%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA082^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 07:45:52 AM UTC 2026
% Result : Theorem 0.19s 0.27s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 20
% Syntax : Number of formulae : 139 ( 24 unt; 0 typ; 17 def)
% Number of atoms : 707 ( 163 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 747 ( 138 ~; 145 |; 37 &; 392 @)
% ( 13 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 31 usr; 23 con; 0-4 aty)
% ( 0 !!; 9 ??; 0 @@+; 0 @@-)
% Number of variables : 71 ( 0 sgn 53 !; 7 ?; 71 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
'type/realax/real': $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
'const/sets/inf': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
thf(func_def_1,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_2,type,
'const/sets/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
'const/sets/EMPTY':
!>[X0: $tType] : ( X0 > $o ) ).
thf(func_def_4,type,
'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
thf(func_def_8,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_9,type,
vAND: $o > $o > $o ).
thf(func_def_10,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_12,type,
sK0: 'type/realax/real' > $o ).
thf(func_def_13,type,
sK1: 'type/realax/real' ).
thf(func_def_14,type,
sF2: $o ).
thf(func_def_15,type,
sF3: 'type/realax/real' ).
thf(func_def_16,type,
sF4: $o ).
thf(func_def_17,type,
sF5: $o ).
thf(func_def_18,type,
sK6: 'type/realax/real' ).
thf(func_def_20,type,
sK8: 'type/realax/real' ).
thf(f1,axiom,
! [X2: 'type/realax/real',X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X2 )
& ( 'const/realax/real_le' @ X0 @ X1 ) )
=> ( 'const/realax/real_le' @ X0 @ X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/realax/REAL_LE_TRANS_') ).
thf(f2,axiom,
! [X0: 'type/realax/real' > $o] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
& ( ( X0 != 'const/sets/EMPTY' ) @ 'type/realax/real' ) )
=> ( ! [X1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 ) )
& ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ X0 ) @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/INF_FINITE_') ).
thf(f3,conjecture,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
& ( ( X0 != 'const/sets/EMPTY' ) @ 'type/realax/real' ) )
=> ? [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
& ( 'const/realax/real_le' @ X2 @ X1 ) )
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/REAL_INF_LE_FINITE_') ).
thf(f4,negated_conjecture,
~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
& ( ( X0 != 'const/sets/EMPTY' ) @ 'type/realax/real' ) )
=> ? [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
& ( 'const/realax/real_le' @ X2 @ X1 ) )
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
& ( ( X0 != 'const/sets/EMPTY' ) @ 'type/realax/real' ) )
=> ? [X2: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
& ( 'const/realax/real_le' @ X2 @ X1 ) )
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 ) ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 )
= ( ?? @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/realax/real_le' @ Y0 @ X1 )
& ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ X0 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X2 @ X0 )
& ( 'const/realax/real_le' @ X1 @ X2 ) )
=> ( 'const/realax/real_le' @ X1 @ X0 ) ),
inference(rectify,[],[f1]) ).
thf(f8,plain,
! [X2: 'type/realax/real',X1: 'type/realax/real',X0: 'type/realax/real'] :
( ( ( $true
= ( 'const/realax/real_le' @ X2 @ X0 ) )
& ( ( 'const/realax/real_le' @ X1 @ X2 )
= $true ) )
=> ( ( 'const/realax/real_le' @ X1 @ X0 )
= $true ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
! [X0: 'type/realax/real' > $o] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
& ( ( X0 != 'const/sets/EMPTY' ) @ 'type/realax/real' ) )
=> ( ! [X1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 ) )
& ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ X0 ) @ X0 ) ) ),
inference(rectify,[],[f2]) ).
thf(f10,plain,
! [X0: 'type/realax/real' > $o] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true ) )
=> ( ! [X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
= $true )
=> ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 )
= $true ) )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ X0 ) @ X0 )
= $true ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 )
!= ( ?? @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/realax/real_le' @ Y0 @ X1 )
& ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ X0 ) ) ) )
& ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f12,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 )
!= ( ?? @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/realax/real_le' @ Y0 @ X1 )
& ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ X0 ) ) ) )
& ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) ),
inference(flattening,[],[f11]) ).
thf(f13,plain,
! [X2: 'type/realax/real',X1: 'type/realax/real',X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X0 )
= $true )
| ( $true
!= ( 'const/realax/real_le' @ X2 @ X0 ) )
| ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f14,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X2 @ X0 ) )
| ( ( 'const/realax/real_le' @ X1 @ X0 )
= $true )
| ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true ) ),
inference(flattening,[],[f13]) ).
