(thm)],[f52])).
% 1.29/1.17 thf(f44,plain,(
% 1.29/1.17 spl0_1 | spl0_2),
% 1.29/1.17 inference(avatar_split_clause,[status(thm)],[f21,f31,f27])).
% 1.29/1.17 thf(f21,plain,(
% 1.29/1.17 ((h @ $false) = $true) | ((h @ (!! @ ($o > $o) @ (^[Y0 : $o > $o]: ((Y0 @ (h @ $true)) => (Y0 @ (h @ $false)))))) = $true)),
% 1.29/1.17 inference(binary_proxy_clausification,[status(thm)],[f20])).
% 1.29/1.17 thf(f20,plain,(
% 1.29/1.17 ((h @ (!! @ ($o > $o) @ (^[Y0 : $o > $o]: ((Y0 @ (h @ $true)) => (Y0 @ (h @ $false)))))) != (h @ $false))),
% 1.29/1.17 inference(trivial_inequality_removal,[status(thm)],[f18])).
% 1.29/1.17 thf(f18,plain,(
% 1.29/1.17 ($true = $false) | ((h @ (!! @ ($o > $o) @ (^[Y0 : $o > $o]: ((Y0 @ (h @ $true)) => (Y0 @ (h @ $false)))))) != (h @ $false))),
% 1.29/1.17 inference(constrained_superposition,[status(thm)],[f17,f16])).
% 1.29/1.17 % SZS output end Proof for DTF2THF_14039
% 1.29/1.17 % (14138)------------------------------
% 1.29/1.17 % (14138)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.29/1.17 % (14138)Termination reason: Refutation
% 1.29/1.17
% 1.29/1.17 % (14138)Memory used [KB]: 5884
% 1.29/1.17 % (14138)Time elapsed: 0.017 s
% 1.29/1.17 % (14138)Instructions burned: 41 (million)
% 1.29/1.17 % (14138)------------------------------
% 1.29/1.17 % (14138)------------------------------
% 1.29/1.17 % (14137)Success in time 0.013 s
%------------------------------------------------------------------------------