%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU854^5 : 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 : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:37:35 AM UTC 2026
% Result : Theorem 1.30s 1.12s
% Output : Refutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 72 ( 4 unt; 0 typ; 7 def)
% Number of atoms : 557 ( 170 equ; 0 cnn)
% Maximal formula atoms : 20 ( 7 avg)
% Number of connectives : 660 ( 137 ~; 170 |; 68 &; 254 @)
% ( 11 <=>; 18 =>; 0 <=; 2 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 109 ( 26 ^; 59 !; 24 ?; 109 :)
% 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_11,type,
sK2: a > $o ).
thf(func_def_12,type,
sK3: a ).
thf(func_def_14,type,
ph5:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
sK6: a ).
thf(f147,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f26,f31,f36,f86,f114,f119,f129,f146]) ).
thf(f146,plain,
( ~ spl4_1
| ~ spl4_8
| ~ spl4_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f145]) ).
thf(f145,plain,
( $false
| ~ spl4_1
| ~ spl4_8
| ~ spl4_9 ),
inference(subsumption_resolution,[status(thm)],[f141,f113]) ).
thf(f113,plain,
( ( $true
= ( sK1 @ sK6 ) )
| ~ spl4_8 ),
inference(avatar_component_clause,[status(thm)],[f111]) ).
thf(f111,definition,
( spl4_8
<=> ( $true
= ( sK1 @ sK6 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_8])],[avatar_definition]) ).
thf(f141,plain,
( ( $true
!= ( sK1 @ sK6 ) )
| ~ spl4_1
| ~ spl4_9 ),
inference(trivial_inequality_removal,[status(thm)],[f140]) ).
thf(f140,plain,
( ( $true
!= ( sK1 @ sK6 ) )
| ( $false = $true )
| ~ spl4_1
| ~ spl4_9 ),
inference(superposition,[status(thm)],[f21,f118]) ).
thf(f118,plain,
( ( $false
= ( sK0 @ sK6 ) )
| ~ spl4_9 ),
inference(avatar_component_clause,[status(thm)],[f116]) ).
thf(f116,definition,
( spl4_9
<=> ( $false
= ( sK0 @ sK6 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_9])],[avatar_definition]) ).
thf(f21,plain,
( ! [X5: a] :
( ( $true
= ( sK0 @ X5 ) )
| ( $true
!= ( sK1 @ X5 ) ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[status(thm)],[f20]) ).
thf(f20,definition,
( spl4_1
<=> ! [X5: a] :
( ( $true
!= ( sK1 @ X5 ) )
| ( $true
= ( sK0 @ X5 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition]) ).
thf(f129,plain,
( spl4_2
| ~ spl4_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f128]) ).
thf(f128,plain,
( $false
| spl4_2
| ~ spl4_7 ),
inference(trivial_inequality_removal,[status(thm)],[f123]) ).
thf(f123,plain,
( ( $false = $true )
| spl4_2
| ~ spl4_7 ),
inference(superposition,[status(thm)],[f105,f109]) ).
thf(f109,plain,
( ( $false
= ( sK2 @ sK6 ) )
| ~ spl4_7 ),
inference(avatar_component_clause,[status(thm)],[f107]) ).
thf(f107,definition,
( spl4_7
<=> ( $false
= ( sK2 @ sK6 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_7])],[avatar_definition]) ).
thf(f105,plain,
( ( $true
= ( sK2 @ sK6 ) )
| spl4_2 ),
inference(subsumption_resolution,[status(thm)],[f104,f18]) ).
thf(f18,plain,
! [X3: a] :
( ( $true
= ( sK2 @ X3 ) )
| ( $true
!= ( sK0 @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ! [X3: a] :
( ( $true
= ( sK2 @ X3 ) )
| ( $true
!= ( sK0 @ X3 ) ) )
& ( ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( ~ ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) ) )
!= sK2 )
| ( ( $true
!= ( sK0 @ sK3 ) )
& ( $true
= ( sK1 @ sK3 ) ) ) )
& ( ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( ~ ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) ) )
= sK2 )
| ! [X5: a] :
( ( $true
= ( sK0 @ X5 ) )
| ( $true
!= ( sK1 @ X5 ) ) ) )
& ! [X6: a] :
( ( $true
!= ( sK1 @ X6 ) )
| ( $true
= ( sK2 @ X6 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f10,f12,f11]) ).
thf(f11,plain,
( ? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( ( X2 @ X3 )
= $true )
| ( ( X0 @ X3 )
!= $true ) )
& ( ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
| ( ~ ( X1 @ Y0 )
& ( X2 @ Y0 ) ) ) )
!= X2 )
| ? [X4: a] :
( ( ( X0 @ X4 )
!= $true )
& ( ( X1 @ X4 )
= $true ) ) )
& ( ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
| ( ~ ( X1 @ Y0 )
& ( X2 @ Y0 ) ) ) )
= X2 )
| ! [X5: a] :
( ( $true
= ( X0 @ X5 ) )
| ( $true
!= ( X1 @ X5 ) ) ) )
& ! [X6: a] :
( ( $true
!= ( X1 @ X6 ) )
| ( $true
= ( X2 @ X6 ) ) ) )
=> ( ! [X3: a] :
( ( $true
= ( sK2 @ X3 ) )
| ( $true
!= ( sK0 @ X3 ) ) )
& ( ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( ~ ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) ) )
!= sK2 )
| ? [X4: a] :
( ( $true
!= ( sK0 @ X4 ) )
& ( ( sK1 @ X4 )
= $true ) ) )
& ( ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( ~ ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) ) )
= sK2 )
| ! [X5: a] :
( ( $true
= ( sK0 @ X5 ) )
| ( $true
!= ( sK1 @ X5 ) ) ) )
& ! [X6: a] :
( ( $true
!= ( sK1 @ X6 ) )
| ( $true
= ( sK2 @ X6 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ? [X4: a] :
( ( $true
!= ( sK0 @ X4 ) )
& ( ( sK1 @ X4 )
= $true ) )
=> ( ( $true
!= ( sK0 @ sK3 ) )
& ( $true
= ( sK1 @ sK3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( ( X2 @ X3 )
= $true )
| ( ( X0 @ X3 )
!= $true ) )
& ( ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
| ( ~ ( X1 @ Y0 )
& ( X2 @ Y0 ) ) ) )
!= X2 )
| ? [X4: a] :
( ( ( X0 @ X4 )
!= $true )
& ( ( X1 @ X4 )
= $true ) ) )
& ( ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
| ( ~ ( X1 @ Y0 )
& ( X2 @ Y0 ) ) ) )
= X2 )
| ! [X5: a] :
( ( $true
= ( X0 @ X5 ) )
| ( $true
!= ( X1 @ X5 ) ) ) )
& ! [X6: a] :
( ( $true
!= ( X1 @ X6 ) )
| ( $true
= ( X2 @ X6 ) ) ) ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X4: a] :
( ( ( X2 @ X4 )
= $true )
| ( ( X0 @ X4 )
!= $true ) )
& ( ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
| ( ~ ( X1 @ Y0 )
& ( X2 @ Y0 ) ) ) )
!= X2 )
| ? [X5: a] :
( ( $true
!= ( X0 @ X5 ) )
& ( $true
= ( X1 @ X5 ) ) ) )
& ( ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
| ( ~ ( X1 @ Y0 )
& ( X2 @ Y0 ) ) ) )
= X2 )
| ! [X5: a] :
( ( $true
= ( X0 @ X5 ) )
| ( $true
!= ( X1 @ X5 ) ) ) )
& ! [X3: a] :
( ( ( X1 @ X3 )
!= $true )
| ( ( X2 @ X3 )
= $true ) ) ),
inference(flattening,[status(thm)],[f8]) ).
