TSTP Solution File: ALG253^1 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : ALG253^1 : TPTP v8.1.2. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : 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 : Sun May 5 04:13:10 EDT 2024
% Result : Theorem 6.84s 1.29s
% Output : Refutation 6.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 59
% Syntax : Number of formulae : 241 ( 160 unt; 26 typ; 0 def)
% Number of atoms : 3093 ( 611 equ; 0 cnn)
% Maximal formula atoms : 4 ( 14 avg)
% Number of connectives : 10665 ( 133 ~; 70 |; 0 &;7151 @)
% ( 5 <=>;1703 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 336 ( 336 >; 0 *; 0 +; 0 <<)
% Number of symbols : 58 ( 54 usr; 40 con; 0-4 aty)
% (1603 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 1741 (1558 ^ 182 !; 0 ?;1741 :)
% ( 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_142,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_143,type,
sK2: term > $o ).
thf(func_def_144,type,
sK3: term ).
thf(func_def_145,type,
sK4: ( term > $o ) > term ).
thf(func_def_146,type,
sK5: ( term > $o ) > term ).
thf(func_def_147,type,
sK6: term > term ).
thf(func_def_148,type,
sK7: subst > term ).
thf(func_def_149,type,
sK8: term ).
thf(f818,plain,
$false,
inference(avatar_sat_refutation,[],[f701,f742,f760,f774,f781,f817]) ).
thf(f817,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f816]) ).
thf(f816,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f815]) ).
thf(f815,plain,
( ( $false = $true )
| ~ spl0_1 ),
inference(backward_demodulation,[],[f804,f814]) ).
thf(f814,plain,
( ( ( sK2 @ ( sK5 @ sK2 ) )
= $false )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f813]) ).
thf(f813,plain,
( ( ( sK2 @ ( sK5 @ sK2 ) )
= $false )
| ( $false = $true )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f812,f802]) ).
thf(f802,plain,
( ( ( sK2 @ sK8 )
= $true )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f800]) ).
thf(f800,plain,
( ( ( ( sK2 @ sK8 )
=> ( ( sK2 @ ( sK5 @ sK2 ) )
=> ( sK2 @ ( ap @ sK8 @ ( sK5 @ sK2 ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f799]) ).
thf(f799,plain,
( ( ( ^ [Y0: term] :
( ( sK2 @ Y0 )
=> ( ( sK2 @ ( sK5 @ sK2 ) )
=> ( sK2 @ ( ap @ Y0 @ ( sK5 @ sK2 ) ) ) ) )
@ sK8 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f798]) ).
thf(f798,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( ( sK2 @ Y0 )
=> ( ( sK2 @ ( sK5 @ sK2 ) )
=> ( sK2 @ ( ap @ Y0 @ ( sK5 @ sK2 ) ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f797]) ).
thf(f797,plain,
( ( ( ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ Y1 )
=> ( ( sK2 @ Y0 )
=> ( sK2 @ ( ap @ Y1 @ Y0 ) ) ) ) )
@ ( sK5 @ sK2 ) )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f696]) ).
thf(f696,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ Y1 )
=> ( ( sK2 @ Y0 )
=> ( sK2 @ ( ap @ Y1 @ Y0 ) ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f694]) ).
thf(f694,plain,
( spl0_1
<=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ Y1 )
=> ( ( sK2 @ Y0 )
=> ( sK2 @ ( ap @ Y1 @ Y0 ) ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f812,plain,
( ( ( sK2 @ ( sK5 @ sK2 ) )
= $false )
| ( ( sK2 @ sK8 )
= $false )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f805]) ).
thf(f805,plain,
( ( ( sK2 @ sK8 )
= $false )
| ( ( sK2 @ ( sK5 @ sK2 ) )
= $false )
| ( $false = $true )
| ~ spl0_1 ),
inference(superposition,[],[f803,f678]) ).
thf(f678,plain,
! [X2: term,X1: term] :
( ( ( sK2 @ ( ap @ X1 @ X2 ) )
= $true )
| ( ( sK2 @ X2 )
= $false )
| ( ( sK2 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[],[f677]) ).
thf(f677,plain,
! [X2: term,X1: term] :
( ( $true
= ( ( sK2 @ X2 )
=> ( sK2 @ ( ap @ X1 @ X2 ) ) ) )
| ( ( sK2 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[],[f676]) ).
thf(f676,plain,
! [X2: term,X1: term] :
( ( ( sK2 @ X1 )
=> ( ( sK2 @ X2 )
=> ( sK2 @ ( ap @ X1 @ X2 ) ) ) )
= $true ),
inference(beta_eta_normalization,[],[f675]) ).
thf(f675,plain,
! [X2: term,X1: term] :
( $true
= ( ^ [Y0: term] :
( ( sK2 @ X1 )
=> ( ( sK2 @ Y0 )
=> ( sK2 @ ( ap @ X1 @ Y0 ) ) ) )
@ X2 ) ),
inference(pi_clausification,[],[f674]) ).
thf(f674,plain,
! [X1: term] :
( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( sK2 @ X1 )
=> ( ( sK2 @ Y0 )
=> ( sK2 @ ( ap @ X1 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f673]) ).
thf(f673,plain,
! [X1: term] :
( $true
= ( ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ Y0 )
=> ( ( sK2 @ Y1 )
=> ( sK2 @ ( ap @ Y0 @ Y1 ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[],[f585]) ).
thf(f585,plain,
( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ Y0 )
=> ( ( sK2 @ Y1 )
=> ( sK2 @ ( ap @ Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f582]) ).
thf(f582,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ Y0 )
=> ( ( sK2 @ Y1 )
=> ( sK2 @ ( ap @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ Y1 )
=> ( sK2 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( sK2 @ ( lam @ Y0 ) ) ) )
=> ( !! @ term @ sK2 ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f581]) ).
thf(f581,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK2 @ Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ Y0 )
=> ( ( sK2 @ Y1 )
=> ( sK2 @ ( ap @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ Y1 )
=> ( sK2 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( sK2 @ ( lam @ Y0 ) ) ) )
=> ( !! @ term @ sK2 ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f580]) ).
thf(f580,plain,
( ( ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[],[f578]) ).
thf(f578,plain,
( $false
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f576]) ).
thf(f576,plain,
( ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f574]) ).
thf(f574,plain,
( ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f572]) ).
thf(f572,plain,
( ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f570]) ).
thf(f570,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f568]) ).
thf(f568,plain,
( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f566]) ).
thf(f566,plain,
( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f564]) ).
thf(f564,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f562]) ).
thf(f562,plain,
( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f560]) ).
thf(f560,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f558]) ).
thf(f558,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f556]) ).
thf(f556,plain,
( $false
= ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f554]) ).
thf(f554,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f552]) ).
thf(f552,plain,
( ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f549]) ).
thf(f549,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f547]) ).
thf(f547,plain,
( ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f545]) ).
thf(f545,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f543]) ).
thf(f543,plain,
( $false
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y1 @ Y0 ) @ Y2 )
= ( push @ ( sub @ Y1 @ Y2 ) @ ( comp @ Y0 @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f541]) ).
thf(f541,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y1 @ Y0 ) @ Y2 )
= ( push @ ( sub @ Y1 @ Y2 ) @ ( comp @ Y0 @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f539]) ).
thf(f539,plain,
( $false
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y1 @ Y0 ) @ Y2 )
= ( push @ ( sub @ Y1 @ Y2 ) @ ( comp @ Y0 @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f537]) ).
thf(f537,plain,
( $false
= ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y1 @ Y0 ) @ Y2 )
= ( push @ ( sub @ Y1 @ Y2 ) @ ( comp @ Y0 @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f535]) ).
thf(f535,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y2 ) @ Y1 )
= ( sub @ Y0 @ ( comp @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y1 @ Y0 ) @ Y2 )
= ( push @ ( sub @ Y1 @ Y2 ) @ ( comp @ Y0 @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f533]) ).
thf(f533,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) )
= ( sub @ ( lam @ Y0 ) @ Y1 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y2 ) @ Y1 )
= ( sub @ Y0 @ ( comp @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y1 @ Y0 ) @ Y2 )
= ( push @ ( sub @ Y1 @ Y2 ) @ ( comp @ Y0 @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f531]) ).
thf(f531,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) )
= ( sub @ ( lam @ Y0 ) @ Y1 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y2 ) @ Y1 )
= ( sub @ Y0 @ ( comp @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y1 @ Y0 ) @ Y2 )
= ( push @ ( sub @ Y1 @ Y2 ) @ ( comp @ Y0 @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f529]) ).
thf(f529,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ one @ ( push @ Y1 @ Y0 ) )
= Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) )
= ( sub @ ( lam @ Y0 ) @ Y1 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y2 ) @ Y1 )
= ( sub @ Y0 @ ( comp @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y1 @ Y0 ) @ Y2 )
= ( push @ ( sub @ Y1 @ Y2 ) @ ( comp @ Y0 @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f528]) ).
thf(f528,plain,
( $false
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( ap @ Y1 @ Y2 ) @ Y0 )
= ( ap @ ( sub @ Y1 @ Y0 ) @ ( sub @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ one @ ( push @ Y1 @ Y0 ) )
= Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) )
= ( sub @ ( lam @ Y0 ) @ Y1 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y2 ) @ Y1 )
= ( sub @ Y0 @ ( comp @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y1 @ Y0 ) @ Y2 )
= ( push @ ( sub @ Y1 @ Y2 ) @ ( comp @ Y0 @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f527]) ).
thf(f527,plain,
( ( ~ ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( ap @ Y1 @ Y2 ) @ Y0 )
= ( ap @ ( sub @ Y1 @ Y0 ) @ ( sub @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ one @ ( push @ Y1 @ Y0 ) )
= Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) )
= ( sub @ ( lam @ Y0 ) @ Y1 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y2 ) @ Y1 )
= ( sub @ Y0 @ ( comp @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y1 @ Y0 ) @ Y2 )
= ( push @ ( sub @ Y1 @ Y2 ) @ ( comp @ Y0 @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[],[f526]) ).
thf(f526,plain,
( ( ~ ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( ap @ Y1 @ Y2 ) @ Y0 )
= ( ap @ ( sub @ Y1 @ Y0 ) @ ( sub @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ one @ ( push @ Y1 @ Y0 ) )
= Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) )
= ( sub @ ( lam @ Y0 ) @ Y1 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y2 ) @ Y1 )
= ( sub @ Y0 @ ( comp @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y1 @ Y0 ) @ Y2 )
= ( push @ ( sub @ Y1 @ Y2 ) @ ( comp @ Y0 @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f337,f517]) ).
thf(f517,plain,
( induction2_gthm
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( ap @ Y1 @ Y2 ) @ Y0 )
= ( ap @ ( sub @ Y1 @ Y0 ) @ ( sub @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ one @ ( push @ Y1 @ Y0 ) )
= Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) )
= ( sub @ ( lam @ Y0 ) @ Y1 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y2 ) @ Y1 )
= ( sub @ Y0 @ ( comp @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y1 @ Y0 ) @ Y2 )
= ( push @ ( sub @ Y1 @ Y2 ) @ ( comp @ Y0 @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f368,f428,f419,f384,f435,f410,f366,f351,f379,f352,f361,f385,f420,f356,f363,f394,f395,f409,f365,f348,f396,f389,f380,f422,f353,f390,f417]) ).
thf(f417,plain,
( induction2
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f259]) ).
thf(f259,plain,
( induction2
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f258]) ).
thf(f258,plain,
! [X0: term > $o] :
( ( ! [X1: term] :
( ( var @ X1 )
=> ( X0 @ X1 ) )
=> ( ! [X2: term,X3: term] :
( ( X0 @ X3 )
=> ( ( X0 @ X2 )
=> ( X0 @ ( ap @ X3 @ X2 ) ) ) )
=> ( ! [X4: term] :
( ! [X5: term] :
( ( X0 @ X5 )
=> ( X0 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X0 @ ( lam @ X4 ) ) )
=> ! [X6: term] : ( X0 @ X6 ) ) ) )
= induction2 ),
inference(rectify,[],[f46]) ).
thf(f46,axiom,
! [X5: term > $o] :
( ( ! [X0: term] :
( ( var @ X0 )
=> ( X5 @ X0 ) )
=> ( ! [X1: term,X0: term] :
( ( X5 @ X0 )
=> ( ( X5 @ X1 )
=> ( X5 @ ( ap @ X0 @ X1 ) ) ) )
=> ( ! [X0: term] :
( ! [X1: term] :
( ( X5 @ X1 )
=> ( X5 @ ( sub @ X0 @ ( push @ X1 @ id ) ) ) )
=> ( X5 @ ( lam @ X0 ) ) )
=> ! [X0: term] : ( X5 @ X0 ) ) ) )
= induction2 ),
file('/export/starexec/sandbox2/tmp/tmp.MYatKX2vKv/Vampire---4.8_3619',induction2) ).
thf(f390,plain,
( induction2lem
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f171]) ).
thf(f171,plain,
( induction2lem
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f170]) ).
thf(f170,plain,
! [X0: term > $o] :
( ( ! [X1: term,X2: term] :
( ( X0 @ X1 )
=> ( ( X0 @ X2 )
=> ( X0 @ ( ap @ X1 @ X2 ) ) ) )
=> ( ! [X3: term] :
( ! [X4: term] :
( ( X0 @ X4 )
=> ( X0 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X0 @ ( lam @ X3 ) ) )
=> ! [X5: term,X6: subst] :
( ! [X7: term] :
( ( var @ X7 )
=> ( X0 @ ( sub @ X7 @ X6 ) ) )
=> ( X0 @ ( sub @ X5 @ X6 ) ) ) ) )
= induction2lem ),
inference(rectify,[],[f43]) ).
thf(f43,axiom,
! [X5: term > $o] :
( ( ! [X0: term,X1: term] :
( ( X5 @ X0 )
=> ( ( X5 @ X1 )
=> ( X5 @ ( ap @ X0 @ X1 ) ) ) )
=> ( ! [X0: term] :
( ! [X1: term] :
( ( X5 @ X1 )
=> ( X5 @ ( sub @ X0 @ ( push @ X1 @ id ) ) ) )
=> ( X5 @ ( lam @ X0 ) ) )
=> ! [X0: term,X2: subst] :
( ! [X1: term] :
( ( var @ X1 )
=> ( X5 @ ( sub @ X1 @ X2 ) ) )
=> ( X5 @ ( sub @ X0 @ X2 ) ) ) ) )
= induction2lem ),
file('/export/starexec/sandbox2/tmp/tmp.MYatKX2vKv/Vampire---4.8_3619',induction2lem) ).
thf(f353,plain,
( pushprop
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f267]) ).
