%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV428^1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 08:38:37 AM UTC 2026
% Result : Theorem 0.23s 0.32s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 11
% Syntax : Number of formulae : 102 ( 22 unt; 0 typ; 5 def)
% Number of atoms : 537 ( 132 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 661 ( 136 ~; 151 |; 30 &; 324 @)
% ( 5 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 134 ( 134 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 21 usr; 9 con; 0-4 aty)
% ( 0 !!; 9 ??; 0 @@+; 0 @@-)
% Number of variables : 162 ( 0 sgn 92 !; 12 ?; 162 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
eps: ( $i > $o ) > $i ).
thf(func_def_2,type,
epsio: ( ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_3,type,
setunion: ( ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_4,type,
choosenonempty: ( ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_5,type,
c: ( $i > $o ) > $o ).
thf(func_def_7,type,
vAND: $o > $o > $o ).
thf(func_def_8,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_13,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_14,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
vNOT: $o > $o ).
thf(func_def_17,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_18,type,
sK1: ( ( $i > $o ) > $o ) > $i > $i > $o ).
thf(f1,axiom,
! [X0: $i > $o] :
( ? [X1: $i] : ( X0 @ X1 )
=> ( X0 @ ( eps @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choiceax) ).
thf(f2,axiom,
! [X0: ( $i > $o ) > $o] :
( ? [X1: $i > $o] : ( X0 @ X1 )
=> ( X0 @ ( epsio @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choiceaxio) ).
thf(f3,axiom,
( ( ^ [X0: ( $i > $o ) > $o,X1: $i] :
? [X2: $i > $o] :
( ( X0 @ X2 )
& ( X2 @ X1 ) ) )
= setunion ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setuniond) ).
thf(f4,axiom,
( ( ^ [X0: ( $i > $o ) > $o] :
( epsio
@ ^ [X1: $i > $o] :
( ( X1 @ ( eps @ X1 ) )
& ( X0 @ X1 ) ) ) )
= choosenonempty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choosenonemptyd) ).
thf(f5,axiom,
setunion @ c @ a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ca) ).
thf(f6,conjecture,
( ( c @ ( choosenonempty @ c ) )
& ? [X0: $i] : ( choosenonempty @ c @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f7,negated_conjecture,
~ ( ( c @ ( choosenonempty @ c ) )
& ? [X0: $i] : ( choosenonempty @ c @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f8,plain,
( ( ^ [X0: ( $i > $o ) > $o] :
( epsio
@ ^ [X1: $i > $o] :
( ( X1 @ ( eps @ X1 ) )
& ( X0 @ X1 ) ) ) )
= choosenonempty ),
inference(rectify,[],[f4]) ).
thf(f9,plain,
( choosenonempty
= ( ^ [Y0: ( $i > $o ) > $o] :
( epsio
@ ^ [Y1: $i > $o] :
( ( Y0 @ Y1 )
& ( Y1 @ ( eps @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
~ ( ( c @ ( choosenonempty @ c ) )
& ? [X0: $i] : ( choosenonempty @ c @ X0 ) ),
inference(rectify,[],[f7]) ).
thf(f11,plain,
~ ( ( ( c @ ( choosenonempty @ c ) )
= $true )
& ? [X0: $i] :
( ( choosenonempty @ c @ X0 )
= $true ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
( ( ^ [X0: ( $i > $o ) > $o,X1: $i] :
? [X2: $i > $o] :
( ( X0 @ X2 )
& ( X2 @ X1 ) ) )
= setunion ),
inference(rectify,[],[f3]) ).
thf(f13,plain,
( setunion
= ( ^ [Y0: ( $i > $o ) > $o,Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y1 )
& ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
! [X0: ( $i > $o ) > $o] :
( ? [X1: $i > $o] : ( X0 @ X1 )
=> ( X0 @ ( epsio @ X0 ) ) ),
inference(rectify,[],[f2]) ).
thf(f15,plain,
! [X0: ( $i > $o ) > $o] :
( ? [X1: $i > $o] :
( ( X0 @ X1 )
= $true )
=> ( ( X0 @ ( epsio @ X0 ) )
= $true ) ),
inference(fool_elimination,[],[f14]) ).
