TSTP Solution File: ALG268^2 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : ALG268^2 : 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n029.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 18:20:43 EDT 2024
% Result : Theorem 0.18s 0.52s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 35
% Syntax : Number of formulae : 135 ( 65 unt; 26 typ; 0 def)
% Number of atoms : 917 ( 205 equ; 0 cnn)
% Maximal formula atoms : 4 ( 8 avg)
% Number of connectives : 4397 ( 30 ~; 40 |; 0 &;3539 @)
% ( 2 <=>; 356 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 394 ( 394 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 29 usr; 17 con; 0-4 aty)
% ( 430 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 605 ( 492 ^ 112 !; 0 ?; 605 :)
% ( 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_141,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_142,type,
sK2: subst > term > subst > $o ).
thf(func_def_143,type,
sK3: term ).
thf(func_def_144,type,
sK4: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_145,type,
sK5: ( subst > term > subst > $o ) > term > term ).
thf(func_def_146,type,
sK6: subst ).
thf(func_def_147,type,
sK7: subst ).
thf(func_def_148,type,
sK8: term ).
thf(f1056,plain,
$false,
inference(avatar_sat_refutation,[],[f967,f981,f1055]) ).
thf(f1055,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f1054]) ).
thf(f1054,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f1053]) ).
thf(f1053,plain,
( ( $true = $false )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f1052]) ).
thf(f1052,plain,
( ( ( ( sub @ ( sK4 @ sK2 @ sK7 @ sK8 ) @ sK6 )
= ( sub @ ( sK4 @ sK2 @ sK7 @ sK8 ) @ sK6 ) )
= $false )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f1051,f790]) ).
thf(f790,plain,
! [X2: subst,X0: term,X1: subst] :
( ( sub @ ( sK4 @ sK2 @ X2 @ X0 ) @ X1 )
= ( sK4 @ sK2 @ ( comp @ X2 @ X1 ) @ ( sub @ X0 @ X1 ) ) ),
inference(equality_proxy_clausification,[],[f789]) ).
thf(f789,plain,
! [X2: subst,X0: term,X1: subst] :
( $true
= ( ( sub @ ( sK4 @ sK2 @ X2 @ X0 ) @ X1 )
= ( sK4 @ sK2 @ ( comp @ X2 @ X1 ) @ ( sub @ X0 @ X1 ) ) ) ),
inference(beta_eta_normalization,[],[f788]) ).
thf(f788,plain,
! [X2: subst,X0: term,X1: subst] :
( $true
= ( ^ [Y0: subst] :
( ( sub @ ( sK4 @ sK2 @ Y0 @ X0 ) @ X1 )
= ( sK4 @ sK2 @ ( comp @ Y0 @ X1 ) @ ( sub @ X0 @ X1 ) ) )
@ X2 ) ),
inference(pi_clausification,[],[f787]) ).
thf(f787,plain,
! [X0: term,X1: subst] :
( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( ( sub @ ( sK4 @ sK2 @ Y0 @ X0 ) @ X1 )
= ( sK4 @ sK2 @ ( comp @ Y0 @ X1 ) @ ( sub @ X0 @ X1 ) ) ) ) ),
inference(trivial_inequality_removal,[],[f786]) ).
thf(f786,plain,
! [X0: term,X1: subst] :
( ( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( ( sub @ ( sK4 @ sK2 @ Y0 @ X0 ) @ X1 )
= ( sK4 @ sK2 @ ( comp @ Y0 @ X1 ) @ ( sub @ X0 @ X1 ) ) ) ) )
| ( $true = $false ) ),
inference(forward_demodulation,[],[f785,f595]) ).
thf(f595,plain,
( ( sK2 @ id @ ( lam @ sK3 ) @ id )
= $false ),
inference(boolean_simplification,[],[f594]) ).
thf(f594,plain,
( ( $true
=> ( sK2 @ id @ ( lam @ sK3 ) @ id ) )
= $false ),
inference(backward_demodulation,[],[f591,f593]) ).
thf(f593,plain,
( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( sK2 @ id @ Y0 @ id )
=> ( sK2 @ id @ ( sub @ sK3 @ ( push @ Y0 @ id ) ) @ id ) ) ) ),
inference(binary_proxy_clausification,[],[f591]) ).
thf(f591,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( ( sK2 @ id @ Y0 @ id )
=> ( sK2 @ id @ ( sub @ sK3 @ ( push @ Y0 @ id ) ) @ id ) ) )
=> ( sK2 @ id @ ( lam @ sK3 ) @ id ) )
= $false ),
inference(beta_eta_normalization,[],[f590]) ).
thf(f590,plain,
( ( ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( sK2 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( sK2 @ id @ ( lam @ Y0 ) @ id ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[],[f584]) ).
thf(f584,plain,
( ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( sK2 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( sK2 @ id @ ( lam @ Y0 ) @ id ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f582]) ).
thf(f582,plain,
( ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( sK2 @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( sK2 @ id @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( sK2 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( sK2 @ id @ ( lam @ Y0 ) @ id ) ) ) )
= $false ),
inference(boolean_simplification,[],[f581]) ).
thf(f581,plain,
( $false
= ( $true
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( sK2 @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( sK2 @ id @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( sK2 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( sK2 @ id @ ( lam @ Y0 ) @ id ) ) ) ) ) ),
inference(backward_demodulation,[],[f563,f580]) ).
thf(f580,plain,
( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK2 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y0 @ Y3 ) @ Y2 )
=> ( sK2 @ Y1 @ Y0 @ ( comp @ Y3 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f563]) ).
thf(f563,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK2 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y0 @ Y3 ) @ Y2 )
=> ( sK2 @ Y1 @ Y0 @ ( comp @ Y3 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( sK2 @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( sK2 @ id @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( sK2 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( sK2 @ id @ ( lam @ Y0 ) @ id ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f562]) ).
thf(f562,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK2 @ Y1 @ Y2 @ ( comp @ Y3 @ Y0 ) )
=> ( sK2 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK2 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y0 @ Y3 ) @ Y2 )
=> ( sK2 @ Y1 @ Y0 @ ( comp @ Y3 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( sK2 @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( sK2 @ id @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( sK2 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( sK2 @ id @ ( lam @ Y0 ) @ id ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f561]) ).
thf(f561,plain,
( ( ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y3 @ ( comp @ Y4 @ Y1 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y4 @ Y2 ) )
= ( sub @ ( Y1 @ Y3 @ Y4 ) @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( Y1 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ Y1 ) @ id ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[],[f552]) ).
thf(f552,plain,
( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y3 @ ( comp @ Y4 @ Y1 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y4 @ Y2 ) )
= ( sub @ ( Y1 @ Y3 @ Y4 ) @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( Y1 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ Y1 ) @ id ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f543]) ).
thf(f543,plain,
( ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y3 ) @ Y2 )
= ( Y1 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( Y1 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( sub @ Y1 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y3 @ ( comp @ Y4 @ Y1 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y4 @ Y2 ) )
= ( sub @ ( Y1 @ Y3 @ Y4 ) @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( Y1 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ Y1 ) @ id ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f532]) ).