thf(f267,plain,
( pushprop
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f266]) ).
thf(f266,plain,
( pushprop
= ( ! [X0: subst,X1: term,X2: term > $o] :
( ! [X3: term] :
( ( var @ X3 )
=> ( X2 @ ( sub @ X3 @ X0 ) ) )
=> ( ( X2 @ X1 )
=> ! [X4: term] :
( ( var @ X4 )
=> ( X2 @ ( sub @ X4 @ ( push @ X1 @ X0 ) ) ) ) ) ) ) ),
inference(rectify,[],[f39]) ).
thf(f39,axiom,
( pushprop
= ( ! [X2: subst,X0: term,X5: term > $o] :
( ! [X1: term] :
( ( var @ X1 )
=> ( X5 @ ( sub @ X1 @ X2 ) ) )
=> ( ( X5 @ X0 )
=> ! [X1: term] :
( ( var @ X1 )
=> ( X5 @ ( sub @ X1 @ ( push @ X0 @ X2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.MYatKX2vKv/Vampire---4.8_3619',pushprop) ).
thf(f422,plain,
( induction
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f234]) ).
thf(f234,plain,
( induction
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f233]) ).
thf(f233,plain,
( induction
= ( ! [X0: term > $o] :
( ! [X1: term] :
( ( var @ X1 )
=> ( X0 @ X1 ) )
=> ( ! [X2: term,X3: term] :
( ( X0 @ X3 )
=> ( ( X0 @ X2 )
=> ( X0 @ ( ap @ X3 @ X2 ) ) ) )
=> ( ! [X4: term] :
( ( X0 @ X4 )
=> ( X0 @ ( lam @ X4 ) ) )
=> ! [X5: term] : ( X0 @ X5 ) ) ) ) ) ),
inference(rectify,[],[f23]) ).
thf(f23,axiom,
( induction
= ( ! [X5: term > $o] :
( ! [X0: term] :
( ( var @ X0 )
=> ( X5 @ X0 ) )
=> ( ! [X1: term,X0: term] :
( ( X5 @ X0 )
=> ( ( X5 @ X1 )
=> ( X5 @ ( ap @ X0 @ X1 ) ) ) )
=> ( ! [X0: term] :
( ( X5 @ X0 )
=> ( X5 @ ( lam @ X0 ) ) )
=> ! [X0: term] : ( X5 @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.MYatKX2vKv/Vampire---4.8_3619',induction) ).
thf(f380,plain,
( lamnotvar
= ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f289]) ).
thf(f289,plain,
( lamnotvar
= ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) ) ),
inference(fool_elimination,[],[f288]) ).
thf(f288,plain,
! [X0: term] :
( ( ~ ( var @ ( lam @ X0 ) ) )
= lamnotvar ),
inference(rectify,[],[f22]) ).
thf(f22,axiom,
! [X0: term] :
( ( ~ ( var @ ( lam @ X0 ) ) )
= lamnotvar ),
file('/export/starexec/sandbox2/tmp/tmp.MYatKX2vKv/Vampire---4.8_3619',lamnotvar) ).
thf(f389,plain,
( apnotvar
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f330]) ).
thf(f330,plain,
( apnotvar
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f329]) ).
thf(f329,plain,
! [X0: term,X1: term] :
( ( ~ ( var @ ( ap @ X0 @ X1 ) ) )
= apnotvar ),
inference(rectify,[],[f21]) ).
thf(f21,axiom,
! [X0: term,X1: term] :
( ( ~ ( var @ ( ap @ X0 @ X1 ) ) )
= apnotvar ),
file('/export/starexec/sandbox2/tmp/tmp.MYatKX2vKv/Vampire---4.8_3619',apnotvar) ).
thf(f396,plain,
( lamnotap
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f183]) ).
thf(f183,plain,
( lamnotap
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f182]) ).
thf(f182,plain,
( lamnotap
= ( ! [X0: term,X1: term,X2: term] :
( ( ap @ X1 @ X0 )
!= ( lam @ X2 ) ) ) ),
inference(rectify,[],[f20]) ).
thf(f20,axiom,
( lamnotap
= ( ! [X6: term,X1: term,X0: term] :
( ( lam @ X0 )
!= ( ap @ X1 @ X6 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.MYatKX2vKv/Vampire---4.8_3619',lamnotap) ).
thf(f348,plain,
( shinj
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f296]) ).
thf(f296,plain,
( shinj
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f19,axiom,
! [X0: term,X1: term] :
( ( ( ( sub @ X0 @ sh )
= ( sub @ X1 @ sh ) )
=> ( X0 = X1 ) )
= shinj ),
file('/export/starexec/sandbox2/tmp/tmp.MYatKX2vKv/Vampire---4.8_3619',shinj) ).
thf(f365,plain,
( laminj
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f225]) ).
thf(f225,plain,
( laminj
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f18,axiom,
( laminj
= ( ! [X0: term,X1: term] :
( ( ( lam @ X0 )
= ( lam @ X1 ) )
=> ( X0 = X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.MYatKX2vKv/Vampire---4.8_3619',laminj) ).
thf(f409,plain,
( apinj2
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f265]) ).
thf(f265,plain,
( apinj2
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f264]) ).
thf(f264,plain,
( apinj2
= ( ! [X0: term,X1: term,X2: term,X3: term] :
( ( ( ap @ X0 @ X2 )
= ( ap @ X3 @ X1 ) )
=> ( X1 = X2 ) ) ) ),
inference(rectify,[],[f17]) ).
thf(f17,axiom,
( apinj2
= ( ! [X0: term,X7: term,X6: term,X1: term] :
( ( ( ap @ X0 @ X6 )
= ( ap @ X1 @ X7 ) )
=> ( X6 = X7 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.MYatKX2vKv/Vampire---4.8_3619',apinj2) ).
thf(f395,plain,
( apinj1
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y2 = Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f175]) ).
thf(f175,plain,
( apinj1
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y2 = Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f174]) ).
thf(f174,plain,
( apinj1
= ( ! [X0: term,X1: term,X2: term,X3: term] :
( ( ( ap @ X1 @ X2 )
= ( ap @ X3 @ X0 ) )
=> ( X1 = X3 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f16,axiom,
( apinj1
= ( ! [X7: term,X0: term,X6: term,X1: term] :
( ( ( ap @ X0 @ X6 )
= ( ap @ X1 @ X7 ) )
=> ( X0 = X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.MYatKX2vKv/Vampire---4.8_3619',apinj1) ).
thf(f394,plain,
( ulamvarind
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f134]) ).
thf(f134,plain,
( ulamvarind
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f133]) ).
thf(f133,plain,
! [X0: term > $o] :
( ( ( X0 @ one )
=> ( ! [X1: term] :
( ( var @ X1 )
=> ( ( X0 @ X1 )
=> ( X0 @ ( sub @ X1 @ sh ) ) ) )
=> ! [X2: term] :
( ( var @ X2 )
=> ( X0 @ X2 ) ) ) )
= ulamvarind ),
inference(rectify,[],[f15]) ).
thf(f15,axiom,
! [X5: term > $o] :
( ( ( X5 @ one )
=> ( ! [X0: term] :
( ( var @ X0 )
=> ( ( X5 @ X0 )
=> ( X5 @ ( sub @ X0 @ sh ) ) ) )
=> ! [X0: term] :
( ( var @ X0 )
=> ( X5 @ X0 ) ) ) )
= ulamvarind ),
file('/export/starexec/sandbox2/tmp/tmp.MYatKX2vKv/Vampire---4.8_3619',ulamvarind) ).
thf(f363,plain,
( ulamvarsh
= ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) ) ),
inference(cnf_transformation,[],[f221]) ).
thf(f221,plain,
( ulamvarsh
= ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) ) ),
inference(fool_elimination,[],[f220]) ).
thf(f220,plain,
! [X0: term] :
( ( ( var @ X0 )
=> ( var @ ( sub @ X0 @ sh ) ) )
= ulamvarsh ),
inference(rectify,[],[f14]) ).
thf(f14,axiom,
! [X0: term] :
( ( ( var @ X0 )
=> ( var @ ( sub @ X0 @ sh ) ) )
= ulamvarsh ),
file('/export/starexec/sandbox2/tmp/tmp.MYatKX2vKv/Vampire---4.8_3619',ulamvarsh) ).
thf(f356,plain,
( ulamvar1
= ( var @ one ) ),
inference(cnf_transformation,[],[f211]) ).
thf(f211,plain,
( ulamvar1
= ( var @ one ) ),
inference(fool_elimination,[],[f13]) ).
thf(f13,axiom,
( ulamvar1
= ( var @ one ) ),
file('/export/starexec/sandbox2/tmp/tmp.MYatKX2vKv/Vampire---4.8_3619',ulamvar1) ).
thf(f420,plain,
( axscons
= ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) ) ),
inference(cnf_transformation,[],[f202]) ).
thf(f202,plain,
( axscons
= ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) ) ),
inference(fool_elimination,[],[f201]) ).
thf(f201,plain,
( axscons
= ( ! [X0: subst] :
( ( push @ ( sub @ one @ X0 ) @ ( comp @ sh @ X0 ) )
= X0 ) ) ),
inference(rectify,[],[f12]) ).
thf(f12,axiom,
( axscons
= ( ! [X2: subst] :
( ( push @ ( sub @ one @ X2 ) @ ( comp @ sh @ X2 ) )
= X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.MYatKX2vKv/Vampire---4.8_3619',axscons) ).
thf(f385,plain,
( axvarshift
= ( id
= ( push @ one @ sh ) ) ),
inference(cnf_transformation,[],[f237]) ).
thf(f237,plain,
( axvarshift
= ( id
= ( push @ one @ sh ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f11,axiom,
( axvarshift
= ( id
= ( push @ one @ sh ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.MYatKX2vKv/Vampire---4.8_3619',axvarshift) ).
thf(f361,plain,
( axidr
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) ),
inference(cnf_transformation,[],[f159]) ).
thf(f159,plain,
( axidr
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) ),
inference(fool_elimination,[],[f158]) ).
thf(f158,plain,
( axidr
= ( ! [X0: subst] :
( ( comp @ X0 @ id )
= X0 ) ) ),
inference(rectify,[],[f10]) ).
thf(f10,axiom,
( axidr
= ( ! [X2: subst] :
( ( comp @ X2 @ id )
= X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.MYatKX2vKv/Vampire---4.8_3619',axidr) ).
thf(f352,plain,
( axmap
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y1 @ Y0 ) @ Y2 )
= ( push @ ( sub @ Y1 @ Y2 ) @ ( comp @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f126]) ).
thf(f126,plain,
( axmap
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y1 @ Y0 ) @ Y2 )
= ( push @ ( sub @ Y1 @ Y2 ) @ ( comp @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f125]) ).
thf(f125,plain,
! [X0: subst,X1: term,X2: subst] :
( ( ( comp @ ( push @ X1 @ X2 ) @ X0 )
= ( push @ ( sub @ X1 @ X0 ) @ ( comp @ X2 @ X0 ) ) )
= axmap ),
inference(rectify,[],[f9]) ).
thf(f9,axiom,
! [X3: subst,X0: term,X2: subst] :
( ( ( comp @ ( push @ X0 @ X2 ) @ X3 )
= ( push @ ( sub @ X0 @ X3 ) @ ( comp @ X2 @ X3 ) ) )
= axmap ),
file('/export/starexec/sandbox2/tmp/tmp.MYatKX2vKv/Vampire---4.8_3619',axmap) ).
thf(f379,plain,
( axassoc
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f146]) ).
thf(f146,plain,
( axassoc
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f145]) ).
thf(f145,plain,
( axassoc
= ( ! [X0: subst,X1: subst,X2: subst] :
( ( comp @ X2 @ ( comp @ X1 @ X0 ) )
= ( comp @ ( comp @ X2 @ X1 ) @ X0 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f8,axiom,
( axassoc
= ( ! [X4: subst,X3: subst,X2: subst] :
( ( comp @ ( comp @ X2 @ X3 ) @ X4 )
= ( comp @ X2 @ ( comp @ X3 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.MYatKX2vKv/Vampire---4.8_3619',axassoc) ).
thf(f351,plain,
( axshiftcons
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) ) ),
inference(cnf_transformation,[],[f151]) ).
thf(f151,plain,
( axshiftcons
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) ) ),
inference(fool_elimination,[],[f150]) ).
thf(f150,plain,
! [X0: term,X1: subst] :
( ( ( comp @ sh @ ( push @ X0 @ X1 ) )
= X1 )
= axshiftcons ),
inference(rectify,[],[f7]) ).
thf(f7,axiom,
! [X0: term,X2: subst] :
( ( ( comp @ sh @ ( push @ X0 @ X2 ) )
= X2 )
= axshiftcons ),
file('/export/starexec/sandbox2/tmp/tmp.MYatKX2vKv/Vampire---4.8_3619',axshiftcons) ).
thf(f366,plain,
( axidl
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) ),
inference(cnf_transformation,[],[f307]) ).
thf(f307,plain,
( axidl
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) ),
inference(fool_elimination,[],[f306]) ).
thf(f306,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/tmp/tmp.MYatKX2vKv/Vampire---4.8_3619',axidl) ).
thf(f410,plain,
( axclos
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y2 ) @ Y1 )
= ( sub @ Y0 @ ( comp @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f305]) ).
thf(f305,plain,
( axclos
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y2 ) @ Y1 )
= ( sub @ Y0 @ ( comp @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f304]) ).
thf(f304,plain,
! [X0: subst,X1: subst,X2: term] :
( ( ( sub @ ( sub @ X2 @ X0 ) @ X1 )
= ( sub @ X2 @ ( comp @ X0 @ X1 ) ) )
= axclos ),
inference(rectify,[],[f5]) ).
thf(f5,axiom,
! [X2: subst,X3: subst,X0: term] :
( ( ( sub @ ( sub @ X0 @ X2 ) @ X3 )
= ( sub @ X0 @ ( comp @ X2 @ X3 ) ) )
= axclos ),
file('/export/starexec/sandbox2/tmp/tmp.MYatKX2vKv/Vampire---4.8_3619',axclos) ).
thf(f435,plain,
( axabs
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) )
= ( sub @ ( lam @ Y0 ) @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f249]) ).
thf(f249,plain,
( axabs
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) )
= ( sub @ ( lam @ Y0 ) @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f248]) ).
thf(f248,plain,
( axabs
= ( ! [X0: subst,X1: term] :
( ( lam @ ( sub @ X1 @ ( push @ one @ ( comp @ X0 @ sh ) ) ) )
= ( sub @ ( lam @ X1 ) @ X0 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f4,axiom,
( axabs
= ( ! [X2: subst,X0: term] :
( ( sub @ ( lam @ X0 ) @ X2 )
= ( lam @ ( sub @ X0 @ ( push @ one @ ( comp @ X2 @ sh ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.MYatKX2vKv/Vampire---4.8_3619',axabs) ).