thf(f15,plain,
! [X0: 'type/realax/real' > $o] :
( ( ! [X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
!= $true ) )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ X0 ) @ X0 )
= $true ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f16,plain,
! [X0: 'type/realax/real' > $o] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true )
| ( ! [X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
!= $true ) )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ X0 ) @ X0 )
= $true ) ) ),
inference(flattening,[],[f15]) ).
thf(f17,plain,
( ( ( ?? @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/realax/real_le' @ Y0 @ sK1 )
& ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0 ) ) )
!= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK0 ) @ sK1 ) )
& ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 )
= $true )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK0 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f12]) ).
thf(f18,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ X1 )
!= $true )
| ( ( 'const/realax/real_le' @ X2 @ X1 )
= $true )
| ( $true
!= ( 'const/realax/real_le' @ X2 @ X0 ) ) ),
inference(rectify,[],[f14]) ).
thf(f19,plain,
'const/sets/EMPTY' @ ( 'type/realax/real' != sK0 ),
inference(cnf_transformation,[],[f17]) ).
thf(f20,plain,
( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 )
= $true ),
inference(cnf_transformation,[],[f17]) ).
thf(f21,plain,
( ( ?? @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/realax/real_le' @ Y0 @ sK1 )
& ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0 ) ) )
!= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK0 ) @ sK1 ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f22,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X2 @ X1 )
= $true )
| ( ( 'const/realax/real_le' @ X0 @ X1 )
!= $true )
| ( $true
!= ( 'const/realax/real_le' @ X2 @ X0 ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f23,plain,
! [X0: 'type/realax/real' > $o] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ X0 ) @ X0 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f24,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 )
= $true )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f27,definition,
( sF2
= ( ?? @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/realax/real_le' @ Y0 @ sK1 )
& ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
thf(f28,plain,
( ( ?? @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/realax/real_le' @ Y0 @ sK1 )
& ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0 ) ) )
= sF2 ),
inference(reorient_equations,[],[f27]) ).
thf(f29,definition,
( sF3
= ( 'const/sets/inf' @ sK0 ) ),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
thf(f30,definition,
( sF4
= ( 'const/realax/real_le' @ sF3 @ sK1 ) ),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
thf(f31,plain,
sF4 != sF2,
inference(definition_folding,[],[f21,f30,f29,f28]) ).
thf(f32,definition,
( sF5
= ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 ) ),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
thf(f33,plain,
( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 )
= sF5 ),
inference(reorient_equations,[],[f32]) ).
thf(f34,plain,
$true = sF5,
inference(definition_folding,[],[f20,f33]) ).
thf(f35,plain,
( ( $false
= ( 'const/realax/real_le' @ sF3 @ sK1 ) )
| ( sF4 = $true ) ),
inference(iff_proxy_clausification,[],[f30]) ).
thf(f36,plain,
( ( sF4 = $false )
| ( $true
= ( 'const/realax/real_le' @ sF3 @ sK1 ) ) ),
inference(iff_proxy_clausification,[],[f30]) ).
thf(f37,plain,
( ( $true = sF2 )
| ( sF4 = $true ) ),
inference(xor_proxy_clausification,[],[f31]) ).
thf(f38,plain,
( ( $false = sF2 )
| ( sF4 = $false ) ),
inference(xor_proxy_clausification,[],[f31]) ).
thf(f39,plain,
( ( $false = sF2 )
| ( $true
= ( ?? @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/realax/real_le' @ Y0 @ sK1 )
& ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0 ) ) ) ) ),
inference(iff_proxy_clausification,[],[f28]) ).
thf(f40,plain,
( ( $false
= ( ?? @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/realax/real_le' @ Y0 @ sK1 )
& ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0 ) ) ) )
| ( $true = sF2 ) ),
inference(iff_proxy_clausification,[],[f28]) ).
thf(f41,plain,
! [X1: 'type/realax/real'] :
( ( $true = sF2 )
| ( $false
= ( ^ [Y0: 'type/realax/real'] :
( ( 'const/realax/real_le' @ Y0 @ sK1 )
& ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f40]) ).
thf(f42,plain,
! [X1: 'type/realax/real'] :
( ( $false
= ( ( 'const/realax/real_le' @ X1 @ sK1 )
& ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK0 ) ) )
| ( $true = sF2 ) ),
inference(beta-eta_normalization,[],[f41]) ).
