%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO376^5 : TPTP v9.2.1. Released v4.0.0.
% 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 09:54:04 AM UTC 2026
% Result : Theorem 1.45s 1.29s
% Output : Refutation 1.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 13
% Syntax : Number of formulae : 121 ( 20 unt; 0 typ; 12 def)
% Number of atoms : 694 ( 135 equ; 0 cnn)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 493 ( 144 ~; 173 |; 10 &; 150 @)
% ( 12 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 17 con; 0-2 aty)
% Number of variables : 23 ( 23 ^; 0 !; 0 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cG: $o > $o ).
thf(func_def_1,type,
cF: $o > $o ).
thf(func_def_2,type,
cP: ( $o > $o ) > $o ).
thf(func_def_11,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f411,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f33,f39,f58,f68,f123,f139,f161,f197,f233,f235,f315,f323,f353,f362,f401]) ).
thf(f401,plain,
~ spl0_12,
inference(avatar_contradiction_clause,[status(thm)],[f400]) ).
thf(f400,plain,
( $false
| ~ spl0_12 ),
inference(trivial_inequality_removal,[status(thm)],[f392]) ).
thf(f392,plain,
( ( $false = $true )
| ~ spl0_12 ),
inference(superposition,[status(thm)],[f149,f160]) ).
thf(f160,plain,
( ( ( cG @ sK4 )
= $true )
| ~ spl0_12 ),
inference(avatar_component_clause,[status(thm)],[f158]) ).
thf(f158,definition,
( spl0_12
<=> ( ( cG @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition]) ).
thf(f149,plain,
( ( cG @ sK4 )
= $false ),
inference(duplicate_literal_removal,[status(thm)],[f146]) ).
thf(f146,plain,
( ( ( cG @ sK4 )
= $false )
| ( ( cG @ sK4 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f145]) ).
thf(f145,plain,
( ( ( cG @ sK4 )
= $false )
| ( $false
= ( ~ ( cF @ sK4 )
| ( cG @ sK4 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f143]) ).
thf(f143,plain,
( ( cG @ sK4 )
!= ( ~ ( cF @ sK4 )
| ( cG @ sK4 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f142]) ).
thf(f142,plain,
( ( cG @ sK4 )
!= ( ^ [Y0: $o] :
( ~ ( cF @ Y0 )
| ( cG @ Y0 ) )
@ sK4 ) ),
inference(negative_extensionality,[status(thm)],[f71]) ).
thf(f71,plain,
( cG
!= ( ^ [Y0: $o] :
( ~ ( cF @ Y0 )
| ( cG @ Y0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f70]) ).
thf(f70,plain,
( ( $true != $true )
| ( cG
!= ( ^ [Y0: $o] :
( ~ ( cF @ Y0 )
| ( cG @ Y0 ) ) ) ) ),
inference(constrained_superposition,[status(thm)],[f11,f8]) ).
thf(f8,plain,
( ( cP @ cG )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ( $true
!= ( cP
@ ^ [Y0: $o] :
( ~ ( cF @ Y0 )
| ( cG @ Y0 ) ) ) )
& ( $true
!= ( cP
@ ^ [Y0: $o] :
( ( cG @ Y0 )
| ( cF @ Y0 ) ) ) )
& ( ( cP @ cF )
= $true )
& ( ( cP @ cG )
= $true ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ( $true
!= ( cP
@ ^ [Y0: $o] :
( ( cG @ Y0 )
| ( cF @ Y0 ) ) ) )
& ( $true
!= ( cP
@ ^ [Y0: $o] :
( ~ ( cF @ Y0 )
| ( cG @ Y0 ) ) ) )
& ( ( cP @ cF )
= $true )
& ( ( cP @ cG )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ( ( cP @ cF )
= $true )
& ( ( cP @ cG )
= $true ) )
=> ( ( $true
= ( cP
@ ^ [Y0: $o] :
( ( cG @ Y0 )
| ( cF @ Y0 ) ) ) )
| ( $true
= ( cP
@ ^ [Y0: $o] :
( ~ ( cF @ Y0 )
| ( cG @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ( cP @ cF )
& ( cP @ cG ) )
=> ( ( cP
@ ^ [X0: $o] :
( ( cG @ X0 )
| ~ ( cF @ X0 ) ) )
| ( cP
@ ^ [X1: $o] :
( ( cF @ X1 )
| ( cG @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ( cP @ cF )
& ( cP @ cG ) )
=> ( ( cP
@ ^ [X0: $o] :
( ( cG @ X0 )
| ~ ( cF @ X0 ) ) )
| ( cP
@ ^ [X0: $o] :
( ( cF @ X0 )
| ( cG @ X0 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ( cP @ cF )
& ( cP @ cG ) )
=> ( ( cP
@ ^ [X0: $o] :
( ( cG @ X0 )
| ~ ( cF @ X0 ) ) )
| ( cP
@ ^ [X0: $o] :
( ( cF @ X0 )
| ( cG @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.gBESnEnGaI/DTF2THF_9150.p',cTHM627) ).
thf(f11,plain,
( $true
!= ( cP
@ ^ [Y0: $o] :
( ~ ( cF @ Y0 )
| ( cG @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f362,plain,
( spl0_8
| ~ spl0_4
| spl0_7 ),
inference(avatar_split_clause,[status(thm)],[f361,f86,f55,f90]) ).
thf(f90,definition,
( spl0_8
<=> ( $true = sK3 ) ),
introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition]) ).
thf(f55,definition,
( spl0_4
<=> ( ( cF @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f86,definition,
( spl0_7
<=> ( $true = sK2 ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f361,plain,
( ( $true = sK3 )
| ~ spl0_4
| spl0_7 ),
inference(subsumption_resolution,[status(thm)],[f179,f87]) ).
thf(f87,plain,
( ( $true != sK2 )
| spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f86]) ).
thf(f179,plain,
( ( $true = sK3 )
| ( $true = sK2 )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f178]) ).
thf(f178,plain,
( ( sK2 != sK3 )
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f171]) ).
thf(f171,plain,
( ( $false = $true )
| ( sK2 != sK3 )
| ~ spl0_4 ),
inference(constrained_superposition,[status(thm)],[f22,f57]) ).
thf(f57,plain,
( ( ( cF @ sK3 )
= $true )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f55]) ).
thf(f22,plain,
( $false
= ( cF @ sK2 ) ),
inference(duplicate_literal_removal,[status(thm)],[f20]) ).
thf(f20,plain,
( ( $false
= ( cF @ sK2 ) )
| ( $false
= ( cF @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
( ( $false
= ( cF @ sK2 ) )
| ( ( ( cG @ sK2 )
| ( cF @ sK2 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ( cG @ sK2 )
| ( cF @ sK2 ) )
!= ( cF @ sK2 ) ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ^ [Y0: $o] :
( ( cG @ Y0 )
| ( cF @ Y0 ) )
@ sK2 )
!= ( cF @ sK2 ) ),
inference(negative_extensionality,[status(thm)],[f14]) ).
thf(f14,plain,
( cF
!= ( ^ [Y0: $o] :
( ( cG @ Y0 )
| ( cF @ Y0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f12]) ).
thf(f12,plain,
( ( $true != $true )
| ( cF
!= ( ^ [Y0: $o] :
( ( cG @ Y0 )
| ( cF @ Y0 ) ) ) ) ),
inference(constrained_superposition,[status(thm)],[f10,f9]) ).
