TSTP Solution File: ALG254^2 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : ALG254^2 : TPTP v8.2.0. 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 : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 18:20:13 EDT 2024
% Result : Theorem 0.24s 0.47s
% Output : Refutation 0.24s
% 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 : 406 ( 188 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 902 ( 24 ~; 37 |; 19 &; 694 @)
% ( 3 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 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)
% ( 104 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 155 ( 114 ^ 41 !; 0 ?; 155 :)
% 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_142,type,
sK1: subst ).
thf(func_def_143,type,
sK2: subst ).
thf(func_def_144,type,
sK3: subst ).
thf(func_def_145,type,
sK4: subst ).
thf(func_def_146,type,
sK5: subst ).
thf(f577,plain,
$false,
inference(avatar_sat_refutation,[],[f570,f572,f574,f576]) ).
thf(f576,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f575]) ).
thf(f575,plain,
( $false
| spl0_3 ),
inference(subsumption_resolution,[],[f569,f542]) ).
thf(f542,plain,
! [X1: subst] :
( ( comp @ X1 @ id )
= X1 ),
inference(equality_proxy_clausification,[],[f541]) ).
thf(f541,plain,
! [X1: subst] :
( ( ( comp @ X1 @ id )
= X1 )
= $true ),
inference(beta_eta_normalization,[],[f540]) ).
thf(f540,plain,
! [X1: subst] :
( ( ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 )
@ X1 )
= $true ),
inference(pi_clausification,[],[f539]) ).
thf(f539,plain,
( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
= $true ),
inference(binary_proxy_clausification,[],[f529]) ).
thf(f529,plain,
( $false
= ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f524]) ).
thf(f524,plain,
( $false
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f523]) ).
thf(f523,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f377,f510]) ).
thf(f510,plain,
( substmonoid_lthm
= ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f424,f440,f388,f390,f411]) ).
thf(f411,plain,
( substmonoid
= ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f250]) ).
thf(f250,plain,
( substmonoid
= ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f249]) ).
thf(f249,plain,
( ( substmonoid
= ( ! [X0: subst,X1: subst,X2: subst] :
( ( comp @ ( comp @ X1 @ X0 ) @ X2 )
= ( comp @ X1 @ ( comp @ X0 @ X2 ) ) ) ) )
& ! [X3: subst] :
( ( comp @ id @ X3 )
= X3 )
& ! [X4: subst] :
( ( comp @ X4 @ id )
= X4 ) ),
inference(rectify,[],[f49]) ).
thf(f49,axiom,
( ( substmonoid
= ( ! [X3: subst,X2: subst,X4: subst] :
( ( comp @ ( comp @ X2 @ X3 ) @ X4 )
= ( comp @ X2 @ ( comp @ X3 @ X4 ) ) ) ) )
& ! [X2: subst] :
( ( comp @ id @ X2 )
= X2 )
& ! [X2: subst] :
( ( comp @ X2 @ id )
= X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substmonoid) ).
thf(f390,plain,
( axidr
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) ),
inference(cnf_transformation,[],[f204]) ).
thf(f204,plain,
( axidr
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) ),
inference(fool_elimination,[],[f203]) ).
thf(f203,plain,
! [X0: subst] :
( ( ( comp @ X0 @ id )
= X0 )
= axidr ),
inference(rectify,[],[f10]) ).
thf(f10,axiom,
! [X2: subst] :
( ( ( comp @ X2 @ id )
= X2 )
= axidr ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axidr) ).
thf(f388,plain,
( axassoc
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f160]) ).
thf(f160,plain,
( axassoc
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f159]) ).
thf(f159,plain,
! [X0: subst,X1: subst,X2: subst] :
( ( ( comp @ ( comp @ X2 @ X1 ) @ X0 )
= ( comp @ X2 @ ( comp @ X1 @ X0 ) ) )
= axassoc ),
inference(rectify,[],[f8]) ).
thf(f8,axiom,
! [X4: subst,X3: subst,X2: subst] :
( ( ( comp @ ( comp @ X2 @ X3 ) @ X4 )
= ( comp @ X2 @ ( comp @ X3 @ X4 ) ) )
= axassoc ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axassoc) ).
thf(f440,plain,
( axidl
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) ),
inference(cnf_transformation,[],[f136]) ).
