TSTP Solution File: SYO246^5 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO246^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n026.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 : Tue May 21 09:03:38 EDT 2024
% Result : Theorem 0.14s 0.40s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 28
% Syntax : Number of formulae : 126 ( 7 unt; 14 typ; 0 def)
% Number of atoms : 1000 ( 235 equ; 0 cnn)
% Maximal formula atoms : 8 ( 8 avg)
% Number of connectives : 1432 ( 158 ~; 238 |; 100 &; 763 @)
% ( 8 <=>; 91 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 723 ( 723 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 20 usr; 13 con; 0-3 aty)
% ( 36 !!; 38 ??; 0 @@+; 0 @@-)
% Number of variables : 268 ( 106 ^ 114 !; 46 ?; 268 :)
% ( 2 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_2,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_13,type,
sK0: ( ( a > $o ) > $o ) > $o ).
thf(func_def_14,type,
sK1: ( a > $o ) > $o ).
thf(func_def_15,type,
sK2: ( ( a > $o ) > $o ) > a > $o ).
thf(func_def_16,type,
sK3: ( ( ( a > $o ) > $o ) > $o ) > ( ( a > $o ) > $o ) > a > $o ).
thf(func_def_17,type,
sK4: ( ( ( a > $o ) > $o ) > $o ) > ( a > $o ) > $o ).
thf(func_def_19,type,
ph6:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
sK7: a ).
thf(func_def_21,type,
sK8: ( ( ( a > $o ) > $o ) > a > $o ) > ( a > $o ) > $o ).
thf(func_def_22,type,
sK9: ( a > $o ) > $o ).
thf(func_def_23,type,
sK10: ( ( a > $o ) > $o ) > a > $o ).
thf(func_def_24,type,
sK11: ( ( a > $o ) > $o ) > a > $o ).
thf(f260,plain,
$false,
inference(avatar_sat_refutation,[],[f65,f69,f73,f74,f81,f85,f90,f91,f153,f201,f229,f259]) ).
thf(f259,plain,
( ~ spl5_2
| ~ spl5_3
| ~ spl5_5
| ~ spl5_8 ),
inference(avatar_contradiction_clause,[],[f258]) ).
thf(f258,plain,
( $false
| ~ spl5_2
| ~ spl5_3
| ~ spl5_5
| ~ spl5_8 ),
inference(trivial_inequality_removal,[],[f254]) ).
thf(f254,plain,
( ( $false = $true )
| ~ spl5_2
| ~ spl5_3
| ~ spl5_5
| ~ spl5_8 ),
inference(backward_demodulation,[],[f89,f248]) ).
thf(f248,plain,
( ( $false
= ( sK0 @ sK9 ) )
| ~ spl5_2
| ~ spl5_3
| ~ spl5_5
| ~ spl5_8 ),
inference(trivial_inequality_removal,[],[f247]) ).
thf(f247,plain,
( ( $false
= ( sK0 @ sK9 ) )
| ( $false = $true )
| ~ spl5_2
| ~ spl5_3
| ~ spl5_5
| ~ spl5_8 ),
inference(superposition,[],[f68,f243]) ).
thf(f243,plain,
( ( $false
= ( sK11 @ sK9 @ sK7 ) )
| ~ spl5_2
| ~ spl5_5
| ~ spl5_8 ),
inference(trivial_inequality_removal,[],[f242]) ).
thf(f242,plain,
( ( $false
= ( sK11 @ sK9 @ sK7 ) )
| ( $false = $true )
| ~ spl5_2
| ~ spl5_5
| ~ spl5_8 ),
inference(forward_demodulation,[],[f240,f89]) ).
thf(f240,plain,
( ( $false
= ( sK0 @ sK9 ) )
| ( $false
= ( sK11 @ sK9 @ sK7 ) )
| ~ spl5_2
| ~ spl5_5 ),
inference(trivial_inequality_removal,[],[f236]) ).
thf(f236,plain,
( ( $false
= ( sK0 @ sK9 ) )
| ( $false = $true )
| ( $false
= ( sK11 @ sK9 @ sK7 ) )
| ~ spl5_2
| ~ spl5_5 ),
inference(superposition,[],[f64,f77]) ).
thf(f77,plain,
( ! [X2: a > $o] :
( ( $false
= ( sK9 @ X2 ) )
| ( ( X2 @ sK7 )
= $false ) )
| ~ spl5_5 ),
inference(avatar_component_clause,[],[f76]) ).
thf(f76,plain,
( spl5_5
<=> ! [X2: a > $o] :
( ( ( X2 @ sK7 )
= $false )
| ( $false
= ( sK9 @ X2 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_5])]) ).
thf(f64,plain,
( ! [X1: ( a > $o ) > $o] :
( ( $true
= ( X1 @ ( sK11 @ X1 ) ) )
| ( $false
= ( sK0 @ X1 ) ) )
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f63]) ).
thf(f63,plain,
( spl5_2
<=> ! [X1: ( a > $o ) > $o] :
( ( $true
= ( X1 @ ( sK11 @ X1 ) ) )
| ( $false
= ( sK0 @ X1 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).
thf(f68,plain,
( ! [X1: ( a > $o ) > $o] :
( ( ( sK11 @ X1 @ sK7 )
= $true )
| ( $false
= ( sK0 @ X1 ) ) )
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f67]) ).
thf(f67,plain,
( spl5_3
<=> ! [X1: ( a > $o ) > $o] :
( ( ( sK11 @ X1 @ sK7 )
= $true )
| ( $false
= ( sK0 @ X1 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).
thf(f89,plain,
( ( $true
= ( sK0 @ sK9 ) )
| ~ spl5_8 ),
inference(avatar_component_clause,[],[f87]) ).
thf(f87,plain,
( spl5_8
<=> ( $true
= ( sK0 @ sK9 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_8])]) ).
thf(f229,plain,
( ~ spl5_1
| ~ spl5_4
| ~ spl5_5
| ~ spl5_8 ),
inference(avatar_contradiction_clause,[],[f228]) ).
