TSTP Solution File: ALG251^2 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : ALG251^2 : TPTP v8.1.2. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n028.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 : Sun May 5 04:13:09 EDT 2024
% Result : Theorem 0.21s 0.53s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 39
% Syntax : Number of formulae : 167 ( 90 unt; 25 typ; 0 def)
% Number of atoms : 887 ( 263 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 2002 ( 44 ~; 84 |; 0 &;1406 @)
% ( 6 <=>; 237 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 152 ( 152 >; 0 *; 0 +; 0 <<)
% Number of symbols : 38 ( 33 usr; 22 con; 0-4 aty)
% ( 219 !!; 6 ??; 0 @@+; 0 @@-)
% Number of variables : 403 ( 284 ^ 116 !; 2 ?; 403 :)
% ( 1 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
term: $tType ).
thf(type_def_7,type,
subst: $tType ).
thf(func_def_0,type,
term: $tType ).
thf(func_def_1,type,
subst: $tType ).
thf(func_def_2,type,
one: term ).
thf(func_def_3,type,
ap: term > term > term ).
thf(func_def_4,type,
lam: term > term ).
thf(func_def_5,type,
sub: term > subst > term ).
thf(func_def_6,type,
id: subst ).
thf(func_def_7,type,
sh: subst ).
thf(func_def_8,type,
push: term > subst > subst ).
thf(func_def_9,type,
comp: subst > subst > subst ).
thf(func_def_10,type,
var: term > $o ).
thf(func_def_18,type,
hoasap: subst > term > subst > term > term ).
thf(func_def_73,type,
hoaslam: subst > ( subst > term > term ) > term ).
thf(func_def_86,type,
hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).
thf(func_def_107,type,
hoasvar: subst > term > subst > $o ).
thf(func_def_121,type,
pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).
thf(func_def_144,type,
sK1: subst > term > ( term > $o ) > term > $o ).
thf(func_def_145,type,
sK2: ( term > $o ) > term ).
thf(func_def_146,type,
sK3: subst ).
thf(func_def_147,type,
sK4: term > $o ).
thf(func_def_148,type,
sK5: term ).
thf(func_def_149,type,
sK6: term ).
thf(func_def_150,type,
ph7:
!>[X0: $tType] : X0 ).
thf(f1168,plain,
$false,
inference(avatar_sat_refutation,[],[f1087,f1093,f1117,f1164,f1167]) ).
thf(f1167,plain,
~ spl0_15,
inference(avatar_contradiction_clause,[],[f1166]) ).
thf(f1166,plain,
( $false
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f1165]) ).
thf(f1165,plain,
( ( $false = $true )
| ~ spl0_15 ),
inference(backward_demodulation,[],[f601,f1161]) ).
thf(f1161,plain,
( ( $false
= ( var @ sK6 ) )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f1159]) ).
thf(f1159,plain,
( spl0_15
<=> ( $false
= ( var @ sK6 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
thf(f601,plain,
( ( var @ sK6 )
= $true ),
inference(binary_proxy_clausification,[],[f599]) ).
thf(f599,plain,
( $false
= ( ( var @ sK6 )
=> ( sK4 @ ( sub @ sK6 @ ( push @ sK5 @ sK3 ) ) ) ) ),
inference(beta_eta_normalization,[],[f598]) ).
thf(f598,plain,
( $false
= ( ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK4 @ ( sub @ Y0 @ ( push @ sK5 @ sK3 ) ) ) )
@ sK6 ) ),
inference(sigma_clausification,[],[f596]) ).
thf(f596,plain,
( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK4 @ ( sub @ Y0 @ ( push @ sK5 @ sK3 ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f591]) ).
thf(f591,plain,
( $false
= ( ( sK4 @ sK5 )
=> ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK4 @ ( sub @ Y0 @ ( push @ sK5 @ sK3 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f590]) ).
thf(f590,plain,
( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK4 @ ( sub @ Y0 @ sK3 ) ) ) )
=> ( ( sK4 @ sK5 )
=> ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK4 @ ( sub @ Y0 @ ( push @ sK5 @ sK3 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f589]) ).
thf(f589,plain,
( $false
= ( ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( sK4 @ ( sub @ Y1 @ sK3 ) ) ) )
=> ( ( sK4 @ Y0 )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( sK4 @ ( sub @ Y1 @ ( push @ Y0 @ sK3 ) ) ) ) ) ) )
@ sK5 ) ),
inference(sigma_clausification,[],[f588]) ).
thf(f588,plain,
( $false
= ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( sK4 @ ( sub @ Y1 @ sK3 ) ) ) )
=> ( ( sK4 @ Y0 )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( sK4 @ ( sub @ Y1 @ ( push @ Y0 @ sK3 ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f587]) ).
thf(f587,plain,
( $false
= ( ^ [Y0: term > $o] :
( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( var @ Y2 )
=> ( Y0 @ ( sub @ Y2 @ sK3 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !! @ term
@ ^ [Y2: term] :
( ( var @ Y2 )
=> ( Y0 @ ( sub @ Y2 @ ( push @ Y1 @ sK3 ) ) ) ) ) ) ) )
@ sK4 ) ),
inference(sigma_clausification,[],[f586]) ).
thf(f586,plain,
( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( var @ Y2 )
=> ( Y0 @ ( sub @ Y2 @ sK3 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !! @ term
@ ^ [Y2: term] :
( ( var @ Y2 )
=> ( Y0 @ ( sub @ Y2 @ ( push @ Y1 @ sK3 ) ) ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f585]) ).
thf(f585,plain,
( $false
= ( ^ [Y0: subst] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ Y0 ) ) ) )
=> ( ( Y1 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ ( push @ Y2 @ Y0 ) ) ) ) ) ) ) ) )
@ sK3 ) ),
inference(sigma_clausification,[],[f564]) ).
thf(f564,plain,
( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ Y0 ) ) ) )
=> ( ( Y1 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ ( push @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f557]) ).
thf(f557,plain,
( $false
= ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( !! @ subst
@ ^ [Y0: subst] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ Y0 ) ) ) )
=> ( ( Y1 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ ( push @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f548]) ).
thf(f548,plain,
( $false
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( !! @ subst
@ ^ [Y0: subst] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ Y0 ) ) ) )
=> ( ( Y1 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ ( push @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f541]) ).
thf(f541,plain,
( $false
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y2 @ Y0 ) )
= ( sub @ ( sub @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( !! @ subst
@ ^ [Y0: subst] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ Y0 ) ) ) )
=> ( ( Y1 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ ( push @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f539]) ).
thf(f539,plain,
( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y2 @ Y0 ) )
= ( sub @ ( sub @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( !! @ subst
@ ^ [Y0: subst] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ Y0 ) ) ) )
=> ( ( Y1 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ ( push @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f524]) ).
thf(f524,plain,
( $false
= ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y2 @ Y0 ) )
= ( sub @ ( sub @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( !! @ subst
@ ^ [Y0: subst] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ Y0 ) ) ) )
=> ( ( Y1 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ ( push @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f523]) ).
thf(f523,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ subst
@ ^ [Y2: subst] :
( ?? @ ( term > $o )
@ ^ [Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( sub @ Y4 @ ( push @ Y0 @ Y2 ) ) )
= ( Y3 @ Y4 ) ) ) ) ) ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y2 @ Y0 ) )
= ( sub @ ( sub @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( !! @ subst
@ ^ [Y0: subst] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ Y0 ) ) ) )
=> ( ( Y1 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ ( push @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
!= $true ),
inference(beta_eta_normalization,[],[f522]) ).
