TSTP Solution File: ALG253^1 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : ALG253^1 : TPTP v8.2.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 18:20:12 EDT 2024
% Result : Theorem 6.79s 1.25s
% Output : Refutation 6.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 59
% Syntax : Number of formulae : 246 ( 160 unt; 26 typ; 0 def)
% Number of atoms : 3117 ( 619 equ; 0 cnn)
% Maximal formula atoms : 26 ( 14 avg)
% Number of connectives : 10719 ( 138 ~; 78 |; 0 &;7182 @)
% ( 5 <=>;1710 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 334 ( 334 >; 0 *; 0 +; 0 <<)
% Number of symbols : 58 ( 54 usr; 41 con; 0-4 aty)
% (1606 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 1756 (1563 ^ 192 !; 0 ?;1756 :)
% ( 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 > term ).
thf(func_def_147,type,
sK6: subst > term ).
thf(func_def_148,type,
sK7: term ).
thf(func_def_149,type,
sK8: term ).
thf(f846,plain,
$false,
inference(avatar_sat_refutation,[],[f700,f750,f773,f785,f838,f845]) ).
thf(f845,plain,
( ~ spl0_6
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f844]) ).
thf(f844,plain,
( $false
| ~ spl0_6
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f843]) ).
thf(f843,plain,
( ( $true = $false )
| ~ spl0_6
| ~ spl0_7 ),
inference(backward_demodulation,[],[f749,f842]) ).
thf(f842,plain,
( ( $false
= ( var @ ( sK6 @ id ) ) )
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f840]) ).
thf(f840,plain,
( ( $false
= ( var @ ( sK6 @ id ) ) )
| ( $true = $false )
| ~ spl0_7 ),
inference(superposition,[],[f612,f837]) ).
thf(f837,plain,
( ( $false
= ( sK2 @ ( sK6 @ id ) ) )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f835]) ).
thf(f835,plain,
( spl0_7
<=> ( $false
= ( sK2 @ ( sK6 @ id ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
thf(f612,plain,
! [X1: term] :
( ( $true
= ( sK2 @ X1 ) )
| ( ( var @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[],[f611]) ).
thf(f611,plain,
! [X1: term] :
( $true
= ( ( var @ X1 )
=> ( sK2 @ X1 ) ) ),
inference(beta_eta_normalization,[],[f610]) ).
thf(f610,plain,
! [X1: term] :
( $true
= ( ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK2 @ Y0 ) )
@ X1 ) ),
inference(pi_clausification,[],[f583]) ).
thf(f583,plain,
( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK2 @ Y0 ) ) ) ),
inference(binary_proxy_clausification,[],[f581]) ).
thf(f581,plain,
( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK2 @ Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ Y1 )
=> ( ( sK2 @ Y0 )
=> ( sK2 @ ( ap @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ Y1 )
=> ( sK2 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( sK2 @ ( lam @ Y0 ) ) ) )
=> ( !! @ term @ sK2 ) ) ) ) ),
inference(beta_eta_normalization,[],[f580]) ).
thf(f580,plain,
( $false
= ( ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ 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 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) )
@ sK2 ) ),
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 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ 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] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( Y0 @ ( sub @ Y1 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ 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 ) ) ) )
=> ( !! @ 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 @ 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] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( Y0 @ ( sub @ Y1 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ 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 ) ) ) )
=> ( !! @ 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 @ 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] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( Y0 @ ( sub @ Y1 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ 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 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f570]) ).
thf(f570,plain,
( $false
= ( ( !! @ 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 @ 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] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( Y0 @ ( sub @ Y1 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ 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 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f568]) ).
thf(f568,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ 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 @ 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] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( Y0 @ ( sub @ Y1 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ 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 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f566]) ).
thf(f566,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ Y2 @ Y1 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ 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 @ 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] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( Y0 @ ( sub @ Y1 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ 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 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) ) ) ) ) ) ) )
= $false ),
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 @ Y2 @ Y1 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ 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 @ 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] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( Y0 @ ( sub @ Y1 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ 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 ) ) ) )
=> ( !! @ 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 @ Y2 @ Y1 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ 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 @ 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] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( Y0 @ ( sub @ Y1 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ 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 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f560]) ).
thf(f560,plain,
( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y1 @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 @ Y1 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ 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 @ 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] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( Y0 @ ( sub @ Y1 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ 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 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f558]) ).
thf(f558,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y1 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y1 @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 @ Y1 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ 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 @ 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] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( Y0 @ ( sub @ Y1 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ 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 ) ) ) )
=> ( !! @ 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 @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y1 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y1 @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 @ Y1 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ 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 @ 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] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( Y0 @ ( sub @ Y1 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ 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 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f554]) ).
thf(f554,plain,
( $false
= ( ( !! @ 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 @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y1 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y1 @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 @ Y1 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ 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 @ 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] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( Y0 @ ( sub @ Y1 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ 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 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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 @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y1 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y1 @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 @ Y1 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ 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 @ 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] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( Y0 @ ( sub @ Y1 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ 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 ) ) ) )
=> ( !! @ 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 @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y1 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y1 @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 @ Y1 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ 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 @ 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] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( Y0 @ ( sub @ Y1 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ 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 ) ) ) )
=> ( !! @ 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 @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y1 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y1 @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 @ Y1 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ 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 @ 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] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( Y0 @ ( sub @ Y1 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ 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 ) ) ) )
=> ( !! @ 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 @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y1 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y1 @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 @ Y1 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ 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 @ 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] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( Y0 @ ( sub @ Y1 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ 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 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f543]) ).
thf(f543,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( push @ ( sub @ Y2 @ Y0 ) @ ( comp @ Y1 @ Y0 ) )
= ( comp @ ( push @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
=> ( ( !! @ 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 @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y1 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y1 @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 @ Y1 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ 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 @ 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] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( Y0 @ ( sub @ Y1 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ 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 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f541]) ).
thf(f541,plain,
( $false
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y2 ) @ Y1 )
= ( comp @ Y0 @ ( comp @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( push @ ( sub @ Y2 @ Y0 ) @ ( comp @ Y1 @ Y0 ) )
= ( comp @ ( push @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
=> ( ( !! @ 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 @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y1 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y1 @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 @ Y1 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ 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 @ 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] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( Y0 @ ( sub @ Y1 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ 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 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f539]) ).
thf(f539,plain,
( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y2 ) @ Y1 )
= ( comp @ Y0 @ ( comp @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( push @ ( sub @ Y2 @ Y0 ) @ ( comp @ Y1 @ Y0 ) )
= ( comp @ ( push @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
=> ( ( !! @ 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 @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y1 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y1 @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 @ Y1 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ 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 @ 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] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( Y0 @ ( sub @ Y1 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ 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 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f537]) ).
thf(f537,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y2 ) @ Y1 )
= ( comp @ Y0 @ ( comp @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( push @ ( sub @ Y2 @ Y0 ) @ ( comp @ Y1 @ Y0 ) )
= ( comp @ ( push @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
=> ( ( !! @ 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 @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y1 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y1 @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 @ Y1 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ 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 @ 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] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( Y0 @ ( sub @ Y1 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ 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 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f535]) ).
thf(f535,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y2 ) @ Y1 )
= ( comp @ Y0 @ ( comp @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( push @ ( sub @ Y2 @ Y0 ) @ ( comp @ Y1 @ Y0 ) )
= ( comp @ ( push @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
=> ( ( !! @ 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 @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y1 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y1 @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 @ Y1 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ 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 @ 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] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( Y0 @ ( sub @ Y1 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ 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 ) ) ) )
=> ( !! @ 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 ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y2 ) @ Y1 )
= ( comp @ Y0 @ ( comp @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( push @ ( sub @ Y2 @ Y0 ) @ ( comp @ Y1 @ Y0 ) )
= ( comp @ ( push @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
=> ( ( !! @ 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 @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y1 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y1 @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 @ Y1 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ 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 @ 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] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( Y0 @ ( sub @ Y1 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ 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 ) ) ) )
=> ( !! @ 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 ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y2 ) @ Y1 )
= ( comp @ Y0 @ ( comp @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( push @ ( sub @ Y2 @ Y0 ) @ ( comp @ Y1 @ Y0 ) )
= ( comp @ ( push @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
=> ( ( !! @ 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 @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y1 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y1 @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 @ Y1 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ 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 @ 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] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( Y0 @ ( sub @ Y1 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ 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 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f529]) ).