thf(f43,plain,
! [X1: 'type/realax/real'] :
( ( $true = sF2 )
| ( $false
= ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK0 ) )
| ( $false
= ( 'const/realax/real_le' @ X1 @ sK1 ) ) ),
inference(and_proxy_clausification,[],[f42]) ).
thf(f44,plain,
( ( $true
= ( ^ [Y0: 'type/realax/real'] :
( ( 'const/realax/real_le' @ Y0 @ sK1 )
& ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0 ) )
@ sK6 ) )
| ( $false = sF2 ) ),
inference(sigma_proxy_clausification,[],[f39]) ).
thf(f45,plain,
( ( ( ( 'const/realax/real_le' @ sK6 @ sK1 )
& ( 'const/sets/IN' @ 'type/realax/real' @ sK6 @ sK0 ) )
= $true )
| ( $false = sF2 ) ),
inference(beta-eta_normalization,[],[f44]) ).
thf(f46,plain,
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ sK6 @ sK0 ) )
| ( $false = sF2 ) ),
inference(and_proxy_clausification,[],[f45]) ).
thf(f47,plain,
( ( $true
= ( 'const/realax/real_le' @ sK6 @ sK1 ) )
| ( $false = sF2 ) ),
inference(and_proxy_clausification,[],[f45]) ).
thf(f48,plain,
( ( $false = sF5 )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 )
= $true ) ),
inference(iff_proxy_clausification,[],[f33]) ).
thf(f51,definition,
( spl7_1
<=> ( $true
= ( 'const/realax/real_le' @ sF3 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
thf(f52,plain,
( ( $true
!= ( 'const/realax/real_le' @ sF3 @ sK1 ) )
| spl7_1 ),
inference(avatar_component_clause,[],[f51]) ).
thf(f53,plain,
( ( $true
= ( 'const/realax/real_le' @ sF3 @ sK1 ) )
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f51]) ).
thf(f55,definition,
( spl7_2
<=> ( sF4 = $false ) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
thf(f57,plain,
( ( sF4 = $false )
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f55]) ).
thf(f58,plain,
( spl7_1
| spl7_2 ),
inference(avatar_split_clause,[],[f36,f55,f51]) ).
thf(f60,definition,
( spl7_3
<=> ( $false
= ( 'const/realax/real_le' @ sF3 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition]) ).
thf(f62,plain,
( ( $false
= ( 'const/realax/real_le' @ sF3 @ sK1 ) )
| ~ spl7_3 ),
inference(avatar_component_clause,[],[f60]) ).
thf(f64,definition,
( spl7_4
<=> ( sF4 = $true ) ),
introduced(definition,[new_symbols(definition,[spl7_4])],[avatar_definition]) ).
thf(f66,plain,
( ( sF4 = $true )
| ~ spl7_4 ),
inference(avatar_component_clause,[],[f64]) ).
thf(f67,plain,
( spl7_3
| spl7_4 ),
inference(avatar_split_clause,[],[f35,f64,f60]) ).
thf(f69,definition,
( spl7_5
<=> ( $false = sF2 ) ),
introduced(definition,[new_symbols(definition,[spl7_5])],[avatar_definition]) ).
thf(f71,plain,
( ( $false = sF2 )
| ~ spl7_5 ),
inference(avatar_component_clause,[],[f69]) ).
thf(f72,plain,
( spl7_5
| spl7_2 ),
inference(avatar_split_clause,[],[f38,f55,f69]) ).
thf(f74,definition,
( spl7_6
<=> ( $true = sF2 ) ),
introduced(definition,[new_symbols(definition,[spl7_6])],[avatar_definition]) ).
thf(f76,plain,
( ( $true = sF2 )
| ~ spl7_6 ),
inference(avatar_component_clause,[],[f74]) ).
thf(f77,plain,
( spl7_6
| spl7_4 ),
inference(avatar_split_clause,[],[f37,f64,f74]) ).
thf(f79,definition,
( spl7_7
<=> ! [X1: 'type/realax/real'] :
( ( $false
= ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK0 ) )
| ( $false
= ( 'const/realax/real_le' @ X1 @ sK1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl7_7])],[avatar_definition]) ).
thf(f80,plain,
( ! [X1: 'type/realax/real'] :
( ( $false
= ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK0 ) )
| ( $false
= ( 'const/realax/real_le' @ X1 @ sK1 ) ) )
| ~ spl7_7 ),
inference(avatar_component_clause,[],[f79]) ).