thf(f522,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ subst
@ ^ [Y2: subst] :
( ?? @ ( term > $o )
@ ^ [Y3: term > $o] :
( ^ [Y4: term,Y5: subst,Y6: term > $o,Y7: term > $o] :
( !! @ term
@ ^ [Y8: term] :
( ( Y6 @ ( sub @ Y8 @ ( push @ Y4 @ Y5 ) ) )
= ( Y7 @ Y8 ) ) )
@ Y0
@ Y2
@ Y1
@ Y3 ) ) ) ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y2 @ Y0 ) )
= ( sub @ ( sub @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( !! @ subst
@ ^ [Y0: subst] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ Y0 ) ) ) )
=> ( ( Y1 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ ( push @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f347,f494]) ).
thf(f494,plain,
( pushprop_lthm
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ subst
@ ^ [Y2: subst] :
( ?? @ ( term > $o )
@ ^ [Y3: term > $o] :
( ^ [Y4: term,Y5: subst,Y6: term > $o,Y7: term > $o] :
( !! @ term
@ ^ [Y8: term] :
( ( Y6 @ ( sub @ Y8 @ ( push @ Y4 @ Y5 ) ) )
= ( Y7 @ Y8 ) ) )
@ Y0
@ Y2
@ Y1
@ Y3 ) ) ) ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y2 @ Y0 ) )
= ( sub @ ( sub @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( !! @ subst
@ ^ [Y0: subst] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ Y0 ) ) ) )
=> ( ( Y1 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ ( push @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f439,f447,f359,f376,f361,f346,f391,f394]) ).
thf(f394,plain,
( pushprop
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ Y0 ) ) ) )
=> ( ( Y1 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ ( push @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f321]) ).
thf(f321,plain,
( pushprop
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ Y0 ) ) ) )
=> ( ( Y1 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ ( push @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f320]) ).
thf(f320,plain,
( pushprop
= ( ! [X0: term,X1: term > $o,X2: subst] :
( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ ( sub @ X3 @ X2 ) ) )
=> ( ( X1 @ X0 )
=> ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ ( push @ X0 @ X2 ) ) ) ) ) ) ) ),
inference(rectify,[],[f39]) ).
thf(f39,axiom,
( pushprop
= ( ! [X0: term,X5: term > $o,X2: subst] :
( ! [X1: term] :
( ( var @ X1 )
=> ( X5 @ ( sub @ X1 @ X2 ) ) )
=> ( ( X5 @ X0 )
=> ! [X1: term] :
( ( var @ X1 )
=> ( X5 @ ( sub @ X1 @ ( push @ X0 @ X2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.rEC2kAVY5o/Vampire---4.8_9986',pushprop) ).
thf(f391,plain,
( ulamvarind
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f276]) ).
thf(f276,plain,
( ulamvarind
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f275]) ).
thf(f275,plain,
( ulamvarind
= ( ! [X0: term > $o] :
( ( X0 @ one )
=> ( ! [X1: term] :
( ( var @ X1 )
=> ( ( X0 @ X1 )
=> ( X0 @ ( sub @ X1 @ sh ) ) ) )
=> ! [X2: term] :
( ( var @ X2 )
=> ( X0 @ X2 ) ) ) ) ) ),
inference(rectify,[],[f15]) ).
thf(f15,axiom,
( ulamvarind
= ( ! [X5: term > $o] :
( ( X5 @ one )
=> ( ! [X0: term] :
( ( var @ X0 )
=> ( ( X5 @ X0 )
=> ( X5 @ ( sub @ X0 @ sh ) ) ) )
=> ! [X0: term] :
( ( var @ X0 )
=> ( X5 @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.rEC2kAVY5o/Vampire---4.8_9986',ulamvarind) ).
thf(f346,plain,
( axshiftcons
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) ) ),
inference(cnf_transformation,[],[f198]) ).
thf(f198,plain,
( axshiftcons
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) ) ),
inference(fool_elimination,[],[f197]) ).
thf(f197,plain,
( axshiftcons
= ( ! [X0: term,X1: subst] :
( ( comp @ sh @ ( push @ X0 @ X1 ) )
= X1 ) ) ),
inference(rectify,[],[f7]) ).
thf(f7,axiom,
( axshiftcons
= ( ! [X0: term,X2: subst] :
( ( comp @ sh @ ( push @ X0 @ X2 ) )
= X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.rEC2kAVY5o/Vampire---4.8_9986',axshiftcons) ).
thf(f361,plain,
( axclos
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y2 @ Y0 ) )
= ( sub @ ( sub @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f260]) ).
thf(f260,plain,
( axclos
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y2 @ Y0 ) )
= ( sub @ ( sub @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f259]) ).
thf(f259,plain,
( axclos
= ( ! [X0: subst,X1: term,X2: subst] :
( ( sub @ X1 @ ( comp @ X0 @ X2 ) )
= ( sub @ ( sub @ X1 @ X0 ) @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f5,axiom,
( axclos
= ( ! [X2: subst,X0: term,X3: subst] :
( ( sub @ ( sub @ X0 @ X2 ) @ X3 )
= ( sub @ X0 @ ( comp @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.rEC2kAVY5o/Vampire---4.8_9986',axclos) ).
thf(f376,plain,
( axvarcons
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) ) ),
inference(cnf_transformation,[],[f327]) ).
thf(f327,plain,
( axvarcons
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) ) ),
inference(fool_elimination,[],[f326]) ).
thf(f326,plain,
! [X0: subst,X1: term] :
( ( ( sub @ one @ ( push @ X1 @ X0 ) )
= X1 )
= axvarcons ),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
! [X2: subst,X0: term] :
( ( ( sub @ one @ ( push @ X0 @ X2 ) )
= X0 )
= axvarcons ),
file('/export/starexec/sandbox2/tmp/tmp.rEC2kAVY5o/Vampire---4.8_9986',axvarcons) ).
thf(f359,plain,
( ulamvar1
= ( var @ one ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f13,axiom,
( ulamvar1
= ( var @ one ) ),
file('/export/starexec/sandbox2/tmp/tmp.rEC2kAVY5o/Vampire---4.8_9986',ulamvar1) ).
thf(f447,plain,
( pushprop_lem0
= ( !! @ term
@ ^ [Y0: term] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ subst
@ ^ [Y2: subst] :
( ?? @ ( term > $o )
@ ^ [Y3: term > $o] :
( ^ [Y4: term,Y5: subst,Y6: term > $o,Y7: term > $o] :
( !! @ term
@ ^ [Y8: term] :
( ( Y6 @ ( sub @ Y8 @ ( push @ Y4 @ Y5 ) ) )
= ( Y7 @ Y8 ) ) )
@ Y0
@ Y2
@ Y1
@ Y3 ) ) ) ) ) ),
inference(definition_unfolding,[],[f411,f356]) ).
thf(f356,plain,
( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) )
= ( Y3 @ Y4 ) ) ) ) ),
inference(cnf_transformation,[],[f311]) ).
thf(f311,plain,
( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) )
= ( Y3 @ Y4 ) ) ) ) ),
inference(fool_elimination,[],[f310]) ).
thf(f310,plain,
( pushprop_p_and_p_prime
= ( ^ [X0: term,X1: subst,X2: term > $o,X3: term > $o] :
! [X4: term] :
( ( X2 @ ( sub @ X4 @ ( push @ X0 @ X1 ) ) )
<=> ( X3 @ X4 ) ) ) ),
inference(rectify,[],[f24]) ).