thf(f529,plain,
( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) )
=> ( ( !! @ 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 ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y2 ) @ Y1 )
= ( comp @ Y0 @ ( comp @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( push @ ( sub @ Y2 @ Y0 ) @ ( comp @ Y1 @ Y0 ) )
= ( comp @ ( push @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
=> ( ( !! @ 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 @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y1 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y1 @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 @ Y1 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ 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 @ 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] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( Y0 @ ( sub @ Y1 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ 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 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f528]) ).
thf(f528,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( ap @ Y2 @ Y0 ) @ Y1 )
= ( ap @ ( sub @ Y2 @ Y1 ) @ ( sub @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) )
=> ( ( !! @ 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 ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y2 ) @ Y1 )
= ( comp @ Y0 @ ( comp @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( push @ ( sub @ Y2 @ Y0 ) @ ( comp @ Y1 @ Y0 ) )
= ( comp @ ( push @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
=> ( ( !! @ 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 @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y1 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y1 @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 @ Y1 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ 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 @ 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] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( Y0 @ ( sub @ Y1 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ 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 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f527]) ).
thf(f527,plain,
( ( ~ ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( ap @ Y2 @ Y0 ) @ Y1 )
= ( ap @ ( sub @ Y2 @ Y1 ) @ ( sub @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) )
=> ( ( !! @ 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 ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y2 ) @ Y1 )
= ( comp @ Y0 @ ( comp @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( push @ ( sub @ Y2 @ Y0 ) @ ( comp @ Y1 @ Y0 ) )
= ( comp @ ( push @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
=> ( ( !! @ 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 @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y1 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y1 @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 @ Y1 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ 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 @ 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] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( Y0 @ ( sub @ Y1 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ 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 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[],[f526]) ).
thf(f526,plain,
( $true
= ( ~ ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( ap @ Y2 @ Y0 ) @ Y1 )
= ( ap @ ( sub @ Y2 @ Y1 ) @ ( sub @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) )
=> ( ( !! @ 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 ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y2 ) @ Y1 )
= ( comp @ Y0 @ ( comp @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( push @ ( sub @ Y2 @ Y0 ) @ ( comp @ Y1 @ Y0 ) )
= ( comp @ ( push @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
=> ( ( !! @ 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 @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y1 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y1 @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 @ Y1 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ 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 @ 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] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( Y0 @ ( sub @ Y1 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ 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 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f399,f517]) ).
thf(f517,plain,
( induction2_gthm
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( ap @ Y2 @ Y0 ) @ Y1 )
= ( ap @ ( sub @ Y2 @ Y1 ) @ ( sub @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) )
=> ( ( !! @ 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 ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y2 ) @ Y1 )
= ( comp @ Y0 @ ( comp @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( push @ ( sub @ Y2 @ Y0 ) @ ( comp @ Y1 @ Y0 ) )
= ( comp @ ( push @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
=> ( ( !! @ 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 @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y1 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y1 @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 @ Y1 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ 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 @ 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] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( Y0 @ ( sub @ Y1 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ 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 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f354,f423,f432,f445,f406,f412,f437,f440,f371,f407,f359,f433,f378,f416,f366,f400,f393,f447,f349,f357,f425,f427,f347,f368,f441,f369,f377]) ).
thf(f377,plain,
( induction2
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ 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 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f289]) ).
thf(f289,plain,
( induction2
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ 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 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f288]) ).
thf(f288,plain,
! [X0: term > $o] :
( ( ! [X1: term] :
( ( var @ X1 )
=> ( X0 @ X1 ) )
=> ( ! [X2: term,X3: term] :
( ( X0 @ X2 )
=> ( ( X0 @ X3 )
=> ( X0 @ ( ap @ X2 @ X3 ) ) ) )
=> ( ! [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 ) )
=> ( ! [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] : ( X5 @ X0 ) ) ) )
= induction2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',induction2) ).
thf(f369,plain,
( induction2lem
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ 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] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( Y0 @ ( sub @ Y1 @ Y2 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f204]) ).
thf(f204,plain,
( induction2lem
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ 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] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( Y0 @ ( sub @ Y1 @ Y2 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f203]) ).
thf(f203,plain,
! [X0: term > $o] :
( ( ! [X1: term,X2: term] :
( ( X0 @ X2 )
=> ( ( X0 @ X1 )
=> ( X0 @ ( ap @ X2 @ X1 ) ) ) )
=> ( ! [X3: term] :
( ! [X4: term] :
( ( X0 @ X4 )
=> ( X0 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X0 @ ( lam @ X3 ) ) )
=> ! [X5: subst,X6: term] :
( ! [X7: term] :
( ( var @ X7 )
=> ( X0 @ ( sub @ X7 @ X5 ) ) )
=> ( X0 @ ( sub @ X6 @ X5 ) ) ) ) )
= induction2lem ),
inference(rectify,[],[f43]) ).
thf(f43,axiom,
! [X5: term > $o] :
( ( ! [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 ) ) )
=> ! [X2: subst,X0: term] :
( ! [X1: term] :
( ( var @ X1 )
=> ( X5 @ ( sub @ X1 @ X2 ) ) )
=> ( X5 @ ( sub @ X0 @ X2 ) ) ) ) )
= induction2lem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',induction2lem) ).
thf(f441,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,[],[f235]) ).
thf(f235,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,[],[f234]) ).
thf(f234,plain,
! [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 ) ) ) ) ) )
= pushprop ),
inference(rectify,[],[f39]) ).
thf(f39,axiom,
! [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 ) ) ) ) ) )
= pushprop ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop) ).
thf(f368,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,[],[f287]) ).
thf(f287,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,[],[f286]) ).
thf(f286,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/sandbox/benchmark/theBenchmark.p',induction) ).
thf(f347,plain,
( lamnotvar
= ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f244]) ).
thf(f244,plain,
( lamnotvar
= ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) ) ),
inference(fool_elimination,[],[f243]) ).
thf(f243,plain,
! [X0: term] :
( ( ~ ( var @ ( lam @ X0 ) ) )
= lamnotvar ),
inference(rectify,[],[f22]) ).
thf(f22,axiom,
! [X0: term] :
( ( ~ ( var @ ( lam @ X0 ) ) )
= lamnotvar ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamnotvar) ).
thf(f427,plain,
( apnotvar
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f120]) ).
thf(f120,plain,
( apnotvar
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f119]) ).
thf(f119,plain,
( apnotvar
= ( ! [X0: term,X1: term] :
~ ( var @ ( ap @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f21]) ).
thf(f21,axiom,
( apnotvar
= ( ! [X1: term,X0: term] :
~ ( var @ ( ap @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apnotvar) ).
thf(f425,plain,
( lamnotap
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ Y2 @ Y1 )
!= ( lam @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f315]) ).
thf(f315,plain,
( lamnotap
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ Y2 @ Y1 )
!= ( lam @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f314]) ).
thf(f314,plain,
( lamnotap
= ( ! [X0: term,X1: term,X2: term] :
( ( ap @ X0 @ X1 )
!= ( lam @ X2 ) ) ) ),
inference(rectify,[],[f20]) ).
thf(f20,axiom,
( lamnotap
= ( ! [X1: term,X6: term,X0: term] :
( ( lam @ X0 )
!= ( ap @ X1 @ X6 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamnotap) ).
