TSTP Solution File: ALG254^2 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : ALG254^2 : 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n016.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 04:13:11 EDT 2024
% Result : Theorem 0.20s 0.43s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 32
% Syntax : Number of formulae : 99 ( 47 unt; 23 typ; 0 def)
% Number of atoms : 409 ( 190 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 897 ( 22 ~; 37 |; 19 &; 692 @)
% ( 3 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 33 ( 33 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 27 usr; 19 con; 0-4 aty)
% ( 103 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 154 ( 113 ^ 41 !; 0 ?; 154 :)
% 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_141,type,
sK1: subst ).
thf(func_def_142,type,
sK2: subst ).
thf(func_def_143,type,
sK3: subst ).
thf(func_def_144,type,
sK4: subst ).
thf(func_def_145,type,
sK5: subst ).
thf(f576,plain,
$false,
inference(avatar_sat_refutation,[],[f569,f571,f573,f575]) ).
thf(f575,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f574]) ).
thf(f574,plain,
( $false
| spl0_3 ),
inference(subsumption_resolution,[],[f568,f527]) ).
thf(f527,plain,
! [X1: subst] :
( ( comp @ id @ X1 )
= X1 ),
inference(equality_proxy_clausification,[],[f526]) ).
thf(f526,plain,
! [X1: subst] :
( ( ( comp @ id @ X1 )
= X1 )
= $true ),
inference(beta_eta_normalization,[],[f525]) ).
thf(f525,plain,
! [X1: subst] :
( $true
= ( ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 )
@ X1 ) ),
inference(pi_clausification,[],[f524]) ).
thf(f524,plain,
( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) ),
inference(binary_proxy_clausification,[],[f522]) ).
thf(f522,plain,
( $true
!= ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) )
= ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f435,f509]) ).
thf(f509,plain,
( substmonoid_lthm
= ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) )
= ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f369,f393,f384,f418,f414]) ).
thf(f414,plain,
( substmonoid
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) ) ),
inference(cnf_transformation,[],[f161]) ).
thf(f161,plain,
( substmonoid
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) ) ),
inference(fool_elimination,[],[f160]) ).
thf(f160,plain,
( ( substmonoid
= ( ! [X0: subst] :
( ( comp @ id @ X0 )
= X0 ) ) )
& ! [X1: subst] :
( ( comp @ X1 @ id )
= X1 )
& ! [X2: subst,X3: subst,X4: subst] :
( ( comp @ ( comp @ X2 @ X3 ) @ X4 )
= ( comp @ X2 @ ( comp @ X3 @ X4 ) ) ) ),
inference(rectify,[],[f49]) ).
thf(f49,axiom,
( ( substmonoid
= ( ! [X2: subst] :
( ( comp @ id @ X2 )
= X2 ) ) )
& ! [X2: subst] :
( ( comp @ X2 @ id )
= X2 )
& ! [X2: subst,X3: subst,X4: subst] :
( ( comp @ ( comp @ X2 @ X3 ) @ X4 )
= ( comp @ X2 @ ( comp @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ToSfWgMJvw/Vampire---4.8_25659',substmonoid) ).
thf(f418,plain,
( axidr
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) ),
inference(cnf_transformation,[],[f139]) ).
thf(f139,plain,
( axidr
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) ),
inference(fool_elimination,[],[f138]) ).
thf(f138,plain,
( axidr
= ( ! [X0: subst] :
( ( comp @ X0 @ id )
= X0 ) ) ),
inference(rectify,[],[f10]) ).
thf(f10,axiom,
( axidr
= ( ! [X2: subst] :
( ( comp @ X2 @ id )
= X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ToSfWgMJvw/Vampire---4.8_25659',axidr) ).
thf(f384,plain,
( axassoc
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) )
= ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f220]) ).
thf(f220,plain,
( axassoc
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) )
= ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f219]) ).