thf(f9,plain,
( ( cP @ cF )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f10,plain,
( $true
!= ( cP
@ ^ [Y0: $o] :
( ( cG @ Y0 )
| ( cF @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f353,plain,
( ~ spl0_1
| spl0_9
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[status(thm)],[f352]) ).
thf(f352,plain,
( $false
| ~ spl0_1
| spl0_9
| ~ spl0_13 ),
inference(trivial_inequality_removal,[status(thm)],[f346]) ).
thf(f346,plain,
( ( $false = $true )
| ~ spl0_1
| spl0_9
| ~ spl0_13 ),
inference(superposition,[status(thm)],[f334,f195]) ).
thf(f195,plain,
( ( $true = sK4 )
| ~ spl0_13 ),
inference(avatar_component_clause,[status(thm)],[f193]) ).
thf(f193,definition,
( spl0_13
<=> ( $true = sK4 ) ),
introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition]) ).
thf(f334,plain,
( ( $false = sK4 )
| ~ spl0_1
| spl0_9 ),
inference(subsumption_resolution,[status(thm)],[f311,f96]) ).
thf(f96,plain,
( ( $false != sK2 )
| spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f95]) ).
thf(f95,definition,
( spl0_9
<=> ( $false = sK2 ) ),
introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition]) ).
thf(f311,plain,
( ( $false = sK4 )
| ( $false = sK2 )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f309]) ).
thf(f309,plain,
( ( sK4 != sK2 )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f303]) ).
thf(f303,plain,
( ( sK4 != sK2 )
| ( $false = $true )
| ~ spl0_1 ),
inference(constrained_superposition,[status(thm)],[f28,f149]) ).
thf(f28,plain,
( ( $true
= ( cG @ sK2 ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f26]) ).
thf(f26,definition,
( spl0_1
<=> ( $true
= ( cG @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f323,plain,
( ~ spl0_4
| spl0_10
| ~ spl0_11
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[status(thm)],[f322]) ).
thf(f322,plain,
( $false
| ~ spl0_4
| spl0_10
| ~ spl0_11
| ~ spl0_13 ),
inference(trivial_inequality_removal,[status(thm)],[f316]) ).
thf(f316,plain,
( ( $false = $true )
| ~ spl0_4
| spl0_10
| ~ spl0_11
| ~ spl0_13 ),
inference(superposition,[status(thm)],[f195,f285]) ).
thf(f285,plain,
( ( $false = sK4 )
| ~ spl0_4
| spl0_10
| ~ spl0_11 ),
inference(subsumption_resolution,[status(thm)],[f284,f100]) ).
thf(f100,plain,
( ( $false != sK3 )
| spl0_10 ),
inference(avatar_component_clause,[status(thm)],[f99]) ).
thf(f99,definition,
( spl0_10
<=> ( $false = sK3 ) ),
introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition]) ).
thf(f284,plain,
( ( $false = sK3 )
| ( $false = sK4 )
| ~ spl0_4
| ~ spl0_11 ),
inference(binary_proxy_clausification,[status(thm)],[f282]) ).
thf(f282,plain,
( ( sK4 != sK3 )
| ~ spl0_4
| ~ spl0_11 ),
inference(trivial_inequality_removal,[status(thm)],[f274]) ).
thf(f274,plain,
( ( sK4 != sK3 )
| ( $false = $true )
| ~ spl0_4
| ~ spl0_11 ),
inference(constrained_superposition,[status(thm)],[f156,f57]) ).
thf(f156,plain,
( ( $false
= ( cF @ sK4 ) )
| ~ spl0_11 ),
inference(avatar_component_clause,[status(thm)],[f154]) ).
thf(f154,definition,
( spl0_11
<=> ( $false
= ( cF @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition]) ).
thf(f315,plain,
( spl0_13
| ~ spl0_1
| spl0_7 ),
inference(avatar_split_clause,[status(thm)],[f314,f86,f26,f193]) ).
thf(f314,plain,
( ( $true = sK4 )
| ~ spl0_1
| spl0_7 ),
inference(subsumption_resolution,[status(thm)],[f305,f87]) ).
thf(f305,plain,
( ( $true = sK4 )
| ( $true = sK2 )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f304]) ).
thf(f304,plain,
( ( sK4 != sK2 )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f301]) ).
thf(f301,plain,
( ( $false = $true )
| ( sK4 != sK2 )
| ~ spl0_1 ),
inference(constrained_superposition,[status(thm)],[f149,f28]) ).
thf(f235,plain,
( spl0_2
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f234]) ).
thf(f234,plain,
( $false
| spl0_2
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8 ),
inference(subsumption_resolution,[status(thm)],[f226,f128]) ).
thf(f128,plain,
( ( $true
!= ( cF @ $true ) )
| spl0_2
| ~ spl0_7 ),
inference(superposition,[status(thm)],[f31,f88]) ).
thf(f88,plain,
( ( $true = sK2 )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f86]) ).
thf(f31,plain,
( ( $true
!= ( cF @ sK2 ) )
| spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f30]) ).
thf(f30,definition,
( spl0_2
<=> ( $true
= ( cF @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f226,plain,
( ( $true
= ( cF @ $true ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f57,f92]) ).
thf(f92,plain,
( ( $true = sK3 )
| ~ spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f90]) ).
thf(f233,plain,
( ~ spl0_8
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[status(thm)],[f232]) ).
thf(f232,plain,
( $false
| ~ spl0_8
| ~ spl0_10 ),
inference(trivial_inequality_removal,[status(thm)],[f228]) ).
thf(f228,plain,
( ( $false = $true )
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[status(thm)],[f101,f92]) ).
thf(f101,plain,
( ( $false = sK3 )
| ~ spl0_10 ),
inference(avatar_component_clause,[status(thm)],[f99]) ).
thf(f197,plain,
( spl0_13
| spl0_8
| ~ spl0_4
| ~ spl0_11 ),
inference(avatar_split_clause,[status(thm)],[f185,f154,f55,f90,f193]) ).
thf(f185,plain,
( ( $true = sK3 )
| ( $true = sK4 )
| ~ spl0_4
| ~ spl0_11 ),
inference(binary_proxy_clausification,[status(thm)],[f184]) ).
thf(f184,plain,
( ( sK4 != sK3 )
| ~ spl0_4
| ~ spl0_11 ),
inference(trivial_inequality_removal,[status(thm)],[f182]) ).
thf(f182,plain,
( ( $false = $true )
| ( sK4 != sK3 )
| ~ spl0_4
| ~ spl0_11 ),
inference(constrained_superposition,[status(thm)],[f57,f156]) ).
thf(f161,plain,
( spl0_11
| spl0_12 ),
inference(avatar_split_clause,[status(thm)],[f152,f158,f154]) ).
thf(f152,plain,
( ( $false
= ( cF @ sK4 ) )
| ( ( cG @ sK4 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f151]) ).
thf(f151,plain,
( ( ( cG @ sK4 )
= $true )
| ( $true
= ( ~ ( cF @ sK4 ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f150]) ).
thf(f150,plain,
( ( $true
= ( ~ ( cF @ sK4 ) ) )
| ( ( cG @ sK4 )
= $true )
| ( ( cG @ sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f144]) ).