thf(f384,plain,
( axvarid
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ),
inference(cnf_transformation,[],[f308]) ).
thf(f308,plain,
( axvarid
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f3,axiom,
! [X0: term] :
( ( ( sub @ X0 @ id )
= X0 )
= axvarid ),
file('/export/starexec/sandbox2/tmp/tmp.MYatKX2vKv/Vampire---4.8_3619',axvarid) ).
thf(f419,plain,
( axvarcons
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ one @ ( push @ Y1 @ Y0 ) )
= Y1 ) ) ) ),
inference(cnf_transformation,[],[f293]) ).
thf(f293,plain,
( axvarcons
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ one @ ( push @ Y1 @ Y0 ) )
= Y1 ) ) ) ),
inference(fool_elimination,[],[f292]) ).
thf(f292,plain,
! [X0: term,X1: subst] :
( ( ( sub @ one @ ( push @ X0 @ X1 ) )
= X0 )
= axvarcons ),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
! [X0: term,X2: subst] :
( ( ( sub @ one @ ( push @ X0 @ X2 ) )
= X0 )
= axvarcons ),
file('/export/starexec/sandbox2/tmp/tmp.MYatKX2vKv/Vampire---4.8_3619',axvarcons) ).
thf(f428,plain,
( axapp
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( ap @ Y1 @ Y2 ) @ Y0 )
= ( ap @ ( sub @ Y1 @ Y0 ) @ ( sub @ Y2 @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f285]) ).
thf(f285,plain,
( axapp
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( ap @ Y1 @ Y2 ) @ Y0 )
= ( ap @ ( sub @ Y1 @ Y0 ) @ ( sub @ Y2 @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f284]) ).
thf(f284,plain,
( axapp
= ( ! [X0: term,X1: term,X2: subst] :
( ( sub @ ( ap @ X1 @ X0 ) @ X2 )
= ( ap @ ( sub @ X1 @ X2 ) @ ( sub @ X0 @ X2 ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
( axapp
= ( ! [X1: term,X0: term,X2: subst] :
( ( sub @ ( ap @ X0 @ X1 ) @ X2 )
= ( ap @ ( sub @ X0 @ X2 ) @ ( sub @ X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.MYatKX2vKv/Vampire---4.8_3619',axapp) ).
thf(f368,plain,
( induction2_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> induction2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f320]) ).
thf(f320,plain,
( induction2_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> induction2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f319]) ).
thf(f319,plain,
( axapp
=> ( ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> induction2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= induction2_gthm ) ),
inference(rectify,[],[f47]) ).
thf(f47,axiom,
( axapp
=> ( ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> induction2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= induction2_gthm ) ),
file('/export/starexec/sandbox2/tmp/tmp.MYatKX2vKv/Vampire---4.8_3619',induction2_gthm) ).
thf(f337,plain,
( ~ induction2_gthm = $true ),
inference(cnf_transformation,[],[f219]) ).
thf(f219,plain,
( ~ induction2_gthm = $true ),
inference(fool_elimination,[],[f218]) ).
thf(f218,plain,
~ induction2_gthm,
inference(rectify,[],[f115]) ).
thf(f115,negated_conjecture,
~ induction2_gthm,
inference(negated_conjecture,[],[f114]) ).
thf(f114,conjecture,
induction2_gthm,
file('/export/starexec/sandbox2/tmp/tmp.MYatKX2vKv/Vampire---4.8_3619',thm) ).
thf(f803,plain,
( ( $false
= ( sK2 @ ( ap @ sK8 @ ( sK5 @ sK2 ) ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f801]) ).
thf(f801,plain,
( ( $false
= ( ( sK2 @ ( sK5 @ sK2 ) )
=> ( sK2 @ ( ap @ sK8 @ ( sK5 @ sK2 ) ) ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f800]) ).
thf(f804,plain,
( ( ( sK2 @ ( sK5 @ sK2 ) )
= $true )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f801]) ).
thf(f781,plain,
( ~ spl0_5
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f780]) ).
thf(f780,plain,
( $false
| ~ spl0_5
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f779]) ).
thf(f779,plain,
( ( $false = $true )
| ~ spl0_5
| ~ spl0_7 ),
inference(backward_demodulation,[],[f738,f778]) ).
thf(f778,plain,
( ( ( var @ ( sK7 @ id ) )
= $false )
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f775]) ).
thf(f775,plain,
( ( $false = $true )
| ( ( var @ ( sK7 @ id ) )
= $false )
| ~ spl0_7 ),
inference(superposition,[],[f759,f614]) ).
thf(f614,plain,
! [X1: term] :
( ( ( sK2 @ X1 )
= $true )
| ( ( var @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[],[f613]) ).
thf(f613,plain,
! [X1: term] :
( ( ( var @ X1 )
=> ( sK2 @ X1 ) )
= $true ),
inference(beta_eta_normalization,[],[f612]) ).
thf(f612,plain,
! [X1: term] :
( ( ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK2 @ Y0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[],[f583]) ).
thf(f583,plain,
( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK2 @ Y0 ) ) ) ),
inference(binary_proxy_clausification,[],[f581]) ).
thf(f759,plain,
( ( ( sK2 @ ( sK7 @ id ) )
= $false )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f757]) ).
thf(f757,plain,
( spl0_7
<=> ( ( sK2 @ ( sK7 @ id ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
thf(f738,plain,
( ( ( var @ ( sK7 @ id ) )
= $true )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f736]) ).
thf(f736,plain,
( spl0_5
<=> ( ( var @ ( sK7 @ id ) )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
thf(f774,plain,
~ spl0_6,
inference(avatar_contradiction_clause,[],[f773]) ).
thf(f773,plain,
( $false
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f767]) ).
thf(f767,plain,
( ( $false = $true )
| ~ spl0_6 ),
inference(superposition,[],[f596,f741]) ).
thf(f741,plain,
( ! [X0: term] :
( $true
= ( sK2 @ X0 ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f740]) ).
thf(f740,plain,
( spl0_6
<=> ! [X0: term] :
( $true
= ( sK2 @ X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
thf(f596,plain,
( ( sK2 @ sK3 )
= $false ),
inference(sigma_clausification,[],[f586]) ).
thf(f586,plain,
( $false
= ( !! @ term @ sK2 ) ),
inference(binary_proxy_clausification,[],[f584]) ).
thf(f584,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ Y1 )
=> ( sK2 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( sK2 @ ( lam @ Y0 ) ) ) )
=> ( !! @ term @ sK2 ) )
= $false ),
inference(binary_proxy_clausification,[],[f582]) ).
thf(f760,plain,
( spl0_7
| spl0_6
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f755,f698,f740,f757]) ).
thf(f698,plain,
( spl0_2
<=> ! [X0: subst] :
( ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( sK2 @ ( sub @ Y1 @ X0 ) ) ) )
=> ( sK2 @ ( sub @ Y0 @ X0 ) ) ) )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f755,plain,
( ! [X0: term] :
( ( $true
= ( sK2 @ X0 ) )
| ( ( sK2 @ ( sK7 @ id ) )
= $false ) )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f745,f621]) ).
thf(f621,plain,
! [X1: term] :
( ( sub @ X1 @ id )
= X1 ),
inference(equality_proxy_clausification,[],[f620]) ).
thf(f620,plain,
! [X1: term] :
( $true
= ( ( sub @ X1 @ id )
= X1 ) ),
inference(beta_eta_normalization,[],[f619]) ).
thf(f619,plain,
! [X1: term] :
( $true
= ( ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 )
@ X1 ) ),
inference(pi_clausification,[],[f534]) ).
thf(f534,plain,
( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ),
inference(binary_proxy_clausification,[],[f531]) ).
thf(f745,plain,
( ! [X0: term] :
( ( ( sK2 @ ( sK7 @ id ) )
= $false )
| ( ( sK2 @ ( sub @ X0 @ id ) )
= $true ) )
| ~ spl0_2 ),
inference(superposition,[],[f727,f621]) ).
thf(f727,plain,
( ! [X0: subst,X1: term] :
( ( ( sK2 @ ( sub @ ( sK7 @ X0 ) @ X0 ) )
= $false )
| ( ( sK2 @ ( sub @ X1 @ X0 ) )
= $true ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f726]) ).
thf(f726,plain,
( ! [X0: subst,X1: term] :
( ( ( sK2 @ ( sub @ X1 @ X0 ) )
= $true )
| ( ( ( var @ ( sK7 @ X0 ) )
=> ( sK2 @ ( sub @ ( sK7 @ X0 ) @ X0 ) ) )
= $false ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f725]) ).
thf(f725,plain,
( ! [X0: subst,X1: term] :
( ( ( ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK2 @ ( sub @ Y0 @ X0 ) ) )
@ ( sK7 @ X0 ) )
= $false )
| ( ( sK2 @ ( sub @ X1 @ X0 ) )
= $true ) )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f724]) ).
thf(f724,plain,
( ! [X0: subst,X1: term] :
( ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK2 @ ( sub @ Y0 @ X0 ) ) ) )
= $false )
| ( ( sK2 @ ( sub @ X1 @ X0 ) )
= $true ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f723]) ).
thf(f723,plain,
( ! [X0: subst,X1: term] :
( ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK2 @ ( sub @ Y0 @ X0 ) ) ) )
=> ( sK2 @ ( sub @ X1 @ X0 ) ) )
= $true )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f722]) ).
thf(f722,plain,
( ! [X0: subst,X1: term] :
( ( ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( sK2 @ ( sub @ Y1 @ X0 ) ) ) )
=> ( sK2 @ ( sub @ Y0 @ X0 ) ) )
@ X1 )
= $true )
| ~ spl0_2 ),
inference(pi_clausification,[],[f699]) ).
thf(f699,plain,
( ! [X0: subst] :
( ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( sK2 @ ( sub @ Y1 @ X0 ) ) ) )
=> ( sK2 @ ( sub @ Y0 @ X0 ) ) ) )
= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f698]) ).
thf(f742,plain,
( spl0_5
| spl0_6
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f729,f698,f740,f736]) ).
thf(f729,plain,
( ! [X0: term] :
( ( ( var @ ( sK7 @ id ) )
= $true )
| ( $true
= ( sK2 @ X0 ) ) )
| ~ spl0_2 ),
inference(superposition,[],[f728,f621]) ).
thf(f728,plain,
( ! [X0: subst,X1: term] :
( ( ( sK2 @ ( sub @ X1 @ X0 ) )
= $true )
| ( ( var @ ( sK7 @ X0 ) )
= $true ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f726]) ).
thf(f701,plain,
( spl0_2
| spl0_1 ),
inference(avatar_split_clause,[],[f691,f694,f698]) ).
thf(f691,plain,
! [X0: subst] :
( ( ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( sK2 @ ( sub @ Y1 @ X0 ) ) ) )
=> ( sK2 @ ( sub @ Y0 @ X0 ) ) ) )
= $true )
| ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ Y1 )
=> ( ( sK2 @ Y0 )
=> ( sK2 @ ( ap @ Y1 @ Y0 ) ) ) ) ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f688]) ).
thf(f688,plain,
! [X0: subst] :
( ( $false = $true )
| ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ Y1 )
=> ( ( sK2 @ Y0 )
=> ( sK2 @ ( ap @ Y1 @ Y0 ) ) ) ) ) )
= $false )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( sK2 @ ( sub @ Y1 @ X0 ) ) ) )
=> ( sK2 @ ( sub @ Y0 @ X0 ) ) ) )
= $true ) ),
inference(superposition,[],[f587,f595]) ).
thf(f595,plain,
! [X2: subst,X1: term > $o] :
( ( ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( X1 @ Y1 )
=> ( X1 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( X1 @ ( lam @ Y0 ) ) ) )
= $false )
| ( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( X1 @ ( sub @ Y1 @ X2 ) ) ) )
=> ( X1 @ ( sub @ Y0 @ X2 ) ) ) ) )
| ( $false
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( X1 @ Y1 )
=> ( ( X1 @ Y0 )
=> ( X1 @ ( ap @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f594]) ).
thf(f594,plain,
! [X2: subst,X1: term > $o] :
( ( $false
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( X1 @ Y1 )
=> ( ( X1 @ Y0 )
=> ( X1 @ ( ap @ Y1 @ Y0 ) ) ) ) ) ) )
| ( ( ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( var @ Y2 )
=> ( X1 @ ( sub @ Y2 @ Y0 ) ) ) )
=> ( X1 @ ( sub @ Y1 @ Y0 ) ) ) )
@ X2 )
= $true )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( X1 @ Y1 )
=> ( X1 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( X1 @ ( lam @ Y0 ) ) ) )
= $false ) ),
inference(pi_clausification,[],[f593]) ).
thf(f593,plain,
! [X1: term > $o] :
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( var @ Y2 )
=> ( X1 @ ( sub @ Y2 @ Y0 ) ) ) )
=> ( X1 @ ( sub @ Y1 @ Y0 ) ) ) ) )
= $true )
| ( $false
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( X1 @ Y1 )
=> ( ( X1 @ Y0 )
=> ( X1 @ ( ap @ Y1 @ Y0 ) ) ) ) ) ) )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( X1 @ Y1 )
=> ( X1 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( X1 @ ( lam @ Y0 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f592]) ).
thf(f592,plain,
! [X1: term > $o] :
( ( $false
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( X1 @ Y1 )
=> ( ( X1 @ Y0 )
=> ( X1 @ ( ap @ Y1 @ Y0 ) ) ) ) ) ) )
| ( ( ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( X1 @ Y1 )
=> ( X1 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( X1 @ ( lam @ Y0 ) ) ) )
=> ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( var @ Y2 )
=> ( X1 @ ( sub @ Y2 @ Y0 ) ) ) )
=> ( X1 @ ( sub @ Y1 @ Y0 ) ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[],[f591]) ).
thf(f591,plain,
! [X1: term > $o] :
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( X1 @ Y1 )
=> ( ( X1 @ Y0 )
=> ( X1 @ ( ap @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( X1 @ Y1 )
=> ( X1 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( X1 @ ( lam @ Y0 ) ) ) )
=> ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( var @ Y2 )
=> ( X1 @ ( sub @ Y2 @ Y0 ) ) ) )
=> ( X1 @ ( sub @ Y1 @ Y0 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[],[f590]) ).
thf(f590,plain,
! [X1: term > $o] :
( ( ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[],[f579]) ).
thf(f579,plain,
( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f576]) ).
thf(f587,plain,
( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ Y1 )
=> ( sK2 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( sK2 @ ( lam @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f584]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : ALG253^1 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.13/0.14 % 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
% 0.14/0.35 % Computer : n029.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 3 19:56:23 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 This is a TH0_THM_EQU_NAR problem
% 0.14/0.35 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/tmp/tmp.MYatKX2vKv/Vampire---4.8_3619
% 0.21/0.38 % (3767)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on Vampire---4 for (2999ds/27Mi)
% 0.21/0.38 % (3766)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on Vampire---4 for (2999ds/4Mi)
% 0.21/0.38 % (3768)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.21/0.38 % (3769)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.21/0.38 % (3765)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on Vampire---4 for (2999ds/183Mi)
% 0.21/0.38 % (3770)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on Vampire---4 for (2999ds/275Mi)
% 0.21/0.38 % (3772)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.21/0.38 % (3768)Instruction limit reached!