thf(f219,plain,
! [X0: subst,X1: subst,X2: subst] :
( ( ( comp @ X1 @ ( comp @ X0 @ X2 ) )
= ( comp @ ( comp @ X1 @ X0 ) @ X2 ) )
= axassoc ),
inference(rectify,[],[f8]) ).
thf(f8,axiom,
! [X3: subst,X2: subst,X4: subst] :
( ( ( comp @ ( comp @ X2 @ X3 ) @ X4 )
= ( comp @ X2 @ ( comp @ X3 @ X4 ) ) )
= axassoc ),
file('/export/starexec/sandbox/tmp/tmp.ToSfWgMJvw/Vampire---4.8_25659',axassoc) ).
thf(f393,plain,
( axidl
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) ),
inference(cnf_transformation,[],[f290]) ).
thf(f290,plain,
( axidl
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) ),
inference(fool_elimination,[],[f289]) ).
thf(f289,plain,
( axidl
= ( ! [X0: subst] :
( ( comp @ id @ X0 )
= X0 ) ) ),
inference(rectify,[],[f6]) ).
thf(f6,axiom,
( axidl
= ( ! [X2: subst] :
( ( comp @ id @ X2 )
= X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ToSfWgMJvw/Vampire---4.8_25659',axidl) ).
thf(f369,plain,
( substmonoid_lthm
= ( axidl
=> ( axassoc
=> ( axidr
=> substmonoid ) ) ) ),
inference(cnf_transformation,[],[f153]) ).
thf(f153,plain,
( substmonoid_lthm
= ( axidl
=> ( axassoc
=> ( axidr
=> substmonoid ) ) ) ),
inference(fool_elimination,[],[f152]) ).
thf(f152,plain,
( ( substmonoid_lthm = axidl )
=> ( axassoc
=> ( axidr
=> substmonoid ) ) ),
inference(rectify,[],[f51]) ).
thf(f51,axiom,
( ( substmonoid_lthm = axidl )
=> ( axassoc
=> ( axidr
=> substmonoid ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ToSfWgMJvw/Vampire---4.8_25659',substmonoid_lthm) ).
thf(f435,plain,
substmonoid_lthm != $true,
inference(cnf_transformation,[],[f330]) ).
thf(f330,plain,
substmonoid_lthm != $true,
inference(flattening,[],[f284]) ).
thf(f284,plain,
substmonoid_lthm != $true,
inference(fool_elimination,[],[f283]) ).
thf(f283,plain,
~ substmonoid_lthm,
inference(rectify,[],[f115]) ).
thf(f115,negated_conjecture,
~ substmonoid_lthm,
inference(negated_conjecture,[],[f114]) ).
thf(f114,conjecture,
substmonoid_lthm,
file('/export/starexec/sandbox/tmp/tmp.ToSfWgMJvw/Vampire---4.8_25659',thm) ).
thf(f568,plain,
( ( ( comp @ id @ sK3 )
!= sK3 )
| spl0_3 ),
inference(avatar_component_clause,[],[f566]) ).
thf(f566,plain,
( spl0_3
<=> ( ( comp @ id @ sK3 )
= sK3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
thf(f573,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f572]) ).
thf(f572,plain,
( $false
| spl0_2 ),
inference(subsumption_resolution,[],[f564,f536]) ).
thf(f536,plain,
! [X2: subst,X3: subst,X1: subst] :
( ( comp @ X2 @ ( comp @ X3 @ X1 ) )
= ( comp @ ( comp @ X2 @ X3 ) @ X1 ) ),
inference(equality_proxy_clausification,[],[f535]) ).
thf(f535,plain,
! [X2: subst,X3: subst,X1: subst] :
( $true
= ( ( comp @ X2 @ ( comp @ X3 @ X1 ) )
= ( comp @ ( comp @ X2 @ X3 ) @ X1 ) ) ),
inference(beta_eta_normalization,[],[f534]) ).