thf(f24,axiom,
( pushprop_p_and_p_prime
= ( ^ [X0: term,X2: subst,X5: term > $o,X8: term > $o] :
! [X9: term] :
( ( X5 @ ( sub @ X9 @ ( push @ X0 @ X2 ) ) )
<=> ( X8 @ X9 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.rEC2kAVY5o/Vampire---4.8_9986',pushprop_p_and_p_prime) ).
thf(f411,plain,
( pushprop_lem0
= ( !! @ term
@ ^ [Y0: term] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ subst
@ ^ [Y2: subst] :
( ?? @ ( term > $o )
@ ^ [Y3: term > $o] : ( pushprop_p_and_p_prime @ Y0 @ Y2 @ Y1 @ Y3 ) ) ) ) ) ),
inference(cnf_transformation,[],[f149]) ).
thf(f149,plain,
( pushprop_lem0
= ( !! @ term
@ ^ [Y0: term] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ subst
@ ^ [Y2: subst] :
( ?? @ ( term > $o )
@ ^ [Y3: term > $o] : ( pushprop_p_and_p_prime @ Y0 @ Y2 @ Y1 @ Y3 ) ) ) ) ) ),
inference(fool_elimination,[],[f148]) ).
thf(f148,plain,
! [X0: subst,X1: term > $o,X2: term] :
? [X3: term > $o] :
( ( pushprop_p_and_p_prime @ X2 @ X0 @ X1 @ X3 )
= pushprop_lem0 ),
inference(rectify,[],[f25]) ).
thf(f25,axiom,
! [X2: subst,X5: term > $o,X0: term] :
? [X8: term > $o] :
( ( pushprop_p_and_p_prime @ X0 @ X2 @ X5 @ X8 )
= pushprop_lem0 ),
file('/export/starexec/sandbox2/tmp/tmp.rEC2kAVY5o/Vampire---4.8_9986',pushprop_lem0) ).
thf(f439,plain,
( pushprop_lthm
= ( pushprop_lem0
=> ( ulamvar1
=> ( axvarcons
=> ( axclos
=> ( axshiftcons
=> ( ulamvarind
=> pushprop ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f289]) ).
thf(f289,plain,
( pushprop_lthm
= ( pushprop_lem0
=> ( ulamvar1
=> ( axvarcons
=> ( axclos
=> ( axshiftcons
=> ( ulamvarind
=> pushprop ) ) ) ) ) ) ),
inference(fool_elimination,[],[f288]) ).
thf(f288,plain,
( pushprop_lem0
=> ( ( ulamvar1
=> ( axvarcons
=> ( axclos
=> ( axshiftcons
=> ( ulamvarind
=> pushprop ) ) ) ) )
= pushprop_lthm ) ),
inference(rectify,[],[f42]) ).
thf(f42,axiom,
( pushprop_lem0
=> ( ( ulamvar1
=> ( axvarcons
=> ( axclos
=> ( axshiftcons
=> ( ulamvarind
=> pushprop ) ) ) ) )
= pushprop_lthm ) ),
file('/export/starexec/sandbox2/tmp/tmp.rEC2kAVY5o/Vampire---4.8_9986',pushprop_lthm) ).
thf(f347,plain,
pushprop_lthm != $true,
inference(cnf_transformation,[],[f330]) ).
thf(f330,plain,
pushprop_lthm != $true,
inference(flattening,[],[f128]) ).
thf(f128,plain,
pushprop_lthm != $true,
inference(fool_elimination,[],[f127]) ).
thf(f127,plain,
~ pushprop_lthm,
inference(rectify,[],[f115]) ).
thf(f115,negated_conjecture,
~ pushprop_lthm,
inference(negated_conjecture,[],[f114]) ).
thf(f114,conjecture,
pushprop_lthm,
file('/export/starexec/sandbox2/tmp/tmp.rEC2kAVY5o/Vampire---4.8_9986',thm) ).
thf(f1164,plain,
( spl0_15
| spl0_11
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f1139,f1114,f1078,f1159]) ).
thf(f1078,plain,
( spl0_11
<=> ( one = sK6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
thf(f1114,plain,
( spl0_13
<=> ( $false
= ( sK4
@ ( sub
@ ( sK2
@ ^ [Y0: term] : ( sK6 != Y0 ) )
@ sK3 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
thf(f1139,plain,
( ( one = sK6 )
| ( $false
= ( var @ sK6 ) )
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f1134]) ).
thf(f1134,plain,
( ( one = sK6 )
| ( $false
= ( var @ sK6 ) )
| ( $false = $true )
| ~ spl0_13 ),
inference(superposition,[],[f610,f1127]) ).
thf(f1127,plain,
( ( $false
= ( var
@ ( sK2
@ ^ [Y0: term] : ( sK6 != Y0 ) ) ) )
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f1120]) ).
thf(f1120,plain,
( ( $false = $true )
| ( $false
= ( var
@ ( sK2
@ ^ [Y0: term] : ( sK6 != Y0 ) ) ) )
| ~ spl0_13 ),
inference(superposition,[],[f1116,f595]) ).
thf(f595,plain,
! [X1: term] :
( ( ( sK4 @ ( sub @ X1 @ sK3 ) )
= $true )
| ( ( var @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[],[f594]) ).
thf(f594,plain,
! [X1: term] :
( ( ( var @ X1 )
=> ( sK4 @ ( sub @ X1 @ sK3 ) ) )
= $true ),
inference(beta_eta_normalization,[],[f593]) ).
thf(f593,plain,
! [X1: term] :
( ( ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK4 @ ( sub @ Y0 @ sK3 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[],[f592]) ).
thf(f592,plain,
( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK4 @ ( sub @ Y0 @ sK3 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f590]) ).
thf(f1116,plain,
( ( $false
= ( sK4
@ ( sub
@ ( sK2
@ ^ [Y0: term] : ( sK6 != Y0 ) )
@ sK3 ) ) )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f1114]) ).
thf(f610,plain,
! [X0: term] :
( ( ( var
@ ( sK2
@ ^ [Y0: term] : ( X0 != Y0 ) ) )
= $true )
| ( one = X0 )
| ( ( var @ X0 )
= $false ) ),
inference(leibniz_equality_elimination,[],[f576]) ).
thf(f576,plain,
! [X2: term,X1: term > $o] :
( ( ( var @ ( sK2 @ X1 ) )
= $true )
| ( ( X1 @ X2 )
= $true )
| ( $false
= ( var @ X2 ) )
| ( $false
= ( X1 @ one ) ) ),
inference(binary_proxy_clausification,[],[f575]) ).
thf(f575,plain,
! [X2: term,X1: term > $o] :
( ( $false
= ( X1 @ one ) )
| ( ( var @ ( sK2 @ X1 ) )
= $true )
| ( ( ( var @ X2 )
=> ( X1 @ X2 ) )
= $true ) ),
inference(beta_eta_normalization,[],[f574]) ).
thf(f574,plain,
! [X2: term,X1: term > $o] :
( ( ( var @ ( sK2 @ X1 ) )
= $true )
| ( $false
= ( X1 @ one ) )
| ( ( ^ [Y0: term] :
( ( var @ Y0 )
=> ( X1 @ Y0 ) )
@ X2 )
= $true ) ),
inference(pi_clausification,[],[f573]) ).
