%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV447^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:38:38 AM UTC 2026
% Result : Theorem 0.18s 0.26s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 22
% Syntax : Number of formulae : 169 ( 30 unt; 0 typ; 20 def)
% Number of atoms : 788 ( 182 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 641 ( 154 ~; 186 |; 0 &; 277 @)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 41 ( 37 usr; 29 con; 0-4 aty)
% ( 0 !!; 7 ??; 0 @@+; 0 @@-)
% Number of variables : 61 ( 0 sgn 46 !; 6 ?; 61 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
sK0: $tType ).
thf(func_def_0,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_2,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_3,type,
vNOT: $o > $o ).
thf(func_def_4,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_7,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_8,type,
sK1: sK0 > $o ).
thf(func_def_9,type,
sK2: sK0 > $o ).
thf(func_def_12,type,
sF3: $o ).
thf(func_def_13,type,
sF4: $o ).
thf(func_def_14,type,
sF5: $o ).
thf(func_def_15,type,
sK6: sK0 ).
thf(func_def_16,type,
sK7:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_18,type,
sK9: sK0 ).
thf(func_def_19,type,
sK10: sK0 ).
thf(func_def_20,type,
sK11: sK0 ).
thf(func_def_21,type,
sK12: sK0 ).
thf(func_def_22,type,
sK13: sK0 ).
thf(f1,axiom,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= ( X1 @ X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_') ).
thf(f3,conjecture,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( X1 != X2 )
= ( ? [X3: X0] :
( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= ( ~ ( 'const/sets/IN' @ X0 @ X3 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/NOT_EQUAL_SETS_') ).
thf(f4,negated_conjecture,
~ ! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( X1 != X2 )
= ( ? [X3: X0] :
( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= ( ~ ( 'const/sets/IN' @ X0 @ X3 @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
~ ! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( X1 != X2 )
= ( ? [X3: X0] :
( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= ( ~ ( 'const/sets/IN' @ X0 @ X3 @ X1 ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
~ ! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( ?? @ X0
@ ^ [Y0: X0] :
( ( 'const/sets/IN' @ X0 @ Y0 @ X2 )
= ( ~ ( 'const/sets/IN' @ X0 @ Y0 @ X1 ) ) ) )
= ( X1 != X2 ) ),
inference(fool_elimination,[],[f5]) ).
thf(f9,plain,
! [X0: $tType,X1: X0,X2: X0 > $o] :
( ( 'const/sets/IN' @ X0 @ X1 @ X2 )
= ( X2 @ X1 ) ),
inference(rectify,[],[f1]) ).
thf(f10,plain,
? [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ?? @ X0
@ ^ [Y0: X0] :
( ( 'const/sets/IN' @ X0 @ Y0 @ X2 )
= ( ~ ( 'const/sets/IN' @ X0 @ Y0 @ X1 ) ) ) )
!= ( X1 != X2 ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f12,plain,
( ( sK1 != sK2 )
!= ( ?? @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK2 )
= ( ~ ( 'const/sets/IN' @ sK0 @ Y0 @ sK1 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f10]) ).
thf(f14,plain,
( ( sK1 != sK2 )
!= ( ?? @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK2 )
= ( ~ ( 'const/sets/IN' @ sK0 @ Y0 @ sK1 ) ) ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f15,plain,
! [X0: $tType,X2: X0 > $o,X1: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ X2 )
= ( X2 @ X1 ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f18,definition,
( sF3
= ( sK1 = sK2 ) ),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
thf(f19,definition,
( sF4 = ( ~ sF3 ) ),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
thf(f20,plain,
( ( ~ sF3 ) = sF4 ),
inference(reorient_equations,[],[f19]) ).
thf(f21,definition,
( sF5
= ( ?? @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK2 )
= ( ~ ( 'const/sets/IN' @ sK0 @ Y0 @ sK1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
thf(f22,plain,
sF5 != sF4,
inference(definition_folding,[],[f14,f21,f20,f18]) ).
thf(f23,plain,
( ( $true = sF4 )
| ( sF5 = $true ) ),
inference(xor_proxy_clausification,[],[f22]) ).
thf(f24,plain,
( ( $false = sF5 )
| ( $false = sF4 ) ),
inference(xor_proxy_clausification,[],[f22]) ).