thf(f534,plain,
! [X2: subst,X3: subst,X1: subst] :
( ( ^ [Y0: subst] :
( ( comp @ X2 @ ( comp @ Y0 @ X1 ) )
= ( comp @ ( comp @ X2 @ Y0 ) @ X1 ) )
@ X3 )
= $true ),
inference(pi_clausification,[],[f533]) ).
thf(f533,plain,
! [X2: subst,X1: subst] :
( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ X2 @ ( comp @ Y0 @ X1 ) )
= ( comp @ ( comp @ X2 @ Y0 ) @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[],[f532]) ).
thf(f532,plain,
! [X2: subst,X1: subst] :
( $true
= ( ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ Y0 @ ( comp @ Y1 @ X1 ) )
= ( comp @ ( comp @ Y0 @ Y1 ) @ X1 ) ) )
@ X2 ) ),
inference(pi_clausification,[],[f531]) ).
thf(f531,plain,
! [X1: subst] :
( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ Y0 @ ( comp @ Y1 @ X1 ) )
= ( comp @ ( comp @ Y0 @ Y1 ) @ X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[],[f530]) ).
thf(f530,plain,
! [X1: subst] :
( ( ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) )
= ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[],[f529]) ).
thf(f529,plain,
( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) )
= ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f523]) ).
thf(f523,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) )
= ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f522]) ).
thf(f564,plain,
( ( ( comp @ sK5 @ ( comp @ sK4 @ sK1 ) )
!= ( comp @ ( comp @ sK5 @ sK4 ) @ sK1 ) )
| spl0_2 ),
inference(avatar_component_clause,[],[f562]) ).
thf(f562,plain,
( spl0_2
<=> ( ( comp @ sK5 @ ( comp @ sK4 @ sK1 ) )
= ( comp @ ( comp @ sK5 @ sK4 ) @ sK1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f571,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f570]) ).
thf(f570,plain,
( $false
| spl0_1 ),
inference(subsumption_resolution,[],[f560,f541]) ).
thf(f541,plain,
! [X1: subst] :
( ( comp @ X1 @ id )
= X1 ),
inference(equality_proxy_clausification,[],[f540]) ).
thf(f540,plain,
! [X1: subst] :
( $true
= ( ( comp @ X1 @ id )
= X1 ) ),
inference(beta_eta_normalization,[],[f539]) ).
thf(f539,plain,
! [X1: subst] :
( $true
= ( ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 )
@ X1 ) ),
inference(pi_clausification,[],[f538]) ).
thf(f538,plain,
( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) ),
inference(binary_proxy_clausification,[],[f528]) ).
thf(f528,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f523]) ).
thf(f560,plain,
( ( ( comp @ sK2 @ id )
!= sK2 )
| spl0_1 ),
inference(avatar_component_clause,[],[f558]) ).
thf(f558,plain,
( spl0_1
<=> ( ( comp @ sK2 @ id )
= sK2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f569,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f556,f566,f562,f558]) ).
thf(f556,plain,
( ( ( comp @ sK5 @ ( comp @ sK4 @ sK1 ) )
!= ( comp @ ( comp @ sK5 @ sK4 ) @ sK1 ) )
| ( ( comp @ id @ sK3 )
!= sK3 )
| ( ( comp @ sK2 @ id )
!= sK2 ) ),
inference(equality_proxy_clausification,[],[f555]) ).
thf(f555,plain,
( ( ( comp @ sK2 @ id )
!= sK2 )
| ( ( comp @ id @ sK3 )
!= sK3 )
| ( $false
= ( ( comp @ ( comp @ sK5 @ sK4 ) @ sK1 )
= ( comp @ sK5 @ ( comp @ sK4 @ sK1 ) ) ) ) ),
inference(equality_proxy_clausification,[],[f554]) ).
thf(f554,plain,
( ( ( comp @ id @ sK3 )
!= sK3 )
| ( ( ( comp @ sK2 @ id )
= sK2 )
= $false )
| ( $false
= ( ( comp @ ( comp @ sK5 @ sK4 ) @ sK1 )
= ( comp @ sK5 @ ( comp @ sK4 @ sK1 ) ) ) ) ),
inference(beta_eta_normalization,[],[f553]) ).