thf(f8,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X4: a] :
( ( ( X2 @ X4 )
= $true )
| ( ( X0 @ X4 )
!= $true ) )
& ( ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
| ( ~ ( X1 @ Y0 )
& ( X2 @ Y0 ) ) ) )
!= X2 )
| ? [X5: a] :
( ( $true
!= ( X0 @ X5 ) )
& ( $true
= ( X1 @ X5 ) ) ) )
& ( ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
| ( ~ ( X1 @ Y0 )
& ( X2 @ Y0 ) ) ) )
= X2 )
| ! [X5: a] :
( ( $true
= ( X0 @ X5 ) )
| ( $true
!= ( X1 @ X5 ) ) ) )
& ! [X3: a] :
( ( ( X1 @ X3 )
!= $true )
| ( ( X2 @ X3 )
= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X4: a] :
( ( ( X2 @ X4 )
= $true )
| ( ( X0 @ X4 )
!= $true ) )
& ( ! [X5: a] :
( ( $true
= ( X0 @ X5 ) )
| ( $true
!= ( X1 @ X5 ) ) )
<~> ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
| ( ~ ( X1 @ Y0 )
& ( X2 @ Y0 ) ) ) )
= X2 ) )
& ! [X3: a] :
( ( ( X1 @ X3 )
!= $true )
| ( ( X2 @ X3 )
= $true ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X5: a] :
( ( $true
= ( X0 @ X5 ) )
| ( $true
!= ( X1 @ X5 ) ) )
<~> ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
| ( ~ ( X1 @ Y0 )
& ( X2 @ Y0 ) ) ) )
= X2 ) )
& ! [X3: a] :
( ( ( X1 @ X3 )
!= $true )
| ( ( X2 @ X3 )
= $true ) )
& ! [X4: a] :
( ( ( X2 @ X4 )
= $true )
| ( ( X0 @ X4 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( ( X1 @ X3 )
= $true )
=> ( ( X2 @ X3 )
= $true ) )
& ! [X4: a] :
( ( ( X0 @ X4 )
= $true )
=> ( ( X2 @ X4 )
= $true ) ) )
=> ( ! [X5: a] :
( ( $true
= ( X1 @ X5 ) )
=> ( $true
= ( X0 @ X5 ) ) )
<=> ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
| ( ~ ( X1 @ Y0 )
& ( X2 @ Y0 ) ) ) )
= X2 ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
& ! [X4: a] :
( ( X0 @ X4 )
=> ( X2 @ X4 ) ) )
=> ( ! [X5: a] :
( ( X1 @ X5 )
=> ( X0 @ X5 ) )
<=> ( X2
= ( ^ [X6: a] :
( ( ( X2 @ X6 )
& ~ ( X1 @ X6 ) )
| ( X0 @ X6 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a > $o,X0: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( X0 @ X3 )
=> ( X2 @ X3 ) )
& ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
=> ( ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) )
<=> ( X2
= ( ^ [X4: a] :
( ( ( X2 @ X4 )
& ~ ( X0 @ X4 ) )
| ( X1 @ X4 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: a > $o,X0: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( X0 @ X3 )
=> ( X2 @ X3 ) )
& ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
=> ( ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) )
<=> ( X2
= ( ^ [X4: a] :
( ( ( X2 @ X4 )
& ~ ( X0 @ X4 ) )
| ( X1 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PBLsnQ9ley/DTF2THF_29652.p',cGAZING_THM34_pme) ).
thf(f104,plain,
( ( $true
= ( sK0 @ sK6 ) )
| ( $true
= ( sK2 @ sK6 ) )
| spl4_2 ),
inference(duplicate_literal_removal,[status(thm)],[f101]) ).
thf(f101,plain,
( ( $true
= ( sK2 @ sK6 ) )
| ( $true
= ( sK0 @ sK6 ) )
| ( $true
= ( sK2 @ sK6 ) )
| spl4_2 ),
inference(binary_proxy_clausification,[status(thm)],[f100]) ).
thf(f100,plain,
( ( $true
= ( sK0 @ sK6 ) )
| ( $true
= ( sK2 @ sK6 ) )
| ( $true
= ( ~ ( sK1 @ sK6 )
& ( sK2 @ sK6 ) ) )
| spl4_2 ),
inference(binary_proxy_clausification,[status(thm)],[f93]) ).
thf(f93,plain,
( ( $true
= ( sK2 @ sK6 ) )
| ( $true
= ( ( sK0 @ sK6 )
| ( ~ ( sK1 @ sK6 )
& ( sK2 @ sK6 ) ) ) )
| spl4_2 ),
inference(binary_proxy_clausification,[status(thm)],[f92]) ).
thf(f92,plain,
( ( ( ( sK0 @ sK6 )
| ( ~ ( sK1 @ sK6 )
& ( sK2 @ sK6 ) ) )
!= ( sK2 @ sK6 ) )
| spl4_2 ),
inference(beta_eta_normalization,[status(thm)],[f91]) ).
thf(f91,plain,
( ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( ~ ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) )
@ sK6 )
!= ( sK2 @ sK6 ) )
| spl4_2 ),
inference(negative_extensionality,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( ~ ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) ) )
!= sK2 )
| spl4_2 ),
inference(avatar_component_clause,[status(thm)],[f23]) ).
thf(f23,definition,
( spl4_2
<=> ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( ~ ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) ) )
= sK2 ) ),
introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition]) ).
thf(f119,plain,
( spl4_9
| spl4_7
| spl4_2 ),
inference(avatar_split_clause,[status(thm)],[f96,f23,f107,f116]) ).
thf(f96,plain,
( ( $false
= ( sK0 @ sK6 ) )
| ( $false
= ( sK2 @ sK6 ) )
| spl4_2 ),
inference(binary_proxy_clausification,[status(thm)],[f94]) ).
