%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV493^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:41:22 AM UTC 2026
% Result : Theorem 1.67s 1.38s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 8
% Syntax : Number of formulae : 93 ( 39 unt; 0 typ; 4 def)
% Number of atoms : 738 ( 122 equ; 0 cnn)
% Maximal formula atoms : 9 ( 7 avg)
% Number of connectives : 1300 ( 73 ~; 44 |; 71 &; 882 @)
% ( 4 <=>; 119 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 15 usr; 11 con; 0-3 aty)
% ( 86 !!; 21 ??; 0 @@+; 0 @@-)
% Number of variables : 165 ( 117 ^; 44 !; 4 ?; 165 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
'type/realax/real': $tType ).
thf(func_def_0,type,
'type/realax/real': $tType ).
thf(func_def_1,type,
'const/sets/inf': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
thf(func_def_2,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
'const/sets/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_4,type,
'const/sets/EMPTY':
!>[X0: $tType] : ( X0 > $o ) ).
thf(func_def_5,type,
'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
thf(func_def_21,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
sK2: 'type/realax/real' > $o ).
thf(func_def_23,type,
sK3: 'type/realax/real' ).
thf(func_def_24,type,
sK4: 'type/realax/real' ).
thf(func_def_25,type,
sK5: 'type/realax/real' > 'type/realax/real' ).
thf(func_def_26,type,
sK6: 'type/realax/real' ).
thf(f328,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f106,f191,f201,f212,f327]) ).
thf(f327,plain,
( ~ spl0_6
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f326]) ).
thf(f326,plain,
( $false
| ~ spl0_6
| ~ spl0_8 ),
inference(trivial_inequality_removal,[status(thm)],[f325]) ).
thf(f325,plain,
( ( $true = $false )
| ~ spl0_6
| ~ spl0_8 ),
inference(backward_demodulation,[status(thm)],[f234,f313]) ).
thf(f313,plain,
( ( ( 'const/sets/IN' @ 'type/realax/real' @ sK6 @ sK2 )
= $false )
| ~ spl0_6
| ~ spl0_8 ),
inference(backward_demodulation,[status(thm)],[f105,f312]) ).
thf(f312,plain,
( ( sK6
= ( 'const/sets/inf' @ sK2 ) )
| ~ spl0_8 ),
inference(equality_proxy_clausification,[status(thm)],[f282]) ).
thf(f282,plain,
( ( $true
= ( ( 'const/sets/inf' @ sK2 )
= sK6 ) )
| ~ spl0_8 ),
inference(backward_demodulation,[status(thm)],[f273,f281]) ).
thf(f281,plain,
( ( $true
= ( 'const/realax/real_le' @ sK6 @ ( 'const/sets/inf' @ sK2 ) ) )
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f279]) ).
thf(f279,plain,
( ( $true
= ( $true
=> ( 'const/realax/real_le' @ sK6 @ ( 'const/sets/inf' @ sK2 ) ) ) )
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f261,f236]) ).
thf(f236,plain,
( $true
= ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2 )
=> ( 'const/realax/real_le' @ sK6 @ Y0 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f235]) ).
thf(f235,plain,
( ( $true
& ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2 )
=> ( 'const/realax/real_le' @ sK6 @ Y0 ) ) ) )
= $true ),
inference(backward_demodulation,[status(thm)],[f186,f234]) ).
thf(f186,plain,
( $true
= ( ( 'const/sets/IN' @ 'type/realax/real' @ sK6 @ sK2 )
& ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2 )
=> ( 'const/realax/real_le' @ sK6 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f184]) ).
thf(f184,plain,
( $true
= ( ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2 )
& ( !! @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2 )
=> ( 'const/realax/real_le' @ Y0 @ Y1 ) ) ) )
@ sK6 ) ),
inference(sigma_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
( $true
= ( ?? @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2 )
& ( !! @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2 )
=> ( 'const/realax/real_le' @ Y0 @ Y1 ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f60]) ).
thf(f60,plain,
( $true
= ( $true
=> ( ?? @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2 )
& ( !! @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2 )
=> ( 'const/realax/real_le' @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f59,f56]) ).
thf(f56,plain,
( $true
= ( ~ ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f55]) ).
thf(f55,plain,
( $true
= ( $true
& ~ ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) ) ) ),
inference(backward_demodulation,[status(thm)],[f46,f54]) ).
thf(f54,plain,
( $true
= ( 'const/sets/FINITE' @ 'type/realax/real' @ sK2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
( $true
= ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK2 )
& ~ ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
( $false
= ( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK2 )
& ~ ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) ) )
=> ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ sK2 ) @ sK2 )
& ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f43]) ).
thf(f43,plain,
( ( ^ [Y0: 'type/realax/real' > $o] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ Y0 )
& ~ ( 'const/sets/EMPTY' @ ( 'type/realax/real' = Y0 ) ) )
=> ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ Y0 ) @ Y0 )
& ( !! @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y1 @ Y0 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ Y0 ) @ Y1 ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
( $false
= ( !! @ ( 'type/realax/real' > $o )
@ ^ [Y0: 'type/realax/real' > $o] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ Y0 )
& ~ ( 'const/sets/EMPTY' @ ( 'type/realax/real' = Y0 ) ) )
=> ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ Y0 ) @ Y0 )
& ( !! @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y1 @ Y0 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ Y0 ) @ Y1 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
( $true
= ( ~ ( !! @ ( 'type/realax/real' > $o )
@ ^ [Y0: 'type/realax/real' > $o] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ Y0 )
& ~ ( 'const/sets/EMPTY' @ ( 'type/realax/real' = Y0 ) ) )
=> ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ Y0 ) @ Y0 )
& ( !! @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y1 @ Y0 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ Y0 ) @ Y1 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( $true
= ( ~ ( !! @ ( 'type/realax/real' > $o )
@ ^ [Y0: 'type/realax/real' > $o] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ Y0 )
& ~ ( 'const/sets/EMPTY' @ ( 'type/realax/real' = Y0 ) ) )
=> ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ Y0 ) @ Y0 )
& ( !! @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y1 @ Y0 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ Y0 ) @ Y1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ! [X0: 'type/realax/real' > $o] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( '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,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ! [X0: 'type/realax/real' > $o] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( '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(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
! [X0: 'type/realax/real' > $o] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( '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/sandbox/tmp/tmp.ecFsokLpz9/DTF2THF_14497.p','thm/sets/INF_FINITE_') ).
thf(f59,plain,
( $true
= ( ~ ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
=> ( ?? @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2 )
& ( !! @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2 )
=> ( 'const/realax/real_le' @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f58]) ).
thf(f58,plain,
( $true
= ( ( ~ ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
& $true )
=> ( ?? @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2 )
& ( !! @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2 )
=> ( 'const/realax/real_le' @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(superposition,[status(thm)],[f38,f54]) ).
thf(f38,plain,
! [X1: 'type/realax/real' > $o] :
( $true
= ( ( ~ ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X1 ) )
& ( 'const/sets/FINITE' @ 'type/realax/real' @ X1 ) )
=> ( ?? @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ X1 )
& ( !! @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y1 @ X1 )
=> ( 'const/realax/real_le' @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f37]) ).
thf(f37,plain,
! [X1: 'type/realax/real' > $o] :
( $true
= ( ^ [Y0: 'type/realax/real' > $o] :
( ( ~ ( 'const/sets/EMPTY' @ ( 'type/realax/real' = Y0 ) )
& ( 'const/sets/FINITE' @ 'type/realax/real' @ Y0 ) )
=> ( ?? @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y1 @ Y0 )
& ( !! @ 'type/realax/real'
@ ^ [Y2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y2 @ Y0 )
=> ( 'const/realax/real_le' @ Y1 @ Y2 ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
( ( !! @ ( 'type/realax/real' > $o )
@ ^ [Y0: 'type/realax/real' > $o] :
( ( ~ ( 'const/sets/EMPTY' @ ( 'type/realax/real' = Y0 ) )
& ( 'const/sets/FINITE' @ 'type/realax/real' @ Y0 ) )
=> ( ?? @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y1 @ Y0 )
& ( !! @ 'type/realax/real'
@ ^ [Y2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y2 @ Y0 )
=> ( 'const/realax/real_le' @ Y1 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( !! @ ( 'type/realax/real' > $o )
@ ^ [Y0: 'type/realax/real' > $o] :
( ( ~ ( 'const/sets/EMPTY' @ ( 'type/realax/real' = Y0 ) )
& ( 'const/sets/FINITE' @ 'type/realax/real' @ Y0 ) )
=> ( ?? @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y1 @ Y0 )
& ( !! @ 'type/realax/real'
@ ^ [Y2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y2 @ Y0 )
=> ( 'const/realax/real_le' @ Y1 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: 'type/realax/real' > $o] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ? [X1: 'type/realax/real'] :
( ! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_le' @ X1 @ X2 ) )
& ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X0: 'type/realax/real' > $o] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ? [X1: 'type/realax/real'] :
( ! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_le' @ X1 @ X2 ) )
& ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ecFsokLpz9/DTF2THF_14497.p','thm/sets/INF_FINITE_LEMMA_') ).
thf(f261,plain,
( ! [X1: 'type/realax/real'] :
( $true
= ( ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2 )
=> ( 'const/realax/real_le' @ X1 @ Y0 ) ) )
=> ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK2 ) ) ) )
| ~ spl0_8 ),
inference(beta_eta_normalization,[status(thm)],[f258]) ).
thf(f258,plain,
( ! [X1: 'type/realax/real'] :
( $true
= ( ^ [Y0: 'type/realax/real'] :
( ( !! @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2 )
=> ( 'const/realax/real_le' @ Y0 @ Y1 ) ) )
=> ( 'const/realax/real_le' @ Y0 @ ( 'const/sets/inf' @ sK2 ) ) )
@ X1 ) )
| ~ spl0_8 ),
inference(pi_clausification,[status(thm)],[f216]) ).