thf(f357,plain,
( shinj
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f187]) ).
thf(f187,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/sandbox/benchmark/theBenchmark.p',shinj) ).
thf(f349,plain,
( laminj
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f321]) ).
thf(f321,plain,
( laminj
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f18,axiom,
! [X0: term,X1: term] :
( ( ( ( lam @ X0 )
= ( lam @ X1 ) )
=> ( X0 = X1 ) )
= laminj ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',laminj) ).
thf(f447,plain,
( apinj2
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y1 @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f299]) ).
thf(f299,plain,
( apinj2
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y1 @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f298]) ).
thf(f298,plain,
! [X0: term,X1: term,X2: term,X3: term] :
( ( ( ( ap @ X0 @ X1 )
= ( ap @ X2 @ X3 ) )
=> ( X1 = X3 ) )
= apinj2 ),
inference(rectify,[],[f17]) ).
thf(f17,axiom,
! [X1: term,X7: term,X0: term,X6: term] :
( ( ( ( ap @ X0 @ X6 )
= ( ap @ X1 @ X7 ) )
=> ( X6 = X7 ) )
= apinj2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apinj2) ).
thf(f393,plain,
( apinj1
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y1 = Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f328]) ).
thf(f328,plain,
( apinj1
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y1 = Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f327]) ).
thf(f327,plain,
( apinj1
= ( ! [X0: term,X1: term,X2: term,X3: term] :
( ( ( ap @ X3 @ X1 )
= ( ap @ X2 @ X0 ) )
=> ( X2 = X3 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f16,axiom,
( apinj1
= ( ! [X6: term,X7: term,X0: term,X1: term] :
( ( ( ap @ X0 @ X6 )
= ( ap @ X1 @ X7 ) )
=> ( X0 = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apinj1) ).
thf(f400,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,[],[f172]) ).
thf(f172,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,[],[f171]) ).
thf(f171,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/sandbox/benchmark/theBenchmark.p',ulamvarind) ).
thf(f366,plain,
( ulamvarsh
= ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) ) ),
inference(cnf_transformation,[],[f297]) ).
thf(f297,plain,
( ulamvarsh
= ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) ) ),
inference(fool_elimination,[],[f296]) ).
thf(f296,plain,
( ulamvarsh
= ( ! [X0: term] :
( ( var @ X0 )
=> ( var @ ( sub @ X0 @ sh ) ) ) ) ),
inference(rectify,[],[f14]) ).
thf(f14,axiom,
( ulamvarsh
= ( ! [X0: term] :
( ( var @ X0 )
=> ( var @ ( sub @ X0 @ sh ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ulamvarsh) ).
thf(f416,plain,
( ulamvar1
= ( var @ one ) ),
inference(cnf_transformation,[],[f129]) ).
thf(f129,plain,
( ulamvar1
= ( var @ one ) ),
inference(fool_elimination,[],[f13]) ).
thf(f13,axiom,
( ulamvar1
= ( var @ one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ulamvar1) ).
thf(f378,plain,
( axscons
= ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) ) ),
inference(cnf_transformation,[],[f221]) ).
thf(f221,plain,
( axscons
= ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) ) ),
inference(fool_elimination,[],[f220]) ).
thf(f220,plain,
! [X0: subst] :
( ( ( push @ ( sub @ one @ X0 ) @ ( comp @ sh @ X0 ) )
= X0 )
= axscons ),
inference(rectify,[],[f12]) ).
thf(f12,axiom,
! [X2: subst] :
( ( ( push @ ( sub @ one @ X2 ) @ ( comp @ sh @ X2 ) )
= X2 )
= axscons ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axscons) ).
thf(f433,plain,
( axvarshift
= ( id
= ( push @ one @ sh ) ) ),
inference(cnf_transformation,[],[f213]) ).
thf(f213,plain,
( axvarshift
= ( id
= ( push @ one @ sh ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f11,axiom,
( axvarshift
= ( id
= ( push @ one @ sh ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axvarshift) ).
thf(f359,plain,
( axidr
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) ),
inference(cnf_transformation,[],[f217]) ).
thf(f217,plain,
( axidr
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) ),
inference(fool_elimination,[],[f216]) ).
thf(f216,plain,
! [X0: subst] :
( ( ( comp @ X0 @ id )
= X0 )
= axidr ),
inference(rectify,[],[f10]) ).
thf(f10,axiom,
! [X2: subst] :
( ( ( comp @ X2 @ id )
= X2 )
= axidr ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axidr) ).
thf(f407,plain,
( axmap
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( push @ ( sub @ Y2 @ Y0 ) @ ( comp @ Y1 @ Y0 ) )
= ( comp @ ( push @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f248]) ).
thf(f248,plain,
( axmap
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( push @ ( sub @ Y2 @ Y0 ) @ ( comp @ Y1 @ Y0 ) )
= ( comp @ ( push @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f247]) ).
thf(f247,plain,
( axmap
= ( ! [X0: term,X1: subst,X2: subst] :
( ( push @ ( sub @ X0 @ X2 ) @ ( comp @ X1 @ X2 ) )
= ( comp @ ( push @ X0 @ X1 ) @ X2 ) ) ) ),
inference(rectify,[],[f9]) ).
thf(f9,axiom,
( axmap
= ( ! [X0: term,X2: subst,X3: subst] :
( ( comp @ ( push @ X0 @ X2 ) @ X3 )
= ( push @ ( sub @ X0 @ X3 ) @ ( comp @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axmap) ).
thf(f371,plain,
( axassoc
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y2 ) @ Y1 )
= ( comp @ Y0 @ ( comp @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f210]) ).
thf(f210,plain,
( axassoc
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y2 ) @ Y1 )
= ( comp @ Y0 @ ( comp @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f209]) ).
thf(f209,plain,
! [X0: subst,X1: subst,X2: subst] :
( ( ( comp @ ( comp @ X2 @ X0 ) @ X1 )
= ( comp @ X2 @ ( comp @ X0 @ X1 ) ) )
= axassoc ),
inference(rectify,[],[f8]) ).
thf(f8,axiom,
! [X3: subst,X4: subst,X2: subst] :
( ( ( comp @ ( comp @ X2 @ X3 ) @ X4 )
= ( comp @ X2 @ ( comp @ X3 @ X4 ) ) )
= axassoc ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axassoc) ).
thf(f440,plain,
( axshiftcons
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) ) ),
inference(cnf_transformation,[],[f146]) ).
thf(f146,plain,
( axshiftcons
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) ) ),
inference(fool_elimination,[],[f145]) ).
thf(f145,plain,
( axshiftcons
= ( ! [X0: subst,X1: term] :
( ( comp @ sh @ ( push @ X1 @ X0 ) )
= X0 ) ) ),
inference(rectify,[],[f7]) ).
thf(f7,axiom,
( axshiftcons
= ( ! [X2: subst,X0: term] :
( ( comp @ sh @ ( push @ X0 @ X2 ) )
= X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axshiftcons) ).
thf(f437,plain,
( axidl
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) ),
inference(cnf_transformation,[],[f196]) ).
thf(f196,plain,
( axidl
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) ),
inference(fool_elimination,[],[f195]) ).
thf(f195,plain,
! [X0: subst] :
( ( ( comp @ id @ X0 )
= X0 )
= axidl ),
inference(rectify,[],[f6]) ).
thf(f6,axiom,
! [X2: subst] :
( ( ( comp @ id @ X2 )
= X2 )
= axidl ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axidl) ).
thf(f412,plain,
( axclos
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f330]) ).
thf(f330,plain,
( axclos
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f329]) ).