thf(f25,plain,
( ( $false = sF4 )
| ( ( ~ sF3 ) = $true ) ),
inference(iff_proxy_clausification,[],[f20]) ).
thf(f26,plain,
( ( $false = ( ~ sF3 ) )
| ( $true = sF4 ) ),
inference(iff_proxy_clausification,[],[f20]) ).
thf(f27,plain,
( ( $true = sF4 )
| ( sF3 = $true ) ),
inference(not_proxy_clausification,[],[f26]) ).
thf(f28,plain,
( ( $false = sF4 )
| ( $false = sF3 ) ),
inference(not_proxy_clausification,[],[f25]) ).
thf(f29,plain,
( ( $false
= ( sK1 = sK2 ) )
| ( sF3 = $true ) ),
inference(iff_proxy_clausification,[],[f18]) ).
thf(f30,plain,
( ( $false = sF3 )
| ( ( sK1 = sK2 )
= $true ) ),
inference(iff_proxy_clausification,[],[f18]) ).
thf(f31,plain,
( ( sK2 = sK1 )
| ( $false = sF3 ) ),
inference(equality_proxy_clausification,[],[f30]) ).
thf(f32,plain,
( ( sF3 = $true )
| ( sK2 != sK1 ) ),
inference(equality_proxy_clausification,[],[f29]) ).
thf(f33,plain,
( ( $false
= ( ?? @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK2 )
= ( ~ ( 'const/sets/IN' @ sK0 @ Y0 @ sK1 ) ) ) ) )
| ( sF5 = $true ) ),
inference(iff_proxy_clausification,[],[f21]) ).
thf(f34,plain,
( ( $false = sF5 )
| ( ( ?? @ sK0
@ ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK2 )
= ( ~ ( 'const/sets/IN' @ sK0 @ Y0 @ sK1 ) ) ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f21]) ).
thf(f35,plain,
( ( ( ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK2 )
= ( ~ ( 'const/sets/IN' @ sK0 @ Y0 @ sK1 ) ) )
@ sK6 )
= $true )
| ( $false = sF5 ) ),
inference(sigma_proxy_clausification,[],[f34]) ).
thf(f36,plain,
( ( $false = sF5 )
| ( ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK2 )
= ( ~ ( 'const/sets/IN' @ sK0 @ sK6 @ sK1 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f35]) ).
thf(f37,plain,
( ( ( ~ ( 'const/sets/IN' @ sK0 @ sK6 @ sK1 ) )
= ( 'const/sets/IN' @ sK0 @ sK6 @ sK2 ) )
| ( $false = sF5 ) ),
inference(equality_proxy_clausification,[],[f36]) ).
thf(f38,plain,
( ( $false = sF5 )
| ( ( ~ ( 'const/sets/IN' @ sK0 @ sK6 @ sK1 ) )
= $true )
| ( $false
= ( 'const/sets/IN' @ sK0 @ sK6 @ sK2 ) ) ),
inference(iff_proxy_clausification,[],[f37]) ).
thf(f39,plain,
( ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK2 )
= $true )
| ( $false
= ( ~ ( 'const/sets/IN' @ sK0 @ sK6 @ sK1 ) ) )
| ( $false = sF5 ) ),
inference(iff_proxy_clausification,[],[f37]) ).
thf(f40,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK6 @ sK1 ) )
| ( $false = sF5 )
| ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK2 )
= $true ) ),
inference(not_proxy_clausification,[],[f39]) ).
thf(f41,plain,
( ( $false = sF5 )
| ( $false
= ( 'const/sets/IN' @ sK0 @ sK6 @ sK2 ) )
| ( $false
= ( 'const/sets/IN' @ sK0 @ sK6 @ sK1 ) ) ),
inference(not_proxy_clausification,[],[f38]) ).
thf(f42,plain,
! [X1: sK0] :
( ( $false
= ( ^ [Y0: sK0] :
( ( 'const/sets/IN' @ sK0 @ Y0 @ sK2 )
= ( ~ ( 'const/sets/IN' @ sK0 @ Y0 @ sK1 ) ) )
@ X1 ) )
| ( sF5 = $true ) ),
inference(pi_proxy_clausification,[],[f33]) ).