thf(f228,plain,
( $false
| ~ spl5_1
| ~ spl5_4
| ~ spl5_5
| ~ spl5_8 ),
inference(trivial_inequality_removal,[],[f224]) ).
thf(f224,plain,
( ( $false = $true )
| ~ spl5_1
| ~ spl5_4
| ~ spl5_5
| ~ spl5_8 ),
inference(backward_demodulation,[],[f89,f222]) ).
thf(f222,plain,
( ( $false
= ( sK0 @ sK9 ) )
| ~ spl5_1
| ~ spl5_4
| ~ spl5_5
| ~ spl5_8 ),
inference(trivial_inequality_removal,[],[f221]) ).
thf(f221,plain,
( ( $false
= ( sK0 @ sK9 ) )
| ( $false = $true )
| ~ spl5_1
| ~ spl5_4
| ~ spl5_5
| ~ spl5_8 ),
inference(superposition,[],[f72,f217]) ).
thf(f217,plain,
( ( $false
= ( sK10 @ sK9 @ sK7 ) )
| ~ spl5_1
| ~ spl5_5
| ~ spl5_8 ),
inference(trivial_inequality_removal,[],[f216]) ).
thf(f216,plain,
( ( $false = $true )
| ( $false
= ( sK10 @ sK9 @ sK7 ) )
| ~ spl5_1
| ~ spl5_5
| ~ spl5_8 ),
inference(forward_demodulation,[],[f215,f89]) ).
thf(f215,plain,
( ( $false
= ( sK0 @ sK9 ) )
| ( $false
= ( sK10 @ sK9 @ sK7 ) )
| ~ spl5_1
| ~ spl5_5 ),
inference(trivial_inequality_removal,[],[f211]) ).
thf(f211,plain,
( ( $false = $true )
| ( $false
= ( sK0 @ sK9 ) )
| ( $false
= ( sK10 @ sK9 @ sK7 ) )
| ~ spl5_1
| ~ spl5_5 ),
inference(superposition,[],[f61,f77]) ).
thf(f61,plain,
( ! [X2: ( a > $o ) > $o] :
( ( ( X2 @ ( sK10 @ X2 ) )
= $true )
| ( $false
= ( sK0 @ X2 ) ) )
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f60]) ).
thf(f60,plain,
( spl5_1
<=> ! [X2: ( a > $o ) > $o] :
( ( $false
= ( sK0 @ X2 ) )
| ( ( X2 @ ( sK10 @ X2 ) )
= $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).
thf(f72,plain,
( ! [X2: ( a > $o ) > $o] :
( ( $true
= ( sK10 @ X2 @ sK7 ) )
| ( $false
= ( sK0 @ X2 ) ) )
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f71]) ).
thf(f71,plain,
( spl5_4
<=> ! [X2: ( a > $o ) > $o] :
( ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( sK10 @ X2 @ sK7 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_4])]) ).
thf(f201,plain,
( ~ spl5_1
| ~ spl5_4
| ~ spl5_6
| ~ spl5_7 ),
inference(avatar_contradiction_clause,[],[f200]) ).
thf(f200,plain,
( $false
| ~ spl5_1
| ~ spl5_4
| ~ spl5_6
| ~ spl5_7 ),
inference(trivial_inequality_removal,[],[f193]) ).
thf(f193,plain,
( ( $false = $true )
| ~ spl5_1
| ~ spl5_4
| ~ spl5_6
| ~ spl5_7 ),
inference(superposition,[],[f191,f84]) ).
thf(f84,plain,
( ! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( sK0 @ ( sK8 @ X1 ) )
= $true )
| ~ spl5_7 ),
inference(avatar_component_clause,[],[f83]) ).
thf(f83,plain,
( spl5_7
<=> ! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( sK0 @ ( sK8 @ X1 ) )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_7])]) ).
thf(f191,plain,
( ( $false
= ( sK0 @ ( sK8 @ sK10 ) ) )
| ~ spl5_1
| ~ spl5_4
| ~ spl5_6
| ~ spl5_7 ),
inference(trivial_inequality_removal,[],[f190]) ).
thf(f190,plain,
( ( $false = $true )
| ( $false
= ( sK0 @ ( sK8 @ sK10 ) ) )
| ~ spl5_1
| ~ spl5_4
| ~ spl5_6
| ~ spl5_7 ),
inference(superposition,[],[f72,f186]) ).
thf(f186,plain,
( ( $false
= ( sK10 @ ( sK8 @ sK10 ) @ sK7 ) )
| ~ spl5_1
| ~ spl5_6
| ~ spl5_7 ),
inference(trivial_inequality_removal,[],[f185]) ).
thf(f185,plain,
( ( $false = $true )
| ( $false
= ( sK10 @ ( sK8 @ sK10 ) @ sK7 ) )
| ~ spl5_1
| ~ spl5_6
| ~ spl5_7 ),
inference(forward_demodulation,[],[f184,f84]) ).
thf(f184,plain,
( ( $false
= ( sK0 @ ( sK8 @ sK10 ) ) )
| ( $false
= ( sK10 @ ( sK8 @ sK10 ) @ sK7 ) )
| ~ spl5_1
| ~ spl5_6 ),
inference(trivial_inequality_removal,[],[f179]) ).
thf(f179,plain,
( ( $false = $true )
| ( $false
= ( sK0 @ ( sK8 @ sK10 ) ) )
| ( $false
= ( sK10 @ ( sK8 @ sK10 ) @ sK7 ) )
| ~ spl5_1
| ~ spl5_6 ),
inference(superposition,[],[f61,f80]) ).
thf(f80,plain,
( ! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( $false
= ( sK8 @ X1 @ ( X1 @ ( sK8 @ X1 ) ) ) )
| ( $false
= ( X1 @ ( sK8 @ X1 ) @ sK7 ) ) )
| ~ spl5_6 ),
inference(avatar_component_clause,[],[f79]) ).
thf(f79,plain,
( spl5_6
<=> ! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( $false
= ( X1 @ ( sK8 @ X1 ) @ sK7 ) )
| ( $false
= ( sK8 @ X1 @ ( X1 @ ( sK8 @ X1 ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_6])]) ).