% 0.21/0.38 % (3768)------------------------------
% 0.21/0.38 % (3768)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (3769)Instruction limit reached!
% 0.21/0.38 % (3769)------------------------------
% 0.21/0.38 % (3769)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (3768)Termination reason: Unknown
% 0.21/0.38 % (3768)Termination phase: shuffling
% 0.21/0.38
% 0.21/0.38 % (3768)Memory used [KB]: 1279
% 0.21/0.38 % (3768)Time elapsed: 0.004 s
% 0.21/0.38 % (3768)Instructions burned: 3 (million)
% 0.21/0.38 % (3768)------------------------------
% 0.21/0.38 % (3768)------------------------------
% 0.21/0.38 % (3769)Termination reason: Unknown
% 0.21/0.38 % (3769)Termination phase: shuffling
% 0.21/0.38
% 0.21/0.38 % (3769)Memory used [KB]: 1279
% 0.21/0.38 % (3769)Time elapsed: 0.004 s
% 0.21/0.38 % (3769)Instructions burned: 3 (million)
% 0.21/0.38 % (3769)------------------------------
% 0.21/0.38 % (3769)------------------------------
% 0.21/0.38 % (3772)Instruction limit reached!
% 0.21/0.38 % (3772)------------------------------
% 0.21/0.38 % (3772)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (3772)Termination reason: Unknown
% 0.21/0.38 % (3772)Termination phase: shuffling
% 0.21/0.38
% 0.21/0.38 % (3772)Memory used [KB]: 1279
% 0.21/0.38 % (3772)Time elapsed: 0.004 s
% 0.21/0.38 % (3772)Instructions burned: 3 (million)
% 0.21/0.38 % (3772)------------------------------
% 0.21/0.38 % (3772)------------------------------
% 0.21/0.38 % (3766)Instruction limit reached!
% 0.21/0.38 % (3766)------------------------------
% 0.21/0.38 % (3766)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (3766)Termination reason: Unknown
% 0.21/0.38 % (3766)Termination phase: shuffling
% 0.21/0.38
% 0.21/0.38 % (3766)Memory used [KB]: 1279
% 0.21/0.38 % (3766)Time elapsed: 0.005 s
% 0.21/0.38 % (3766)Instructions burned: 5 (million)
% 0.21/0.38 % (3766)------------------------------
% 0.21/0.38 % (3766)------------------------------
% 0.21/0.39 % (3771)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.21/0.40 % (3767)Instruction limit reached!
% 0.21/0.40 % (3767)------------------------------
% 0.21/0.40 % (3767)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (3767)Termination reason: Unknown
% 0.21/0.40 % (3767)Termination phase: Property scanning
% 0.21/0.40
% 0.21/0.40 % (3767)Memory used [KB]: 1791
% 0.21/0.40 % (3767)Time elapsed: 0.016 s
% 0.21/0.40 % (3767)Instructions burned: 27 (million)
% 0.21/0.40 % (3767)------------------------------
% 0.21/0.40 % (3767)------------------------------
% 0.21/0.40 % (3770)Refutation not found, incomplete strategy
% 0.21/0.40 % (3770)------------------------------
% 0.21/0.40 % (3770)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (3770)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.40
% 0.21/0.40
% 0.21/0.40 % (3770)Memory used [KB]: 6140
% 0.21/0.40 % (3770)Time elapsed: 0.018 s
% 0.21/0.40 % (3770)Instructions burned: 27 (million)
% 0.21/0.40 % (3770)------------------------------
% 0.21/0.40 % (3770)------------------------------
% 0.21/0.40 % (3773)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on Vampire---4 for (2999ds/37Mi)
% 0.21/0.40 % (3774)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on Vampire---4 for (2999ds/15Mi)
% 0.21/0.40 % (3776)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on Vampire---4 for (2999ds/1041Mi)
% 0.21/0.40 % (3771)Instruction limit reached!
% 0.21/0.40 % (3771)------------------------------
% 0.21/0.40 % (3771)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (3771)Termination reason: Unknown
% 0.21/0.40 % (3771)Termination phase: Property scanning
% 0.21/0.40
% 0.21/0.40 % (3771)Memory used [KB]: 1663
% 0.21/0.40 % (3771)Time elapsed: 0.012 s
% 0.21/0.40 % (3771)Instructions burned: 19 (million)
% 0.21/0.40 % (3771)------------------------------
% 0.21/0.40 % (3771)------------------------------
% 0.21/0.40 % (3775)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.21/0.40 % (3775)Instruction limit reached!
% 0.21/0.40 % (3775)------------------------------
% 0.21/0.40 % (3775)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (3775)Termination reason: Unknown
% 0.21/0.40 % (3775)Termination phase: shuffling
% 0.21/0.40
% 0.21/0.40 % (3775)Memory used [KB]: 1279
% 0.21/0.40 % (3775)Time elapsed: 0.004 s
% 0.21/0.40 % (3775)Instructions burned: 3 (million)
% 0.21/0.40 % (3775)------------------------------
% 0.21/0.40 % (3775)------------------------------
% 0.21/0.41 % (3774)Instruction limit reached!
% 0.21/0.41 % (3774)------------------------------
% 0.21/0.41 % (3774)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (3774)Termination reason: Unknown
% 0.21/0.41 % (3774)Termination phase: Property scanning
% 0.21/0.41
% 0.21/0.41 % (3774)Memory used [KB]: 1663
% 0.21/0.41 % (3774)Time elapsed: 0.012 s
% 0.21/0.41 % (3774)Instructions burned: 16 (million)
% 0.21/0.41 % (3774)------------------------------
% 0.21/0.41 % (3774)------------------------------
% 0.21/0.41 % (3778)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on Vampire---4 for (2999ds/7Mi)
% 0.21/0.41 % (3779)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on Vampire---4 for (2999ds/16Mi)
% 0.21/0.41 % (3778)Instruction limit reached!
% 0.21/0.41 % (3778)------------------------------
% 0.21/0.41 % (3778)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (3778)Termination reason: Unknown
% 0.21/0.41 % (3778)Termination phase: shuffling
% 0.21/0.41
% 0.21/0.41 % (3778)Memory used [KB]: 1407
% 0.21/0.41 % (3778)Time elapsed: 0.006 s
% 0.21/0.41 % (3778)Instructions burned: 8 (million)
% 0.21/0.41 % (3778)------------------------------
% 0.21/0.41 % (3778)------------------------------
% 0.21/0.42 % (3780)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.21/0.42 % (3773)Instruction limit reached!
% 0.21/0.42 % (3773)------------------------------
% 0.21/0.42 % (3773)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (3773)Termination reason: Unknown
% 0.21/0.42 % (3773)Termination phase: Property scanning
% 0.21/0.42
% 0.21/0.42 % (3773)Memory used [KB]: 1791
% 0.21/0.42 % (3773)Time elapsed: 0.020 s
% 0.21/0.42 % (3773)Instructions burned: 38 (million)
% 0.21/0.42 % (3773)------------------------------
% 0.21/0.42 % (3773)------------------------------
% 0.21/0.42 % (3780)Instruction limit reached!
% 0.21/0.42 % (3780)------------------------------
% 0.21/0.42 % (3780)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (3780)Termination reason: Unknown
% 0.21/0.42 % (3780)Termination phase: shuffling
% 0.21/0.42
% 0.21/0.42 % (3780)Memory used [KB]: 1279
% 0.21/0.42 % (3780)Time elapsed: 0.004 s
% 0.21/0.42 % (3780)Instructions burned: 5 (million)
% 0.21/0.42 % (3780)------------------------------
% 0.21/0.42 % (3780)------------------------------
% 0.21/0.42 % (3781)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.21/0.42 % (3781)Instruction limit reached!
% 0.21/0.42 % (3781)------------------------------
% 0.21/0.42 % (3781)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (3781)Termination reason: Unknown
% 0.21/0.42 % (3781)Termination phase: shuffling
% 0.21/0.42
% 0.21/0.42 % (3781)Memory used [KB]: 1279
% 0.21/0.42 % (3781)Time elapsed: 0.004 s
% 0.21/0.42 % (3781)Instructions burned: 4 (million)
% 0.21/0.42 % (3781)------------------------------
% 0.21/0.42 % (3781)------------------------------
% 0.21/0.42 % (3779)Instruction limit reached!
% 0.21/0.42 % (3779)------------------------------
% 0.21/0.42 % (3779)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (3779)Termination reason: Unknown
% 0.21/0.42 % (3779)Termination phase: shuffling
% 0.21/0.42
% 0.21/0.42 % (3779)Memory used [KB]: 1535
% 0.21/0.42 % (3779)Time elapsed: 0.010 s
% 0.21/0.42 % (3779)Instructions burned: 16 (million)
% 0.21/0.42 % (3779)------------------------------
% 0.21/0.42 % (3779)------------------------------
% 0.21/0.42 % (3782)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on Vampire---4 for (2999ds/7Mi)
% 0.21/0.43 % (3782)Instruction limit reached!
% 0.21/0.43 % (3782)------------------------------
% 0.21/0.43 % (3782)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43 % (3782)Termination reason: Unknown
% 0.21/0.43 % (3782)Termination phase: shuffling
% 0.21/0.43
% 0.21/0.43 % (3782)Memory used [KB]: 1407
% 0.21/0.43 % (3782)Time elapsed: 0.006 s
% 0.21/0.43 % (3782)Instructions burned: 8 (million)
% 0.21/0.43 % (3782)------------------------------
% 0.21/0.43 % (3782)------------------------------
% 0.21/0.43 % (3783)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.21/0.43 % (3785)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.21/0.43 % (3783)Instruction limit reached!
% 0.21/0.43 % (3783)------------------------------
% 0.21/0.43 % (3783)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43 % (3783)Termination reason: Unknown
% 0.21/0.43 % (3783)Termination phase: shuffling
% 0.21/0.43
% 0.21/0.43 % (3783)Memory used [KB]: 1279
% 0.21/0.43 % (3783)Time elapsed: 0.004 s
% 0.21/0.43 % (3783)Instructions burned: 4 (million)
% 0.21/0.43 % (3783)------------------------------
% 0.21/0.43 % (3783)------------------------------
% 0.21/0.43 % (3784)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on Vampire---4 for (2999ds/4Mi)
% 0.21/0.43 % (3784)Instruction limit reached!
% 0.21/0.43 % (3784)------------------------------
% 0.21/0.43 % (3784)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43 % (3784)Termination reason: Unknown
% 0.21/0.43 % (3784)Termination phase: shuffling
% 0.21/0.43
% 0.21/0.43 % (3784)Memory used [KB]: 1279
% 0.21/0.43 % (3784)Time elapsed: 0.004 s
% 0.21/0.43 % (3784)Instructions burned: 5 (million)
% 0.21/0.43 % (3784)------------------------------
% 0.21/0.43 % (3784)------------------------------
% 0.21/0.43 % (3785)Instruction limit reached!
% 0.21/0.43 % (3785)------------------------------
% 0.21/0.43 % (3785)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43 % (3785)Termination reason: Unknown
% 0.21/0.43 % (3785)Termination phase: shuffling
% 0.21/0.43
% 0.21/0.43 % (3785)Memory used [KB]: 1663
% 0.21/0.43 % (3785)Time elapsed: 0.007 s
% 0.21/0.43 % (3785)Instructions burned: 20 (million)
% 0.21/0.44 % (3785)------------------------------
% 0.21/0.44 % (3785)------------------------------
% 0.21/0.44 % (3787)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on Vampire---4 for (2999ds/6Mi)
% 0.21/0.44 % (3786)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on Vampire---4 for (2999ds/710Mi)
% 0.21/0.44 % (3787)Instruction limit reached!
% 0.21/0.44 % (3787)------------------------------
% 0.21/0.44 % (3787)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.44 % (3787)Termination reason: Unknown
% 0.21/0.44 % (3787)Termination phase: shuffling
% 0.21/0.44
% 0.21/0.44 % (3787)Memory used [KB]: 1279
% 0.21/0.44 % (3787)Time elapsed: 0.005 s
% 0.21/0.44 % (3787)Instructions burned: 6 (million)
% 0.21/0.44 % (3787)------------------------------
% 0.21/0.44 % (3787)------------------------------
% 0.21/0.44 % (3791)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on Vampire---4 for (2999ds/6Mi)
% 0.21/0.45 % (3791)Instruction limit reached!
% 0.21/0.45 % (3791)------------------------------
% 0.21/0.45 % (3791)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.45 % (3791)Termination reason: Unknown
% 0.21/0.45 % (3791)Termination phase: shuffling
% 0.21/0.45
% 0.21/0.45 % (3791)Memory used [KB]: 1279
% 0.21/0.45 % (3791)Time elapsed: 0.003 s
% 0.21/0.45 % (3791)Instructions burned: 7 (million)
% 0.21/0.45 % (3791)------------------------------
% 0.21/0.45 % (3791)------------------------------
% 0.21/0.45 % (3788)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on Vampire---4 for (2999ds/902Mi)
% 0.21/0.45 % (3789)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on Vampire---4 for (2999ds/21Mi)
% 0.21/0.45 % (3790)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on Vampire---4 for (2999ds/5Mi)
% 0.21/0.45 % (3790)Instruction limit reached!
% 0.21/0.45 % (3790)------------------------------
% 0.21/0.45 % (3790)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.45 % (3790)Termination reason: Unknown
% 0.21/0.45 % (3790)Termination phase: shuffling
% 0.21/0.45
% 0.21/0.45 % (3790)Memory used [KB]: 1279
% 0.21/0.45 % (3790)Time elapsed: 0.005 s
% 0.21/0.45 % (3790)Instructions burned: 6 (million)
% 0.21/0.45 % (3790)------------------------------
% 0.21/0.45 % (3790)------------------------------
% 0.21/0.45 % (3793)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on Vampire---4 for (2999ds/779Mi)
% 0.21/0.45 % (3792)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on Vampire---4 for (2999ds/377Mi)
% 0.21/0.46 % (3789)Instruction limit reached!
