%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ANA082^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n013.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 07:46:01 AM UTC 2026
% Result : Theorem 0.19s 0.26s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 8
% Syntax : Number of formulae : 75 ( 6 unt; 0 typ; 5 def)
% Number of atoms : 519 ( 128 equ; 0 cnn)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 648 ( 96 ~; 98 |; 35 &; 394 @)
% ( 5 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 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 : 23 ( 19 usr; 11 con; 0-4 aty)
% ( 0 !!; 7 ??; 0 @@+; 0 @@-)
% Number of variables : 70 ( 0 sgn 54 !; 7 ?; 70 :)
% 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,
sK2: 'type/realax/real' ).
thf(func_def_16,type,
sK4: 'type/realax/real' ).
thf(f1,axiom,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X2 )
& ( 'const/realax/real_le' @ X0 @ X1 ) )
=> ( 'const/realax/real_le' @ X0 @ X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/realax/REAL_LE_TRANS_') ).
thf(f2,axiom,
! [X0: 'type/realax/real' > $o] :
( ( ( ( X0 != 'const/sets/EMPTY' ) @ 'type/realax/real' )
& ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 ) )
=> ( ! [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/sandbox2/benchmark/theBenchmark.p','thm/sets/INF_FINITE_') ).
thf(f3,conjecture,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( ( X0 != 'const/sets/EMPTY' ) @ 'type/realax/real' )
& ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 ) )
=> ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 )
= ( ? [X2: 'type/realax/real'] :
( ( 'const/realax/real_le' @ X2 @ X1 )
& ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/REAL_INF_LE_FINITE_') ).
thf(f4,negated_conjecture,
~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( ( X0 != 'const/sets/EMPTY' ) @ 'type/realax/real' )
& ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 ) )
=> ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 )
= ( ? [X2: 'type/realax/real'] :
( ( 'const/realax/real_le' @ X2 @ X1 )
& ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X2 )
& ( 'const/realax/real_le' @ X0 @ X1 ) )
=> ( 'const/realax/real_le' @ X0 @ X2 ) ),
inference(rectify,[],[f1]) ).
thf(f6,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( ( 'const/realax/real_le' @ X1 @ X2 )
= $true )
& ( ( 'const/realax/real_le' @ X0 @ X1 )
= $true ) )
=> ( ( 'const/realax/real_le' @ X0 @ X2 )
= $true ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
! [X0: 'type/realax/real' > $o] :
( ( ( ( X0 != 'const/sets/EMPTY' ) @ 'type/realax/real' )
& ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 ) )
=> ( ! [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(f8,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,[],[f7]) ).
thf(f9,plain,
~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( ( X0 != 'const/sets/EMPTY' ) @ 'type/realax/real' )
& ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 ) )
=> ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 )
= ( ? [X2: 'type/realax/real'] :
( ( 'const/realax/real_le' @ X2 @ X1 )
& ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f10,plain,
~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true ) )
=> ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 )
= ( ?? @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ X0 )
& ( 'const/realax/real_le' @ Y0 @ X1 ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ X2 )
= $true )
| ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true )
| ( ( 'const/realax/real_le' @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f12,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ X2 )
= $true )
| ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true )
| ( ( 'const/realax/real_le' @ X0 @ X1 )
!= $true ) ),
inference(flattening,[],[f11]) ).
thf(f13,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,[],[f8]) ).
thf(f14,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(flattening,[],[f13]) ).
thf(f15,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/sets/IN' @ 'type/realax/real' @ Y0 @ X0 )
& ( 'const/realax/real_le' @ Y0 @ X1 ) ) ) )
& ( '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,X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 )
!= ( ?? @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ X0 )
& ( 'const/realax/real_le' @ Y0 @ X1 ) ) ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true ) ),
inference(flattening,[],[f15]) ).
thf(f17,plain,
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK0 ) @ sK1 )
!= ( ?? @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0 )
& ( 'const/realax/real_le' @ Y0 @ sK1 ) ) ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK0 ) )
& ( $true
= ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f16]) ).
thf(f18,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ X2 )
= $true )
| ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true )
| ( ( 'const/realax/real_le' @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f19,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,[],[f14]) ).
thf(f20,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/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f21,plain,
( $true
= ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f22,plain,
'const/sets/EMPTY' @ ( 'type/realax/real' != sK0 ),
inference(cnf_transformation,[],[f17]) ).
thf(f23,plain,
( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK0 ) @ sK1 )
!= ( ?? @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0 )
& ( 'const/realax/real_le' @ Y0 @ sK1 ) ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f26,plain,
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK0 ) @ sK1 ) )
| ( $true
= ( ?? @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0 )
& ( 'const/realax/real_le' @ Y0 @ sK1 ) ) ) ) ),
inference(xor_proxy_clausification,[],[f23]) ).
