TSTP Solution File: SEV493^1 by Vampire---4.9
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%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEV493^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n018.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 : Mon Jun 24 16:04:06 EDT 2024
% Result : Theorem 0.20s 0.44s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 8
% Syntax : Number of formulae : 92 ( 39 unt; 0 typ; 0 def)
% Number of atoms : 734 ( 121 equ; 0 cnn)
% Maximal formula atoms : 9 ( 7 avg)
% Number of connectives : 1300 ( 72 ~; 43 |; 70 &; 883 @)
% ( 4 <=>; 120 =>; 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)
% ( 87 !!; 21 ??; 0 @@+; 0 @@-)
% Number of variables : 166 ( 118 ^ 44 !; 4 ?; 166 :)
% 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(f338,plain,
$false,
inference(avatar_sat_refutation,[],[f108,f198,f208,f323,f337]) ).
thf(f337,plain,
~ spl0_8,
inference(avatar_contradiction_clause,[],[f336]) ).
thf(f336,plain,
( $false
| ~ spl0_8 ),
inference(trivial_inequality_removal,[],[f335]) ).
thf(f335,plain,
( ( $false = $true )
| ~ spl0_8 ),
inference(backward_demodulation,[],[f214,f332]) ).
thf(f332,plain,
( ! [X1: 'type/realax/real'] :
( ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2 )
=> ( 'const/realax/real_le' @ X1 @ Y0 ) ) )
= $false )
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f330]) ).
thf(f330,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_8 ),
inference(pi_clausification,[],[f207]) ).
thf(f207,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_8 ),
inference(avatar_component_clause,[],[f206]) ).
thf(f206,plain,
( spl0_8
<=> ( $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(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
thf(f214,plain,
( ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2 )
=> ( 'const/realax/real_le' @ sK6 @ Y0 ) ) )
= $true ),
inference(boolean_simplification,[],[f213]) ).
thf(f213,plain,
( $true
= ( $true
& ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2 )
=> ( 'const/realax/real_le' @ sK6 @ Y0 ) ) ) ) ),
inference(backward_demodulation,[],[f193,f212]) ).
thf(f212,plain,
( ( 'const/sets/IN' @ 'type/realax/real' @ sK6 @ sK2 )
= $true ),
inference(binary_proxy_clausification,[],[f193]) ).
thf(f193,plain,
( ( ( '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 ) ) ) )
= $true ),
inference(beta_eta_normalization,[],[f191]) ).
thf(f191,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,[],[f61]) ).
thf(f61,plain,
( ( ?? @ '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 ) ) ) ) )
= $true ),
inference(boolean_simplification,[],[f60]) ).
thf(f60,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 ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[],[f59,f56]) ).
thf(f56,plain,
( $true
= ( ~ ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) ) ) ),
inference(boolean_simplification,[],[f55]) ).
thf(f55,plain,
( ( $true
& ~ ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) ) )
= $true ),
inference(backward_demodulation,[],[f46,f54]) ).
thf(f54,plain,
( $true
= ( 'const/sets/FINITE' @ 'type/realax/real' @ sK2 ) ),
inference(binary_proxy_clausification,[],[f46]) ).
thf(f46,plain,
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK2 )
& ~ ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f44]) ).
thf(f44,plain,
( ( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK2 )
& ~ ( 'const/sets/EMPTY' @ ( 'type/realax/real' = 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 ) ) )
& ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ sK2 ) @ sK2 ) ) )
= $false ),
inference(beta_eta_normalization,[],[f43]) ).
thf(f43,plain,
( $false
= ( ^ [Y0: 'type/realax/real' > $o] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ Y0 )
& ~ ( 'const/sets/EMPTY' @ ( 'type/realax/real' = 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 ) ) )
& ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ Y0 ) @ Y0 ) ) )
@ sK2 ) ),
inference(sigma_clausification,[],[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 ) ) )
=> ( ( !! @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y1 @ Y0 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ Y0 ) @ Y1 ) ) )
& ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ Y0 ) @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f21]) ).
thf(f21,plain,
( ( ~ ( !! @ ( 'type/realax/real' > $o )
@ ^ [Y0: 'type/realax/real' > $o] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ Y0 )
& ~ ( 'const/sets/EMPTY' @ ( 'type/realax/real' = 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 ) ) )
& ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ Y0 ) @ Y0 ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f9]) ).