thf(f94,plain,
( ( $false
= ( sK2 @ sK6 ) )
| ( $false
= ( ( sK0 @ sK6 )
| ( ~ ( sK1 @ sK6 )
& ( sK2 @ sK6 ) ) ) )
| spl4_2 ),
inference(binary_proxy_clausification,[status(thm)],[f92]) ).
thf(f114,plain,
( spl4_7
| spl4_8
| spl4_2 ),
inference(avatar_split_clause,[status(thm)],[f99,f23,f111,f107]) ).
thf(f99,plain,
( ( $false
= ( sK2 @ sK6 ) )
| ( $true
= ( sK1 @ sK6 ) )
| spl4_2 ),
inference(not_proxy_clausification,[status(thm)],[f98]) ).
thf(f98,plain,
( ( $false
= ( sK2 @ sK6 ) )
| ( $false
= ( ~ ( sK1 @ sK6 ) ) )
| spl4_2 ),
inference(duplicate_literal_removal,[status(thm)],[f97]) ).
thf(f97,plain,
( ( $false
= ( sK2 @ sK6 ) )
| ( $false
= ( ~ ( sK1 @ sK6 ) ) )
| ( $false
= ( sK2 @ sK6 ) )
| spl4_2 ),
inference(binary_proxy_clausification,[status(thm)],[f95]) ).
thf(f95,plain,
( ( $false
= ( ~ ( sK1 @ sK6 )
& ( sK2 @ sK6 ) ) )
| ( $false
= ( sK2 @ sK6 ) )
| spl4_2 ),
inference(binary_proxy_clausification,[status(thm)],[f94]) ).
thf(f86,plain,
( ~ spl4_2
| ~ spl4_3
| spl4_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f85]) ).
thf(f85,plain,
( $false
| ~ spl4_2
| ~ spl4_3
| spl4_4 ),
inference(subsumption_resolution,[status(thm)],[f79,f30]) ).
thf(f30,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[status(thm)],[f28]) ).
thf(f28,definition,
( spl4_3
<=> ( $true
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition]) ).
thf(f79,plain,
( ( $true
!= ( sK1 @ sK3 ) )
| ~ spl4_2
| ~ spl4_3
| spl4_4 ),
inference(trivial_inequality_removal,[status(thm)],[f76]) ).
thf(f76,plain,
( ( $false = $true )
| ( $true
!= ( sK1 @ sK3 ) )
| ~ spl4_2
| ~ spl4_3
| spl4_4 ),
inference(superposition,[status(thm)],[f74,f14]) ).
thf(f14,plain,
! [X6: a] :
( ( $true
= ( sK2 @ X6 ) )
| ( $true
!= ( sK1 @ X6 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f74,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ~ spl4_2
| ~ spl4_3
| spl4_4 ),
inference(trivial_inequality_removal,[status(thm)],[f73]) ).
thf(f73,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false = $true )
| ~ spl4_2
| ~ spl4_3
| spl4_4 ),
inference(forward_demodulation,[status(thm)],[f71,f30]) ).
thf(f71,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ~ spl4_2
| spl4_4 ),
inference(trivial_inequality_removal,[status(thm)],[f68]) ).
thf(f68,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $true != $true )
| ( $false
= ( sK1 @ sK3 ) )
| ~ spl4_2
| spl4_4 ),
inference(superposition,[status(thm)],[f35,f44]) ).
thf(f44,plain,
( ! [X1: a] :
( ( $true
= ( sK0 @ X1 ) )
| ( $false
= ( sK1 @ X1 ) )
| ( $false
= ( sK2 @ X1 ) ) )
| ~ spl4_2 ),
inference(not_proxy_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
( ! [X1: a] :
( ( $false
= ( sK2 @ X1 ) )
| ( $true
= ( ~ ( sK1 @ X1 ) ) )
| ( $true
= ( sK0 @ X1 ) ) )
| ~ spl4_2 ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
( ! [X1: a] :
( ( $true
= ( sK0 @ X1 ) )
| ( $false
= ( sK2 @ X1 ) )
| ( $true
= ( ~ ( sK1 @ X1 )
& ( sK2 @ X1 ) ) ) )
| ~ spl4_2 ),
inference(binary_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
( ! [X1: a] :
( ( $false
= ( sK2 @ X1 ) )
| ( $true
= ( ( sK0 @ X1 )
| ( ~ ( sK1 @ X1 )
& ( sK2 @ X1 ) ) ) ) )
| ~ spl4_2 ),
inference(binary_proxy_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
( ! [X1: a] :
( ( sK2 @ X1 )
= ( ( sK0 @ X1 )
| ( ~ ( sK1 @ X1 )
& ( sK2 @ X1 ) ) ) )
| ~ spl4_2 ),
inference(beta_eta_normalization,[status(thm)],[f37]) ).
thf(f37,plain,
( ! [X1: a] :
( ( sK2 @ X1 )
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( ~ ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) )
@ X1 ) )
| ~ spl4_2 ),
inference(argument_congruence,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( ~ ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) ) )
= sK2 )
| ~ spl4_2 ),
inference(avatar_component_clause,[status(thm)],[f23]) ).
thf(f35,plain,
( ( $true
!= ( sK0 @ sK3 ) )
| spl4_4 ),
inference(avatar_component_clause,[status(thm)],[f33]) ).
thf(f33,definition,
( spl4_4
<=> ( $true
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition]) ).
thf(f36,plain,
( ~ spl4_2
| ~ spl4_4 ),
inference(avatar_split_clause,[status(thm)],[f17,f33,f23]) ).
thf(f17,plain,
( ( $true
!= ( sK0 @ sK3 ) )
| ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( ~ ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) ) )
!= sK2 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f31,plain,
( ~ spl4_2
| spl4_3 ),
inference(avatar_split_clause,[status(thm)],[f16,f28,f23]) ).
thf(f16,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( ~ ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) ) )
!= sK2 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f26,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[status(thm)],[f15,f23,f20]) ).
thf(f15,plain,
! [X5: a] :
( ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( ~ ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) ) )
= sK2 )
| ( $true
!= ( sK1 @ X5 ) )
| ( $true
= ( sK0 @ X5 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU854^5 : 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
% 0.15/0.33 % Computer : n005.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 12:35:29 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
% 0.17/0.44 ---- Original DTF file ---
% 0.17/0.44 thf(spec,logic,$$dhol).
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 % File : SEU854^5 : TPTP v9.2.1. Released v4.0.0.
% 0.17/0.44 % Domain : Set Theory
% 0.17/0.44 % Problem : TPS problem GAZING-THM34
% 0.17/0.44 % Version : Especial.