thf(f532,plain,
( ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y3 ) @ Y2 )
= ( Y1 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( Y1 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( sub @ Y1 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y3 @ ( comp @ Y4 @ Y1 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y4 @ Y2 ) )
= ( sub @ ( Y1 @ Y3 @ Y4 ) @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( Y1 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ Y1 ) @ id ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f529]) ).
thf(f529,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y3 ) @ Y2 )
= ( Y1 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( Y1 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( sub @ Y1 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y3 @ ( comp @ Y4 @ Y1 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y4 @ Y2 ) )
= ( sub @ ( Y1 @ Y3 @ Y4 ) @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( Y1 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ Y1 ) @ id ) ) ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f528]) ).
thf(f528,plain,
( $true
= ( ~ ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y3 ) @ Y2 )
= ( Y1 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( Y1 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( sub @ Y1 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y3 @ ( comp @ Y4 @ Y1 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y4 @ Y2 ) )
= ( sub @ ( Y1 @ Y3 @ Y4 ) @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( Y1 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ Y1 ) @ id ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f527]) ).
thf(f527,plain,
( $true
= ( ~ ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y3 ) @ Y2 )
= ( Y1 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id
@ ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) )
@ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( sub @ Y1 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y3 @ ( comp @ Y4 @ Y1 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y4 @ Y2 ) )
= ( sub @ ( Y1 @ Y3 @ Y4 ) @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id
@ ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) )
@ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ Y1 ) @ id ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f439,f504]) ).
thf(f504,plain,
( hoasinduction_lem3_lthm
= ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y3 ) @ Y2 )
= ( Y1 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id
@ ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) )
@ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( sub @ Y1 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y3 @ ( comp @ Y4 @ Y1 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y4 @ Y2 ) )
= ( sub @ ( Y1 @ Y3 @ Y4 ) @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id
@ ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) )
@ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ Y1 ) @ id ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f449,f358,f434,f479,f470]) ).
thf(f470,plain,
( hoasinduction_lem3
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y3 @ ( comp @ Y4 @ Y1 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y4 @ Y2 ) )
= ( sub @ ( Y1 @ Y3 @ Y4 ) @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id
@ ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) )
@ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ Y1 ) @ id ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f364,f424]) ).
thf(f424,plain,
( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( lam @ ( Y1 @ sh @ one ) ) ) ),
inference(cnf_transformation,[],[f158]) ).
thf(f158,plain,
( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( lam @ ( Y1 @ sh @ one ) ) ) ),
inference(fool_elimination,[],[f157]) ).
thf(f157,plain,
( ( ^ [X0: subst,X1: subst > term > term] : ( lam @ ( X1 @ sh @ one ) ) )
= hoaslam ),
inference(rectify,[],[f56]) ).
thf(f56,axiom,
( ( ^ [X2: subst,X10: subst > term > term] : ( lam @ ( X10 @ sh @ one ) ) )
= hoaslam ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoaslam) ).
thf(f364,plain,
( hoasinduction_lem3
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y3 @ ( comp @ Y4 @ Y1 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y4 @ Y2 ) )
= ( sub @ ( Y1 @ Y3 @ Y4 ) @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id
@ ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) )
@ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ Y1 ) @ id ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f144]) ).
thf(f144,plain,
( hoasinduction_lem3
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y3 @ ( comp @ Y4 @ Y1 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y4 @ Y2 ) )
= ( sub @ ( Y1 @ Y3 @ Y4 ) @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id
@ ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) )
@ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ Y1 ) @ id ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f143]) ).
thf(f143,plain,
! [X0: subst > term > subst > $o] :
( ( ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( X0 @ X3 @ X2 @ ( comp @ X1 @ X4 ) )
=> ( X0 @ ( comp @ X3 @ X1 ) @ ( sub @ X2 @ X1 ) @ X4 ) )
=> ( ! [X5: subst,X6: subst,X7: subst,X8: term] :
( ( X0 @ ( comp @ X7 @ X5 ) @ ( sub @ X8 @ X5 ) @ X6 )
=> ( X0 @ X7 @ X8 @ ( comp @ X5 @ X6 ) ) )
=> ( ! [X9: subst > term > term] :
( ! [X10: term,X11: subst,X12: subst] :
( ( X9 @ ( comp @ X11 @ X12 ) @ ( sub @ X10 @ X12 ) )
= ( sub @ ( X9 @ X11 @ X10 ) @ X12 ) )
=> ( ! [X13: term] :
( ( X0 @ id @ X13 @ id )
=> ( X0 @ id @ ( X9 @ id @ X13 ) @ id ) )
=> ( X0 @ id
@ ( hoaslam @ id
@ ^ [X14: subst,X15: term] : ( X9 @ X14 @ X15 ) )
@ id ) ) )
=> ! [X16: term] :
( ! [X17: term] :
( ( X0 @ id @ X17 @ id )
=> ( X0 @ id @ ( sub @ X16 @ ( push @ X17 @ id ) ) @ id ) )
=> ( X0 @ id @ ( lam @ X16 ) @ id ) ) ) ) )
= hoasinduction_lem3 ),
inference(rectify,[],[f99]) ).
thf(f99,axiom,
! [X5: subst > term > subst > $o] :
( ( ! [X4: subst,X0: term,X2: subst,X3: subst] :
( ( X5 @ X2 @ X0 @ ( comp @ X4 @ X3 ) )
=> ( X5 @ ( comp @ X2 @ X4 ) @ ( sub @ X0 @ X4 ) @ X3 ) )
=> ( ! [X4: subst,X3: subst,X2: subst,X0: term] :
( ( X5 @ ( comp @ X2 @ X4 ) @ ( sub @ X0 @ X4 ) @ X3 )
=> ( X5 @ X2 @ X0 @ ( comp @ X4 @ X3 ) ) )
=> ( ! [X10: subst > term > term] :
( ! [X0: term,X2: subst,X3: subst] :
( ( sub @ ( X10 @ X2 @ X0 ) @ X3 )
= ( X10 @ ( comp @ X2 @ X3 ) @ ( sub @ X0 @ X3 ) ) )
=> ( ! [X0: term] :
( ( X5 @ id @ X0 @ id )
=> ( X5 @ id @ ( X10 @ id @ X0 ) @ id ) )
=> ( X5 @ id
@ ( hoaslam @ id
@ ^ [X2: subst,X0: term] : ( X10 @ X2 @ X0 ) )
@ id ) ) )
=> ! [X0: term] :
( ! [X1: term] :
( ( X5 @ id @ X1 @ id )
=> ( X5 @ id @ ( sub @ X0 @ ( push @ X1 @ id ) ) @ id ) )
=> ( X5 @ id @ ( lam @ X0 ) @ id ) ) ) ) )
= hoasinduction_lem3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3) ).
thf(f479,plain,
( hoasinduction_lem3aa
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y3 ) @ Y2 )
= ( Y1 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id
@ ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) )
@ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( sub @ Y1 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) ) ),
inference(definition_unfolding,[],[f342,f424]) ).
thf(f342,plain,
( hoasinduction_lem3aa
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y3 ) @ Y2 )
= ( Y1 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id
@ ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) )
@ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( sub @ Y1 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) ) ),
inference(cnf_transformation,[],[f332]) ).
thf(f332,plain,
( hoasinduction_lem3aa
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y3 ) @ Y2 )
= ( Y1 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id
@ ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) )
@ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( sub @ Y1 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) ) ),
inference(fool_elimination,[],[f331]) ).