thf(f27,plain,
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK0 ) @ sK1 )
= $false )
| ( ( ?? @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0 )
& ( 'const/realax/real_le' @ Y0 @ sK1 ) ) )
= $false ) ),
inference(xor_proxy_clausification,[],[f23]) ).
thf(f28,plain,
! [X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK0 ) @ sK1 )
= $false )
| ( $false
= ( ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0 )
& ( 'const/realax/real_le' @ Y0 @ sK1 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f27]) ).
thf(f29,plain,
! [X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK0 ) @ sK1 )
= $false )
| ( $false
= ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK0 )
& ( 'const/realax/real_le' @ X1 @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f28]) ).
thf(f30,plain,
! [X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK0 ) @ sK1 )
= $false )
| ( $false
= ( 'const/realax/real_le' @ X1 @ sK1 ) )
| ( $false
= ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK0 ) ) ),
inference(and_proxy_clausification,[],[f29]) ).
thf(f31,plain,
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK0 ) @ sK1 ) )
| ( $true
= ( ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0 )
& ( 'const/realax/real_le' @ Y0 @ sK1 ) )
@ sK2 ) ) ),
inference(sigma_proxy_clausification,[],[f26]) ).
thf(f32,plain,
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK0 ) @ sK1 ) )
| ( $true
= ( ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0 )
& ( 'const/realax/real_le' @ sK2 @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f31]) ).
thf(f33,plain,
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK0 ) @ sK1 ) )
| ( $true
= ( 'const/realax/real_le' @ sK2 @ sK1 ) ) ),
inference(and_proxy_clausification,[],[f32]) ).
thf(f34,plain,
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK0 ) @ sK1 ) )
| ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0 ) ) ),
inference(and_proxy_clausification,[],[f32]) ).
thf(f36,definition,
( spl3_1
<=> ! [X1: 'type/realax/real'] :
( ( $false
= ( 'const/realax/real_le' @ X1 @ sK1 ) )
| ( $false
= ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f37,plain,
( ! [X1: 'type/realax/real'] :
( ( $false
= ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK0 ) )
| ( $false
= ( 'const/realax/real_le' @ X1 @ sK1 ) ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f36]) ).
thf(f39,definition,
( spl3_2
<=> ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK0 ) @ sK1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f40,plain,
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK0 ) @ sK1 )
!= $false )
| spl3_2 ),
inference(avatar_component_clause,[],[f39]) ).
thf(f41,plain,
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK0 ) @ sK1 )
= $false )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f39]) ).
thf(f42,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f30,f39,f36]) ).
thf(f44,definition,
( spl3_3
<=> ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
thf(f46,plain,
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0 ) )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f44]) ).
thf(f48,definition,
( spl3_4
<=> ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK0 ) @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
thf(f50,plain,
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK0 ) @ sK1 ) )
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f48]) ).
thf(f51,plain,
( spl3_3
| spl3_4 ),
inference(avatar_split_clause,[],[f34,f48,f44]) ).
thf(f53,definition,
( spl3_5
<=> ( $true
= ( 'const/realax/real_le' @ sK2 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
thf(f55,plain,
( ( $true
= ( 'const/realax/real_le' @ sK2 @ sK1 ) )
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f53]) ).
thf(f56,plain,
( spl3_5
| spl3_4 ),
inference(avatar_split_clause,[],[f33,f48,f53]) ).
thf(f57,plain,
( ( $true = $false )
| ~ spl3_2
| ~ spl3_4 ),
inference(forward_demodulation,[],[f50,f41]) ).
thf(f58,plain,
( $false
| ~ spl3_2
| ~ spl3_4 ),
inference(trivial_inequality_removal,[],[f57]) ).
thf(f59,plain,
( ~ spl3_2
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[],[f58]) ).
thf(f110,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( $true != $true )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 ) )
| ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true ) ),
inference(constrained_superposition,[],[f18,f20]) ).
thf(f114,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 ) )
| ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f110]) ).
thf(f115,plain,
( ( $true = $false )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK0 ) @ sK1 )
= $false )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( $true
!= ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 ) )
| ~ spl3_1 ),
inference(constrained_superposition,[],[f37,f19]) ).
thf(f120,plain,
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK0 ) @ sK1 )
= $false )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( $true
!= ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 ) )
| ~ spl3_1 ),
inference(trivial_inequality_removal,[],[f115]) ).
thf(f122,plain,
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( $true
!= ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 ) )
| ~ spl3_1
| spl3_2 ),
inference(forward_subsumption_resolution,[],[f120,f40]) ).