thf(f144,plain,
( ( ( cG @ sK4 )
= $true )
| ( $true
= ( ~ ( cF @ sK4 )
| ( cG @ sK4 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f143]) ).
thf(f139,plain,
( ~ spl0_7
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f138]) ).
thf(f138,plain,
( $false
| ~ spl0_7
| ~ spl0_9 ),
inference(trivial_inequality_removal,[status(thm)],[f132]) ).
thf(f132,plain,
( ( $false = $true )
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[status(thm)],[f88,f97]) ).
thf(f97,plain,
( ( $false = sK2 )
| ~ spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f95]) ).
thf(f123,plain,
( ~ spl0_3
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f122]) ).
thf(f122,plain,
( $false
| ~ spl0_3
| ~ spl0_5 ),
inference(trivial_inequality_removal,[status(thm)],[f112]) ).
thf(f112,plain,
( ( $false = $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[status(thm)],[f53,f62]) ).
thf(f62,plain,
( ( $false
= ( cG @ sK3 ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f60]) ).
thf(f60,definition,
( spl0_5
<=> ( $false
= ( cG @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f53,plain,
( ( $true
= ( cG @ sK3 ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f51]) ).
thf(f51,definition,
( spl0_3
<=> ( $true
= ( cG @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f68,plain,
spl0_5,
inference(avatar_split_clause,[status(thm)],[f47,f60]) ).
thf(f47,plain,
( $false
= ( cG @ sK3 ) ),
inference(duplicate_literal_removal,[status(thm)],[f46]) ).
thf(f46,plain,
( ( $false
= ( cG @ sK3 ) )
| ( $false
= ( cG @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
( ( ( ( cG @ sK3 )
| ( cF @ sK3 ) )
= $false )
| ( $false
= ( cG @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
( ( ( cG @ sK3 )
| ( cF @ sK3 ) )
!= ( cG @ sK3 ) ),
inference(beta_eta_normalization,[status(thm)],[f41]) ).
thf(f41,plain,
( ( ^ [Y0: $o] :
( ( cG @ Y0 )
| ( cF @ Y0 ) )
@ sK3 )
!= ( cG @ sK3 ) ),
inference(negative_extensionality,[status(thm)],[f15]) ).
thf(f15,plain,
( cG
!= ( ^ [Y0: $o] :
( ( cG @ Y0 )
| ( cF @ Y0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f13]) ).
thf(f13,plain,
( ( $true != $true )
| ( cG
!= ( ^ [Y0: $o] :
( ( cG @ Y0 )
| ( cF @ Y0 ) ) ) ) ),
inference(constrained_superposition,[status(thm)],[f10,f8]) ).
thf(f58,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f49,f55,f51]) ).
thf(f49,plain,
( ( ( cF @ sK3 )
= $true )
| ( $true
= ( cG @ sK3 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f48]) ).
thf(f48,plain,
( ( ( cF @ sK3 )
= $true )
| ( $true
= ( cG @ sK3 ) )
| ( $true
= ( cG @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
( ( ( ( cG @ sK3 )
| ( cF @ sK3 ) )
= $true )
| ( $true
= ( cG @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f42]) ).
thf(f39,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f38]) ).
thf(f38,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f34]) ).
thf(f34,plain,
( ( $false = $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f22,f32]) ).
thf(f32,plain,
( ( $true
= ( cF @ sK2 ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f30]) ).
thf(f33,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f24,f30,f26]) ).
thf(f24,plain,
( ( $true
= ( cF @ sK2 ) )
| ( $true
= ( cG @ sK2 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f23]) ).
thf(f23,plain,
( ( $true
= ( cF @ sK2 ) )
| ( $true
= ( cG @ sK2 ) )
| ( $true
= ( cF @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
( ( $true
= ( cF @ sK2 ) )
| ( ( ( cG @ sK2 )
| ( cF @ sK2 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO376^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/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 14:29:14 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : SYO376^5 : TPTP v9.2.1. Released v4.0.0.
% 0.20/0.46 % Domain : Syntactic
% 0.20/0.46 % Problem : TPS problem from EXTENSIONALITY
% 0.20/0.46 % Version : Especial.
% 0.20/0.46 % English :
% 0.20/0.46
% 0.20/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.46 % Source : [Bro09]
% 0.20/0.46 % Names : tps_0807 [Bro09]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % Rating : 0.25 v8.2.0, 0.27 v8.1.0, 0.25 v7.4.0, 0.33 v7.3.0, 0.40 v7.2.0, 0.38 v7.1.0, 0.43 v7.0.0, 0.38 v6.4.0, 0.43 v6.3.0, 0.50 v6.2.0, 0.67 v6.1.0, 0.50 v6.0.0, 0.33 v5.5.0, 0.00 v5.4.0, 0.25 v5.3.0, 0.50 v5.1.0, 0.75 v5.0.0, 0.50 v4.1.0, 1.00 v4.0.1, 0.67 v4.0.0
% 0.20/0.46 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.20/0.46 % Number of atoms : 10 ( 0 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 10 ( 10 avg)
% 0.20/0.46 % Number of connectives : 14 ( 1 ~; 3 |; 1 &; 8 @)
% 0.20/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 8 ( 8 avg)
% 0.20/0.46 % Number of types : 1 ( 0 usr)
% 0.20/0.46 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 3 ( 3 usr; 0 con; 1-1 aty)
% 0.20/0.46 % Number of variables : 2 ( 2 ^; 0 !; 0 ?; 2 :)
% 0.20/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.20/0.46
% 0.20/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 thf(cG,type,
% 0.20/0.46 cG: $o > $o ).
% 0.20/0.46
% 0.20/0.46 thf(cF,type,
% 0.20/0.46 cF: $o > $o ).
% 0.20/0.46
% 0.20/0.46 thf(cP,type,
% 0.20/0.46 cP: ( $o > $o ) > $o ).
% 0.20/0.46
% 0.20/0.46 thf(cTHM627,conjecture,
% 0.20/0.46 ( ( ( cP @ cF )
% 0.20/0.46 & ( cP @ cG ) )
% 0.20/0.46 => ( ( cP
% 0.20/0.46 @ ^ [Xx: $o] :
% 0.20/0.46 ( ( cF @ Xx )
% 0.20/0.46 | ( cG @ Xx ) ) )
% 0.20/0.46 | ( cP
% 0.20/0.46 @ ^ [Xx: $o] :
% 0.20/0.46 ( ~ ( cF @ Xx )
% 0.20/0.46 | ( cG @ Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 ------------------------
% 1.45/1.25 ---- Embedded in THF ---
% 1.45/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.45/1.25 %%% Generated on Tue Feb 24 14:29:15 EST 2026
% 1.45/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.45/1.25 %%% Logic specification used:
% 1.45/1.25 %%% thf(spec, logic, $$dhol).
% 1.45/1.25
% 1.45/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.gBESnEnGaI/DTF2DTF9150.p
% See solution above
% 1.45/1.25 ------------------------
% 1.45/1.26 ---- Cleaned THF ---
% 1.45/1.26 thf(cG,type,
% 1.45/1.26 cG: $o > $o ).
% 1.45/1.26
% 1.45/1.26 thf(cF,type,
% 1.45/1.26 cF: $o > $o ).
% 1.45/1.26
% 1.45/1.26 thf(cP,type,
% 1.45/1.26 cP: ( $o > $o ) > $o ).