thf(f573,plain,
! [X1: term > $o] :
( ( $false
= ( X1 @ one ) )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( X1 @ Y0 ) ) )
= $true )
| ( ( var @ ( sK2 @ X1 ) )
= $true ) ),
inference(binary_proxy_clausification,[],[f571]) ).
thf(f571,plain,
! [X1: term > $o] :
( ( $false
= ( X1 @ one ) )
| ( $false
= ( ( var @ ( sK2 @ X1 ) )
=> ( ( X1 @ ( sK2 @ X1 ) )
=> ( X1 @ ( sub @ ( sK2 @ X1 ) @ sh ) ) ) ) )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( X1 @ Y0 ) ) )
= $true ) ),
inference(beta_eta_normalization,[],[f570]) ).
thf(f570,plain,
! [X1: term > $o] :
( ( $false
= ( X1 @ one ) )
| ( $false
= ( ^ [Y0: term] :
( ( var @ Y0 )
=> ( ( X1 @ Y0 )
=> ( X1 @ ( sub @ Y0 @ sh ) ) ) )
@ ( sK2 @ X1 ) ) )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( X1 @ Y0 ) ) )
= $true ) ),
inference(sigma_clausification,[],[f569]) ).
thf(f569,plain,
! [X1: term > $o] :
( ( $false
= ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( ( X1 @ Y0 )
=> ( X1 @ ( sub @ Y0 @ sh ) ) ) ) ) )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( X1 @ Y0 ) ) )
= $true )
| ( $false
= ( X1 @ one ) ) ),
inference(binary_proxy_clausification,[],[f568]) ).
thf(f568,plain,
! [X1: term > $o] :
( ( ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( ( X1 @ Y0 )
=> ( X1 @ ( sub @ Y0 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( X1 @ Y0 ) ) ) )
= $true )
| ( $false
= ( X1 @ one ) ) ),
inference(binary_proxy_clausification,[],[f567]) ).
thf(f567,plain,
! [X1: term > $o] :
( ( ( X1 @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( ( X1 @ Y0 )
=> ( X1 @ ( sub @ Y0 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( X1 @ Y0 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[],[f566]) ).
thf(f566,plain,
! [X1: term > $o] :
( ( ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[],[f565]) ).
thf(f565,plain,
( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f557]) ).
thf(f1117,plain,
( spl0_11
| spl0_13
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f1112,f1082,f1114,f1078]) ).
thf(f1082,plain,
( spl0_12
<=> ! [X0: term] :
( $false
= ( sK4 @ ( sub @ sK6 @ ( push @ X0 @ sK3 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
thf(f1112,plain,
( ( one = sK6 )
| ( $false
= ( sK4
@ ( sub
@ ( sK2
@ ^ [Y0: term] : ( sK6 != Y0 ) )
@ sK3 ) ) )
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f1111]) ).
thf(f1111,plain,
( ( $false = $true )
| ( $false
= ( sK4
@ ( sub
@ ( sK2
@ ^ [Y0: term] : ( sK6 != Y0 ) )
@ sK3 ) ) )
| ( one = sK6 )
| ~ spl0_12 ),
inference(forward_demodulation,[],[f1106,f601]) ).
thf(f1106,plain,
( ( $false
= ( sK4
@ ( sub
@ ( sK2
@ ^ [Y0: term] : ( sK6 != Y0 ) )
@ sK3 ) ) )
| ( $false
= ( var @ sK6 ) )
| ( one = sK6 )
| ~ spl0_12 ),
inference(superposition,[],[f1083,f954]) ).
thf(f954,plain,
! [X2: term,X0: term,X1: subst] :
( ( ( sub
@ ( sK2
@ ^ [Y0: term] : ( X2 != Y0 ) )
@ X1 )
= ( sub @ X2 @ ( push @ X0 @ X1 ) ) )
| ( one = X2 )
| ( $false
= ( var @ X2 ) ) ),
inference(superposition,[],[f847,f563]) ).
thf(f563,plain,
! [X2: term,X1: subst] :
( ( comp @ sh @ ( push @ X2 @ X1 ) )
= X1 ),
inference(equality_proxy_clausification,[],[f562]) ).
thf(f562,plain,
! [X2: term,X1: subst] :
( ( ( comp @ sh @ ( push @ X2 @ X1 ) )
= X1 )
= $true ),
inference(beta_eta_normalization,[],[f561]) ).
thf(f561,plain,
! [X2: term,X1: subst] :
( ( ^ [Y0: term] :
( ( comp @ sh @ ( push @ Y0 @ X1 ) )
= X1 )
@ X2 )
= $true ),
inference(pi_clausification,[],[f560]) ).
thf(f560,plain,
! [X1: subst] :
( ( !! @ term
@ ^ [Y0: term] :
( ( comp @ sh @ ( push @ Y0 @ X1 ) )
= X1 ) )
= $true ),
inference(beta_eta_normalization,[],[f559]) ).
thf(f559,plain,
! [X1: subst] :
( ( ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[],[f558]) ).
thf(f558,plain,
( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f548]) ).
thf(f847,plain,
! [X0: term,X1: subst] :
( ( ( sub @ X0 @ X1 )
= ( sub
@ ( sK2
@ ^ [Y0: term] : ( X0 != Y0 ) )
@ ( comp @ sh @ X1 ) ) )
| ( ( var @ X0 )
= $false )
| ( one = X0 ) ),
inference(superposition,[],[f556,f795]) ).
thf(f795,plain,
! [X0: term] :
( ( ( sub
@ ( sK2
@ ^ [Y0: term] : ( X0 != Y0 ) )
@ sh )
= X0 )
| ( one = X0 )
| ( ( var @ X0 )
= $false ) ),
inference(equality_proxy_clausification,[],[f794]) ).
thf(f794,plain,
! [X0: term] :
( ( ( var @ X0 )
= $false )
| ( ( X0 = one )
= $true )
| ( ( sub
@ ( sK2
@ ^ [Y0: term] : ( X0 != Y0 ) )
@ sh )
= X0 ) ),
inference(not_proxy_clausification,[],[f793]) ).
thf(f793,plain,
! [X0: term] :
( ( $false
= ( X0 != one ) )
| ( ( var @ X0 )
= $false )
| ( ( sub
@ ( sK2
@ ^ [Y0: term] : ( X0 != Y0 ) )
@ sh )
= X0 ) ),
inference(beta_eta_normalization,[],[f783]) ).
thf(f783,plain,
! [X0: term] :
( ( ( sub
@ ( sK2
@ ^ [Y0: term] : ( X0 != Y0 ) )
@ sh )
= X0 )
| ( $false
= ( ^ [Y0: term] : ( X0 != Y0 )
@ one ) )
| ( ( var @ X0 )
= $false ) ),
inference(leibniz_equality_elimination,[],[f584]) ).
thf(f584,plain,
! [X2: term,X1: term > $o] :
( ( $false
= ( X1 @ ( sub @ ( sK2 @ X1 ) @ sh ) ) )
| ( ( X1 @ X2 )
= $true )
| ( $false
= ( var @ X2 ) )
| ( $false
= ( X1 @ one ) ) ),
inference(binary_proxy_clausification,[],[f583]) ).
thf(f583,plain,
! [X2: term,X1: term > $o] :
( ( $false
= ( X1 @ ( sub @ ( sK2 @ X1 ) @ sh ) ) )
| ( $false
= ( X1 @ one ) )
| ( ( ( var @ X2 )
=> ( X1 @ X2 ) )
= $true ) ),
inference(beta_eta_normalization,[],[f582]) ).