thf(f43,plain,
! [X1: sK0] :
( ( sF5 = $true )
| ( $false
= ( ( 'const/sets/IN' @ sK0 @ X1 @ sK2 )
= ( ~ ( 'const/sets/IN' @ sK0 @ X1 @ sK1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f42]) ).
thf(f44,plain,
! [X1: sK0] :
( ( sF5 = $true )
| ( ( ~ ( 'const/sets/IN' @ sK0 @ X1 @ sK1 ) )
!= ( 'const/sets/IN' @ sK0 @ X1 @ sK2 ) ) ),
inference(equality_proxy_clausification,[],[f43]) ).
thf(f45,plain,
! [X1: sK0] :
( ( ( 'const/sets/IN' @ sK0 @ X1 @ sK2 )
= $true )
| ( ( ~ ( 'const/sets/IN' @ sK0 @ X1 @ sK1 ) )
= $true )
| ( sF5 = $true ) ),
inference(xor_proxy_clausification,[],[f44]) ).
thf(f46,plain,
! [X1: sK0] :
( ( sF5 = $true )
| ( $false
= ( 'const/sets/IN' @ sK0 @ X1 @ sK2 ) )
| ( $false
= ( ~ ( 'const/sets/IN' @ sK0 @ X1 @ sK1 ) ) ) ),
inference(xor_proxy_clausification,[],[f44]) ).
thf(f47,plain,
! [X1: sK0] :
( ( $true
= ( 'const/sets/IN' @ sK0 @ X1 @ sK1 ) )
| ( $false
= ( 'const/sets/IN' @ sK0 @ X1 @ sK2 ) )
| ( sF5 = $true ) ),
inference(not_proxy_clausification,[],[f46]) ).
thf(f48,plain,
! [X1: sK0] :
( ( $false
= ( 'const/sets/IN' @ sK0 @ X1 @ sK1 ) )
| ( ( 'const/sets/IN' @ sK0 @ X1 @ sK2 )
= $true )
| ( sF5 = $true ) ),
inference(not_proxy_clausification,[],[f45]) ).
thf(f63,plain,
! [X0: $tType,X2: X0 > $o,X1: X0] :
( ( ( 'const/sets/IN' @ X0 @ X1 @ X2 )
= $true )
| ( $false
= ( X2 @ X1 ) ) ),
inference(iff_proxy_clausification,[],[f15]) ).
thf(f64,plain,
! [X0: $tType,X2: X0 > $o,X1: X0] :
( ( $false
= ( 'const/sets/IN' @ X0 @ X1 @ X2 ) )
| ( ( X2 @ X1 )
= $true ) ),
inference(iff_proxy_clausification,[],[f15]) ).
thf(f66,definition,
( spl8_1
<=> ( $false = sF5 ) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
thf(f68,plain,
( ( $false = sF5 )
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f66]) ).
thf(f70,definition,
( spl8_2
<=> ( $false = sF4 ) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
thf(f72,plain,
( ( $false = sF4 )
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f70]) ).
thf(f73,plain,
( spl8_1
| spl8_2 ),
inference(avatar_split_clause,[],[f24,f70,f66]) ).
thf(f75,definition,
( spl8_3
<=> ( $true = sF4 ) ),
introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition]) ).
thf(f77,plain,
( ( $true = sF4 )
| ~ spl8_3 ),
inference(avatar_component_clause,[],[f75]) ).
thf(f79,definition,
( spl8_4
<=> ( sF5 = $true ) ),
introduced(definition,[new_symbols(definition,[spl8_4])],[avatar_definition]) ).
thf(f81,plain,
( ( sF5 = $true )
| ~ spl8_4 ),
inference(avatar_component_clause,[],[f79]) ).
thf(f82,plain,
( spl8_3
| spl8_4 ),
inference(avatar_split_clause,[],[f23,f79,f75]) ).
thf(f84,definition,
( spl8_5
<=> ( sF3 = $true ) ),
introduced(definition,[new_symbols(definition,[spl8_5])],[avatar_definition]) ).
thf(f86,plain,
( ( sF3 = $true )
| ~ spl8_5 ),
inference(avatar_component_clause,[],[f84]) ).
thf(f87,plain,
( spl8_3
| spl8_5 ),
inference(avatar_split_clause,[],[f27,f84,f75]) ).