% 1.45/1.26
% 1.45/1.26 thf(cTHM627,conjecture,
% 1.45/1.26 ( ( ( cP @ cF )
% 1.45/1.26 & ( cP @ cG ) )
% 1.45/1.26 => ( ( cP
% 1.45/1.26 @ ^ [Xx: $o] :
% 1.45/1.26 ( ( cF @ Xx )
% 1.45/1.26 | ( cG @ Xx ) ) )
% 1.45/1.26 | ( cP
% 1.45/1.26 @ ^ [Xx: $o] :
% 1.45/1.26 ( ~ ( cF @ Xx )
% 1.45/1.26 | ( cG @ Xx ) ) ) ) ) ).
% 1.45/1.26 ------------------------
% 1.45/1.27 % (9303)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_9150 for (2999ds/27Mi)
% 1.45/1.27 % (9302)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_9150 for (2999ds/4Mi)
% 1.45/1.27 % (9303)Refutation not found, incomplete strategy
% 1.45/1.27 % (9303)------------------------------
% 1.45/1.27 % (9303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.27 % (9303)Termination reason: Refutation not found, incomplete strategy
% 1.45/1.27
% 1.45/1.27
% 1.45/1.27 % (9303)Memory used [KB]: 5500
% 1.45/1.27 % (9303)Time elapsed: 0.002 s
% 1.45/1.27 % (9303)Instructions burned: 2 (million)
% 1.45/1.27 % (9303)------------------------------
% 1.45/1.27 % (9303)------------------------------
% 1.45/1.27 % (9302)Refutation not found, incomplete strategy
% 1.45/1.27 % (9302)------------------------------
% 1.45/1.27 % (9302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.27 % (9302)Termination reason: Refutation not found, incomplete strategy
% 1.45/1.27
% 1.45/1.27
% 1.45/1.27 % (9302)Memory used [KB]: 5500
% 1.45/1.27 % (9302)Time elapsed: 0.002 s
% 1.45/1.27 % (9302)Instructions burned: 2 (million)
% 1.45/1.27 % (9302)------------------------------
% 1.45/1.27 % (9302)------------------------------
% 1.45/1.28 % (9305)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_9150 for (2999ds/2Mi)
% 1.45/1.28 % (9305)Instruction limit reached!
% 1.45/1.28 % (9305)------------------------------
% 1.45/1.28 % (9305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.28 % (9305)Termination reason: Unknown
% 1.45/1.28 % (9305)Termination phase: Saturation
% 1.45/1.28
% 1.45/1.28 % (9305)Memory used [KB]: 5500
% 1.45/1.28 % (9305)Time elapsed: 0.003 s
% 1.45/1.28 % (9305)Instructions burned: 2 (million)
% 1.45/1.28 % (9301)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_9150 for (2999ds/183Mi)
% 1.45/1.28 % (9305)------------------------------
% 1.45/1.28 % (9305)------------------------------
% 1.45/1.28 % (9304)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_9150 for (2999ds/2Mi)
% 1.45/1.28 % (9307)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_9150 for (2999ds/18Mi)
% 1.45/1.28 % (9306)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_9150 for (2999ds/275Mi)
% 1.45/1.28 % (9304)Refutation not found, incomplete strategy
% 1.45/1.28 % (9304)------------------------------
% 1.45/1.28 % (9304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.28 % (9304)Termination reason: Refutation not found, incomplete strategy
% 1.45/1.28
% 1.45/1.28
% 1.45/1.28 % (9304)Memory used [KB]: 5500
% 1.45/1.28 % (9304)Time elapsed: 0.003 s
% 1.45/1.28 % (9304)Instructions burned: 1 (million)
% 1.45/1.28 % (9304)------------------------------
% 1.45/1.28 % (9304)------------------------------
% 1.45/1.28 % (9306)Refutation not found, incomplete strategy
% 1.45/1.28 % (9306)------------------------------
% 1.45/1.28 % (9306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.28 % (9306)Termination reason: Refutation not found, incomplete strategy
% 1.45/1.28
% 1.45/1.28
% 1.45/1.28 % (9306)Memory used [KB]: 5500
% 1.45/1.28 % (9306)Time elapsed: 0.003 s
% 1.45/1.28 % (9306)Instructions burned: 1 (million)
% 1.45/1.28 % (9306)------------------------------
% 1.45/1.28 % (9306)------------------------------
% 1.45/1.28 % (9308)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_9150 for (2999ds/3Mi)
% 1.45/1.28 % (9308)Refutation not found, incomplete strategy
% 1.45/1.28 % (9308)------------------------------
% 1.45/1.28 % (9308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.28 % (9308)Termination reason: Refutation not found, incomplete strategy
% 1.45/1.28
% 1.45/1.28
% 1.45/1.28 % (9308)Memory used [KB]: 5500
% 1.45/1.28 % (9308)Time elapsed: 0.002 s
% 1.45/1.28 % (9308)Instructions burned: 2 (million)
% 1.45/1.28 % (9308)------------------------------
% 1.45/1.28 % (9308)------------------------------
% 1.45/1.28 % (9309)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_9150 for (2999ds/37Mi)
% 1.45/1.29 % (9307)Refutation not found, incomplete strategy
% 1.45/1.29 % (9307)------------------------------
% 1.45/1.29 % (9307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.29 % (9307)Termination reason: Refutation not found, incomplete strategy
% 1.45/1.29
% 1.45/1.29
% 1.45/1.29 % (9307)Memory used [KB]: 5500
% 1.45/1.29 % (9307)Time elapsed: 0.008 s
% 1.45/1.29 % (9307)Instructions burned: 8 (million)
% 1.45/1.29 % (9307)------------------------------
% 1.45/1.29 % (9307)------------------------------
% 1.45/1.29 % (9309)Refutation not found, incomplete strategy
% 1.45/1.29 % (9309)------------------------------
% 1.45/1.29 % (9309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.29 % (9309)Termination reason: Refutation not found, incomplete strategy
% 1.45/1.29
% 1.45/1.29
% 1.45/1.29 % (9309)Memory used [KB]: 5628
% 1.45/1.29 % (9309)Time elapsed: 0.007 s
% 1.45/1.29 % (9309)Instructions burned: 12 (million)
% 1.45/1.29 % (9309)------------------------------
% 1.45/1.29 % (9309)------------------------------
% 1.45/1.29 % (9301)First to succeed.
% 1.45/1.29 % (9301)Refutation found. Thanks to Tanya!
% 1.45/1.29 % SZS status Theorem for DTF2THF_9150
% 1.45/1.29 % SZS output start Proof for DTF2THF_9150
% 1.45/1.29 thf(func_def_0, type, cG: $o > $o).
% 1.45/1.29 thf(func_def_1, type, cF: $o > $o).
% 1.45/1.29 thf(func_def_2, type, cP: ($o > $o) > $o).
% 1.45/1.29 thf(func_def_11, type, ph1: !>[X0: $tType]:(X0)).
% 1.45/1.29 thf(f411,plain,(
% 1.45/1.29 $false),
% 1.45/1.29 inference(avatar_sat_refutation,[status(thm)],[f33,f39,f58,f68,f123,f139,f161,f197,f233,f235,f315,f323,f353,f362,f401])).
% 1.45/1.29 thf(f401,plain,(
% 1.45/1.29 ~spl0_12),
% 1.45/1.29 inference(avatar_contradiction_clause,[status(thm)],[f400])).