thf(f216,plain,
( ( $true
= ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( !! @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2 )
=> ( 'const/realax/real_le' @ Y0 @ Y1 ) ) )
=> ( 'const/realax/real_le' @ Y0 @ ( 'const/sets/inf' @ sK2 ) ) ) ) )
| ~ spl0_8 ),
inference(binary_proxy_clausification,[status(thm)],[f200]) ).
thf(f200,plain,
( ( $true
= ( ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( !! @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2 )
=> ( 'const/realax/real_le' @ Y0 @ Y1 ) ) )
=> ( 'const/realax/real_le' @ Y0 @ ( 'const/sets/inf' @ sK2 ) ) ) )
& ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ Y0 ) ) ) ) )
| ~ spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f199]) ).
thf(f199,definition,
( spl0_8
<=> ( $true
= ( ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( !! @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2 )
=> ( 'const/realax/real_le' @ Y0 @ Y1 ) ) )
=> ( 'const/realax/real_le' @ Y0 @ ( 'const/sets/inf' @ sK2 ) ) ) )
& ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition]) ).
thf(f273,plain,
( ( ( ( 'const/sets/inf' @ sK2 )
= sK6 )
= ( 'const/realax/real_le' @ sK6 @ ( 'const/sets/inf' @ sK2 ) ) )
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f268]) ).
thf(f268,plain,
( ( ( ( 'const/sets/inf' @ sK2 )
= sK6 )
= ( $true
& ( 'const/realax/real_le' @ sK6 @ ( 'const/sets/inf' @ sK2 ) ) ) )
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f32,f240]) ).
thf(f240,plain,
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ sK6 ) )
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f239]) ).
thf(f239,plain,
( ( $true
= ( $true
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ sK6 ) ) )
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f223,f234]) ).
thf(f223,plain,
( ! [X1: 'type/realax/real'] :
( $true
= ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK2 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X1 ) ) )
| ~ spl0_8 ),
inference(beta_eta_normalization,[status(thm)],[f221]) ).
thf(f221,plain,
( ! [X1: 'type/realax/real'] :
( $true
= ( ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ Y0 ) )
@ X1 ) )
| ~ spl0_8 ),
inference(pi_clausification,[status(thm)],[f220]) ).
thf(f220,plain,
( ( $true
= ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ Y0 ) ) ) )
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f219]) ).
thf(f219,plain,
( ( ( $true
& ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ Y0 ) ) ) )
= $true )
| ~ spl0_8 ),
inference(backward_demodulation,[status(thm)],[f200,f216]) ).
thf(f32,plain,
! [X2: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X2 @ X1 )
& ( 'const/realax/real_le' @ X1 @ X2 ) )
= ( X2 = X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
! [X2: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( ( 'const/realax/real_le' @ X2 @ X1 )
& ( 'const/realax/real_le' @ X1 @ X2 ) )
= ( X2 = X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f30]) ).
thf(f30,plain,
! [X2: 'type/realax/real',X1: 'type/realax/real'] :
( ( ^ [Y0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ Y0 @ X1 )
& ( 'const/realax/real_le' @ X1 @ Y0 ) )
= ( Y0 = X1 ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
! [X1: 'type/realax/real'] :
( ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ Y0 @ X1 )
& ( 'const/realax/real_le' @ X1 @ Y0 ) )
= ( Y0 = X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f28]) ).
thf(f28,plain,
! [X1: 'type/realax/real'] :
( $true
= ( ^ [Y0: 'type/realax/real'] :
( !! @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ Y1 @ Y0 )
& ( 'const/realax/real_le' @ Y0 @ Y1 ) )
= ( Y1 = Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
( $true
= ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( !! @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ Y1 @ Y0 )
& ( 'const/realax/real_le' @ Y0 @ Y1 ) )
= ( Y1 = Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( $true
= ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( !! @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ Y1 @ Y0 )
& ( 'const/realax/real_le' @ Y0 @ Y1 ) )
= ( Y1 = Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/realax/real_le' @ X1 @ X0 )
& ( ( 'const/realax/real_le' @ X0 @ X1 )
= ( X0 = X1 ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/realax/real_le' @ X1 @ X0 )
& ( ( 'const/realax/real_le' @ X0 @ X1 )
= ( X0 = X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ecFsokLpz9/DTF2THF_14497.p','thm/realax/REAL_LE_ANTISYM_') ).
thf(f105,plain,
( ( $false
= ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ sK2 ) @ sK2 ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f104]) ).
thf(f104,definition,
( spl0_6
<=> ( $false
= ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ sK2 ) @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f234,plain,
( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ sK6 @ sK2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f186]) ).
thf(f212,plain,
~ spl0_7,
inference(avatar_contradiction_clause,[status(thm)],[f211]) ).
thf(f211,plain,
( $false
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f210]) ).
thf(f210,plain,
( ( $true = $false )
| ~ spl0_7 ),
inference(boolean_simplification,[status(thm)],[f209]) ).
thf(f209,plain,
( ( $true
= ( ( 'const/sets/IN' @ 'type/realax/real' @ sK6 @ sK2 )
& $false ) )
| ~ spl0_7 ),
inference(backward_demodulation,[status(thm)],[f186,f206]) ).
thf(f206,plain,
( ! [X1: 'type/realax/real'] :
( $false
= ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2 )
=> ( 'const/realax/real_le' @ X1 @ Y0 ) ) ) )
| ~ spl0_7 ),
inference(beta_eta_normalization,[status(thm)],[f204]) ).
thf(f204,plain,
( ! [X1: 'type/realax/real'] :
( $false
= ( ^ [Y0: 'type/realax/real'] :
( !! @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2 )
=> ( 'const/realax/real_le' @ Y0 @ Y1 ) ) )
@ X1 ) )
| ~ spl0_7 ),
inference(pi_clausification,[status(thm)],[f197]) ).
thf(f197,plain,
( ( $false
= ( ?? @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( !! @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2 )
=> ( 'const/realax/real_le' @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f196]) ).
thf(f196,definition,
( spl0_7
<=> ( $false
= ( ?? @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( !! @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2 )
=> ( 'const/realax/real_le' @ Y0 @ Y1 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f201,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[status(thm)],[f194,f199,f196]) ).
thf(f194,plain,
( ( $false
= ( ?? @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( !! @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2 )
=> ( 'const/realax/real_le' @ Y0 @ Y1 ) ) ) ) )
| ( $true
= ( ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( !! @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2 )
=> ( 'const/realax/real_le' @ Y0 @ Y1 ) ) )
=> ( 'const/realax/real_le' @ Y0 @ ( 'const/sets/inf' @ sK2 ) ) ) )
& ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f66]) ).
thf(f66,plain,
( ( ( ?? @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( !! @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2 )
=> ( 'const/realax/real_le' @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( !! @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2 )
=> ( 'const/realax/real_le' @ Y0 @ Y1 ) ) )
=> ( 'const/realax/real_le' @ Y0 @ ( 'const/sets/inf' @ sK2 ) ) ) )
& ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ Y0 ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f63]) ).
thf(f63,plain,
( $true
= ( ( ( ?? @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( !! @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2 )
=> ( 'const/realax/real_le' @ Y0 @ Y1 ) ) ) )
& $true )
=> ( ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( !! @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2 )
=> ( 'const/realax/real_le' @ Y0 @ Y1 ) ) )
=> ( 'const/realax/real_le' @ Y0 @ ( 'const/sets/inf' @ sK2 ) ) ) )
& ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ Y0 ) ) ) ) ) ),
inference(superposition,[status(thm)],[f52,f56]) ).
thf(f52,plain,
! [X1: 'type/realax/real' > $o] :
( $true
= ( ( ( ?? @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( !! @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y1 @ X1 )
=> ( 'const/realax/real_le' @ Y0 @ Y1 ) ) ) )
& ~ ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X1 ) ) )
=> ( ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( !! @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y1 @ X1 )
=> ( 'const/realax/real_le' @ Y0 @ Y1 ) ) )
=> ( 'const/realax/real_le' @ Y0 @ ( 'const/sets/inf' @ X1 ) ) ) )
& ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ X1 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X1 ) @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f51]) ).
thf(f51,plain,
! [X1: 'type/realax/real' > $o] :
( $true
= ( ^ [Y0: 'type/realax/real' > $o] :
( ( ( ?? @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( !! @ 'type/realax/real'
@ ^ [Y2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y2 @ Y0 )
=> ( 'const/realax/real_le' @ Y1 @ Y2 ) ) ) )
& ~ ( 'const/sets/EMPTY' @ ( 'type/realax/real' = Y0 ) ) )
=> ( ( !! @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( !! @ 'type/realax/real'
@ ^ [Y2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y2 @ Y0 )
=> ( 'const/realax/real_le' @ Y1 @ Y2 ) ) )
=> ( 'const/realax/real_le' @ Y1 @ ( 'const/sets/inf' @ Y0 ) ) ) )
& ( !! @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y1 @ Y0 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ Y0 ) @ Y1 ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
( $true
= ( !! @ ( 'type/realax/real' > $o )
@ ^ [Y0: 'type/realax/real' > $o] :
( ( ( ?? @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( !! @ 'type/realax/real'
@ ^ [Y2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y2 @ Y0 )
=> ( 'const/realax/real_le' @ Y1 @ Y2 ) ) ) )
& ~ ( 'const/sets/EMPTY' @ ( 'type/realax/real' = Y0 ) ) )
=> ( ( !! @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( !! @ 'type/realax/real'
@ ^ [Y2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y2 @ Y0 )
=> ( 'const/realax/real_le' @ Y1 @ Y2 ) ) )
=> ( 'const/realax/real_le' @ Y1 @ ( 'const/sets/inf' @ Y0 ) ) ) )
& ( !! @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y1 @ Y0 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ Y0 ) @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( $true
= ( !! @ ( 'type/realax/real' > $o )
@ ^ [Y0: 'type/realax/real' > $o] :
( ( ( ?? @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( !! @ 'type/realax/real'
@ ^ [Y2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y2 @ Y0 )
=> ( 'const/realax/real_le' @ Y1 @ Y2 ) ) ) )
& ~ ( 'const/sets/EMPTY' @ ( 'type/realax/real' = Y0 ) ) )
=> ( ( !! @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( !! @ 'type/realax/real'
@ ^ [Y2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y2 @ Y0 )
=> ( 'const/realax/real_le' @ Y1 @ Y2 ) ) )
=> ( 'const/realax/real_le' @ Y1 @ ( 'const/sets/inf' @ Y0 ) ) ) )
& ( !! @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y1 @ Y0 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ Y0 ) @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: 'type/realax/real' > $o] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ? [X1: 'type/realax/real'] :
! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_le' @ X1 @ X2 ) ) )
=> ( ! [X3: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X3 ) )
& ! [X4: 'type/realax/real'] :
( ! [X5: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
=> ( 'const/realax/real_le' @ X4 @ X5 ) )
=> ( 'const/realax/real_le' @ X4 @ ( 'const/sets/inf' @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: 'type/realax/real' > $o] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ? [X1: 'type/realax/real'] :
! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_le' @ X1 @ X2 ) ) )
=> ( ! [X1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 ) )
& ! [X1: 'type/realax/real'] :
( ! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_le' @ X1 @ X2 ) )
=> ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ecFsokLpz9/DTF2THF_14497.p','thm/sets/INF_') ).