% 0.17/0.44 % English :
% 0.17/0.44
% 0.17/0.44 % Refs : [Bar92] Barker-Plummer D (1992), Gazing: An Approach to the Pr
% 0.17/0.44 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.17/0.44 % Source : [Bro09]
% 0.17/0.44 % Names : tps_0418 [Bro09]
% 0.17/0.44 % : 34 [Bar92]
% 0.17/0.44 % : GAZING-THM34 [TPS]
% 0.17/0.44
% 0.17/0.44 % Status : Theorem
% 0.17/0.44 % Rating : 0.00 v8.2.0, 0.15 v8.1.0, 0.09 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, 0.00 v6.1.0, 0.14 v5.5.0, 0.17 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
% 0.17/0.44 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.17/0.44 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.17/0.44 % Maximal formula atoms : 1 ( 1 avg)
% 0.17/0.44 % Number of connectives : 18 ( 1 ~; 1 |; 2 &; 9 @)
% 0.17/0.44 % ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% 0.17/0.44 % Maximal formula depth : 9 ( 9 avg)
% 0.17/0.44 % Number of types : 2 ( 1 usr)
% 0.17/0.44 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.17/0.44 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.17/0.44 % Number of variables : 7 ( 1 ^; 6 !; 0 ?; 7 :)
% 0.17/0.44 % SPC : TH0_THM_EQU_NAR
% 0.17/0.44
% 0.17/0.44 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.17/0.44 % project in the Department of Mathematical Sciences at Carnegie
% 0.17/0.44 % Mellon University. Distributed under the Creative Commons copyleft
% 0.17/0.44 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.17/0.44 % : Polymorphic definitions expanded.
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 thf(a_type,type,
% 0.17/0.44 a: $tType ).
% 0.17/0.44
% 0.17/0.44 thf(cGAZING_THM34_pme,conjecture,
% 0.17/0.44 ! [S: a > $o,T: a > $o,U: a > $o] :
% 0.17/0.44 ( ( ! [Xx: a] :
% 0.17/0.44 ( ( S @ Xx )
% 0.17/0.44 => ( U @ Xx ) )
% 0.17/0.44 & ! [Xx: a] :
% 0.17/0.44 ( ( T @ Xx )
% 0.17/0.44 => ( U @ Xx ) ) )
% 0.17/0.44 => ( ! [Xx: a] :
% 0.17/0.44 ( ( S @ Xx )
% 0.17/0.44 => ( T @ Xx ) )
% 0.17/0.44 <=> ( ( ^ [Xz: a] :
% 0.17/0.44 ( ( ( U @ Xz )
% 0.17/0.44 & ~ ( S @ Xz ) )
% 0.17/0.44 | ( T @ Xz ) ) )
% 0.17/0.44 = U ) ) ) ).
% 0.17/0.44
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 ------------------------
% 1.12/1.10 ---- Embedded in THF ---
% 1.12/1.10 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.12/1.10 %%% Generated on Tue Feb 24 12:35:30 EST 2026
% 1.12/1.10 %%% using '$$dhol' embedding, version 1.3.0.
% 1.12/1.10 %%% Logic specification used:
% 1.12/1.10 %%% thf(spec, logic, $$dhol).
% 1.12/1.10
% 1.12/1.10 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.PBLsnQ9ley/DTF2DTF29652.p
% See solution above
% 1.12/1.10 ------------------------
% 1.12/1.11 ---- Cleaned THF ---
% 1.12/1.11 thf(a_type,type,
% 1.12/1.11 a: $tType ).
% 1.12/1.11
% 1.12/1.11 thf(cGAZING_THM34_pme,conjecture,
% 1.12/1.11 ! [S: a > $o,T: a > $o,U: a > $o] :
% 1.12/1.11 ( ( ! [Xx: a] :
% 1.12/1.11 ( ( S @ Xx )
% 1.12/1.11 => ( U @ Xx ) )
% 1.12/1.11 & ! [Xx: a] :
% 1.12/1.11 ( ( T @ Xx )
% 1.12/1.11 => ( U @ Xx ) ) )
% 1.12/1.11 => ( ! [Xx: a] :
% 1.12/1.11 ( ( S @ Xx )
% 1.12/1.11 => ( T @ Xx ) )
% 1.12/1.11 <=> ( ( ^ [Xz: a] :
% 1.12/1.11 ( ( ( U @ Xz )
% 1.12/1.11 & ~ ( S @ Xz ) )
% 1.12/1.11 | ( T @ Xz ) ) )
% 1.12/1.11 = U ) ) ) ).
% 1.12/1.11 ------------------------
% 1.30/1.12 % (29783)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_29652 for (3000ds/18Mi)
% 1.30/1.12 % (29780)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_29652 for (3000ds/2Mi)
% 1.30/1.12 % (29781)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_29652 for (3000ds/2Mi)
% 1.30/1.12 % (29777)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_29652 for (3000ds/183Mi)
% 1.30/1.12 % (29782)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_29652 for (3000ds/275Mi)
% 1.30/1.12 % (29778)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_29652 for (3000ds/4Mi)
% 1.30/1.12 % (29779)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_29652 for (3000ds/27Mi)
% 1.30/1.12 % (29780)Instruction limit reached!
% 1.30/1.12 % (29780)------------------------------
% 1.30/1.12 % (29780)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.30/1.12 % (29780)Termination reason: Unknown
% 1.30/1.12 % (29780)Termination phase: Saturation
% 1.30/1.12
% 1.30/1.12 % (29780)Memory used [KB]: 5500
% 1.30/1.12 % (29780)Time elapsed: 0.003 s
% 1.30/1.12 % (29780)Instructions burned: 2 (million)
% 1.30/1.12 % (29780)------------------------------
% 1.30/1.12 % (29780)------------------------------
% 1.30/1.12 % (29781)Instruction limit reached!
% 1.30/1.12 % (29781)------------------------------
% 1.30/1.12 % (29781)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.30/1.12 % (29781)Termination reason: Unknown
% 1.30/1.12 % (29781)Termination phase: Saturation
% 1.30/1.12
% 1.30/1.12 % (29781)Memory used [KB]: 5500
% 1.30/1.12 % (29781)Time elapsed: 0.003 s
% 1.30/1.12 % (29781)Instructions burned: 3 (million)
% 1.30/1.12 % (29781)------------------------------
% 1.30/1.12 % (29781)------------------------------
% 1.30/1.12 % (29778)Instruction limit reached!
% 1.30/1.12 % (29778)------------------------------
% 1.30/1.12 % (29778)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.30/1.12 % (29778)Termination reason: Unknown
% 1.30/1.12 % (29778)Termination phase: Saturation
% 1.30/1.12
% 1.30/1.12 % (29778)Memory used [KB]: 5500
% 1.30/1.12 % (29778)Time elapsed: 0.003 s
% 1.30/1.12 % (29778)Instructions burned: 4 (million)
% 1.30/1.12 % (29778)------------------------------
% 1.30/1.12 % (29778)------------------------------
% 1.30/1.12 % (29782)First to succeed.
% 1.30/1.12 % (29777)Also succeeded, but the first one will report.
% 1.30/1.12 % (29782)Refutation found. Thanks to Tanya!