thf(f89,definition,
( spl8_6
<=> ( $false = sF3 ) ),
introduced(definition,[new_symbols(definition,[spl8_6])],[avatar_definition]) ).
thf(f91,plain,
( ( $false = sF3 )
| ~ spl8_6 ),
inference(avatar_component_clause,[],[f89]) ).
thf(f92,plain,
( spl8_6
| spl8_2 ),
inference(avatar_split_clause,[],[f28,f70,f89]) ).
thf(f94,definition,
( spl8_7
<=> ( sK2 = sK1 ) ),
introduced(definition,[new_symbols(definition,[spl8_7])],[avatar_definition]) ).
thf(f95,plain,
( ( sK2 != sK1 )
| spl8_7 ),
inference(avatar_component_clause,[],[f94]) ).
thf(f96,plain,
( ( sK2 = sK1 )
| ~ spl8_7 ),
inference(avatar_component_clause,[],[f94]) ).
thf(f97,plain,
( spl8_7
| spl8_6 ),
inference(avatar_split_clause,[],[f31,f89,f94]) ).
thf(f98,plain,
( spl8_5
| ~ spl8_7 ),
inference(avatar_split_clause,[],[f32,f94,f84]) ).
thf(f100,definition,
( spl8_8
<=> ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl8_8])],[avatar_definition]) ).
thf(f102,plain,
( ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK2 )
= $true )
| ~ spl8_8 ),
inference(avatar_component_clause,[],[f100]) ).
thf(f104,definition,
( spl8_9
<=> ( $true
= ( 'const/sets/IN' @ sK0 @ sK6 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_9])],[avatar_definition]) ).
thf(f106,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK6 @ sK1 ) )
| ~ spl8_9 ),
inference(avatar_component_clause,[],[f104]) ).
thf(f107,plain,
( spl8_8
| spl8_9
| spl8_1 ),
inference(avatar_split_clause,[],[f40,f66,f104,f100]) ).
thf(f109,definition,
( spl8_10
<=> ( $false
= ( 'const/sets/IN' @ sK0 @ sK6 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_10])],[avatar_definition]) ).
thf(f111,plain,
( ( $false
= ( 'const/sets/IN' @ sK0 @ sK6 @ sK2 ) )
| ~ spl8_10 ),
inference(avatar_component_clause,[],[f109]) ).
thf(f113,definition,
( spl8_11
<=> ( $false
= ( 'const/sets/IN' @ sK0 @ sK6 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_11])],[avatar_definition]) ).
thf(f115,plain,
( ( $false
= ( 'const/sets/IN' @ sK0 @ sK6 @ sK1 ) )
| ~ spl8_11 ),
inference(avatar_component_clause,[],[f113]) ).
thf(f116,plain,
( spl8_1
| spl8_10
| spl8_11 ),
inference(avatar_split_clause,[],[f41,f113,f109,f66]) ).
thf(f118,definition,
( spl8_12
<=> ! [X1: sK0] :
( ( $true
= ( 'const/sets/IN' @ sK0 @ X1 @ sK1 ) )
| ( $false
= ( 'const/sets/IN' @ sK0 @ X1 @ sK2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl8_12])],[avatar_definition]) ).
thf(f119,plain,
( ! [X1: sK0] :
( ( $true
= ( 'const/sets/IN' @ sK0 @ X1 @ sK1 ) )
| ( $false
= ( 'const/sets/IN' @ sK0 @ X1 @ sK2 ) ) )
| ~ spl8_12 ),
inference(avatar_component_clause,[],[f118]) ).
thf(f120,plain,
( spl8_4
| spl8_12 ),
inference(avatar_split_clause,[],[f47,f118,f79]) ).
thf(f122,definition,
( spl8_13
<=> ! [X1: sK0] :
( ( $false
= ( 'const/sets/IN' @ sK0 @ X1 @ sK1 ) )
| ( ( 'const/sets/IN' @ sK0 @ X1 @ sK2 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl8_13])],[avatar_definition]) ).
thf(f123,plain,
( ! [X1: sK0] :
( ( $false
= ( 'const/sets/IN' @ sK0 @ X1 @ sK1 ) )
| ( ( 'const/sets/IN' @ sK0 @ X1 @ sK2 )
= $true ) )
| ~ spl8_13 ),
inference(avatar_component_clause,[],[f122]) ).