thf(f136,plain,
( axidl
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) ),
inference(fool_elimination,[],[f135]) ).
thf(f135,plain,
! [X0: subst] :
( ( ( comp @ id @ X0 )
= X0 )
= axidl ),
inference(rectify,[],[f6]) ).
thf(f6,axiom,
! [X2: subst] :
( ( ( comp @ id @ X2 )
= X2 )
= axidl ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axidl) ).
thf(f424,plain,
( substmonoid_lthm
= ( axidl
=> ( axassoc
=> ( axidr
=> substmonoid ) ) ) ),
inference(cnf_transformation,[],[f222]) ).
thf(f222,plain,
( substmonoid_lthm
= ( axidl
=> ( axassoc
=> ( axidr
=> substmonoid ) ) ) ),
inference(fool_elimination,[],[f221]) ).
thf(f221,plain,
( ( substmonoid_lthm = axidl )
=> ( axassoc
=> ( axidr
=> substmonoid ) ) ),
inference(rectify,[],[f51]) ).
thf(f51,axiom,
( ( substmonoid_lthm = axidl )
=> ( axassoc
=> ( axidr
=> substmonoid ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substmonoid_lthm) ).
thf(f377,plain,
substmonoid_lthm != $true,
inference(cnf_transformation,[],[f331]) ).
thf(f331,plain,
substmonoid_lthm != $true,
inference(flattening,[],[f244]) ).
thf(f244,plain,
substmonoid_lthm != $true,
inference(fool_elimination,[],[f243]) ).
thf(f243,plain,
~ substmonoid_lthm,
inference(rectify,[],[f115]) ).
thf(f115,negated_conjecture,
~ substmonoid_lthm,
inference(negated_conjecture,[],[f114]) ).
thf(f114,conjecture,
substmonoid_lthm,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(f569,plain,
( ( ( comp @ sK5 @ id )
!= sK5 )
| spl0_3 ),
inference(avatar_component_clause,[],[f567]) ).
thf(f567,plain,
( spl0_3
<=> ( ( comp @ sK5 @ id )
= sK5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
thf(f574,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f573]) ).
thf(f573,plain,
( $false
| spl0_2 ),
inference(subsumption_resolution,[],[f565,f537]) ).
thf(f537,plain,
! [X2: subst,X3: subst,X1: subst] :
( ( comp @ X1 @ ( comp @ X2 @ X3 ) )
= ( comp @ ( comp @ X1 @ X2 ) @ X3 ) ),
inference(equality_proxy_clausification,[],[f536]) ).
thf(f536,plain,
! [X2: subst,X3: subst,X1: subst] :
( ( ( comp @ ( comp @ X1 @ X2 ) @ X3 )
= ( comp @ X1 @ ( comp @ X2 @ X3 ) ) )
= $true ),
inference(beta_eta_normalization,[],[f535]) ).
thf(f535,plain,
! [X2: subst,X3: subst,X1: subst] :
( ( ^ [Y0: subst] :
( ( comp @ ( comp @ X1 @ X2 ) @ Y0 )
= ( comp @ X1 @ ( comp @ X2 @ Y0 ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[],[f534]) ).
thf(f534,plain,
! [X2: subst,X1: subst] :
( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ ( comp @ X1 @ X2 ) @ Y0 )
= ( comp @ X1 @ ( comp @ X2 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[],[f533]) ).
thf(f533,plain,
! [X2: subst,X1: subst] :
( ( ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ ( comp @ X1 @ Y0 ) @ Y1 )
= ( comp @ X1 @ ( comp @ Y0 @ Y1 ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[],[f532]) ).
thf(f532,plain,
! [X1: subst] :
( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ ( comp @ X1 @ Y0 ) @ Y1 )
= ( comp @ X1 @ ( comp @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[],[f531]) ).
thf(f531,plain,
! [X1: subst] :
( ( ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[],[f530]) ).
thf(f530,plain,
( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f524]) ).
thf(f565,plain,
( ( ( comp @ ( comp @ sK3 @ sK4 ) @ sK2 )
!= ( comp @ sK3 @ ( comp @ sK4 @ sK2 ) ) )
| spl0_2 ),
inference(avatar_component_clause,[],[f563]) ).