thf(f553,plain,
( ( ( ^ [Y0: subst] :
( ( comp @ ( comp @ Y0 @ sK4 ) @ sK1 )
= ( comp @ Y0 @ ( comp @ sK4 @ sK1 ) ) )
@ sK5 )
= $false )
| ( ( ( comp @ sK2 @ id )
= sK2 )
= $false )
| ( ( comp @ id @ sK3 )
!= sK3 ) ),
inference(sigma_clausification,[],[f552]) ).
thf(f552,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ ( comp @ Y0 @ sK4 ) @ sK1 )
= ( comp @ Y0 @ ( comp @ sK4 @ sK1 ) ) ) )
= $false )
| ( ( comp @ id @ sK3 )
!= sK3 )
| ( ( ( comp @ sK2 @ id )
= sK2 )
= $false ) ),
inference(beta_eta_normalization,[],[f551]) ).
thf(f551,plain,
( ( ( ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ ( comp @ Y1 @ Y0 ) @ sK1 )
= ( comp @ Y1 @ ( comp @ Y0 @ sK1 ) ) ) )
@ sK4 )
= $false )
| ( ( comp @ id @ sK3 )
!= sK3 )
| ( ( ( comp @ sK2 @ id )
= sK2 )
= $false ) ),
inference(sigma_clausification,[],[f550]) ).
thf(f550,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ ( comp @ Y1 @ Y0 ) @ sK1 )
= ( comp @ Y1 @ ( comp @ Y0 @ sK1 ) ) ) ) )
= $false )
| ( ( comp @ id @ sK3 )
!= sK3 )
| ( ( ( comp @ sK2 @ id )
= sK2 )
= $false ) ),
inference(equality_proxy_clausification,[],[f549]) ).
thf(f549,plain,
( ( ( ( comp @ id @ sK3 )
= sK3 )
= $false )
| ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ ( comp @ Y1 @ Y0 ) @ sK1 )
= ( comp @ Y1 @ ( comp @ Y0 @ sK1 ) ) ) ) )
= $false )
| ( ( ( comp @ sK2 @ id )
= sK2 )
= $false ) ),
inference(beta_eta_normalization,[],[f548]) ).
thf(f548,plain,
( ( ( ( comp @ sK2 @ id )
= sK2 )
= $false )
| ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ ( comp @ Y1 @ Y0 ) @ sK1 )
= ( comp @ Y1 @ ( comp @ Y0 @ sK1 ) ) ) ) )
= $false )
| ( ( ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 )
@ sK3 )
= $false ) ),
inference(sigma_clausification,[],[f547]) ).
thf(f547,plain,
( ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
| ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ ( comp @ Y1 @ Y0 ) @ sK1 )
= ( comp @ Y1 @ ( comp @ Y0 @ sK1 ) ) ) ) )
= $false )
| ( ( ( comp @ sK2 @ id )
= sK2 )
= $false ) ),
inference(beta_eta_normalization,[],[f546]) ).
thf(f546,plain,
( ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
| ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ ( comp @ Y1 @ Y0 ) @ sK1 )
= ( comp @ Y1 @ ( comp @ Y0 @ sK1 ) ) ) ) )
= $false )
| ( ( ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 )
@ sK2 )
= $false ) ),
inference(sigma_clausification,[],[f545]) ).
thf(f545,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
= $false )
| ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
| ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ ( comp @ Y1 @ Y0 ) @ sK1 )
= ( comp @ Y1 @ ( comp @ Y0 @ sK1 ) ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[],[f544]) ).
thf(f544,plain,
( ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
| ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
= $false )
| ( ( ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) )
@ sK1 )
= $false ) ),
inference(sigma_clausification,[],[f543]) ).
thf(f543,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
| ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f542]) ).
thf(f542,plain,
( ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
= $false )
| ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) ) ),
inference(binary_proxy_clausification,[],[f537]) ).
thf(f537,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f528]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : ALG254^2 : TPTP v8.1.2. Bugfixed v5.2.0.