thf(f331,plain,
! [X0: subst > term > subst > $o] :
( ( ! [X1: subst > term > term] :
( ! [X2: subst,X3: term,X4: subst] :
( ( sub @ ( X1 @ X2 @ X3 ) @ X4 )
= ( X1 @ ( comp @ X2 @ X4 ) @ ( sub @ X3 @ X4 ) ) )
=> ( ! [X5: term] :
( ( X0 @ id @ X5 @ id )
=> ( X0 @ id @ ( X1 @ id @ X5 ) @ id ) )
=> ( X0 @ id
@ ( hoaslam @ id
@ ^ [X6: subst,X7: term] : ( X1 @ X6 @ X7 ) )
@ id ) ) )
=> ! [X8: term] :
( ! [X9: term] :
( ( X0 @ id @ X9 @ id )
=> ( X0 @ id @ ( sub @ X8 @ ( push @ X9 @ id ) ) @ id ) )
=> ( X0 @ id @ ( lam @ ( sub @ X8 @ ( push @ one @ sh ) ) ) @ id ) ) )
= hoasinduction_lem3aa ),
inference(rectify,[],[f96]) ).
thf(f96,axiom,
! [X5: subst > term > subst > $o] :
( ( ! [X10: subst > term > term] :
( ! [X2: subst,X0: term,X3: subst] :
( ( sub @ ( X10 @ X2 @ X0 ) @ X3 )
= ( X10 @ ( comp @ X2 @ X3 ) @ ( sub @ X0 @ X3 ) ) )
=> ( ! [X0: term] :
( ( X5 @ id @ X0 @ id )
=> ( X5 @ id @ ( X10 @ id @ X0 ) @ id ) )
=> ( X5 @ id
@ ( hoaslam @ id
@ ^ [X2: subst,X0: term] : ( X10 @ X2 @ X0 ) )
@ id ) ) )
=> ! [X0: term] :
( ! [X1: term] :
( ( X5 @ id @ X1 @ id )
=> ( X5 @ id @ ( sub @ X0 @ ( push @ X1 @ id ) ) @ id ) )
=> ( X5 @ id @ ( lam @ ( sub @ X0 @ ( push @ one @ sh ) ) ) @ id ) ) )
= hoasinduction_lem3aa ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3aa) ).
thf(f434,plain,
( axvarshift
= ( id
= ( push @ one @ sh ) ) ),
inference(cnf_transformation,[],[f198]) ).
thf(f198,plain,
( axvarshift
= ( id
= ( push @ one @ sh ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f11,axiom,
( ( id
= ( push @ one @ sh ) )
= axvarshift ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axvarshift) ).
thf(f358,plain,
( axvarid
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ),
inference(cnf_transformation,[],[f205]) ).
thf(f205,plain,
( axvarid
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f3,axiom,
( axvarid
= ( ! [X0: term] :
( ( sub @ X0 @ id )
= X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axvarid) ).
thf(f449,plain,
( hoasinduction_lem3_lthm
= ( axvarid
=> ( axvarshift
=> ( hoasinduction_lem3aa
=> hoasinduction_lem3 ) ) ) ),
inference(cnf_transformation,[],[f330]) ).
thf(f330,plain,
( hoasinduction_lem3_lthm
= ( axvarid
=> ( axvarshift
=> ( hoasinduction_lem3aa
=> hoasinduction_lem3 ) ) ) ),
inference(fool_elimination,[],[f329]) ).
thf(f329,plain,
( ( hoasinduction_lem3_lthm = axvarid )
=> ( axvarshift
=> ( hoasinduction_lem3aa
=> hoasinduction_lem3 ) ) ),
inference(rectify,[],[f101]) ).
thf(f101,axiom,
( ( hoasinduction_lem3_lthm = axvarid )
=> ( axvarshift
=> ( hoasinduction_lem3aa
=> hoasinduction_lem3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3_lthm) ).
thf(f439,plain,
( $true = ~ hoasinduction_lem3_lthm ),
inference(cnf_transformation,[],[f230]) ).
thf(f230,plain,
( $true = ~ hoasinduction_lem3_lthm ),
inference(fool_elimination,[],[f229]) ).
thf(f229,plain,
~ hoasinduction_lem3_lthm,
inference(rectify,[],[f115]) ).
thf(f115,negated_conjecture,
~ hoasinduction_lem3_lthm,
inference(negated_conjecture,[],[f114]) ).
thf(f114,conjecture,
hoasinduction_lem3_lthm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f785,plain,
! [X0: term,X1: subst] :
( ( ( sK2 @ id @ ( lam @ sK3 ) @ id )
= $true )
| ( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( ( sub @ ( sK4 @ sK2 @ Y0 @ X0 ) @ X1 )
= ( sK4 @ sK2 @ ( comp @ Y0 @ X1 ) @ ( sub @ X0 @ X1 ) ) ) ) ) ),
inference(boolean_simplification,[],[f783]) ).
thf(f783,plain,
! [X0: term,X1: subst] :
( ( $true
= ( $true
=> ( sK2 @ id @ ( lam @ sK3 ) @ id ) ) )
| ( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( ( sub @ ( sK4 @ sK2 @ Y0 @ X0 ) @ X1 )
= ( sK4 @ sK2 @ ( comp @ Y0 @ X1 ) @ ( sub @ X0 @ X1 ) ) ) ) ) ),
inference(superposition,[],[f739,f593]) ).
thf(f739,plain,
! [X2: term,X3: subst,X1: subst > term > subst > $o,X4: term] :
( ( ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ id @ Y0 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ Y0 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
= $true )
| ( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( ( sub @ ( sK4 @ X1 @ Y0 @ X4 ) @ X3 )
= ( sK4 @ X1 @ ( comp @ Y0 @ X3 ) @ ( sub @ X4 @ X3 ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f738]) ).
thf(f738,plain,
! [X2: term,X3: subst,X1: subst > term > subst > $o,X4: term] :
( ( ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ id @ Y0 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ Y0 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
= $true )
| ( $true
= ( ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( sK4 @ X1 @ Y1 @ Y0 ) @ X3 )
= ( sK4 @ X1 @ ( comp @ Y1 @ X3 ) @ ( sub @ Y0 @ X3 ) ) ) )
@ X4 ) ) ),
inference(pi_clausification,[],[f719]) ).
thf(f719,plain,
! [X2: term,X3: subst,X1: subst > term > subst > $o] :
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( sK4 @ X1 @ Y1 @ Y0 ) @ X3 )
= ( sK4 @ X1 @ ( comp @ Y1 @ X3 ) @ ( sub @ Y0 @ X3 ) ) ) ) )
= $true )
| ( ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ id @ Y0 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ Y0 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
= $true ) ),
inference(beta_eta_normalization,[],[f717]) ).
thf(f717,plain,
! [X2: term,X3: subst,X1: subst > term > subst > $o] :
( ( ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ id @ Y0 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ Y0 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
= $true )
| ( $true
= ( ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sK4 @ X1 @ Y2 @ Y1 ) @ Y0 )
= ( sK4 @ X1 @ ( comp @ Y2 @ Y0 ) @ ( sub @ Y1 @ Y0 ) ) ) ) )
@ X3 ) ) ),
inference(pi_clausification,[],[f699]) ).