thf(f153,plain,
( ~ spl5_2
| ~ spl5_3
| ~ spl5_6
| ~ spl5_7 ),
inference(avatar_contradiction_clause,[],[f152]) ).
thf(f152,plain,
( $false
| ~ spl5_2
| ~ spl5_3
| ~ spl5_6
| ~ spl5_7 ),
inference(trivial_inequality_removal,[],[f146]) ).
thf(f146,plain,
( ( $false = $true )
| ~ spl5_2
| ~ spl5_3
| ~ spl5_6
| ~ spl5_7 ),
inference(superposition,[],[f84,f143]) ).
thf(f143,plain,
( ( $false
= ( sK0 @ ( sK8 @ sK11 ) ) )
| ~ spl5_2
| ~ spl5_3
| ~ spl5_6
| ~ spl5_7 ),
inference(trivial_inequality_removal,[],[f141]) ).
thf(f141,plain,
( ( $false = $true )
| ( $false
= ( sK0 @ ( sK8 @ sK11 ) ) )
| ~ spl5_2
| ~ spl5_3
| ~ spl5_6
| ~ spl5_7 ),
inference(superposition,[],[f138,f68]) ).
thf(f138,plain,
( ( $false
= ( sK11 @ ( sK8 @ sK11 ) @ sK7 ) )
| ~ spl5_2
| ~ spl5_6
| ~ spl5_7 ),
inference(trivial_inequality_removal,[],[f137]) ).
thf(f137,plain,
( ( $false = $true )
| ( $false
= ( sK11 @ ( sK8 @ sK11 ) @ sK7 ) )
| ~ spl5_2
| ~ spl5_6
| ~ spl5_7 ),
inference(forward_demodulation,[],[f135,f84]) ).
thf(f135,plain,
( ( $false
= ( sK11 @ ( sK8 @ sK11 ) @ sK7 ) )
| ( $false
= ( sK0 @ ( sK8 @ sK11 ) ) )
| ~ spl5_2
| ~ spl5_6 ),
inference(trivial_inequality_removal,[],[f130]) ).
thf(f130,plain,
( ( $false
= ( sK11 @ ( sK8 @ sK11 ) @ sK7 ) )
| ( $false = $true )
| ( $false
= ( sK0 @ ( sK8 @ sK11 ) ) )
| ~ spl5_2
| ~ spl5_6 ),
inference(superposition,[],[f80,f64]) ).
thf(f91,plain,
( spl5_7
| spl5_8 ),
inference(avatar_split_clause,[],[f35,f87,f83]) ).
thf(f35,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( ( sK0 @ ( sK8 @ X1 ) )
= $true )
| ( $true
= ( sK0 @ sK9 ) ) ),
inference(binary_proxy_clausification,[],[f33]) ).
thf(f33,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( $false
= ( ( sK0 @ ( sK8 @ X1 ) )
=> ( ( X1 @ ( sK8 @ X1 ) @ sK7 )
& ( sK8 @ X1 @ ( X1 @ ( sK8 @ X1 ) ) ) ) ) )
| ( $true
= ( sK0 @ sK9 ) ) ),
inference(binary_proxy_clausification,[],[f31]) ).
thf(f31,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( $false
= ( ( sK0 @ sK9 )
=> ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK7 )
& ( sK9 @ Y0 ) ) ) ) )
| ( $false
= ( ( sK0 @ ( sK8 @ X1 ) )
=> ( ( X1 @ ( sK8 @ X1 ) @ sK7 )
& ( sK8 @ X1 @ ( X1 @ ( sK8 @ X1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f30]) ).
thf(f30,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( $false
= ( ^ [Y0: ( a > $o ) > $o] :
( ( sK0 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ sK7 )
& ( Y0 @ Y1 ) ) ) )
@ sK9 ) )
| ( $false
= ( ( sK0 @ ( sK8 @ X1 ) )
=> ( ( X1 @ ( sK8 @ X1 ) @ sK7 )
& ( sK8 @ X1 @ ( X1 @ ( sK8 @ X1 ) ) ) ) ) ) ),
inference(sigma_clausification,[],[f29]) ).
thf(f29,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( $false
= ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK0 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ sK7 )
& ( Y0 @ Y1 ) ) ) ) ) )
| ( $false
= ( ( sK0 @ ( sK8 @ X1 ) )
=> ( ( X1 @ ( sK8 @ X1 ) @ sK7 )
& ( sK8 @ X1 @ ( X1 @ ( sK8 @ X1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f28]) ).
thf(f28,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( $false
= ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK0 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ sK7 )
& ( Y0 @ Y1 ) ) ) ) ) )
| ( ( ^ [Y0: ( a > $o ) > $o] :
( ( sK0 @ Y0 )
=> ( ( X1 @ Y0 @ sK7 )
& ( Y0 @ ( X1 @ Y0 ) ) ) )
@ ( sK8 @ X1 ) )
= $false ) ),
inference(sigma_clausification,[],[f27]) ).
thf(f27,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK0 @ Y0 )
=> ( ( X1 @ Y0 @ sK7 )
& ( Y0 @ ( X1 @ Y0 ) ) ) ) )
= $false )
| ( $false
= ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK0 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ sK7 )
& ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f26]) ).
thf(f26,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( $false
= ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK0 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ sK7 )
& ( Y0 @ Y1 ) ) ) ) ) )
| ( $false
= ( ^ [Y0: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( sK0 @ Y1 )
=> ( ( Y0 @ Y1 @ sK7 )
& ( Y1 @ ( Y0 @ Y1 ) ) ) ) )
@ X1 ) ) ),
inference(pi_clausification,[],[f25]) ).
thf(f25,plain,
( ( $false
= ( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y0: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( sK0 @ Y1 )
=> ( ( Y0 @ Y1 @ sK7 )
& ( Y1 @ ( Y0 @ Y1 ) ) ) ) ) ) )
| ( $false
= ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK0 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ sK7 )
& ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f23]) ).