thf(f563,plain,
( spl0_2
<=> ( ( comp @ ( comp @ sK3 @ sK4 ) @ sK2 )
= ( comp @ sK3 @ ( comp @ sK4 @ sK2 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f572,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f571]) ).
thf(f571,plain,
( $false
| spl0_1 ),
inference(subsumption_resolution,[],[f561,f528]) ).
thf(f528,plain,
! [X1: subst] :
( ( comp @ id @ X1 )
= X1 ),
inference(equality_proxy_clausification,[],[f527]) ).
thf(f527,plain,
! [X1: subst] :
( ( ( comp @ id @ X1 )
= X1 )
= $true ),
inference(beta_eta_normalization,[],[f526]) ).
thf(f526,plain,
! [X1: subst] :
( ( ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 )
@ X1 )
= $true ),
inference(pi_clausification,[],[f525]) ).
thf(f525,plain,
( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
= $true ),
inference(binary_proxy_clausification,[],[f523]) ).
thf(f561,plain,
( ( sK1
!= ( comp @ id @ sK1 ) )
| spl0_1 ),
inference(avatar_component_clause,[],[f559]) ).
thf(f559,plain,
( spl0_1
<=> ( sK1
= ( comp @ id @ sK1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f570,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f557,f567,f563,f559]) ).
thf(f557,plain,
( ( ( comp @ ( comp @ sK3 @ sK4 ) @ sK2 )
!= ( comp @ sK3 @ ( comp @ sK4 @ sK2 ) ) )
| ( ( comp @ sK5 @ id )
!= sK5 )
| ( sK1
!= ( comp @ id @ sK1 ) ) ),
inference(equality_proxy_clausification,[],[f556]) ).
thf(f556,plain,
( ( sK1
!= ( comp @ id @ sK1 ) )
| ( $false
= ( ( comp @ sK5 @ id )
= sK5 ) )
| ( ( comp @ ( comp @ sK3 @ sK4 ) @ sK2 )
!= ( comp @ sK3 @ ( comp @ sK4 @ sK2 ) ) ) ),
inference(equality_proxy_clausification,[],[f555]) ).
thf(f555,plain,
( ( $false
= ( ( comp @ ( comp @ sK3 @ sK4 ) @ sK2 )
= ( comp @ sK3 @ ( comp @ sK4 @ sK2 ) ) ) )
| ( sK1
!= ( comp @ id @ sK1 ) )
| ( $false
= ( ( comp @ sK5 @ id )
= sK5 ) ) ),
inference(beta_eta_normalization,[],[f554]) ).
thf(f554,plain,
( ( $false
= ( ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 )
@ sK5 ) )
| ( sK1
!= ( comp @ id @ sK1 ) )
| ( $false
= ( ( comp @ ( comp @ sK3 @ sK4 ) @ sK2 )
= ( comp @ sK3 @ ( comp @ sK4 @ sK2 ) ) ) ) ),
inference(sigma_clausification,[],[f553]) ).
thf(f553,plain,
( ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
| ( $false
= ( ( comp @ ( comp @ sK3 @ sK4 ) @ sK2 )
= ( comp @ sK3 @ ( comp @ sK4 @ sK2 ) ) ) )
| ( sK1
!= ( comp @ id @ sK1 ) ) ),
inference(beta_eta_normalization,[],[f552]) ).
thf(f552,plain,
( ( ( ^ [Y0: subst] :
( ( comp @ ( comp @ sK3 @ Y0 ) @ sK2 )
= ( comp @ sK3 @ ( comp @ Y0 @ sK2 ) ) )
@ sK4 )
= $false )
| ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
| ( sK1
!= ( comp @ id @ sK1 ) ) ),
inference(sigma_clausification,[],[f551]) ).
thf(f551,plain,
( ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ ( comp @ sK3 @ Y0 ) @ sK2 )
= ( comp @ sK3 @ ( comp @ Y0 @ sK2 ) ) ) ) )
| ( sK1
!= ( comp @ id @ sK1 ) )
| ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) ) ),
inference(beta_eta_normalization,[],[f550]) ).
thf(f550,plain,
( ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
| ( $false
= ( ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ sK2 )
= ( comp @ Y0 @ ( comp @ Y1 @ sK2 ) ) ) )
@ sK3 ) )
| ( sK1
!= ( comp @ id @ sK1 ) ) ),
inference(sigma_clausification,[],[f549]) ).