thf(f699,plain,
! [X2: term,X1: subst > term > subst > $o] :
( ( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sK4 @ X1 @ Y2 @ Y1 ) @ Y0 )
= ( sK4 @ X1 @ ( comp @ Y2 @ Y0 ) @ ( sub @ Y1 @ Y0 ) ) ) ) ) ) )
| ( ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ id @ Y0 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ Y0 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
= $true ) ),
inference(forward_demodulation,[],[f698,f540]) ).
thf(f540,plain,
! [X1: term] :
( ( sub @ X1 @ id )
= X1 ),
inference(equality_proxy_clausification,[],[f539]) ).
thf(f539,plain,
! [X1: term] :
( $true
= ( ( sub @ X1 @ id )
= X1 ) ),
inference(beta_eta_normalization,[],[f538]) ).
thf(f538,plain,
! [X1: term] :
( $true
= ( ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 )
@ X1 ) ),
inference(pi_clausification,[],[f533]) ).
thf(f533,plain,
( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ),
inference(binary_proxy_clausification,[],[f529]) ).
thf(f698,plain,
! [X2: term,X1: subst > term > subst > $o] :
( ( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sK4 @ X1 @ Y2 @ Y1 ) @ Y0 )
= ( sK4 @ X1 @ ( comp @ Y2 @ Y0 ) @ ( sub @ Y1 @ Y0 ) ) ) ) ) ) )
| ( $true
= ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ id @ Y0 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ Y0 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ id ) ) @ id ) ) ) ),
inference(forward_demodulation,[],[f696,f549]) ).
thf(f549,plain,
( id
= ( push @ one @ sh ) ),
inference(equality_proxy_clausification,[],[f544]) ).
thf(f544,plain,
( $true
= ( id
= ( push @ one @ sh ) ) ),
inference(binary_proxy_clausification,[],[f532]) ).
thf(f696,plain,
! [X2: term,X1: subst > term > subst > $o] :
( ( $true
= ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ id @ Y0 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ Y0 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) )
| ( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sK4 @ X1 @ Y2 @ Y1 ) @ Y0 )
= ( sK4 @ X1 @ ( comp @ Y2 @ Y0 ) @ ( sub @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f694]) ).
thf(f694,plain,
! [X2: term,X1: subst > term > subst > $o] :
( ( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sK4 @ X1 @ Y2 @ Y1 ) @ Y0 )
= ( sK4 @ X1 @ ( comp @ Y2 @ Y0 ) @ ( sub @ Y1 @ Y0 ) ) ) ) ) ) )
| ( ( ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( X1 @ id @ Y1 @ id )
=> ( X1 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ Y0 @ ( push @ one @ sh ) ) ) @ id ) )
@ X2 )
= $true ) ),
inference(pi_clausification,[],[f641]) ).
thf(f641,plain,
! [X1: subst > term > subst > $o] :
( ( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( X1 @ id @ Y1 @ id )
=> ( X1 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ Y0 @ ( push @ one @ sh ) ) ) @ id ) ) ) )
| ( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sK4 @ X1 @ Y2 @ Y1 ) @ Y0 )
= ( sK4 @ X1 @ ( comp @ Y2 @ Y0 ) @ ( sub @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f635]) ).
thf(f635,plain,
! [X1: subst > term > subst > $o] :
( ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sK4 @ X1 @ Y2 @ Y1 ) @ Y0 )
= ( sK4 @ X1 @ ( comp @ Y2 @ Y0 ) @ ( sub @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ id @ Y0 @ id )
=> ( X1 @ id @ ( sK4 @ X1 @ id @ Y0 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sK4 @ X1 @ sh @ one ) ) @ id ) ) )
= $false )
| ( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( X1 @ id @ Y1 @ id )
=> ( X1 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ Y0 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) ),
inference(beta_eta_normalization,[],[f632]) ).
thf(f632,plain,
! [X1: subst > term > subst > $o] :
( ( ( ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( X1 @ id @ Y1 @ id )
=> ( X1 @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) )
@ ( sK4 @ X1 ) )
= $false )
| ( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( X1 @ id @ Y1 @ id )
=> ( X1 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ Y0 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) ),
inference(sigma_clausification,[],[f560]) ).
thf(f560,plain,
! [X1: subst > term > subst > $o] :
( ( $false
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( X1 @ id @ Y1 @ id )
=> ( X1 @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) ) )
| ( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( X1 @ id @ Y1 @ id )
=> ( X1 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ Y0 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) ),
inference(binary_proxy_clausification,[],[f559]) ).
thf(f559,plain,
! [X1: subst > term > subst > $o] :
( $true
= ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( X1 @ id @ Y1 @ id )
=> ( X1 @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( X1 @ id @ Y1 @ id )
=> ( X1 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ Y0 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) ),
inference(beta_eta_normalization,[],[f558]) ).
thf(f558,plain,
! [X1: subst > term > subst > $o] :
( $true
= ( ^ [Y0: subst > term > subst > $o] :
( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y3 ) @ Y2 )
= ( Y1 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( Y1 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( sub @ Y1 @ ( push @ one @ sh ) ) ) @ id ) ) ) )
@ X1 ) ),
inference(pi_clausification,[],[f553]) ).
thf(f553,plain,
( $true
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y3 ) @ Y2 )
= ( Y1 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( Y1 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( sub @ Y1 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f543]) ).
thf(f1051,plain,
( ( ( ( sK4 @ sK2 @ ( comp @ sK7 @ sK6 ) @ ( sub @ sK8 @ sK6 ) )
= ( sub @ ( sK4 @ sK2 @ sK7 @ sK8 ) @ sK6 ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f1050]) ).
thf(f1050,plain,
( ( ( ^ [Y0: term] :
( ( sK4 @ sK2 @ ( comp @ sK7 @ sK6 ) @ ( sub @ Y0 @ sK6 ) )
= ( sub @ ( sK4 @ sK2 @ sK7 @ Y0 ) @ sK6 ) )
@ sK8 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f1049]) ).
thf(f1049,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( ( sK4 @ sK2 @ ( comp @ sK7 @ sK6 ) @ ( sub @ Y0 @ sK6 ) )
= ( sub @ ( sK4 @ sK2 @ sK7 @ Y0 ) @ sK6 ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f1048]) ).
thf(f1048,plain,
( ( ( ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sK4 @ sK2 @ ( comp @ Y0 @ sK6 ) @ ( sub @ Y1 @ sK6 ) )
= ( sub @ ( sK4 @ sK2 @ Y0 @ Y1 ) @ sK6 ) ) )
@ sK7 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f1046]) ).
thf(f1046,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sK4 @ sK2 @ ( comp @ Y0 @ sK6 ) @ ( sub @ Y1 @ sK6 ) )
= ( sub @ ( sK4 @ sK2 @ Y0 @ Y1 ) @ sK6 ) ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f1044]) ).
thf(f1044,plain,
( ( $false
= ( ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sK4 @ sK2 @ ( comp @ Y1 @ Y0 ) @ ( sub @ Y2 @ Y0 ) )
= ( sub @ ( sK4 @ sK2 @ Y1 @ Y2 ) @ Y0 ) ) ) )
@ sK6 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f1041]) ).