thf(f9,plain,
( ( ~ ( !! @ ( 'type/realax/real' > $o )
@ ^ [Y0: 'type/realax/real' > $o] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ Y0 )
& ~ ( 'const/sets/EMPTY' @ ( 'type/realax/real' = 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 ) ) )
& ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ Y0 ) @ Y0 ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f8]) ).
thf(f8,plain,
~ ! [X0: 'type/realax/real' > $o] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 ) )
=> ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ X0 ) @ X0 )
& ! [X1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f6,negated_conjecture,
~ ! [X0: 'type/realax/real' > $o] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 ) )
=> ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ X0 ) @ X0 )
& ! [X1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 ) ) ) ),
inference(negated_conjecture,[],[f5]) ).
thf(f5,conjecture,
! [X0: 'type/realax/real' > $o] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 ) )
=> ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ X0 ) @ X0 )
& ! [X1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/INF_FINITE_') ).
thf(f59,plain,
( ( ~ ( '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 ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[],[f58]) ).
thf(f58,plain,
( ( ( ~ ( '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 ) ) ) ) ) )
= $true ),
inference(superposition,[],[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,[],[f37]) ).
thf(f37,plain,
! [X1: '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 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[],[f18]) ).
thf(f18,plain,
( $true
= ( !! @ ( '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 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f11,plain,
( $true
= ( !! @ ( '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 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f10,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,[],[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/sandbox2/benchmark/theBenchmark.p','thm/sets/INF_FINITE_LEMMA_') ).
thf(f323,plain,
( ~ spl0_6
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f322]) ).
thf(f322,plain,
( $false
| ~ spl0_6
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f321]) ).
thf(f321,plain,
( ( $false = $true )
| ~ spl0_6
| ~ spl0_7 ),
inference(backward_demodulation,[],[f212,f309]) ).
thf(f309,plain,
( ( $false
= ( 'const/sets/IN' @ 'type/realax/real' @ sK6 @ sK2 ) )
| ~ spl0_6
| ~ spl0_7 ),
inference(backward_demodulation,[],[f107,f308]) ).
thf(f308,plain,
( ( sK6
= ( 'const/sets/inf' @ sK2 ) )
| ~ spl0_7 ),
inference(equality_proxy_clausification,[],[f294]) ).
thf(f294,plain,
( ( $true
= ( sK6
= ( 'const/sets/inf' @ sK2 ) ) )
| ~ spl0_7 ),
inference(backward_demodulation,[],[f240,f292]) ).
thf(f292,plain,
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ sK6 )
= $true )
| ~ spl0_7 ),
inference(boolean_simplification,[],[f290]) ).
thf(f290,plain,
( ( ( $true
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ sK6 ) )
= $true )
| ~ spl0_7 ),
inference(superposition,[],[f268,f212]) ).
thf(f268,plain,
( ! [X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK2 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X1 ) )
= $true )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f264]) ).
thf(f264,plain,
( ! [X1: 'type/realax/real'] :
( ( ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ Y0 ) )
@ X1 )
= $true )
| ~ spl0_7 ),
inference(pi_clausification,[],[f215]) ).
thf(f215,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 ) ) )
= $true )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f204]) ).
thf(f204,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 ) ) )
=> ( '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 )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f203]) ).
thf(f203,plain,
( spl0_7
<=> ( ( ( !! @ '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 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
thf(f240,plain,
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ sK6 )
= ( sK6
= ( 'const/sets/inf' @ sK2 ) ) )
| ~ spl0_7 ),
inference(boolean_simplification,[],[f237]) ).
thf(f237,plain,
( ( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ sK6 )
& $true )
= ( sK6
= ( 'const/sets/inf' @ sK2 ) ) )
| ~ spl0_7 ),
inference(superposition,[],[f32,f234]) ).
thf(f234,plain,
( ( ( 'const/realax/real_le' @ sK6 @ ( 'const/sets/inf' @ sK2 ) )
= $true )
| ~ spl0_7 ),
inference(boolean_simplification,[],[f233]) ).