thf(f124,plain,
( spl8_4
| spl8_13 ),
inference(avatar_split_clause,[],[f48,f122,f79]) ).
thf(f125,plain,
( ( $false = $true )
| ~ spl8_2
| ~ spl8_3 ),
inference(forward_demodulation,[],[f77,f72]) ).
thf(f126,plain,
( $false
| ~ spl8_2
| ~ spl8_3 ),
inference(trivial_inequality_removal,[],[f125]) ).
thf(f127,plain,
( ~ spl8_2
| ~ spl8_3 ),
inference(avatar_contradiction_clause,[],[f126]) ).
thf(f129,plain,
( ( $false = $true )
| ~ spl8_1
| ~ spl8_4 ),
inference(forward_demodulation,[],[f81,f68]) ).
thf(f130,plain,
( $false
| ~ spl8_1
| ~ spl8_4 ),
inference(trivial_inequality_removal,[],[f129]) ).
thf(f131,plain,
( ~ spl8_1
| ~ spl8_4 ),
inference(avatar_contradiction_clause,[],[f130]) ).
thf(f133,plain,
( ( ( sK2 @ sK9 )
!= ( sK1 @ sK9 ) )
| spl8_7 ),
inference(negative_extensionality,[],[f95]) ).
thf(f134,plain,
( ( ( sK1 @ sK9 )
= $true )
| ( ( sK2 @ sK9 )
= $true )
| spl8_7 ),
inference(xor_proxy_clausification,[],[f133]) ).
thf(f135,plain,
( ( $false
= ( sK2 @ sK9 ) )
| ( $false
= ( sK1 @ sK9 ) )
| spl8_7 ),
inference(xor_proxy_clausification,[],[f133]) ).
thf(f137,definition,
( spl8_14
<=> ( $false
= ( sK1 @ sK9 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_14])],[avatar_definition]) ).
thf(f138,plain,
( ( $false
!= ( sK1 @ sK9 ) )
| spl8_14 ),
inference(avatar_component_clause,[],[f137]) ).
thf(f139,plain,
( ( $false
= ( sK1 @ sK9 ) )
| ~ spl8_14 ),
inference(avatar_component_clause,[],[f137]) ).
thf(f141,definition,
( spl8_15
<=> ( $false
= ( sK2 @ sK9 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_15])],[avatar_definition]) ).
thf(f143,plain,
( ( $false
= ( sK2 @ sK9 ) )
| ~ spl8_15 ),
inference(avatar_component_clause,[],[f141]) ).
thf(f144,plain,
( spl8_14
| spl8_15
| spl8_7 ),
inference(avatar_split_clause,[],[f135,f94,f141,f137]) ).
thf(f146,definition,
( spl8_16
<=> ( ( sK2 @ sK9 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl8_16])],[avatar_definition]) ).
thf(f148,plain,
( ( ( sK2 @ sK9 )
= $true )
| ~ spl8_16 ),
inference(avatar_component_clause,[],[f146]) ).
thf(f150,definition,
( spl8_17
<=> ( ( sK1 @ sK9 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl8_17])],[avatar_definition]) ).
thf(f152,plain,
( ( ( sK1 @ sK9 )
= $true )
| ~ spl8_17 ),
inference(avatar_component_clause,[],[f150]) ).
thf(f153,plain,
( spl8_16
| spl8_17
| spl8_7 ),
inference(avatar_split_clause,[],[f134,f94,f150,f146]) ).
thf(f154,plain,
( ( $false = $true )
| ~ spl8_5
| ~ spl8_6 ),
inference(forward_demodulation,[],[f86,f91]) ).
thf(f155,plain,
( $false
| ~ spl8_5
| ~ spl8_6 ),
inference(trivial_inequality_removal,[],[f154]) ).
thf(f156,plain,
( ~ spl8_5
| ~ spl8_6 ),
inference(avatar_contradiction_clause,[],[f155]) ).
thf(f177,plain,
( ( $false = $true )
| ~ spl8_8
| ~ spl8_10 ),
inference(forward_demodulation,[],[f111,f102]) ).