thf(f329,plain,
! [X0: subst,X1: term,X2: subst] :
( ( ( sub @ X1 @ ( comp @ X2 @ X0 ) )
= ( sub @ ( sub @ X1 @ X2 ) @ X0 ) )
= axclos ),
inference(rectify,[],[f5]) ).
thf(f5,axiom,
! [X3: subst,X0: term,X2: subst] :
( ( ( sub @ ( sub @ X0 @ X2 ) @ X3 )
= ( sub @ X0 @ ( comp @ X2 @ X3 ) ) )
= axclos ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axclos) ).
thf(f406,plain,
( axabs
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) )
= ( sub @ ( lam @ Y0 ) @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f194]) ).
thf(f194,plain,
( axabs
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) )
= ( sub @ ( lam @ Y0 ) @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f193]) ).
thf(f193,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/sandbox/benchmark/theBenchmark.p',axabs) ).
thf(f445,plain,
( axvarid
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ),
inference(cnf_transformation,[],[f236]) ).
thf(f236,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/sandbox/benchmark/theBenchmark.p',axvarid) ).
thf(f432,plain,
( axvarcons
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) ) ),
inference(cnf_transformation,[],[f164]) ).
thf(f164,plain,
( axvarcons
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) ) ),
inference(fool_elimination,[],[f163]) ).
thf(f163,plain,
( axvarcons
= ( ! [X0: subst,X1: term] :
( ( sub @ one @ ( push @ X1 @ X0 ) )
= X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
( axvarcons
= ( ! [X2: subst,X0: term] :
( ( sub @ one @ ( push @ X0 @ X2 ) )
= X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axvarcons) ).
thf(f423,plain,
( axapp
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( ap @ Y2 @ Y0 ) @ Y1 )
= ( ap @ ( sub @ Y2 @ Y1 ) @ ( sub @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f219]) ).
thf(f219,plain,
( axapp
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( ap @ Y2 @ Y0 ) @ Y1 )
= ( ap @ ( sub @ Y2 @ Y1 ) @ ( sub @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f218]) ).
thf(f218,plain,
! [X0: term,X1: subst,X2: term] :
( ( ( sub @ ( ap @ X0 @ X2 ) @ X1 )
= ( ap @ ( sub @ X0 @ X1 ) @ ( sub @ X2 @ X1 ) ) )
= axapp ),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
! [X0: term,X2: subst,X1: term] :
( ( ( sub @ ( ap @ X0 @ X1 ) @ X2 )
= ( ap @ ( sub @ X0 @ X2 ) @ ( sub @ X1 @ X2 ) ) )
= axapp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axapp) ).
thf(f354,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,[],[f258]) ).
thf(f258,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,[],[f257]) ).
thf(f257,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(rectify,[],[f47]) ).
thf(f47,axiom,
( ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',induction2_gthm) ).
thf(f399,plain,
( $true = ~ induction2_gthm ),
inference(cnf_transformation,[],[f227]) ).
thf(f227,plain,
( $true = ~ induction2_gthm ),
inference(fool_elimination,[],[f226]) ).
thf(f226,plain,
~ induction2_gthm,
inference(rectify,[],[f115]) ).
thf(f115,negated_conjecture,
~ induction2_gthm,
inference(negated_conjecture,[],[f114]) ).
thf(f114,conjecture,
induction2_gthm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f749,plain,
( ( $true
= ( var @ ( sK6 @ id ) ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f747]) ).
thf(f747,plain,
( spl0_6
<=> ( $true
= ( var @ ( sK6 @ id ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
thf(f838,plain,
( spl0_7
| spl0_5
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f833,f696,f744,f835]) ).
thf(f744,plain,
( spl0_5
<=> ! [X0: term] :
( ( sK2 @ X0 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
thf(f696,plain,
( spl0_2
<=> ! [X0: term] :
( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( sK2 @ ( sub @ Y1 @ Y0 ) ) ) )
=> ( sK2 @ ( sub @ X0 @ Y0 ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f833,plain,
( ! [X0: term] :
( ( $false
= ( sK2 @ ( sK6 @ id ) ) )
| ( ( sK2 @ X0 )
= $true ) )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f823,f619]) ).
thf(f619,plain,
! [X1: term] :
( ( sub @ X1 @ id )
= X1 ),
inference(equality_proxy_clausification,[],[f618]) ).
thf(f618,plain,
! [X1: term] :
( $true
= ( ( sub @ X1 @ id )
= X1 ) ),
inference(beta_eta_normalization,[],[f617]) ).
thf(f617,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(f823,plain,
( ! [X0: term] :
( ( $true
= ( sK2 @ ( sub @ X0 @ id ) ) )
| ( $false
= ( sK2 @ ( sK6 @ id ) ) ) )
| ~ spl0_2 ),
inference(superposition,[],[f813,f619]) ).
thf(f813,plain,
( ! [X0: term,X1: subst] :
( ( ( sK2 @ ( sub @ ( sK6 @ X1 ) @ X1 ) )
= $false )
| ( $true
= ( sK2 @ ( sub @ X0 @ X1 ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f812]) ).
thf(f812,plain,
( ! [X0: term,X1: subst] :
( ( $true
= ( sK2 @ ( sub @ X0 @ X1 ) ) )
| ( ( ( var @ ( sK6 @ X1 ) )
=> ( sK2 @ ( sub @ ( sK6 @ X1 ) @ X1 ) ) )
= $false ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f811]) ).
thf(f811,plain,
( ! [X0: term,X1: subst] :
( ( $true
= ( sK2 @ ( sub @ X0 @ X1 ) ) )
| ( $false
= ( ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK2 @ ( sub @ Y0 @ X1 ) ) )
@ ( sK6 @ X1 ) ) ) )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f810]) ).
thf(f810,plain,
( ! [X0: term,X1: subst] :
( ( $false
= ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK2 @ ( sub @ Y0 @ X1 ) ) ) ) )
| ( $true
= ( sK2 @ ( sub @ X0 @ X1 ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f809]) ).
thf(f809,plain,
( ! [X0: term,X1: subst] :
( $true
= ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK2 @ ( sub @ Y0 @ X1 ) ) ) )
=> ( sK2 @ ( sub @ X0 @ X1 ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f808]) ).
thf(f808,plain,
( ! [X0: term,X1: subst] :
( $true
= ( ^ [Y0: subst] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( sK2 @ ( sub @ Y1 @ Y0 ) ) ) )
=> ( sK2 @ ( sub @ X0 @ Y0 ) ) )
@ X1 ) )
| ~ spl0_2 ),
inference(pi_clausification,[],[f697]) ).
thf(f697,plain,
( ! [X0: term] :
( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( sK2 @ ( sub @ Y1 @ Y0 ) ) ) )
=> ( sK2 @ ( sub @ X0 @ Y0 ) ) ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f696]) ).
thf(f785,plain,
~ spl0_5,
inference(avatar_contradiction_clause,[],[f784]) ).
thf(f784,plain,
( $false
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f777]) ).
thf(f777,plain,
( ( $true = $false )
| ~ spl0_5 ),
inference(superposition,[],[f745,f596]) ).
thf(f596,plain,
( ( sK2 @ sK3 )
= $false ),
inference(sigma_clausification,[],[f586]) ).
thf(f586,plain,
( $false
= ( !! @ term @ sK2 ) ),
inference(binary_proxy_clausification,[],[f584]) ).
thf(f584,plain,
( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ Y1 )
=> ( sK2 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( sK2 @ ( lam @ Y0 ) ) ) )
=> ( !! @ term @ sK2 ) ) ),
inference(binary_proxy_clausification,[],[f582]) ).
thf(f582,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ Y1 )
=> ( ( sK2 @ Y0 )
=> ( sK2 @ ( ap @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ 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(f745,plain,
( ! [X0: term] :
( ( sK2 @ X0 )
= $true )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f744]) ).
thf(f773,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f772]) ).