thf(f191,plain,
~ spl0_5,
inference(avatar_contradiction_clause,[status(thm)],[f190]) ).
thf(f190,plain,
( $false
| ~ spl0_5 ),
inference(trivial_inequality_removal,[status(thm)],[f189]) ).
thf(f189,plain,
( ( $true = $false )
| ~ spl0_5 ),
inference(boolean_simplification,[status(thm)],[f188]) ).
thf(f188,plain,
( ( $true
= ( ( 'const/sets/IN' @ 'type/realax/real' @ sK6 @ sK2 )
& $false ) )
| ~ spl0_5 ),
inference(forward_demodulation,[status(thm)],[f186,f149]) ).
thf(f149,plain,
( ! [X1: 'type/realax/real'] :
( $false
= ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2 )
=> ( 'const/realax/real_le' @ X1 @ Y0 ) ) ) )
| ~ spl0_5 ),
inference(beta_eta_normalization,[status(thm)],[f147]) ).
thf(f147,plain,
( ! [X1: 'type/realax/real'] :
( $false
= ( ^ [Y0: 'type/realax/real'] :
( !! @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2 )
=> ( 'const/realax/real_le' @ Y0 @ Y1 ) ) )
@ X1 ) )
| ~ spl0_5 ),
inference(pi_clausification,[status(thm)],[f144]) ).
thf(f144,plain,
( ( $false
= ( ?? @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( !! @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2 )
=> ( 'const/realax/real_le' @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_5 ),
inference(not_proxy_clausification,[status(thm)],[f110]) ).
thf(f110,plain,
( ( $true
= ( ~ ( ?? @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( !! @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2 )
=> ( 'const/realax/real_le' @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_5 ),
inference(boolean_simplification,[status(thm)],[f109]) ).
thf(f109,plain,
( ( ( ( ?? @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( !! @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2 )
=> ( 'const/realax/real_le' @ Y0 @ Y1 ) ) ) )
=> $false )
= $true )
| ~ spl0_5 ),
inference(boolean_simplification,[status(thm)],[f107]) ).
thf(f107,plain,
( ( $true
= ( ( ?? @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( !! @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2 )
=> ( 'const/realax/real_le' @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( !! @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2 )
=> ( 'const/realax/real_le' @ Y0 @ Y1 ) ) )
=> ( 'const/realax/real_le' @ Y0 @ ( 'const/sets/inf' @ sK2 ) ) ) )
& $false ) ) )
| ~ spl0_5 ),
inference(backward_demodulation,[status(thm)],[f66,f102]) ).
thf(f102,plain,
( ( ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ Y0 ) ) )
= $false )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f101]) ).
thf(f101,definition,
( spl0_5
<=> ( ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ Y0 ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f106,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[status(thm)],[f99,f104,f101]) ).
thf(f99,plain,
( ( $false
= ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ sK2 ) @ sK2 ) )
| ( ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ Y0 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ sK2 ) @ sK2 )
& ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ Y0 ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV493^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n009.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:47:55 EST 2026
% 0.17/0.35 % CPUTime :
% 0.17/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.28/0.47 ---- Original DTF file ---
% 0.28/0.47 thf(spec,logic,$$dhol).
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 % File : SEV493^1 : TPTP v9.2.1. Released v7.0.0.
% 0.28/0.47 % Domain : Analysis
% 0.28/0.47 % Problem : INF_FINITE
% 0.28/0.47 % Version : Especial.
% 0.28/0.47 % English :
% 0.28/0.47
% 0.28/0.47 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.28/0.47 % Source : [Kal16]
% 0.28/0.47 % Names : INF_FINITE_.p [Kal16]
% 0.28/0.47
% 0.28/0.47 % Status : Theorem
% 0.28/0.47 % Rating : 0.00 v7.1.0
% 0.28/0.47 % Syntax : Number of formulae : 11 ( 1 unt; 6 typ; 0 def)
% 0.28/0.47 % Number of atoms : 27 ( 5 equ; 0 cnn)
% 0.28/0.47 % Maximal formula atoms : 8 ( 5 avg)
% 0.28/0.47 % Number of connectives : 72 ( 3 ~; 1 |; 7 &; 52 @)
% 0.28/0.47 % ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% 0.28/0.47 % Maximal formula depth : 11 ( 8 avg)
% 0.28/0.47 % Number of types : 2 ( 1 usr)
% 0.28/0.47 % Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% 0.28/0.47 % Number of symbols : 6 ( 5 usr; 0 con; 1-3 aty)
% 0.28/0.47 % Number of variables : 18 ( 0 ^; 13 !; 2 ?; 18 :)
% 0.28/0.47 % ( 3 !>; 0 ?*; 0 @-; 0 @+)
% 0.28/0.47 % SPC : TH1_THM_EQU_NAR
% 0.28/0.47
% 0.28/0.47 % Comments : Exported from core HOL Light.
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 thf('thf_type_type/realax/real',type,
% 0.28/0.47 'type/realax/real': $tType ).
% 0.28/0.47
% 0.28/0.47 thf('thf_const_const/sets/inf',type,
% 0.28/0.47 'const/sets/inf': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
% 0.28/0.47
% 0.28/0.47 thf('thf_const_const/sets/IN',type,
% 0.28/0.47 'const/sets/IN':
% 0.28/0.47 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.28/0.47
% 0.28/0.47 thf('thf_const_const/sets/FINITE',type,
% 0.28/0.47 'const/sets/FINITE':
% 0.28/0.47 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 0.28/0.47
% 0.28/0.47 thf('thf_const_const/sets/EMPTY',type,
% 0.28/0.47 'const/sets/EMPTY':
% 0.28/0.47 !>[A: $tType] : ( A > $o ) ).
% 0.28/0.47
% 0.28/0.47 thf('thf_const_const/realax/real_le',type,
% 0.28/0.47 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
% 0.28/0.47
% 0.28/0.47 thf('thm/sets/INF_',axiom,
% 0.28/0.47 ! [A: 'type/realax/real' > $o] :
% 0.28/0.47 ( ( ( A
% 0.28/0.47 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 0.28/0.47 & ? [A0: 'type/realax/real'] :
% 0.28/0.47 ! [A1: 'type/realax/real'] :
% 0.28/0.47 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 0.28/0.47 => ( 'const/realax/real_le' @ A0 @ A1 ) ) )
% 0.28/0.47 => ( ! [A0: 'type/realax/real'] :
% 0.28/0.47 ( ( 'const/sets/IN' @ 'type/realax/real' @ A0 @ A )
% 0.28/0.47 => ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ A0 ) )
% 0.28/0.47 & ! [A0: 'type/realax/real'] :
% 0.28/0.47 ( ! [A1: 'type/realax/real'] :
% 0.28/0.47 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 0.28/0.47 => ( 'const/realax/real_le' @ A0 @ A1 ) )
% 0.28/0.47 => ( 'const/realax/real_le' @ A0 @ ( 'const/sets/inf' @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf('thm/realax/REAL_LE_TOTAL_',axiom,
% 0.28/0.47 ! [A: 'type/realax/real',A0: 'type/realax/real'] :
% 0.28/0.47 ( ( 'const/realax/real_le' @ A @ A0 )
% 0.28/0.47 | ( 'const/realax/real_le' @ A0 @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 thf('thm/realax/REAL_LE_ANTISYM_',axiom,
% 0.28/0.47 ! [A: 'type/realax/real',A0: 'type/realax/real'] :
% 0.28/0.47 ( ( ( 'const/realax/real_le' @ A @ A0 )
% 0.28/0.47 & ( 'const/realax/real_le' @ A0 @ A ) )
% 0.28/0.47 = ( A = A0 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf('thm/sets/INF_FINITE_LEMMA_',axiom,
% 0.28/0.47 ! [A: 'type/realax/real' > $o] :
% 0.28/0.47 ( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
% 0.28/0.47 & ( A
% 0.28/0.47 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) ) )
% 0.28/0.47 => ? [A0: 'type/realax/real'] :
% 0.28/0.47 ( ( 'const/sets/IN' @ 'type/realax/real' @ A0 @ A )
% 0.28/0.47 & ! [A1: 'type/realax/real'] :
% 0.28/0.47 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 0.28/0.47 => ( 'const/realax/real_le' @ A0 @ A1 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf('thm/sets/INF_FINITE_',conjecture,
% 0.28/0.47 ! [A: 'type/realax/real' > $o] :
% 0.28/0.47 ( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
% 0.28/0.47 & ( A
% 0.28/0.47 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) ) )
% 0.28/0.47 => ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ A ) @ A )
% 0.28/0.47 & ! [A0: 'type/realax/real'] :
% 0.28/0.47 ( ( 'const/sets/IN' @ 'type/realax/real' @ A0 @ A )
% 0.28/0.47 => ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ A0 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 ------------------------
% 1.67/1.32 ---- Embedded in THF ---
% 1.67/1.32 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.67/1.32 %%% Generated on Tue Feb 24 12:47:56 EST 2026
% 1.67/1.32 %%% using '$$dhol' embedding, version 1.3.0.