thf(f582,plain,
! [X2: term,X1: term > $o] :
( ( $false
= ( X1 @ ( sub @ ( sK2 @ X1 ) @ sh ) ) )
| ( ( ^ [Y0: term] :
( ( var @ Y0 )
=> ( X1 @ Y0 ) )
@ X2 )
= $true )
| ( $false
= ( X1 @ one ) ) ),
inference(pi_clausification,[],[f577]) ).
thf(f577,plain,
! [X1: term > $o] :
( ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( X1 @ Y0 ) ) )
= $true )
| ( $false
= ( X1 @ one ) )
| ( $false
= ( X1 @ ( sub @ ( sK2 @ X1 ) @ sh ) ) ) ),
inference(binary_proxy_clausification,[],[f572]) ).
thf(f572,plain,
! [X1: term > $o] :
( ( $false
= ( ( X1 @ ( sK2 @ X1 ) )
=> ( X1 @ ( sub @ ( sK2 @ X1 ) @ sh ) ) ) )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( X1 @ Y0 ) ) )
= $true )
| ( $false
= ( X1 @ one ) ) ),
inference(binary_proxy_clausification,[],[f571]) ).
thf(f556,plain,
! [X2: term,X3: subst,X1: subst] :
( ( sub @ ( sub @ X2 @ X3 ) @ X1 )
= ( sub @ X2 @ ( comp @ X3 @ X1 ) ) ),
inference(equality_proxy_clausification,[],[f555]) ).
thf(f555,plain,
! [X2: term,X3: subst,X1: subst] :
( ( ( sub @ X2 @ ( comp @ X3 @ X1 ) )
= ( sub @ ( sub @ X2 @ X3 ) @ X1 ) )
= $true ),
inference(beta_eta_normalization,[],[f554]) ).
thf(f554,plain,
! [X2: term,X3: subst,X1: subst] :
( ( ^ [Y0: subst] :
( ( sub @ X2 @ ( comp @ Y0 @ X1 ) )
= ( sub @ ( sub @ X2 @ Y0 ) @ X1 ) )
@ X3 )
= $true ),
inference(pi_clausification,[],[f553]) ).
thf(f553,plain,
! [X2: term,X1: subst] :
( ( !! @ subst
@ ^ [Y0: subst] :
( ( sub @ X2 @ ( comp @ Y0 @ X1 ) )
= ( sub @ ( sub @ X2 @ Y0 ) @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[],[f552]) ).
thf(f552,plain,
! [X2: term,X1: subst] :
( ( ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ X1 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ X1 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[],[f551]) ).
thf(f551,plain,
! [X1: subst] :
( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ X1 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[],[f550]) ).
thf(f550,plain,
! [X1: subst] :
( ( ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y2 @ Y0 ) )
= ( sub @ ( sub @ Y1 @ Y2 ) @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[],[f549]) ).
thf(f549,plain,
( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y2 @ Y0 ) )
= ( sub @ ( sub @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f541]) ).
thf(f1083,plain,
( ! [X0: term] :
( $false
= ( sK4 @ ( sub @ sK6 @ ( push @ X0 @ sK3 ) ) ) )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f1082]) ).
thf(f1093,plain,
~ spl0_11,
inference(avatar_contradiction_clause,[],[f1092]) ).
thf(f1092,plain,
( $false
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f1091]) ).
thf(f1091,plain,
( ( $false = $true )
| ~ spl0_11 ),
inference(backward_demodulation,[],[f597,f1090]) ).
thf(f1090,plain,
( ( $false
= ( sK4 @ sK5 ) )
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1089,f547]) ).
thf(f547,plain,
! [X2: subst,X1: term] :
( ( sub @ one @ ( push @ X1 @ X2 ) )
= X1 ),
inference(equality_proxy_clausification,[],[f546]) ).
thf(f546,plain,
! [X2: subst,X1: term] :
( ( ( sub @ one @ ( push @ X1 @ X2 ) )
= X1 )
= $true ),
inference(beta_eta_normalization,[],[f545]) ).
thf(f545,plain,
! [X2: subst,X1: term] :
( ( ^ [Y0: subst] :
( ( sub @ one @ ( push @ X1 @ Y0 ) )
= X1 )
@ X2 )
= $true ),
inference(pi_clausification,[],[f544]) ).
thf(f544,plain,
! [X1: term] :
( ( !! @ subst
@ ^ [Y0: subst] :
( ( sub @ one @ ( push @ X1 @ Y0 ) )
= X1 ) )
= $true ),
inference(beta_eta_normalization,[],[f543]) ).
thf(f543,plain,
! [X1: term] :
( ( ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[],[f542]) ).
thf(f542,plain,
( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f539]) ).
thf(f1089,plain,
( ( $false
= ( sK4 @ ( sub @ one @ ( push @ sK5 @ sK3 ) ) ) )
| ~ spl0_11 ),
inference(backward_demodulation,[],[f600,f1080]) ).
thf(f1080,plain,
( ( one = sK6 )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f1078]) ).
thf(f600,plain,
( $false
= ( sK4 @ ( sub @ sK6 @ ( push @ sK5 @ sK3 ) ) ) ),
inference(binary_proxy_clausification,[],[f599]) ).
thf(f597,plain,
( ( sK4 @ sK5 )
= $true ),
inference(binary_proxy_clausification,[],[f591]) ).
thf(f1087,plain,
( spl0_11
| spl0_12 ),
inference(avatar_split_clause,[],[f1086,f1082,f1078]) ).
thf(f1086,plain,
! [X0: term] :
( ( $false
= ( sK4 @ ( sub @ sK6 @ ( push @ X0 @ sK3 ) ) ) )
| ( one = sK6 ) ),
inference(trivial_inequality_removal,[],[f1085]) ).
thf(f1085,plain,
! [X0: term] :
( ( $false
= ( sK4 @ ( sub @ sK6 @ ( push @ X0 @ sK3 ) ) ) )
| ( one = sK6 )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f1051,f601]) ).
thf(f1051,plain,
! [X0: term] :
( ( $false
= ( var @ sK6 ) )
| ( one = sK6 )
| ( $false
= ( sK4 @ ( sub @ sK6 @ ( push @ X0 @ sK3 ) ) ) ) ),
inference(superposition,[],[f600,f986]) ).
thf(f986,plain,
! [X2: term,X3: term,X0: term,X1: subst] :
( ( ( sub @ X0 @ ( push @ X3 @ X1 ) )
= ( sub @ X0 @ ( push @ X2 @ X1 ) ) )
| ( ( var @ X0 )
= $false )
| ( one = X0 ) ),
inference(duplicate_literal_removal,[],[f961]) ).
thf(f961,plain,
! [X2: term,X3: term,X0: term,X1: subst] :
( ( one = X0 )
| ( ( var @ X0 )
= $false )
| ( ( sub @ X0 @ ( push @ X3 @ X1 ) )
= ( sub @ X0 @ ( push @ X2 @ X1 ) ) )
| ( ( var @ X0 )
= $false )
| ( one = X0 ) ),
inference(superposition,[],[f954,f954]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : ALG251^2 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.13/0.15 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.35 % Computer : n028.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 3 19:58:23 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.35 This is a TH0_THM_EQU_NAR problem
% 0.15/0.36 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/sandbox2/tmp/tmp.rEC2kAVY5o/Vampire---4.8_9986
% 0.15/0.39 % (10143)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on Vampire---4 for (2999ds/183Mi)
% 0.15/0.39 % (10144)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 Vampire---4 for (2999ds/4Mi)
% 0.15/0.39 % (10145)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 Vampire---4 for (2999ds/27Mi)
% 0.15/0.39 % (10146)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.15/0.39 % (10148)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on Vampire---4 for (2999ds/275Mi)
% 0.15/0.39 % (10149)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.15/0.39 % (10146)Instruction limit reached!