thf(f1041,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sK4 @ sK2 @ ( comp @ Y1 @ Y0 ) @ ( sub @ Y2 @ Y0 ) )
= ( sub @ ( sK4 @ sK2 @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(not_proxy_clausification,[],[f963]) ).
thf(f963,plain,
( ( $true
= ( ~ ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sK4 @ sK2 @ ( comp @ Y1 @ Y0 ) @ ( sub @ Y2 @ Y0 ) )
= ( sub @ ( sK4 @ sK2 @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f962]) ).
thf(f962,plain,
( spl0_1
<=> ( $true
= ( ~ ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sK4 @ sK2 @ ( comp @ Y1 @ Y0 ) @ ( sub @ Y2 @ Y0 ) )
= ( sub @ ( sK4 @ sK2 @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f981,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f980]) ).
thf(f980,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f979]) ).
thf(f979,plain,
( ( $true = $false )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f978]) ).
thf(f978,plain,
( ( $true = ~ $true )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f972,f593]) ).
thf(f972,plain,
( ( $true
= ( ~ ( !! @ term
@ ^ [Y0: term] :
( ( sK2 @ id @ Y0 @ id )
=> ( sK2 @ id @ ( sub @ sK3 @ ( push @ Y0 @ id ) ) @ id ) ) ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f969]) ).
thf(f969,plain,
( ( $true
= ( ( !! @ term
@ ^ [Y0: term] :
( ( sK2 @ id @ Y0 @ id )
=> ( sK2 @ id @ ( sub @ sK3 @ ( push @ Y0 @ id ) ) @ id ) ) )
=> $false ) )
| ~ spl0_2 ),
inference(superposition,[],[f966,f595]) ).
thf(f966,plain,
( ! [X0: term] :
( $true
= ( ( !! @ term
@ ^ [Y0: term] :
( ( sK2 @ id @ Y0 @ id )
=> ( sK2 @ id @ ( sub @ X0 @ ( push @ Y0 @ id ) ) @ id ) ) )
=> ( sK2 @ id @ ( lam @ X0 ) @ id ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f965]) ).
thf(f965,plain,
( spl0_2
<=> ! [X0: term] :
( $true
= ( ( !! @ term
@ ^ [Y0: term] :
( ( sK2 @ id @ Y0 @ id )
=> ( sK2 @ id @ ( sub @ X0 @ ( push @ Y0 @ id ) ) @ id ) ) )
=> ( sK2 @ id @ ( lam @ X0 ) @ id ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f967,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f959,f965,f962]) ).
thf(f959,plain,
! [X0: term] :
( ( $true
= ( ~ ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sK4 @ sK2 @ ( comp @ Y1 @ Y0 ) @ ( sub @ Y2 @ Y0 ) )
= ( sub @ ( sK4 @ sK2 @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) ) )
| ( $true
= ( ( !! @ term
@ ^ [Y0: term] :
( ( sK2 @ id @ Y0 @ id )
=> ( sK2 @ id @ ( sub @ X0 @ ( push @ Y0 @ id ) ) @ id ) ) )
=> ( sK2 @ id @ ( lam @ X0 ) @ id ) ) ) ),
inference(boolean_simplification,[],[f957]) ).
thf(f957,plain,
! [X0: term] :
( ( $true
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sK4 @ sK2 @ ( comp @ Y1 @ Y0 ) @ ( sub @ Y2 @ Y0 ) )
= ( sub @ ( sK4 @ sK2 @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
=> $false ) )
| ( $true
= ( ( !! @ term
@ ^ [Y0: term] :
( ( sK2 @ id @ Y0 @ id )
=> ( sK2 @ id @ ( sub @ X0 @ ( push @ Y0 @ id ) ) @ id ) ) )
=> ( sK2 @ id @ ( lam @ X0 ) @ id ) ) ) ),
inference(superposition,[],[f613,f932]) ).
thf(f932,plain,
! [X2: term,X1: subst > term > subst > $o] :
( ( ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ id @ Y0 @ id )
=> ( X1 @ id @ ( sK4 @ X1 @ id @ Y0 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sK4 @ X1 @ sh @ one ) ) @ id ) )
= $false )
| ( ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ id @ Y0 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ Y0 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) )
= $true ) ),
inference(forward_demodulation,[],[f931,f540]) ).
thf(f931,plain,
! [X2: term,X1: subst > term > subst > $o] :
( ( ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ id @ Y0 @ id )
=> ( X1 @ id @ ( sK4 @ X1 @ id @ Y0 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sK4 @ X1 @ sh @ one ) ) @ id ) )
= $false )
| ( $true
= ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ id @ Y0 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ Y0 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ id ) ) @ id ) ) ) ),
inference(forward_demodulation,[],[f929,f549]) ).
thf(f929,plain,
! [X2: term,X1: subst > term > subst > $o] :
( ( $true
= ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ id @ Y0 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ Y0 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) )
| ( ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ id @ Y0 @ id )
=> ( X1 @ id @ ( sK4 @ X1 @ id @ Y0 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sK4 @ X1 @ sh @ one ) ) @ id ) )
= $false ) ),
inference(beta_eta_normalization,[],[f927]) ).
thf(f927,plain,
! [X2: term,X1: subst > term > subst > $o] :
( ( ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ id @ Y0 @ id )
=> ( X1 @ id @ ( sK4 @ X1 @ id @ Y0 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sK4 @ X1 @ sh @ one ) ) @ id ) )
= $false )
| ( ( ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( X1 @ id @ Y1 @ id )
=> ( X1 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ Y0 @ ( push @ one @ sh ) ) ) @ id ) )
@ X2 )
= $true ) ),
inference(pi_clausification,[],[f640]) ).
thf(f640,plain,
! [X1: subst > term > subst > $o] :
( ( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( X1 @ id @ Y1 @ id )
=> ( X1 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sub @ Y0 @ ( push @ one @ sh ) ) ) @ id ) ) ) )
| ( ( ( !! @ term
@ ^ [Y0: term] :
( ( X1 @ id @ Y0 @ id )
=> ( X1 @ id @ ( sK4 @ X1 @ id @ Y0 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( sK4 @ X1 @ sh @ one ) ) @ id ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f635]) ).
thf(f613,plain,
! [X1: subst > term > term] :
( $true
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( X1 @ ( comp @ Y1 @ Y0 ) @ ( sub @ Y2 @ Y0 ) )
= ( sub @ ( X1 @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sK2 @ id @ Y0 @ id )
=> ( sK2 @ id @ ( X1 @ id @ Y0 ) @ id ) ) )
=> ( sK2 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id ) ) ) ),
inference(beta_eta_normalization,[],[f612]) ).
thf(f612,plain,
! [X1: subst > term > term] :
( $true
= ( ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( sK2 @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( sK2 @ id @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) )
@ X1 ) ),
inference(pi_clausification,[],[f585]) ).
thf(f585,plain,
( $true
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( sK2 @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( sK2 @ id @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) ) ),
inference(binary_proxy_clausification,[],[f582]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ALG268^2 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.12/0.13 % 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
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat May 18 23:20:38 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.12/0.33 This is a TH0_THM_EQU_NAR problem
% 0.12/0.34 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.36 % (18204)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)
% 0.18/0.36 % (18202)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)
% 0.18/0.36 % (18203)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.18/0.36 % (18200)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.18/0.36 % (18206)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.18/0.36 % (18201)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)
% 0.18/0.36 % (18205)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)
% 0.18/0.36 % (18207)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)
% 0.18/0.37 % (18203)Instruction limit reached!