thf(f23,plain,
( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK0 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ sK7 )
& ( Y0 @ Y1 ) ) ) ) )
!= ( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y0: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( sK0 @ Y1 )
=> ( ( Y0 @ Y1 @ sK7 )
& ( Y1 @ ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f22]) ).
thf(f22,plain,
( ( ^ [Y0: a] :
( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y2: ( a > $o ) > $o] :
( ( sK0 @ Y2 )
=> ( ( Y1 @ Y2 @ Y0 )
& ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) )
@ sK7 )
!= ( ^ [Y0: a] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( sK0 @ Y1 )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y0 )
& ( Y1 @ Y2 ) ) ) ) )
@ sK7 ) ),
inference(negative_extensionality,[],[f19]) ).
thf(f19,plain,
( ( ^ [Y0: a] :
( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y2: ( a > $o ) > $o] :
( ( sK0 @ Y2 )
=> ( ( Y1 @ Y2 @ Y0 )
& ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) )
!= ( ^ [Y0: a] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( sK0 @ Y1 )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y0 )
& ( Y1 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f14,plain,
( ( ( ^ [Y0: a] :
( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y2: ( a > $o ) > $o] :
( ( sK0 @ Y2 )
=> ( ( Y1 @ Y2 @ Y0 )
& ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) )
!= ( ^ [Y0: a] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( sK0 @ Y1 )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y0 )
& ( Y1 @ Y2 ) ) ) ) ) ) )
& ( $true
= ( sK0 @ sK1 ) )
& ! [X2: ( a > $o ) > $o] :
( ( ( sK0 @ X2 )
!= $true )
| ( ( X2 @ ( sK2 @ X2 ) )
= $true ) )
& ! [X4: ( ( a > $o ) > $o ) > $o] :
( ! [X6: ( a > $o ) > $o] :
( ( ( X4 @ X6 )
!= $true )
| ( ( X6 @ ( sK3 @ X4 @ X6 ) )
= $true ) )
| ( ( $true
= ( X4 @ ( sK4 @ X4 ) ) )
& ! [X8: a > $o] :
( $true
!= ( sK4 @ X4 @ X8 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f8,f13,f12,f11,f10,f9]) ).
thf(f9,plain,
( ? [X0: ( ( a > $o ) > $o ) > $o] :
( ( ( ^ [Y0: a] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( X0 @ Y1 )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y0 )
& ( Y1 @ Y2 ) ) ) ) ) )
!= ( ^ [Y0: a] :
( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y2: ( a > $o ) > $o] :
( ( X0 @ Y2 )
=> ( ( Y1 @ Y2 @ Y0 )
& ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) ) )
& ? [X1: ( a > $o ) > $o] :
( ( X0 @ X1 )
= $true )
& ! [X2: ( a > $o ) > $o] :
( ( $true
!= ( X0 @ X2 ) )
| ? [X3: a > $o] :
( ( X2 @ X3 )
= $true ) ) )
=> ( ( ( ^ [Y0: a] :
( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y2: ( a > $o ) > $o] :
( ( sK0 @ Y2 )
=> ( ( Y1 @ Y2 @ Y0 )
& ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) )
!= ( ^ [Y0: a] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( sK0 @ Y1 )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y0 )
& ( Y1 @ Y2 ) ) ) ) ) ) )
& ? [X1: ( a > $o ) > $o] :
( ( sK0 @ X1 )
= $true )
& ! [X2: ( a > $o ) > $o] :
( ( ( sK0 @ X2 )
!= $true )
| ? [X3: a > $o] :
( ( X2 @ X3 )
= $true ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f10,plain,
( ? [X1: ( a > $o ) > $o] :
( ( sK0 @ X1 )
= $true )
=> ( $true
= ( sK0 @ sK1 ) ) ),
introduced(choice_axiom,[]) ).
thf(f11,plain,
! [X2: ( a > $o ) > $o] :
( ? [X3: a > $o] :
( ( X2 @ X3 )
= $true )
=> ( ( X2 @ ( sK2 @ X2 ) )
= $true ) ),
introduced(choice_axiom,[]) ).
thf(f12,plain,
! [X4: ( ( a > $o ) > $o ) > $o] :
( ? [X5: ( ( a > $o ) > $o ) > a > $o] :
! [X6: ( a > $o ) > $o] :
( ( ( X4 @ X6 )
!= $true )
| ( $true
= ( X6 @ ( X5 @ X6 ) ) ) )
=> ! [X6: ( a > $o ) > $o] :
( ( ( X4 @ X6 )
!= $true )
| ( ( X6 @ ( sK3 @ X4 @ X6 ) )
= $true ) ) ),
introduced(choice_axiom,[]) ).