thf(f233,plain,
( ( ( $true
=> ( 'const/realax/real_le' @ sK6 @ ( 'const/sets/inf' @ sK2 ) ) )
= $true )
| ~ spl0_7 ),
inference(superposition,[],[f224,f214]) ).
thf(f224,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_7 ),
inference(beta_eta_normalization,[],[f221]) ).
thf(f221,plain,
( ! [X1: '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 ) ) )
@ X1 )
= $true )
| ~ spl0_7 ),
inference(pi_clausification,[],[f220]) ).
thf(f220,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 ) ) )
=> ( 'const/realax/real_le' @ Y0 @ ( 'const/sets/inf' @ sK2 ) ) ) )
= $true )
| ~ spl0_7 ),
inference(boolean_simplification,[],[f219]) ).
thf(f219,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 ) ) )
=> ( 'const/realax/real_le' @ Y0 @ ( 'const/sets/inf' @ sK2 ) ) ) )
& $true )
= $true )
| ~ spl0_7 ),
inference(backward_demodulation,[],[f204,f215]) ).
thf(f32,plain,
! [X2: 'type/realax/real',X1: 'type/realax/real'] :
( ( X2 = X1 )
= ( ( 'const/realax/real_le' @ X1 @ X2 )
& ( 'const/realax/real_le' @ X2 @ X1 ) ) ),
inference(equality_proxy_clausification,[],[f31]) ).
thf(f31,plain,
! [X2: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( X2 = X1 )
= ( ( 'const/realax/real_le' @ X1 @ X2 )
& ( 'const/realax/real_le' @ X2 @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[],[f30]) ).
thf(f30,plain,
! [X2: 'type/realax/real',X1: 'type/realax/real'] :
( ( ^ [Y0: 'type/realax/real'] :
( ( Y0 = X1 )
= ( ( 'const/realax/real_le' @ X1 @ Y0 )
& ( 'const/realax/real_le' @ Y0 @ X1 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[],[f29]) ).
thf(f29,plain,
! [X1: 'type/realax/real'] :
( ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( Y0 = X1 )
= ( ( 'const/realax/real_le' @ X1 @ Y0 )
& ( 'const/realax/real_le' @ Y0 @ X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[],[f28]) ).
thf(f28,plain,
! [X1: 'type/realax/real'] :
( ( ^ [Y0: 'type/realax/real'] :
( !! @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( Y1 = Y0 )
= ( ( 'const/realax/real_le' @ Y0 @ Y1 )
& ( 'const/realax/real_le' @ Y1 @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[],[f22]) ).
thf(f22,plain,
( ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( !! @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( Y1 = Y0 )
= ( ( 'const/realax/real_le' @ Y0 @ Y1 )
& ( 'const/realax/real_le' @ Y1 @ Y0 ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f13]) ).
thf(f13,plain,
( ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( !! @ 'type/realax/real'
@ ^ [Y1: 'type/realax/real'] :
( ( Y1 = Y0 )
= ( ( 'const/realax/real_le' @ Y0 @ Y1 )
& ( 'const/realax/real_le' @ Y1 @ Y0 ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f12]) ).
thf(f12,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( X0 = X1 )
= ( 'const/realax/real_le' @ X0 @ X1 ) )
& ( 'const/realax/real_le' @ X1 @ X0 ) ),
inference(rectify,[],[f3]) ).
thf(f3,axiom,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( X0 = X1 )
= ( 'const/realax/real_le' @ X0 @ X1 ) )
& ( 'const/realax/real_le' @ X1 @ X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/realax/REAL_LE_ANTISYM_') ).
thf(f107,plain,
( ( $false
= ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ sK2 ) @ sK2 ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f106]) ).
thf(f106,plain,
( spl0_6
<=> ( $false
= ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ sK2 ) @ sK2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
thf(f208,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f201,f206,f203]) ).
thf(f201,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 ) ) )
=> ( '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 )
| ( $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 ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[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,[],[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 ) ) ) ) )
=> ( ( !! @ '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(superposition,[],[f52,f56]) ).
thf(f52,plain,
! [X1: 'type/realax/real' > $o] :
( ( ( ~ ( '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 ) ) ) ) )
=> ( ( !! @ '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 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[],[f51]) ).