thf(f124,plain,
( ( $true
!= ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 ) )
| ~ spl3_1
| spl3_2 ),
inference(forward_subsumption_resolution,[],[f122,f22]) ).
thf(f127,plain,
( $false
| ~ spl3_1
| spl3_2 ),
inference(forward_subsumption_resolution,[],[f124,f21]) ).
thf(f128,plain,
( ~ spl3_1
| spl3_2 ),
inference(avatar_contradiction_clause,[],[f127]) ).
thf(f417,plain,
( ! [X0: 'type/realax/real'] :
( ( $true = $false )
| ( $true
!= ( 'const/realax/real_le' @ X0 @ sK1 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK0 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( $true
!= ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 ) ) )
| ~ spl3_2 ),
inference(constrained_superposition,[],[f41,f114]) ).
thf(f418,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X0 @ sK1 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK0 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( $true
!= ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 ) ) )
| ~ spl3_2 ),
inference(trivial_inequality_removal,[],[f417]) ).
thf(f442,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X0 @ sK1 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK0 ) )
| ( $true
!= ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 ) ) )
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f418,f22]) ).
thf(f444,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK0 ) )
| ( $true
!= ( 'const/realax/real_le' @ X0 @ sK1 ) ) )
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f442,f21]) ).
thf(f463,plain,
( ( $true != $true )
| ( $true
!= ( 'const/realax/real_le' @ sK2 @ sK1 ) )
| ~ spl3_2
| ~ spl3_3 ),
inference(constrained_superposition,[],[f444,f46]) ).
thf(f467,plain,
( ( $true
!= ( 'const/realax/real_le' @ sK2 @ sK1 ) )
| ~ spl3_2
| ~ spl3_3 ),
inference(trivial_inequality_removal,[],[f463]) ).
thf(f469,plain,
( $false
| ~ spl3_2
| ~ spl3_3
| ~ spl3_5 ),
inference(forward_subsumption_resolution,[],[f467,f55]) ).
thf(f470,plain,
( ~ spl3_2
| ~ spl3_3
| ~ spl3_5 ),
inference(avatar_contradiction_clause,[],[f469]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f42]) ).
cnf(s2,plain,
( spl3_3
| spl3_4 ),
inference(sat_conversion,[],[f51]) ).
cnf(s3,plain,
( spl3_4
| spl3_5 ),
inference(sat_conversion,[],[f56]) ).
cnf(s4,plain,
( ~ spl3_2
| ~ spl3_4 ),
inference(sat_conversion,[],[f59]) ).
cnf(s9,plain,
( ~ spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f128]) ).
cnf(s12,plain,
( ~ spl3_2
| ~ spl3_3
| ~ spl3_5 ),
inference(sat_conversion,[],[f470]) ).
cnf(s13,plain,
~ spl3_2,
inference(rat,[],[s12,s2,s3,s4]) ).
cnf(s14,plain,
~ spl3_1,
inference(rat,[],[s9,s13]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s1,s13,s14]) ).
thf(f474,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA082^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.17 % Computer : n013.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 17:40:06 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 Running first-order model finding
% 0.09/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.26 % (2427167)Will run a generic schedule for satisfiability detection.
% 0.19/0.26 % (2427176)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=328280323:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.26 % (2427176)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.26 % (2427173)% WARNING: option uhcvi not known.
% 0.19/0.26 % (2427173)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=700670318:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.26 % (2427172)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1133182386_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.26 % (2427174)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3673751121:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.26 % (2427175)dis+10_1_sil=32000:sp=arity:random_seed=274473914:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.26 % (2427173)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.26 % (2427173)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.26 % Exception at run slice level% (2427177)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4285140678:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.26
% 0.19/0.26 % (2427178)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4049648556:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.26 % (2427176) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2427167-2427176"...
% 0.19/0.26 % (2427176)...printing done.
% 0.19/0.26 % (2427176)Refutation found. Thanks to Tanya!
% 0.19/0.26 % SZS status Theorem for theBenchmark
% 0.19/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.26 % (2427176)------------------------------
% 0.19/0.26 % (2427176)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.26 % (2427176)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.26 % (2427176)CaDiCaL version: 2.1.3
% 0.19/0.26 % (2427176)Termination reason: Refutation
% 0.19/0.26 % (2427176)Time elapsed: 0.012 s
% 0.19/0.26 % (2427176)Peak memory usage: 12 MB
% 0.19/0.26 % (2427176)Instructions burned: 42 (million)
% 0.19/0.26 % (2427167)Success in time 0.043 s
% 0.19/0.26 % Vampire exiting
%------------------------------------------------------------------------------