thf(f13,plain,
! [X4: ( ( a > $o ) > $o ) > $o] :
( ? [X7: ( a > $o ) > $o] :
( ( ( X4 @ X7 )
= $true )
& ! [X8: a > $o] :
( ( X7 @ X8 )
!= $true ) )
=> ( ( $true
= ( X4 @ ( sK4 @ X4 ) ) )
& ! [X8: a > $o] :
( $true
!= ( sK4 @ X4 @ X8 ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f8,plain,
( ? [X0: ( ( a > $o ) > $o ) > $o] :
( ( ( ^ [Y0: a] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( X0 @ Y1 )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y0 )
& ( Y1 @ Y2 ) ) ) ) ) )
!= ( ^ [Y0: a] :
( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y2: ( a > $o ) > $o] :
( ( X0 @ Y2 )
=> ( ( Y1 @ Y2 @ Y0 )
& ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) ) )
& ? [X1: ( a > $o ) > $o] :
( ( X0 @ X1 )
= $true )
& ! [X2: ( a > $o ) > $o] :
( ( $true
!= ( X0 @ X2 ) )
| ? [X3: a > $o] :
( ( X2 @ X3 )
= $true ) ) )
& ! [X4: ( ( a > $o ) > $o ) > $o] :
( ? [X5: ( ( a > $o ) > $o ) > a > $o] :
! [X6: ( a > $o ) > $o] :
( ( ( X4 @ X6 )
!= $true )
| ( $true
= ( X6 @ ( X5 @ X6 ) ) ) )
| ? [X7: ( a > $o ) > $o] :
( ( ( X4 @ X7 )
= $true )
& ! [X8: a > $o] :
( ( X7 @ X8 )
!= $true ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f7,plain,
( ? [X5: ( ( a > $o ) > $o ) > $o] :
( ( ( ^ [Y0: a] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( X5 @ Y1 )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y0 )
& ( Y1 @ Y2 ) ) ) ) ) )
!= ( ^ [Y0: a] :
( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y2: ( a > $o ) > $o] :
( ( X5 @ Y2 )
=> ( ( Y1 @ Y2 @ Y0 )
& ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) ) )
& ? [X8: ( a > $o ) > $o] :
( ( X5 @ X8 )
= $true )
& ! [X6: ( a > $o ) > $o] :
( ( ( X5 @ X6 )
!= $true )
| ? [X7: a > $o] :
( ( X6 @ X7 )
= $true ) ) )
& ! [X0: ( ( a > $o ) > $o ) > $o] :
( ? [X3: ( ( a > $o ) > $o ) > a > $o] :
! [X4: ( a > $o ) > $o] :
( ( ( X0 @ X4 )
!= $true )
| ( $true
= ( X4 @ ( X3 @ X4 ) ) ) )
| ? [X1: ( a > $o ) > $o] :
( ( ( X0 @ X1 )
= $true )
& ! [X2: a > $o] :
( ( X1 @ X2 )
!= $true ) ) ) ),
inference(flattening,[],[f6]) ).
thf(f6,plain,
( ? [X5: ( ( a > $o ) > $o ) > $o] :
( ( ( ^ [Y0: a] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( X5 @ Y1 )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y0 )
& ( Y1 @ Y2 ) ) ) ) ) )
!= ( ^ [Y0: a] :
( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y2: ( a > $o ) > $o] :
( ( X5 @ Y2 )
=> ( ( Y1 @ Y2 @ Y0 )
& ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) ) )
& ? [X8: ( a > $o ) > $o] :
( ( X5 @ X8 )
= $true )
& ! [X6: ( a > $o ) > $o] :
( ( ( X5 @ X6 )
!= $true )
| ? [X7: a > $o] :
( ( X6 @ X7 )
= $true ) ) )
& ! [X0: ( ( a > $o ) > $o ) > $o] :
( ? [X3: ( ( a > $o ) > $o ) > a > $o] :
! [X4: ( a > $o ) > $o] :
( ( ( X0 @ X4 )
!= $true )
| ( $true
= ( X4 @ ( X3 @ X4 ) ) ) )
| ? [X1: ( a > $o ) > $o] :
( ( ( X0 @ X1 )
= $true )
& ! [X2: a > $o] :
( ( X1 @ X2 )
!= $true ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f5,plain,
~ ( ! [X0: ( ( a > $o ) > $o ) > $o] :
( ! [X1: ( a > $o ) > $o] :
( ( ( X0 @ X1 )
= $true )
=> ? [X2: a > $o] :
( ( X1 @ X2 )
= $true ) )
=> ? [X3: ( ( a > $o ) > $o ) > a > $o] :
! [X4: ( a > $o ) > $o] :
( ( ( X0 @ X4 )
= $true )
=> ( $true
= ( X4 @ ( X3 @ X4 ) ) ) ) )
=> ! [X5: ( ( a > $o ) > $o ) > $o] :
( ( ? [X8: ( a > $o ) > $o] :
( ( X5 @ X8 )
= $true )
& ! [X6: ( a > $o ) > $o] :
( ( ( X5 @ X6 )
= $true )
=> ? [X7: a > $o] :
( ( X6 @ X7 )
= $true ) ) )
=> ( ( ^ [Y0: a] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( X5 @ Y1 )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y0 )
& ( Y1 @ Y2 ) ) ) ) ) )
= ( ^ [Y0: a] :
( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y2: ( a > $o ) > $o] :
( ( X5 @ Y2 )
=> ( ( Y1 @ Y2 @ Y0 )
& ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
~ ( ! [X0: ( ( a > $o ) > $o ) > $o] :
( ! [X1: ( a > $o ) > $o] :
( ( X0 @ X1 )
=> ? [X2: a > $o] : ( X1 @ X2 ) )
=> ? [X3: ( ( a > $o ) > $o ) > a > $o] :
! [X4: ( a > $o ) > $o] :
( ( X0 @ X4 )
=> ( X4 @ ( X3 @ X4 ) ) ) )
=> ! [X5: ( ( a > $o ) > $o ) > $o] :
( ( ! [X6: ( a > $o ) > $o] :
( ( X5 @ X6 )
=> ? [X7: a > $o] : ( X6 @ X7 ) )
& ? [X8: ( a > $o ) > $o] : ( X5 @ X8 ) )