% 1.30/1.12 % SZS status Theorem for DTF2THF_29652
% 1.30/1.12 % SZS output start Proof for DTF2THF_29652
% 1.30/1.12 thf(type_def_5, type, a: $tType).
% 1.30/1.12 thf(func_def_0, type, a: $tType).
% 1.30/1.12 thf(func_def_9, type, sK0: a > $o).
% 1.30/1.12 thf(func_def_10, type, sK1: a > $o).
% 1.30/1.12 thf(func_def_11, type, sK2: a > $o).
% 1.30/1.12 thf(func_def_12, type, sK3: a).
% 1.30/1.12 thf(func_def_14, type, ph5: !>[X0: $tType]:(X0)).
% 1.30/1.12 thf(func_def_15, type, sK6: a).
% 1.30/1.12 thf(f147,plain,(
% 1.30/1.12 $false),
% 1.30/1.12 inference(avatar_sat_refutation,[status(thm)],[f26,f31,f36,f86,f114,f119,f129,f146])).
% 1.30/1.12 thf(f146,plain,(
% 1.30/1.12 ~spl4_1 | ~spl4_8 | ~spl4_9),
% 1.30/1.12 inference(avatar_contradiction_clause,[status(thm)],[f145])).
% 1.30/1.12 thf(f145,plain,(
% 1.30/1.12 $false | (~spl4_1 | ~spl4_8 | ~spl4_9)),
% 1.30/1.12 inference(subsumption_resolution,[status(thm)],[f141,f113])).
% 1.30/1.12 thf(f113,plain,(
% 1.30/1.12 ($true = (sK1 @ sK6)) | ~spl4_8),
% 1.30/1.12 inference(avatar_component_clause,[status(thm)],[f111])).
% 1.30/1.12 thf(f111,definition,(
% 1.30/1.12 spl4_8 <=> ($true = (sK1 @ sK6))),
% 1.30/1.12 introduced(definition,[new_symbols(naming,[spl4_8])],[avatar_definition])).
% 1.30/1.12 thf(f141,plain,(
% 1.30/1.12 ($true != (sK1 @ sK6)) | (~spl4_1 | ~spl4_9)),
% 1.30/1.12 inference(trivial_inequality_removal,[status(thm)],[f140])).
% 1.30/1.12 thf(f140,plain,(
% 1.30/1.12 ($true != (sK1 @ sK6)) | ($false = $true) | (~spl4_1 | ~spl4_9)),
% 1.30/1.12 inference(superposition,[status(thm)],[f21,f118])).
% 1.30/1.12 thf(f118,plain,(
% 1.30/1.12 ($false = (sK0 @ sK6)) | ~spl4_9),
% 1.30/1.12 inference(avatar_component_clause,[status(thm)],[f116])).
% 1.30/1.12 thf(f116,definition,(
% 1.30/1.12 spl4_9 <=> ($false = (sK0 @ sK6))),
% 1.30/1.12 introduced(definition,[new_symbols(naming,[spl4_9])],[avatar_definition])).
% 1.30/1.12 thf(f21,plain,(
% 1.30/1.12 ( ! [X5 : a] : (($true = (sK0 @ X5)) | ($true != (sK1 @ X5))) ) | ~spl4_1),
% 1.30/1.12 inference(avatar_component_clause,[status(thm)],[f20])).
% 1.30/1.12 thf(f20,definition,(
% 1.30/1.12 spl4_1 <=> ! [X5 : a] : (($true != (sK1 @ X5)) | ($true = (sK0 @ X5)))),
% 1.30/1.12 introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition])).
% 1.30/1.12 thf(f129,plain,(
% 1.30/1.12 spl4_2 | ~spl4_7),
% 1.30/1.12 inference(avatar_contradiction_clause,[status(thm)],[f128])).
% 1.30/1.12 thf(f128,plain,(
% 1.30/1.12 $false | (spl4_2 | ~spl4_7)),
% 1.30/1.12 inference(trivial_inequality_removal,[status(thm)],[f123])).
% 1.30/1.12 thf(f123,plain,(
% 1.30/1.12 ($false = $true) | (spl4_2 | ~spl4_7)),
% 1.30/1.12 inference(superposition,[status(thm)],[f105,f109])).
% 1.30/1.12 thf(f109,plain,(
% 1.30/1.12 ($false = (sK2 @ sK6)) | ~spl4_7),
% 1.30/1.12 inference(avatar_component_clause,[status(thm)],[f107])).
% 1.30/1.12 thf(f107,definition,(
% 1.30/1.12 spl4_7 <=> ($false = (sK2 @ sK6))),
% 1.30/1.12 introduced(definition,[new_symbols(naming,[spl4_7])],[avatar_definition])).
% 1.30/1.12 thf(f105,plain,(
% 1.30/1.12 ($true = (sK2 @ sK6)) | spl4_2),
% 1.30/1.12 inference(subsumption_resolution,[status(thm)],[f104,f18])).
% 1.30/1.12 thf(f18,plain,(
% 1.30/1.12 ( ! [X3 : a] : (($true = (sK2 @ X3)) | ($true != (sK0 @ X3))) )),
% 1.30/1.12 inference(cnf_transformation,[status(thm)],[f13])).
% 1.30/1.12 thf(f13,plain,(
% 1.30/1.12 ! [X3 : a] : (($true = (sK2 @ X3)) | ($true != (sK0 @ X3))) & (((^[Y0 : a]: ((sK0 @ Y0) | ((~ (sK1 @ Y0)) & (sK2 @ Y0)))) != sK2) | (($true != (sK0 @ sK3)) & ($true = (sK1 @ sK3)))) & (((^[Y0 : a]: ((sK0 @ Y0) | ((~ (sK1 @ Y0)) & (sK2 @ Y0)))) = sK2) | ! [X5 : a] : (($true = (sK0 @ X5)) | ($true != (sK1 @ X5)))) & ! [X6 : a] : (($true != (sK1 @ X6)) | ($true = (sK2 @ X6)))),
% 1.30/1.12 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f10,f12,f11])).
% 1.30/1.12 thf(f11,plain,(
% 1.30/1.12 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (! [X3 : a] : (((X2 @ X3) = $true) | ((X0 @ X3) != $true)) & (((^[Y0 : a]: ((X0 @ Y0) | ((~ (X1 @ Y0)) & (X2 @ Y0)))) != X2) | ? [X4 : a] : (((X0 @ X4) != $true) & ((X1 @ X4) = $true))) & (((^[Y0 : a]: ((X0 @ Y0) | ((~ (X1 @ Y0)) & (X2 @ Y0)))) = X2) | ! [X5 : a] : (($true = (X0 @ X5)) | ($true != (X1 @ X5)))) & ! [X6 : a] : (($true != (X1 @ X6)) | ($true = (X2 @ X6)))) => (! [X3 : a] : (($true = (sK2 @ X3)) | ($true != (sK0 @ X3))) & (((^[Y0 : a]: ((sK0 @ Y0) | ((~ (sK1 @ Y0)) & (sK2 @ Y0)))) != sK2) | ? [X4 : a] : (($true != (sK0 @ X4)) & ((sK1 @ X4) = $true))) & (((^[Y0 : a]: ((sK0 @ Y0) | ((~ (sK1 @ Y0)) & (sK2 @ Y0)))) = sK2) | ! [X5 : a] : (($true = (sK0 @ X5)) | ($true != (sK1 @ X5)))) & ! [X6 : a] : (($true != (sK1 @ X6)) | ($true = (sK2 @ X6))))),
% 1.30/1.12 introduced(definition,[],[choice_axiom])).