% 0.15/0.39 % (10146)------------------------------
% 0.15/0.39 % (10146)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (10146)Termination reason: Unknown
% 0.15/0.39 % (10146)Termination phase: shuffling
% 0.15/0.39
% 0.15/0.39 % (10146)Memory used [KB]: 1279
% 0.15/0.39 % (10146)Time elapsed: 0.004 s
% 0.15/0.39 % (10146)Instructions burned: 3 (million)
% 0.15/0.39 % (10146)------------------------------
% 0.15/0.39 % (10146)------------------------------
% 0.15/0.39 % (10144)Instruction limit reached!
% 0.15/0.39 % (10144)------------------------------
% 0.15/0.39 % (10144)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (10144)Termination reason: Unknown
% 0.15/0.39 % (10144)Termination phase: shuffling
% 0.15/0.39
% 0.15/0.39 % (10144)Memory used [KB]: 1279
% 0.15/0.39 % (10144)Time elapsed: 0.005 s
% 0.15/0.39 % (10144)Instructions burned: 5 (million)
% 0.15/0.39 % (10144)------------------------------
% 0.15/0.39 % (10144)------------------------------
% 0.15/0.39 % (10147)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.15/0.39 % (10147)Instruction limit reached!
% 0.15/0.39 % (10147)------------------------------
% 0.15/0.39 % (10147)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (10147)Termination reason: Unknown
% 0.15/0.39 % (10147)Termination phase: shuffling
% 0.15/0.39
% 0.15/0.39 % (10147)Memory used [KB]: 1279
% 0.15/0.39 % (10147)Time elapsed: 0.004 s
% 0.15/0.39 % (10147)Instructions burned: 2 (million)
% 0.15/0.39 % (10147)------------------------------
% 0.15/0.39 % (10147)------------------------------
% 0.15/0.40 % (10149)Instruction limit reached!
% 0.15/0.40 % (10149)------------------------------
% 0.15/0.40 % (10149)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (10149)Termination reason: Unknown
% 0.15/0.40 % (10149)Termination phase: Property scanning
% 0.15/0.40
% 0.15/0.40 % (10149)Memory used [KB]: 1663
% 0.15/0.40 % (10149)Time elapsed: 0.013 s
% 0.15/0.40 % (10149)Instructions burned: 19 (million)
% 0.15/0.40 % (10149)------------------------------
% 0.15/0.40 % (10149)------------------------------
% 0.15/0.40 % (10150)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.15/0.40 % (10145)Instruction limit reached!
% 0.15/0.40 % (10145)------------------------------
% 0.15/0.40 % (10145)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (10145)Termination reason: Unknown
% 0.15/0.40 % (10145)Termination phase: Property scanning
% 0.15/0.40
% 0.15/0.40 % (10145)Memory used [KB]: 1791
% 0.15/0.40 % (10145)Time elapsed: 0.016 s
% 0.15/0.40 % (10145)Instructions burned: 27 (million)
% 0.15/0.40 % (10145)------------------------------
% 0.15/0.40 % (10145)------------------------------
% 0.15/0.40 % (10150)Instruction limit reached!
% 0.15/0.40 % (10150)------------------------------
% 0.15/0.40 % (10150)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (10150)Termination reason: Unknown
% 0.15/0.40 % (10150)Termination phase: shuffling
% 0.15/0.40
% 0.15/0.40 % (10150)Memory used [KB]: 1279
% 0.15/0.40 % (10150)Time elapsed: 0.004 s
% 0.15/0.40 % (10150)Instructions burned: 3 (million)
% 0.15/0.40 % (10150)------------------------------
% 0.15/0.40 % (10150)------------------------------
% 0.15/0.40 % (10148)Refutation not found, incomplete strategy
% 0.15/0.40 % (10148)------------------------------
% 0.15/0.40 % (10148)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (10148)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.40
% 0.15/0.40
% 0.15/0.40 % (10148)Memory used [KB]: 6140
% 0.15/0.40 % (10148)Time elapsed: 0.018 s
% 0.15/0.40 % (10148)Instructions burned: 26 (million)
% 0.15/0.40 % (10148)------------------------------
% 0.15/0.40 % (10148)------------------------------
% 0.15/0.40 % (10151)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 Vampire---4 for (2999ds/37Mi)
% 0.15/0.40 % (10152)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 Vampire---4 for (2999ds/15Mi)
% 0.15/0.41 % (10153)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.15/0.41 % (10153)Instruction limit reached!
% 0.15/0.41 % (10153)------------------------------
% 0.15/0.41 % (10153)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.41 % (10153)Termination reason: Unknown
% 0.15/0.41 % (10153)Termination phase: shuffling
% 0.15/0.41
% 0.15/0.41 % (10153)Memory used [KB]: 1279
% 0.15/0.41 % (10153)Time elapsed: 0.004 s
% 0.15/0.41 % (10153)Instructions burned: 4 (million)
% 0.15/0.41 % (10153)------------------------------
% 0.15/0.41 % (10153)------------------------------
% 0.15/0.41 % (10154)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 Vampire---4 for (2999ds/1041Mi)
% 0.15/0.41 % (10152)Instruction limit reached!
% 0.15/0.41 % (10152)------------------------------
% 0.15/0.41 % (10152)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.41 % (10152)Termination reason: Unknown
% 0.15/0.41 % (10152)Termination phase: Property scanning
% 0.15/0.41
% 0.15/0.41 % (10152)Memory used [KB]: 1663
% 0.15/0.41 % (10152)Time elapsed: 0.012 s
% 0.15/0.41 % (10152)Instructions burned: 16 (million)
% 0.15/0.41 % (10152)------------------------------
% 0.15/0.41 % (10152)------------------------------
% 0.15/0.42 % (10156)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on Vampire---4 for (2999ds/16Mi)
% 0.15/0.42 % (10155)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on Vampire---4 for (2999ds/7Mi)
% 0.15/0.42 % (10157)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 Vampire---4 for (2999ds/3Mi)
% 0.15/0.42 % (10157)Instruction limit reached!
% 0.15/0.42 % (10157)------------------------------
% 0.15/0.42 % (10157)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.42 % (10157)Termination reason: Unknown
% 0.15/0.42 % (10157)Termination phase: shuffling
% 0.15/0.42
% 0.15/0.42 % (10157)Memory used [KB]: 1279
% 0.15/0.42 % (10157)Time elapsed: 0.004 s
% 0.15/0.42 % (10157)Instructions burned: 3 (million)
% 0.15/0.42 % (10157)------------------------------
% 0.15/0.42 % (10157)------------------------------
% 0.15/0.42 % (10151)Instruction limit reached!
% 0.15/0.42 % (10151)------------------------------
% 0.15/0.42 % (10151)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.42 % (10151)Termination reason: Unknown
% 0.15/0.42 % (10151)Termination phase: Property scanning
% 0.15/0.42
% 0.15/0.42 % (10151)Memory used [KB]: 1791
% 0.15/0.42 % (10151)Time elapsed: 0.020 s
% 0.15/0.42 % (10151)Instructions burned: 38 (million)
% 0.15/0.42 % (10151)------------------------------
% 0.15/0.42 % (10151)------------------------------
% 0.15/0.42 % (10155)Instruction limit reached!
