%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU856^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/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 09:37:36 AM UTC 2026
% Result : Theorem 1.78s 1.50s
% Output : Refutation 1.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 94 ( 1 unt; 0 typ; 10 def)
% Number of atoms : 503 ( 114 equ; 0 cnn)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 571 ( 163 ~; 161 |; 58 &; 173 @)
% ( 14 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 15 con; 0-2 aty)
% Number of variables : 69 ( 42 ^; 21 !; 6 ?; 69 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_9,type,
sK0: a > $o ).
thf(func_def_10,type,
sK1: a > $o ).
thf(func_def_12,type,
ph3:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
sK4: a ).
thf(func_def_14,type,
sK5: a ).
thf(func_def_15,type,
sK6: a ).
thf(f216,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f20,f21,f33,f42,f56,f77,f111,f121,f122,f137,f140,f150,f202,f215]) ).
thf(f215,plain,
( ~ spl2_4
| ~ spl2_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f214]) ).
thf(f214,plain,
( $false
| ~ spl2_4
| ~ spl2_6 ),
inference(trivial_inequality_removal,[status(thm)],[f211]) ).
thf(f211,plain,
( ( $false = $true )
| ~ spl2_4
| ~ spl2_6 ),
inference(superposition,[status(thm)],[f32,f41]) ).
thf(f41,plain,
( ( ( sK0 @ sK4 )
= $false )
| ~ spl2_6 ),
inference(avatar_component_clause,[status(thm)],[f39]) ).
thf(f39,definition,
( spl2_6
<=> ( ( sK0 @ sK4 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl2_6])],[avatar_definition]) ).
thf(f32,plain,
( ( ( sK0 @ sK4 )
= $true )
| ~ spl2_4 ),
inference(avatar_component_clause,[status(thm)],[f30]) ).
thf(f30,definition,
( spl2_4
<=> ( ( sK0 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition]) ).
thf(f202,plain,
( spl2_6
| ~ spl2_2
| ~ spl2_5 ),
inference(avatar_split_clause,[status(thm)],[f193,f35,f17,f39]) ).
thf(f17,definition,
( spl2_2
<=> ( ( ^ [Y0: a] :
( ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
= ( ^ [Y0: a] : $false ) ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f35,definition,
( spl2_5
<=> ( ( sK1 @ sK4 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl2_5])],[avatar_definition]) ).
thf(f193,plain,
( ( ( sK0 @ sK4 )
= $false )
| ~ spl2_2
| ~ spl2_5 ),
inference(trivial_inequality_removal,[status(thm)],[f188]) ).
thf(f188,plain,
( ( ( sK0 @ sK4 )
= $false )
| ( $false = $true )
| ~ spl2_2
| ~ spl2_5 ),
inference(superposition,[status(thm)],[f37,f181]) ).
thf(f181,plain,
( ! [X1: a] :
( ( ( sK1 @ X1 )
= $true )
| ( ( sK0 @ X1 )
= $false ) )
| ~ spl2_2 ),
inference(not_proxy_clausification,[status(thm)],[f180]) ).
thf(f180,plain,
( ! [X1: a] :
( ( ( ~ ( sK1 @ X1 ) )
= $false )
| ( ( sK0 @ X1 )
= $false ) )
| ~ spl2_2 ),
inference(binary_proxy_clausification,[status(thm)],[f179]) ).
thf(f179,plain,
( ! [X1: a] :
( $false
= ( ~ ( sK1 @ X1 )
& ( sK0 @ X1 ) ) )
| ~ spl2_2 ),
inference(binary_proxy_clausification,[status(thm)],[f177]) ).
thf(f177,plain,
( ! [X1: a] :
( $false
= ( ( ~ ( sK1 @ X1 )
& ( sK0 @ X1 ) )
| ( ~ ( sK0 @ X1 )
& ( sK1 @ X1 ) ) ) )
| ~ spl2_2 ),
inference(beta_eta_normalization,[status(thm)],[f176]) ).
thf(f176,plain,
( ! [X1: a] :
( ( ^ [Y0: a] : $false
@ X1 )
= ( ^ [Y0: a] :
( ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
@ X1 ) )
| ~ spl2_2 ),
inference(argument_congruence,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ( ^ [Y0: a] :
( ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
= ( ^ [Y0: a] : $false ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f17]) ).
thf(f37,plain,
( ( ( sK1 @ sK4 )
= $false )
| ~ spl2_5 ),
inference(avatar_component_clause,[status(thm)],[f35]) ).
thf(f150,plain,
( ~ spl2_1
| spl2_9
| ~ spl2_10 ),
inference(avatar_contradiction_clause,[status(thm)],[f149]) ).
thf(f149,plain,
( $false
| ~ spl2_1
| spl2_9
| ~ spl2_10 ),
inference(subsumption_resolution,[status(thm)],[f145,f114]) ).
thf(f114,plain,
( ( ( sK0 @ sK5 )
!= $false )
| spl2_9 ),
inference(avatar_component_clause,[status(thm)],[f113]) ).
thf(f113,definition,
( spl2_9
<=> ( ( sK0 @ sK5 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl2_9])],[avatar_definition]) ).
thf(f145,plain,
( ( ( sK0 @ sK5 )
= $false )
| ~ spl2_1
| ~ spl2_10 ),
inference(trivial_inequality_removal,[status(thm)],[f144]) ).
thf(f144,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( $false = $true )
| ~ spl2_1
| ~ spl2_10 ),
inference(superposition,[status(thm)],[f80,f120]) ).
thf(f120,plain,
( ( ( sK1 @ sK5 )
= $false )
| ~ spl2_10 ),
inference(avatar_component_clause,[status(thm)],[f118]) ).
thf(f118,definition,
( spl2_10
<=> ( ( sK1 @ sK5 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl2_10])],[avatar_definition]) ).
thf(f80,plain,
( ! [X1: a] :
( ( ( sK1 @ X1 )
= $true )
| ( ( sK0 @ X1 )
= $false ) )
| ~ spl2_1 ),
inference(binary_proxy_clausification,[status(thm)],[f78]) ).
thf(f78,plain,
( ! [X1: a] :
( ( sK0 @ X1 )
= ( sK1 @ X1 ) )
| ~ spl2_1 ),
inference(argument_congruence,[status(thm)],[f14]) ).
thf(f14,plain,
( ( sK1 = sK0 )
| ~ spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f13]) ).
thf(f13,definition,
( spl2_1
<=> ( sK1 = sK0 ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f140,plain,
( ~ spl2_7
| ~ spl2_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f139]) ).
thf(f139,plain,
( $false
| ~ spl2_7
| ~ spl2_9 ),
inference(trivial_inequality_removal,[status(thm)],[f138]) ).
thf(f138,plain,
( ( $false = $true )
| ~ spl2_7
| ~ spl2_9 ),
inference(forward_demodulation,[status(thm)],[f106,f115]) ).
thf(f115,plain,
( ( ( sK0 @ sK5 )
= $false )
| ~ spl2_9 ),
inference(avatar_component_clause,[status(thm)],[f113]) ).