thf(f81,plain,
( spl7_7
| spl7_6 ),
inference(avatar_split_clause,[],[f43,f74,f79]) ).
thf(f83,definition,
( spl7_8
<=> ( $true
= ( 'const/realax/real_le' @ sK6 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_8])],[avatar_definition]) ).
thf(f85,plain,
( ( $true
= ( 'const/realax/real_le' @ sK6 @ sK1 ) )
| ~ spl7_8 ),
inference(avatar_component_clause,[],[f83]) ).
thf(f86,plain,
( spl7_8
| spl7_5 ),
inference(avatar_split_clause,[],[f47,f69,f83]) ).
thf(f88,definition,
( spl7_9
<=> ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ sK6 @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_9])],[avatar_definition]) ).
thf(f90,plain,
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ sK6 @ sK0 ) )
| ~ spl7_9 ),
inference(avatar_component_clause,[],[f88]) ).
thf(f91,plain,
( spl7_9
| spl7_5 ),
inference(avatar_split_clause,[],[f46,f69,f88]) ).
thf(f93,definition,
( spl7_10
<=> ( $true = sF5 ) ),
introduced(definition,[new_symbols(definition,[spl7_10])],[avatar_definition]) ).
thf(f95,plain,
( ( $true = sF5 )
| ~ spl7_10 ),
inference(avatar_component_clause,[],[f93]) ).
thf(f102,definition,
( spl7_12
<=> ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl7_12])],[avatar_definition]) ).
thf(f106,definition,
( spl7_13
<=> ( $false = sF5 ) ),
introduced(definition,[new_symbols(definition,[spl7_13])],[avatar_definition]) ).
thf(f108,plain,
( ( $false = sF5 )
| ~ spl7_13 ),
inference(avatar_component_clause,[],[f106]) ).
thf(f109,plain,
( spl7_12
| spl7_13 ),
inference(avatar_split_clause,[],[f48,f106,f102]) ).
thf(f110,plain,
spl7_10,
inference(avatar_split_clause,[],[f34,f93]) ).
thf(f132,plain,
( ( $true = $false )
| ~ spl7_5
| ~ spl7_6 ),
inference(forward_demodulation,[],[f76,f71]) ).
thf(f133,plain,
( $false
| ~ spl7_5
| ~ spl7_6 ),
inference(trivial_inequality_removal,[],[f132]) ).
thf(f134,plain,
( ~ spl7_5
| ~ spl7_6 ),
inference(avatar_contradiction_clause,[],[f133]) ).
thf(f136,plain,
( ( $true = $false )
| ~ spl7_2
| ~ spl7_4 ),
inference(forward_demodulation,[],[f66,f57]) ).
thf(f137,plain,
( $false
| ~ spl7_2
| ~ spl7_4 ),
inference(trivial_inequality_removal,[],[f136]) ).
thf(f138,plain,
( ~ spl7_2
| ~ spl7_4 ),
inference(avatar_contradiction_clause,[],[f137]) ).
thf(f152,plain,
( ( $true = $false )
| ~ spl7_1
| ~ spl7_3 ),
inference(forward_demodulation,[],[f62,f53]) ).
thf(f153,plain,
( $false
| ~ spl7_1
| ~ spl7_3 ),
inference(trivial_inequality_removal,[],[f152]) ).
thf(f154,plain,
( ~ spl7_1
| ~ spl7_3 ),
inference(avatar_contradiction_clause,[],[f153]) ).
thf(f159,plain,
( ( $true = $false )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 )
!= $true )
| ( $false
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK0 ) @ sK1 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ~ spl7_7 ),
inference(constrained_superposition,[],[f23,f80]) ).
thf(f161,plain,
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( $false
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK0 ) @ sK1 ) )
| ~ spl7_7 ),
inference(trivial_inequality_removal,[],[f159]) ).
thf(f177,plain,
( ( $true = $false )
| ~ spl7_10
| ~ spl7_13 ),
inference(forward_demodulation,[],[f108,f95]) ).
thf(f178,plain,
( $false
| ~ spl7_10
| ~ spl7_13 ),
inference(trivial_inequality_removal,[],[f177]) ).
thf(f179,plain,
( ~ spl7_10
| ~ spl7_13 ),
inference(avatar_contradiction_clause,[],[f178]) ).
thf(f185,plain,
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 )
!= $true )
| ( $false
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK0 ) @ sK1 ) )
| ~ spl7_7 ),
inference(forward_subsumption_resolution,[],[f161,f19]) ).