% 1.45/1.29 thf(f400,plain,(
% 1.45/1.29 $false | ~spl0_12),
% 1.45/1.29 inference(trivial_inequality_removal,[status(thm)],[f392])).
% 1.45/1.29 thf(f392,plain,(
% 1.45/1.29 ($false = $true) | ~spl0_12),
% 1.45/1.29 inference(superposition,[status(thm)],[f149,f160])).
% 1.45/1.29 thf(f160,plain,(
% 1.45/1.29 ((cG @ sK4) = $true) | ~spl0_12),
% 1.45/1.29 inference(avatar_component_clause,[status(thm)],[f158])).
% 1.45/1.29 thf(f158,definition,(
% 1.45/1.29 spl0_12 <=> ((cG @ sK4) = $true)),
% 1.45/1.29 introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition])).
% 1.45/1.29 thf(f149,plain,(
% 1.45/1.29 ((cG @ sK4) = $false)),
% 1.45/1.29 inference(duplicate_literal_removal,[status(thm)],[f146])).
% 1.45/1.29 thf(f146,plain,(
% 1.45/1.29 ((cG @ sK4) = $false) | ((cG @ sK4) = $false)),
% 1.45/1.29 inference(binary_proxy_clausification,[status(thm)],[f145])).
% 1.45/1.29 thf(f145,plain,(
% 1.45/1.29 ((cG @ sK4) = $false) | ($false = ((~ (cF @ sK4)) | (cG @ sK4)))),
% 1.45/1.29 inference(binary_proxy_clausification,[status(thm)],[f143])).
% 1.45/1.29 thf(f143,plain,(
% 1.45/1.29 ((cG @ sK4) != ((~ (cF @ sK4)) | (cG @ sK4)))),
% 1.45/1.29 inference(beta_eta_normalization,[status(thm)],[f142])).
% 1.45/1.29 thf(f142,plain,(
% 1.45/1.29 ((cG @ sK4) != ((^[Y0 : $o]: ((~ (cF @ Y0)) | (cG @ Y0))) @ sK4))),
% 1.45/1.29 inference(negative_extensionality,[status(thm)],[f71])).
% 1.45/1.29 thf(f71,plain,(
% 1.45/1.29 (cG != (^[Y0 : $o]: ((~ (cF @ Y0)) | (cG @ Y0))))),
% 1.45/1.29 inference(trivial_inequality_removal,[status(thm)],[f70])).
% 1.45/1.29 thf(f70,plain,(
% 1.45/1.29 ($true != $true) | (cG != (^[Y0 : $o]: ((~ (cF @ Y0)) | (cG @ Y0))))),
% 1.45/1.29 inference(constrained_superposition,[status(thm)],[f11,f8])).
% 1.45/1.29 thf(f8,plain,(
% 1.45/1.29 ((cP @ cG) = $true)),
% 1.45/1.29 inference(cnf_transformation,[status(thm)],[f7])).
% 1.45/1.29 thf(f7,plain,(
% 1.45/1.29 ($true != (cP @ (^[Y0 : $o]: ((~ (cF @ Y0)) | (cG @ Y0))))) & ($true != (cP @ (^[Y0 : $o]: ((cG @ Y0) | (cF @ Y0))))) & ((cP @ cF) = $true) & ((cP @ cG) = $true)),
% 1.45/1.29 inference(flattening,[status(thm)],[f6])).
% 1.45/1.29 thf(f6,plain,(
% 1.45/1.29 (($true != (cP @ (^[Y0 : $o]: ((cG @ Y0) | (cF @ Y0))))) & ($true != (cP @ (^[Y0 : $o]: ((~ (cF @ Y0)) | (cG @ Y0)))))) & (((cP @ cF) = $true) & ((cP @ cG) = $true))),
% 1.45/1.29 inference(ennf_transformation,[status(thm)],[f5])).
% 1.45/1.29 thf(f5,plain,(
% 1.45/1.29 ~((((cP @ cF) = $true) & ((cP @ cG) = $true)) => (($true = (cP @ (^[Y0 : $o]: ((cG @ Y0) | (cF @ Y0))))) | ($true = (cP @ (^[Y0 : $o]: ((~ (cF @ Y0)) | (cG @ Y0)))))))),
% 1.45/1.29 inference(fool_elimination,[status(thm)],[f4])).
% 1.45/1.29 thf(f4,plain,(
% 1.45/1.29 ~(((cP @ cF) & (cP @ cG)) => ((cP @ (^[X0 : $o] : ((cG @ X0) | ~(cF @ X0)))) | (cP @ (^[X1 : $o] : ((cF @ X1) | (cG @ X1))))))),
% 1.45/1.29 inference(rectify,[status(thm)],[f2])).
% 1.45/1.29 thf(f2,negated_conjecture,(
% 1.45/1.29 ~(((cP @ cF) & (cP @ cG)) => ((cP @ (^[X0 : $o] : ((cG @ X0) | ~(cF @ X0)))) | (cP @ (^[X0 : $o] : ((cF @ X0) | (cG @ X0))))))),
% 1.45/1.29 inference(negated_conjecture,[status(cth)],[f1])).
% 1.45/1.29 thf(f1,conjecture,(
% 1.45/1.29 ((cP @ cF) & (cP @ cG)) => ((cP @ (^[X0 : $o] : ((cG @ X0) | ~(cF @ X0)))) | (cP @ (^[X0 : $o] : ((cF @ X0) | (cG @ X0)))))),
% 1.45/1.29 file('/export/starexec/sandbox2/tmp/tmp.gBESnEnGaI/DTF2THF_9150.p',cTHM627)).
% 1.45/1.29 thf(f11,plain,(
% 1.45/1.29 ($true != (cP @ (^[Y0 : $o]: ((~ (cF @ Y0)) | (cG @ Y0)))))),
% 1.45/1.29 inference(cnf_transformation,[status(thm)],[f7])).
% 1.45/1.29 thf(f362,plain,(
% 1.45/1.29 spl0_8 | ~spl0_4 | spl0_7),
% 1.45/1.29 inference(avatar_split_clause,[status(thm)],[f361,f86,f55,f90])).
% 1.45/1.29 thf(f90,definition,(
% 1.45/1.29 spl0_8 <=> ($true = sK3)),
% 1.45/1.29 introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition])).
% 1.45/1.29 thf(f55,definition,(
% 1.45/1.29 spl0_4 <=> ((cF @ sK3) = $true)),
% 1.45/1.29 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.45/1.29 thf(f86,definition,(
% 1.45/1.29 spl0_7 <=> ($true = sK2)),
% 1.45/1.29 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 1.45/1.29 thf(f361,plain,(
% 1.45/1.29 ($true = sK3) | (~spl0_4 | spl0_7)),
% 1.45/1.29 inference(subsumption_resolution,[status(thm)],[f179,f87])).
% 1.45/1.29 thf(f87,plain,(
% 1.45/1.29 ($true != sK2) | spl0_7),
% 1.45/1.29 inference(avatar_component_clause,[status(thm)],[f86])).
% 1.45/1.29 thf(f179,plain,(
% 1.45/1.29 ($true = sK3) | ($true = sK2) | ~spl0_4),
% 1.45/1.29 inference(binary_proxy_clausification,[status(thm)],[f178])).