% 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 : n016.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 : Fri May 3 19:56:23 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 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/tmp/tmp.ToSfWgMJvw/Vampire---4.8_25659
% 0.14/0.38 % (25921)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)
% 0.14/0.39 % (25917)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)
% 0.14/0.39 % (25916)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)
% 0.14/0.39 % (25918)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)
% 0.14/0.39 % (25919)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.14/0.39 % (25920)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)
% 0.14/0.39 % (25922)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.14/0.39 % (25923)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)
% 0.14/0.39 % (25919)Instruction limit reached!
% 0.14/0.39 % (25919)------------------------------
% 0.14/0.39 % (25919)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (25919)Termination reason: Unknown
% 0.14/0.39 % (25919)Termination phase: shuffling
% 0.14/0.39
% 0.14/0.39 % (25919)Memory used [KB]: 1279
% 0.14/0.39 % (25919)Time elapsed: 0.004 s
% 0.14/0.39 % (25919)Instructions burned: 3 (million)
% 0.14/0.39 % (25919)------------------------------
% 0.14/0.39 % (25919)------------------------------
% 0.14/0.39 % (25920)Instruction limit reached!
% 0.14/0.39 % (25920)------------------------------
% 0.14/0.39 % (25920)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (25920)Termination reason: Unknown
% 0.14/0.39 % (25920)Termination phase: shuffling
% 0.14/0.39
% 0.14/0.39 % (25920)Memory used [KB]: 1279
% 0.14/0.39 % (25920)Time elapsed: 0.004 s
% 0.14/0.39 % (25920)Instructions burned: 3 (million)
% 0.14/0.39 % (25920)------------------------------
% 0.14/0.39 % (25920)------------------------------
% 0.14/0.39 % (25923)Instruction limit reached!
% 0.14/0.39 % (25923)------------------------------
% 0.14/0.39 % (25923)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (25923)Termination reason: Unknown
% 0.14/0.39 % (25923)Termination phase: shuffling
% 0.14/0.39
% 0.14/0.39 % (25923)Memory used [KB]: 1279
% 0.14/0.39 % (25923)Time elapsed: 0.004 s
% 0.14/0.39 % (25917)Instruction limit reached!
% 0.14/0.39 % (25917)------------------------------
% 0.14/0.39 % (25917)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (25917)Termination reason: Unknown
% 0.14/0.39 % (25917)Termination phase: shuffling
% 0.14/0.39
% 0.14/0.39 % (25917)Memory used [KB]: 1279
% 0.14/0.39 % (25917)Time elapsed: 0.005 s
% 0.14/0.39 % (25917)Instructions burned: 5 (million)
% 0.14/0.39 % (25917)------------------------------
% 0.14/0.39 % (25917)------------------------------
% 0.14/0.39 % (25923)Instructions burned: 3 (million)
% 0.14/0.39 % (25923)------------------------------
% 0.14/0.39 % (25923)------------------------------
% 0.14/0.40 % (25921)Refutation not found, incomplete strategy
% 0.14/0.40 % (25921)------------------------------
% 0.14/0.40 % (25921)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (25921)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.40
% 0.14/0.40
% 0.14/0.40 % (25921)Memory used [KB]: 6140
% 0.14/0.40 % (25921)Time elapsed: 0.014 s
% 0.14/0.40 % (25921)Instructions burned: 26 (million)
% 0.14/0.40 % (25921)------------------------------
% 0.14/0.40 % (25921)------------------------------
% 0.14/0.40 % (25922)Instruction limit reached!