thf(f106,plain,
( ( ( sK0 @ sK5 )
= $true )
| ~ spl2_7 ),
inference(avatar_component_clause,[status(thm)],[f104]) ).
thf(f104,definition,
( spl2_7
<=> ( ( sK0 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_7])],[avatar_definition]) ).
thf(f137,plain,
( ~ spl2_1
| ~ spl2_8
| ~ spl2_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f136]) ).
thf(f136,plain,
( $false
| ~ spl2_1
| ~ spl2_8
| ~ spl2_9 ),
inference(trivial_inequality_removal,[status(thm)],[f135]) ).
thf(f135,plain,
( ( $false = $true )
| ~ spl2_1
| ~ spl2_8
| ~ spl2_9 ),
inference(forward_demodulation,[status(thm)],[f130,f115]) ).
thf(f130,plain,
( ( ( sK0 @ sK5 )
= $true )
| ~ spl2_1
| ~ spl2_8 ),
inference(trivial_inequality_removal,[status(thm)],[f128]) ).
thf(f128,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( $false = $true )
| ~ spl2_1
| ~ spl2_8 ),
inference(superposition,[status(thm)],[f110,f79]) ).
thf(f79,plain,
( ! [X1: a] :
( ( ( sK1 @ X1 )
= $false )
| ( ( sK0 @ X1 )
= $true ) )
| ~ spl2_1 ),
inference(binary_proxy_clausification,[status(thm)],[f78]) ).
thf(f110,plain,
( ( ( sK1 @ sK5 )
= $true )
| ~ spl2_8 ),
inference(avatar_component_clause,[status(thm)],[f108]) ).
thf(f108,definition,
( spl2_8
<=> ( ( sK1 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_8])],[avatar_definition]) ).
thf(f122,plain,
( spl2_10
| spl2_9
| spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f98,f17,f113,f118]) ).
thf(f98,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( ( sK1 @ sK5 )
= $false )
| spl2_2 ),
inference(not_proxy_clausification,[status(thm)],[f97]) ).
thf(f97,plain,
( ( ( ~ ( sK0 @ sK5 ) )
= $true )
| ( ( sK1 @ sK5 )
= $false )
| spl2_2 ),
inference(not_proxy_clausification,[status(thm)],[f96]) ).
thf(f96,plain,
( ( ( ~ ( sK1 @ sK5 ) )
= $true )
| ( ( ~ ( sK0 @ sK5 ) )
= $true )
| spl2_2 ),
inference(binary_proxy_clausification,[status(thm)],[f94]) ).
thf(f94,plain,
( ( ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) )
= $true )
| ( ( ~ ( sK1 @ sK5 ) )
= $true )
| spl2_2 ),
inference(binary_proxy_clausification,[status(thm)],[f92]) ).
thf(f92,plain,
( ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
= $true )
| ( ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) )
= $true )
| spl2_2 ),
inference(binary_proxy_clausification,[status(thm)],[f91]) ).
thf(f91,plain,
( ( ( ( ~ ( sK1 @ sK5 )
& ( sK0 @ sK5 ) )
| ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) ) )
!= $false )
| spl2_2 ),
inference(beta_eta_normalization,[status(thm)],[f90]) ).
thf(f90,plain,
( ( ( ^ [Y0: a] :
( ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
@ sK5 )
!= ( ^ [Y0: a] : $false
@ sK5 ) )
| spl2_2 ),
inference(negative_extensionality,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ( ^ [Y0: a] :
( ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
!= ( ^ [Y0: a] : $false ) )
| spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f17]) ).
thf(f121,plain,
( spl2_10
| spl2_8
| spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f99,f17,f108,f118]) ).
thf(f99,plain,
( ( ( sK1 @ sK5 )
= $true )
| ( ( sK1 @ sK5 )
= $false )
| spl2_2 ),
inference(not_proxy_clausification,[status(thm)],[f95]) ).
thf(f95,plain,
( ( ( sK1 @ sK5 )
= $true )
| ( ( ~ ( sK1 @ sK5 ) )
= $true )
| spl2_2 ),
inference(binary_proxy_clausification,[status(thm)],[f94]) ).
thf(f111,plain,
( spl2_7
| spl2_8
| spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f100,f17,f108,f104]) ).
thf(f100,plain,
( ( ( sK1 @ sK5 )
= $true )
| ( ( sK0 @ sK5 )
= $true )
| spl2_2 ),
inference(binary_proxy_clausification,[status(thm)],[f93]) ).
thf(f93,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( ( ~ ( sK0 @ sK5 )
& ( sK1 @ sK5 ) )
= $true )
| spl2_2 ),
inference(binary_proxy_clausification,[status(thm)],[f92]) ).
thf(f77,plain,
( ~ spl2_2
| ~ spl2_3
| ~ spl2_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f76]) ).
thf(f76,plain,
( $false
| ~ spl2_2
| ~ spl2_3
| ~ spl2_6 ),
inference(trivial_inequality_removal,[status(thm)],[f75]) ).
thf(f75,plain,
( ( $false = $true )
| ~ spl2_2
| ~ spl2_3
| ~ spl2_6 ),
inference(forward_demodulation,[status(thm)],[f64,f41]) ).
thf(f64,plain,
( ( ( sK0 @ sK4 )
= $true )
| ~ spl2_2
| ~ spl2_3 ),
inference(trivial_inequality_removal,[status(thm)],[f59]) ).
thf(f59,plain,
( ( ( sK0 @ sK4 )
= $true )
| ( $false = $true )
| ~ spl2_2
| ~ spl2_3 ),
inference(superposition,[status(thm)],[f50,f28]) ).
thf(f28,plain,
( ( ( sK1 @ sK4 )
= $true )
| ~ spl2_3 ),
inference(avatar_component_clause,[status(thm)],[f26]) ).
thf(f26,definition,
( spl2_3
<=> ( ( sK1 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition]) ).
thf(f50,plain,
( ! [X1: a] :
( ( ( sK1 @ X1 )
= $false )
| ( ( sK0 @ X1 )
= $true ) )
| ~ spl2_2 ),
inference(not_proxy_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
( ! [X1: a] :
( ( ( ~ ( sK0 @ X1 ) )
= $false )
| ( ( sK1 @ X1 )
= $false ) )
| ~ spl2_2 ),
inference(binary_proxy_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
( ! [X1: a] :
( ( ~ ( sK0 @ X1 )
& ( sK1 @ X1 ) )
= $false )
| ~ spl2_2 ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
( ! [X1: a] :
( $false
= ( ( ~ ( sK1 @ X1 )
& ( sK0 @ X1 ) )
| ( ~ ( sK0 @ X1 )
& ( sK1 @ X1 ) ) ) )
| ~ spl2_2 ),
inference(beta_eta_normalization,[status(thm)],[f43]) ).
thf(f43,plain,
( ! [X1: a] :
( ( ^ [Y0: a] : $false
@ X1 )
= ( ^ [Y0: a] :
( ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
@ X1 ) )
| ~ spl2_2 ),
inference(argument_congruence,[status(thm)],[f18]) ).