% 0.21/0.46 % (3789)------------------------------
% 0.21/0.46 % (3789)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.46 % (3789)Termination reason: Unknown
% 0.21/0.46 % (3789)Termination phase: shuffling
% 0.21/0.46
% 0.21/0.46 % (3789)Memory used [KB]: 1663
% 0.21/0.46 % (3789)Time elapsed: 0.013 s
% 0.21/0.46 % (3789)Instructions burned: 21 (million)
% 0.21/0.46 % (3789)------------------------------
% 0.21/0.46 % (3789)------------------------------
% 0.21/0.46 % (3786)Refutation not found, incomplete strategy
% 0.21/0.46 % (3786)------------------------------
% 0.21/0.46 % (3786)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.46 % (3786)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.46
% 0.21/0.46
% 0.21/0.46 % (3786)Memory used [KB]: 6268
% 0.21/0.46 % (3786)Time elapsed: 0.027 s
% 0.21/0.46 % (3786)Instructions burned: 27 (million)
% 0.21/0.46 % (3786)------------------------------
% 0.21/0.46 % (3786)------------------------------
% 0.21/0.47 % (3794)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on Vampire---4 for (2999ds/19Mi)
% 0.21/0.48 % (3765)Instruction limit reached!
% 0.21/0.48 % (3765)------------------------------
% 0.21/0.48 % (3765)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.48 % (3765)Termination reason: Unknown
% 0.21/0.48 % (3765)Termination phase: Saturation
% 0.21/0.48
% 0.21/0.48 % (3765)Memory used [KB]: 7291
% 0.21/0.48 % (3765)Time elapsed: 0.095 s
% 0.21/0.48 % (3765)Instructions burned: 184 (million)
% 0.21/0.48 % (3765)------------------------------
% 0.21/0.48 % (3765)------------------------------
% 0.21/0.48 % (3794)Instruction limit reached!
% 0.21/0.48 % (3794)------------------------------
% 0.21/0.48 % (3794)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.48 % (3794)Termination reason: Unknown
% 0.21/0.48 % (3794)Termination phase: shuffling
% 0.21/0.48
% 0.21/0.48 % (3794)Memory used [KB]: 1663
% 0.21/0.48 % (3794)Time elapsed: 0.012 s
% 0.21/0.48 % (3794)Instructions burned: 20 (million)
% 0.21/0.48 % (3794)------------------------------
% 0.21/0.48 % (3794)------------------------------
% 0.21/0.48 % (3796)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on Vampire---4 for (2998ds/17Mi)
% 0.21/0.48 % (3796)Instruction limit reached!
% 0.21/0.48 % (3796)------------------------------
% 0.21/0.48 % (3796)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.48 % (3796)Termination reason: Unknown
% 0.21/0.48 % (3796)Termination phase: shuffling
% 0.21/0.48
% 0.21/0.48 % (3796)Memory used [KB]: 1663
% 0.21/0.48 % (3796)Time elapsed: 0.007 s
% 0.21/0.48 % (3796)Instructions burned: 18 (million)
% 0.21/0.48 % (3796)------------------------------
% 0.21/0.48 % (3796)------------------------------
% 0.21/0.49 % (3795)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on Vampire---4 for (2998ds/879Mi)
% 0.21/0.49 % (3798)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on Vampire---4 for (2998ds/30Mi)
% 0.21/0.49 % (3797)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2998ds/3Mi)
% 0.21/0.49 % (3797)Instruction limit reached!
% 0.21/0.49 % (3797)------------------------------
% 0.21/0.49 % (3797)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.49 % (3797)Termination reason: Unknown
% 0.21/0.49 % (3797)Termination phase: shuffling
% 0.21/0.49
% 0.21/0.49 % (3797)Memory used [KB]: 1279
% 0.21/0.49 % (3797)Time elapsed: 0.003 s
% 0.21/0.49 % (3797)Instructions burned: 4 (million)
% 0.21/0.49 % (3797)------------------------------
% 0.21/0.49 % (3797)------------------------------
% 0.21/0.50 % (3799)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on Vampire---4 for (2998ds/127Mi)
% 0.21/0.50 % (3798)Instruction limit reached!
% 0.21/0.50 % (3798)------------------------------
% 0.21/0.50 % (3798)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.50 % (3798)Termination reason: Unknown
% 0.21/0.50 % (3798)Termination phase: Property scanning
% 0.21/0.50
% 0.21/0.50 % (3798)Memory used [KB]: 1791
% 0.21/0.50 % (3798)Time elapsed: 0.011 s
% 0.21/0.50 % (3798)Instructions burned: 33 (million)
% 0.21/0.50 % (3798)------------------------------
% 0.21/0.50 % (3798)------------------------------
% 0.21/0.50 % (3800)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on Vampire---4 for (2998ds/100Mi)
% 0.21/0.51 % (3801)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2998ds/3Mi)
% 0.21/0.51 % (3801)Instruction limit reached!
% 0.21/0.51 % (3801)------------------------------
% 0.21/0.51 % (3801)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.51 % (3801)Termination reason: Unknown
% 0.21/0.51 % (3801)Termination phase: shuffling
% 0.21/0.51
% 0.21/0.51 % (3801)Memory used [KB]: 1279
% 0.21/0.51 % (3801)Time elapsed: 0.002 s
% 0.21/0.51 % (3801)Instructions burned: 3 (million)
% 0.21/0.51 % (3801)------------------------------
% 0.21/0.51 % (3801)------------------------------
% 0.21/0.51 % (3795)Refutation not found, incomplete strategy
% 0.21/0.51 % (3795)------------------------------
% 0.21/0.51 % (3795)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.51 % (3795)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.51
% 0.21/0.51
% 0.21/0.51 % (3795)Memory used [KB]: 6268
% 0.21/0.51 % (3795)Time elapsed: 0.024 s
% 0.21/0.51 % (3795)Instructions burned: 59 (million)
% 0.21/0.51 % (3795)------------------------------
% 0.21/0.51 % (3795)------------------------------
% 0.21/0.52 % (3802)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on Vampire---4 for (2998ds/20Mi)
% 0.21/0.52 % (3803)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on Vampire---4 for (2998ds/86Mi)
% 0.21/0.52 % (3802)Instruction limit reached!
% 0.21/0.52 % (3802)------------------------------
% 0.21/0.52 % (3802)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.52 % (3802)Termination reason: Unknown
% 0.21/0.52 % (3802)Termination phase: Property scanning
% 0.21/0.52
% 0.21/0.52 % (3802)Memory used [KB]: 1663
% 0.21/0.52 % (3802)Time elapsed: 0.008 s
% 0.21/0.52 % (3802)Instructions burned: 22 (million)
% 0.21/0.52 % (3802)------------------------------
% 0.21/0.52 % (3802)------------------------------
% 0.21/0.53 % (3800)Instruction limit reached!
% 0.21/0.53 % (3800)------------------------------
% 0.21/0.53 % (3800)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.53 % (3800)Termination reason: Unknown
% 0.21/0.53 % (3800)Termination phase: Saturation
% 0.21/0.53
% 0.21/0.53 % (3800)Memory used [KB]: 6524
% 0.21/0.53 % (3800)Time elapsed: 0.027 s
% 0.21/0.53 % (3800)Instructions burned: 100 (million)
% 0.21/0.53 % (3800)------------------------------
% 0.21/0.53 % (3800)------------------------------
% 0.21/0.53 % (3804)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on Vampire---4 for (2998ds/107Mi)
% 0.21/0.54 % (3805)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on Vampire---4 for (2998ds/39Mi)
% 0.21/0.54 % (3803)Instruction limit reached!
% 0.21/0.54 % (3803)------------------------------
% 0.21/0.54 % (3803)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.54 % (3803)Termination reason: Unknown
% 0.21/0.54 % (3803)Termination phase: Saturation
% 0.21/0.54
% 0.21/0.54 % (3803)Memory used [KB]: 2046
% 0.21/0.54 % (3803)Time elapsed: 0.023 s
% 0.21/0.54 % (3803)Instructions burned: 87 (million)
% 0.21/0.54 % (3803)------------------------------
% 0.21/0.54 % (3803)------------------------------
% 0.21/0.55 % (3805)Instruction limit reached!
% 0.21/0.55 % (3805)------------------------------
% 0.21/0.55 % (3805)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.55 % (3805)Termination reason: Unknown
% 0.21/0.55 % (3805)Termination phase: Property scanning
% 0.21/0.55
% 0.21/0.55 % (3805)Memory used [KB]: 1791
% 0.21/0.55 % (3805)Time elapsed: 0.012 s
% 0.21/0.55 % (3805)Instructions burned: 40 (million)
% 0.21/0.55 % (3805)------------------------------
% 0.21/0.55 % (3805)------------------------------
% 0.21/0.55 % (3806)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on Vampire---4 for (2998ds/448Mi)
% 0.21/0.55 % (3799)Instruction limit reached!
% 0.21/0.55 % (3799)------------------------------
% 0.21/0.55 % (3799)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.55 % (3799)Termination reason: Unknown
% 0.21/0.55 % (3799)Termination phase: Saturation
% 0.21/0.55
% 0.21/0.55 % (3799)Memory used [KB]: 6652
% 0.21/0.55 % (3799)Time elapsed: 0.053 s
% 0.21/0.55 % (3799)Instructions burned: 129 (million)
% 0.21/0.55 % (3799)------------------------------
% 0.21/0.55 % (3799)------------------------------
% 0.21/0.56 % (3807)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on Vampire---4 for (2998ds/46Mi)
% 1.58/0.56 % (3808)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on Vampire---4 for (2998ds/98Mi)
% 1.58/0.56 % (3804)Instruction limit reached!
% 1.58/0.56 % (3804)------------------------------
% 1.58/0.56 % (3804)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.58/0.56 % (3804)Termination reason: Unknown
% 1.58/0.56 % (3804)Termination phase: Saturation
% 1.58/0.56
% 1.58/0.56 % (3804)Memory used [KB]: 6524
% 1.58/0.56 % (3804)Time elapsed: 0.031 s
% 1.58/0.56 % (3804)Instructions burned: 109 (million)
% 1.58/0.56 % (3804)------------------------------
% 1.58/0.56 % (3804)------------------------------
% 1.58/0.57 % (3807)Instruction limit reached!
% 1.58/0.57 % (3807)------------------------------
% 1.58/0.57 % (3807)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.58/0.57 % (3807)Termination reason: Unknown
% 1.58/0.57 % (3807)Termination phase: SInE selection
% 1.58/0.57
% 1.58/0.57 % (3807)Memory used [KB]: 1791
% 1.58/0.57 % (3807)Time elapsed: 0.014 s
% 1.58/0.57 % (3807)Instructions burned: 48 (million)
% 1.58/0.57 % (3807)------------------------------
% 1.58/0.57 % (3807)------------------------------
% 1.58/0.57 % (3809)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on Vampire---4 for (2998ds/507Mi)
% 1.72/0.58 % (3810)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on Vampire---4 for (2997ds/149Mi)
% 1.72/0.58 % (3808)Instruction limit reached!
% 1.72/0.58 % (3808)------------------------------
% 1.72/0.58 % (3808)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.72/0.58 % (3808)Termination reason: Unknown
% 1.72/0.58 % (3808)Termination phase: Saturation
% 1.72/0.58
% 1.72/0.58 % (3808)Memory used [KB]: 2046
% 1.72/0.58 % (3808)Time elapsed: 0.026 s
% 1.72/0.58 % (3808)Instructions burned: 98 (million)
% 1.72/0.58 % (3808)------------------------------
% 1.72/0.58 % (3808)------------------------------
% 1.72/0.59 % (3811)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on Vampire---4 for (2997ds/39Mi)
% 1.72/0.59 % (3792)Instruction limit reached!
% 1.72/0.59 % (3792)------------------------------
% 1.72/0.59 % (3792)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.72/0.59 % (3792)Termination reason: Unknown
% 1.72/0.59 % (3792)Termination phase: Saturation
% 1.72/0.59
% 1.72/0.59 % (3792)Memory used [KB]: 7419
% 1.72/0.59 % (3792)Time elapsed: 0.140 s
% 1.72/0.59 % (3792)Instructions burned: 377 (million)
% 1.72/0.59 % (3792)------------------------------
% 1.72/0.59 % (3792)------------------------------
% 1.72/0.60 % (3812)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on Vampire---4 for (2997ds/6Mi)
% 1.72/0.60 % (3811)Instruction limit reached!
% 1.72/0.60 % (3811)------------------------------
% 1.72/0.60 % (3811)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.72/0.60 % (3811)Termination reason: Unknown
% 1.72/0.60 % (3811)Termination phase: Property scanning
% 1.72/0.60
% 1.72/0.60 % (3811)Memory used [KB]: 1791
% 1.72/0.60 % (3811)Time elapsed: 0.012 s
% 1.72/0.60 % (3811)Instructions burned: 40 (million)
% 1.72/0.60 % (3811)------------------------------
% 1.72/0.60 % (3811)------------------------------
% 1.72/0.60 % (3812)Instruction limit reached!
% 1.72/0.60 % (3812)------------------------------
% 1.72/0.60 % (3812)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.72/0.60 % (3812)Termination reason: Unknown
% 1.72/0.60 % (3812)Termination phase: shuffling
% 1.72/0.60
% 1.72/0.60 % (3812)Memory used [KB]: 1279
% 1.72/0.60 % (3812)Time elapsed: 0.003 s
% 1.72/0.60 % (3812)Instructions burned: 6 (million)
% 1.72/0.60 % (3812)------------------------------
% 1.72/0.60 % (3812)------------------------------
% 1.72/0.61 % (3813)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on Vampire---4 for (2997ds/1087Mi)
% 1.72/0.61 % (3814)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on Vampire---4 for (2997ds/47Mi)
% 1.72/0.62 % (3813)Refutation not found, incomplete strategy
% 1.72/0.62 % (3813)------------------------------
% 1.72/0.62 % (3813)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.72/0.62 % (3813)Termination reason: Refutation not found, incomplete strategy
% 1.72/0.62
% 1.72/0.62
% 1.72/0.62 % (3813)Memory used [KB]: 6268
% 1.72/0.62 % (3813)Time elapsed: 0.010 s
% 1.72/0.62 % (3813)Instructions burned: 28 (million)
% 1.72/0.62 % (3813)------------------------------
% 1.72/0.62 % (3813)------------------------------
% 1.72/0.62 % (3810)Instruction limit reached!