% 1.67/1.32 %%% Logic specification used:
% 1.67/1.32 %%% thf(spec, logic, $$dhol).
% 1.67/1.32
% 1.67/1.32 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.ecFsokLpz9/DTF2DTF14497.p
% See solution above
% 1.67/1.32 ------------------------
% 1.67/1.33 ---- Cleaned THF ---
% 1.67/1.33 thf('thf_type_type/realax/real',type,
% 1.67/1.33 'type/realax/real': $tType ).
% 1.67/1.33
% 1.67/1.33 thf('thf_const_const/sets/inf',type,
% 1.67/1.33 'const/sets/inf': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
% 1.67/1.33
% 1.67/1.33 thf('thf_const_const/sets/IN',type,
% 1.67/1.33 'const/sets/IN':
% 1.67/1.33 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 1.67/1.33
% 1.67/1.33 thf('thf_const_const/sets/FINITE',type,
% 1.67/1.33 'const/sets/FINITE':
% 1.67/1.33 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 1.67/1.33
% 1.67/1.33 thf('thf_const_const/sets/EMPTY',type,
% 1.67/1.33 'const/sets/EMPTY':
% 1.67/1.33 !>[A: $tType] : ( A > $o ) ).
% 1.67/1.33
% 1.67/1.33 thf('thf_const_const/realax/real_le',type,
% 1.67/1.33 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
% 1.67/1.33
% 1.67/1.33 thf('thm/sets/INF_',axiom,
% 1.67/1.33 ! [A: 'type/realax/real' > $o] :
% 1.67/1.33 ( ( ( A
% 1.67/1.33 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
% 1.67/1.33 & ? [A0: 'type/realax/real'] :
% 1.67/1.33 ! [A1: 'type/realax/real'] :
% 1.67/1.33 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 1.67/1.33 => ( 'const/realax/real_le' @ A0 @ A1 ) ) )
% 1.67/1.33 => ( ! [A0: 'type/realax/real'] :
% 1.67/1.33 ( ( 'const/sets/IN' @ 'type/realax/real' @ A0 @ A )
% 1.67/1.33 => ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ A0 ) )
% 1.67/1.33 & ! [A0: 'type/realax/real'] :
% 1.67/1.33 ( ! [A1: 'type/realax/real'] :
% 1.67/1.33 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 1.67/1.33 => ( 'const/realax/real_le' @ A0 @ A1 ) )
% 1.67/1.33 => ( 'const/realax/real_le' @ A0 @ ( 'const/sets/inf' @ A ) ) ) ) ) ).
% 1.67/1.33
% 1.67/1.33 thf('thm/realax/REAL_LE_TOTAL_',axiom,
% 1.67/1.33 ! [A: 'type/realax/real',A0: 'type/realax/real'] :
% 1.67/1.33 ( ( 'const/realax/real_le' @ A @ A0 )
% 1.67/1.33 | ( 'const/realax/real_le' @ A0 @ A ) ) ).
% 1.67/1.33
% 1.67/1.33 thf('thm/realax/REAL_LE_ANTISYM_',axiom,
% 1.67/1.33 ! [A: 'type/realax/real',A0: 'type/realax/real'] :
% 1.67/1.33 ( ( ( 'const/realax/real_le' @ A @ A0 )
% 1.67/1.33 & ( 'const/realax/real_le' @ A0 @ A ) )
% 1.67/1.33 = ( A = A0 ) ) ).
% 1.67/1.33
% 1.67/1.33 thf('thm/sets/INF_FINITE_LEMMA_',axiom,
% 1.67/1.33 ! [A: 'type/realax/real' > $o] :
% 1.67/1.33 ( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
% 1.67/1.33 & ( A
% 1.67/1.33 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) ) )
% 1.67/1.33 => ? [A0: 'type/realax/real'] :
% 1.67/1.33 ( ( 'const/sets/IN' @ 'type/realax/real' @ A0 @ A )
% 1.67/1.33 & ! [A1: 'type/realax/real'] :
% 1.67/1.33 ( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
% 1.67/1.33 => ( 'const/realax/real_le' @ A0 @ A1 ) ) ) ) ).
% 1.67/1.33
% 1.67/1.33 thf('thm/sets/INF_FINITE_',conjecture,
% 1.67/1.33 ! [A: 'type/realax/real' > $o] :
% 1.67/1.33 ( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
% 1.67/1.33 & ( A
% 1.67/1.33 != ( 'const/sets/EMPTY' @ 'type/realax/real' ) ) )
% 1.67/1.33 => ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ A ) @ A )
% 1.67/1.33 & ! [A0: 'type/realax/real'] :
% 1.67/1.33 ( ( 'const/sets/IN' @ 'type/realax/real' @ A0 @ A )
% 1.67/1.33 => ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ A0 ) ) ) ) ).
% 1.67/1.33 ------------------------
% 1.67/1.34 % (14597)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_14497 for (3000ds/2Mi)
% 1.67/1.34 % (14594)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_14497 for (3000ds/183Mi)
% 1.67/1.34 % (14597)Instruction limit reached!
% 1.67/1.34 % (14597)------------------------------
% 1.67/1.34 % (14597)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.34 % (14597)Termination reason: Unknown
% 1.67/1.34 % (14597)Termination phase: Property scanning
% 1.67/1.34
% 1.67/1.34 % (14597)Memory used [KB]: 895
% 1.67/1.34 % (14597)Time elapsed: 0.002 s
% 1.67/1.34 % (14597)Instructions burned: 2 (million)
% 1.67/1.34 % (14597)------------------------------
% 1.67/1.34 % (14597)------------------------------
% 1.67/1.35 % (14598)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_14497 for (3000ds/2Mi)
% 1.67/1.35 % (14599)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_14497 for (3000ds/275Mi)
% 1.67/1.35 % (14598)Instruction limit reached!
% 1.67/1.35 % (14598)------------------------------
% 1.67/1.35 % (14598)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.35 % (14598)Termination reason: Unknown
% 1.67/1.35 % (14598)Termination phase: shuffling
% 1.67/1.35
% 1.67/1.35 % (14598)Memory used [KB]: 895
% 1.67/1.35 % (14598)Time elapsed: 0.002 s
% 1.67/1.35 % (14598)Instructions burned: 2 (million)
% 1.67/1.35 % (14598)------------------------------
% 1.67/1.35 % (14598)------------------------------
% 1.67/1.35 % (14596)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_14497 for (3000ds/27Mi)
% 1.67/1.35 % (14595)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_14497 for (3000ds/4Mi)
% 1.67/1.35 % (14599)Refutation not found, incomplete strategy
% 1.67/1.35 % (14599)------------------------------
% 1.67/1.35 % (14599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.35 % (14599)Termination reason: Refutation not found, incomplete strategy
% 1.67/1.35
% 1.67/1.35
% 1.67/1.35 % (14599)Memory used [KB]: 5500
% 1.67/1.35 % (14599)Time elapsed: 0.005 s
% 1.67/1.35 % (14599)Instructions burned: 5 (million)
% 1.67/1.35 % (14599)------------------------------
% 1.67/1.35 % (14599)------------------------------
% 1.67/1.35 % (14601)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_14497 for (2999ds/3Mi)
% 1.67/1.35 % (14595)Instruction limit reached!
% 1.67/1.35 % (14595)------------------------------
% 1.67/1.35 % (14595)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.35 % (14595)Termination reason: Unknown
% 1.67/1.35 % (14595)Termination phase: Saturation
% 1.67/1.35
% 1.67/1.35 % (14595)Memory used [KB]: 5500
% 1.67/1.35 % (14595)Time elapsed: 0.005 s
% 1.67/1.35 % (14595)Instructions burned: 5 (million)
% 1.67/1.35 % (14595)------------------------------
% 1.67/1.35 % (14595)------------------------------
% 1.67/1.35 % (14601)Instruction limit reached!
% 1.67/1.35 % (14601)------------------------------
% 1.67/1.35 % (14601)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.35 % (14601)Termination reason: Unknown
% 1.67/1.35 % (14601)Termination phase: Saturation
% 1.67/1.35
% 1.67/1.35 % (14601)Memory used [KB]: 5500
% 1.67/1.35 % (14601)Time elapsed: 0.002 s
% 1.67/1.35 % (14601)Instructions burned: 3 (million)
% 1.67/1.35 % (14601)------------------------------
% 1.67/1.35 % (14601)------------------------------
% 1.67/1.36 % (14600)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_14497 for (3000ds/18Mi)
% 1.67/1.36 % (14605)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_14497 for (2999ds/1041Mi)
% 1.67/1.36 % (14600)Instruction limit reached!
% 1.67/1.36 % (14600)------------------------------
% 1.67/1.36 % (14600)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.36 % (14600)Termination reason: Unknown
% 1.67/1.36 % (14600)Termination phase: Saturation
% 1.67/1.36
% 1.67/1.36 % (14600)Memory used [KB]: 5628
% 1.67/1.36 % (14600)Time elapsed: 0.033 s
% 1.67/1.36 % (14600)Instructions burned: 19 (million)
% 1.67/1.36 % (14600)------------------------------
% 1.67/1.36 % (14600)------------------------------
% 1.67/1.37 % (14596)Instruction limit reached!