% 1.30/1.12 thf(f12,plain,(
% 1.30/1.12 ? [X4 : a] : (($true != (sK0 @ X4)) & ((sK1 @ X4) = $true)) => (($true != (sK0 @ sK3)) & ($true = (sK1 @ sK3)))),
% 1.30/1.12 introduced(definition,[],[choice_axiom])).
% 1.30/1.12 thf(f10,plain,(
% 1.30/1.12 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (! [X3 : a] : (((X2 @ X3) = $true) | ((X0 @ X3) != $true)) & (((^[Y0 : a]: ((X0 @ Y0) | ((~ (X1 @ Y0)) & (X2 @ Y0)))) != X2) | ? [X4 : a] : (((X0 @ X4) != $true) & ((X1 @ X4) = $true))) & (((^[Y0 : a]: ((X0 @ Y0) | ((~ (X1 @ Y0)) & (X2 @ Y0)))) = X2) | ! [X5 : a] : (($true = (X0 @ X5)) | ($true != (X1 @ X5)))) & ! [X6 : a] : (($true != (X1 @ X6)) | ($true = (X2 @ X6))))),
% 1.30/1.12 inference(rectify,[status(thm)],[f9])).
% 1.30/1.12 thf(f9,plain,(
% 1.30/1.12 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (! [X4 : a] : (((X2 @ X4) = $true) | ((X0 @ X4) != $true)) & (((^[Y0 : a]: ((X0 @ Y0) | ((~ (X1 @ Y0)) & (X2 @ Y0)))) != X2) | ? [X5 : a] : (($true != (X0 @ X5)) & ($true = (X1 @ X5)))) & (((^[Y0 : a]: ((X0 @ Y0) | ((~ (X1 @ Y0)) & (X2 @ Y0)))) = X2) | ! [X5 : a] : (($true = (X0 @ X5)) | ($true != (X1 @ X5)))) & ! [X3 : a] : (((X1 @ X3) != $true) | ((X2 @ X3) = $true)))),
% 1.30/1.12 inference(flattening,[status(thm)],[f8])).
% 1.30/1.12 thf(f8,plain,(
% 1.30/1.12 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (! [X4 : a] : (((X2 @ X4) = $true) | ((X0 @ X4) != $true)) & ((((^[Y0 : a]: ((X0 @ Y0) | ((~ (X1 @ Y0)) & (X2 @ Y0)))) != X2) | ? [X5 : a] : (($true != (X0 @ X5)) & ($true = (X1 @ X5)))) & (((^[Y0 : a]: ((X0 @ Y0) | ((~ (X1 @ Y0)) & (X2 @ Y0)))) = X2) | ! [X5 : a] : (($true = (X0 @ X5)) | ($true != (X1 @ X5))))) & ! [X3 : a] : (((X1 @ X3) != $true) | ((X2 @ X3) = $true)))),
% 1.30/1.12 inference(nnf_transformation,[status(thm)],[f7])).
% 1.30/1.12 thf(f7,plain,(
% 1.30/1.12 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (! [X4 : a] : (((X2 @ X4) = $true) | ((X0 @ X4) != $true)) & (! [X5 : a] : (($true = (X0 @ X5)) | ($true != (X1 @ X5))) <~> ((^[Y0 : a]: ((X0 @ Y0) | ((~ (X1 @ Y0)) & (X2 @ Y0)))) = X2)) & ! [X3 : a] : (((X1 @ X3) != $true) | ((X2 @ X3) = $true)))),
% 1.30/1.12 inference(flattening,[status(thm)],[f6])).
% 1.30/1.12 thf(f6,plain,(
% 1.30/1.12 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((! [X5 : a] : (($true = (X0 @ X5)) | ($true != (X1 @ X5))) <~> ((^[Y0 : a]: ((X0 @ Y0) | ((~ (X1 @ Y0)) & (X2 @ Y0)))) = X2)) & (! [X3 : a] : (((X1 @ X3) != $true) | ((X2 @ X3) = $true)) & ! [X4 : a] : (((X2 @ X4) = $true) | ((X0 @ X4) != $true))))),
% 1.30/1.12 inference(ennf_transformation,[status(thm)],[f5])).
% 1.30/1.12 thf(f5,plain,(
% 1.30/1.12 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((! [X3 : a] : (((X1 @ X3) = $true) => ((X2 @ X3) = $true)) & ! [X4 : a] : (((X0 @ X4) = $true) => ((X2 @ X4) = $true))) => (! [X5 : a] : (($true = (X1 @ X5)) => ($true = (X0 @ X5))) <=> ((^[Y0 : a]: ((X0 @ Y0) | ((~ (X1 @ Y0)) & (X2 @ Y0)))) = X2)))),
% 1.30/1.12 inference(fool_elimination,[status(thm)],[f4])).
% 1.30/1.12 thf(f4,plain,(
% 1.30/1.12 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((! [X3 : a] : ((X1 @ X3) => (X2 @ X3)) & ! [X4 : a] : ((X0 @ X4) => (X2 @ X4))) => (! [X5 : a] : ((X1 @ X5) => (X0 @ X5)) <=> (X2 = (^[X6 : a] : (((X2 @ X6) & ~(X1 @ X6)) | (X0 @ X6))))))),
% 1.30/1.12 inference(rectify,[status(thm)],[f2])).
% 1.30/1.12 thf(f2,negated_conjecture,(
% 1.30/1.12 ~! [X1 : a > $o,X0 : a > $o,X2 : a > $o] : ((! [X3 : a] : ((X0 @ X3) => (X2 @ X3)) & ! [X3 : a] : ((X1 @ X3) => (X2 @ X3))) => (! [X3 : a] : ((X0 @ X3) => (X1 @ X3)) <=> (X2 = (^[X4 : a] : (((X2 @ X4) & ~(X0 @ X4)) | (X1 @ X4))))))),
% 1.30/1.12 inference(negated_conjecture,[status(cth)],[f1])).