% 0.14/0.40 % (25922)------------------------------
% 0.14/0.40 % (25922)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (25922)Termination reason: Unknown
% 0.14/0.40 % (25922)Termination phase: Property scanning
% 0.14/0.40
% 0.14/0.40 % (25922)Memory used [KB]: 1663
% 0.14/0.40 % (25922)Time elapsed: 0.013 s
% 0.14/0.40 % (25922)Instructions burned: 18 (million)
% 0.14/0.40 % (25922)------------------------------
% 0.14/0.40 % (25922)------------------------------
% 0.14/0.40 % (25918)Instruction limit reached!
% 0.14/0.40 % (25918)------------------------------
% 0.14/0.40 % (25918)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (25918)Termination reason: Unknown
% 0.14/0.40 % (25918)Termination phase: Property scanning
% 0.14/0.40
% 0.14/0.40 % (25918)Memory used [KB]: 1791
% 0.14/0.40 % (25918)Time elapsed: 0.016 s
% 0.14/0.40 % (25918)Instructions burned: 27 (million)
% 0.14/0.40 % (25918)------------------------------
% 0.14/0.40 % (25918)------------------------------
% 0.14/0.40 % (25924)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)
% 0.14/0.40 % (25925)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)
% 0.14/0.40 % (25926)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)
% 0.14/0.40 % (25927)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)
% 0.14/0.41 % (25926)Instruction limit reached!
% 0.14/0.41 % (25926)------------------------------
% 0.14/0.41 % (25926)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.41 % (25926)Termination reason: Unknown
% 0.14/0.41 % (25926)Termination phase: shuffling
% 0.14/0.41
% 0.14/0.41 % (25926)Memory used [KB]: 1279
% 0.14/0.41 % (25926)Time elapsed: 0.004 s
% 0.14/0.41 % (25926)Instructions burned: 4 (million)
% 0.14/0.41 % (25926)------------------------------
% 0.14/0.41 % (25926)------------------------------
% 0.14/0.41 % (25928)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)
% 0.14/0.41 % (25928)Instruction limit reached!
% 0.14/0.41 % (25928)------------------------------
% 0.14/0.41 % (25928)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.41 % (25928)Termination reason: Unknown
% 0.14/0.41 % (25928)Termination phase: shuffling
% 0.14/0.41
% 0.14/0.41 % (25928)Memory used [KB]: 1279
% 0.14/0.41 % (25928)Time elapsed: 0.004 s
% 0.14/0.41 % (25928)Instructions burned: 7 (million)
% 0.14/0.41 % (25928)------------------------------
% 0.14/0.41 % (25928)------------------------------
% 0.14/0.41 % (25929)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)
% 0.14/0.41 % (25925)Instruction limit reached!
% 0.14/0.41 % (25925)------------------------------
% 0.14/0.41 % (25925)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.41 % (25925)Termination reason: Unknown
% 0.14/0.41 % (25925)Termination phase: Property scanning
% 0.14/0.41
% 0.14/0.41 % (25925)Memory used [KB]: 1663
% 0.14/0.41 % (25925)Time elapsed: 0.012 s
% 0.14/0.41 % (25925)Instructions burned: 16 (million)
% 0.14/0.41 % (25925)------------------------------
% 0.14/0.41 % (25925)------------------------------
% 0.14/0.42 % (25930)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)
% 0.14/0.42 % (25930)Instruction limit reached!
% 0.14/0.42 % (25930)------------------------------
% 0.14/0.42 % (25930)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.42 % (25930)Termination reason: Unknown
% 0.14/0.42 % (25930)Termination phase: shuffling
% 0.14/0.42
% 0.14/0.42 % (25930)Memory used [KB]: 1279
% 0.14/0.42 % (25930)Time elapsed: 0.004 s
% 0.14/0.42 % (25930)Instructions burned: 4 (million)
% 0.14/0.42 % (25930)------------------------------
% 0.14/0.42 % (25930)------------------------------
% 0.14/0.42 % (25929)Instruction limit reached!