=> ( ( ^ [X9: a] :
? [X10: ( ( a > $o ) > $o ) > a > $o] :
! [X11: ( a > $o ) > $o] :
( ( X5 @ X11 )
=> ( ( X11 @ ( X10 @ X11 ) )
& ( X10 @ X11 @ X9 ) ) ) )
= ( ^ [X12: a] :
! [X13: ( a > $o ) > $o] :
( ( X5 @ X13 )
=> ? [X14: a > $o] :
( ( X13 @ X14 )
& ( X14 @ X12 ) ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: ( ( a > $o ) > $o ) > $o] :
( ! [X1: ( a > $o ) > $o] :
( ( X0 @ X1 )
=> ? [X2: a > $o] : ( X1 @ X2 ) )
=> ? [X3: ( ( a > $o ) > $o ) > a > $o] :
! [X1: ( a > $o ) > $o] :
( ( X0 @ X1 )
=> ( X1 @ ( X3 @ X1 ) ) ) )
=> ! [X4: ( ( a > $o ) > $o ) > $o] :
( ( ! [X1: ( a > $o ) > $o] :
( ( X4 @ X1 )
=> ? [X5: a > $o] : ( X1 @ X5 ) )
& ? [X1: ( a > $o ) > $o] : ( X4 @ X1 ) )
=> ( ( ^ [X6: a] :
? [X3: ( ( a > $o ) > $o ) > a > $o] :
! [X7: ( a > $o ) > $o] :
( ( X4 @ X7 )
=> ( ( X7 @ ( X3 @ X7 ) )
& ( X3 @ X7 @ X6 ) ) ) )
= ( ^ [X6: a] :
! [X7: ( a > $o ) > $o] :
( ( X4 @ X7 )
=> ? [X8: a > $o] :
( ( X7 @ X8 )
& ( X8 @ X6 ) ) ) ) ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
( ! [X0: ( ( a > $o ) > $o ) > $o] :
( ! [X1: ( a > $o ) > $o] :
( ( X0 @ X1 )
=> ? [X2: a > $o] : ( X1 @ X2 ) )
=> ? [X3: ( ( a > $o ) > $o ) > a > $o] :
! [X1: ( a > $o ) > $o] :
( ( X0 @ X1 )
=> ( X1 @ ( X3 @ X1 ) ) ) )
=> ! [X4: ( ( a > $o ) > $o ) > $o] :
( ( ! [X1: ( a > $o ) > $o] :
( ( X4 @ X1 )
=> ? [X5: a > $o] : ( X1 @ X5 ) )
& ? [X1: ( a > $o ) > $o] : ( X4 @ X1 ) )
=> ( ( ^ [X6: a] :
? [X3: ( ( a > $o ) > $o ) > a > $o] :
! [X7: ( a > $o ) > $o] :
( ( X4 @ X7 )
=> ( ( X7 @ ( X3 @ X7 ) )
& ( X3 @ X7 @ X6 ) ) ) )
= ( ^ [X6: a] :
! [X7: ( a > $o ) > $o] :
( ( X4 @ X7 )
=> ? [X8: a > $o] :
( ( X7 @ X8 )
& ( X8 @ X6 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM535) ).
thf(f90,plain,
( spl5_6
| spl5_8 ),
inference(avatar_split_clause,[],[f36,f87,f79]) ).
thf(f36,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( $false
= ( X1 @ ( sK8 @ X1 ) @ sK7 ) )
| ( $false
= ( sK8 @ X1 @ ( X1 @ ( sK8 @ X1 ) ) ) )
| ( $true
= ( sK0 @ sK9 ) ) ),
inference(binary_proxy_clausification,[],[f34]) ).
thf(f34,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( $false
= ( ( X1 @ ( sK8 @ X1 ) @ sK7 )
& ( sK8 @ X1 @ ( X1 @ ( sK8 @ X1 ) ) ) ) )
| ( $true
= ( sK0 @ sK9 ) ) ),
inference(binary_proxy_clausification,[],[f33]) ).
thf(f85,plain,
( spl5_7
| spl5_5 ),
inference(avatar_split_clause,[],[f41,f76,f83]) ).
thf(f41,plain,
! [X2: a > $o,X1: ( ( a > $o ) > $o ) > a > $o] :
( ( ( sK0 @ ( sK8 @ X1 ) )
= $true )
| ( ( X2 @ sK7 )
= $false )
| ( $false
= ( sK9 @ X2 ) ) ),
inference(binary_proxy_clausification,[],[f39]) ).
thf(f39,plain,
! [X2: a > $o,X1: ( ( a > $o ) > $o ) > a > $o] :
( ( $false
= ( sK9 @ X2 ) )
| ( $false
= ( ( sK0 @ ( sK8 @ X1 ) )
=> ( ( X1 @ ( sK8 @ X1 ) @ sK7 )
& ( sK8 @ X1 @ ( X1 @ ( sK8 @ X1 ) ) ) ) ) )
| ( ( X2 @ sK7 )
= $false ) ),
inference(binary_proxy_clausification,[],[f38]) ).
thf(f38,plain,
! [X2: a > $o,X1: ( ( a > $o ) > $o ) > a > $o] :
( ( $false
= ( ( X2 @ sK7 )
& ( sK9 @ X2 ) ) )
| ( $false
= ( ( sK0 @ ( sK8 @ X1 ) )
=> ( ( X1 @ ( sK8 @ X1 ) @ sK7 )
& ( sK8 @ X1 @ ( X1 @ ( sK8 @ X1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f37]) ).
thf(f37,plain,
! [X2: a > $o,X1: ( ( a > $o ) > $o ) > a > $o] :
( ( $false
= ( ( sK0 @ ( sK8 @ X1 ) )
=> ( ( X1 @ ( sK8 @ X1 ) @ sK7 )
& ( sK8 @ X1 @ ( X1 @ ( sK8 @ X1 ) ) ) ) ) )
| ( $false
= ( ^ [Y0: a > $o] :
( ( Y0 @ sK7 )
& ( sK9 @ Y0 ) )
@ X2 ) ) ),
inference(pi_clausification,[],[f32]) ).
thf(f32,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( $false
= ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK7 )
& ( sK9 @ Y0 ) ) ) )
| ( $false
= ( ( sK0 @ ( sK8 @ X1 ) )
=> ( ( X1 @ ( sK8 @ X1 ) @ sK7 )
& ( sK8 @ X1 @ ( X1 @ ( sK8 @ X1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f31]) ).
thf(f81,plain,
( spl5_5
| spl5_6 ),
inference(avatar_split_clause,[],[f42,f79,f76]) ).
thf(f42,plain,
! [X2: a > $o,X1: ( ( a > $o ) > $o ) > a > $o] :
( ( ( X2 @ sK7 )
= $false )
| ( $false
= ( X1 @ ( sK8 @ X1 ) @ sK7 ) )
| ( $false
= ( sK8 @ X1 @ ( X1 @ ( sK8 @ X1 ) ) ) )
| ( $false
= ( sK9 @ X2 ) ) ),
inference(binary_proxy_clausification,[],[f40]) ).