% 1.30/1.12 thf(f1,conjecture,(
% 1.30/1.12 ! [X1 : a > $o,X0 : a > $o,X2 : a > $o] : ((! [X3 : a] : ((X0 @ X3) => (X2 @ X3)) & ! [X3 : a] : ((X1 @ X3) => (X2 @ X3))) => (! [X3 : a] : ((X0 @ X3) => (X1 @ X3)) <=> (X2 = (^[X4 : a] : (((X2 @ X4) & ~(X0 @ X4)) | (X1 @ X4))))))),
% 1.30/1.12 file('/export/starexec/sandbox/tmp/tmp.PBLsnQ9ley/DTF2THF_29652.p',cGAZING_THM34_pme)).
% 1.30/1.12 thf(f104,plain,(
% 1.30/1.12 ($true = (sK0 @ sK6)) | ($true = (sK2 @ sK6)) | spl4_2),
% 1.30/1.12 inference(duplicate_literal_removal,[status(thm)],[f101])).
% 1.30/1.12 thf(f101,plain,(
% 1.30/1.12 ($true = (sK2 @ sK6)) | ($true = (sK0 @ sK6)) | ($true = (sK2 @ sK6)) | spl4_2),
% 1.30/1.12 inference(binary_proxy_clausification,[status(thm)],[f100])).
% 1.30/1.12 thf(f100,plain,(
% 1.30/1.12 ($true = (sK0 @ sK6)) | ($true = (sK2 @ sK6)) | ($true = ((~ (sK1 @ sK6)) & (sK2 @ sK6))) | spl4_2),
% 1.30/1.12 inference(binary_proxy_clausification,[status(thm)],[f93])).
% 1.30/1.12 thf(f93,plain,(
% 1.30/1.12 ($true = (sK2 @ sK6)) | ($true = ((sK0 @ sK6) | ((~ (sK1 @ sK6)) & (sK2 @ sK6)))) | spl4_2),
% 1.30/1.12 inference(binary_proxy_clausification,[status(thm)],[f92])).
% 1.30/1.12 thf(f92,plain,(
% 1.30/1.12 (((sK0 @ sK6) | ((~ (sK1 @ sK6)) & (sK2 @ sK6))) != (sK2 @ sK6)) | spl4_2),
% 1.30/1.12 inference(beta_eta_normalization,[status(thm)],[f91])).
% 1.30/1.12 thf(f91,plain,(
% 1.30/1.12 (((^[Y0 : a]: ((sK0 @ Y0) | ((~ (sK1 @ Y0)) & (sK2 @ Y0)))) @ sK6) != (sK2 @ sK6)) | spl4_2),
% 1.30/1.12 inference(negative_extensionality,[status(thm)],[f24])).
% 1.30/1.12 thf(f24,plain,(
% 1.30/1.12 ((^[Y0 : a]: ((sK0 @ Y0) | ((~ (sK1 @ Y0)) & (sK2 @ Y0)))) != sK2) | spl4_2),
% 1.30/1.12 inference(avatar_component_clause,[status(thm)],[f23])).
% 1.30/1.12 thf(f23,definition,(
% 1.30/1.12 spl4_2 <=> ((^[Y0 : a]: ((sK0 @ Y0) | ((~ (sK1 @ Y0)) & (sK2 @ Y0)))) = sK2)),
% 1.30/1.12 introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition])).
% 1.30/1.12 thf(f119,plain,(
% 1.30/1.12 spl4_9 | spl4_7 | spl4_2),
% 1.30/1.12 inference(avatar_split_clause,[status(thm)],[f96,f23,f107,f116])).
% 1.30/1.12 thf(f96,plain,(
% 1.30/1.12 ($false = (sK0 @ sK6)) | ($false = (sK2 @ sK6)) | spl4_2),
% 1.30/1.12 inference(binary_proxy_clausification,[status(thm)],[f94])).
% 1.30/1.12 thf(f94,plain,(
% 1.30/1.12 ($false = (sK2 @ sK6)) | ($false = ((sK0 @ sK6) | ((~ (sK1 @ sK6)) & (sK2 @ sK6)))) | spl4_2),
% 1.30/1.12 inference(binary_proxy_clausification,[status(thm)],[f92])).
% 1.30/1.12 thf(f114,plain,(
% 1.30/1.12 spl4_7 | spl4_8 | spl4_2),
% 1.30/1.12 inference(avatar_split_clause,[status(thm)],[f99,f23,f111,f107])).
% 1.30/1.12 thf(f99,plain,(
% 1.30/1.12 ($false = (sK2 @ sK6)) | ($true = (sK1 @ sK6)) | spl4_2),
% 1.30/1.12 inference(not_proxy_clausification,[status(thm)],[f98])).
% 1.30/1.12 thf(f98,plain,(
% 1.30/1.12 ($false = (sK2 @ sK6)) | ($false = (~ (sK1 @ sK6))) | spl4_2),
% 1.30/1.12 inference(duplicate_literal_removal,[status(thm)],[f97])).
% 1.30/1.12 thf(f97,plain,(
% 1.30/1.12 ($false = (sK2 @ sK6)) | ($false = (~ (sK1 @ sK6))) | ($false = (sK2 @ sK6)) | spl4_2),
% 1.30/1.12 inference(binary_proxy_clausification,[status(thm)],[f95])).
% 1.30/1.12 thf(f95,plain,(
% 1.30/1.12 ($false = ((~ (sK1 @ sK6)) & (sK2 @ sK6))) | ($false = (sK2 @ sK6)) | spl4_2),
% 1.30/1.12 inference(binary_proxy_clausification,[status(thm)],[f94])).
% 1.30/1.12 thf(f86,plain,(
% 1.30/1.12 ~spl4_2 | ~spl4_3 | spl4_4),
% 1.30/1.12 inference(avatar_contradiction_clause,[status(thm)],[f85])).
% 1.30/1.12 thf(f85,plain,(
% 1.30/1.12 $false | (~spl4_2 | ~spl4_3 | spl4_4)),
% 1.30/1.12 inference(subsumption_resolution,[status(thm)],[f79,f30])).
% 1.30/1.12 thf(f30,plain,(
% 1.30/1.12 ($true = (sK1 @ sK3)) | ~spl4_3),
% 1.30/1.12 inference(avatar_component_clause,[status(thm)],[f28])).
% 1.30/1.12 thf(f28,definition,(
% 1.30/1.12 spl4_3 <=> ($true = (sK1 @ sK3))),
% 1.30/1.12 introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition])).
% 1.30/1.12 thf(f79,plain,(
% 1.30/1.12 ($true != (sK1 @ sK3)) | (~spl4_2 | ~spl4_3 | spl4_4)),
% 1.30/1.12 inference(trivial_inequality_removal,[status(thm)],[f76])).
% 1.30/1.12 thf(f76,plain,(
% 1.30/1.12 ($false = $true) | ($true != (sK1 @ sK3)) | (~spl4_2 | ~spl4_3 | spl4_4)),
% 1.30/1.12 inference(superposition,[status(thm)],[f74,f14])).