% 1.72/0.62 % (3810)------------------------------
% 1.72/0.62 % (3810)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.72/0.62 % (3810)Termination reason: Unknown
% 1.72/0.62 % (3810)Termination phase: Saturation
% 1.72/0.62
% 1.72/0.62 % (3810)Memory used [KB]: 6908
% 1.72/0.62 % (3810)Time elapsed: 0.046 s
% 1.72/0.62 % (3810)Instructions burned: 149 (million)
% 1.72/0.62 % (3810)------------------------------
% 1.72/0.62 % (3810)------------------------------
% 1.72/0.62 % (3814)Instruction limit reached!
% 1.72/0.62 % (3814)------------------------------
% 1.72/0.62 % (3814)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.72/0.62 % (3814)Termination reason: Unknown
% 1.72/0.62 % (3814)Termination phase: Property scanning
% 1.72/0.62
% 1.72/0.62 % (3814)Memory used [KB]: 1791
% 1.72/0.62 % (3814)Time elapsed: 0.014 s
% 1.72/0.62 % (3814)Instructions burned: 47 (million)
% 1.72/0.62 % (3814)------------------------------
% 1.72/0.62 % (3814)------------------------------
% 1.72/0.63 % (3815)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on Vampire---4 for (2997ds/44Mi)
% 1.72/0.63 % (3816)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on Vampire---4 for (2997ds/432Mi)
% 1.72/0.63 % (3817)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on Vampire---4 for (2997ds/62Mi)
% 2.08/0.65 % (3815)Instruction limit reached!
% 2.08/0.65 % (3815)------------------------------
% 2.08/0.65 % (3815)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.08/0.65 % (3815)Termination reason: Unknown
% 2.08/0.65 % (3815)Termination phase: SInE selection
% 2.08/0.65
% 2.08/0.65 % (3815)Memory used [KB]: 1791
% 2.08/0.65 % (3815)Time elapsed: 0.018 s
% 2.08/0.65 % (3815)Instructions burned: 45 (million)
% 2.08/0.65 % (3815)------------------------------
% 2.08/0.65 % (3815)------------------------------
% 2.08/0.65 % (3817)Instruction limit reached!
% 2.08/0.65 % (3817)------------------------------
% 2.08/0.65 % (3817)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.08/0.65 % (3817)Termination reason: Unknown
% 2.08/0.65 % (3817)Termination phase: Function definition elimination
% 2.08/0.65
% 2.08/0.65 % (3817)Memory used [KB]: 1791
% 2.08/0.65 % (3817)Time elapsed: 0.018 s
% 2.08/0.65 % (3817)Instructions burned: 64 (million)
% 2.08/0.65 % (3817)------------------------------
% 2.08/0.65 % (3817)------------------------------
% 2.18/0.66 % (3818)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on Vampire---4 for (2997ds/31Mi)
% 2.18/0.66 % (3819)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on Vampire---4 for (2996ds/96Mi)
% 2.18/0.66 % (3818)Instruction limit reached!
% 2.18/0.66 % (3818)------------------------------
% 2.18/0.66 % (3818)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.18/0.66 % (3818)Termination reason: Unknown
% 2.18/0.66 % (3818)Termination phase: Property scanning
% 2.18/0.66
% 2.18/0.66 % (3818)Memory used [KB]: 1791
% 2.18/0.66 % (3818)Time elapsed: 0.010 s
% 2.18/0.66 % (3818)Instructions burned: 32 (million)
% 2.18/0.66 % (3818)------------------------------
% 2.18/0.66 % (3818)------------------------------
% 2.18/0.67 % (3820)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on Vampire---4 for (2996ds/453Mi)
% 2.18/0.68 % (3819)Instruction limit reached!
% 2.18/0.68 % (3819)------------------------------
% 2.18/0.68 % (3819)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.18/0.68 % (3819)Termination reason: Unknown
% 2.18/0.68 % (3819)Termination phase: Saturation
% 2.18/0.68
% 2.18/0.68 % (3819)Memory used [KB]: 6524
% 2.18/0.68 % (3819)Time elapsed: 0.026 s
% 2.18/0.68 % (3819)Instructions burned: 99 (million)
% 2.18/0.68 % (3819)------------------------------
% 2.18/0.68 % (3819)------------------------------
% 2.18/0.69 % (3821)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on Vampire---4 for (2996ds/71Mi)
% 2.18/0.70 % (3806)Instruction limit reached!
% 2.18/0.70 % (3806)------------------------------
% 2.18/0.70 % (3806)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.18/0.70 % (3806)Termination reason: Unknown
% 2.18/0.70 % (3806)Termination phase: Saturation
% 2.18/0.70
% 2.18/0.70 % (3806)Memory used [KB]: 7291
% 2.18/0.70 % (3806)Time elapsed: 0.152 s
% 2.18/0.70 % (3806)Instructions burned: 448 (million)
% 2.18/0.70 % (3806)------------------------------
% 2.18/0.70 % (3806)------------------------------
% 2.18/0.71 % (3822)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on Vampire---4 for (2996ds/83Mi)
% 2.18/0.71 % (3821)Instruction limit reached!
% 2.18/0.71 % (3821)------------------------------
% 2.18/0.71 % (3821)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.18/0.71 % (3821)Termination reason: Unknown
% 2.18/0.71 % (3821)Termination phase: Function definition elimination
% 2.18/0.71
% 2.18/0.71 % (3821)Memory used [KB]: 1918
% 2.18/0.71 % (3821)Time elapsed: 0.020 s
% 2.18/0.71 % (3821)Instructions burned: 73 (million)
% 2.18/0.71 % (3821)------------------------------
% 2.18/0.71 % (3821)------------------------------
% 2.60/0.72 % (3823)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on Vampire---4 for (2996ds/11Mi)
% 2.60/0.72 % (3823)Instruction limit reached!
% 2.60/0.72 % (3823)------------------------------
% 2.60/0.72 % (3823)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.60/0.72 % (3823)Termination reason: Unknown
% 2.60/0.72 % (3823)Termination phase: shuffling
% 2.60/0.72
% 2.60/0.72 % (3823)Memory used [KB]: 1535
% 2.60/0.72 % (3823)Time elapsed: 0.005 s
% 2.60/0.72 % (3823)Instructions burned: 13 (million)
% 2.60/0.72 % (3823)------------------------------
% 2.60/0.72 % (3823)------------------------------
% 2.60/0.72 % (3822)Refutation not found, incomplete strategy
% 2.60/0.72 % (3822)------------------------------
% 2.60/0.72 % (3822)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.60/0.72 % (3822)Termination reason: Refutation not found, incomplete strategy
% 2.60/0.72
% 2.60/0.72
% 2.60/0.72 % (3822)Memory used [KB]: 6268
% 2.60/0.72 % (3822)Time elapsed: 0.017 s
% 2.60/0.72 % (3822)Instructions burned: 58 (million)
% 2.60/0.72 % (3822)------------------------------
% 2.60/0.72 % (3822)------------------------------
% 2.60/0.73 % (3824)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on Vampire---4 for (2996ds/41Mi)
% 2.60/0.73 % (3825)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on Vampire---4 for (2996ds/6Mi)
% 2.60/0.73 % (3793)Instruction limit reached!
% 2.60/0.73 % (3793)------------------------------
% 2.60/0.73 % (3793)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.60/0.73 % (3793)Termination reason: Unknown
% 2.60/0.73 % (3793)Termination phase: Saturation
% 2.60/0.73
% 2.60/0.73 % (3793)Memory used [KB]: 7931
% 2.60/0.73 % (3793)Time elapsed: 0.277 s
% 2.60/0.73 % (3793)Instructions burned: 779 (million)
% 2.60/0.73 % (3793)------------------------------
% 2.60/0.73 % (3793)------------------------------
% 2.60/0.73 % (3825)Instruction limit reached!
% 2.60/0.73 % (3825)------------------------------
% 2.60/0.73 % (3825)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.60/0.73 % (3825)Termination reason: Unknown
% 2.60/0.73 % (3825)Termination phase: shuffling
% 2.60/0.73
% 2.60/0.73 % (3825)Memory used [KB]: 1279
% 2.60/0.73 % (3825)Time elapsed: 0.003 s
% 2.60/0.73 % (3825)Instructions burned: 6 (million)
% 2.60/0.73 % (3825)------------------------------
% 2.60/0.73 % (3825)------------------------------
% 2.60/0.74 % (3824)Instruction limit reached!
% 2.60/0.74 % (3824)------------------------------
% 2.60/0.74 % (3824)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.60/0.74 % (3824)Termination reason: Unknown
% 2.60/0.74 % (3824)Termination phase: Property scanning
% 2.60/0.74
% 2.60/0.74 % (3824)Memory used [KB]: 1791
% 2.60/0.74 % (3824)Time elapsed: 0.012 s
% 2.60/0.74 % (3824)Instructions burned: 41 (million)
% 2.60/0.74 % (3824)------------------------------
% 2.60/0.74 % (3824)------------------------------
% 2.60/0.74 % (3826)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on Vampire---4 for (2996ds/150Mi)
% 2.60/0.74 % (3827)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on Vampire---4 for (2996ds/343Mi)
% 2.60/0.75 % (3809)Instruction limit reached!
% 2.60/0.75 % (3809)------------------------------
% 2.60/0.75 % (3809)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.60/0.75 % (3809)Termination reason: Unknown
% 2.60/0.75 % (3809)Termination phase: Saturation
% 2.60/0.75
% 2.60/0.75 % (3809)Memory used [KB]: 7164
% 2.60/0.75 % (3809)Time elapsed: 0.180 s
% 2.60/0.75 % (3809)Instructions burned: 507 (million)
% 2.60/0.75 % (3809)------------------------------
% 2.60/0.75 % (3809)------------------------------
% 2.60/0.75 % (3828)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on Vampire---4 for (2996ds/109Mi)
% 2.96/0.76 % (3829)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on Vampire---4 for (2996ds/253Mi)
% 2.96/0.76 % (3816)Instruction limit reached!
% 2.96/0.76 % (3816)------------------------------
% 2.96/0.76 % (3816)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.96/0.76 % (3816)Termination reason: Unknown
% 2.96/0.76 % (3816)Termination phase: Saturation
% 2.96/0.76
% 2.96/0.76 % (3816)Memory used [KB]: 2942
% 2.96/0.76 % (3816)Time elapsed: 0.155 s
% 2.96/0.76 % (3816)Instructions burned: 432 (million)
% 2.96/0.76 % (3816)------------------------------
% 2.96/0.76 % (3816)------------------------------
% 2.96/0.77 % (3829)Refutation not found, incomplete strategy
% 2.96/0.77 % (3829)------------------------------
% 2.96/0.77 % (3829)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.96/0.77 % (3829)Termination reason: Refutation not found, incomplete strategy
% 2.96/0.77
% 2.96/0.77
% 2.96/0.77 % (3829)Memory used [KB]: 6140
% 2.96/0.77 % (3829)Time elapsed: 0.011 s
% 2.96/0.77 % (3829)Instructions burned: 29 (million)
% 2.96/0.77 % (3829)------------------------------
% 2.96/0.77 % (3829)------------------------------
% 2.96/0.77 % (3830)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on Vampire---4 for (2995ds/140Mi)
% 2.96/0.78 % (3831)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on Vampire---4 for (2995ds/614Mi)
% 2.96/0.78 % (3788)Instruction limit reached!
% 2.96/0.78 % (3788)------------------------------
% 2.96/0.78 % (3788)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.96/0.78 % (3788)Termination reason: Unknown
% 2.96/0.78 % (3788)Termination phase: Saturation
% 2.96/0.78
% 2.96/0.78 % (3788)Memory used [KB]: 8443
% 2.96/0.78 % (3788)Time elapsed: 0.323 s
% 2.96/0.78 % (3788)Instructions burned: 903 (million)
% 2.96/0.78 % (3788)------------------------------
% 2.96/0.78 % (3788)------------------------------
% 2.96/0.78 % (3828)Instruction limit reached!
% 2.96/0.78 % (3828)------------------------------
% 2.96/0.78 % (3828)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.96/0.78 % (3828)Termination reason: Unknown
% 2.96/0.78 % (3828)Termination phase: Saturation
% 2.96/0.78
% 2.96/0.78 % (3828)Memory used [KB]: 6524
% 2.96/0.78 % (3828)Time elapsed: 0.030 s
% 2.96/0.78 % (3828)Instructions burned: 111 (million)
% 2.96/0.78 % (3828)------------------------------
% 2.96/0.78 % (3828)------------------------------
% 2.96/0.78 % (3776)Instruction limit reached!
% 2.96/0.78 % (3776)------------------------------
% 2.96/0.78 % (3776)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.96/0.78 % (3776)Termination reason: Unknown
% 2.96/0.78 % (3776)Termination phase: Saturation
% 2.96/0.78
% 2.96/0.78 % (3776)Memory used [KB]: 9850
% 2.96/0.78 % (3776)Time elapsed: 0.406 s
% 2.96/0.78 % (3776)Instructions burned: 1041 (million)
% 2.96/0.78 % (3776)------------------------------
% 2.96/0.78 % (3776)------------------------------
% 2.96/0.78 % (3826)Instruction limit reached!
% 2.96/0.78 % (3826)------------------------------
% 2.96/0.78 % (3826)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.96/0.78 % (3826)Termination reason: Unknown
% 2.96/0.78 % (3826)Termination phase: Property scanning
% 2.96/0.78
% 2.96/0.78 % (3826)Memory used [KB]: 3070
% 2.96/0.78 % (3826)Time elapsed: 0.043 s
% 2.96/0.78 % (3826)Instructions burned: 152 (million)
% 2.96/0.78 % (3826)------------------------------
% 2.96/0.78 % (3826)------------------------------
% 2.96/0.79 % (3830)Refutation not found, incomplete strategy
% 2.96/0.79 % (3830)------------------------------
% 2.96/0.79 % (3830)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.96/0.79 % (3830)Termination reason: Refutation not found, incomplete strategy
% 2.96/0.79
% 2.96/0.79
% 2.96/0.79 % (3830)Memory used [KB]: 6268
% 2.96/0.79 % (3830)Time elapsed: 0.015 s
% 2.96/0.79 % (3830)Instructions burned: 51 (million)
% 2.96/0.79 % (3830)------------------------------
% 2.96/0.79 % (3830)------------------------------
% 2.96/0.79 % (3833)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on Vampire---4 for (2995ds/339Mi)
% 2.96/0.79 % (3834)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=283:si=on:rtra=on_0 on Vampire---4 for (2995ds/283Mi)
% 2.96/0.79 % (3832)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on Vampire---4 for (2995ds/202Mi)
% 2.96/0.79 % (3835)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on Vampire---4 for (2995ds/134Mi)
% 2.96/0.79 % (3836)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on Vampire---4 for (2995ds/298Mi)
% 2.96/0.81 % (3832)Refutation not found, incomplete strategy
% 2.96/0.81 % (3832)------------------------------
% 2.96/0.81 % (3832)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.96/0.81 % (3832)Termination reason: Refutation not found, incomplete strategy
% 2.96/0.81
% 2.96/0.81
% 2.96/0.81 % (3832)Memory used [KB]: 6140
% 2.96/0.81 % (3832)Time elapsed: 0.016 s
% 2.96/0.81 % (3832)Instructions burned: 29 (million)
% 2.96/0.81 % (3832)------------------------------
% 2.96/0.81 % (3832)------------------------------
% 2.96/0.82 % (3820)Instruction limit reached!