thf(f56,plain,
( ~ spl2_3
| ~ spl2_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f55]) ).
thf(f55,plain,
( $false
| ~ spl2_3
| ~ spl2_5 ),
inference(trivial_inequality_removal,[status(thm)],[f51]) ).
thf(f51,plain,
( ( $false = $true )
| ~ spl2_3
| ~ spl2_5 ),
inference(superposition,[status(thm)],[f37,f28]) ).
thf(f42,plain,
( spl2_5
| spl2_6
| spl2_1 ),
inference(avatar_split_clause,[status(thm)],[f24,f13,f39,f35]) ).
thf(f24,plain,
( ( ( sK1 @ sK4 )
= $false )
| ( ( sK0 @ sK4 )
= $false )
| spl2_1 ),
inference(binary_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ( sK1 @ sK4 )
!= ( sK0 @ sK4 ) )
| spl2_1 ),
inference(negative_extensionality,[status(thm)],[f15]) ).
thf(f15,plain,
( ( sK1 != sK0 )
| spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f13]) ).
thf(f33,plain,
( spl2_3
| spl2_4
| spl2_1 ),
inference(avatar_split_clause,[status(thm)],[f23,f13,f30,f26]) ).
thf(f23,plain,
( ( ( sK1 @ sK4 )
= $true )
| ( ( sK0 @ sK4 )
= $true )
| spl2_1 ),
inference(binary_proxy_clausification,[status(thm)],[f22]) ).
thf(f21,plain,
( spl2_2
| spl2_1 ),
inference(avatar_split_clause,[status(thm)],[f10,f13,f17]) ).
thf(f10,plain,
( ( ( ^ [Y0: a] :
( ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
= ( ^ [Y0: a] : $false ) )
| ( sK1 = sK0 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ( sK1 != sK0 )
| ( ( ^ [Y0: a] :
( ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
!= ( ^ [Y0: a] : $false ) ) )
& ( ( sK1 = sK0 )
| ( ( ^ [Y0: a] :
( ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
= ( ^ [Y0: a] : $false ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f8]) ).
thf(f8,plain,
( ? [X0: a > $o,X1: a > $o] :
( ( ( X0 != X1 )
| ( ( ^ [Y0: a] :
( ( ~ ( X1 @ Y0 )
& ( X0 @ Y0 ) )
| ( ~ ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) )
!= ( ^ [Y0: a] : $false ) ) )
& ( ( X0 = X1 )
| ( ( ^ [Y0: a] :
( ( ~ ( X1 @ Y0 )
& ( X0 @ Y0 ) )
| ( ~ ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) )
= ( ^ [Y0: a] : $false ) ) ) )
=> ( ( ( sK1 != sK0 )
| ( ( ^ [Y0: a] :
( ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
!= ( ^ [Y0: a] : $false ) ) )
& ( ( sK1 = sK0 )
| ( ( ^ [Y0: a] :
( ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
= ( ^ [Y0: a] : $false ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
? [X0: a > $o,X1: a > $o] :
( ( ( X0 != X1 )
| ( ( ^ [Y0: a] :
( ( ~ ( X1 @ Y0 )
& ( X0 @ Y0 ) )
| ( ~ ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) )
!= ( ^ [Y0: a] : $false ) ) )
& ( ( X0 = X1 )
| ( ( ^ [Y0: a] :
( ( ~ ( X1 @ Y0 )
& ( X0 @ Y0 ) )
| ( ~ ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) )
= ( ^ [Y0: a] : $false ) ) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o] :
( ( ( ^ [Y0: a] :
( ( ~ ( X1 @ Y0 )
& ( X0 @ Y0 ) )
| ( ~ ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) )
= ( ^ [Y0: a] : $false ) )
<~> ( X0 = X1 ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( X0 = X1 )
<=> ( ( ^ [Y0: a] :
( ( ~ ( X1 @ Y0 )
& ( X0 @ Y0 ) )
| ( ~ ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) )
= ( ^ [Y0: a] : $false ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( X0 = X1 )
<=> ( ( ^ [X2: a] :
( ( ( X1 @ X2 )
& ~ ( X0 @ X2 ) )
| ( ( X0 @ X2 )
& ~ ( X1 @ X2 ) ) ) )
= ( ^ [X3: a] : $false ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a > $o,X0: a > $o] :
( ( X0 = X1 )
<=> ( ( ^ [X2: a] :
( ( ( X0 @ X2 )
& ~ ( X1 @ X2 ) )
| ( ( X1 @ X2 )
& ~ ( X0 @ X2 ) ) ) )
= ( ^ [X3: a] : $false ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: a > $o,X0: a > $o] :
( ( X0 = X1 )
<=> ( ( ^ [X2: a] :
( ( ( X0 @ X2 )
& ~ ( X1 @ X2 ) )
| ( ( X1 @ X2 )
& ~ ( X0 @ X2 ) ) ) )
= ( ^ [X3: a] : $false ) ) ),
file('/export/starexec/sandbox/tmp/tmp.BwkXj8rEJz/DTF2THF_30461.p',cGAZING_THM46_pme) ).
thf(f20,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f11,f17,f13]) ).
thf(f11,plain,
( ( ( ^ [Y0: a] :
( ( ~ ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
!= ( ^ [Y0: a] : $false ) )
| ( sK1 != sK0 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU856^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n029.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 12:35:44 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.49 ---- Original DTF file ---
% 0.29/0.49 thf(spec,logic,$$dhol).
% 0.29/0.49 %------------------------------------------------------------------------------
% 0.29/0.49 % File : SEU856^5 : TPTP v9.2.1. Released v4.0.0.
% 0.29/0.49 % Domain : Set Theory
% 0.29/0.49 % Problem : TPS problem GAZING-THM46
% 0.29/0.49 % Version : Especial.
% 0.29/0.49 % English :
% 0.29/0.49
% 0.29/0.49 % Refs : [Bar92] Barker-Plummer D (1992), Gazing: An Approach to the Pr
% 0.29/0.49 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.49 % Source : [Bro09]
% 0.29/0.49 % Names : tps_0450 [Bro09]
% 0.29/0.49 % : 46 [Bar92]
% 0.29/0.49 % : GAZING-THM46 [TPS]
% 0.29/0.49
% 0.29/0.49 % Status : Theorem
% 0.29/0.49 % Rating : 0.00 v8.2.0, 0.15 v8.1.0, 0.18 v7.5.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v6.0.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.29/0.49 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.29/0.49 % Number of atoms : 3 ( 2 equ; 0 cnn)
% 0.29/0.49 % Maximal formula atoms : 2 ( 3 avg)
% 0.29/0.49 % Number of connectives : 10 ( 2 ~; 1 |; 2 &; 4 @)
% 0.29/0.49 % ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% 0.29/0.49 % Maximal formula depth : 4 ( 4 avg)
% 0.29/0.49 % Number of types : 2 ( 1 usr)
% 0.29/0.49 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.29/0.49 % Number of symbols : 2 ( 0 usr; 1 con; 0-2 aty)
% 0.29/0.49 % Number of variables : 4 ( 2 ^; 2 !; 0 ?; 4 :)
% 0.29/0.49 % SPC : TH0_THM_EQU_NAR
% 0.29/0.49
% 0.29/0.49 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.29/0.49 % project in the Department of Mathematical Sciences at Carnegie
% 0.29/0.49 % Mellon University. Distributed under the Creative Commons copyleft
% 0.29/0.49 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.29/0.49 % : Polymorphic definitions expanded.