thf(f178,plain,
( $false
| ~ spl8_8
| ~ spl8_10 ),
inference(trivial_inequality_removal,[],[f177]) ).
thf(f179,plain,
( ~ spl8_8
| ~ spl8_10 ),
inference(avatar_contradiction_clause,[],[f178]) ).
thf(f334,plain,
( ( $false = $true )
| ~ spl8_15
| ~ spl8_16 ),
inference(forward_demodulation,[],[f148,f143]) ).
thf(f335,plain,
( $false
| ~ spl8_15
| ~ spl8_16 ),
inference(trivial_inequality_removal,[],[f334]) ).
thf(f336,plain,
( ~ spl8_15
| ~ spl8_16 ),
inference(avatar_contradiction_clause,[],[f335]) ).
thf(f390,plain,
( ( ( 'const/sets/IN' @ sK0 @ sK6 @ sK2 )
= $true )
| ~ spl8_7
| ~ spl8_9 ),
inference(forward_demodulation,[],[f106,f96]) ).
thf(f393,plain,
( ( $false
= ( 'const/sets/IN' @ sK0 @ sK6 @ sK2 ) )
| ~ spl8_7
| ~ spl8_11 ),
inference(forward_demodulation,[],[f115,f96]) ).
thf(f394,plain,
( spl8_8
| ~ spl8_7
| ~ spl8_9 ),
inference(avatar_split_clause,[],[f390,f104,f94,f100]) ).
thf(f395,plain,
( spl8_10
| ~ spl8_7
| ~ spl8_11 ),
inference(avatar_split_clause,[],[f393,f113,f94,f109]) ).
thf(f396,plain,
( ( $false = $true )
| ~ spl8_14
| ~ spl8_17 ),
inference(forward_demodulation,[],[f152,f139]) ).
thf(f397,plain,
( $false
| ~ spl8_14
| ~ spl8_17 ),
inference(trivial_inequality_removal,[],[f396]) ).
thf(f398,plain,
( ~ spl8_14
| ~ spl8_17 ),
inference(avatar_contradiction_clause,[],[f397]) ).
thf(f456,plain,
( ! [X0: sK0] :
( ( $true
= ( sK1 @ X0 ) )
| ( $false = $true )
| ( $false
= ( 'const/sets/IN' @ sK0 @ X0 @ sK2 ) ) )
| ~ spl8_12 ),
inference(constrained_superposition,[],[f119,f64]) ).
thf(f458,plain,
( ! [X0: sK0] :
( ( $false
= ( 'const/sets/IN' @ sK0 @ X0 @ sK2 ) )
| ( $true
= ( sK1 @ X0 ) ) )
| ~ spl8_12 ),
inference(trivial_inequality_removal,[],[f456]) ).
thf(f464,plain,
( ! [X0: sK0] :
( ( $false = $true )
| ( $true
= ( sK1 @ X0 ) )
| ( $false
= ( sK2 @ X0 ) ) )
| ~ spl8_12 ),
inference(constrained_superposition,[],[f63,f458]) ).
thf(f465,plain,
( ! [X0: sK0] :
( ( $true
= ( sK1 @ X0 ) )
| ( $false
= ( sK2 @ X0 ) ) )
| ~ spl8_12 ),
inference(trivial_inequality_removal,[],[f464]) ).
thf(f476,plain,
( ! [X0: sK0] :
( ( $false
= ( sK1 @ X0 ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ X0 @ sK2 ) )
| ( $false = $true ) )
| ~ spl8_13 ),
inference(constrained_superposition,[],[f63,f123]) ).
thf(f479,plain,
( ! [X0: sK0] :
( ( $true
= ( 'const/sets/IN' @ sK0 @ X0 @ sK2 ) )
| ( $false
= ( sK1 @ X0 ) ) )
| ~ spl8_13 ),
inference(trivial_inequality_removal,[],[f476]) ).
thf(f490,plain,
( ! [X0: sK0] :
( ( $true
= ( sK2 @ X0 ) )
| ( $false = $true )
| ( $false
= ( sK1 @ X0 ) ) )
| ~ spl8_13 ),
inference(constrained_superposition,[],[f64,f479]) ).