% 0.14/0.42 % (25929)------------------------------
% 0.14/0.42 % (25929)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.42 % (25929)Termination reason: Unknown
% 0.14/0.42 % (25929)Termination phase: shuffling
% 0.14/0.42
% 0.14/0.42 % (25929)Memory used [KB]: 1535
% 0.14/0.42 % (25929)Time elapsed: 0.010 s
% 0.14/0.42 % (25931)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)
% 0.14/0.42 % (25929)Instructions burned: 16 (million)
% 0.14/0.42 % (25929)------------------------------
% 0.14/0.42 % (25929)------------------------------
% 0.14/0.42 % (25924)Instruction limit reached!
% 0.14/0.42 % (25924)------------------------------
% 0.14/0.42 % (25924)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.42 % (25924)Termination reason: Unknown
% 0.14/0.42 % (25924)Termination phase: Property scanning
% 0.14/0.42
% 0.14/0.42 % (25924)Memory used [KB]: 1791
% 0.14/0.42 % (25924)Time elapsed: 0.020 s
% 0.14/0.42 % (25924)Instructions burned: 38 (million)
% 0.14/0.42 % (25924)------------------------------
% 0.14/0.42 % (25924)------------------------------
% 0.20/0.42 % (25931)Instruction limit reached!
% 0.20/0.42 % (25931)------------------------------
% 0.20/0.42 % (25931)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.42 % (25931)Termination reason: Unknown
% 0.20/0.42 % (25931)Termination phase: shuffling
% 0.20/0.42
% 0.20/0.42 % (25931)Memory used [KB]: 1279
% 0.20/0.42 % (25931)Time elapsed: 0.004 s
% 0.20/0.42 % (25931)Instructions burned: 4 (million)
% 0.20/0.42 % (25931)------------------------------
% 0.20/0.42 % (25931)------------------------------
% 0.20/0.42 % (25932)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)
% 0.20/0.43 % (25916)First to succeed.
% 0.20/0.43 % (25932)Instruction limit reached!
% 0.20/0.43 % (25932)------------------------------
% 0.20/0.43 % (25932)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.43 % (25932)Termination reason: Unknown
% 0.20/0.43 % (25932)Termination phase: shuffling
% 0.20/0.43
% 0.20/0.43 % (25932)Memory used [KB]: 1407
% 0.20/0.43 % (25932)Time elapsed: 0.004 s
% 0.20/0.43 % (25932)Instructions burned: 7 (million)
% 0.20/0.43 % (25932)------------------------------
% 0.20/0.43 % (25932)------------------------------
% 0.20/0.43 % (25933)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)
% 0.20/0.43 % (25933)Instruction limit reached!
% 0.20/0.43 % (25933)------------------------------
% 0.20/0.43 % (25933)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.43 % (25933)Termination reason: Unknown
% 0.20/0.43 % (25933)Termination phase: shuffling
% 0.20/0.43
% 0.20/0.43 % (25933)Memory used [KB]: 1279
% 0.20/0.43 % (25933)Time elapsed: 0.004 s
% 0.20/0.43 % (25933)Instructions burned: 4 (million)
% 0.20/0.43 % (25933)------------------------------
% 0.20/0.43 % (25933)------------------------------
% 0.20/0.43 % (25916)Refutation found. Thanks to Tanya!
% 0.20/0.43 % SZS status Theorem for Vampire---4
% 0.20/0.43 % SZS output start Proof for Vampire---4
% See solution above
% 0.20/0.43 % (25916)------------------------------
% 0.20/0.43 % (25916)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.43 % (25916)Termination reason: Refutation
% 0.20/0.43
% 0.20/0.43 % (25916)Memory used [KB]: 6524
% 0.20/0.43 % (25916)Time elapsed: 0.044 s
% 0.20/0.43 % (25916)Instructions burned: 87 (million)
% 0.20/0.43 % (25916)------------------------------
% 0.20/0.43 % (25916)------------------------------
% 0.20/0.43 % (25915)Success in time 0.07 s
% 0.20/0.43 % Vampire---4.8 exiting
%------------------------------------------------------------------------------