% 0.29/0.49 %------------------------------------------------------------------------------
% 0.29/0.49 thf(a_type,type,
% 0.29/0.49 a: $tType ).
% 0.29/0.49
% 0.29/0.49 thf(cGAZING_THM46_pme,conjecture,
% 0.29/0.49 ! [S: a > $o,T: a > $o] :
% 0.29/0.49 ( ( S = T )
% 0.29/0.49 <=> ( ( ^ [Xz: a] :
% 0.29/0.49 ( ( ( T @ Xz )
% 0.29/0.49 & ~ ( S @ Xz ) )
% 0.29/0.49 | ( ( S @ Xz )
% 0.29/0.49 & ~ ( T @ Xz ) ) ) )
% 0.29/0.49 = ( ^ [Xx: a] : $false ) ) ) ).
% 0.29/0.49
% 0.29/0.49 %------------------------------------------------------------------------------
% 0.29/0.49 ------------------------
% 1.64/1.46 ---- Embedded in THF ---
% 1.64/1.46 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.64/1.46 %%% Generated on Tue Feb 24 12:35:45 EST 2026
% 1.64/1.46 %%% using '$$dhol' embedding, version 1.3.0.
% 1.64/1.46 %%% Logic specification used:
% 1.64/1.46 %%% thf(spec, logic, $$dhol).
% 1.64/1.46
% 1.64/1.46 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.BwkXj8rEJz/DTF2DTF30461.p
% See solution above
% 1.64/1.46 ------------------------
% 1.64/1.47 ---- Cleaned THF ---
% 1.64/1.47 thf(a_type,type,
% 1.64/1.47 a: $tType ).
% 1.64/1.47
% 1.64/1.47 thf(cGAZING_THM46_pme,conjecture,
% 1.64/1.47 ! [S: a > $o,T: a > $o] :
% 1.64/1.47 ( ( S = T )
% 1.64/1.47 <=> ( ( ^ [Xz: a] :
% 1.64/1.47 ( ( ( T @ Xz )
% 1.64/1.47 & ~ ( S @ Xz ) )
% 1.64/1.47 | ( ( S @ Xz )
% 1.64/1.47 & ~ ( T @ Xz ) ) ) )
% 1.64/1.47 = ( ^ [Xx: a] : $false ) ) ) ).
% 1.64/1.47 ------------------------
% 1.64/1.49 % (30562)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30461 for (3000ds/2Mi)
% 1.64/1.49 % (30560)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_30461 for (3000ds/4Mi)
% 1.64/1.49 % (30563)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_30461 for (3000ds/2Mi)
% 1.64/1.49 % (30561)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_30461 for (3000ds/27Mi)
% 1.64/1.49 % (30564)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_30461 for (3000ds/275Mi)
% 1.64/1.49 % (30565)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30461 for (3000ds/18Mi)
% 1.64/1.49 % (30559)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30461 for (3000ds/183Mi)
% 1.64/1.49 % (30562)Instruction limit reached!
% 1.64/1.49 % (30562)------------------------------
% 1.64/1.49 % (30562)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.49 % (30562)Termination reason: Unknown
% 1.64/1.49 % (30562)Termination phase: Saturation
% 1.64/1.49
% 1.64/1.49 % (30562)Memory used [KB]: 5373
% 1.64/1.49 % (30562)Time elapsed: 0.003 s
% 1.64/1.49 % (30562)Instructions burned: 2 (million)
% 1.64/1.49 % (30562)------------------------------
% 1.64/1.49 % (30562)------------------------------
% 1.64/1.49 % (30563)Instruction limit reached!
% 1.64/1.49 % (30563)------------------------------
% 1.64/1.49 % (30563)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.49 % (30563)Termination reason: Unknown
% 1.64/1.49 % (30563)Termination phase: Saturation
% 1.64/1.49
% 1.64/1.49 % (30563)Memory used [KB]: 5373
% 1.64/1.49 % (30563)Time elapsed: 0.003 s
% 1.64/1.49 % (30563)Instructions burned: 2 (million)
% 1.64/1.49 % (30563)------------------------------
% 1.64/1.49 % (30563)------------------------------
% 1.64/1.49 % (30560)Instruction limit reached!
% 1.64/1.49 % (30560)------------------------------
% 1.64/1.49 % (30560)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.49 % (30560)Termination reason: Unknown
% 1.64/1.49 % (30560)Termination phase: Saturation
% 1.64/1.49
% 1.64/1.49 % (30560)Memory used [KB]: 5500
% 1.64/1.49 % (30560)Time elapsed: 0.005 s
% 1.64/1.49 % (30560)Instructions burned: 4 (million)
% 1.64/1.49 % (30560)------------------------------
% 1.64/1.49 % (30560)------------------------------
% 1.64/1.50 % (30564)First to succeed.
% 1.78/1.50 % (30559)Also succeeded, but the first one will report.
% 1.78/1.50 % (30561)Also succeeded, but the first one will report.
% 1.78/1.50 % (30564)Refutation found. Thanks to Tanya!
% 1.78/1.50 % SZS status Theorem for DTF2THF_30461
% 1.78/1.50 % SZS output start Proof for DTF2THF_30461
% 1.78/1.50 thf(type_def_5, type, a: $tType).
% 1.78/1.50 thf(func_def_0, type, a: $tType).
% 1.78/1.50 thf(func_def_9, type, sK0: a > $o).
% 1.78/1.50 thf(func_def_10, type, sK1: a > $o).
% 1.78/1.50 thf(func_def_12, type, ph3: !>[X0: $tType]:(X0)).
% 1.78/1.50 thf(func_def_13, type, sK4: a).
% 1.78/1.50 thf(func_def_14, type, sK5: a).
% 1.78/1.50 thf(func_def_15, type, sK6: a).
% 1.78/1.50 thf(f216,plain,(
% 1.78/1.50 $false),
% 1.78/1.50 inference(avatar_sat_refutation,[status(thm)],[f20,f21,f33,f42,f56,f77,f111,f121,f122,f137,f140,f150,f202,f215])).
% 1.78/1.50 thf(f215,plain,(
% 1.78/1.50 ~spl2_4 | ~spl2_6),
% 1.78/1.50 inference(avatar_contradiction_clause,[status(thm)],[f214])).
% 1.78/1.50 thf(f214,plain,(
% 1.78/1.50 $false | (~spl2_4 | ~spl2_6)),
% 1.78/1.50 inference(trivial_inequality_removal,[status(thm)],[f211])).