thf(f772,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f771]) ).
thf(f771,plain,
( ( $true = $false )
| ~ spl0_1 ),
inference(backward_demodulation,[],[f758,f770]) ).
thf(f770,plain,
( ( ( sK2 @ sK8 )
= $false )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f769]) ).
thf(f769,plain,
( ( ( sK2 @ sK8 )
= $false )
| ( $true = $false )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f768,f756]) ).
thf(f756,plain,
( ( $true
= ( sK2 @ sK7 ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f754]) ).
thf(f754,plain,
( ( $false
= ( ( sK2 @ sK7 )
=> ( ( sK2 @ sK8 )
=> ( sK2 @ ( ap @ sK7 @ sK8 ) ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f753]) ).
thf(f753,plain,
( ( ( ^ [Y0: term] :
( ( sK2 @ sK7 )
=> ( ( sK2 @ Y0 )
=> ( sK2 @ ( ap @ sK7 @ Y0 ) ) ) )
@ sK8 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f752]) ).
thf(f752,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( ( sK2 @ sK7 )
=> ( ( sK2 @ Y0 )
=> ( sK2 @ ( ap @ sK7 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f751]) ).
thf(f751,plain,
( ( $false
= ( ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ Y0 )
=> ( ( sK2 @ Y1 )
=> ( sK2 @ ( ap @ Y0 @ Y1 ) ) ) ) )
@ sK7 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f694]) ).
thf(f694,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ Y0 )
=> ( ( sK2 @ Y1 )
=> ( sK2 @ ( ap @ Y0 @ Y1 ) ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f692]) ).
thf(f692,plain,
( spl0_1
<=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ Y0 )
=> ( ( sK2 @ Y1 )
=> ( sK2 @ ( ap @ Y0 @ Y1 ) ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f768,plain,
( ( ( sK2 @ sK7 )
= $false )
| ( ( sK2 @ sK8 )
= $false )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f761]) ).
thf(f761,plain,
( ( ( sK2 @ sK8 )
= $false )
| ( $true = $false )
| ( ( sK2 @ sK7 )
= $false )
| ~ spl0_1 ),
inference(superposition,[],[f757,f676]) ).
thf(f676,plain,
! [X2: term,X1: term] :
( ( $true
= ( sK2 @ ( ap @ X2 @ X1 ) ) )
| ( ( sK2 @ X1 )
= $false )
| ( $false
= ( sK2 @ X2 ) ) ),
inference(binary_proxy_clausification,[],[f675]) ).
thf(f675,plain,
! [X2: term,X1: term] :
( ( $false
= ( sK2 @ X2 ) )
| ( $true
= ( ( sK2 @ X1 )
=> ( sK2 @ ( ap @ X2 @ X1 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f674]) ).
thf(f674,plain,
! [X2: term,X1: term] :
( $true
= ( ( sK2 @ X2 )
=> ( ( sK2 @ X1 )
=> ( sK2 @ ( ap @ X2 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[],[f673]) ).
thf(f673,plain,
! [X2: term,X1: term] :
( $true
= ( ^ [Y0: term] :
( ( sK2 @ Y0 )
=> ( ( sK2 @ X1 )
=> ( sK2 @ ( ap @ Y0 @ X1 ) ) ) )
@ X2 ) ),
inference(pi_clausification,[],[f672]) ).
thf(f672,plain,
! [X1: term] :
( ( !! @ term
@ ^ [Y0: term] :
( ( sK2 @ Y0 )
=> ( ( sK2 @ X1 )
=> ( sK2 @ ( ap @ Y0 @ X1 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[],[f671]) ).
thf(f671,plain,
! [X1: term] :
( $true
= ( ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ Y1 )
=> ( ( sK2 @ Y0 )
=> ( sK2 @ ( ap @ Y1 @ Y0 ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[],[f585]) ).
thf(f585,plain,
( $true
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ Y1 )
=> ( ( sK2 @ Y0 )
=> ( sK2 @ ( ap @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f582]) ).
thf(f757,plain,
( ( ( sK2 @ ( ap @ sK7 @ sK8 ) )
= $false )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f755]) ).
thf(f755,plain,
( ( $false
= ( ( sK2 @ sK8 )
=> ( sK2 @ ( ap @ sK7 @ sK8 ) ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f754]) ).
thf(f758,plain,
( ( $true
= ( sK2 @ sK8 ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f755]) ).
thf(f750,plain,
( spl0_5
| spl0_6
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f737,f696,f747,f744]) ).
thf(f737,plain,
( ! [X0: term] :
( ( $true
= ( var @ ( sK6 @ id ) ) )
| ( ( sK2 @ X0 )
= $true ) )
| ~ spl0_2 ),
inference(superposition,[],[f736,f619]) ).
thf(f736,plain,
( ! [X0: term,X1: subst] :
( ( $true
= ( sK2 @ ( sub @ X0 @ X1 ) ) )
| ( $true
= ( var @ ( sK6 @ X1 ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f734]) ).
thf(f734,plain,
( ! [X0: term,X1: subst] :
( ( $true
= ( sK2 @ ( sub @ X0 @ X1 ) ) )
| ( ( ( var @ ( sK6 @ X1 ) )
=> ( sK2 @ ( sub @ ( sK6 @ X1 ) @ X1 ) ) )
= $false ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f733]) ).
thf(f733,plain,
( ! [X0: term,X1: subst] :
( ( $true
= ( sK2 @ ( sub @ X0 @ X1 ) ) )
| ( $false
= ( ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK2 @ ( sub @ Y0 @ X1 ) ) )
@ ( sK6 @ X1 ) ) ) )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f732]) ).
thf(f732,plain,
( ! [X0: term,X1: subst] :
( ( $false
= ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK2 @ ( sub @ Y0 @ X1 ) ) ) ) )
| ( $true
= ( sK2 @ ( sub @ X0 @ X1 ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f731]) ).
thf(f731,plain,
( ! [X0: term,X1: subst] :
( $true
= ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK2 @ ( sub @ Y0 @ X1 ) ) ) )
=> ( sK2 @ ( sub @ X0 @ X1 ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f730]) ).
thf(f730,plain,
( ! [X0: term,X1: subst] :
( $true
= ( ^ [Y0: subst] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( sK2 @ ( sub @ Y1 @ Y0 ) ) ) )
=> ( sK2 @ ( sub @ X0 @ Y0 ) ) )
@ X1 ) )
| ~ spl0_2 ),
inference(pi_clausification,[],[f697]) ).
thf(f700,plain,
( spl0_2
| spl0_1 ),
inference(avatar_split_clause,[],[f688,f692,f696]) ).
thf(f688,plain,
! [X0: term] :
( ( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( sK2 @ ( sub @ Y1 @ Y0 ) ) ) )
=> ( sK2 @ ( sub @ X0 @ Y0 ) ) ) ) )
| ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ Y0 )
=> ( ( sK2 @ Y1 )
=> ( sK2 @ ( ap @ Y0 @ Y1 ) ) ) ) ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f686]) ).
thf(f686,plain,
! [X0: term] :
( ( $true = $false )
| ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ Y0 )
=> ( ( sK2 @ Y1 )
=> ( sK2 @ ( ap @ Y0 @ Y1 ) ) ) ) ) )
= $false )
| ( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( sK2 @ ( sub @ Y1 @ Y0 ) ) ) )
=> ( sK2 @ ( sub @ X0 @ Y0 ) ) ) ) ) ),
inference(superposition,[],[f587,f595]) ).
thf(f595,plain,
! [X2: term,X1: term > $o] :
( ( ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( X1 @ Y1 )
=> ( X1 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( X1 @ ( lam @ Y0 ) ) ) )
= $false )
| ( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( X1 @ ( sub @ Y1 @ Y0 ) ) ) )
=> ( X1 @ ( sub @ X2 @ Y0 ) ) ) ) )
| ( $false
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( X1 @ Y0 )
=> ( ( X1 @ Y1 )
=> ( X1 @ ( ap @ Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f594]) ).