thf(f16,plain,
setunion @ c @ a,
inference(rectify,[],[f5]) ).
thf(f17,plain,
( ( setunion @ c @ a )
= $true ),
inference(fool_elimination,[],[f16]) ).
thf(f18,plain,
! [X0: $i > $o] :
( ? [X1: $i] : ( X0 @ X1 )
=> ( X0 @ ( eps @ X0 ) ) ),
inference(rectify,[],[f1]) ).
thf(f19,plain,
! [X0: $i > $o] :
( ? [X1: $i] :
( ( X0 @ X1 )
= $true )
=> ( ( X0 @ ( eps @ X0 ) )
= $true ) ),
inference(fool_elimination,[],[f18]) ).
thf(f20,plain,
! [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ X1 )
!= $true )
| ( ( X0 @ ( eps @ X0 ) )
= $true ) ),
inference(ennf_transformation,[],[f19]) ).
thf(f21,plain,
( ( ( c @ ( choosenonempty @ c ) )
!= $true )
| ! [X0: $i] :
( ( choosenonempty @ c @ X0 )
!= $true ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f22,plain,
! [X0: ( $i > $o ) > $o] :
( ! [X1: $i > $o] :
( ( X0 @ X1 )
!= $true )
| ( ( X0 @ ( epsio @ X0 ) )
= $true ) ),
inference(ennf_transformation,[],[f15]) ).
thf(f23,plain,
! [X0: ( $i > $o ) > $o,X1: $i > $o] :
( ( ( X0 @ ( epsio @ X0 ) )
= $true )
| ( ( X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f24,plain,
( setunion
= ( ^ [Y0: ( $i > $o ) > $o,Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y1 )
& ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f25,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ ( eps @ X0 ) )
= $true )
| ( ( X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f26,plain,
( choosenonempty
= ( ^ [Y0: ( $i > $o ) > $o] :
( epsio
@ ^ [Y1: $i > $o] :
( ( Y0 @ Y1 )
& ( Y1 @ ( eps @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f27,plain,
! [X0: $i] :
( ( ( choosenonempty @ c @ X0 )
!= $true )
| ( ( c @ ( choosenonempty @ c ) )
!= $true ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f28,plain,
( ( setunion @ c @ a )
= $true ),
inference(cnf_transformation,[],[f17]) ).
thf(f31,definition,
( spl0_1
<=> ( setunion
= ( ^ [Y0: ( $i > $o ) > $o,Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y1 )
& ( Y0 @ Y2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f33,plain,
( ( setunion
= ( ^ [Y0: ( $i > $o ) > $o,Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y1 )
& ( Y0 @ Y2 ) ) ) ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f31]) ).
thf(f34,plain,
spl0_1,
inference(avatar_split_clause,[],[f24,f31]) ).
thf(f36,definition,
( spl0_2
<=> ( ( c @ ( choosenonempty @ c ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f38,plain,
( ( ( c @ ( choosenonempty @ c ) )
!= $true )
| spl0_2 ),
inference(avatar_component_clause,[],[f36]) ).
thf(f40,definition,
( spl0_3
<=> ! [X0: $i] :
( ( choosenonempty @ c @ X0 )
!= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
thf(f41,plain,
( ! [X0: $i] :
( ( choosenonempty @ c @ X0 )
!= $true )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f40]) ).
thf(f42,plain,
( ~ spl0_2
| spl0_3 ),
inference(avatar_split_clause,[],[f27,f40,f36]) ).
thf(f44,definition,
( spl0_4
<=> ( choosenonempty
= ( ^ [Y0: ( $i > $o ) > $o] :
( epsio
@ ^ [Y1: $i > $o] :
( ( Y0 @ Y1 )
& ( Y1 @ ( eps @ Y1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
thf(f46,plain,
( ( choosenonempty
= ( ^ [Y0: ( $i > $o ) > $o] :
( epsio
@ ^ [Y1: $i > $o] :
( ( Y0 @ Y1 )
& ( Y1 @ ( eps @ Y1 ) ) ) ) ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f44]) ).
thf(f47,plain,
spl0_4,
inference(avatar_split_clause,[],[f26,f44]) ).