thf(f493,plain,
( ! [X0: sK0] :
( ( $true
= ( sK2 @ X0 ) )
| ( $false
= ( sK1 @ X0 ) ) )
| ~ spl8_13 ),
inference(trivial_inequality_removal,[],[f490]) ).
thf(f495,plain,
( ( $false = $true )
| ( $false
= ( sK1 @ sK9 ) )
| ~ spl8_13
| ~ spl8_15 ),
inference(constrained_superposition,[],[f493,f143]) ).
thf(f514,plain,
( ( $false
= ( sK1 @ sK9 ) )
| ~ spl8_13
| ~ spl8_15 ),
inference(trivial_inequality_removal,[],[f495]) ).
thf(f537,plain,
( $false
| ~ spl8_13
| spl8_14
| ~ spl8_15 ),
inference(forward_subsumption_resolution,[],[f514,f138]) ).
thf(f538,plain,
( ~ spl8_13
| spl8_14
| ~ spl8_15 ),
inference(avatar_contradiction_clause,[],[f537]) ).
thf(f555,plain,
( ( $false
= ( sK2 @ sK9 ) )
| ( $false = $true )
| ~ spl8_12
| ~ spl8_14 ),
inference(constrained_superposition,[],[f139,f465]) ).
thf(f558,plain,
( ( $false
= ( sK2 @ sK9 ) )
| ~ spl8_12
| ~ spl8_14 ),
inference(trivial_inequality_removal,[],[f555]) ).
thf(f561,plain,
( spl8_15
| ~ spl8_12
| ~ spl8_14 ),
inference(avatar_split_clause,[],[f558,f137,f118,f141]) ).
cnf(s1,plain,
( spl8_1
| spl8_2 ),
inference(sat_conversion,[],[f73]) ).
cnf(s2,plain,
( spl8_3
| spl8_4 ),
inference(sat_conversion,[],[f82]) ).
cnf(s3,plain,
( spl8_3
| spl8_5 ),
inference(sat_conversion,[],[f87]) ).
cnf(s4,plain,
( spl8_2
| spl8_6 ),
inference(sat_conversion,[],[f92]) ).
cnf(s5,plain,
( spl8_6
| spl8_7 ),
inference(sat_conversion,[],[f97]) ).
cnf(s6,plain,
( spl8_5
| ~ spl8_7 ),
inference(sat_conversion,[],[f98]) ).
cnf(s7,plain,
( spl8_1
| spl8_8
| spl8_9 ),
inference(sat_conversion,[],[f107]) ).
cnf(s8,plain,
( spl8_1
| spl8_10
| spl8_11 ),
inference(sat_conversion,[],[f116]) ).
cnf(s9,plain,
( spl8_4
| spl8_12 ),
inference(sat_conversion,[],[f120]) ).
cnf(s10,plain,
( spl8_4
| spl8_13 ),
inference(sat_conversion,[],[f124]) ).
cnf(s11,plain,
( ~ spl8_2
| ~ spl8_3 ),
inference(sat_conversion,[],[f127]) ).
cnf(s12,plain,
( ~ spl8_1
| ~ spl8_4 ),
inference(sat_conversion,[],[f131]) ).
cnf(s13,plain,
( spl8_7
| spl8_14
| spl8_15 ),
inference(sat_conversion,[],[f144]) ).
cnf(s14,plain,
( spl8_7
| spl8_16
| spl8_17 ),
inference(sat_conversion,[],[f153]) ).
cnf(s15,plain,
( ~ spl8_5
| ~ spl8_6 ),
inference(sat_conversion,[],[f156]) ).
cnf(s16,plain,
( ~ spl8_8
| ~ spl8_10 ),
inference(sat_conversion,[],[f179]) ).
cnf(s36,plain,
( ~ spl8_15
| ~ spl8_16 ),
inference(sat_conversion,[],[f336]) ).
cnf(s42,plain,
( ~ spl8_7
| spl8_8
| ~ spl8_9 ),
inference(sat_conversion,[],[f394]) ).
cnf(s43,plain,
( ~ spl8_7
| spl8_10
| ~ spl8_11 ),
inference(sat_conversion,[],[f395]) ).
cnf(s44,plain,
( ~ spl8_14
| ~ spl8_17 ),
inference(sat_conversion,[],[f398]) ).