% 1.67/1.37 % (14596)------------------------------
% 1.67/1.37 % (14596)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.37 % (14596)Termination reason: Unknown
% 1.67/1.37 % (14596)Termination phase: Saturation
% 1.67/1.37
% 1.67/1.37 % (14596)Memory used [KB]: 5628
% 1.67/1.37 % (14596)Time elapsed: 0.020 s
% 1.67/1.37 % (14596)Instructions burned: 27 (million)
% 1.67/1.37 % (14596)------------------------------
% 1.67/1.37 % (14596)------------------------------
% 1.67/1.37 % (14603)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_14497 for (2999ds/15Mi)
% 1.67/1.37 % (14602)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_14497 for (2999ds/37Mi)
% 1.67/1.37 % (14604)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_14497 for (2999ds/3Mi)
% 1.67/1.37 % (14604)Instruction limit reached!
% 1.67/1.37 % (14604)------------------------------
% 1.67/1.37 % (14604)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.37 % (14604)Termination reason: Unknown
% 1.67/1.37 % (14604)Termination phase: Saturation
% 1.67/1.37
% 1.67/1.37 % (14604)Memory used [KB]: 5500
% 1.67/1.37 % (14604)Time elapsed: 0.004 s
% 1.67/1.37 % (14604)Instructions burned: 3 (million)
% 1.67/1.37 % (14604)------------------------------
% 1.67/1.37 % (14604)------------------------------
% 1.67/1.37 % (14606)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_14497 for (2999ds/7Mi)
% 1.67/1.38 % (14603)Instruction limit reached!
% 1.67/1.38 % (14603)------------------------------
% 1.67/1.38 % (14603)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.38 % (14603)Termination reason: Unknown
% 1.67/1.38 % (14603)Termination phase: Saturation
% 1.67/1.38
% 1.67/1.38 % (14603)Memory used [KB]: 5628
% 1.67/1.38 % (14603)Time elapsed: 0.011 s
% 1.67/1.38 % (14603)Instructions burned: 16 (million)
% 1.67/1.38 % (14603)------------------------------
% 1.67/1.38 % (14603)------------------------------
% 1.67/1.38 % (14606)Instruction limit reached!
% 1.67/1.38 % (14606)------------------------------
% 1.67/1.38 % (14606)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.38 % (14606)Termination reason: Unknown
% 1.67/1.38 % (14606)Termination phase: Saturation
% 1.67/1.38
% 1.67/1.38 % (14606)Memory used [KB]: 1023
% 1.67/1.38 % (14606)Time elapsed: 0.005 s
% 1.67/1.38 % (14606)Instructions burned: 8 (million)
% 1.67/1.38 % (14606)------------------------------
% 1.67/1.38 % (14606)------------------------------
% 1.67/1.38 % (14605)First to succeed.
% 1.67/1.38 % (14605)Refutation found. Thanks to Tanya!
% 1.67/1.38 % SZS status Theorem for DTF2THF_14497
% 1.67/1.38 % SZS output start Proof for DTF2THF_14497
% 1.67/1.38 thf(type_def_5, type, 'type/realax/real': $tType).
% 1.67/1.38 thf(func_def_0, type, 'type/realax/real': $tType).
% 1.67/1.38 thf(func_def_1, type, 'const/sets/inf': ('type/realax/real' > $o) > 'type/realax/real').
% 1.67/1.38 thf(func_def_2, type, 'const/sets/IN': !>[X0: $tType]:(X0 > (X0 > $o) > $o)).
% 1.67/1.38 thf(func_def_3, type, 'const/sets/FINITE': !>[X0: $tType]:((X0 > $o) > $o)).
% 1.67/1.38 thf(func_def_4, type, 'const/sets/EMPTY': !>[X0: $tType]:(X0 > $o)).
% 1.67/1.38 thf(func_def_5, type, 'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o).
% 1.67/1.38 thf(func_def_21, type, ph1: !>[X0: $tType]:(X0)).
% 1.67/1.38 thf(func_def_22, type, sK2: 'type/realax/real' > $o).
% 1.67/1.38 thf(func_def_23, type, sK3: 'type/realax/real').
% 1.67/1.38 thf(func_def_24, type, sK4: 'type/realax/real').
% 1.67/1.38 thf(func_def_25, type, sK5: 'type/realax/real' > 'type/realax/real').
% 1.67/1.38 thf(func_def_26, type, sK6: 'type/realax/real').
% 1.67/1.38 thf(f328,plain,(
% 1.67/1.38 $false),
% 1.67/1.38 inference(avatar_sat_refutation,[status(thm)],[f106,f191,f201,f212,f327])).
% 1.67/1.38 thf(f327,plain,(
% 1.67/1.38 ~spl0_6 | ~spl0_8),
% 1.67/1.38 inference(avatar_contradiction_clause,[status(thm)],[f326])).
% 1.67/1.38 thf(f326,plain,(
% 1.67/1.38 $false | (~spl0_6 | ~spl0_8)),
% 1.67/1.38 inference(trivial_inequality_removal,[status(thm)],[f325])).
% 1.67/1.38 thf(f325,plain,(
% 1.67/1.38 ($true = $false) | (~spl0_6 | ~spl0_8)),
% 1.67/1.38 inference(backward_demodulation,[status(thm)],[f234,f313])).
% 1.67/1.38 thf(f313,plain,(
% 1.67/1.38 (('const/sets/IN' @ 'type/realax/real' @ sK6 @ sK2) = $false) | (~spl0_6 | ~spl0_8)),
% 1.67/1.38 inference(backward_demodulation,[status(thm)],[f105,f312])).
% 1.67/1.38 thf(f312,plain,(
% 1.67/1.38 (sK6 = ('const/sets/inf' @ sK2)) | ~spl0_8),
% 1.67/1.38 inference(equality_proxy_clausification,[status(thm)],[f282])).
% 1.67/1.38 thf(f282,plain,(
% 1.67/1.38 ($true = (('const/sets/inf' @ sK2) = sK6)) | ~spl0_8),
% 1.67/1.38 inference(backward_demodulation,[status(thm)],[f273,f281])).
% 1.67/1.38 thf(f281,plain,(
% 1.67/1.38 ($true = ('const/realax/real_le' @ sK6 @ ('const/sets/inf' @ sK2))) | ~spl0_8),
% 1.67/1.38 inference(boolean_simplification,[status(thm)],[f279])).
% 1.67/1.38 thf(f279,plain,(
% 1.67/1.38 ($true = ($true => ('const/realax/real_le' @ sK6 @ ('const/sets/inf' @ sK2)))) | ~spl0_8),
% 1.67/1.38 inference(superposition,[status(thm)],[f261,f236])).
% 1.67/1.38 thf(f236,plain,(
% 1.67/1.38 ($true = (!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2) => ('const/realax/real_le' @ sK6 @ Y0)))))),
% 1.67/1.38 inference(boolean_simplification,[status(thm)],[f235])).
% 1.67/1.38 thf(f235,plain,(
% 1.67/1.38 (($true & (!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2) => ('const/realax/real_le' @ sK6 @ Y0))))) = $true)),
% 1.67/1.38 inference(backward_demodulation,[status(thm)],[f186,f234])).
% 1.67/1.38 thf(f186,plain,(
% 1.67/1.38 ($true = (('const/sets/IN' @ 'type/realax/real' @ sK6 @ sK2) & (!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2) => ('const/realax/real_le' @ sK6 @ Y0))))))),
% 1.67/1.38 inference(beta_eta_normalization,[status(thm)],[f184])).
% 1.67/1.38 thf(f184,plain,(
% 1.67/1.38 ($true = ((^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2) & (!! @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2) => ('const/realax/real_le' @ Y0 @ Y1)))))) @ sK6))),
% 1.67/1.38 inference(sigma_clausification,[status(thm)],[f61])).
% 1.67/1.38 thf(f61,plain,(
% 1.67/1.38 ($true = (?? @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2) & (!! @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2) => ('const/realax/real_le' @ Y0 @ Y1))))))))),
% 1.67/1.38 inference(boolean_simplification,[status(thm)],[f60])).
% 1.67/1.38 thf(f60,plain,(
% 1.67/1.38 ($true = ($true => (?? @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2) & (!! @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2) => ('const/realax/real_le' @ Y0 @ Y1)))))))))),
% 1.67/1.38 inference(forward_demodulation,[status(thm)],[f59,f56])).
% 1.67/1.38 thf(f56,plain,(
% 1.67/1.38 ($true = (~ ('const/sets/EMPTY' @ 'type/realax/real' = sK2)))),
% 1.67/1.38 inference(boolean_simplification,[status(thm)],[f55])).
% 1.67/1.38 thf(f55,plain,(
% 1.67/1.38 ($true = ($true & (~ ('const/sets/EMPTY' @ 'type/realax/real' = sK2))))),
% 1.67/1.38 inference(backward_demodulation,[status(thm)],[f46,f54])).
% 1.67/1.38 thf(f54,plain,(
% 1.67/1.38 ($true = ('const/sets/FINITE' @ 'type/realax/real' @ sK2))),
% 1.67/1.38 inference(binary_proxy_clausification,[status(thm)],[f46])).
% 1.67/1.38 thf(f46,plain,(
% 1.67/1.38 ($true = (('const/sets/FINITE' @ 'type/realax/real' @ sK2) & (~ ('const/sets/EMPTY' @ 'type/realax/real' = sK2))))),
% 1.67/1.38 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.67/1.38 thf(f44,plain,(
% 1.67/1.38 ($false = ((('const/sets/FINITE' @ 'type/realax/real' @ sK2) & (~ ('const/sets/EMPTY' @ 'type/realax/real' = sK2))) => (('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ sK2) @ sK2) & (!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2) => ('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ Y0)))))))),
% 1.67/1.38 inference(beta_eta_normalization,[status(thm)],[f43])).