% 1.45/1.29 thf(f178,plain,(
% 1.45/1.29 (sK2 != sK3) | ~spl0_4),
% 1.45/1.29 inference(trivial_inequality_removal,[status(thm)],[f171])).
% 1.45/1.29 thf(f171,plain,(
% 1.45/1.29 ($false = $true) | (sK2 != sK3) | ~spl0_4),
% 1.45/1.29 inference(constrained_superposition,[status(thm)],[f22,f57])).
% 1.45/1.29 thf(f57,plain,(
% 1.45/1.29 ((cF @ sK3) = $true) | ~spl0_4),
% 1.45/1.29 inference(avatar_component_clause,[status(thm)],[f55])).
% 1.45/1.29 thf(f22,plain,(
% 1.45/1.29 ($false = (cF @ sK2))),
% 1.45/1.29 inference(duplicate_literal_removal,[status(thm)],[f20])).
% 1.45/1.29 thf(f20,plain,(
% 1.45/1.29 ($false = (cF @ sK2)) | ($false = (cF @ sK2))),
% 1.45/1.29 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.45/1.29 thf(f19,plain,(
% 1.45/1.29 ($false = (cF @ sK2)) | (((cG @ sK2) | (cF @ sK2)) = $false)),
% 1.45/1.29 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.45/1.29 thf(f17,plain,(
% 1.45/1.29 (((cG @ sK2) | (cF @ sK2)) != (cF @ sK2))),
% 1.45/1.29 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.45/1.29 thf(f16,plain,(
% 1.45/1.29 (((^[Y0 : $o]: ((cG @ Y0) | (cF @ Y0))) @ sK2) != (cF @ sK2))),
% 1.45/1.29 inference(negative_extensionality,[status(thm)],[f14])).
% 1.45/1.29 thf(f14,plain,(
% 1.45/1.29 (cF != (^[Y0 : $o]: ((cG @ Y0) | (cF @ Y0))))),
% 1.45/1.29 inference(trivial_inequality_removal,[status(thm)],[f12])).
% 1.45/1.29 thf(f12,plain,(
% 1.45/1.29 ($true != $true) | (cF != (^[Y0 : $o]: ((cG @ Y0) | (cF @ Y0))))),
% 1.45/1.29 inference(constrained_superposition,[status(thm)],[f10,f9])).
% 1.45/1.29 thf(f9,plain,(
% 1.45/1.29 ((cP @ cF) = $true)),
% 1.45/1.29 inference(cnf_transformation,[status(thm)],[f7])).
% 1.45/1.29 thf(f10,plain,(
% 1.45/1.29 ($true != (cP @ (^[Y0 : $o]: ((cG @ Y0) | (cF @ Y0)))))),
% 1.45/1.29 inference(cnf_transformation,[status(thm)],[f7])).
% 1.45/1.29 thf(f353,plain,(
% 1.45/1.29 ~spl0_1 | spl0_9 | ~spl0_13),
% 1.45/1.29 inference(avatar_contradiction_clause,[status(thm)],[f352])).
% 1.45/1.29 thf(f352,plain,(
% 1.45/1.29 $false | (~spl0_1 | spl0_9 | ~spl0_13)),
% 1.45/1.29 inference(trivial_inequality_removal,[status(thm)],[f346])).
% 1.45/1.29 thf(f346,plain,(
% 1.45/1.29 ($false = $true) | (~spl0_1 | spl0_9 | ~spl0_13)),
% 1.45/1.29 inference(superposition,[status(thm)],[f334,f195])).
% 1.45/1.29 thf(f195,plain,(
% 1.45/1.29 ($true = sK4) | ~spl0_13),
% 1.45/1.29 inference(avatar_component_clause,[status(thm)],[f193])).
% 1.45/1.29 thf(f193,definition,(
% 1.45/1.29 spl0_13 <=> ($true = sK4)),
% 1.45/1.29 introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition])).
% 1.45/1.29 thf(f334,plain,(
% 1.45/1.29 ($false = sK4) | (~spl0_1 | spl0_9)),
% 1.45/1.29 inference(subsumption_resolution,[status(thm)],[f311,f96])).
% 1.45/1.29 thf(f96,plain,(
% 1.45/1.29 ($false != sK2) | spl0_9),
% 1.45/1.29 inference(avatar_component_clause,[status(thm)],[f95])).
% 1.45/1.29 thf(f95,definition,(
% 1.45/1.29 spl0_9 <=> ($false = sK2)),
% 1.45/1.29 introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition])).
% 1.45/1.29 thf(f311,plain,(
% 1.45/1.29 ($false = sK4) | ($false = sK2) | ~spl0_1),
% 1.45/1.29 inference(binary_proxy_clausification,[status(thm)],[f309])).
% 1.45/1.29 thf(f309,plain,(
% 1.45/1.29 (sK4 != sK2) | ~spl0_1),
% 1.45/1.29 inference(trivial_inequality_removal,[status(thm)],[f303])).
% 1.45/1.29 thf(f303,plain,(
% 1.45/1.29 (sK4 != sK2) | ($false = $true) | ~spl0_1),
% 1.45/1.29 inference(constrained_superposition,[status(thm)],[f28,f149])).
% 1.45/1.29 thf(f28,plain,(
% 1.45/1.29 ($true = (cG @ sK2)) | ~spl0_1),
% 1.45/1.29 inference(avatar_component_clause,[status(thm)],[f26])).
% 1.45/1.29 thf(f26,definition,(
% 1.45/1.29 spl0_1 <=> ($true = (cG @ sK2))),
% 1.45/1.29 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.45/1.29 thf(f323,plain,(
% 1.45/1.29 ~spl0_4 | spl0_10 | ~spl0_11 | ~spl0_13),
% 1.45/1.29 inference(avatar_contradiction_clause,[status(thm)],[f322])).
% 1.45/1.29 thf(f322,plain,(
% 1.45/1.29 $false | (~spl0_4 | spl0_10 | ~spl0_11 | ~spl0_13)),
% 1.45/1.29 inference(trivial_inequality_removal,[status(thm)],[f316])).
% 1.45/1.29 thf(f316,plain,(
% 1.45/1.29 ($false = $true) | (~spl0_4 | spl0_10 | ~spl0_11 | ~spl0_13)),
% 1.45/1.29 inference(superposition,[status(thm)],[f195,f285])).
% 1.45/1.29 thf(f285,plain,(
% 1.45/1.29 ($false = sK4) | (~spl0_4 | spl0_10 | ~spl0_11)),
% 1.45/1.29 inference(subsumption_resolution,[status(thm)],[f284,f100])).
% 1.45/1.29 thf(f100,plain,(
% 1.45/1.29 ($false != sK3) | spl0_10),
% 1.45/1.29 inference(avatar_component_clause,[status(thm)],[f99])).
% 1.45/1.29 thf(f99,definition,(
% 1.45/1.29 spl0_10 <=> ($false = sK3)),
% 1.45/1.29 introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition])).
% 1.45/1.29 thf(f284,plain,(
% 1.45/1.29 ($false = sK3) | ($false = sK4) | (~spl0_4 | ~spl0_11)),
% 1.45/1.29 inference(binary_proxy_clausification,[status(thm)],[f282])).