% 1.78/1.50 thf(f211,plain,(
% 1.78/1.50 ($false = $true) | (~spl2_4 | ~spl2_6)),
% 1.78/1.50 inference(superposition,[status(thm)],[f32,f41])).
% 1.78/1.50 thf(f41,plain,(
% 1.78/1.50 ((sK0 @ sK4) = $false) | ~spl2_6),
% 1.78/1.50 inference(avatar_component_clause,[status(thm)],[f39])).
% 1.78/1.50 thf(f39,definition,(
% 1.78/1.50 spl2_6 <=> ((sK0 @ sK4) = $false)),
% 1.78/1.50 introduced(definition,[new_symbols(naming,[spl2_6])],[avatar_definition])).
% 1.78/1.50 thf(f32,plain,(
% 1.78/1.50 ((sK0 @ sK4) = $true) | ~spl2_4),
% 1.78/1.50 inference(avatar_component_clause,[status(thm)],[f30])).
% 1.78/1.50 thf(f30,definition,(
% 1.78/1.50 spl2_4 <=> ((sK0 @ sK4) = $true)),
% 1.78/1.50 introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition])).
% 1.78/1.50 thf(f202,plain,(
% 1.78/1.50 spl2_6 | ~spl2_2 | ~spl2_5),
% 1.78/1.50 inference(avatar_split_clause,[status(thm)],[f193,f35,f17,f39])).
% 1.78/1.50 thf(f17,definition,(
% 1.78/1.50 spl2_2 <=> ((^[Y0 : a]: (((~ (sK1 @ Y0)) & (sK0 @ Y0)) | ((~ (sK0 @ Y0)) & (sK1 @ Y0)))) = (^[Y0 : a]: ($false)))),
% 1.78/1.50 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.78/1.50 thf(f35,definition,(
% 1.78/1.50 spl2_5 <=> ((sK1 @ sK4) = $false)),
% 1.78/1.50 introduced(definition,[new_symbols(naming,[spl2_5])],[avatar_definition])).
% 1.78/1.50 thf(f193,plain,(
% 1.78/1.50 ((sK0 @ sK4) = $false) | (~spl2_2 | ~spl2_5)),
% 1.78/1.50 inference(trivial_inequality_removal,[status(thm)],[f188])).
% 1.78/1.50 thf(f188,plain,(
% 1.78/1.50 ((sK0 @ sK4) = $false) | ($false = $true) | (~spl2_2 | ~spl2_5)),
% 1.78/1.50 inference(superposition,[status(thm)],[f37,f181])).
% 1.78/1.50 thf(f181,plain,(
% 1.78/1.50 ( ! [X1 : a] : (((sK1 @ X1) = $true) | ((sK0 @ X1) = $false)) ) | ~spl2_2),
% 1.78/1.50 inference(not_proxy_clausification,[status(thm)],[f180])).
% 1.78/1.50 thf(f180,plain,(
% 1.78/1.50 ( ! [X1 : a] : (((~ (sK1 @ X1)) = $false) | ((sK0 @ X1) = $false)) ) | ~spl2_2),
% 1.78/1.50 inference(binary_proxy_clausification,[status(thm)],[f179])).
% 1.78/1.50 thf(f179,plain,(
% 1.78/1.50 ( ! [X1 : a] : (($false = ((~ (sK1 @ X1)) & (sK0 @ X1)))) ) | ~spl2_2),
% 1.78/1.50 inference(binary_proxy_clausification,[status(thm)],[f177])).
% 1.78/1.50 thf(f177,plain,(
% 1.78/1.50 ( ! [X1 : a] : (($false = (((~ (sK1 @ X1)) & (sK0 @ X1)) | ((~ (sK0 @ X1)) & (sK1 @ X1))))) ) | ~spl2_2),
% 1.78/1.50 inference(beta_eta_normalization,[status(thm)],[f176])).
% 1.78/1.50 thf(f176,plain,(
% 1.78/1.50 ( ! [X1 : a] : ((((^[Y0 : a]: ($false)) @ X1) = ((^[Y0 : a]: (((~ (sK1 @ Y0)) & (sK0 @ Y0)) | ((~ (sK0 @ Y0)) & (sK1 @ Y0)))) @ X1))) ) | ~spl2_2),
% 1.78/1.50 inference(argument_congruence,[status(thm)],[f18])).
% 1.78/1.50 thf(f18,plain,(
% 1.78/1.50 ((^[Y0 : a]: (((~ (sK1 @ Y0)) & (sK0 @ Y0)) | ((~ (sK0 @ Y0)) & (sK1 @ Y0)))) = (^[Y0 : a]: ($false))) | ~spl2_2),
% 1.78/1.50 inference(avatar_component_clause,[status(thm)],[f17])).
% 1.78/1.50 thf(f37,plain,(
% 1.78/1.50 ((sK1 @ sK4) = $false) | ~spl2_5),
% 1.78/1.50 inference(avatar_component_clause,[status(thm)],[f35])).
% 1.78/1.50 thf(f150,plain,(
% 1.78/1.50 ~spl2_1 | spl2_9 | ~spl2_10),
% 1.78/1.50 inference(avatar_contradiction_clause,[status(thm)],[f149])).
% 1.78/1.50 thf(f149,plain,(
% 1.78/1.50 $false | (~spl2_1 | spl2_9 | ~spl2_10)),
% 1.78/1.50 inference(subsumption_resolution,[status(thm)],[f145,f114])).
% 1.78/1.50 thf(f114,plain,(
% 1.78/1.50 ((sK0 @ sK5) != $false) | spl2_9),
% 1.78/1.50 inference(avatar_component_clause,[status(thm)],[f113])).
% 1.78/1.50 thf(f113,definition,(
% 1.78/1.50 spl2_9 <=> ((sK0 @ sK5) = $false)),
% 1.78/1.50 introduced(definition,[new_symbols(naming,[spl2_9])],[avatar_definition])).
% 1.78/1.50 thf(f145,plain,(
% 1.78/1.50 ((sK0 @ sK5) = $false) | (~spl2_1 | ~spl2_10)),
% 1.78/1.50 inference(trivial_inequality_removal,[status(thm)],[f144])).
% 1.78/1.50 thf(f144,plain,(
% 1.78/1.50 ((sK0 @ sK5) = $false) | ($false = $true) | (~spl2_1 | ~spl2_10)),
% 1.78/1.50 inference(superposition,[status(thm)],[f80,f120])).
% 1.78/1.50 thf(f120,plain,(
% 1.78/1.50 ((sK1 @ sK5) = $false) | ~spl2_10),
% 1.78/1.50 inference(avatar_component_clause,[status(thm)],[f118])).
% 1.78/1.50 thf(f118,definition,(
% 1.78/1.50 spl2_10 <=> ((sK1 @ sK5) = $false)),
% 1.78/1.50 introduced(definition,[new_symbols(naming,[spl2_10])],[avatar_definition])).