cnf(s59,plain,
( ~ spl8_13
| spl8_14
| ~ spl8_15 ),
inference(sat_conversion,[],[f538]) ).
cnf(s72,plain,
( ~ spl8_12
| ~ spl8_14
| spl8_15 ),
inference(sat_conversion,[],[f561]) ).
cnf(s74,plain,
( spl8_8
| spl8_1 ),
inference(rat,[],[s7,s42,s5,s15,s3,s11,s1]) ).
cnf(s75,plain,
spl8_1,
inference(rat,[],[s8,s43,s16,s74,s5,s15,s3,s11,s1]) ).
cnf(s76,plain,
~ spl8_4,
inference(rat,[],[s12,s75]) ).
cnf(s77,plain,
spl8_13,
inference(rat,[],[s10,s76]) ).
cnf(s78,plain,
spl8_12,
inference(rat,[],[s9,s76]) ).
cnf(s79,plain,
spl8_3,
inference(rat,[],[s2,s76]) ).
cnf(s80,plain,
~ spl8_2,
inference(rat,[],[s11,s79]) ).
cnf(s81,plain,
spl8_6,
inference(rat,[],[s4,s80]) ).
cnf(s82,plain,
~ spl8_5,
inference(rat,[],[s15,s81]) ).
cnf(s83,plain,
~ spl8_7,
inference(rat,[],[s6,s82]) ).
cnf(s84,plain,
spl8_14,
inference(rat,[],[s13,s59,s83,s77]) ).
cnf(s85,plain,
spl8_15,
inference(rat,[],[s72,s78,s84]) ).
cnf(s86,plain,
~ spl8_17,
inference(rat,[],[s44,s84]) ).
cnf(s87,plain,
~ spl8_16,
inference(rat,[],[s36,s85]) ).
cnf(s88,plain,
$false,
inference(rat,[],[s14,s83,s87,s86]) ).
thf(f562,plain,
$false,
inference(avatar_sat_refutation,[],[s88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV447^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.17 % Computer : n020.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Tue Sep 29 15:49:18 UTC 2026
% 0.06/0.17 % CPUTime :
% 0.06/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.21 Running higher-order theorem proving
% 0.06/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.26 % (1210369)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.18/0.26 % (1210388)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.18/0.26 % (1210388)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.18/0.26 % (1210388)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=3042306040:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.18/0.26 % (1210381)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2859739783:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.18/0.26 % (1210384)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1431080675:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.18/0.26 % (1210383)lrs+10_16_si=on:nwc=1.5:random_seed=3514458962:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.18/0.26 % (1210386)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=358212714:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.18/0.26 % (1210385)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3472284117:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.18/0.26 % (1210387)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2736660729:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.18/0.26 % (1210388) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1210369-1210388"...
% 0.18/0.26 % (1210384)Refutation not found, incomplete strategy
% 0.18/0.26 % (1210384)------------------------------
% 0.18/0.26 % (1210384)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.26 % (1210384)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.26 % (1210384)CaDiCaL version: 2.1.3
% 0.18/0.26 % (1210384)Termination reason: Refutation not found, incomplete strategy
% 0.18/0.26 % (1210384)Time elapsed: 0.001 s
% 0.18/0.26 % (1210384)Peak memory usage: 12 MB
% 0.18/0.26 % (1210384)Instructions burned: 1 (million)
% 0.18/0.26 % (1210384)------------------------------
% 0.18/0.26 % (1210384)------------------------------
% 0.18/0.26 % (1210388)...printing done.
% 0.18/0.26 % (1210388)Refutation found. Thanks to Tanya!
% 0.18/0.26 % SZS status Theorem for theBenchmark
% 0.18/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.26 % (1210388)------------------------------
% 0.18/0.26 % (1210388)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.26 % (1210388)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.26 % (1210388)CaDiCaL version: 2.1.3
% 0.18/0.26 % (1210388)Termination reason: Refutation
% 0.18/0.26 % (1210388)Time elapsed: 0.009 s
% 0.18/0.26 % (1210388)Peak memory usage: 13 MB
% 0.18/0.26 % (1210388)Instructions burned: 24 (million)
% 0.18/0.26 % (1210369)Success in time 0.036 s
% 0.18/0.26 % Vampire exiting
%------------------------------------------------------------------------------