% 0.18/0.37 % (18203)------------------------------
% 0.18/0.37 % (18203)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.37 % (18203)Termination reason: Unknown
% 0.18/0.37 % (18203)Termination phase: shuffling
% 0.18/0.37
% 0.18/0.37 % (18204)Instruction limit reached!
% 0.18/0.37 % (18204)------------------------------
% 0.18/0.37 % (18204)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.37 % (18204)Termination reason: Unknown
% 0.18/0.37 % (18204)Termination phase: shuffling
% 0.18/0.37
% 0.18/0.37 % (18204)Memory used [KB]: 1279
% 0.18/0.37 % (18204)Time elapsed: 0.003 s
% 0.18/0.37 % (18204)Instructions burned: 3 (million)
% 0.18/0.37 % (18204)------------------------------
% 0.18/0.37 % (18204)------------------------------
% 0.18/0.37 % (18203)Memory used [KB]: 1279
% 0.18/0.37 % (18203)Time elapsed: 0.003 s
% 0.18/0.37 % (18203)Instructions burned: 3 (million)
% 0.18/0.37 % (18203)------------------------------
% 0.18/0.37 % (18203)------------------------------
% 0.18/0.37 % (18207)Instruction limit reached!
% 0.18/0.37 % (18207)------------------------------
% 0.18/0.37 % (18207)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.37 % (18207)Termination reason: Unknown
% 0.18/0.37 % (18207)Termination phase: shuffling
% 0.18/0.37
% 0.18/0.37 % (18207)Memory used [KB]: 1279
% 0.18/0.37 % (18207)Time elapsed: 0.003 s
% 0.18/0.37 % (18207)Instructions burned: 4 (million)
% 0.18/0.37 % (18207)------------------------------
% 0.18/0.37 % (18207)------------------------------
% 0.18/0.37 % (18201)Instruction limit reached!
% 0.18/0.37 % (18201)------------------------------
% 0.18/0.37 % (18201)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.37 % (18201)Termination reason: Unknown
% 0.18/0.37 % (18201)Termination phase: shuffling
% 0.18/0.37
% 0.18/0.37 % (18201)Memory used [KB]: 1279
% 0.18/0.37 % (18201)Time elapsed: 0.004 s
% 0.18/0.37 % (18201)Instructions burned: 5 (million)
% 0.18/0.37 % (18201)------------------------------
% 0.18/0.37 % (18201)------------------------------
% 0.18/0.37 % (18206)Instruction limit reached!
% 0.18/0.37 % (18206)------------------------------
% 0.18/0.37 % (18206)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.37 % (18206)Termination reason: Unknown
% 0.18/0.37 % (18206)Termination phase: Property scanning
% 0.18/0.37
% 0.18/0.37 % (18206)Memory used [KB]: 1663
% 0.18/0.37 % (18206)Time elapsed: 0.011 s
% 0.18/0.37 % (18206)Instructions burned: 19 (million)
% 0.18/0.37 % (18206)------------------------------
% 0.18/0.37 % (18206)------------------------------
% 0.18/0.38 % (18202)Instruction limit reached!
% 0.18/0.38 % (18202)------------------------------
% 0.18/0.38 % (18202)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.38 % (18202)Termination reason: Unknown
% 0.18/0.38 % (18202)Termination phase: Property scanning
% 0.18/0.38
% 0.18/0.38 % (18202)Memory used [KB]: 1791
% 0.18/0.38 % (18202)Time elapsed: 0.014 s
% 0.18/0.38 % (18202)Instructions burned: 27 (million)
% 0.18/0.38 % (18202)------------------------------
% 0.18/0.38 % (18202)------------------------------
% 0.18/0.38 % (18208)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)
% 0.18/0.38 % (18211)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)
% 0.18/0.38 % (18210)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)
% 0.18/0.38 % (18209)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)
% 0.18/0.38 % (18210)Instruction limit reached!
% 0.18/0.38 % (18210)------------------------------
% 0.18/0.38 % (18210)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.38 % (18210)Termination reason: Unknown
% 0.18/0.38 % (18210)Termination phase: shuffling
% 0.18/0.38
% 0.18/0.38 % (18210)Memory used [KB]: 1279
% 0.18/0.38 % (18210)Time elapsed: 0.003 s
% 0.18/0.38 % (18210)Instructions burned: 4 (million)
% 0.18/0.38 % (18210)------------------------------
% 0.18/0.38 % (18210)------------------------------
% 0.18/0.39 % (18205)Refutation not found, incomplete strategy
% 0.18/0.39 % (18205)------------------------------
% 0.18/0.39 % (18205)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.39 % (18205)Termination reason: Refutation not found, incomplete strategy
% 0.18/0.39
% 0.18/0.39
% 0.18/0.39 % (18205)Memory used [KB]: 6268
% 0.18/0.39 % (18205)Time elapsed: 0.022 s
% 0.18/0.39 % (18205)Instructions burned: 36 (million)
% 0.18/0.39 % (18205)------------------------------
% 0.18/0.39 % (18205)------------------------------
% 0.18/0.39 % (18209)Instruction limit reached!
% 0.18/0.39 % (18209)------------------------------
% 0.18/0.39 % (18209)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.39 % (18209)Termination reason: Unknown
% 0.18/0.39 % (18209)Termination phase: Property scanning
% 0.18/0.39
% 0.18/0.39 % (18209)Memory used [KB]: 1663
% 0.18/0.39 % (18209)Time elapsed: 0.009 s
% 0.18/0.39 % (18209)Instructions burned: 15 (million)
% 0.18/0.39 % (18209)------------------------------
% 0.18/0.39 % (18209)------------------------------
% 0.18/0.39 % (18212)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.18/0.39 % (18213)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.18/0.39 % (18212)Instruction limit reached!
% 0.18/0.39 % (18212)------------------------------
% 0.18/0.39 % (18212)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.39 % (18212)Termination reason: Unknown
% 0.18/0.39 % (18212)Termination phase: shuffling
% 0.18/0.39
% 0.18/0.39 % (18212)Memory used [KB]: 1407
% 0.18/0.39 % (18212)Time elapsed: 0.006 s
% 0.18/0.39 % (18212)Instructions burned: 8 (million)
% 0.18/0.39 % (18212)------------------------------
% 0.18/0.39 % (18212)------------------------------
% 0.18/0.40 % (18214)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)
% 0.18/0.40 % (18214)Instruction limit reached!
% 0.18/0.40 % (18214)------------------------------
% 0.18/0.40 % (18214)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.40 % (18214)Termination reason: Unknown
% 0.18/0.40 % (18214)Termination phase: shuffling
% 0.18/0.40
% 0.18/0.40 % (18214)Memory used [KB]: 1279
% 0.18/0.40 % (18208)Instruction limit reached!