% 1.78/1.50 thf(f80,plain,(
% 1.78/1.50 ( ! [X1 : a] : (((sK1 @ X1) = $true) | ((sK0 @ X1) = $false)) ) | ~spl2_1),
% 1.78/1.50 inference(binary_proxy_clausification,[status(thm)],[f78])).
% 1.78/1.50 thf(f78,plain,(
% 1.78/1.50 ( ! [X1 : a] : (((sK0 @ X1) = (sK1 @ X1))) ) | ~spl2_1),
% 1.78/1.50 inference(argument_congruence,[status(thm)],[f14])).
% 1.78/1.50 thf(f14,plain,(
% 1.78/1.50 (sK1 = sK0) | ~spl2_1),
% 1.78/1.50 inference(avatar_component_clause,[status(thm)],[f13])).
% 1.78/1.50 thf(f13,definition,(
% 1.78/1.50 spl2_1 <=> (sK1 = sK0)),
% 1.78/1.50 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.78/1.50 thf(f140,plain,(
% 1.78/1.50 ~spl2_7 | ~spl2_9),
% 1.78/1.50 inference(avatar_contradiction_clause,[status(thm)],[f139])).
% 1.78/1.50 thf(f139,plain,(
% 1.78/1.50 $false | (~spl2_7 | ~spl2_9)),
% 1.78/1.50 inference(trivial_inequality_removal,[status(thm)],[f138])).
% 1.78/1.50 thf(f138,plain,(
% 1.78/1.50 ($false = $true) | (~spl2_7 | ~spl2_9)),
% 1.78/1.50 inference(forward_demodulation,[status(thm)],[f106,f115])).
% 1.78/1.50 thf(f115,plain,(
% 1.78/1.50 ((sK0 @ sK5) = $false) | ~spl2_9),
% 1.78/1.50 inference(avatar_component_clause,[status(thm)],[f113])).
% 1.78/1.50 thf(f106,plain,(
% 1.78/1.50 ((sK0 @ sK5) = $true) | ~spl2_7),
% 1.78/1.50 inference(avatar_component_clause,[status(thm)],[f104])).
% 1.78/1.50 thf(f104,definition,(
% 1.78/1.50 spl2_7 <=> ((sK0 @ sK5) = $true)),
% 1.78/1.50 introduced(definition,[new_symbols(naming,[spl2_7])],[avatar_definition])).
% 1.78/1.50 thf(f137,plain,(
% 1.78/1.50 ~spl2_1 | ~spl2_8 | ~spl2_9),
% 1.78/1.50 inference(avatar_contradiction_clause,[status(thm)],[f136])).
% 1.78/1.50 thf(f136,plain,(
% 1.78/1.50 $false | (~spl2_1 | ~spl2_8 | ~spl2_9)),
% 1.78/1.50 inference(trivial_inequality_removal,[status(thm)],[f135])).
% 1.78/1.50 thf(f135,plain,(
% 1.78/1.50 ($false = $true) | (~spl2_1 | ~spl2_8 | ~spl2_9)),
% 1.78/1.50 inference(forward_demodulation,[status(thm)],[f130,f115])).
% 1.78/1.50 thf(f130,plain,(
% 1.78/1.50 ((sK0 @ sK5) = $true) | (~spl2_1 | ~spl2_8)),
% 1.78/1.50 inference(trivial_inequality_removal,[status(thm)],[f128])).
% 1.78/1.50 thf(f128,plain,(
% 1.78/1.50 ((sK0 @ sK5) = $true) | ($false = $true) | (~spl2_1 | ~spl2_8)),
% 1.78/1.50 inference(superposition,[status(thm)],[f110,f79])).
% 1.78/1.50 thf(f79,plain,(
% 1.78/1.50 ( ! [X1 : a] : (((sK1 @ X1) = $false) | ((sK0 @ X1) = $true)) ) | ~spl2_1),
% 1.78/1.50 inference(binary_proxy_clausification,[status(thm)],[f78])).
% 1.78/1.50 thf(f110,plain,(
% 1.78/1.50 ((sK1 @ sK5) = $true) | ~spl2_8),
% 1.78/1.50 inference(avatar_component_clause,[status(thm)],[f108])).
% 1.78/1.50 thf(f108,definition,(
% 1.78/1.50 spl2_8 <=> ((sK1 @ sK5) = $true)),
% 1.78/1.50 introduced(definition,[new_symbols(naming,[spl2_8])],[avatar_definition])).
% 1.78/1.50 thf(f122,plain,(
% 1.78/1.50 spl2_10 | spl2_9 | spl2_2),
% 1.78/1.50 inference(avatar_split_clause,[status(thm)],[f98,f17,f113,f118])).
% 1.78/1.50 thf(f98,plain,(
% 1.78/1.50 ((sK0 @ sK5) = $false) | ((sK1 @ sK5) = $false) | spl2_2),
% 1.78/1.50 inference(not_proxy_clausification,[status(thm)],[f97])).
% 1.78/1.50 thf(f97,plain,(
% 1.78/1.50 ((~ (sK0 @ sK5)) = $true) | ((sK1 @ sK5) = $false) | spl2_2),
% 1.78/1.50 inference(not_proxy_clausification,[status(thm)],[f96])).
% 1.78/1.50 thf(f96,plain,(
% 1.78/1.50 ((~ (sK1 @ sK5)) = $true) | ((~ (sK0 @ sK5)) = $true) | spl2_2),
% 1.78/1.50 inference(binary_proxy_clausification,[status(thm)],[f94])).
% 1.78/1.50 thf(f94,plain,(
% 1.78/1.50 (((~ (sK0 @ sK5)) & (sK1 @ sK5)) = $true) | ((~ (sK1 @ sK5)) = $true) | spl2_2),
% 1.78/1.50 inference(binary_proxy_clausification,[status(thm)],[f92])).
% 1.78/1.50 thf(f92,plain,(
% 1.78/1.50 (((~ (sK1 @ sK5)) & (sK0 @ sK5)) = $true) | (((~ (sK0 @ sK5)) & (sK1 @ sK5)) = $true) | spl2_2),
% 1.78/1.50 inference(binary_proxy_clausification,[status(thm)],[f91])).
% 1.78/1.50 thf(f91,plain,(
% 1.78/1.50 ((((~ (sK1 @ sK5)) & (sK0 @ sK5)) | ((~ (sK0 @ sK5)) & (sK1 @ sK5))) != $false) | spl2_2),
% 1.78/1.50 inference(beta_eta_normalization,[status(thm)],[f90])).
% 1.78/1.50 thf(f90,plain,(
% 1.78/1.50 (((^[Y0 : a]: (((~ (sK1 @ Y0)) & (sK0 @ Y0)) | ((~ (sK0 @ Y0)) & (sK1 @ Y0)))) @ sK5) != ((^[Y0 : a]: ($false)) @ sK5)) | spl2_2),
% 1.78/1.50 inference(negative_extensionality,[status(thm)],[f19])).