thf(f49,definition,
( spl0_5
<=> ( ( setunion @ c @ a )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
thf(f51,plain,
( ( ( setunion @ c @ a )
= $true )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f49]) ).
thf(f52,plain,
spl0_5,
inference(avatar_split_clause,[],[f28,f49]) ).
thf(f56,plain,
! [X2: $i > $o,X1: $i] :
( ( ( ^ [Y0: $i] :
~ ( X2 @ Y0 )
@ X1 )
!= $true )
| ( $true
= ( ^ [Y0: $i] :
~ ( X2 @ Y0 )
@ ( eps
@ ^ [Y0: $i] :
~ ( X2 @ Y0 ) ) ) ) ),
inference(primitive_instantiation,[],[f25]) ).
thf(f57,plain,
! [X2: $i > $o,X1: $i] :
( ( ( ~ ( X2 @ X1 ) )
!= $true )
| ( ( ~ ( X2
@ ( eps
@ ^ [Y0: $i] :
~ ( X2 @ Y0 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f56]) ).
thf(f58,plain,
! [X2: $i > $o,X1: $i] :
( ( ( ~ ( X2
@ ( eps
@ ^ [Y0: $i] :
~ ( X2 @ Y0 ) ) ) )
= $true )
| ( ( X2 @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f57]) ).
thf(f59,plain,
! [X2: $i > $o,X1: $i] :
( ( ( X2
@ ( eps
@ ^ [Y0: $i] :
~ ( X2 @ Y0 ) ) )
= $false )
| ( ( X2 @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f58]) ).
thf(f80,plain,
( ! [X1: ( $i > $o ) > $o] :
( ( ^ [Y0: ( $i > $o ) > $o,Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y1 )
& ( Y0 @ Y2 ) ) )
@ X1 )
= ( setunion @ X1 ) )
| ~ spl0_1 ),
inference(argument_congruence,[],[f33]) ).
thf(f81,plain,
( ! [X1: ( $i > $o ) > $o] :
( ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( X1 @ Y1 ) ) ) )
= ( setunion @ X1 ) )
| ~ spl0_1 ),
inference(beta-eta_normalization,[],[f80]) ).
thf(f82,plain,
( ! [X1: ( $i > $o ) > $o] :
( ( ^ [Y0: ( $i > $o ) > $o] :
( epsio
@ ^ [Y1: $i > $o] :
( ( Y0 @ Y1 )
& ( Y1 @ ( eps @ Y1 ) ) ) )
@ X1 )
= ( choosenonempty @ X1 ) )
| ~ spl0_4 ),
inference(argument_congruence,[],[f46]) ).
thf(f83,plain,
( ! [X1: ( $i > $o ) > $o] :
( ( choosenonempty @ X1 )
= ( epsio
@ ^ [Y0: $i > $o] :
( ( X1 @ Y0 )
& ( Y0 @ ( eps @ Y0 ) ) ) ) )
| ~ spl0_4 ),
inference(beta-eta_normalization,[],[f82]) ).
thf(f87,plain,
! [X3: $i > $o,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
~ ( X3 @ Y0 )
@ ( eps
@ ^ [Y0: $i] :
~ ( ^ [Y1: $i] :
~ ( X3 @ Y1 )
@ Y0 ) ) ) )
| ( ( ^ [Y0: $i] :
~ ( X3 @ Y0 )
@ X1 )
= $true ) ),
inference(primitive_instantiation,[],[f59]) ).
thf(f91,plain,
! [X3: $i > $o,X1: $i] :
( ( $true
= ( ~ ( X3 @ X1 ) ) )
| ( $false
= ( ~ ( X3
@ ( eps
@ ^ [Y0: $i] :
~ ~ ( X3 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f87]) ).
thf(f92,plain,
! [X3: $i > $o,X1: $i] :
( ( $false
= ( ~ ( X3
@ ( eps
@ ^ [Y0: $i] :
~ ~ ( X3 @ Y0 ) ) ) ) )
| ( ( X3 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f91]) ).
thf(f93,plain,
! [X3: $i > $o,X1: $i] :
( ( ( X3
@ ( eps
@ ^ [Y0: $i] :
~ ~ ( X3 @ Y0 ) ) )
= $true )
| ( ( X3 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f92]) ).