% 1.30/1.12 thf(f14,plain,(
% 1.30/1.12 ( ! [X6 : a] : (($true = (sK2 @ X6)) | ($true != (sK1 @ X6))) )),
% 1.30/1.12 inference(cnf_transformation,[status(thm)],[f13])).
% 1.30/1.12 thf(f74,plain,(
% 1.30/1.12 ($false = (sK2 @ sK3)) | (~spl4_2 | ~spl4_3 | spl4_4)),
% 1.30/1.12 inference(trivial_inequality_removal,[status(thm)],[f73])).
% 1.30/1.12 thf(f73,plain,(
% 1.30/1.12 ($false = (sK2 @ sK3)) | ($false = $true) | (~spl4_2 | ~spl4_3 | spl4_4)),
% 1.30/1.13 inference(forward_demodulation,[status(thm)],[f71,f30])).
% 1.30/1.13 thf(f71,plain,(
% 1.30/1.13 ($false = (sK1 @ sK3)) | ($false = (sK2 @ sK3)) | (~spl4_2 | spl4_4)),
% 1.30/1.13 inference(trivial_inequality_removal,[status(thm)],[f68])).
% 1.30/1.13 thf(f68,plain,(
% 1.30/1.13 ($false = (sK2 @ sK3)) | ($true != $true) | ($false = (sK1 @ sK3)) | (~spl4_2 | spl4_4)),
% 1.30/1.13 inference(superposition,[status(thm)],[f35,f44])).
% 1.30/1.13 thf(f44,plain,(
% 1.30/1.13 ( ! [X1 : a] : (($true = (sK0 @ X1)) | ($false = (sK1 @ X1)) | ($false = (sK2 @ X1))) ) | ~spl4_2),
% 1.30/1.13 inference(not_proxy_clausification,[status(thm)],[f43])).
% 1.30/1.13 thf(f43,plain,(
% 1.30/1.13 ( ! [X1 : a] : (($false = (sK2 @ X1)) | ($true = (~ (sK1 @ X1))) | ($true = (sK0 @ X1))) ) | ~spl4_2),
% 1.30/1.13 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 1.30/1.13 thf(f41,plain,(
% 1.30/1.13 ( ! [X1 : a] : (($true = (sK0 @ X1)) | ($false = (sK2 @ X1)) | ($true = ((~ (sK1 @ X1)) & (sK2 @ X1)))) ) | ~spl4_2),
% 1.30/1.13 inference(binary_proxy_clausification,[status(thm)],[f40])).
% 1.30/1.13 thf(f40,plain,(
% 1.30/1.13 ( ! [X1 : a] : (($false = (sK2 @ X1)) | ($true = ((sK0 @ X1) | ((~ (sK1 @ X1)) & (sK2 @ X1))))) ) | ~spl4_2),
% 1.30/1.13 inference(binary_proxy_clausification,[status(thm)],[f38])).
% 1.30/1.13 thf(f38,plain,(
% 1.30/1.13 ( ! [X1 : a] : (((sK2 @ X1) = ((sK0 @ X1) | ((~ (sK1 @ X1)) & (sK2 @ X1))))) ) | ~spl4_2),
% 1.30/1.13 inference(beta_eta_normalization,[status(thm)],[f37])).
% 1.30/1.13 thf(f37,plain,(
% 1.30/1.13 ( ! [X1 : a] : (((sK2 @ X1) = ((^[Y0 : a]: ((sK0 @ Y0) | ((~ (sK1 @ Y0)) & (sK2 @ Y0)))) @ X1))) ) | ~spl4_2),
% 1.30/1.13 inference(argument_congruence,[status(thm)],[f25])).
% 1.30/1.13 thf(f25,plain,(
% 1.30/1.13 ((^[Y0 : a]: ((sK0 @ Y0) | ((~ (sK1 @ Y0)) & (sK2 @ Y0)))) = sK2) | ~spl4_2),
% 1.30/1.13 inference(avatar_component_clause,[status(thm)],[f23])).
% 1.30/1.13 thf(f35,plain,(
% 1.30/1.13 ($true != (sK0 @ sK3)) | spl4_4),
% 1.30/1.13 inference(avatar_component_clause,[status(thm)],[f33])).
% 1.30/1.13 thf(f33,definition,(
% 1.30/1.13 spl4_4 <=> ($true = (sK0 @ sK3))),
% 1.30/1.13 introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition])).
% 1.30/1.13 thf(f36,plain,(
% 1.30/1.13 ~spl4_2 | ~spl4_4),
% 1.30/1.13 inference(avatar_split_clause,[status(thm)],[f17,f33,f23])).
% 1.30/1.13 thf(f17,plain,(
% 1.30/1.13 ($true != (sK0 @ sK3)) | ((^[Y0 : a]: ((sK0 @ Y0) | ((~ (sK1 @ Y0)) & (sK2 @ Y0)))) != sK2)),
% 1.30/1.13 inference(cnf_transformation,[status(thm)],[f13])).
% 1.30/1.13 thf(f31,plain,(
% 1.30/1.13 ~spl4_2 | spl4_3),
% 1.30/1.13 inference(avatar_split_clause,[status(thm)],[f16,f28,f23])).
% 1.30/1.13 thf(f16,plain,(
% 1.30/1.13 ($true = (sK1 @ sK3)) | ((^[Y0 : a]: ((sK0 @ Y0) | ((~ (sK1 @ Y0)) & (sK2 @ Y0)))) != sK2)),
% 1.30/1.13 inference(cnf_transformation,[status(thm)],[f13])).
% 1.30/1.13 thf(f26,plain,(
% 1.30/1.13 spl4_1 | spl4_2),
% 1.30/1.13 inference(avatar_split_clause,[status(thm)],[f15,f23,f20])).
% 1.30/1.13 thf(f15,plain,(
% 1.30/1.13 ( ! [X5 : a] : (((^[Y0 : a]: ((sK0 @ Y0) | ((~ (sK1 @ Y0)) & (sK2 @ Y0)))) = sK2) | ($true != (sK1 @ X5)) | ($true = (sK0 @ X5))) )),
% 1.30/1.13 inference(cnf_transformation,[status(thm)],[f13])).
% 1.30/1.13 % SZS output end Proof for DTF2THF_29652
% 1.30/1.13 % (29782)------------------------------
% 1.30/1.13 % (29782)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.30/1.13 % (29782)Termination reason: Refutation
% 1.30/1.13
% 1.30/1.13 % (29782)Memory used [KB]: 5500
% 1.30/1.13 % (29782)Time elapsed: 0.006 s
% 1.30/1.13 % (29782)Instructions burned: 8 (million)
% 1.30/1.13 % (29782)------------------------------
% 1.30/1.13 % (29782)------------------------------
% 1.30/1.13 % (29775)Success in time 0.014 s
%------------------------------------------------------------------------------