thf(f594,plain,
! [X2: term,X1: term > $o] :
( ( $false
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( X1 @ Y0 )
=> ( ( X1 @ Y1 )
=> ( X1 @ ( ap @ Y0 @ Y1 ) ) ) ) ) ) )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( X1 @ Y1 )
=> ( X1 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( X1 @ ( lam @ Y0 ) ) ) )
= $false )
| ( $true
= ( ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( !! @ term
@ ^ [Y2: term] :
( ( var @ Y2 )
=> ( X1 @ ( sub @ Y2 @ Y1 ) ) ) )
=> ( X1 @ ( sub @ Y0 @ Y1 ) ) ) )
@ X2 ) ) ),
inference(pi_clausification,[],[f593]) ).
thf(f593,plain,
! [X1: term > $o] :
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( !! @ term
@ ^ [Y2: term] :
( ( var @ Y2 )
=> ( X1 @ ( sub @ Y2 @ Y1 ) ) ) )
=> ( X1 @ ( sub @ Y0 @ Y1 ) ) ) ) )
= $true )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( X1 @ Y1 )
=> ( X1 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( X1 @ ( lam @ Y0 ) ) ) )
= $false )
| ( $false
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( X1 @ Y0 )
=> ( ( X1 @ Y1 )
=> ( X1 @ ( ap @ Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f592]) ).
thf(f592,plain,
! [X1: term > $o] :
( ( $false
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( X1 @ Y0 )
=> ( ( X1 @ Y1 )
=> ( X1 @ ( ap @ Y0 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( X1 @ Y1 )
=> ( X1 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( X1 @ ( lam @ Y0 ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( !! @ term
@ ^ [Y2: term] :
( ( var @ Y2 )
=> ( X1 @ ( sub @ Y2 @ Y1 ) ) ) )
=> ( X1 @ ( sub @ Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f591]) ).
thf(f591,plain,
! [X1: term > $o] :
( $true
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( X1 @ Y0 )
=> ( ( X1 @ Y1 )
=> ( X1 @ ( ap @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( X1 @ Y1 )
=> ( X1 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( X1 @ ( lam @ Y0 ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( !! @ term
@ ^ [Y2: term] :
( ( var @ Y2 )
=> ( X1 @ ( sub @ Y2 @ Y1 ) ) ) )
=> ( X1 @ ( sub @ Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f590]) ).
thf(f590,plain,
! [X1: term > $o] :
( $true
= ( ^ [Y0: term > $o] :
( ( !! @ 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] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( Y0 @ ( sub @ Y1 @ Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[],[f579]) ).
thf(f579,plain,
( $true
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ 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] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( Y0 @ ( sub @ Y1 @ Y2 ) ) ) ) ) ) ) ) ),
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
% 0.07/0.12 % Problem : ALG253^1 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.07/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.35 % Computer : n016.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat May 18 22:54:23 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/sandbox/benchmark/theBenchmark.p
% 0.14/0.38 % (27748)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.22/0.38 % (27748)Instruction limit reached!
% 0.22/0.38 % (27748)------------------------------
% 0.22/0.38 % (27748)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.38 % (27748)Termination reason: Unknown
% 0.22/0.38 % (27748)Termination phase: shuffling
% 0.22/0.38
% 0.22/0.38 % (27748)Memory used [KB]: 1279
% 0.22/0.38 % (27748)Time elapsed: 0.003 s
% 0.22/0.38 % (27748)Instructions burned: 3 (million)
% 0.22/0.38 % (27748)------------------------------
% 0.22/0.38 % (27748)------------------------------
% 0.22/0.38 % (27747)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.22/0.38 % (27745)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.22/0.38 % (27749)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.22/0.38 % (27746)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.22/0.38 % (27750)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.22/0.38 % (27751)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.22/0.38 % (27752)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.22/0.38 % (27749)Instruction limit reached!
% 0.22/0.38 % (27749)------------------------------
% 0.22/0.38 % (27749)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.38 % (27749)Termination reason: Unknown
% 0.22/0.38 % (27749)Termination phase: shuffling
% 0.22/0.38
% 0.22/0.38 % (27749)Memory used [KB]: 1279
% 0.22/0.38 % (27749)Time elapsed: 0.004 s
% 0.22/0.38 % (27749)Instructions burned: 3 (million)
% 0.22/0.38 % (27749)------------------------------
% 0.22/0.38 % (27749)------------------------------
% 0.22/0.38 % (27752)Instruction limit reached!
% 0.22/0.38 % (27752)------------------------------
% 0.22/0.38 % (27752)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.38 % (27752)Termination reason: Unknown
% 0.22/0.38 % (27752)Termination phase: shuffling
% 0.22/0.38
% 0.22/0.38 % (27752)Memory used [KB]: 1279
% 0.22/0.38 % (27752)Time elapsed: 0.004 s
% 0.22/0.38 % (27752)Instructions burned: 3 (million)
% 0.22/0.38 % (27752)------------------------------
% 0.22/0.38 % (27752)------------------------------
% 0.22/0.38 % (27746)Instruction limit reached!
% 0.22/0.38 % (27746)------------------------------
% 0.22/0.38 % (27746)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.38 % (27746)Termination reason: Unknown
% 0.22/0.38 % (27746)Termination phase: shuffling
% 0.22/0.38
% 0.22/0.38 % (27746)Memory used [KB]: 1279
% 0.22/0.38 % (27746)Time elapsed: 0.004 s
% 0.22/0.38 % (27746)Instructions burned: 5 (million)
% 0.22/0.38 % (27746)------------------------------
% 0.22/0.38 % (27746)------------------------------
% 0.22/0.39 % (27753)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.22/0.39 % (27751)Instruction limit reached!
% 0.22/0.39 % (27751)------------------------------
% 0.22/0.39 % (27751)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.39 % (27751)Termination reason: Unknown
% 0.22/0.39 % (27751)Termination phase: Property scanning
% 0.22/0.39
% 0.22/0.39 % (27751)Memory used [KB]: 1663
% 0.22/0.39 % (27751)Time elapsed: 0.013 s
% 0.22/0.39 % (27751)Instructions burned: 18 (million)
% 0.22/0.39 % (27751)------------------------------
% 0.22/0.39 % (27751)------------------------------
% 0.22/0.39 % (27747)Instruction limit reached!
% 0.22/0.39 % (27747)------------------------------
% 0.22/0.39 % (27747)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.39 % (27747)Termination reason: Unknown
% 0.22/0.39 % (27747)Termination phase: Property scanning
% 0.22/0.39
% 0.22/0.40 % (27747)Memory used [KB]: 1791
% 0.22/0.40 % (27747)Time elapsed: 0.016 s
% 0.22/0.40 % (27747)Instructions burned: 28 (million)
% 0.22/0.40 % (27747)------------------------------
% 0.22/0.40 % (27747)------------------------------
% 0.22/0.40 % (27750)Refutation not found, incomplete strategy
% 0.22/0.40 % (27750)------------------------------
% 0.22/0.40 % (27750)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.40 % (27754)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.22/0.40 % (27750)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.40
% 0.22/0.40
% 0.22/0.40 % (27750)Memory used [KB]: 6140
% 0.22/0.40 % (27750)Time elapsed: 0.018 s
% 0.22/0.40 % (27750)Instructions burned: 27 (million)
% 0.22/0.40 % (27750)------------------------------
% 0.22/0.40 % (27750)------------------------------
% 0.22/0.40 % (27755)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.22/0.40 % (27756)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.22/0.40 % (27755)Instruction limit reached!