thf(f40,plain,
! [X2: a > $o,X1: ( ( a > $o ) > $o ) > a > $o] :
( ( $false
= ( ( X1 @ ( sK8 @ X1 ) @ sK7 )
& ( sK8 @ X1 @ ( X1 @ ( sK8 @ X1 ) ) ) ) )
| ( ( X2 @ sK7 )
= $false )
| ( $false
= ( sK9 @ X2 ) ) ),
inference(binary_proxy_clausification,[],[f39]) ).
thf(f74,plain,
( spl5_4
| spl5_3 ),
inference(avatar_split_clause,[],[f56,f67,f71]) ).
thf(f56,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( sK10 @ X2 @ sK7 ) )
| ( $false
= ( sK0 @ X1 ) )
| ( ( sK11 @ X1 @ sK7 )
= $true ) ),
inference(binary_proxy_clausification,[],[f54]) ).
thf(f54,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( $false
= ( sK0 @ X1 ) )
| ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( sK10 @ X2 @ sK7 ) )
| ( ( ( sK11 @ X1 @ sK7 )
& ( X1 @ ( sK11 @ X1 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[],[f52]) ).
thf(f52,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( $true
= ( ( sK10 @ X2 @ sK7 )
& ( X2 @ ( sK10 @ X2 ) ) ) )
| ( ( ( sK11 @ X1 @ sK7 )
& ( X1 @ ( sK11 @ X1 ) ) )
= $true )
| ( $false
= ( sK0 @ X1 ) )
| ( $false
= ( sK0 @ X2 ) ) ),
inference(binary_proxy_clausification,[],[f51]) ).
thf(f51,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( ( ( sK0 @ X2 )
=> ( ( sK10 @ X2 @ sK7 )
& ( X2 @ ( sK10 @ X2 ) ) ) )
= $true )
| ( ( ( sK11 @ X1 @ sK7 )
& ( X1 @ ( sK11 @ X1 ) ) )
= $true )
| ( $false
= ( sK0 @ X1 ) ) ),
inference(beta_eta_normalization,[],[f50]) ).
thf(f50,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( ( ( sK0 @ X2 )
=> ( ( sK10 @ X2 @ sK7 )
& ( X2 @ ( sK10 @ X2 ) ) ) )
= $true )
| ( ( ^ [Y0: a > $o] :
( ( Y0 @ sK7 )
& ( X1 @ Y0 ) )
@ ( sK11 @ X1 ) )
= $true )
| ( $false
= ( sK0 @ X1 ) ) ),
inference(sigma_clausification,[],[f49]) ).
thf(f49,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK7 )
& ( X1 @ Y0 ) ) )
= $true )
| ( $false
= ( sK0 @ X1 ) )
| ( ( ( sK0 @ X2 )
=> ( ( sK10 @ X2 @ sK7 )
& ( X2 @ ( sK10 @ X2 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[],[f48]) ).
thf(f48,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( ( ( sK0 @ X1 )
=> ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK7 )
& ( X1 @ Y0 ) ) ) )
= $true )
| ( ( ( sK0 @ X2 )
=> ( ( sK10 @ X2 @ sK7 )
& ( X2 @ ( sK10 @ X2 ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[],[f47]) ).
thf(f47,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( ( ( sK0 @ X1 )
=> ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK7 )
& ( X1 @ Y0 ) ) ) )
= $true )
| ( ( ^ [Y0: ( a > $o ) > $o] :
( ( sK0 @ Y0 )
=> ( ( sK10 @ Y0 @ sK7 )
& ( Y0 @ ( sK10 @ Y0 ) ) ) )
@ X2 )
= $true ) ),
inference(pi_clausification,[],[f46]) ).
thf(f46,plain,
! [X1: ( a > $o ) > $o] :
( ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK0 @ Y0 )
=> ( ( sK10 @ Y0 @ sK7 )
& ( Y0 @ ( sK10 @ Y0 ) ) ) ) )
= $true )
| ( ( ( sK0 @ X1 )
=> ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK7 )
& ( X1 @ Y0 ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[],[f45]) ).
thf(f45,plain,
! [X1: ( a > $o ) > $o] :
( ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK0 @ Y0 )
=> ( ( sK10 @ Y0 @ sK7 )
& ( Y0 @ ( sK10 @ Y0 ) ) ) ) )
= $true )
| ( ( ^ [Y0: ( a > $o ) > $o] :
( ( sK0 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ sK7 )
& ( Y0 @ Y1 ) ) ) )
@ X1 )
= $true ) ),
inference(pi_clausification,[],[f44]) ).
thf(f44,plain,
( ( $true
= ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK0 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ sK7 )
& ( Y0 @ Y1 ) ) ) ) ) )
| ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK0 @ Y0 )
=> ( ( sK10 @ Y0 @ sK7 )
& ( Y0 @ ( sK10 @ Y0 ) ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[],[f43]) ).
thf(f43,plain,
( ( $true
= ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK0 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ sK7 )
& ( Y0 @ Y1 ) ) ) ) ) )
| ( ( ^ [Y0: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( sK0 @ Y1 )
=> ( ( Y0 @ Y1 @ sK7 )
& ( Y1 @ ( Y0 @ Y1 ) ) ) ) )
@ sK10 )
= $true ) ),
inference(sigma_clausification,[],[f24]) ).
thf(f24,plain,
( ( $true
= ( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y0: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( sK0 @ Y1 )
=> ( ( Y0 @ Y1 @ sK7 )
& ( Y1 @ ( Y0 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK0 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ sK7 )
& ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f23]) ).
thf(f73,plain,
( spl5_4
| spl5_2 ),
inference(avatar_split_clause,[],[f55,f63,f71]) ).
thf(f55,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( $true
= ( X1 @ ( sK11 @ X1 ) ) )
| ( $false
= ( sK0 @ X1 ) )
| ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( sK10 @ X2 @ sK7 ) ) ),
inference(binary_proxy_clausification,[],[f54]) ).
thf(f69,plain,
( spl5_1
| spl5_3 ),
inference(avatar_split_clause,[],[f58,f67,f60]) ).