thf(f187,plain,
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 )
!= $true )
| ( $false
= ( 'const/realax/real_le' @ sF3 @ sK1 ) )
| ~ spl7_7 ),
inference(forward_demodulation,[],[f185,f29]) ).
thf(f189,plain,
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 )
!= $true )
| ( $true = $false )
| ~ spl7_1
| ~ spl7_7 ),
inference(forward_demodulation,[],[f187,f53]) ).
thf(f190,plain,
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 )
!= $true )
| ~ spl7_1
| ~ spl7_7 ),
inference(trivial_inequality_removal,[],[f189]) ).
thf(f193,plain,
( ~ spl7_12
| ~ spl7_1
| ~ spl7_7 ),
inference(avatar_split_clause,[],[f190,f79,f51,f102]) ).
thf(f215,plain,
! [X0: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ sF3 @ X0 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK0 ) )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) ) ),
inference(constrained_superposition,[],[f24,f29]) ).
thf(f216,plain,
! [X0: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ sF3 @ X0 ) )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 )
!= $true )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK0 ) ) ),
inference(forward_subsumption_resolution,[],[f215,f19]) ).
thf(f218,definition,
( spl7_21
<=> ! [X0: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ sF3 @ X0 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl7_21])],[avatar_definition]) ).
thf(f219,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK0 ) )
| ( $true
= ( 'const/realax/real_le' @ sF3 @ X0 ) ) )
| ~ spl7_21 ),
inference(avatar_component_clause,[],[f218]) ).
thf(f220,plain,
( spl7_21
| ~ spl7_12 ),
inference(avatar_split_clause,[],[f216,f102,f218]) ).
thf(f251,plain,
( ! [X0: 'type/realax/real'] :
( ( $true != $true )
| ( $true
!= ( 'const/realax/real_le' @ sF3 @ X0 ) )
| ( $true
!= ( 'const/realax/real_le' @ X0 @ sK1 ) ) )
| spl7_1 ),
inference(constrained_superposition,[],[f52,f22]) ).
thf(f254,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ sF3 @ X0 ) )
| ( $true
!= ( 'const/realax/real_le' @ X0 @ sK1 ) ) )
| spl7_1 ),
inference(trivial_inequality_removal,[],[f251]) ).
thf(f265,plain,
( ( $true
= ( 'const/realax/real_le' @ sF3 @ sK6 ) )
| ( $true != $true )
| ~ spl7_9
| ~ spl7_21 ),
inference(constrained_superposition,[],[f219,f90]) ).
thf(f266,plain,
( ( $true
= ( 'const/realax/real_le' @ sF3 @ sK6 ) )
| ~ spl7_9
| ~ spl7_21 ),
inference(trivial_inequality_removal,[],[f265]) ).
thf(f272,plain,
( ( $true
!= ( 'const/realax/real_le' @ sK6 @ sK1 ) )
| ( $true != $true )
| spl7_1
| ~ spl7_9
| ~ spl7_21 ),
inference(constrained_superposition,[],[f254,f266]) ).
thf(f277,plain,
( ( $true
!= ( 'const/realax/real_le' @ sK6 @ sK1 ) )
| spl7_1
| ~ spl7_9
| ~ spl7_21 ),
inference(trivial_inequality_removal,[],[f272]) ).
thf(f278,plain,
( $false
| spl7_1
| ~ spl7_8
| ~ spl7_9
| ~ spl7_21 ),
inference(forward_subsumption_resolution,[],[f277,f85]) ).
thf(f279,plain,
( spl7_1
| ~ spl7_8
| ~ spl7_9
| ~ spl7_21 ),
inference(avatar_contradiction_clause,[],[f278]) ).
cnf(s1,plain,
( spl7_1
| spl7_2 ),
inference(sat_conversion,[],[f58]) ).
cnf(s2,plain,
( spl7_3
| spl7_4 ),
inference(sat_conversion,[],[f67]) ).
cnf(s3,plain,
( spl7_2
| spl7_5 ),
inference(sat_conversion,[],[f72]) ).
cnf(s4,plain,
( spl7_4
| spl7_6 ),
inference(sat_conversion,[],[f77]) ).
cnf(s5,plain,
( spl7_6
| spl7_7 ),
inference(sat_conversion,[],[f81]) ).
cnf(s6,plain,
( spl7_5
| spl7_8 ),
inference(sat_conversion,[],[f86]) ).