% 2.96/0.82 % (3820)------------------------------
% 2.96/0.82 % (3820)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.96/0.82 % (3820)Termination reason: Unknown
% 2.96/0.82 % (3820)Termination phase: Saturation
% 2.96/0.82
% 2.96/0.82 % (3820)Memory used [KB]: 7547
% 2.96/0.82 % (3820)Time elapsed: 0.150 s
% 2.96/0.82 % (3820)Instructions burned: 453 (million)
% 2.96/0.82 % (3820)------------------------------
% 2.96/0.82 % (3820)------------------------------
% 2.96/0.82 % (3847)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on Vampire---4 for (2995ds/192Mi)
% 2.96/0.83 % (3850)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on Vampire---4 for (2995ds/258Mi)
% 3.48/0.84 % (3835)Instruction limit reached!
% 3.48/0.84 % (3835)------------------------------
% 3.48/0.84 % (3835)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.48/0.84 % (3835)Termination reason: Unknown
% 3.48/0.84 % (3835)Termination phase: Saturation
% 3.48/0.84
% 3.48/0.84 % (3835)Memory used [KB]: 6652
% 3.48/0.84 % (3835)Time elapsed: 0.050 s
% 3.48/0.84 % (3835)Instructions burned: 135 (million)
% 3.48/0.84 % (3835)------------------------------
% 3.48/0.84 % (3835)------------------------------
% 3.48/0.85 % (3855)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on Vampire---4 for (2995ds/90Mi)
% 3.48/0.87 % (3827)Instruction limit reached!
% 3.48/0.87 % (3827)------------------------------
% 3.48/0.87 % (3827)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.48/0.87 % (3827)Termination reason: Unknown
% 3.48/0.87 % (3827)Termination phase: Saturation
% 3.48/0.87
% 3.48/0.87 % (3827)Memory used [KB]: 7675
% 3.48/0.87 % (3827)Time elapsed: 0.127 s
% 3.48/0.87 % (3827)Instructions burned: 345 (million)
% 3.48/0.87 % (3827)------------------------------
% 3.48/0.87 % (3827)------------------------------
% 3.48/0.87 % (3855)Instruction limit reached!
% 3.48/0.87 % (3855)------------------------------
% 3.48/0.87 % (3855)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.48/0.87 % (3855)Termination reason: Unknown
% 3.48/0.87 % (3855)Termination phase: Saturation
% 3.48/0.87
% 3.48/0.87 % (3855)Memory used [KB]: 6652
% 3.48/0.87 % (3855)Time elapsed: 0.023 s
% 3.48/0.87 % (3855)Instructions burned: 91 (million)
% 3.48/0.87 % (3855)------------------------------
% 3.48/0.87 % (3855)------------------------------
% 3.70/0.88 % (3866)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on Vampire---4 for (2994ds/231Mi)
% 3.70/0.88 % (3847)Instruction limit reached!
% 3.70/0.88 % (3847)------------------------------
% 3.70/0.88 % (3847)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.70/0.88 % (3847)Termination reason: Unknown
% 3.70/0.88 % (3847)Termination phase: Saturation
% 3.70/0.88
% 3.70/0.88 % (3847)Memory used [KB]: 7036
% 3.70/0.88 % (3847)Time elapsed: 0.057 s
% 3.70/0.88 % (3847)Instructions burned: 194 (million)
% 3.70/0.88 % (3847)------------------------------
% 3.70/0.88 % (3847)------------------------------
% 3.70/0.88 % (3868)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on Vampire---4 for (2994ds/458Mi)
% 3.70/0.88 % (3833)Instruction limit reached!
% 3.70/0.88 % (3833)------------------------------
% 3.70/0.88 % (3833)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.70/0.88 % (3833)Termination reason: Unknown
% 3.70/0.88 % (3833)Termination phase: Saturation
% 3.70/0.88
% 3.70/0.88 % (3833)Memory used [KB]: 7036
% 3.70/0.88 % (3833)Time elapsed: 0.091 s
% 3.70/0.88 % (3833)Instructions burned: 341 (million)
% 3.70/0.88 % (3833)------------------------------
% 3.70/0.88 % (3833)------------------------------
% 3.70/0.88 % (3834)Instruction limit reached!
% 3.70/0.88 % (3834)------------------------------
% 3.70/0.88 % (3834)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.70/0.88 % (3834)Termination reason: Unknown
% 3.70/0.88 % (3834)Termination phase: Saturation
% 3.70/0.88
% 3.70/0.88 % (3834)Memory used [KB]: 6908
% 3.70/0.88 % (3834)Time elapsed: 0.093 s
% 3.70/0.88 % (3834)Instructions burned: 284 (million)
% 3.70/0.88 % (3834)------------------------------
% 3.70/0.88 % (3834)------------------------------
% 3.70/0.89 % (3873)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on Vampire---4 for (2994ds/31Mi)
% 3.70/0.89 % (3874)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on Vampire---4 for (2994ds/297Mi)
% 3.70/0.89 % (3876)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on Vampire---4 for (2994ds/987Mi)
% 3.70/0.90 % (3873)Instruction limit reached!
% 3.70/0.90 % (3873)------------------------------
% 3.70/0.90 % (3873)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.70/0.90 % (3873)Termination reason: Unknown
% 3.70/0.90 % (3873)Termination phase: Property scanning
% 3.70/0.90
% 3.70/0.90 % (3873)Memory used [KB]: 1791
% 3.70/0.90 % (3873)Time elapsed: 0.010 s
% 3.70/0.90 % (3873)Instructions burned: 34 (million)
% 3.70/0.90 % (3873)------------------------------
% 3.70/0.90 % (3873)------------------------------
% 3.70/0.90 % (3836)Instruction limit reached!
% 3.70/0.90 % (3836)------------------------------
% 3.70/0.90 % (3836)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.70/0.90 % (3836)Termination reason: Unknown
% 3.70/0.90 % (3836)Termination phase: Saturation
% 3.70/0.90
% 3.70/0.90 % (3836)Memory used [KB]: 7036
% 3.70/0.90 % (3836)Time elapsed: 0.107 s
% 3.70/0.90 % (3836)Instructions burned: 299 (million)
% 3.70/0.90 % (3836)------------------------------
% 3.70/0.90 % (3836)------------------------------
% 3.70/0.90 % (3882)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on Vampire---4 for (2994ds/182Mi)
% 3.70/0.91 % (3850)Instruction limit reached!
% 3.70/0.91 % (3850)------------------------------
% 3.70/0.91 % (3850)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.70/0.91 % (3850)Termination reason: Unknown
% 3.70/0.91 % (3850)Termination phase: Saturation
% 3.70/0.91
% 3.70/0.91 % (3850)Memory used [KB]: 7164
% 3.70/0.91 % (3850)Time elapsed: 0.074 s
% 3.70/0.91 % (3850)Instructions burned: 258 (million)
% 3.70/0.91 % (3850)------------------------------
% 3.70/0.91 % (3850)------------------------------
% 3.70/0.91 % (3885)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on Vampire---4 for (2994ds/182Mi)
% 3.70/0.91 % (3889)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on Vampire---4 for (2994ds/154Mi)
% 4.19/0.95 % (3866)Instruction limit reached!
% 4.19/0.95 % (3866)------------------------------
% 4.19/0.95 % (3866)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.19/0.95 % (3882)Instruction limit reached!
% 4.19/0.95 % (3882)------------------------------
% 4.19/0.95 % (3882)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.19/0.95 % (3882)Termination reason: Unknown
% 4.19/0.95 % (3882)Termination phase: Saturation
% 4.19/0.95
% 4.19/0.95 % (3882)Memory used [KB]: 7164
% 4.19/0.95 % (3882)Time elapsed: 0.048 s
% 4.19/0.95 % (3882)Instructions burned: 183 (million)
% 4.19/0.95 % (3882)------------------------------
% 4.19/0.95 % (3882)------------------------------
% 4.19/0.95 % (3866)Termination reason: Unknown
% 4.19/0.95 % (3866)Termination phase: Saturation
% 4.19/0.95
% 4.19/0.95 % (3866)Memory used [KB]: 7931
% 4.19/0.95 % (3866)Time elapsed: 0.074 s
% 4.19/0.95 % (3866)Instructions burned: 231 (million)
% 4.19/0.95 % (3866)------------------------------
% 4.19/0.95 % (3866)------------------------------
% 4.19/0.95 % (3889)Instruction limit reached!
% 4.19/0.95 % (3889)------------------------------
% 4.19/0.95 % (3889)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.19/0.95 % (3889)Termination reason: Unknown
% 4.19/0.95 % (3889)Termination phase: Saturation
% 4.19/0.95
% 4.19/0.95 % (3889)Memory used [KB]: 6652
% 4.19/0.95 % (3889)Time elapsed: 0.040 s
% 4.19/0.95 % (3889)Instructions burned: 156 (million)
% 4.19/0.95 % (3889)------------------------------
% 4.19/0.95 % (3889)------------------------------
% 4.38/0.96 % (3909)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on Vampire---4 for (2994ds/79Mi)
% 4.38/0.96 % (3910)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on Vampire---4 for (2994ds/216Mi)
% 4.38/0.96 % (3913)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on Vampire---4 for (2994ds/114Mi)
% 4.38/0.96 % (3885)Instruction limit reached!
% 4.38/0.96 % (3885)------------------------------
% 4.38/0.96 % (3885)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.38/0.96 % (3885)Termination reason: Unknown
% 4.38/0.96 % (3885)Termination phase: Saturation
% 4.38/0.96
% 4.38/0.96 % (3885)Memory used [KB]: 9466
% 4.38/0.96 % (3885)Time elapsed: 0.057 s
% 4.38/0.96 % (3885)Instructions burned: 184 (million)
% 4.38/0.96 % (3885)------------------------------
% 4.38/0.96 % (3885)------------------------------
% 4.38/0.96 % (3874)Instruction limit reached!
% 4.38/0.96 % (3874)------------------------------
% 4.38/0.96 % (3874)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.38/0.96 % (3874)Termination reason: Unknown
% 4.38/0.96 % (3874)Termination phase: Saturation
% 4.38/0.96
% 4.38/0.96 % (3874)Memory used [KB]: 6652
% 4.38/0.96 % (3874)Time elapsed: 0.078 s
% 4.38/0.96 % (3874)Instructions burned: 299 (million)
% 4.38/0.96 % (3874)------------------------------
% 4.38/0.96 % (3874)------------------------------
% 4.38/0.97 % (3918)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on Vampire---4 for (2993ds/922Mi)
% 4.38/0.97 % (3920)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on Vampire---4 for (2993ds/182Mi)
% 4.38/0.97 % (3831)Instruction limit reached!
% 4.38/0.97 % (3831)------------------------------
% 4.38/0.97 % (3831)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.38/0.97 % (3831)Termination reason: Unknown
% 4.38/0.97 % (3831)Termination phase: Saturation
% 4.38/0.97
% 4.38/0.97 % (3831)Memory used [KB]: 7675
% 4.38/0.97 % (3831)Time elapsed: 0.198 s
% 4.38/0.97 % (3831)Instructions burned: 614 (million)
% 4.38/0.97 % (3831)------------------------------
% 4.38/0.97 % (3831)------------------------------
% 4.38/0.98 % (3909)Instruction limit reached!
% 4.38/0.98 % (3909)------------------------------
% 4.38/0.98 % (3909)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.38/0.98 % (3909)Termination reason: Unknown
% 4.38/0.98 % (3909)Termination phase: Function definition elimination
% 4.38/0.98
% 4.38/0.98 % (3909)Memory used [KB]: 2046
% 4.38/0.98 % (3909)Time elapsed: 0.020 s
% 4.38/0.98 % (3909)Instructions burned: 81 (million)
% 4.38/0.98 % (3909)------------------------------
% 4.38/0.98 % (3909)------------------------------
% 4.38/0.98 % (3918)Refutation not found, incomplete strategy
% 4.38/0.98 % (3918)------------------------------
% 4.38/0.98 % (3918)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.38/0.98 % (3918)Termination reason: Refutation not found, incomplete strategy
% 4.38/0.98
% 4.38/0.98
% 4.38/0.98 % (3918)Memory used [KB]: 6268
% 4.38/0.98 % (3918)Time elapsed: 0.010 s
% 4.38/0.98 % (3918)Instructions burned: 28 (million)
% 4.38/0.98 % (3918)------------------------------
% 4.38/0.98 % (3918)------------------------------
% 4.38/0.98 % (3923)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on Vampire---4 for (2993ds/164Mi)
% 4.38/0.98 % (3925)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on Vampire---4 for (2993ds/50Mi)
% 4.38/0.99 % (3913)Refutation not found, incomplete strategy
% 4.38/0.99 % (3913)------------------------------
% 4.38/0.99 % (3913)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.38/0.99 % (3913)Termination reason: Refutation not found, incomplete strategy
% 4.38/0.99
% 4.38/0.99
% 4.38/0.99 % (3913)Memory used [KB]: 6652
% 4.38/0.99 % (3913)Time elapsed: 0.025 s
% 4.38/0.99 % (3913)Instructions burned: 101 (million)
% 4.38/0.99 % (3913)------------------------------
% 4.38/0.99 % (3913)------------------------------
% 4.38/0.99 % (3926)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on Vampire---4 for (2993ds/368Mi)
% 4.38/0.99 % (3928)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on Vampire---4 for (2993ds/1021Mi)
% 4.38/1.00 % (3925)Instruction limit reached!