% 1.45/1.29 thf(f282,plain,(
% 1.45/1.29 (sK4 != sK3) | (~spl0_4 | ~spl0_11)),
% 1.45/1.29 inference(trivial_inequality_removal,[status(thm)],[f274])).
% 1.45/1.29 thf(f274,plain,(
% 1.45/1.29 (sK4 != sK3) | ($false = $true) | (~spl0_4 | ~spl0_11)),
% 1.45/1.29 inference(constrained_superposition,[status(thm)],[f156,f57])).
% 1.45/1.29 thf(f156,plain,(
% 1.45/1.29 ($false = (cF @ sK4)) | ~spl0_11),
% 1.45/1.29 inference(avatar_component_clause,[status(thm)],[f154])).
% 1.45/1.29 thf(f154,definition,(
% 1.45/1.29 spl0_11 <=> ($false = (cF @ sK4))),
% 1.45/1.29 introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition])).
% 1.45/1.29 thf(f315,plain,(
% 1.45/1.29 spl0_13 | ~spl0_1 | spl0_7),
% 1.45/1.29 inference(avatar_split_clause,[status(thm)],[f314,f86,f26,f193])).
% 1.45/1.29 thf(f314,plain,(
% 1.45/1.29 ($true = sK4) | (~spl0_1 | spl0_7)),
% 1.45/1.29 inference(subsumption_resolution,[status(thm)],[f305,f87])).
% 1.45/1.29 thf(f305,plain,(
% 1.45/1.29 ($true = sK4) | ($true = sK2) | ~spl0_1),
% 1.45/1.29 inference(binary_proxy_clausification,[status(thm)],[f304])).
% 1.45/1.29 thf(f304,plain,(
% 1.45/1.29 (sK4 != sK2) | ~spl0_1),
% 1.45/1.29 inference(trivial_inequality_removal,[status(thm)],[f301])).
% 1.45/1.29 thf(f301,plain,(
% 1.45/1.29 ($false = $true) | (sK4 != sK2) | ~spl0_1),
% 1.45/1.29 inference(constrained_superposition,[status(thm)],[f149,f28])).
% 1.45/1.29 thf(f235,plain,(
% 1.45/1.29 spl0_2 | ~spl0_4 | ~spl0_7 | ~spl0_8),
% 1.45/1.29 inference(avatar_contradiction_clause,[status(thm)],[f234])).
% 1.45/1.29 thf(f234,plain,(
% 1.45/1.29 $false | (spl0_2 | ~spl0_4 | ~spl0_7 | ~spl0_8)),
% 1.45/1.29 inference(subsumption_resolution,[status(thm)],[f226,f128])).
% 1.45/1.29 thf(f128,plain,(
% 1.45/1.29 ($true != (cF @ $true)) | (spl0_2 | ~spl0_7)),
% 1.45/1.29 inference(superposition,[status(thm)],[f31,f88])).
% 1.45/1.29 thf(f88,plain,(
% 1.45/1.29 ($true = sK2) | ~spl0_7),
% 1.45/1.29 inference(avatar_component_clause,[status(thm)],[f86])).
% 1.45/1.29 thf(f31,plain,(
% 1.45/1.29 ($true != (cF @ sK2)) | spl0_2),
% 1.45/1.29 inference(avatar_component_clause,[status(thm)],[f30])).
% 1.45/1.29 thf(f30,definition,(
% 1.45/1.29 spl0_2 <=> ($true = (cF @ sK2))),
% 1.45/1.29 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.45/1.29 thf(f226,plain,(
% 1.45/1.29 ($true = (cF @ $true)) | (~spl0_4 | ~spl0_8)),
% 1.45/1.29 inference(superposition,[status(thm)],[f57,f92])).
% 1.45/1.29 thf(f92,plain,(
% 1.45/1.29 ($true = sK3) | ~spl0_8),
% 1.45/1.29 inference(avatar_component_clause,[status(thm)],[f90])).
% 1.45/1.29 thf(f233,plain,(
% 1.45/1.29 ~spl0_8 | ~spl0_10),
% 1.45/1.29 inference(avatar_contradiction_clause,[status(thm)],[f232])).
% 1.45/1.29 thf(f232,plain,(
% 1.45/1.29 $false | (~spl0_8 | ~spl0_10)),
% 1.45/1.29 inference(trivial_inequality_removal,[status(thm)],[f228])).
% 1.45/1.29 thf(f228,plain,(
% 1.45/1.29 ($false = $true) | (~spl0_8 | ~spl0_10)),
% 1.45/1.29 inference(superposition,[status(thm)],[f101,f92])).
% 1.45/1.29 thf(f101,plain,(
% 1.45/1.29 ($false = sK3) | ~spl0_10),
% 1.45/1.29 inference(avatar_component_clause,[status(thm)],[f99])).
% 1.45/1.29 thf(f197,plain,(
% 1.45/1.29 spl0_13 | spl0_8 | ~spl0_4 | ~spl0_11),
% 1.45/1.29 inference(avatar_split_clause,[status(thm)],[f185,f154,f55,f90,f193])).
% 1.45/1.29 thf(f185,plain,(
% 1.45/1.29 ($true = sK3) | ($true = sK4) | (~spl0_4 | ~spl0_11)),
% 1.45/1.29 inference(binary_proxy_clausification,[status(thm)],[f184])).
% 1.45/1.29 thf(f184,plain,(
% 1.45/1.29 (sK4 != sK3) | (~spl0_4 | ~spl0_11)),
% 1.45/1.29 inference(trivial_inequality_removal,[status(thm)],[f182])).
% 1.45/1.29 thf(f182,plain,(
% 1.45/1.29 ($false = $true) | (sK4 != sK3) | (~spl0_4 | ~spl0_11)),
% 1.45/1.29 inference(constrained_superposition,[status(thm)],[f57,f156])).
% 1.45/1.29 thf(f161,plain,(
% 1.45/1.29 spl0_11 | spl0_12),
% 1.45/1.29 inference(avatar_split_clause,[status(thm)],[f152,f158,f154])).
% 1.45/1.29 thf(f152,plain,(
% 1.45/1.29 ($false = (cF @ sK4)) | ((cG @ sK4) = $true)),
% 1.45/1.29 inference(not_proxy_clausification,[status(thm)],[f151])).
% 1.45/1.29 thf(f151,plain,(
% 1.45/1.29 ((cG @ sK4) = $true) | ($true = (~ (cF @ sK4)))),
% 1.45/1.29 inference(duplicate_literal_removal,[status(thm)],[f150])).
% 1.45/1.29 thf(f150,plain,(
% 1.45/1.29 ($true = (~ (cF @ sK4))) | ((cG @ sK4) = $true) | ((cG @ sK4) = $true)),
% 1.45/1.29 inference(binary_proxy_clausification,[status(thm)],[f144])).
% 1.45/1.29 thf(f144,plain,(
% 1.45/1.29 ((cG @ sK4) = $true) | ($true = ((~ (cF @ sK4)) | (cG @ sK4)))),
% 1.45/1.29 inference(binary_proxy_clausification,[status(thm)],[f143])).
% 1.45/1.29 thf(f139,plain,(
% 1.45/1.29 ~spl0_7 | ~spl0_9),
% 1.45/1.29 inference(avatar_contradiction_clause,[status(thm)],[f138])).
% 1.45/1.29 thf(f138,plain,(
% 1.45/1.29 $false | (~spl0_7 | ~spl0_9)),
% 1.45/1.29 inference(trivial_inequality_removal,[status(thm)],[f132])).