% 1.78/1.50 thf(f19,plain,(
% 1.78/1.50 ((^[Y0 : a]: (((~ (sK1 @ Y0)) & (sK0 @ Y0)) | ((~ (sK0 @ Y0)) & (sK1 @ Y0)))) != (^[Y0 : a]: ($false))) | spl2_2),
% 1.78/1.50 inference(avatar_component_clause,[status(thm)],[f17])).
% 1.78/1.50 thf(f121,plain,(
% 1.78/1.50 spl2_10 | spl2_8 | spl2_2),
% 1.78/1.50 inference(avatar_split_clause,[status(thm)],[f99,f17,f108,f118])).
% 1.78/1.50 thf(f99,plain,(
% 1.78/1.50 ((sK1 @ sK5) = $true) | ((sK1 @ sK5) = $false) | spl2_2),
% 1.78/1.50 inference(not_proxy_clausification,[status(thm)],[f95])).
% 1.78/1.50 thf(f95,plain,(
% 1.78/1.50 ((sK1 @ sK5) = $true) | ((~ (sK1 @ sK5)) = $true) | spl2_2),
% 1.78/1.50 inference(binary_proxy_clausification,[status(thm)],[f94])).
% 1.78/1.50 thf(f111,plain,(
% 1.78/1.50 spl2_7 | spl2_8 | spl2_2),
% 1.78/1.50 inference(avatar_split_clause,[status(thm)],[f100,f17,f108,f104])).
% 1.78/1.50 thf(f100,plain,(
% 1.78/1.50 ((sK1 @ sK5) = $true) | ((sK0 @ sK5) = $true) | spl2_2),
% 1.78/1.50 inference(binary_proxy_clausification,[status(thm)],[f93])).
% 1.78/1.50 thf(f93,plain,(
% 1.78/1.50 ((sK0 @ sK5) = $true) | (((~ (sK0 @ sK5)) & (sK1 @ sK5)) = $true) | spl2_2),
% 1.78/1.50 inference(binary_proxy_clausification,[status(thm)],[f92])).
% 1.78/1.50 thf(f77,plain,(
% 1.78/1.50 ~spl2_2 | ~spl2_3 | ~spl2_6),
% 1.78/1.50 inference(avatar_contradiction_clause,[status(thm)],[f76])).
% 1.78/1.50 thf(f76,plain,(
% 1.78/1.50 $false | (~spl2_2 | ~spl2_3 | ~spl2_6)),
% 1.78/1.50 inference(trivial_inequality_removal,[status(thm)],[f75])).
% 1.78/1.50 thf(f75,plain,(
% 1.78/1.50 ($false = $true) | (~spl2_2 | ~spl2_3 | ~spl2_6)),
% 1.78/1.50 inference(forward_demodulation,[status(thm)],[f64,f41])).
% 1.78/1.50 thf(f64,plain,(
% 1.78/1.50 ((sK0 @ sK4) = $true) | (~spl2_2 | ~spl2_3)),
% 1.78/1.50 inference(trivial_inequality_removal,[status(thm)],[f59])).
% 1.78/1.50 thf(f59,plain,(
% 1.78/1.50 ((sK0 @ sK4) = $true) | ($false = $true) | (~spl2_2 | ~spl2_3)),
% 1.78/1.50 inference(superposition,[status(thm)],[f50,f28])).
% 1.78/1.50 thf(f28,plain,(
% 1.78/1.50 ((sK1 @ sK4) = $true) | ~spl2_3),
% 1.78/1.50 inference(avatar_component_clause,[status(thm)],[f26])).
% 1.78/1.50 thf(f26,definition,(
% 1.78/1.50 spl2_3 <=> ((sK1 @ sK4) = $true)),
% 1.78/1.50 introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition])).
% 1.78/1.50 thf(f50,plain,(
% 1.78/1.50 ( ! [X1 : a] : (((sK1 @ X1) = $false) | ((sK0 @ X1) = $true)) ) | ~spl2_2),
% 1.78/1.50 inference(not_proxy_clausification,[status(thm)],[f49])).
% 1.78/1.50 thf(f49,plain,(
% 1.78/1.50 ( ! [X1 : a] : (((~ (sK0 @ X1)) = $false) | ((sK1 @ X1) = $false)) ) | ~spl2_2),
% 1.78/1.50 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 1.78/1.50 thf(f45,plain,(
% 1.78/1.50 ( ! [X1 : a] : ((((~ (sK0 @ X1)) & (sK1 @ X1)) = $false)) ) | ~spl2_2),
% 1.78/1.50 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.78/1.50 thf(f44,plain,(
% 1.78/1.50 ( ! [X1 : a] : (($false = (((~ (sK1 @ X1)) & (sK0 @ X1)) | ((~ (sK0 @ X1)) & (sK1 @ X1))))) ) | ~spl2_2),
% 1.78/1.50 inference(beta_eta_normalization,[status(thm)],[f43])).
% 1.78/1.50 thf(f43,plain,(
% 1.78/1.50 ( ! [X1 : a] : ((((^[Y0 : a]: ($false)) @ X1) = ((^[Y0 : a]: (((~ (sK1 @ Y0)) & (sK0 @ Y0)) | ((~ (sK0 @ Y0)) & (sK1 @ Y0)))) @ X1))) ) | ~spl2_2),
% 1.78/1.50 inference(argument_congruence,[status(thm)],[f18])).
% 1.78/1.50 thf(f56,plain,(
% 1.78/1.50 ~spl2_3 | ~spl2_5),
% 1.78/1.50 inference(avatar_contradiction_clause,[status(thm)],[f55])).
% 1.78/1.50 thf(f55,plain,(
% 1.78/1.50 $false | (~spl2_3 | ~spl2_5)),
% 1.78/1.50 inference(trivial_inequality_removal,[status(thm)],[f51])).
% 1.78/1.50 thf(f51,plain,(
% 1.78/1.50 ($false = $true) | (~spl2_3 | ~spl2_5)),
% 1.78/1.50 inference(superposition,[status(thm)],[f37,f28])).
% 1.78/1.50 thf(f42,plain,(
% 1.78/1.50 spl2_5 | spl2_6 | spl2_1),
% 1.78/1.50 inference(avatar_split_clause,[status(thm)],[f24,f13,f39,f35])).
% 1.78/1.50 thf(f24,plain,(
% 1.78/1.50 ((sK1 @ sK4) = $false) | ((sK0 @ sK4) = $false) | spl2_1),
% 1.78/1.50 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 1.78/1.50 thf(f22,plain,(
% 1.78/1.50 ((sK1 @ sK4) != (sK0 @ sK4)) | spl2_1),
% 1.78/1.50 inference(negative_extensionality,[status(thm)],[f15])).
% 1.78/1.50 thf(f15,plain,(
% 1.78/1.50 (sK1 != sK0) | spl2_1),
% 1.78/1.50 inference(avatar_component_clause,[status(thm)],[f13])).
% 1.78/1.50 thf(f33,plain,(
% 1.78/1.50 spl2_3 | spl2_4 | spl2_1),
% 1.78/1.50 inference(avatar_split_clause,[status(thm)],[f23,f13,f30,f26])).