% 4.38/1.00 % (3925)------------------------------
% 4.38/1.00 % (3925)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.38/1.00 % (3925)Termination reason: Unknown
% 4.38/1.00 % (3925)Termination phase: Property scanning
% 4.38/1.00
% 4.38/1.00 % (3925)Memory used [KB]: 1791
% 4.38/1.00 % (3925)Time elapsed: 0.014 s
% 4.38/1.00 % (3925)Instructions burned: 53 (million)
% 4.38/1.00 % (3925)------------------------------
% 4.38/1.00 % (3925)------------------------------
% 4.38/1.00 % (3923)Refutation not found, incomplete strategy
% 4.38/1.00 % (3923)------------------------------
% 4.38/1.00 % (3923)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.38/1.00 % (3923)Termination reason: Refutation not found, incomplete strategy
% 4.38/1.00
% 4.38/1.00
% 4.38/1.00 % (3923)Memory used [KB]: 1791
% 4.38/1.00 % (3923)Time elapsed: 0.017 s
% 4.38/1.00 % (3923)Instructions burned: 61 (million)
% 4.38/1.00 % (3923)------------------------------
% 4.38/1.00 % (3923)------------------------------
% 4.38/1.00 % (3935)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on Vampire---4 for (2993ds/267Mi)
% 4.38/1.01 % (3937)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on Vampire---4 for (2993ds/204Mi)
% 4.38/1.01 % (3910)Instruction limit reached!
% 4.38/1.01 % (3910)------------------------------
% 4.38/1.01 % (3910)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.38/1.01 % (3910)Termination reason: Unknown
% 4.38/1.01 % (3910)Termination phase: Saturation
% 4.38/1.01
% 4.38/1.01 % (3910)Memory used [KB]: 6524
% 4.38/1.01 % (3910)Time elapsed: 0.053 s
% 4.38/1.01 % (3910)Instructions burned: 218 (million)
% 4.38/1.01 % (3910)------------------------------
% 4.38/1.01 % (3910)------------------------------
% 4.91/1.02 % (3920)Instruction limit reached!
% 4.91/1.02 % (3920)------------------------------
% 4.91/1.02 % (3920)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.91/1.02 % (3920)Termination reason: Unknown
% 4.91/1.02 % (3920)Termination phase: Saturation
% 4.91/1.02
% 4.91/1.02 % (3920)Memory used [KB]: 6652
% 4.91/1.02 % (3920)Time elapsed: 0.046 s
% 4.91/1.02 % (3920)Instructions burned: 182 (million)
% 4.91/1.02 % (3920)------------------------------
% 4.91/1.02 % (3920)------------------------------
% 4.91/1.02 % (3868)Instruction limit reached!
% 4.91/1.02 % (3868)------------------------------
% 4.91/1.02 % (3868)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.91/1.02 % (3868)Termination reason: Unknown
% 4.91/1.02 % (3868)Termination phase: Saturation
% 4.91/1.02
% 4.91/1.02 % (3868)Memory used [KB]: 7931
% 4.91/1.02 % (3868)Time elapsed: 0.139 s
% 4.91/1.02 % (3868)Instructions burned: 459 (million)
% 4.91/1.02 % (3868)------------------------------
% 4.91/1.02 % (3868)------------------------------
% 4.91/1.02 % (3948)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on Vampire---4 for (2993ds/26Mi)
% 4.91/1.02 % (3948)Instruction limit reached!
% 4.91/1.02 % (3948)------------------------------
% 4.91/1.02 % (3948)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.91/1.02 % (3948)Termination reason: Unknown
% 4.91/1.02 % (3948)Termination phase: shuffling
% 4.91/1.02
% 4.91/1.02 % (3948)Memory used [KB]: 1791
% 4.91/1.02 % (3948)Time elapsed: 0.008 s
% 4.91/1.02 % (3948)Instructions burned: 26 (million)
% 4.91/1.02 % (3948)------------------------------
% 4.91/1.02 % (3948)------------------------------
% 4.91/1.02 % (3953)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on Vampire---4 for (2993ds/53Mi)
% 4.91/1.03 % (3954)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on Vampire---4 for (2993ds/4436Mi)
% 4.91/1.03 % (3958)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on Vampire---4 for (2993ds/1539Mi)
% 4.91/1.03 % (3954)Refutation not found, incomplete strategy
% 4.91/1.03 % (3954)------------------------------
% 4.91/1.03 % (3954)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.91/1.03 % (3954)Termination reason: Refutation not found, incomplete strategy
% 4.91/1.03
% 4.91/1.03
% 4.91/1.03 % (3954)Memory used [KB]: 6268
% 4.91/1.03 % (3954)Time elapsed: 0.010 s
% 4.91/1.03 % (3954)Instructions burned: 28 (million)
% 4.91/1.03 % (3954)------------------------------
% 4.91/1.03 % (3954)------------------------------
% 4.91/1.04 % (3953)Instruction limit reached!
% 4.91/1.04 % (3953)------------------------------
% 4.91/1.04 % (3953)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.91/1.04 % (3953)Termination reason: Unknown
% 4.91/1.04 % (3953)Termination phase: Property scanning
% 4.91/1.04
% 4.91/1.04 % (3953)Memory used [KB]: 1791
% 4.91/1.04 % (3953)Time elapsed: 0.014 s
% 4.91/1.04 % (3953)Instructions burned: 53 (million)
% 4.91/1.04 % (3953)------------------------------
% 4.91/1.04 % (3953)------------------------------
% 4.91/1.04 % (3969)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on Vampire---4 for (2993ds/408Mi)
% 4.91/1.05 % (3972)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on Vampire---4 for (2993ds/5205Mi)
% 5.66/1.07 % (3935)Instruction limit reached!
% 5.66/1.07 % (3935)------------------------------
% 5.66/1.07 % (3935)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 5.66/1.07 % (3935)Termination reason: Unknown
% 5.66/1.07 % (3935)Termination phase: Saturation
% 5.66/1.07
% 5.66/1.07 % (3935)Memory used [KB]: 6908
% 5.66/1.07 % (3935)Time elapsed: 0.070 s
% 5.66/1.07 % (3935)Instructions burned: 267 (million)
% 5.66/1.07 % (3935)------------------------------
% 5.66/1.07 % (3935)------------------------------
% 5.66/1.07 % (3937)Instruction limit reached!
% 5.66/1.07 % (3937)------------------------------
% 5.66/1.07 % (3937)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 5.66/1.07 % (3937)Termination reason: Unknown
% 5.66/1.07 % (3937)Termination phase: Saturation
% 5.66/1.07
% 5.66/1.07 % (3937)Memory used [KB]: 6780
% 5.66/1.07 % (3937)Time elapsed: 0.087 s
% 5.66/1.07 % (3937)Instructions burned: 204 (million)
% 5.66/1.07 % (3937)------------------------------
% 5.66/1.07 % (3937)------------------------------
% 5.66/1.08 % (3998)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on Vampire---4 for (2992ds/1913Mi)
% 5.66/1.08 % (3999)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on Vampire---4 for (2992ds/4350Mi)
% 5.66/1.08 % (3926)Instruction limit reached!
% 5.66/1.08 % (3926)------------------------------
% 5.66/1.08 % (3926)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 5.66/1.08 % (3926)Termination reason: Unknown
% 5.66/1.08 % (3926)Termination phase: Saturation
% 5.66/1.08
% 5.66/1.08 % (3926)Memory used [KB]: 6908
% 5.66/1.08 % (3926)Time elapsed: 0.097 s
% 5.66/1.08 % (3926)Instructions burned: 369 (million)
% 5.66/1.08 % (3926)------------------------------
% 5.66/1.08 % (3926)------------------------------
% 5.66/1.09 % (4001)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on Vampire---4 for (2992ds/68Mi)
% 5.66/1.10 % (3999)Refutation not found, incomplete strategy
% 5.66/1.10 % (3999)------------------------------
% 5.66/1.10 % (3999)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 5.66/1.10 % (3999)Termination reason: Refutation not found, incomplete strategy
% 5.66/1.10
% 5.66/1.10
% 5.66/1.10 % (3999)Memory used [KB]: 6268
% 5.66/1.10 % (3999)Time elapsed: 0.015 s
% 5.66/1.10 % (3999)Instructions burned: 53 (million)
% 5.66/1.10 % (3999)------------------------------
% 5.66/1.10 % (3999)------------------------------
% 5.66/1.10 % (4008)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on Vampire---4 for (2992ds/358Mi)
% 5.66/1.11 % (4001)Instruction limit reached!
% 5.66/1.11 % (4001)------------------------------
% 5.66/1.11 % (4001)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 5.66/1.11 % (4001)Termination reason: Unknown
% 5.66/1.11 % (4001)Termination phase: Function definition elimination
% 5.66/1.11
% 5.66/1.11 % (4001)Memory used [KB]: 1791
% 5.66/1.11 % (4001)Time elapsed: 0.019 s
% 5.66/1.11 % (4001)Instructions burned: 72 (million)
% 5.66/1.11 % (4001)------------------------------
% 5.66/1.11 % (4001)------------------------------
% 5.66/1.12 % (4018)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on Vampire---4 for (2992ds/31Mi)
% 5.66/1.13 % (4018)Instruction limit reached!
% 5.66/1.13 % (4018)------------------------------
% 5.66/1.13 % (4018)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 5.66/1.13 % (4018)Termination reason: Unknown
% 5.66/1.13 % (4018)Termination phase: Property scanning
% 5.66/1.13
% 5.66/1.13 % (4018)Memory used [KB]: 1791
% 5.66/1.13 % (4018)Time elapsed: 0.010 s
% 5.66/1.13 % (4018)Instructions burned: 33 (million)
% 5.66/1.13 % (4018)------------------------------
% 5.66/1.13 % (4018)------------------------------
% 5.66/1.13 % (4024)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on Vampire---4 for (2992ds/279Mi)
% 6.20/1.17 % (3969)Instruction limit reached!
% 6.20/1.17 % (3969)------------------------------
% 6.20/1.17 % (3969)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.20/1.17 % (3969)Termination reason: Unknown
% 6.20/1.17 % (3969)Termination phase: Saturation
% 6.20/1.17
% 6.20/1.17 % (3969)Memory used [KB]: 9466
% 6.20/1.17 % (3969)Time elapsed: 0.149 s
% 6.20/1.17 % (3969)Instructions burned: 408 (million)
% 6.20/1.17 % (3969)------------------------------
% 6.20/1.17 % (3969)------------------------------
% 6.20/1.18 % (4039)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on Vampire---4 for (2991ds/258Mi)
% 6.20/1.18 % (3876)Instruction limit reached!
% 6.20/1.18 % (3876)------------------------------
% 6.20/1.18 % (3876)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.20/1.18 % (3876)Termination reason: Unknown
% 6.20/1.18 % (3876)Termination phase: Saturation
% 6.20/1.18
% 6.20/1.18 % (3876)Memory used [KB]: 9083
% 6.20/1.18 % (3876)Time elapsed: 0.290 s
% 6.20/1.18 % (3876)Instructions burned: 988 (million)
% 6.20/1.18 % (3876)------------------------------
% 6.20/1.18 % (3876)------------------------------
% 6.20/1.19 % (4040)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on Vampire---4 for (2991ds/26Mi)
% 6.38/1.19 % (4040)Instruction limit reached!
% 6.38/1.19 % (4040)------------------------------
% 6.38/1.19 % (4040)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.38/1.19 % (4040)Termination reason: Unknown
% 6.38/1.19 % (4040)Termination phase: Property scanning
% 6.38/1.19
% 6.38/1.19 % (4040)Memory used [KB]: 1791
% 6.38/1.19 % (4040)Time elapsed: 0.009 s
% 6.38/1.19 % (4040)Instructions burned: 29 (million)
% 6.38/1.19 % (4040)------------------------------
% 6.38/1.19 % (4040)------------------------------
% 6.38/1.20 % (4041)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on Vampire---4 for (2991ds/995Mi)
% 6.38/1.21 % (4008)Instruction limit reached!
% 6.38/1.21 % (4008)------------------------------
% 6.38/1.21 % (4008)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.38/1.21 % (4008)Termination reason: Unknown
% 6.38/1.21 % (4008)Termination phase: Saturation
% 6.38/1.21
% 6.38/1.21 % (4008)Memory used [KB]: 7164
% 6.38/1.21 % (4008)Time elapsed: 0.106 s
% 6.38/1.21 % (4008)Instructions burned: 359 (million)
% 6.38/1.21 % (4008)------------------------------
% 6.38/1.21 % (4008)------------------------------
% 6.38/1.21 % (4024)Instruction limit reached!
% 6.38/1.21 % (4024)------------------------------
% 6.38/1.21 % (4024)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.38/1.21 % (4024)Termination reason: Unknown
% 6.38/1.21 % (4024)Termination phase: Saturation
% 6.38/1.21
% 6.38/1.21 % (4024)Memory used [KB]: 6908
% 6.38/1.21 % (4024)Time elapsed: 0.082 s
% 6.38/1.21 % (4024)Instructions burned: 281 (million)
% 6.38/1.21 % (4024)------------------------------
% 6.38/1.21 % (4024)------------------------------
% 6.38/1.22 % (4044)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on Vampire---4 for (2991ds/373Mi)
% 6.38/1.22 % (4047)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on Vampire---4 for (2991ds/253Mi)
% 6.73/1.24 % (4039)Instruction limit reached!
% 6.73/1.24 % (4039)------------------------------
% 6.73/1.24 % (4039)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.73/1.24 % (4039)Termination reason: Unknown
% 6.73/1.24 % (4039)Termination phase: Saturation
% 6.73/1.24
% 6.73/1.24 % (4039)Memory used [KB]: 7291
% 6.73/1.24 % (4039)Time elapsed: 0.067 s
% 6.73/1.24 % (4039)Instructions burned: 261 (million)
% 6.73/1.24 % (4039)------------------------------
% 6.73/1.24 % (4039)------------------------------
% 6.84/1.25 % (4057)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on Vampire---4 for (2991ds/832Mi)
% 6.84/1.28 % (4047)First to succeed.
% 6.84/1.29 % (4047)Refutation found. Thanks to Tanya!
% 6.84/1.29 % SZS status Theorem for Vampire---4
% 6.84/1.29 % SZS output start Proof for Vampire---4
% See solution above
% 6.84/1.29 % (4047)------------------------------
% 6.84/1.29 % (4047)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.84/1.29 % (4047)Termination reason: Refutation
% 6.84/1.29
% 6.84/1.29 % (4047)Memory used [KB]: 7931
% 6.84/1.29 % (4047)Time elapsed: 0.067 s
% 6.84/1.29 % (4047)Instructions burned: 191 (million)
% 6.84/1.29 % (4047)------------------------------
% 6.84/1.29 % (4047)------------------------------
% 6.84/1.29 % (3764)Success in time 0.937 s
% 6.84/1.29 % Vampire---4.8 exiting
%------------------------------------------------------------------------------