thf(f58,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( ( sK11 @ X1 @ sK7 )
= $true )
| ( ( X2 @ ( sK10 @ X2 ) )
= $true )
| ( $false
= ( sK0 @ X1 ) )
| ( $false
= ( sK0 @ X2 ) ) ),
inference(binary_proxy_clausification,[],[f53]) ).
thf(f53,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( ( X2 @ ( sK10 @ X2 ) )
= $true )
| ( $false
= ( sK0 @ X2 ) )
| ( ( ( sK11 @ X1 @ sK7 )
& ( X1 @ ( sK11 @ X1 ) ) )
= $true )
| ( $false
= ( sK0 @ X1 ) ) ),
inference(binary_proxy_clausification,[],[f52]) ).
thf(f65,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f57,f63,f60]) ).
thf(f57,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( X1 @ ( sK11 @ X1 ) ) )
| ( ( X2 @ ( sK10 @ X2 ) )
= $true )
| ( $false
= ( sK0 @ X1 ) ) ),
inference(binary_proxy_clausification,[],[f53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO246^5 : TPTP v8.2.0. Released v4.0.0.
% 0.12/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.35 % Computer : n026.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon May 20 10:37:38 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 This is a TH0_THM_EQU_NAR problem
% 0.14/0.36 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.37 % (4370)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.37 % (4371)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)
% 0.14/0.37 % (4372)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)
% 0.14/0.37 % (4374)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)
% 0.14/0.38 % (4375)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)
% 0.14/0.38 % (4376)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.38 % (4377)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)
% 0.14/0.38 % (4374)Instruction limit reached!
% 0.14/0.38 % (4374)------------------------------
% 0.14/0.38 % (4374)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (4374)Termination reason: Unknown
% 0.14/0.38 % (4374)Termination phase: Property scanning
% 0.14/0.38
% 0.14/0.38 % (4374)Memory used [KB]: 895
% 0.14/0.38 % (4374)Time elapsed: 0.003 s
% 0.14/0.38 % (4374)Instructions burned: 2 (million)
% 0.14/0.38 % (4374)------------------------------
% 0.14/0.38 % (4374)------------------------------
% 0.14/0.38 % (4377)Instruction limit reached!
% 0.14/0.38 % (4377)------------------------------
% 0.14/0.38 % (4377)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (4377)Termination reason: Unknown
% 0.14/0.38 % (4377)Termination phase: Saturation
% 0.14/0.38
% 0.14/0.38 % (4377)Memory used [KB]: 5500
% 0.14/0.38 % (4377)Time elapsed: 0.005 s
% 0.14/0.38 % (4377)Instructions burned: 3 (million)
% 0.14/0.38 % (4377)------------------------------
% 0.14/0.38 % (4377)------------------------------
% 0.14/0.38 % (4371)Instruction limit reached!
% 0.14/0.38 % (4371)------------------------------
% 0.14/0.38 % (4371)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (4371)Termination reason: Unknown
% 0.14/0.38 % (4371)Termination phase: Saturation
% 0.14/0.38
% 0.14/0.38 % (4371)Memory used [KB]: 5500
% 0.14/0.38 % (4371)Time elapsed: 0.006 s
% 0.14/0.38 % (4371)Instructions burned: 5 (million)
% 0.14/0.38 % (4371)------------------------------
% 0.14/0.38 % (4371)------------------------------
% 0.14/0.38 % (4373)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.38 % (4373)Instruction limit reached!
% 0.14/0.38 % (4373)------------------------------
% 0.14/0.38 % (4373)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (4373)Termination reason: Unknown
% 0.14/0.38 % (4373)Termination phase: Preprocessing 3
% 0.14/0.38
% 0.14/0.38 % (4373)Memory used [KB]: 895
% 0.14/0.38 % (4373)Time elapsed: 0.003 s
% 0.14/0.38 % (4373)Instructions burned: 2 (million)
% 0.14/0.38 % (4373)------------------------------
% 0.14/0.38 % (4373)------------------------------
% 0.14/0.39 % (4376)Instruction limit reached!
% 0.14/0.39 % (4376)------------------------------
% 0.14/0.39 % (4376)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (4376)Termination reason: Unknown
% 0.14/0.39 % (4376)Termination phase: Saturation
% 0.14/0.39
% 0.14/0.39 % (4376)Memory used [KB]: 5628
% 0.14/0.39 % (4376)Time elapsed: 0.014 s
% 0.14/0.39 % (4376)Instructions burned: 19 (million)
% 0.14/0.39 % (4376)------------------------------
% 0.14/0.39 % (4376)------------------------------
% 0.14/0.39 % (4378)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)
% 0.14/0.39 % (4379)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)
% 0.14/0.39 % (4380)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)
% 0.14/0.39 % (4372)First to succeed.
% 0.14/0.40 % (4380)Instruction limit reached!
% 0.14/0.40 % (4380)------------------------------
% 0.14/0.40 % (4380)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (4380)Termination reason: Unknown
% 0.14/0.40 % (4380)Termination phase: Saturation
% 0.14/0.40
% 0.14/0.40 % (4380)Memory used [KB]: 5500
% 0.14/0.40 % (4380)Time elapsed: 0.004 s
% 0.14/0.40 % (4380)Instructions burned: 3 (million)
% 0.14/0.40 % (4380)------------------------------
% 0.14/0.40 % (4380)------------------------------
% 0.14/0.40 % (4381)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)
% 0.14/0.40 % (4372)Refutation found. Thanks to Tanya!
% 0.14/0.40 % SZS status Theorem for theBenchmark
% 0.14/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.40 % (4372)------------------------------
% 0.14/0.40 % (4372)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (4372)Termination reason: Refutation
% 0.14/0.40
% 0.14/0.40 % (4372)Memory used [KB]: 5756
% 0.14/0.40 % (4372)Time elapsed: 0.026 s
% 0.14/0.40 % (4372)Instructions burned: 26 (million)
% 0.14/0.40 % (4372)------------------------------
% 0.14/0.40 % (4372)------------------------------
% 0.14/0.40 % (4369)Success in time 0.028 s
% 0.14/0.40 % Vampire---4.8 exiting
%------------------------------------------------------------------------------