thf(f549,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ sK2 )
= ( comp @ Y0 @ ( comp @ Y1 @ sK2 ) ) ) ) )
= $false )
| ( sK1
!= ( comp @ id @ sK1 ) )
| ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) ) ),
inference(equality_proxy_clausification,[],[f548]) ).
thf(f548,plain,
( ( $false
= ( ( comp @ id @ sK1 )
= sK1 ) )
| ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
| ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ sK2 )
= ( comp @ Y0 @ ( comp @ Y1 @ sK2 ) ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[],[f547]) ).
thf(f547,plain,
( ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
| ( ( ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) )
@ sK2 )
= $false )
| ( $false
= ( ( comp @ id @ sK1 )
= sK1 ) ) ),
inference(sigma_clausification,[],[f546]) ).
thf(f546,plain,
( ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) )
| ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
| ( $false
= ( ( comp @ id @ sK1 )
= sK1 ) ) ),
inference(beta_eta_normalization,[],[f545]) ).
thf(f545,plain,
( ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
| ( $false
= ( ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 )
@ sK1 ) )
| ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(sigma_clausification,[],[f544]) ).
thf(f544,plain,
( ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
| ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) )
| ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) ) ),
inference(binary_proxy_clausification,[],[f543]) ).
thf(f543,plain,
( ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
= $false )
| ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f538]) ).
thf(f538,plain,
( $false
= ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f529]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ALG254^2 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.07/0.15 % 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
% 0.15/0.39 % Computer : n025.cluster.edu
% 0.15/0.39 % Model : x86_64 x86_64
% 0.15/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.39 % Memory : 8042.1875MB
% 0.15/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.39 % CPULimit : 300
% 0.15/0.39 % WCLimit : 300
% 0.15/0.39 % DateTime : Sat May 18 22:54:53 EDT 2024
% 0.15/0.39 % CPUTime :
% 0.15/0.39 This is a TH0_THM_EQU_NAR problem
% 0.15/0.40 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/benchmark/theBenchmark.p
% 0.15/0.43 % (10864)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.15/0.43 % (10858)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.43 % (10860)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.15/0.43 % (10861)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.43 % (10863)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.15/0.43 % (10859)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.15/0.43 % (10862)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.43 % (10865)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.15/0.43 % (10861)Instruction limit reached!
% 0.15/0.43 % (10861)------------------------------
% 0.15/0.43 % (10861)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.43 % (10861)Termination reason: Unknown
% 0.15/0.43 % (10861)Termination phase: shuffling
% 0.15/0.43 % (10862)Instruction limit reached!
% 0.15/0.43 % (10862)------------------------------
% 0.15/0.43 % (10862)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.43 % (10862)Termination reason: Unknown
% 0.15/0.43 % (10862)Termination phase: shuffling
% 0.15/0.43
% 0.15/0.43 % (10862)Memory used [KB]: 1279
% 0.15/0.43 % (10862)Time elapsed: 0.003 s
% 0.15/0.43 % (10862)Instructions burned: 3 (million)
% 0.15/0.43 % (10862)------------------------------
% 0.15/0.43 % (10862)------------------------------
% 0.15/0.43
% 0.15/0.43 % (10861)Memory used [KB]: 1279
% 0.15/0.43 % (10861)Time elapsed: 0.003 s
% 0.15/0.43 % (10861)Instructions burned: 3 (million)
% 0.15/0.43 % (10861)------------------------------
% 0.15/0.43 % (10861)------------------------------
% 0.15/0.43 % (10865)Instruction limit reached!
% 0.15/0.43 % (10865)------------------------------
% 0.15/0.43 % (10865)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.43 % (10865)Termination reason: Unknown
% 0.15/0.43 % (10865)Termination phase: shuffling
% 0.15/0.43
% 0.15/0.43 % (10865)Memory used [KB]: 1279
% 0.15/0.43 % (10865)Time elapsed: 0.003 s
% 0.15/0.43 % (10865)Instructions burned: 3 (million)
% 0.15/0.43 % (10865)------------------------------
% 0.15/0.43 % (10865)------------------------------
% 0.15/0.43 % (10859)Instruction limit reached!