thf(f51,plain,
! [X1: 'type/realax/real' > $o] :
( ( ^ [Y0: 'type/realax/real' > $o] :
( ( ~ ( '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 ) ) ) ) )
=> ( ( !! @ '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 )
= $true ),
inference(pi_clausification,[],[f19]) ).
thf(f19,plain,
( $true
= ( !! @ ( 'type/realax/real' > $o )
@ ^ [Y0: 'type/realax/real' > $o] :
( ( ~ ( '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 ) ) ) ) )
=> ( ( !! @ '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,[],[f17]) ).
thf(f17,plain,
( $true
= ( !! @ ( 'type/realax/real' > $o )
@ ^ [Y0: 'type/realax/real' > $o] :
( ( ~ ( '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 ) ) ) ) )
=> ( ( !! @ '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,[],[f16]) ).
thf(f16,plain,
! [X0: 'type/realax/real' > $o] :
( ( ? [X1: 'type/realax/real'] :
! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_le' @ X1 @ X2 ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ! [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,[],[f1]) ).
thf(f1,axiom,
! [X0: 'type/realax/real' > $o] :
( ( ? [X1: 'type/realax/real'] :
! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_le' @ X1 @ X2 ) )
& ( 'const/sets/EMPTY' @ ( '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 ) )
& ! [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/sandbox2/benchmark/theBenchmark.p','thm/sets/INF_') ).
thf(f198,plain,
~ spl0_5,
inference(avatar_contradiction_clause,[],[f197]) ).
thf(f197,plain,
( $false
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f196]) ).
thf(f196,plain,
( ( $false = $true )
| ~ spl0_5 ),
inference(boolean_simplification,[],[f195]) ).
thf(f195,plain,
( ( ( ( 'const/sets/IN' @ 'type/realax/real' @ sK6 @ sK2 )
& $false )
= $true )
| ~ spl0_5 ),
inference(forward_demodulation,[],[f193,f154]) ).
thf(f154,plain,
( ! [X1: 'type/realax/real'] :
( ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK2 )
=> ( 'const/realax/real_le' @ X1 @ Y0 ) ) )
= $false )
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f150]) ).
thf(f150,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,[],[f137]) ).
thf(f137,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,[],[f112]) ).
thf(f112,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 ) ) ) ) )
= $true )
| ~ spl0_5 ),
inference(boolean_simplification,[],[f111]) ).
thf(f111,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,[],[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 ) ) ) )
=> ( ( !! @ '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 ) )
= $true )
| ~ spl0_5 ),
inference(backward_demodulation,[],[f66,f104]) ).
thf(f104,plain,
( ( $false
= ( !! @ '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_5 ),
inference(avatar_component_clause,[],[f103]) ).
thf(f103,plain,
( spl0_5
<=> ( $false
= ( !! @ '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(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
thf(f108,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f101,f106,f103]) ).
thf(f101,plain,
( ( $false
= ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ sK2 ) @ sK2 ) )
| ( $false
= ( !! @ '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,[],[f45]) ).
thf(f45,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 ) ) )
& ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ sK2 ) @ sK2 ) )
= $false ),
inference(binary_proxy_clausification,[],[f44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEV493^1 : TPTP v8.2.0. Released v7.0.0.
% 0.07/0.12 % Command : run_vampire %s %d THM
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 21 19:16:09 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.12/0.35 This is a TH1_THM_EQU_NAR problem
% 0.12/0.35 Running higher-order theorem proving
% 0.12/0.35 Running /export/starexec/sandbox2/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox2/benchmark/theBenchmark.p -m 16384 -t 300
% 0.12/0.37 % (15536)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.12/0.37 % (15537)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 theBenchmark for (2999ds/4Mi)
% 0.12/0.37 % (15539)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.12/0.37 % (15538)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 theBenchmark for (2999ds/27Mi)
% 0.20/0.37 % (15540)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.37 % (15541)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.20/0.37 % (15542)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.20/0.38 % (15539)Instruction limit reached!
% 0.20/0.38 % (15539)------------------------------
% 0.20/0.38 % (15539)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.38 % (15539)Termination reason: Unknown
% 0.20/0.38 % (15539)Termination phase: Preprocessing 3
% 0.20/0.38
% 0.20/0.38 % (15539)Memory used [KB]: 1023
% 0.20/0.38 % (15539)Time elapsed: 0.003 s
% 0.20/0.38 % (15539)Instructions burned: 2 (million)
% 0.20/0.38 % (15539)------------------------------
% 0.20/0.38 % (15539)------------------------------
% 0.20/0.38 % (15540)Instruction limit reached!