% 0.18/0.40 % (18208)------------------------------
% 0.18/0.40 % (18208)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.40 % (18208)Termination reason: Unknown
% 0.18/0.40 % (18208)Termination phase: Property scanning
% 0.18/0.40
% 0.18/0.40 % (18208)Memory used [KB]: 1791
% 0.18/0.40 % (18208)Time elapsed: 0.019 s
% 0.18/0.40 % (18208)Instructions burned: 37 (million)
% 0.18/0.40 % (18208)------------------------------
% 0.18/0.40 % (18208)------------------------------
% 0.18/0.40 % (18214)Time elapsed: 0.003 s
% 0.18/0.40 % (18214)Instructions burned: 3 (million)
% 0.18/0.40 % (18214)------------------------------
% 0.18/0.40 % (18214)------------------------------
% 0.18/0.40 % (18213)Instruction limit reached!
% 0.18/0.40 % (18213)------------------------------
% 0.18/0.40 % (18213)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.40 % (18213)Termination reason: Unknown
% 0.18/0.40 % (18213)Termination phase: shuffling
% 0.18/0.40
% 0.18/0.40 % (18213)Memory used [KB]: 1535
% 0.18/0.40 % (18213)Time elapsed: 0.009 s
% 0.18/0.40 % (18213)Instructions burned: 16 (million)
% 0.18/0.40 % (18213)------------------------------
% 0.18/0.40 % (18213)------------------------------
% 0.18/0.40 % (18215)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)
% 0.18/0.40 % (18216)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)
% 0.18/0.40 % (18215)Instruction limit reached!
% 0.18/0.40 % (18215)------------------------------
% 0.18/0.40 % (18215)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.40 % (18215)Termination reason: Unknown
% 0.18/0.40 % (18215)Termination phase: shuffling
% 0.18/0.40
% 0.18/0.40 % (18215)Memory used [KB]: 1279
% 0.18/0.40 % (18215)Time elapsed: 0.004 s
% 0.18/0.40 % (18215)Instructions burned: 4 (million)
% 0.18/0.40 % (18215)------------------------------
% 0.18/0.40 % (18215)------------------------------
% 0.18/0.40 % (18216)Instruction limit reached!
% 0.18/0.40 % (18216)------------------------------
% 0.18/0.40 % (18216)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.40 % (18216)Termination reason: Unknown
% 0.18/0.40 % (18216)Termination phase: shuffling
% 0.18/0.40
% 0.18/0.40 % (18216)Memory used [KB]: 1407
% 0.18/0.40 % (18216)Time elapsed: 0.005 s
% 0.18/0.40 % (18216)Instructions burned: 7 (million)
% 0.18/0.40 % (18216)------------------------------
% 0.18/0.40 % (18216)------------------------------
% 0.18/0.41 % (18217)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)
% 0.18/0.41 % (18217)Instruction limit reached!
% 0.18/0.41 % (18217)------------------------------
% 0.18/0.41 % (18217)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.41 % (18217)Termination reason: Unknown
% 0.18/0.41 % (18217)Termination phase: shuffling
% 0.18/0.41
% 0.18/0.41 % (18217)Memory used [KB]: 1279
% 0.18/0.41 % (18217)Time elapsed: 0.003 s
% 0.18/0.41 % (18217)Instructions burned: 3 (million)
% 0.18/0.41 % (18217)------------------------------
% 0.18/0.41 % (18217)------------------------------
% 0.18/0.41 % (18218)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.18/0.41 % (18219)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.18/0.41 % (18220)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.18/0.41 % (18218)Instruction limit reached!
% 0.18/0.41 % (18218)------------------------------
% 0.18/0.41 % (18218)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.41 % (18218)Termination reason: Unknown
% 0.18/0.41 % (18218)Termination phase: shuffling
% 0.18/0.41
% 0.18/0.41 % (18218)Memory used [KB]: 1279
% 0.18/0.41 % (18218)Time elapsed: 0.005 s
% 0.18/0.41 % (18218)Instructions burned: 5 (million)
% 0.18/0.41 % (18218)------------------------------
% 0.18/0.41 % (18218)------------------------------
% 0.18/0.42 % (18221)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.18/0.42 % (18222)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 theBenchmark for (2999ds/902Mi)
% 0.18/0.42 % (18219)Instruction limit reached!
% 0.18/0.42 % (18219)------------------------------
% 0.18/0.42 % (18219)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.42 % (18219)Termination reason: Unknown
% 0.18/0.42 % (18219)Termination phase: shuffling
% 0.18/0.42
% 0.18/0.42 % (18219)Memory used [KB]: 1663
% 0.18/0.42 % (18219)Time elapsed: 0.010 s
% 0.18/0.42 % (18219)Instructions burned: 19 (million)
% 0.18/0.42 % (18219)------------------------------
% 0.18/0.42 % (18219)------------------------------
% 0.18/0.42 % (18221)Instruction limit reached!
% 0.18/0.42 % (18221)------------------------------
% 0.18/0.42 % (18221)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.42 % (18221)Termination reason: Unknown
% 0.18/0.42 % (18221)Termination phase: shuffling
% 0.18/0.42
% 0.18/0.42 % (18221)Memory used [KB]: 1407
% 0.18/0.42 % (18221)Time elapsed: 0.006 s
% 0.18/0.42 % (18221)Instructions burned: 7 (million)
% 0.18/0.42 % (18221)------------------------------
% 0.18/0.42 % (18221)------------------------------
% 0.18/0.42 % (18223)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 theBenchmark for (2999ds/21Mi)
% 0.18/0.43 % (18220)Refutation not found, incomplete strategy
% 0.18/0.43 % (18220)------------------------------
% 0.18/0.43 % (18220)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.43 % (18220)Termination reason: Refutation not found, incomplete strategy
% 0.18/0.43
% 0.18/0.43
% 0.18/0.43 % (18220)Memory used [KB]: 6140
% 0.18/0.43 % (18220)Time elapsed: 0.015 s
% 0.18/0.43 % (18220)Instructions burned: 25 (million)
% 0.18/0.43 % (18220)------------------------------
% 0.18/0.43 % (18220)------------------------------
% 0.18/0.43 % (18224)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.18/0.43 % (18224)Instruction limit reached!
% 0.18/0.43 % (18224)------------------------------
% 0.18/0.43 % (18224)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.43 % (18224)Termination reason: Unknown
% 0.18/0.43 % (18224)Termination phase: shuffling
% 0.18/0.43
% 0.18/0.43 % (18224)Memory used [KB]: 1279
% 0.18/0.43 % (18224)Time elapsed: 0.005 s
% 0.18/0.43 % (18224)Instructions burned: 6 (million)
% 0.18/0.43 % (18224)------------------------------
% 0.18/0.43 % (18224)------------------------------
% 0.18/0.43 % (18223)Instruction limit reached!
% 0.18/0.43 % (18223)------------------------------
% 0.18/0.43 % (18223)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.43 % (18223)Termination reason: Unknown
% 0.18/0.43 % (18223)Termination phase: shuffling
% 0.18/0.43
% 0.18/0.43 % (18223)Memory used [KB]: 1663
% 0.18/0.43 % (18223)Time elapsed: 0.011 s
% 0.18/0.43 % (18223)Instructions burned: 21 (million)
% 0.18/0.43 % (18223)------------------------------
% 0.18/0.43 % (18223)------------------------------
% 0.18/0.43 % (18225)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 theBenchmark for (2999ds/6Mi)
% 0.18/0.44 % (18226)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2999ds/377Mi)
% 0.18/0.44 % (18225)Instruction limit reached!