% 1.78/1.50 thf(f23,plain,(
% 1.78/1.50 ((sK1 @ sK4) = $true) | ((sK0 @ sK4) = $true) | spl2_1),
% 1.78/1.50 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 1.78/1.50 thf(f21,plain,(
% 1.78/1.50 spl2_2 | spl2_1),
% 1.78/1.50 inference(avatar_split_clause,[status(thm)],[f10,f13,f17])).
% 1.78/1.50 thf(f10,plain,(
% 1.78/1.50 ((^[Y0 : a]: (((~ (sK1 @ Y0)) & (sK0 @ Y0)) | ((~ (sK0 @ Y0)) & (sK1 @ Y0)))) = (^[Y0 : a]: ($false))) | (sK1 = sK0)),
% 1.78/1.50 inference(cnf_transformation,[status(thm)],[f9])).
% 1.78/1.50 thf(f9,plain,(
% 1.78/1.50 ((sK1 != sK0) | ((^[Y0 : a]: (((~ (sK1 @ Y0)) & (sK0 @ Y0)) | ((~ (sK0 @ Y0)) & (sK1 @ Y0)))) != (^[Y0 : a]: ($false)))) & ((sK1 = sK0) | ((^[Y0 : a]: (((~ (sK1 @ Y0)) & (sK0 @ Y0)) | ((~ (sK0 @ Y0)) & (sK1 @ Y0)))) = (^[Y0 : a]: ($false))))),
% 1.78/1.50 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f8])).
% 1.78/1.50 thf(f8,plain,(
% 1.78/1.50 ? [X0 : a > $o,X1 : a > $o] : (((X0 != X1) | ((^[Y0 : a]: (((~ (X1 @ Y0)) & (X0 @ Y0)) | ((~ (X0 @ Y0)) & (X1 @ Y0)))) != (^[Y0 : a]: ($false)))) & ((X0 = X1) | ((^[Y0 : a]: (((~ (X1 @ Y0)) & (X0 @ Y0)) | ((~ (X0 @ Y0)) & (X1 @ Y0)))) = (^[Y0 : a]: ($false))))) => (((sK1 != sK0) | ((^[Y0 : a]: (((~ (sK1 @ Y0)) & (sK0 @ Y0)) | ((~ (sK0 @ Y0)) & (sK1 @ Y0)))) != (^[Y0 : a]: ($false)))) & ((sK1 = sK0) | ((^[Y0 : a]: (((~ (sK1 @ Y0)) & (sK0 @ Y0)) | ((~ (sK0 @ Y0)) & (sK1 @ Y0)))) = (^[Y0 : a]: ($false)))))),
% 1.78/1.50 introduced(definition,[],[choice_axiom])).
% 1.78/1.50 thf(f7,plain,(
% 1.78/1.50 ? [X0 : a > $o,X1 : a > $o] : (((X0 != X1) | ((^[Y0 : a]: (((~ (X1 @ Y0)) & (X0 @ Y0)) | ((~ (X0 @ Y0)) & (X1 @ Y0)))) != (^[Y0 : a]: ($false)))) & ((X0 = X1) | ((^[Y0 : a]: (((~ (X1 @ Y0)) & (X0 @ Y0)) | ((~ (X0 @ Y0)) & (X1 @ Y0)))) = (^[Y0 : a]: ($false)))))),
% 1.78/1.50 inference(nnf_transformation,[status(thm)],[f6])).
% 1.78/1.50 thf(f6,plain,(
% 1.78/1.50 ? [X0 : a > $o,X1 : a > $o] : (((^[Y0 : a]: (((~ (X1 @ Y0)) & (X0 @ Y0)) | ((~ (X0 @ Y0)) & (X1 @ Y0)))) = (^[Y0 : a]: ($false))) <~> (X0 = X1))),
% 1.78/1.50 inference(ennf_transformation,[status(thm)],[f5])).
% 1.78/1.50 thf(f5,plain,(
% 1.78/1.50 ~! [X0 : a > $o,X1 : a > $o] : ((X0 = X1) <=> ((^[Y0 : a]: (((~ (X1 @ Y0)) & (X0 @ Y0)) | ((~ (X0 @ Y0)) & (X1 @ Y0)))) = (^[Y0 : a]: ($false))))),
% 1.78/1.50 inference(fool_elimination,[status(thm)],[f4])).
% 1.78/1.50 thf(f4,plain,(
% 1.78/1.50 ~! [X0 : a > $o,X1 : a > $o] : ((X0 = X1) <=> ((^[X2 : a] : (((X1 @ X2) & ~(X0 @ X2)) | ((X0 @ X2) & ~(X1 @ X2)))) = (^[X3 : a] : ($false))))),
% 1.78/1.50 inference(rectify,[status(thm)],[f2])).
% 1.78/1.50 thf(f2,negated_conjecture,(
% 1.78/1.50 ~! [X1 : a > $o,X0 : a > $o] : ((X0 = X1) <=> ((^[X2 : a] : (((X0 @ X2) & ~(X1 @ X2)) | ((X1 @ X2) & ~(X0 @ X2)))) = (^[X3 : a] : ($false))))),
% 1.78/1.50 inference(negated_conjecture,[status(cth)],[f1])).
% 1.78/1.50 thf(f1,conjecture,(
% 1.78/1.50 ! [X1 : a > $o,X0 : a > $o] : ((X0 = X1) <=> ((^[X2 : a] : (((X0 @ X2) & ~(X1 @ X2)) | ((X1 @ X2) & ~(X0 @ X2)))) = (^[X3 : a] : ($false))))),
% 1.78/1.50 file('/export/starexec/sandbox/tmp/tmp.BwkXj8rEJz/DTF2THF_30461.p',cGAZING_THM46_pme)).
% 1.78/1.50 thf(f20,plain,(
% 1.78/1.50 ~spl2_1 | ~spl2_2),
% 1.78/1.50 inference(avatar_split_clause,[status(thm)],[f11,f17,f13])).
% 1.78/1.50 thf(f11,plain,(
% 1.78/1.50 ((^[Y0 : a]: (((~ (sK1 @ Y0)) & (sK0 @ Y0)) | ((~ (sK0 @ Y0)) & (sK1 @ Y0)))) != (^[Y0 : a]: ($false))) | (sK1 != sK0)),
% 1.78/1.50 inference(cnf_transformation,[status(thm)],[f9])).
% 1.78/1.50 % SZS output end Proof for DTF2THF_30461
% 1.78/1.50 % (30564)------------------------------
% 1.78/1.50 % (30564)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.78/1.50 % (30564)Termination reason: Refutation
% 1.78/1.50
% 1.78/1.50 % (30564)Memory used [KB]: 5628
% 1.78/1.50 % (30564)Time elapsed: 0.010 s
% 1.78/1.50 % (30564)Instructions burned: 10 (million)
% 1.78/1.50 % (30564)------------------------------
% 1.78/1.50 % (30564)------------------------------
% 1.78/1.50 % (30558)Success in time 0.024 s
%------------------------------------------------------------------------------