% 0.20/0.38 % (15540)------------------------------
% 0.20/0.38 % (15540)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.38 % (15540)Termination reason: Unknown
% 0.20/0.38 % (15540)Termination phase: Preprocessing 1
% 0.20/0.38
% 0.20/0.38 % (15540)Memory used [KB]: 1023
% 0.20/0.38 % (15540)Time elapsed: 0.003 s
% 0.20/0.38 % (15540)Instructions burned: 2 (million)
% 0.20/0.38 % (15540)------------------------------
% 0.20/0.38 % (15540)------------------------------
% 0.20/0.38 % (15537)Instruction limit reached!
% 0.20/0.38 % (15537)------------------------------
% 0.20/0.38 % (15537)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.38 % (15537)Termination reason: Unknown
% 0.20/0.38 % (15537)Termination phase: Saturation
% 0.20/0.38
% 0.20/0.38 % (15537)Memory used [KB]: 5500
% 0.20/0.38 % (15537)Time elapsed: 0.005 s
% 0.20/0.38 % (15537)Instructions burned: 5 (million)
% 0.20/0.38 % (15537)------------------------------
% 0.20/0.38 % (15537)------------------------------
% 0.20/0.38 % (15541)Refutation not found, incomplete strategy
% 0.20/0.38 % (15541)------------------------------
% 0.20/0.38 % (15541)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.38 % (15541)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.38
% 0.20/0.38
% 0.20/0.38 % (15541)Memory used [KB]: 5500
% 0.20/0.38 % (15541)Time elapsed: 0.006 s
% 0.20/0.38 % (15541)Instructions burned: 5 (million)
% 0.20/0.38 % (15541)------------------------------
% 0.20/0.38 % (15541)------------------------------
% 0.20/0.39 % (15542)Instruction limit reached!
% 0.20/0.39 % (15542)------------------------------
% 0.20/0.39 % (15542)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.39 % (15542)Termination reason: Unknown
% 0.20/0.39 % (15542)Termination phase: Saturation
% 0.20/0.39
% 0.20/0.39 % (15542)Memory used [KB]: 5628
% 0.20/0.39 % (15542)Time elapsed: 0.015 s
% 0.20/0.39 % (15542)Instructions burned: 18 (million)
% 0.20/0.39 % (15542)------------------------------
% 0.20/0.39 % (15542)------------------------------
% 0.20/0.39 % (15553)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.39 % (15554)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 theBenchmark for (2999ds/37Mi)
% 0.20/0.39 % (15553)Instruction limit reached!
% 0.20/0.39 % (15553)------------------------------
% 0.20/0.39 % (15553)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.39 % (15556)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 theBenchmark for (2999ds/15Mi)
% 0.20/0.39 % (15553)Termination reason: Unknown
% 0.20/0.39 % (15553)Termination phase: Property scanning
% 0.20/0.39
% 0.20/0.39 % (15553)Memory used [KB]: 1023
% 0.20/0.39 % (15553)Time elapsed: 0.004 s
% 0.20/0.39 % (15553)Instructions burned: 3 (million)
% 0.20/0.39 % (15553)------------------------------
% 0.20/0.39 % (15553)------------------------------
% 0.20/0.39 % (15538)Instruction limit reached!
% 0.20/0.39 % (15538)------------------------------
% 0.20/0.39 % (15538)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.39 % (15538)Termination reason: Unknown
% 0.20/0.39 % (15538)Termination phase: Saturation
% 0.20/0.39
% 0.20/0.39 % (15538)Memory used [KB]: 5628
% 0.20/0.39 % (15538)Time elapsed: 0.022 s
% 0.20/0.39 % (15538)Instructions burned: 27 (million)
% 0.20/0.39 % (15538)------------------------------
% 0.20/0.39 % (15538)------------------------------
% 0.20/0.40 % (15558)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.40 % (15558)Instruction limit reached!