% 0.15/0.42 % (10155)------------------------------
% 0.15/0.42 % (10155)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.42 % (10155)Termination reason: Unknown
% 0.15/0.42 % (10155)Termination phase: shuffling
% 0.15/0.42
% 0.15/0.42 % (10155)Memory used [KB]: 1407
% 0.15/0.42 % (10155)Time elapsed: 0.006 s
% 0.15/0.42 % (10155)Instructions burned: 8 (million)
% 0.15/0.42 % (10155)------------------------------
% 0.15/0.42 % (10155)------------------------------
% 0.21/0.42 % (10156)Instruction limit reached!
% 0.21/0.42 % (10156)------------------------------
% 0.21/0.42 % (10156)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (10156)Termination reason: Unknown
% 0.21/0.42 % (10156)Termination phase: shuffling
% 0.21/0.42
% 0.21/0.42 % (10156)Memory used [KB]: 1535
% 0.21/0.42 % (10156)Time elapsed: 0.010 s
% 0.21/0.42 % (10156)Instructions burned: 16 (million)
% 0.21/0.42 % (10156)------------------------------
% 0.21/0.42 % (10156)------------------------------
% 0.21/0.43 % (10158)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 Vampire---4 for (2999ds/3Mi)
% 0.21/0.43 % (10158)Instruction limit reached!
% 0.21/0.43 % (10158)------------------------------
% 0.21/0.43 % (10158)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43 % (10158)Termination reason: Unknown
% 0.21/0.43 % (10158)Termination phase: shuffling
% 0.21/0.43
% 0.21/0.43 % (10158)Memory used [KB]: 1279
% 0.21/0.43 % (10158)Time elapsed: 0.004 s
% 0.21/0.43 % (10158)Instructions burned: 5 (million)
% 0.21/0.43 % (10158)------------------------------
% 0.21/0.43 % (10158)------------------------------
% 0.21/0.43 % (10159)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on Vampire---4 for (2999ds/7Mi)
% 0.21/0.43 % (10159)Instruction limit reached!
% 0.21/0.43 % (10159)------------------------------
% 0.21/0.43 % (10159)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43 % (10159)Termination reason: Unknown
% 0.21/0.43 % (10159)Termination phase: shuffling
% 0.21/0.43
% 0.21/0.43 % (10159)Memory used [KB]: 1407
% 0.21/0.43 % (10159)Time elapsed: 0.006 s
% 0.21/0.43 % (10159)Instructions burned: 8 (million)
% 0.21/0.43 % (10159)------------------------------
% 0.21/0.43 % (10159)------------------------------
% 0.21/0.43 % (10160)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.21/0.44 % (10162)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.21/0.44 % (10160)Instruction limit reached!
% 0.21/0.44 % (10160)------------------------------
% 0.21/0.44 % (10160)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.44 % (10160)Termination reason: Unknown
% 0.21/0.44 % (10160)Termination phase: shuffling
% 0.21/0.44
% 0.21/0.44 % (10160)Memory used [KB]: 1279
% 0.21/0.44 % (10160)Time elapsed: 0.004 s
% 0.21/0.44 % (10160)Instructions burned: 4 (million)
% 0.21/0.44 % (10160)------------------------------
% 0.21/0.44 % (10160)------------------------------
% 0.21/0.44 % (10161)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on Vampire---4 for (2999ds/4Mi)
% 0.21/0.44 % (10163)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on Vampire---4 for (2999ds/710Mi)
% 0.21/0.44 % (10161)Instruction limit reached!
% 0.21/0.44 % (10161)------------------------------
% 0.21/0.44 % (10161)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.44 % (10161)Termination reason: Unknown
% 0.21/0.44 % (10161)Termination phase: shuffling
% 0.21/0.44
% 0.21/0.44 % (10161)Memory used [KB]: 1279
% 0.21/0.44 % (10161)Time elapsed: 0.004 s
% 0.21/0.44 % (10161)Instructions burned: 4 (million)
% 0.21/0.44 % (10161)------------------------------
% 0.21/0.44 % (10161)------------------------------
% 0.21/0.44 % (10164)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on Vampire---4 for (2999ds/6Mi)
% 0.21/0.44 % (10162)Instruction limit reached!
% 0.21/0.44 % (10162)------------------------------
% 0.21/0.44 % (10162)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.44 % (10162)Termination reason: Unknown
% 0.21/0.44 % (10162)Termination phase: shuffling
% 0.21/0.44
% 0.21/0.44 % (10162)Memory used [KB]: 1663
% 0.21/0.44 % (10162)Time elapsed: 0.011 s
% 0.21/0.44 % (10162)Instructions burned: 18 (million)
% 0.21/0.44 % (10162)------------------------------
% 0.21/0.44 % (10162)------------------------------
% 0.21/0.45 % (10164)Instruction limit reached!
% 0.21/0.45 % (10164)------------------------------
% 0.21/0.45 % (10164)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.45 % (10164)Termination reason: Unknown
% 0.21/0.45 % (10164)Termination phase: shuffling
% 0.21/0.45
% 0.21/0.45 % (10164)Memory used [KB]: 1279
% 0.21/0.45 % (10164)Time elapsed: 0.005 s
% 0.21/0.45 % (10164)Instructions burned: 6 (million)
% 0.21/0.45 % (10164)------------------------------
% 0.21/0.45 % (10164)------------------------------
% 0.21/0.45 % (10165)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on Vampire---4 for (2999ds/902Mi)
% 0.21/0.45 % (10166)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on Vampire---4 for (2999ds/21Mi)
% 0.21/0.45 % (10163)Refutation not found, incomplete strategy
% 0.21/0.45 % (10163)------------------------------
% 0.21/0.45 % (10163)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.45 % (10163)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.45
% 0.21/0.45
% 0.21/0.45 % (10163)Memory used [KB]: 6140
% 0.21/0.45 % (10163)Time elapsed: 0.017 s
% 0.21/0.45 % (10163)Instructions burned: 26 (million)
% 0.21/0.45 % (10163)------------------------------
% 0.21/0.45 % (10163)------------------------------
% 0.21/0.45 % (10167)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on Vampire---4 for (2999ds/5Mi)
% 0.21/0.46 % (10167)Instruction limit reached!
% 0.21/0.46 % (10167)------------------------------
% 0.21/0.46 % (10167)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.46 % (10167)Termination reason: Unknown
% 0.21/0.46 % (10167)Termination phase: shuffling
% 0.21/0.46
% 0.21/0.46 % (10167)Memory used [KB]: 1279
% 0.21/0.46 % (10167)Time elapsed: 0.005 s
% 0.21/0.46 % (10167)Instructions burned: 6 (million)
% 0.21/0.46 % (10167)------------------------------
% 0.21/0.46 % (10167)------------------------------
% 0.21/0.46 % (10169)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on Vampire---4 for (2999ds/377Mi)
% 0.21/0.46 % (10168)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on Vampire---4 for (2999ds/6Mi)
% 0.21/0.47 % (10168)Instruction limit reached!
% 0.21/0.47 % (10168)------------------------------
% 0.21/0.47 % (10168)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.47 % (10168)Termination reason: Unknown
% 0.21/0.47 % (10168)Termination phase: shuffling
% 0.21/0.47
% 0.21/0.47 % (10168)Memory used [KB]: 1407
% 0.21/0.47 % (10168)Time elapsed: 0.007 s
% 0.21/0.47 % (10168)Instructions burned: 7 (million)
% 0.21/0.47 % (10168)------------------------------
% 0.21/0.47 % (10168)------------------------------
% 0.21/0.47 % (10166)Instruction limit reached!