% 0.15/0.43 % (10859)------------------------------
% 0.15/0.43 % (10859)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.43 % (10859)Termination reason: Unknown
% 0.15/0.43 % (10859)Termination phase: shuffling
% 0.15/0.43
% 0.15/0.43 % (10859)Memory used [KB]: 1279
% 0.15/0.43 % (10859)Time elapsed: 0.004 s
% 0.15/0.43 % (10859)Instructions burned: 5 (million)
% 0.15/0.43 % (10859)------------------------------
% 0.15/0.43 % (10859)------------------------------
% 0.15/0.44 % (10864)Instruction limit reached!
% 0.15/0.44 % (10864)------------------------------
% 0.15/0.44 % (10864)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.44 % (10864)Termination reason: Unknown
% 0.15/0.44 % (10864)Termination phase: Property scanning
% 0.15/0.44
% 0.15/0.44 % (10864)Memory used [KB]: 1663
% 0.15/0.44 % (10864)Time elapsed: 0.012 s
% 0.15/0.44 % (10864)Instructions burned: 19 (million)
% 0.15/0.44 % (10864)------------------------------
% 0.15/0.44 % (10864)------------------------------
% 0.15/0.44 % (10860)Instruction limit reached!
% 0.15/0.44 % (10860)------------------------------
% 0.15/0.44 % (10860)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.44 % (10860)Termination reason: Unknown
% 0.15/0.44 % (10860)Termination phase: Property scanning
% 0.15/0.44
% 0.15/0.44 % (10860)Memory used [KB]: 1791
% 0.15/0.44 % (10860)Time elapsed: 0.015 s
% 0.15/0.44 % (10860)Instructions burned: 28 (million)
% 0.15/0.44 % (10860)------------------------------
% 0.15/0.44 % (10860)------------------------------
% 0.15/0.44 % (10863)Refutation not found, incomplete strategy
% 0.15/0.44 % (10863)------------------------------
% 0.15/0.44 % (10863)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.44 % (10863)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.44
% 0.15/0.44
% 0.15/0.44 % (10863)Memory used [KB]: 6140
% 0.15/0.44 % (10863)Time elapsed: 0.017 s
% 0.15/0.44 % (10863)Instructions burned: 26 (million)
% 0.15/0.44 % (10863)------------------------------
% 0.15/0.44 % (10863)------------------------------
% 0.15/0.44 % (10866)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.15/0.44 % (10867)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.15/0.44 % (10868)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.15/0.44 % (10869)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.15/0.44 % (10868)Instruction limit reached!
% 0.15/0.44 % (10868)------------------------------
% 0.15/0.44 % (10868)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.44 % (10868)Termination reason: Unknown
% 0.15/0.44 % (10868)Termination phase: shuffling
% 0.15/0.44
% 0.15/0.44 % (10868)Memory used [KB]: 1279
% 0.15/0.45 % (10868)Time elapsed: 0.004 s
% 0.15/0.45 % (10868)Instructions burned: 4 (million)
% 0.15/0.45 % (10868)------------------------------
% 0.15/0.45 % (10868)------------------------------
% 0.15/0.45 % (10867)Instruction limit reached!
% 0.15/0.45 % (10867)------------------------------
% 0.15/0.45 % (10867)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.45 % (10867)Termination reason: Unknown
% 0.15/0.45 % (10867)Termination phase: Property scanning
% 0.15/0.45
% 0.15/0.45 % (10867)Memory used [KB]: 1663
% 0.15/0.45 % (10867)Time elapsed: 0.010 s
% 0.15/0.45 % (10867)Instructions burned: 15 (million)
% 0.15/0.45 % (10867)------------------------------
% 0.15/0.45 % (10867)------------------------------
% 0.15/0.45 % (10870)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.15/0.45 % (10871)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.15/0.45 % (10870)Instruction limit reached!
% 0.15/0.45 % (10870)------------------------------
% 0.15/0.45 % (10870)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.45 % (10870)Termination reason: Unknown
% 0.15/0.45 % (10870)Termination phase: shuffling
% 0.15/0.45
% 0.15/0.45 % (10870)Memory used [KB]: 1407
% 0.15/0.45 % (10870)Time elapsed: 0.006 s
% 0.15/0.45 % (10870)Instructions burned: 8 (million)
% 0.15/0.45 % (10870)------------------------------
% 0.15/0.45 % (10870)------------------------------
% 0.15/0.46 % (10872)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.15/0.46 % (10872)Instruction limit reached!