thf(f94,plain,
! [X3: $i > $o,X1: $i] :
( ( ( X3 @ X1 )
= $false )
| ( ( X3
@ ( eps
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) )
= $true ) ),
inference(boolean_simplification,[],[f93]) ).
thf(f95,plain,
! [X3: $i > $o,X1: $i] :
( ( $true
= ( X3 @ ( eps @ X3 ) ) )
| ( ( X3 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f94]) ).
thf(f125,plain,
( ! [X2: $i,X1: ( $i > $o ) > $o] :
( ( setunion @ X1 @ X2 )
= ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( X1 @ Y1 ) ) )
@ X2 ) )
| ~ spl0_1 ),
inference(argument_congruence,[],[f81]) ).
thf(f127,plain,
( ! [X2: $i,X1: ( $i > $o ) > $o] :
( ( $false
= ( setunion @ X1 @ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( Y1 @ Y0 )
& ( X1 @ Y1 ) ) )
@ X2 ) ) )
| ~ spl0_1 ),
inference(iff_proxy_clausification,[],[f125]) ).
thf(f128,plain,
( ! [X2: $i,X1: ( $i > $o ) > $o] :
( ( $false
= ( setunion @ X1 @ X2 ) )
| ( $true
= ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0 @ X2 )
& ( X1 @ Y0 ) ) ) ) )
| ~ spl0_1 ),
inference(beta-eta_normalization,[],[f127]) ).
thf(f129,plain,
( ! [X2: $i,X1: ( $i > $o ) > $o] :
( ( $false
= ( setunion @ X1 @ X2 ) )
| ( $true
= ( ^ [Y0: $i > $o] :
( ( Y0 @ X2 )
& ( X1 @ Y0 ) )
@ ( sK1 @ X1 @ X2 ) ) ) )
| ~ spl0_1 ),
inference(sigma_proxy_clausification,[],[f128]) ).
thf(f130,plain,
( ! [X2: $i,X1: ( $i > $o ) > $o] :
( ( $false
= ( setunion @ X1 @ X2 ) )
| ( $true
= ( ( sK1 @ X1 @ X2 @ X2 )
& ( X1 @ ( sK1 @ X1 @ X2 ) ) ) ) )
| ~ spl0_1 ),
inference(beta-eta_normalization,[],[f129]) ).
thf(f131,plain,
( ! [X2: $i,X1: ( $i > $o ) > $o] :
( ( $true
= ( X1 @ ( sK1 @ X1 @ X2 ) ) )
| ( $false
= ( setunion @ X1 @ X2 ) ) )
| ~ spl0_1 ),
inference(and_proxy_clausification,[],[f130]) ).
thf(f132,plain,
( ! [X2: $i,X1: ( $i > $o ) > $o] :
( ( ( sK1 @ X1 @ X2 @ X2 )
= $true )
| ( $false
= ( setunion @ X1 @ X2 ) ) )
| ~ spl0_1 ),
inference(and_proxy_clausification,[],[f130]) ).
thf(f138,plain,
( ! [X0: ( $i > $o ) > $o,X1: $i > $o] :
( ( $true
= ( ^ [Y0: $i > $o] :
( ( X0 @ Y0 )
& ( Y0 @ ( eps @ Y0 ) ) )
@ ( choosenonempty @ X0 ) ) )
| ( ( ^ [Y0: $i > $o] :
( ( X0 @ Y0 )
& ( Y0 @ ( eps @ Y0 ) ) )
@ X1 )
!= $true ) )
| ~ spl0_4 ),
inference(superposition,[],[f23,f83]) ).
thf(f139,plain,
( ! [X0: ( $i > $o ) > $o,X1: $i > $o] :
( ( $true
!= ( ( X0 @ X1 )
& ( X1 @ ( eps @ X1 ) ) ) )
| ( $true
= ( ( X0 @ ( choosenonempty @ X0 ) )
& ( choosenonempty @ X0 @ ( eps @ ( choosenonempty @ X0 ) ) ) ) ) )
| ~ spl0_4 ),
inference(beta-eta_normalization,[],[f138]) ).