% 1.67/1.38 thf(f43,plain,(
% 1.67/1.38 (((^[Y0 : 'type/realax/real' > $o]: ((('const/sets/FINITE' @ 'type/realax/real' @ Y0) & (~ ('const/sets/EMPTY' @ 'type/realax/real' = Y0))) => (('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ Y0) @ Y0) & (!! @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y1 @ Y0) => ('const/realax/real_le' @ ('const/sets/inf' @ Y0) @ Y1))))))) @ sK2) = $false)),
% 1.67/1.38 inference(sigma_clausification,[status(thm)],[f40])).
% 1.67/1.38 thf(f40,plain,(
% 1.67/1.38 ($false = (!! @ ('type/realax/real' > $o) @ (^[Y0 : 'type/realax/real' > $o]: ((('const/sets/FINITE' @ 'type/realax/real' @ Y0) & (~ ('const/sets/EMPTY' @ 'type/realax/real' = Y0))) => (('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ Y0) @ Y0) & (!! @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y1 @ Y0) => ('const/realax/real_le' @ ('const/sets/inf' @ Y0) @ Y1)))))))))),
% 1.67/1.38 inference(not_proxy_clausification,[status(thm)],[f19])).
% 1.67/1.38 thf(f19,plain,(
% 1.67/1.38 ($true = (~ (!! @ ('type/realax/real' > $o) @ (^[Y0 : 'type/realax/real' > $o]: ((('const/sets/FINITE' @ 'type/realax/real' @ Y0) & (~ ('const/sets/EMPTY' @ 'type/realax/real' = Y0))) => (('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ Y0) @ Y0) & (!! @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y1 @ Y0) => ('const/realax/real_le' @ ('const/sets/inf' @ Y0) @ Y1))))))))))),
% 1.67/1.38 inference(cnf_transformation,[status(thm)],[f11])).
% 1.67/1.38 thf(f11,plain,(
% 1.67/1.38 ($true = (~ (!! @ ('type/realax/real' > $o) @ (^[Y0 : 'type/realax/real' > $o]: ((('const/sets/FINITE' @ 'type/realax/real' @ Y0) & (~ ('const/sets/EMPTY' @ 'type/realax/real' = Y0))) => (('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ Y0) @ Y0) & (!! @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y1 @ Y0) => ('const/realax/real_le' @ ('const/sets/inf' @ Y0) @ Y1))))))))))),
% 1.67/1.38 inference(fool_elimination,[status(thm)],[f10])).
% 1.67/1.38 thf(f10,plain,(
% 1.67/1.38 ~! [X0 : 'type/realax/real' > $o] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ('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)))),
% 1.67/1.38 inference(rectify,[status(thm)],[f6])).
% 1.67/1.38 thf(f6,negated_conjecture,(
% 1.67/1.38 ~! [X0 : 'type/realax/real' > $o] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ('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)))),
% 1.67/1.38 inference(negated_conjecture,[status(cth)],[f5])).
% 1.67/1.38 thf(f5,conjecture,(
% 1.67/1.38 ! [X0 : 'type/realax/real' > $o] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ('const/sets/FINITE' @ 'type/realax/real' @ X0)) => (! [X1 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) => ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1)) & ('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ X0) @ X0)))),
% 1.67/1.38 file('/export/starexec/sandbox/tmp/tmp.ecFsokLpz9/DTF2THF_14497.p','thm/sets/INF_FINITE_')).
% 1.67/1.38 thf(f59,plain,(
% 1.67/1.38 ($true = ((~ ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) => (?? @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2) & (!! @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2) => ('const/realax/real_le' @ Y0 @ Y1)))))))))),
% 1.67/1.38 inference(boolean_simplification,[status(thm)],[f58])).
% 1.67/1.38 thf(f58,plain,(
% 1.67/1.38 ($true = (((~ ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) & $true) => (?? @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2) & (!! @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2) => ('const/realax/real_le' @ Y0 @ Y1)))))))))),
% 1.67/1.38 inference(superposition,[status(thm)],[f38,f54])).
% 1.67/1.38 thf(f38,plain,(
% 1.67/1.38 ( ! [X1 : 'type/realax/real' > $o] : (($true = (((~ ('const/sets/EMPTY' @ 'type/realax/real' = X1)) & ('const/sets/FINITE' @ 'type/realax/real' @ X1)) => (?? @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ X1) & (!! @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y1 @ X1) => ('const/realax/real_le' @ Y0 @ Y1)))))))))) )),
% 1.67/1.38 inference(beta_eta_normalization,[status(thm)],[f37])).
% 1.67/1.38 thf(f37,plain,(
% 1.67/1.38 ( ! [X1 : 'type/realax/real' > $o] : (($true = ((^[Y0 : 'type/realax/real' > $o]: (((~ ('const/sets/EMPTY' @ 'type/realax/real' = Y0)) & ('const/sets/FINITE' @ 'type/realax/real' @ Y0)) => (?? @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y1 @ Y0) & (!! @ 'type/realax/real' @ (^[Y2 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y2 @ Y0) => ('const/realax/real_le' @ Y1 @ Y2))))))))) @ X1))) )),
% 1.67/1.38 inference(pi_clausification,[status(thm)],[f18])).
% 1.67/1.38 thf(f18,plain,(
% 1.67/1.38 ((!! @ ('type/realax/real' > $o) @ (^[Y0 : 'type/realax/real' > $o]: (((~ ('const/sets/EMPTY' @ 'type/realax/real' = Y0)) & ('const/sets/FINITE' @ 'type/realax/real' @ Y0)) => (?? @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y1 @ Y0) & (!! @ 'type/realax/real' @ (^[Y2 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y2 @ Y0) => ('const/realax/real_le' @ Y1 @ Y2)))))))))) = $true)),
% 1.67/1.38 inference(cnf_transformation,[status(thm)],[f15])).
% 1.67/1.38 thf(f15,plain,(
% 1.67/1.38 ((!! @ ('type/realax/real' > $o) @ (^[Y0 : 'type/realax/real' > $o]: (((~ ('const/sets/EMPTY' @ 'type/realax/real' = Y0)) & ('const/sets/FINITE' @ 'type/realax/real' @ Y0)) => (?? @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y1 @ Y0) & (!! @ 'type/realax/real' @ (^[Y2 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y2 @ Y0) => ('const/realax/real_le' @ Y1 @ Y2)))))))))) = $true)),
% 1.67/1.38 inference(fool_elimination,[status(thm)],[f14])).
% 1.67/1.38 thf(f14,plain,(
% 1.67/1.38 ! [X0 : 'type/realax/real' > $o] : ((('const/sets/FINITE' @ 'type/realax/real' @ X0) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => ? [X1 : 'type/realax/real'] : (! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X1 @ X2)) & ('const/sets/IN' @ 'type/realax/real' @ X1 @ X0)))),
% 1.67/1.38 inference(rectify,[status(thm)],[f4])).
% 1.67/1.38 thf(f4,axiom,(
% 1.67/1.38 ! [X0 : 'type/realax/real' > $o] : ((('const/sets/FINITE' @ 'type/realax/real' @ X0) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => ? [X1 : 'type/realax/real'] : (! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X1 @ X2)) & ('const/sets/IN' @ 'type/realax/real' @ X1 @ X0)))),
% 1.67/1.38 file('/export/starexec/sandbox/tmp/tmp.ecFsokLpz9/DTF2THF_14497.p','thm/sets/INF_FINITE_LEMMA_')).
% 1.67/1.38 thf(f261,plain,(
% 1.67/1.38 ( ! [X1 : 'type/realax/real'] : (($true = ((!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2) => ('const/realax/real_le' @ X1 @ Y0)))) => ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ sK2))))) ) | ~spl0_8),
% 1.67/1.38 inference(beta_eta_normalization,[status(thm)],[f258])).
% 1.67/1.38 thf(f258,plain,(
% 1.67/1.38 ( ! [X1 : 'type/realax/real'] : (($true = ((^[Y0 : 'type/realax/real']: ((!! @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2) => ('const/realax/real_le' @ Y0 @ Y1)))) => ('const/realax/real_le' @ Y0 @ ('const/sets/inf' @ sK2)))) @ X1))) ) | ~spl0_8),
% 1.67/1.38 inference(pi_clausification,[status(thm)],[f216])).
% 1.67/1.38 thf(f216,plain,(
% 1.67/1.38 ($true = (!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: ((!! @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2) => ('const/realax/real_le' @ Y0 @ Y1)))) => ('const/realax/real_le' @ Y0 @ ('const/sets/inf' @ sK2)))))) | ~spl0_8),
% 1.67/1.38 inference(binary_proxy_clausification,[status(thm)],[f200])).
% 1.67/1.38 thf(f200,plain,(
% 1.67/1.38 ($true = ((!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: ((!! @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2) => ('const/realax/real_le' @ Y0 @ Y1)))) => ('const/realax/real_le' @ Y0 @ ('const/sets/inf' @ sK2))))) & (!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2) => ('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ Y0)))))) | ~spl0_8),
% 1.67/1.38 inference(avatar_component_clause,[status(thm)],[f199])).
% 1.67/1.38 thf(f199,definition,(
% 1.67/1.38 spl0_8 <=> ($true = ((!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: ((!! @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2) => ('const/realax/real_le' @ Y0 @ Y1)))) => ('const/realax/real_le' @ Y0 @ ('const/sets/inf' @ sK2))))) & (!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2) => ('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ Y0))))))),
% 1.67/1.38 introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition])).