% 0.22/0.40 % (27755)------------------------------
% 0.22/0.40 % (27755)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.40 % (27755)Termination reason: Unknown
% 0.22/0.40 % (27755)Termination phase: shuffling
% 0.22/0.40
% 0.22/0.40 % (27755)Memory used [KB]: 1279
% 0.22/0.40 % (27755)Time elapsed: 0.004 s
% 0.22/0.40 % (27755)Instructions burned: 4 (million)
% 0.22/0.40 % (27755)------------------------------
% 0.22/0.40 % (27755)------------------------------
% 0.22/0.41 % (27753)Instruction limit reached!
% 0.22/0.41 % (27753)------------------------------
% 0.22/0.41 % (27753)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.41 % (27753)Termination reason: Unknown
% 0.22/0.41 % (27753)Termination phase: Property scanning
% 0.22/0.41
% 0.22/0.41 % (27753)Memory used [KB]: 1791
% 0.22/0.41 % (27753)Time elapsed: 0.016 s
% 0.22/0.41 % (27753)Instructions burned: 38 (million)
% 0.22/0.41 % (27753)------------------------------
% 0.22/0.41 % (27753)------------------------------
% 0.22/0.41 % (27757)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.22/0.41 % (27754)Instruction limit reached!
% 0.22/0.41 % (27754)------------------------------
% 0.22/0.41 % (27754)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.41 % (27754)Termination reason: Unknown
% 0.22/0.41 % (27754)Termination phase: Property scanning
% 0.22/0.41
% 0.22/0.41 % (27754)Memory used [KB]: 1663
% 0.22/0.41 % (27754)Time elapsed: 0.012 s
% 0.22/0.41 % (27754)Instructions burned: 17 (million)
% 0.22/0.41 % (27754)------------------------------
% 0.22/0.41 % (27754)------------------------------
% 0.22/0.41 % (27758)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.22/0.41 % (27757)Instruction limit reached!
% 0.22/0.41 % (27757)------------------------------
% 0.22/0.41 % (27757)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.41 % (27757)Termination reason: Unknown
% 0.22/0.41 % (27757)Termination phase: shuffling
% 0.22/0.41
% 0.22/0.41 % (27757)Memory used [KB]: 1407
% 0.22/0.41 % (27757)Time elapsed: 0.006 s
% 0.22/0.41 % (27757)Instructions burned: 8 (million)
% 0.22/0.41 % (27757)------------------------------
% 0.22/0.41 % (27757)------------------------------
% 0.22/0.41 % (27759)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.22/0.42 % (27760)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.22/0.42 % (27759)Instruction limit reached!
% 0.22/0.42 % (27759)------------------------------
% 0.22/0.42 % (27759)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (27759)Termination reason: Unknown
% 0.22/0.42 % (27759)Termination phase: shuffling
% 0.22/0.42
% 0.22/0.42 % (27759)Memory used [KB]: 1279
% 0.22/0.42 % (27759)Time elapsed: 0.004 s
% 0.22/0.42 % (27759)Instructions burned: 4 (million)
% 0.22/0.42 % (27759)------------------------------
% 0.22/0.42 % (27759)------------------------------
% 0.22/0.42 % (27760)Instruction limit reached!
% 0.22/0.42 % (27760)------------------------------
% 0.22/0.42 % (27760)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (27760)Termination reason: Unknown
% 0.22/0.42 % (27760)Termination phase: shuffling
% 0.22/0.42
% 0.22/0.42 % (27760)Memory used [KB]: 1279
% 0.22/0.42 % (27760)Time elapsed: 0.004 s
% 0.22/0.42 % (27760)Instructions burned: 3 (million)
% 0.22/0.42 % (27760)------------------------------
% 0.22/0.42 % (27760)------------------------------
% 0.22/0.42 % (27758)Instruction limit reached!
% 0.22/0.42 % (27758)------------------------------
% 0.22/0.42 % (27758)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (27758)Termination reason: Unknown
% 0.22/0.42 % (27758)Termination phase: shuffling
% 0.22/0.42
% 0.22/0.42 % (27758)Memory used [KB]: 1535
% 0.22/0.42 % (27758)Time elapsed: 0.010 s
% 0.22/0.42 % (27758)Instructions burned: 16 (million)
% 0.22/0.42 % (27758)------------------------------
% 0.22/0.42 % (27758)------------------------------
% 0.22/0.42 % (27761)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.22/0.42 % (27761)Instruction limit reached!
% 0.22/0.42 % (27761)------------------------------
% 0.22/0.42 % (27761)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (27761)Termination reason: Unknown
% 0.22/0.42 % (27761)Termination phase: shuffling
% 0.22/0.42
% 0.22/0.42 % (27761)Memory used [KB]: 1279
% 0.22/0.42 % (27761)Time elapsed: 0.004 s
% 0.22/0.42 % (27761)Instructions burned: 7 (million)
% 0.22/0.42 % (27761)------------------------------
% 0.22/0.42 % (27761)------------------------------
% 0.22/0.42 % (27762)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.22/0.42 % (27762)Instruction limit reached!
% 0.22/0.42 % (27762)------------------------------
% 0.22/0.42 % (27762)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (27762)Termination reason: Unknown
% 0.22/0.42 % (27762)Termination phase: shuffling
% 0.22/0.42
% 0.22/0.42 % (27762)Memory used [KB]: 1279
% 0.22/0.42 % (27762)Time elapsed: 0.004 s
% 0.22/0.42 % (27762)Instructions burned: 4 (million)
% 0.22/0.42 % (27762)------------------------------
% 0.22/0.42 % (27762)------------------------------
% 0.22/0.43 % (27763)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.22/0.43 % (27763)Instruction limit reached!
% 0.22/0.43 % (27763)------------------------------
% 0.22/0.43 % (27763)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.43 % (27763)Termination reason: Unknown
% 0.22/0.43 % (27763)Termination phase: shuffling
% 0.22/0.43
% 0.22/0.43 % (27763)Memory used [KB]: 1279
% 0.22/0.43 % (27763)Time elapsed: 0.004 s
% 0.22/0.43 % (27763)Instructions burned: 4 (million)
% 0.22/0.43 % (27763)------------------------------
% 0.22/0.43 % (27763)------------------------------
% 0.22/0.43 % (27764)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.22/0.43 % (27765)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.22/0.43 % (27766)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.22/0.43 % (27767)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on theBenchmark for (2999ds/902Mi)
% 0.22/0.44 % (27766)Instruction limit reached!
% 0.22/0.44 % (27766)------------------------------
% 0.22/0.44 % (27766)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.44 % (27766)Termination reason: Unknown
% 0.22/0.44 % (27766)Termination phase: shuffling
% 0.22/0.44
% 0.22/0.44 % (27766)Memory used [KB]: 1279
% 0.22/0.44 % (27766)Time elapsed: 0.005 s
% 0.22/0.44 % (27766)Instructions burned: 6 (million)
% 0.22/0.44 % (27766)------------------------------
% 0.22/0.44 % (27766)------------------------------
% 0.22/0.44 % (27764)Instruction limit reached!
% 0.22/0.44 % (27764)------------------------------
% 0.22/0.44 % (27764)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.44 % (27764)Termination reason: Unknown
% 0.22/0.44 % (27764)Termination phase: shuffling
% 0.22/0.44
% 0.22/0.44 % (27764)Memory used [KB]: 1663
% 0.22/0.44 % (27764)Time elapsed: 0.011 s
% 0.22/0.44 % (27764)Instructions burned: 18 (million)
% 0.22/0.44 % (27764)------------------------------
% 0.22/0.44 % (27764)------------------------------
% 0.22/0.44 % (27768)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on theBenchmark for (2999ds/21Mi)
% 0.22/0.44 % (27769)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.22/0.45 % (27769)Instruction limit reached!