thf(f140,plain,
( ! [X0: ( $i > $o ) > $o,X1: $i > $o] :
( ( ( X0 @ X1 )
= $false )
| ( $true
= ( ( X0 @ ( choosenonempty @ X0 ) )
& ( choosenonempty @ X0 @ ( eps @ ( choosenonempty @ X0 ) ) ) ) )
| ( ( X1 @ ( eps @ X1 ) )
= $false ) )
| ~ spl0_4 ),
inference(and_proxy_clausification,[],[f139]) ).
thf(f141,plain,
( ! [X0: ( $i > $o ) > $o,X1: $i > $o] :
( ( $true
= ( choosenonempty @ X0 @ ( eps @ ( choosenonempty @ X0 ) ) ) )
| ( ( X1 @ ( eps @ X1 ) )
= $false )
| ( ( X0 @ X1 )
= $false ) )
| ~ spl0_4 ),
inference(and_proxy_clausification,[],[f140]) ).
thf(f142,plain,
( ! [X0: ( $i > $o ) > $o,X1: $i > $o] :
( ( $true
= ( X0 @ ( choosenonempty @ X0 ) ) )
| ( ( X1 @ ( eps @ X1 ) )
= $false )
| ( ( X0 @ X1 )
= $false ) )
| ~ spl0_4 ),
inference(and_proxy_clausification,[],[f140]) ).
thf(f312,plain,
( ! [X0: $i > $o] :
( ( ( c @ X0 )
= $false )
| ( $true != $true )
| ( ( X0 @ ( eps @ X0 ) )
= $false ) )
| ~ spl0_3
| ~ spl0_4 ),
inference(superposition,[],[f41,f141]) ).
thf(f316,plain,
( ! [X0: $i > $o] :
( ( ( X0 @ ( eps @ X0 ) )
= $false )
| ( ( c @ X0 )
= $false ) )
| ~ spl0_3
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f312]) ).
thf(f348,plain,
( ! [X0: $i > $o,X1: $i] :
( ( $true = $false )
| ( ( c @ X0 )
= $false )
| ( ( X0 @ X1 )
= $false ) )
| ~ spl0_3
| ~ spl0_4 ),
inference(superposition,[],[f95,f316]) ).
thf(f350,plain,
( ! [X0: $i > $o,X1: $i] :
( ( ( c @ X0 )
= $false )
| ( ( X0 @ X1 )
= $false ) )
| ~ spl0_3
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f348]) ).
thf(f444,plain,
( ! [X0: $i,X1: $i] :
( ( ( sK1 @ c @ X0 @ X1 )
= $false )
| ( $true = $false )
| ( $false
= ( setunion @ c @ X0 ) ) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4 ),
inference(superposition,[],[f131,f350]) ).
thf(f451,plain,
( ! [X0: $i,X1: $i] :
( ( ( sK1 @ c @ X0 @ X1 )
= $false )
| ( $false
= ( setunion @ c @ X0 ) ) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f444]) ).
thf(f456,plain,
( ! [X0: $i] :
( ( $false
= ( setunion @ c @ X0 ) )
| ( $true = $false )
| ( $false
= ( setunion @ c @ X0 ) ) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4 ),
inference(superposition,[],[f132,f451]) ).
thf(f461,plain,
( ! [X0: $i] :
( ( $false
= ( setunion @ c @ X0 ) )
| ( $true = $false ) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4 ),
inference(duplicate_literal_removal,[],[f456]) ).
thf(f462,plain,
( ! [X0: $i] :
( $false
= ( setunion @ c @ X0 ) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f461]) ).
thf(f468,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(superposition,[],[f462,f51]) ).
thf(f482,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f468]) ).
thf(f483,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f482]) ).
thf(f503,plain,
( ! [X0: $i > $o] :
( ( ( X0 @ ( eps @ X0 ) )
= $false )
| ( $true != $true )
| ( ( c @ X0 )
= $false ) )
| spl0_2
| ~ spl0_4 ),
inference(superposition,[],[f38,f142]) ).
thf(f504,plain,
( ! [X0: $i > $o] :
( ( ( X0 @ ( eps @ X0 ) )
= $false )
| ( ( c @ X0 )
= $false ) )
| spl0_2
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f503]) ).