% 0.15/0.46 % (10872)------------------------------
% 0.15/0.46 % (10872)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.46 % (10872)Termination reason: Unknown
% 0.15/0.46 % (10872)Termination phase: shuffling
% 0.15/0.46
% 0.15/0.46 % (10872)Memory used [KB]: 1279
% 0.15/0.46 % (10872)Time elapsed: 0.004 s
% 0.15/0.46 % (10872)Instructions burned: 4 (million)
% 0.15/0.46 % (10872)------------------------------
% 0.15/0.46 % (10872)------------------------------
% 0.15/0.46 % (10873)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.24/0.46 % (10866)Instruction limit reached!
% 0.24/0.46 % (10866)------------------------------
% 0.24/0.46 % (10866)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.46 % (10866)Termination reason: Unknown
% 0.24/0.46 % (10866)Termination phase: Property scanning
% 0.24/0.46
% 0.24/0.46 % (10866)Memory used [KB]: 1791
% 0.24/0.46 % (10866)Time elapsed: 0.020 s
% 0.24/0.46 % (10866)Instructions burned: 38 (million)
% 0.24/0.46 % (10866)------------------------------
% 0.24/0.46 % (10866)------------------------------
% 0.24/0.46 % (10873)Instruction limit reached!
% 0.24/0.46 % (10873)------------------------------
% 0.24/0.46 % (10873)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.46 % (10873)Termination reason: Unknown
% 0.24/0.46 % (10873)Termination phase: shuffling
% 0.24/0.46
% 0.24/0.46 % (10873)Memory used [KB]: 1279
% 0.24/0.46 % (10873)Time elapsed: 0.004 s
% 0.24/0.46 % (10873)Instructions burned: 4 (million)
% 0.24/0.46 % (10873)------------------------------
% 0.24/0.46 % (10873)------------------------------
% 0.24/0.46 % (10871)Instruction limit reached!
% 0.24/0.46 % (10871)------------------------------
% 0.24/0.46 % (10871)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.46 % (10871)Termination reason: Unknown
% 0.24/0.46 % (10871)Termination phase: shuffling
% 0.24/0.46
% 0.24/0.46 % (10871)Memory used [KB]: 1535
% 0.24/0.46 % (10871)Time elapsed: 0.010 s
% 0.24/0.46 % (10871)Instructions burned: 16 (million)
% 0.24/0.46 % (10871)------------------------------
% 0.24/0.46 % (10871)------------------------------
% 0.24/0.47 % (10874)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.24/0.47 % (10858)First to succeed.
% 0.24/0.47 % (10874)Instruction limit reached!
% 0.24/0.47 % (10874)------------------------------
% 0.24/0.47 % (10874)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.47 % (10874)Termination reason: Unknown
% 0.24/0.47 % (10875)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.24/0.47 % (10874)Termination phase: shuffling
% 0.24/0.47
% 0.24/0.47 % (10874)Memory used [KB]: 1407
% 0.24/0.47 % (10874)Time elapsed: 0.006 s
% 0.24/0.47 % (10874)Instructions burned: 8 (million)
% 0.24/0.47 % (10874)------------------------------
% 0.24/0.47 % (10874)------------------------------
% 0.24/0.47 % (10858)Refutation found. Thanks to Tanya!
% 0.24/0.47 % SZS status Theorem for theBenchmark
% 0.24/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.47 % (10858)------------------------------
% 0.24/0.47 % (10858)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.47 % (10858)Termination reason: Refutation
% 0.24/0.47
% 0.24/0.47 % (10858)Memory used [KB]: 6524
% 0.24/0.47 % (10858)Time elapsed: 0.043 s
% 0.24/0.47 % (10858)Instructions burned: 86 (million)
% 0.24/0.47 % (10858)------------------------------
% 0.24/0.47 % (10858)------------------------------
% 0.24/0.47 % (10857)Success in time 0.061 s
% 0.24/0.47 % Vampire---4.8 exiting
%------------------------------------------------------------------------------