% 0.21/0.47 % (10166)------------------------------
% 0.21/0.47 % (10166)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.47 % (10166)Termination reason: Unknown
% 0.21/0.47 % (10166)Termination phase: shuffling
% 0.21/0.47
% 0.21/0.47 % (10166)Memory used [KB]: 1663
% 0.21/0.47 % (10166)Time elapsed: 0.019 s
% 0.21/0.47 % (10166)Instructions burned: 21 (million)
% 0.21/0.47 % (10166)------------------------------
% 0.21/0.47 % (10166)------------------------------
% 0.21/0.47 % (10170)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on Vampire---4 for (2999ds/779Mi)
% 0.21/0.47 % (10171)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on Vampire---4 for (2999ds/19Mi)
% 0.21/0.47 % (10143)Instruction limit reached!
% 0.21/0.47 % (10143)------------------------------
% 0.21/0.47 % (10143)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.47 % (10143)Termination reason: Unknown
% 0.21/0.47 % (10143)Termination phase: Saturation
% 0.21/0.47
% 0.21/0.47 % (10143)Memory used [KB]: 7419
% 0.21/0.47 % (10143)Time elapsed: 0.088 s
% 0.21/0.47 % (10143)Instructions burned: 183 (million)
% 0.21/0.47 % (10143)------------------------------
% 0.21/0.47 % (10143)------------------------------
% 0.21/0.48 % (10171)Instruction limit reached!
% 0.21/0.48 % (10171)------------------------------
% 0.21/0.48 % (10171)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.48 % (10171)Termination reason: Unknown
% 0.21/0.48 % (10171)Termination phase: shuffling
% 0.21/0.48
% 0.21/0.48 % (10171)Memory used [KB]: 1663
% 0.21/0.48 % (10171)Time elapsed: 0.010 s
% 0.21/0.48 % (10171)Instructions burned: 21 (million)
% 0.21/0.48 % (10171)------------------------------
% 0.21/0.48 % (10171)------------------------------
% 0.21/0.48 % (10173)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on Vampire---4 for (2998ds/17Mi)
% 0.21/0.48 % (10174)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2998ds/3Mi)
% 0.21/0.48 % (10172)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on Vampire---4 for (2998ds/879Mi)
% 0.21/0.49 % (10174)Instruction limit reached!
% 0.21/0.49 % (10174)------------------------------
% 0.21/0.49 % (10174)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.49 % (10174)Termination reason: Unknown
% 0.21/0.49 % (10174)Termination phase: shuffling
% 0.21/0.49
% 0.21/0.49 % (10174)Memory used [KB]: 1279
% 0.21/0.49 % (10174)Time elapsed: 0.003 s
% 0.21/0.49 % (10174)Instructions burned: 5 (million)
% 0.21/0.49 % (10174)------------------------------
% 0.21/0.49 % (10174)------------------------------
% 0.21/0.49 % (10175)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on Vampire---4 for (2998ds/30Mi)
% 0.21/0.49 % (10173)Instruction limit reached!
% 0.21/0.49 % (10173)------------------------------
% 0.21/0.49 % (10173)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.49 % (10173)Termination reason: Unknown
% 0.21/0.49 % (10173)Termination phase: shuffling
% 0.21/0.49
% 0.21/0.49 % (10173)Memory used [KB]: 1535
% 0.21/0.49 % (10173)Time elapsed: 0.007 s
% 0.21/0.49 % (10173)Instructions burned: 17 (million)
% 0.21/0.49 % (10173)------------------------------
% 0.21/0.49 % (10173)------------------------------
% 0.21/0.49 % (10176)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on Vampire---4 for (2998ds/127Mi)
% 0.21/0.50 % (10175)Instruction limit reached!
% 0.21/0.50 % (10175)------------------------------
% 0.21/0.50 % (10175)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.50 % (10175)Termination reason: Unknown
% 0.21/0.50 % (10175)Termination phase: Property scanning
% 0.21/0.50
% 0.21/0.50 % (10175)Memory used [KB]: 1791
% 0.21/0.50 % (10175)Time elapsed: 0.010 s
% 0.21/0.50 % (10175)Instructions burned: 32 (million)
% 0.21/0.50 % (10175)------------------------------
% 0.21/0.50 % (10175)------------------------------
% 0.21/0.50 % (10172)Refutation not found, incomplete strategy
% 0.21/0.50 % (10172)------------------------------
% 0.21/0.50 % (10172)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.50 % (10172)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.50
% 0.21/0.50
% 0.21/0.50 % (10172)Memory used [KB]: 6268
% 0.21/0.50 % (10172)Time elapsed: 0.017 s
% 0.21/0.50 % (10172)Instructions burned: 56 (million)
% 0.21/0.50 % (10172)------------------------------
% 0.21/0.50 % (10172)------------------------------
% 0.21/0.50 % (10177)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on Vampire---4 for (2998ds/100Mi)
% 0.21/0.50 % (10178)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2998ds/3Mi)
% 0.21/0.51 % (10178)Instruction limit reached!
% 0.21/0.51 % (10178)------------------------------
% 0.21/0.51 % (10178)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.51 % (10178)Termination reason: Unknown
% 0.21/0.51 % (10178)Termination phase: shuffling
% 0.21/0.51
% 0.21/0.51 % (10178)Memory used [KB]: 1279
% 0.21/0.51 % (10178)Time elapsed: 0.002 s
% 0.21/0.51 % (10178)Instructions burned: 3 (million)
% 0.21/0.51 % (10178)------------------------------
% 0.21/0.51 % (10178)------------------------------
% 0.21/0.51 % (10179)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on Vampire---4 for (2998ds/20Mi)
% 0.21/0.51 % (10180)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on Vampire---4 for (2998ds/86Mi)
% 0.21/0.52 % (10179)Instruction limit reached!
% 0.21/0.52 % (10179)------------------------------
% 0.21/0.52 % (10179)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.52 % (10179)Termination reason: Unknown
% 0.21/0.52 % (10179)Termination phase: Property scanning
% 0.21/0.52
% 0.21/0.52 % (10179)Memory used [KB]: 1663
% 0.21/0.52 % (10179)Time elapsed: 0.008 s
% 0.21/0.52 % (10179)Instructions burned: 21 (million)
% 0.21/0.52 % (10179)------------------------------
% 0.21/0.52 % (10179)------------------------------
% 0.21/0.52 % (10169)First to succeed.
% 0.21/0.53 % (10169)Refutation found. Thanks to Tanya!
% 0.21/0.53 % SZS status Theorem for Vampire---4
% 0.21/0.53 % SZS output start Proof for Vampire---4
% See solution above
% 0.21/0.53 % (10169)------------------------------
% 0.21/0.53 % (10169)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.53 % (10169)Termination reason: Refutation
% 0.21/0.53
% 0.21/0.53 % (10169)Memory used [KB]: 7036
% 0.21/0.53 % (10169)Time elapsed: 0.067 s
% 0.21/0.53 % (10169)Instructions burned: 182 (million)
% 0.21/0.53 % (10169)------------------------------
% 0.21/0.53 % (10169)------------------------------
% 0.21/0.53 % (10142)Success in time 0.16 s
% 0.21/0.53 % Vampire---4.8 exiting
%------------------------------------------------------------------------------