thf(f522,plain,
( ! [X0: $i > $o,X1: $i] :
( ( ( X0 @ X1 )
!= $true )
| ( ( c @ X0 )
= $false )
| ( $true = $false ) )
| spl0_2
| ~ spl0_4 ),
inference(superposition,[],[f25,f504]) ).
thf(f528,plain,
( ! [X0: $i > $o,X1: $i] :
( ( ( c @ X0 )
= $false )
| ( ( X0 @ X1 )
!= $true ) )
| spl0_2
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f522]) ).
thf(f693,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( setunion @ c @ X0 ) )
| ( ( sK1 @ c @ X0 @ X1 )
!= $true )
| ( $true = $false ) )
| ~ spl0_1
| spl0_2
| ~ spl0_4 ),
inference(superposition,[],[f528,f131]) ).
thf(f701,plain,
( ! [X0: $i,X1: $i] :
( ( ( sK1 @ c @ X0 @ X1 )
!= $true )
| ( $false
= ( setunion @ c @ X0 ) ) )
| ~ spl0_1
| spl0_2
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f693]) ).
thf(f711,plain,
( ! [X0: $i] :
( ( $false
= ( setunion @ c @ X0 ) )
| ( $false
= ( setunion @ c @ X0 ) )
| ( $true != $true ) )
| ~ spl0_1
| spl0_2
| ~ spl0_4 ),
inference(superposition,[],[f701,f132]) ).
thf(f719,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( $false
= ( setunion @ c @ X0 ) ) )
| ~ spl0_1
| spl0_2
| ~ spl0_4 ),
inference(duplicate_literal_removal,[],[f711]) ).
thf(f720,plain,
( ! [X0: $i] :
( $false
= ( setunion @ c @ X0 ) )
| ~ spl0_1
| spl0_2
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f719]) ).
thf(f723,plain,
( ( $true = $false )
| ~ spl0_1
| spl0_2
| ~ spl0_4
| ~ spl0_5 ),
inference(superposition,[],[f720,f51]) ).
thf(f734,plain,
( $false
| ~ spl0_1
| spl0_2
| ~ spl0_4
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f723]) ).
thf(f735,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_4
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f734]) ).
cnf(s1,plain,
spl0_1,
inference(sat_conversion,[],[f34]) ).
cnf(s2,plain,
( ~ spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f42]) ).
cnf(s3,plain,
spl0_4,
inference(sat_conversion,[],[f47]) ).
cnf(s4,plain,
spl0_5,
inference(sat_conversion,[],[f52]) ).
cnf(s15,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f483]) ).
cnf(s17,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f735]) ).
cnf(s18,plain,
spl0_2,
inference(rat,[],[s17,s4,s3,s1]) ).
cnf(s19,plain,
~ spl0_3,
inference(rat,[],[s15,s4,s3,s1]) ).
cnf(s20,plain,
$false,
inference(rat,[],[s2,s19,s18]) ).
thf(f742,plain,
$false,
inference(avatar_sat_refutation,[],[s20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV428^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.18 % Computer : n014.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 15:46:45 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running higher-order theorem proving
% 0.10/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.23/0.32 % (2835632)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.32 % (2835645)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.32 % (2835645)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
% 0.23/0.32 % (2835645)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=1529786616:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.32 % (2835641)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=199408170:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.32 % (2835642)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=2072447020: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)
% 0.23/0.32 % (2835645)Refutation not found, incomplete strategy
% 0.23/0.32 % (2835645)------------------------------
% 0.23/0.32 % (2835645)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.32 % (2835645)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.32 % (2835645)CaDiCaL version: 2.1.3
% 0.23/0.32 % (2835645)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.32 % (2835645)Time elapsed: 0.002 s
% 0.23/0.32 % (2835645)Peak memory usage: 12 MB
% 0.23/0.32 % (2835645)Instructions burned: 4 (million)
% 0.23/0.32 % (2835639)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1640204711:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.32 % (2835641)Instruction limit reached!