% 0.20/0.40 % (15558)------------------------------
% 0.20/0.40 % (15558)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.40 % (15558)Termination reason: Unknown
% 0.20/0.40 % (15558)Termination phase: Saturation
% 0.20/0.40
% 0.20/0.40 % (15558)Memory used [KB]: 1023
% 0.20/0.40 % (15558)Time elapsed: 0.004 s
% 0.20/0.40 % (15558)Instructions burned: 3 (million)
% 0.20/0.40 % (15558)------------------------------
% 0.20/0.40 % (15558)------------------------------
% 0.20/0.40 % (15561)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 theBenchmark for (2999ds/1041Mi)
% 0.20/0.41 % (15556)Instruction limit reached!
% 0.20/0.41 % (15556)------------------------------
% 0.20/0.41 % (15556)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.41 % (15556)Termination reason: Unknown
% 0.20/0.41 % (15556)Termination phase: Saturation
% 0.20/0.41
% 0.20/0.41 % (15556)Memory used [KB]: 5756
% 0.20/0.41 % (15556)Time elapsed: 0.014 s
% 0.20/0.41 % (15556)Instructions burned: 15 (million)
% 0.20/0.41 % (15556)------------------------------
% 0.20/0.41 % (15556)------------------------------
% 0.20/0.41 % (15563)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.41 % (15564)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.20/0.41 % (15566)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.41 % (15563)Instruction limit reached!
% 0.20/0.41 % (15563)------------------------------
% 0.20/0.41 % (15563)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.41 % (15563)Termination reason: Unknown
% 0.20/0.41 % (15563)Termination phase: Saturation
% 0.20/0.41
% 0.20/0.41 % (15563)Memory used [KB]: 1023
% 0.20/0.41 % (15563)Time elapsed: 0.007 s
% 0.20/0.41 % (15563)Instructions burned: 7 (million)
% 0.20/0.41 % (15563)------------------------------
% 0.20/0.41 % (15563)------------------------------
% 0.20/0.42 % (15566)Instruction limit reached!
% 0.20/0.42 % (15566)------------------------------
% 0.20/0.42 % (15566)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.42 % (15566)Termination reason: Unknown
% 0.20/0.42 % (15566)Termination phase: Twee Goal Transformation
% 0.20/0.42
% 0.20/0.42 % (15566)Memory used [KB]: 1023
% 0.20/0.42 % (15566)Time elapsed: 0.004 s
% 0.20/0.42 % (15566)Instructions burned: 3 (million)
% 0.20/0.42 % (15566)------------------------------
% 0.20/0.42 % (15566)------------------------------
% 0.20/0.42 % (15554)Instruction limit reached!
% 0.20/0.42 % (15554)------------------------------
% 0.20/0.42 % (15554)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.42 % (15554)Termination reason: Unknown
% 0.20/0.42 % (15554)Termination phase: Saturation
% 0.20/0.42
% 0.20/0.42 % (15554)Memory used [KB]: 5628
% 0.20/0.42 % (15554)Time elapsed: 0.028 s
% 0.20/0.42 % (15554)Instructions burned: 37 (million)
% 0.20/0.42 % (15554)------------------------------
% 0.20/0.42 % (15554)------------------------------
% 0.20/0.42 % (15571)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.42 % (15564)Instruction limit reached!
% 0.20/0.42 % (15564)------------------------------
% 0.20/0.42 % (15564)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.42 % (15564)Termination reason: Unknown
% 0.20/0.42 % (15564)Termination phase: Saturation
% 0.20/0.42
% 0.20/0.42 % (15564)Memory used [KB]: 5756
% 0.20/0.42 % (15564)Time elapsed: 0.014 s
% 0.20/0.42 % (15564)Instructions burned: 16 (million)
% 0.20/0.42 % (15564)------------------------------
% 0.20/0.42 % (15564)------------------------------
% 0.20/0.42 % (15571)Instruction limit reached!
% 0.20/0.42 % (15571)------------------------------
% 0.20/0.42 % (15571)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.42 % (15571)Termination reason: Unknown
% 0.20/0.42 % (15571)Termination phase: Property scanning
% 0.20/0.42
% 0.20/0.42 % (15571)Memory used [KB]: 1023
% 0.20/0.42 % (15571)Time elapsed: 0.004 s
% 0.20/0.42 % (15571)Instructions burned: 3 (million)
% 0.20/0.42 % (15571)------------------------------
% 0.20/0.42 % (15571)------------------------------
% 0.20/0.43 % (15576)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.43 % (15536)Instruction limit reached!