cnf(s7,plain,
( spl7_5
| spl7_9 ),
inference(sat_conversion,[],[f91]) ).
cnf(s9,plain,
( spl7_12
| spl7_13 ),
inference(sat_conversion,[],[f109]) ).
cnf(s10,plain,
spl7_10,
inference(sat_conversion,[],[f110]) ).
cnf(s13,plain,
( ~ spl7_5
| ~ spl7_6 ),
inference(sat_conversion,[],[f134]) ).
cnf(s14,plain,
( ~ spl7_2
| ~ spl7_4 ),
inference(sat_conversion,[],[f138]) ).
cnf(s15,plain,
( ~ spl7_1
| ~ spl7_3 ),
inference(sat_conversion,[],[f154]) ).
cnf(s18,plain,
( ~ spl7_10
| ~ spl7_13 ),
inference(sat_conversion,[],[f179]) ).
cnf(s20,plain,
( ~ spl7_1
| ~ spl7_7
| ~ spl7_12 ),
inference(sat_conversion,[],[f193]) ).
cnf(s28,plain,
( ~ spl7_12
| spl7_21 ),
inference(sat_conversion,[],[f220]) ).
cnf(s32,plain,
( spl7_1
| ~ spl7_8
| ~ spl7_9
| ~ spl7_21 ),
inference(sat_conversion,[],[f279]) ).
cnf(s33,plain,
~ spl7_13,
inference(rat,[],[s18,s10]) ).
cnf(s34,plain,
spl7_12,
inference(rat,[],[s9,s33]) ).
cnf(s35,plain,
spl7_21,
inference(rat,[],[s28,s34]) ).
cnf(s38,plain,
spl7_1,
inference(rat,[],[s32,s6,s7,s13,s4,s14,s1,s35]) ).
cnf(s39,plain,
~ spl7_7,
inference(rat,[],[s20,s34,s38]) ).
cnf(s40,plain,
~ spl7_3,
inference(rat,[],[s15,s38]) ).
cnf(s41,plain,
spl7_6,
inference(rat,[],[s5,s39]) ).
cnf(s42,plain,
spl7_4,
inference(rat,[],[s2,s40]) ).
cnf(s43,plain,
~ spl7_5,
inference(rat,[],[s13,s41]) ).
cnf(s44,plain,
~ spl7_2,
inference(rat,[],[s14,s42]) ).
cnf(s47,plain,
$false,
inference(rat,[],[s3,s43,s44]) ).
thf(f280,plain,
$false,
inference(avatar_sat_refutation,[],[s47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA082^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n004.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 17:40:37 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.23 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
% 0.19/0.27 % (1618339)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.27 % (1618350)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.19/0.27 % (1618350)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
% 0.19/0.27 % (1618350)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=1489918670:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.19/0.27 % (1618348)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3255801024:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.19/0.27 % (1618344)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=809089182:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.19/0.27 % (1618346)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=306224795:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.19/0.27 % (1618345)lrs+10_16_si=on:nwc=1.5:random_seed=380039598:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.19/0.27 % (1618350) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1618339-1618350"...
% 0.19/0.27 % (1618346)Refutation not found, incomplete strategy
% 0.19/0.27 % (1618346)------------------------------
% 0.19/0.27 % (1618346)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (1618346)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (1618346)CaDiCaL version: 2.1.3
% 0.19/0.27 % (1618346)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.27 % (1618346)Time elapsed: 0.002 s
% 0.19/0.27 % (1618346)Peak memory usage: 12 MB
% 0.19/0.27 % (1618346)Instructions burned: 2 (million)
% 0.19/0.27 % (1618350)...printing done.
% 0.19/0.27 % (1618346)------------------------------
% 0.19/0.27 % (1618346)------------------------------
% 0.19/0.27 % (1618350)Refutation found. Thanks to Tanya!
% 0.19/0.27 % SZS status Theorem for theBenchmark
% 0.19/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.27 % (1618350)------------------------------
% 0.19/0.27 % (1618350)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (1618350)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (1618350)CaDiCaL version: 2.1.3
% 0.19/0.27 % (1618350)Termination reason: Refutation
% 0.19/0.27 % (1618350)Time elapsed: 0.005 s
% 0.19/0.27 % (1618350)Peak memory usage: 13 MB
% 0.19/0.27 % (1618350)Instructions burned: 14 (million)
% 0.19/0.27 % (1618339)Success in time 0.039 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------