% 0.18/0.44 % (18225)------------------------------
% 0.18/0.44 % (18225)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.44 % (18225)Termination reason: Unknown
% 0.18/0.44 % (18225)Termination phase: shuffling
% 0.18/0.44
% 0.18/0.44 % (18225)Memory used [KB]: 1279
% 0.18/0.44 % (18225)Time elapsed: 0.005 s
% 0.18/0.44 % (18225)Instructions burned: 6 (million)
% 0.18/0.44 % (18225)------------------------------
% 0.18/0.44 % (18225)------------------------------
% 0.18/0.44 % (18227)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 theBenchmark for (2999ds/779Mi)
% 0.18/0.45 % (18229)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on theBenchmark for (2999ds/879Mi)
% 0.18/0.45 % (18228)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 theBenchmark for (2999ds/19Mi)
% 0.18/0.45 % (18200)Instruction limit reached!
% 0.18/0.45 % (18200)------------------------------
% 0.18/0.45 % (18200)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.45 % (18200)Termination reason: Unknown
% 0.18/0.45 % (18200)Termination phase: Saturation
% 0.18/0.45
% 0.18/0.45 % (18200)Memory used [KB]: 7036
% 0.18/0.45 % (18200)Time elapsed: 0.085 s
% 0.18/0.45 % (18200)Instructions burned: 183 (million)
% 0.18/0.45 % (18200)------------------------------
% 0.18/0.45 % (18200)------------------------------
% 0.18/0.45 % (18230)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2999ds/17Mi)
% 0.18/0.46 % (18228)Instruction limit reached!
% 0.18/0.46 % (18228)------------------------------
% 0.18/0.46 % (18228)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.46 % (18228)Termination reason: Unknown
% 0.18/0.46 % (18228)Termination phase: shuffling
% 0.18/0.46
% 0.18/0.46 % (18228)Memory used [KB]: 1663
% 0.18/0.46 % (18228)Time elapsed: 0.011 s
% 0.18/0.46 % (18228)Instructions burned: 20 (million)
% 0.18/0.46 % (18228)------------------------------
% 0.18/0.46 % (18228)------------------------------
% 0.18/0.46 % (18230)Instruction limit reached!
% 0.18/0.46 % (18230)------------------------------
% 0.18/0.46 % (18230)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.46 % (18230)Termination reason: Unknown
% 0.18/0.46 % (18230)Termination phase: shuffling
% 0.18/0.46
% 0.18/0.46 % (18230)Memory used [KB]: 1535
% 0.18/0.46 % (18230)Time elapsed: 0.010 s
% 0.18/0.46 % (18230)Instructions burned: 18 (million)
% 0.18/0.46 % (18230)------------------------------
% 0.18/0.46 % (18230)------------------------------
% 0.18/0.46 % (18231)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi)
% 0.18/0.46 % (18231)Instruction limit reached!
% 0.18/0.46 % (18231)------------------------------
% 0.18/0.46 % (18231)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.46 % (18231)Termination reason: Unknown
% 0.18/0.46 % (18231)Termination phase: shuffling
% 0.18/0.46
% 0.18/0.46 % (18231)Memory used [KB]: 1279
% 0.18/0.46 % (18231)Time elapsed: 0.004 s
% 0.18/0.46 % (18231)Instructions burned: 3 (million)
% 0.18/0.46 % (18231)------------------------------
% 0.18/0.46 % (18231)------------------------------
% 0.18/0.47 % (18232)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on theBenchmark for (2998ds/30Mi)
% 0.18/0.47 % (18229)Refutation not found, incomplete strategy
% 0.18/0.47 % (18229)------------------------------
% 0.18/0.47 % (18229)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.47 % (18229)Termination reason: Refutation not found, incomplete strategy
% 0.18/0.47
% 0.18/0.47
% 0.18/0.47 % (18229)Memory used [KB]: 6268
% 0.18/0.47 % (18229)Time elapsed: 0.026 s
% 0.18/0.47 % (18229)Instructions burned: 56 (million)
% 0.18/0.47 % (18229)------------------------------
% 0.18/0.47 % (18229)------------------------------
% 0.18/0.47 % (18233)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on theBenchmark for (2998ds/127Mi)
% 0.18/0.48 % (18234)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on theBenchmark for (2998ds/100Mi)
% 0.18/0.48 % (18232)Instruction limit reached!
% 0.18/0.48 % (18232)------------------------------
% 0.18/0.48 % (18232)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.48 % (18232)Termination reason: Unknown
% 0.18/0.48 % (18232)Termination phase: Property scanning
% 0.18/0.48
% 0.18/0.48 % (18232)Memory used [KB]: 1791
% 0.18/0.48 % (18232)Time elapsed: 0.016 s
% 0.18/0.48 % (18232)Instructions burned: 30 (million)
% 0.18/0.48 % (18232)------------------------------
% 0.18/0.48 % (18232)------------------------------
% 0.18/0.49 % (18235)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 theBenchmark for (2998ds/3Mi)
% 0.18/0.49 % (18235)Instruction limit reached!
% 0.18/0.49 % (18235)------------------------------
% 0.18/0.49 % (18235)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.49 % (18235)Termination reason: Unknown
% 0.18/0.49 % (18235)Termination phase: shuffling
% 0.18/0.49
% 0.18/0.49 % (18235)Memory used [KB]: 1279
% 0.18/0.49 % (18235)Time elapsed: 0.003 s
% 0.18/0.49 % (18235)Instructions burned: 3 (million)
% 0.18/0.49 % (18235)------------------------------
% 0.18/0.49 % (18235)------------------------------
% 0.18/0.50 % (18236)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 theBenchmark for (2998ds/20Mi)
% 0.18/0.50 % (18237)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 theBenchmark for (2998ds/86Mi)
% 0.18/0.50 % (18211)First to succeed.
% 0.18/0.51 % (18236)Instruction limit reached!
% 0.18/0.51 % (18236)------------------------------
% 0.18/0.51 % (18236)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.51 % (18236)Termination reason: Unknown
% 0.18/0.51 % (18236)Termination phase: Property scanning
% 0.18/0.51
% 0.18/0.51 % (18236)Memory used [KB]: 1663
% 0.18/0.51 % (18236)Time elapsed: 0.013 s
% 0.18/0.51 % (18236)Instructions burned: 21 (million)
% 0.18/0.51 % (18236)------------------------------
% 0.18/0.51 % (18236)------------------------------
% 0.18/0.52 % (18211)Refutation found. Thanks to Tanya!
% 0.18/0.52 % SZS status Theorem for theBenchmark
% 0.18/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.52 % (18211)------------------------------
% 0.18/0.52 % (18211)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.52 % (18211)Termination reason: Refutation
% 0.18/0.52
% 0.18/0.52 % (18211)Memory used [KB]: 7419
% 0.18/0.52 % (18211)Time elapsed: 0.135 s
% 0.18/0.52 % (18211)Instructions burned: 254 (million)
% 0.18/0.52 % (18211)------------------------------
% 0.18/0.52 % (18211)------------------------------
% 0.18/0.52 % (18199)Success in time 0.172 s
% 0.18/0.52 % Vampire---4.8 exiting
%------------------------------------------------------------------------------