% 0.20/0.43 % (15536)------------------------------
% 0.20/0.43 % (15536)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.43 % (15536)Termination reason: Unknown
% 0.20/0.43 % (15536)Termination phase: Saturation
% 0.20/0.43
% 0.20/0.43 % (15536)Memory used [KB]: 6140
% 0.20/0.43 % (15536)Time elapsed: 0.065 s
% 0.20/0.43 % (15536)Instructions burned: 184 (million)
% 0.20/0.43 % (15536)------------------------------
% 0.20/0.43 % (15536)------------------------------
% 0.20/0.43 % (15577)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.43 % (15577)Instruction limit reached!
% 0.20/0.43 % (15577)------------------------------
% 0.20/0.43 % (15577)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.43 % (15577)Termination reason: Unknown
% 0.20/0.43 % (15577)Termination phase: Saturation
% 0.20/0.43
% 0.20/0.43 % (15577)Memory used [KB]: 5500
% 0.20/0.43 % (15577)Time elapsed: 0.004 s
% 0.20/0.43 % (15577)Instructions burned: 3 (million)
% 0.20/0.43 % (15577)------------------------------
% 0.20/0.43 % (15577)------------------------------
% 0.20/0.43 % (15579)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.20/0.43 % (15576)Instruction limit reached!
% 0.20/0.43 % (15576)------------------------------
% 0.20/0.43 % (15576)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.43 % (15576)Termination reason: Unknown
% 0.20/0.43 % (15576)Termination phase: Saturation
% 0.20/0.43
% 0.20/0.43 % (15576)Memory used [KB]: 5500
% 0.20/0.43 % (15576)Time elapsed: 0.007 s
% 0.20/0.43 % (15576)Instructions burned: 7 (million)
% 0.20/0.43 % (15576)------------------------------
% 0.20/0.43 % (15576)------------------------------
% 0.20/0.44 % (15579)Instruction limit reached!
% 0.20/0.44 % (15579)------------------------------
% 0.20/0.44 % (15579)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.44 % (15579)Termination reason: Unknown
% 0.20/0.44 % (15579)Termination phase: Saturation
% 0.20/0.44
% 0.20/0.44 % (15579)Memory used [KB]: 5500
% 0.20/0.44 % (15579)Time elapsed: 0.005 s
% 0.20/0.44 % (15579)Instructions burned: 4 (million)
% 0.20/0.44 % (15579)------------------------------
% 0.20/0.44 % (15579)------------------------------
% 0.20/0.44 % (15581)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.20/0.44 % (15561)First to succeed.
% 0.20/0.44 % (15583)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.20/0.44 % (15587)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.20/0.44 % (15587)Instruction limit reached!
% 0.20/0.44 % (15587)------------------------------
% 0.20/0.44 % (15587)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.44 % (15587)Termination reason: Unknown
% 0.20/0.44 % (15587)Termination phase: Saturation
% 0.20/0.44
% 0.20/0.44 % (15587)Memory used [KB]: 5500
% 0.20/0.44 % (15587)Time elapsed: 0.004 s
% 0.20/0.44 % (15587)Instructions burned: 7 (million)
% 0.20/0.44 % (15587)------------------------------
% 0.20/0.44 % (15587)------------------------------
% 0.20/0.44 % (15561)Refutation found. Thanks to Tanya!
% 0.20/0.44 % SZS status Theorem for theBenchmark
% 0.20/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.44 % (15561)------------------------------
% 0.20/0.44 % (15561)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.20/0.44 % (15561)Termination reason: Refutation
% 0.20/0.44
% 0.20/0.44 % (15561)Memory used [KB]: 5884
% 0.20/0.44 % (15561)Time elapsed: 0.040 s
% 0.20/0.44 % (15561)Instructions burned: 48 (million)
% 0.20/0.44 % (15561)------------------------------
% 0.20/0.44 % (15561)------------------------------
% 0.20/0.44 % (15533)Success in time 0.075 s
%------------------------------------------------------------------------------