% 1.45/1.29 thf(f132,plain,(
% 1.45/1.29 ($false = $true) | (~spl0_7 | ~spl0_9)),
% 1.45/1.29 inference(superposition,[status(thm)],[f88,f97])).
% 1.45/1.29 thf(f97,plain,(
% 1.45/1.29 ($false = sK2) | ~spl0_9),
% 1.45/1.29 inference(avatar_component_clause,[status(thm)],[f95])).
% 1.45/1.29 thf(f123,plain,(
% 1.45/1.29 ~spl0_3 | ~spl0_5),
% 1.45/1.29 inference(avatar_contradiction_clause,[status(thm)],[f122])).
% 1.45/1.29 thf(f122,plain,(
% 1.45/1.29 $false | (~spl0_3 | ~spl0_5)),
% 1.45/1.29 inference(trivial_inequality_removal,[status(thm)],[f112])).
% 1.45/1.29 thf(f112,plain,(
% 1.45/1.29 ($false = $true) | (~spl0_3 | ~spl0_5)),
% 1.45/1.29 inference(superposition,[status(thm)],[f53,f62])).
% 1.45/1.29 thf(f62,plain,(
% 1.45/1.29 ($false = (cG @ sK3)) | ~spl0_5),
% 1.45/1.29 inference(avatar_component_clause,[status(thm)],[f60])).
% 1.45/1.29 thf(f60,definition,(
% 1.45/1.29 spl0_5 <=> ($false = (cG @ sK3))),
% 1.45/1.29 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.45/1.29 thf(f53,plain,(
% 1.45/1.29 ($true = (cG @ sK3)) | ~spl0_3),
% 1.45/1.29 inference(avatar_component_clause,[status(thm)],[f51])).
% 1.45/1.29 thf(f51,definition,(
% 1.45/1.29 spl0_3 <=> ($true = (cG @ sK3))),
% 1.45/1.29 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.45/1.29 thf(f68,plain,(
% 1.45/1.29 spl0_5),
% 1.45/1.29 inference(avatar_split_clause,[status(thm)],[f47,f60])).
% 1.45/1.30 thf(f47,plain,(
% 1.45/1.30 ($false = (cG @ sK3))),
% 1.45/1.30 inference(duplicate_literal_removal,[status(thm)],[f46])).
% 1.45/1.30 thf(f46,plain,(
% 1.45/1.30 ($false = (cG @ sK3)) | ($false = (cG @ sK3))),
% 1.45/1.30 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.45/1.30 thf(f44,plain,(
% 1.45/1.30 (((cG @ sK3) | (cF @ sK3)) = $false) | ($false = (cG @ sK3))),
% 1.45/1.30 inference(binary_proxy_clausification,[status(thm)],[f42])).
% 1.45/1.30 thf(f42,plain,(
% 1.45/1.30 (((cG @ sK3) | (cF @ sK3)) != (cG @ sK3))),
% 1.45/1.30 inference(beta_eta_normalization,[status(thm)],[f41])).
% 1.45/1.30 thf(f41,plain,(
% 1.45/1.30 (((^[Y0 : $o]: ((cG @ Y0) | (cF @ Y0))) @ sK3) != (cG @ sK3))),
% 1.45/1.30 inference(negative_extensionality,[status(thm)],[f15])).
% 1.45/1.30 thf(f15,plain,(
% 1.45/1.30 (cG != (^[Y0 : $o]: ((cG @ Y0) | (cF @ Y0))))),
% 1.45/1.30 inference(trivial_inequality_removal,[status(thm)],[f13])).
% 1.45/1.30 thf(f13,plain,(
% 1.45/1.30 ($true != $true) | (cG != (^[Y0 : $o]: ((cG @ Y0) | (cF @ Y0))))),
% 1.45/1.30 inference(constrained_superposition,[status(thm)],[f10,f8])).
% 1.45/1.30 thf(f58,plain,(
% 1.45/1.30 spl0_3 | spl0_4),
% 1.45/1.30 inference(avatar_split_clause,[status(thm)],[f49,f55,f51])).
% 1.45/1.30 thf(f49,plain,(
% 1.45/1.30 ((cF @ sK3) = $true) | ($true = (cG @ sK3))),
% 1.45/1.30 inference(duplicate_literal_removal,[status(thm)],[f48])).
% 1.45/1.30 thf(f48,plain,(
% 1.45/1.30 ((cF @ sK3) = $true) | ($true = (cG @ sK3)) | ($true = (cG @ sK3))),
% 1.45/1.30 inference(binary_proxy_clausification,[status(thm)],[f43])).
% 1.45/1.30 thf(f43,plain,(
% 1.45/1.30 (((cG @ sK3) | (cF @ sK3)) = $true) | ($true = (cG @ sK3))),
% 1.45/1.30 inference(binary_proxy_clausification,[status(thm)],[f42])).
% 1.45/1.30 thf(f39,plain,(
% 1.45/1.30 ~spl0_2),
% 1.45/1.30 inference(avatar_contradiction_clause,[status(thm)],[f38])).
% 1.45/1.30 thf(f38,plain,(
% 1.45/1.30 $false | ~spl0_2),
% 1.45/1.30 inference(trivial_inequality_removal,[status(thm)],[f34])).
% 1.45/1.30 thf(f34,plain,(
% 1.45/1.30 ($false = $true) | ~spl0_2),
% 1.45/1.30 inference(superposition,[status(thm)],[f22,f32])).
% 1.45/1.30 thf(f32,plain,(
% 1.45/1.30 ($true = (cF @ sK2)) | ~spl0_2),
% 1.45/1.30 inference(avatar_component_clause,[status(thm)],[f30])).
% 1.45/1.30 thf(f33,plain,(
% 1.45/1.30 spl0_1 | spl0_2),
% 1.45/1.30 inference(avatar_split_clause,[status(thm)],[f24,f30,f26])).
% 1.45/1.30 thf(f24,plain,(
% 1.45/1.30 ($true = (cF @ sK2)) | ($true = (cG @ sK2))),
% 1.45/1.30 inference(duplicate_literal_removal,[status(thm)],[f23])).
% 1.45/1.30 thf(f23,plain,(
% 1.45/1.30 ($true = (cF @ sK2)) | ($true = (cG @ sK2)) | ($true = (cF @ sK2))),
% 1.45/1.30 inference(binary_proxy_clausification,[status(thm)],[f18])).
% 1.45/1.30 thf(f18,plain,(
% 1.45/1.30 ($true = (cF @ sK2)) | (((cG @ sK2) | (cF @ sK2)) = $true)),
% 1.45/1.30 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.45/1.30 % SZS output end Proof for DTF2THF_9150
% 1.45/1.30 % (9301)------------------------------
% 1.45/1.30 % (9301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.30 % (9301)Termination reason: Refutation
% 1.45/1.30
% 1.45/1.30 % (9301)Memory used [KB]: 5628
% 1.45/1.30 % (9301)Time elapsed: 0.016 s
% 1.45/1.30 % (9301)Instructions burned: 16 (million)
% 1.45/1.30 % (9301)------------------------------
% 1.45/1.30 % (9301)------------------------------
% 1.45/1.30 % (9300)Success in time 0.019 s
%------------------------------------------------------------------------------