% 1.67/1.38 thf(f273,plain,(
% 1.67/1.38 ((('const/sets/inf' @ sK2) = sK6) = ('const/realax/real_le' @ sK6 @ ('const/sets/inf' @ sK2))) | ~spl0_8),
% 1.67/1.38 inference(boolean_simplification,[status(thm)],[f268])).
% 1.67/1.38 thf(f268,plain,(
% 1.67/1.38 ((('const/sets/inf' @ sK2) = sK6) = ($true & ('const/realax/real_le' @ sK6 @ ('const/sets/inf' @ sK2)))) | ~spl0_8),
% 1.67/1.38 inference(superposition,[status(thm)],[f32,f240])).
% 1.67/1.38 thf(f240,plain,(
% 1.67/1.38 ($true = ('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ sK6)) | ~spl0_8),
% 1.67/1.38 inference(boolean_simplification,[status(thm)],[f239])).
% 1.67/1.38 thf(f239,plain,(
% 1.67/1.38 ($true = ($true => ('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ sK6))) | ~spl0_8),
% 1.67/1.38 inference(superposition,[status(thm)],[f223,f234])).
% 1.67/1.38 thf(f223,plain,(
% 1.67/1.38 ( ! [X1 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK2) => ('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ X1)))) ) | ~spl0_8),
% 1.67/1.38 inference(beta_eta_normalization,[status(thm)],[f221])).
% 1.67/1.38 thf(f221,plain,(
% 1.67/1.38 ( ! [X1 : 'type/realax/real'] : (($true = ((^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2) => ('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ Y0))) @ X1))) ) | ~spl0_8),
% 1.67/1.38 inference(pi_clausification,[status(thm)],[f220])).
% 1.67/1.38 thf(f220,plain,(
% 1.67/1.38 ($true = (!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2) => ('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ Y0))))) | ~spl0_8),
% 1.67/1.38 inference(boolean_simplification,[status(thm)],[f219])).
% 1.67/1.38 thf(f219,plain,(
% 1.67/1.38 (($true & (!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2) => ('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ Y0))))) = $true) | ~spl0_8),
% 1.67/1.38 inference(backward_demodulation,[status(thm)],[f200,f216])).
% 1.67/1.38 thf(f32,plain,(
% 1.67/1.38 ( ! [X2 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X2 @ X1) & ('const/realax/real_le' @ X1 @ X2)) = (X2 = X1))) )),
% 1.67/1.38 inference(equality_proxy_clausification,[status(thm)],[f31])).
% 1.67/1.38 thf(f31,plain,(
% 1.67/1.38 ( ! [X2 : 'type/realax/real',X1 : 'type/realax/real'] : ((((('const/realax/real_le' @ X2 @ X1) & ('const/realax/real_le' @ X1 @ X2)) = (X2 = X1)) = $true)) )),
% 1.67/1.38 inference(beta_eta_normalization,[status(thm)],[f30])).
% 1.67/1.38 thf(f30,plain,(
% 1.67/1.38 ( ! [X2 : 'type/realax/real',X1 : 'type/realax/real'] : ((((^[Y0 : 'type/realax/real']: ((('const/realax/real_le' @ Y0 @ X1) & ('const/realax/real_le' @ X1 @ Y0)) = (Y0 = X1))) @ X2) = $true)) )),
% 1.67/1.38 inference(pi_clausification,[status(thm)],[f29])).
% 1.67/1.38 thf(f29,plain,(
% 1.67/1.38 ( ! [X1 : 'type/realax/real'] : (((!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: ((('const/realax/real_le' @ Y0 @ X1) & ('const/realax/real_le' @ X1 @ Y0)) = (Y0 = X1)))) = $true)) )),
% 1.67/1.38 inference(beta_eta_normalization,[status(thm)],[f28])).
% 1.67/1.38 thf(f28,plain,(
% 1.67/1.38 ( ! [X1 : 'type/realax/real'] : (($true = ((^[Y0 : 'type/realax/real']: (!! @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: ((('const/realax/real_le' @ Y1 @ Y0) & ('const/realax/real_le' @ Y0 @ Y1)) = (Y1 = Y0))))) @ X1))) )),
% 1.67/1.38 inference(pi_clausification,[status(thm)],[f22])).
% 1.67/1.38 thf(f22,plain,(
% 1.67/1.38 ($true = (!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (!! @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: ((('const/realax/real_le' @ Y1 @ Y0) & ('const/realax/real_le' @ Y0 @ Y1)) = (Y1 = Y0)))))))),
% 1.67/1.38 inference(cnf_transformation,[status(thm)],[f13])).
% 1.67/1.38 thf(f13,plain,(
% 1.67/1.38 ($true = (!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (!! @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: ((('const/realax/real_le' @ Y1 @ Y0) & ('const/realax/real_le' @ Y0 @ Y1)) = (Y1 = Y0)))))))),
% 1.67/1.38 inference(fool_elimination,[status(thm)],[f12])).
% 1.67/1.38 thf(f12,plain,(
% 1.67/1.38 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/realax/real_le' @ X1 @ X0) & ('const/realax/real_le' @ X0 @ X1) = (X0 = X1))),
% 1.67/1.38 inference(rectify,[status(thm)],[f3])).
% 1.67/1.38 thf(f3,axiom,(
% 1.67/1.38 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/realax/real_le' @ X1 @ X0) & ('const/realax/real_le' @ X0 @ X1) = (X0 = X1))),
% 1.67/1.38 file('/export/starexec/sandbox/tmp/tmp.ecFsokLpz9/DTF2THF_14497.p','thm/realax/REAL_LE_ANTISYM_')).
% 1.67/1.38 thf(f105,plain,(
% 1.67/1.38 ($false = ('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ sK2) @ sK2)) | ~spl0_6),
% 1.67/1.38 inference(avatar_component_clause,[status(thm)],[f104])).
% 1.67/1.38 thf(f104,definition,(
% 1.67/1.38 spl0_6 <=> ($false = ('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ sK2) @ sK2))),
% 1.67/1.38 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.67/1.38 thf(f234,plain,(
% 1.67/1.38 ($true = ('const/sets/IN' @ 'type/realax/real' @ sK6 @ sK2))),
% 1.67/1.38 inference(binary_proxy_clausification,[status(thm)],[f186])).
% 1.67/1.38 thf(f212,plain,(
% 1.67/1.38 ~spl0_7),
% 1.67/1.38 inference(avatar_contradiction_clause,[status(thm)],[f211])).
% 1.67/1.38 thf(f211,plain,(
% 1.67/1.38 $false | ~spl0_7),
% 1.67/1.38 inference(trivial_inequality_removal,[status(thm)],[f210])).
% 1.67/1.38 thf(f210,plain,(
% 1.67/1.38 ($true = $false) | ~spl0_7),
% 1.67/1.38 inference(boolean_simplification,[status(thm)],[f209])).
% 1.67/1.38 thf(f209,plain,(
% 1.67/1.38 ($true = (('const/sets/IN' @ 'type/realax/real' @ sK6 @ sK2) & $false)) | ~spl0_7),
% 1.67/1.38 inference(backward_demodulation,[status(thm)],[f186,f206])).
% 1.67/1.38 thf(f206,plain,(
% 1.67/1.38 ( ! [X1 : 'type/realax/real'] : (($false = (!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2) => ('const/realax/real_le' @ X1 @ Y0)))))) ) | ~spl0_7),
% 1.67/1.38 inference(beta_eta_normalization,[status(thm)],[f204])).
% 1.67/1.38 thf(f204,plain,(
% 1.67/1.38 ( ! [X1 : 'type/realax/real'] : (($false = ((^[Y0 : 'type/realax/real']: (!! @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2) => ('const/realax/real_le' @ Y0 @ Y1))))) @ X1))) ) | ~spl0_7),
% 1.67/1.38 inference(pi_clausification,[status(thm)],[f197])).
% 1.67/1.38 thf(f197,plain,(
% 1.67/1.38 ($false = (?? @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (!! @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2) => ('const/realax/real_le' @ Y0 @ Y1))))))) | ~spl0_7),
% 1.67/1.38 inference(avatar_component_clause,[status(thm)],[f196])).
% 1.67/1.38 thf(f196,definition,(
% 1.67/1.38 spl0_7 <=> ($false = (?? @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (!! @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2) => ('const/realax/real_le' @ Y0 @ Y1)))))))),
% 1.67/1.38 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 1.67/1.38 thf(f201,plain,(
% 1.67/1.38 spl0_7 | spl0_8),
% 1.67/1.38 inference(avatar_split_clause,[status(thm)],[f194,f199,f196])).
% 1.67/1.38 thf(f194,plain,(
% 1.67/1.38 ($false = (?? @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (!! @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2) => ('const/realax/real_le' @ Y0 @ Y1))))))) | ($true = ((!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: ((!! @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2) => ('const/realax/real_le' @ Y0 @ Y1)))) => ('const/realax/real_le' @ Y0 @ ('const/sets/inf' @ sK2))))) & (!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2) => ('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ Y0))))))),
% 1.67/1.38 inference(binary_proxy_clausification,[status(thm)],[f66])).
% 1.67/1.38 thf(f66,plain,(
% 1.67/1.38 (((?? @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (!! @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2) => ('const/realax/real_le' @ Y0 @ Y1)))))) => ((!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: ((!! @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2) => ('const/realax/real_le' @ Y0 @ Y1)))) => ('const/realax/real_le' @ Y0 @ ('const/sets/inf' @ sK2))))) & (!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2) => ('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ Y0)))))) = $true)),
% 1.67/1.38 inference(boolean_simplification,[status(thm)],[f63])).
% 1.67/1.38 thf(f63,plain,(
% 1.67/1.38 ($true = (((?? @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (!! @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2) => ('const/realax/real_le' @ Y0 @ Y1)))))) & $true) => ((!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: ((!! @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2) => ('const/realax/real_le' @ Y0 @ Y1)))) => ('const/realax/real_le' @ Y0 @ ('const/sets/inf' @ sK2))))) & (!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2) => ('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ Y0)))))))),
% 1.67/1.38 inference(superposition,[status(thm)],[f52,f56])).