% 0.23/0.32 % (2835641)------------------------------
% 0.23/0.32 % (2835641)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.32 % (2835641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.32 % (2835641)CaDiCaL version: 2.1.3
% 0.23/0.32 % (2835641)Termination reason: Instruction limit
% 0.23/0.32 % (2835641)Termination phase: Saturation
% 0.23/0.32 % (2835641)Time elapsed: 0.003 s
% 0.23/0.32 % (2835641)Peak memory usage: 12 MB
% 0.23/0.32 % (2835641)Instructions burned: 3 (million)
% 0.23/0.32 % (2835644)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2031578929:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.32 % (2835643)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2255116052:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.32 % (2835640)lrs+10_16_si=on:nwc=1.5:random_seed=3866033917:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.32 % (2835661)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2206914583:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.23/0.32 % (2835661)Instruction limit reached!
% 0.23/0.32 % (2835661)------------------------------
% 0.23/0.32 % (2835661)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.32 % (2835661)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.32 % (2835661)CaDiCaL version: 2.1.3
% 0.23/0.32 % (2835661)Termination reason: Instruction limit
% 0.23/0.32 % (2835661)Termination phase: Saturation
% 0.23/0.32 % (2835661)Time elapsed: 0.002 s
% 0.23/0.32 % (2835661)Peak memory usage: 12 MB
% 0.23/0.32 % (2835661)Instructions burned: 6 (million)
% 0.23/0.32 % (2835645)------------------------------
% 0.23/0.32 % (2835645)------------------------------
% 0.23/0.32 % (2835643)Instruction limit reached!
% 0.23/0.32 % (2835643)------------------------------
% 0.23/0.32 % (2835643)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.32 % (2835643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.32 % (2835643)CaDiCaL version: 2.1.3
% 0.23/0.32 % (2835643)Termination reason: Instruction limit
% 0.23/0.32 % (2835643)Termination phase: Saturation
% 0.23/0.32 % (2835643)Time elapsed: 0.015 s
% 0.23/0.32 % (2835643)Peak memory usage: 11 MB
% 0.23/0.32 % (2835643)Instructions burned: 24 (million)
% 0.23/0.32 % (2835640)Instruction limit reached!
% 0.23/0.32 % (2835640)------------------------------
% 0.23/0.32 % (2835640)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.32 % (2835640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.32 % (2835640)CaDiCaL version: 2.1.3
% 0.23/0.32 % (2835640)Termination reason: Instruction limit
% 0.23/0.32 % (2835640)Termination phase: Saturation
% 0.23/0.32 % (2835640)Time elapsed: 0.019 s
% 0.23/0.32 % (2835640)Peak memory usage: 12 MB
% 0.23/0.32 % (2835640)Instructions burned: 18 (million)
% 0.23/0.32 % (2835665)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.23/0.32 % (2835665)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=506294310:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.23/0.32 % (2835665)Instruction limit reached!
% 0.23/0.32 % (2835665)------------------------------
% 0.23/0.32 % (2835665)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.32 % (2835665)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.32 % (2835665)CaDiCaL version: 2.1.3
% 0.23/0.32 % (2835665)Termination reason: Instruction limit
% 0.23/0.32 % (2835665)Termination phase: Saturation
% 0.23/0.32 % (2835665)Time elapsed: 0.003 s
% 0.23/0.32 % (2835665)Peak memory usage: 12 MB
% 0.23/0.32 % (2835665)Instructions burned: 11 (million)
% 0.23/0.32 % (2835642) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2835632-2835642"...
% 0.23/0.32 % (2835664)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2449429304:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.23/0.32 % (2835666)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2104792897:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.23/0.32 % (2835642)...printing done.
% 0.23/0.32 % (2835642)Refutation found. Thanks to Tanya!
% 0.23/0.32 % SZS status Theorem for theBenchmark
% 0.23/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.32 % (2835642)------------------------------
% 0.23/0.32 % (2835642)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.32 % (2835642)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.32 % (2835642)CaDiCaL version: 2.1.3
% 0.23/0.32 % (2835642)Termination reason: Refutation
% 0.23/0.32 % (2835642)Time elapsed: 0.037 s
% 0.23/0.32 % (2835642)Peak memory usage: 13 MB
% 0.23/0.32 % (2835642)Instructions burned: 46 (million)
% 0.23/0.32 % (2835632)Success in time 0.075 s
% 0.23/0.32 % Vampire exiting
%------------------------------------------------------------------------------