% 1.67/1.38 thf(f52,plain,(
% 1.67/1.38 ( ! [X1 : 'type/realax/real' > $o] : (($true = (((?? @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (!! @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y1 @ X1) => ('const/realax/real_le' @ Y0 @ Y1)))))) & (~ ('const/sets/EMPTY' @ 'type/realax/real' = X1))) => ((!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: ((!! @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y1 @ X1) => ('const/realax/real_le' @ Y0 @ Y1)))) => ('const/realax/real_le' @ Y0 @ ('const/sets/inf' @ X1))))) & (!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ X1) => ('const/realax/real_le' @ ('const/sets/inf' @ X1) @ Y0)))))))) )),
% 1.67/1.38 inference(beta_eta_normalization,[status(thm)],[f51])).
% 1.67/1.38 thf(f51,plain,(
% 1.67/1.38 ( ! [X1 : 'type/realax/real' > $o] : (($true = ((^[Y0 : 'type/realax/real' > $o]: (((?? @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: (!! @ 'type/realax/real' @ (^[Y2 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y2 @ Y0) => ('const/realax/real_le' @ Y1 @ Y2)))))) & (~ ('const/sets/EMPTY' @ 'type/realax/real' = Y0))) => ((!! @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: ((!! @ 'type/realax/real' @ (^[Y2 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y2 @ Y0) => ('const/realax/real_le' @ Y1 @ Y2)))) => ('const/realax/real_le' @ Y1 @ ('const/sets/inf' @ Y0))))) & (!! @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y1 @ Y0) => ('const/realax/real_le' @ ('const/sets/inf' @ Y0) @ Y1))))))) @ X1))) )),
% 1.67/1.38 inference(pi_clausification,[status(thm)],[f20])).
% 1.67/1.38 thf(f20,plain,(
% 1.67/1.38 ($true = (!! @ ('type/realax/real' > $o) @ (^[Y0 : 'type/realax/real' > $o]: (((?? @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: (!! @ 'type/realax/real' @ (^[Y2 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y2 @ Y0) => ('const/realax/real_le' @ Y1 @ Y2)))))) & (~ ('const/sets/EMPTY' @ 'type/realax/real' = Y0))) => ((!! @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: ((!! @ 'type/realax/real' @ (^[Y2 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y2 @ Y0) => ('const/realax/real_le' @ Y1 @ Y2)))) => ('const/realax/real_le' @ Y1 @ ('const/sets/inf' @ Y0))))) & (!! @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y1 @ Y0) => ('const/realax/real_le' @ ('const/sets/inf' @ Y0) @ Y1)))))))))),
% 1.67/1.38 inference(cnf_transformation,[status(thm)],[f9])).
% 1.67/1.38 thf(f9,plain,(
% 1.67/1.38 ($true = (!! @ ('type/realax/real' > $o) @ (^[Y0 : 'type/realax/real' > $o]: (((?? @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: (!! @ 'type/realax/real' @ (^[Y2 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y2 @ Y0) => ('const/realax/real_le' @ Y1 @ Y2)))))) & (~ ('const/sets/EMPTY' @ 'type/realax/real' = Y0))) => ((!! @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: ((!! @ 'type/realax/real' @ (^[Y2 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y2 @ Y0) => ('const/realax/real_le' @ Y1 @ Y2)))) => ('const/realax/real_le' @ Y1 @ ('const/sets/inf' @ Y0))))) & (!! @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y1 @ Y0) => ('const/realax/real_le' @ ('const/sets/inf' @ Y0) @ Y1)))))))))),
% 1.67/1.38 inference(fool_elimination,[status(thm)],[f8])).
% 1.67/1.38 thf(f8,plain,(
% 1.67/1.38 ! [X0 : 'type/realax/real' > $o] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ? [X1 : 'type/realax/real'] : ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X1 @ X2))) => (! [X3 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) => ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X3)) & ! [X4 : 'type/realax/real'] : (! [X5 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0) => ('const/realax/real_le' @ X4 @ X5)) => ('const/realax/real_le' @ X4 @ ('const/sets/inf' @ X0)))))),
% 1.67/1.38 inference(rectify,[status(thm)],[f1])).
% 1.67/1.38 thf(f1,axiom,(
% 1.67/1.38 ! [X0 : 'type/realax/real' > $o] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ? [X1 : 'type/realax/real'] : ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X1 @ X2))) => (! [X1 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) => ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1)) & ! [X1 : 'type/realax/real'] : (! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X1 @ X2)) => ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0)))))),
% 1.67/1.38 file('/export/starexec/sandbox/tmp/tmp.ecFsokLpz9/DTF2THF_14497.p','thm/sets/INF_')).
% 1.67/1.38 thf(f191,plain,(
% 1.67/1.38 ~spl0_5),
% 1.67/1.38 inference(avatar_contradiction_clause,[status(thm)],[f190])).
% 1.67/1.38 thf(f190,plain,(
% 1.67/1.38 $false | ~spl0_5),
% 1.67/1.38 inference(trivial_inequality_removal,[status(thm)],[f189])).
% 1.67/1.38 thf(f189,plain,(
% 1.67/1.38 ($true = $false) | ~spl0_5),
% 1.67/1.38 inference(boolean_simplification,[status(thm)],[f188])).
% 1.67/1.38 thf(f188,plain,(
% 1.67/1.38 ($true = (('const/sets/IN' @ 'type/realax/real' @ sK6 @ sK2) & $false)) | ~spl0_5),
% 1.67/1.38 inference(forward_demodulation,[status(thm)],[f186,f149])).
% 1.67/1.38 thf(f149,plain,(
% 1.67/1.38 ( ! [X1 : 'type/realax/real'] : (($false = (!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2) => ('const/realax/real_le' @ X1 @ Y0)))))) ) | ~spl0_5),
% 1.67/1.38 inference(beta_eta_normalization,[status(thm)],[f147])).
% 1.67/1.38 thf(f147,plain,(
% 1.67/1.38 ( ! [X1 : 'type/realax/real'] : (($false = ((^[Y0 : 'type/realax/real']: (!! @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2) => ('const/realax/real_le' @ Y0 @ Y1))))) @ X1))) ) | ~spl0_5),
% 1.67/1.38 inference(pi_clausification,[status(thm)],[f144])).
% 1.67/1.38 thf(f144,plain,(
% 1.67/1.38 ($false = (?? @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (!! @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2) => ('const/realax/real_le' @ Y0 @ Y1))))))) | ~spl0_5),
% 1.67/1.38 inference(not_proxy_clausification,[status(thm)],[f110])).
% 1.67/1.38 thf(f110,plain,(
% 1.67/1.38 ($true = (~ (?? @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (!! @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2) => ('const/realax/real_le' @ Y0 @ Y1)))))))) | ~spl0_5),
% 1.67/1.38 inference(boolean_simplification,[status(thm)],[f109])).
% 1.67/1.38 thf(f109,plain,(
% 1.67/1.38 (((?? @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (!! @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2) => ('const/realax/real_le' @ Y0 @ Y1)))))) => $false) = $true) | ~spl0_5),
% 1.67/1.38 inference(boolean_simplification,[status(thm)],[f107])).
% 1.67/1.38 thf(f107,plain,(
% 1.67/1.38 ($true = ((?? @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (!! @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2) => ('const/realax/real_le' @ Y0 @ Y1)))))) => ((!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: ((!! @ 'type/realax/real' @ (^[Y1 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y1 @ sK2) => ('const/realax/real_le' @ Y0 @ Y1)))) => ('const/realax/real_le' @ Y0 @ ('const/sets/inf' @ sK2))))) & $false))) | ~spl0_5),
% 1.67/1.38 inference(backward_demodulation,[status(thm)],[f66,f102])).
% 1.67/1.38 thf(f102,plain,(
% 1.67/1.38 ((!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2) => ('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ Y0)))) = $false) | ~spl0_5),
% 1.67/1.38 inference(avatar_component_clause,[status(thm)],[f101])).
% 1.67/1.38 thf(f101,definition,(
% 1.67/1.38 spl0_5 <=> ((!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2) => ('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ Y0)))) = $false)),
% 1.67/1.38 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.67/1.38 thf(f106,plain,(
% 1.67/1.38 spl0_5 | spl0_6),
% 1.67/1.38 inference(avatar_split_clause,[status(thm)],[f99,f104,f101])).
% 1.67/1.38 thf(f99,plain,(
% 1.67/1.38 ($false = ('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ sK2) @ sK2)) | ((!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2) => ('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ Y0)))) = $false)),
% 1.67/1.38 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 1.67/1.38 thf(f45,plain,(
% 1.67/1.38 ((('const/sets/IN' @ 'type/realax/real' @ ('const/sets/inf' @ sK2) @ sK2) & (!! @ 'type/realax/real' @ (^[Y0 : 'type/realax/real']: (('const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2) => ('const/realax/real_le' @ ('const/sets/inf' @ sK2) @ Y0))))) = $false)),
% 1.67/1.38 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.67/1.38 % SZS output end Proof for DTF2THF_14497
% 1.67/1.38 % (14605)------------------------------
% 1.67/1.38 % (14605)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.38 % (14605)Termination reason: Refutation
% 1.67/1.38
% 1.67/1.38 % (14605)Memory used [KB]: 5884
% 1.67/1.38 % (14605)Time elapsed: 0.022 s
% 1.67/1.38 % (14605)Instructions burned: 54 (million)
% 1.67/1.38 % (14605)------------------------------
% 1.67/1.38 % (14605)------------------------------
% 1.67/1.38 % (14593)Success in time 0.047 s
%------------------------------------------------------------------------------