% 0.22/0.45 % (27769)------------------------------
% 0.22/0.45 % (27769)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.45 % (27769)Termination reason: Unknown
% 0.22/0.45 % (27769)Termination phase: shuffling
% 0.22/0.45
% 0.22/0.45 % (27769)Memory used [KB]: 1279
% 0.22/0.45 % (27769)Time elapsed: 0.005 s
% 0.22/0.45 % (27769)Instructions burned: 6 (million)
% 0.22/0.45 % (27769)------------------------------
% 0.22/0.45 % (27769)------------------------------
% 0.22/0.45 % (27765)Refutation not found, incomplete strategy
% 0.22/0.45 % (27765)------------------------------
% 0.22/0.45 % (27765)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.45 % (27765)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.45
% 0.22/0.45
% 0.22/0.45 % (27765)Memory used [KB]: 6268
% 0.22/0.45 % (27765)Time elapsed: 0.018 s
% 0.22/0.45 % (27765)Instructions burned: 27 (million)
% 0.22/0.45 % (27765)------------------------------
% 0.22/0.45 % (27765)------------------------------
% 0.22/0.45 % (27768)Instruction limit reached!
% 0.22/0.45 % (27768)------------------------------
% 0.22/0.45 % (27768)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.45 % (27768)Termination reason: Unknown
% 0.22/0.45 % (27768)Termination phase: shuffling
% 0.22/0.45 % (27770)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.22/0.45
% 0.22/0.45 % (27768)Memory used [KB]: 1663
% 0.22/0.45 % (27768)Time elapsed: 0.013 s
% 0.22/0.45 % (27768)Instructions burned: 22 (million)
% 0.22/0.45 % (27768)------------------------------
% 0.22/0.45 % (27768)------------------------------
% 0.22/0.45 % (27770)Instruction limit reached!
% 0.22/0.45 % (27770)------------------------------
% 0.22/0.45 % (27770)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.45 % (27770)Termination reason: Unknown
% 0.22/0.45 % (27770)Termination phase: shuffling
% 0.22/0.45
% 0.22/0.45 % (27770)Memory used [KB]: 1279
% 0.22/0.45 % (27770)Time elapsed: 0.005 s
% 0.22/0.45 % (27770)Instructions burned: 6 (million)
% 0.22/0.45 % (27770)------------------------------
% 0.22/0.45 % (27770)------------------------------
% 0.22/0.45 % (27771)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2999ds/377Mi)
% 0.22/0.46 % (27772)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on theBenchmark for (2999ds/779Mi)
% 0.22/0.46 % (27773)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on theBenchmark for (2999ds/19Mi)
% 0.22/0.47 % (27774)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on theBenchmark for (2999ds/879Mi)
% 0.22/0.47 % (27775)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2999ds/17Mi)
% 0.22/0.47 % (27773)Instruction limit reached!
% 0.22/0.47 % (27773)------------------------------
% 0.22/0.47 % (27773)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.47 % (27773)Termination reason: Unknown
% 0.22/0.47 % (27773)Termination phase: shuffling
% 0.22/0.47
% 0.22/0.47 % (27773)Memory used [KB]: 1663
% 0.22/0.47 % (27773)Time elapsed: 0.012 s
% 0.22/0.47 % (27773)Instructions burned: 20 (million)
% 0.22/0.47 % (27773)------------------------------
% 0.22/0.47 % (27773)------------------------------
% 0.22/0.47 % (27745)Instruction limit reached!
% 0.22/0.47 % (27745)------------------------------
% 0.22/0.47 % (27745)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.47 % (27745)Termination reason: Unknown
% 0.22/0.47 % (27745)Termination phase: Saturation
% 0.22/0.47
% 0.22/0.47 % (27745)Memory used [KB]: 7164
% 0.22/0.47 % (27745)Time elapsed: 0.096 s
% 0.22/0.47 % (27745)Instructions burned: 184 (million)
% 0.22/0.47 % (27745)------------------------------
% 0.22/0.47 % (27745)------------------------------
% 0.22/0.48 % (27775)Instruction limit reached!
% 0.22/0.48 % (27775)------------------------------
% 0.22/0.48 % (27775)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.48 % (27775)Termination reason: Unknown
% 0.22/0.48 % (27775)Termination phase: shuffling
% 0.22/0.48
% 0.22/0.48 % (27775)Memory used [KB]: 1535
% 0.22/0.48 % (27775)Time elapsed: 0.011 s
% 0.22/0.48 % (27775)Instructions burned: 17 (million)
% 0.22/0.48 % (27775)------------------------------
% 0.22/0.48 % (27775)------------------------------
% 0.22/0.49 % (27776)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi)
% 0.22/0.49 % (27776)Instruction limit reached!
% 0.22/0.49 % (27776)------------------------------
% 0.22/0.49 % (27776)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.49 % (27776)Termination reason: Unknown
% 0.22/0.49 % (27776)Termination phase: shuffling
% 0.22/0.49
% 0.22/0.49 % (27776)Memory used [KB]: 1279
% 0.22/0.49 % (27776)Time elapsed: 0.003 s
% 0.22/0.49 % (27776)Instructions burned: 3 (million)
% 0.22/0.49 % (27776)------------------------------
% 0.22/0.49 % (27776)------------------------------
% 0.22/0.49 % (27777)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on theBenchmark for (2998ds/30Mi)
% 0.22/0.49 % (27774)Refutation not found, incomplete strategy
% 0.22/0.49 % (27774)------------------------------
% 0.22/0.49 % (27774)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.49 % (27778)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on theBenchmark for (2998ds/127Mi)
% 0.22/0.49 % (27774)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.49
% 0.22/0.49
% 0.22/0.49 % (27774)Memory used [KB]: 6268
% 0.22/0.49 % (27774)Time elapsed: 0.028 s
% 0.22/0.49 % (27774)Instructions burned: 60 (million)
% 0.22/0.49 % (27774)------------------------------
% 0.22/0.49 % (27774)------------------------------
% 0.22/0.50 % (27779)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on theBenchmark for (2998ds/100Mi)
% 0.22/0.50 % (27780)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi)
% 0.22/0.50 % (27780)Instruction limit reached!
% 0.22/0.50 % (27780)------------------------------
% 0.22/0.50 % (27780)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.50 % (27780)Termination reason: Unknown
% 0.22/0.50 % (27780)Termination phase: shuffling
% 0.22/0.50
% 0.22/0.50 % (27780)Memory used [KB]: 1279
% 0.22/0.50 % (27780)Time elapsed: 0.003 s
% 0.22/0.50 % (27780)Instructions burned: 5 (million)
% 0.22/0.50 % (27780)------------------------------
% 0.22/0.50 % (27780)------------------------------
% 0.22/0.50 % (27777)Instruction limit reached!
% 0.22/0.50 % (27777)------------------------------
% 0.22/0.50 % (27777)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.50 % (27777)Termination reason: Unknown
% 0.22/0.50 % (27777)Termination phase: Property scanning
% 0.22/0.50
% 0.22/0.50 % (27777)Memory used [KB]: 1791
% 0.22/0.50 % (27777)Time elapsed: 0.015 s
% 0.22/0.50 % (27777)Instructions burned: 32 (million)
% 0.22/0.50 % (27777)------------------------------
% 0.22/0.50 % (27777)------------------------------
% 0.22/0.51 % (27781)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on theBenchmark for (2998ds/20Mi)
% 0.22/0.51 % (27782)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on theBenchmark for (2998ds/86Mi)
% 0.22/0.52 % (27781)Instruction limit reached!
% 0.22/0.52 % (27781)------------------------------
% 0.22/0.52 % (27781)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.52 % (27781)Termination reason: Unknown
% 0.22/0.52 % (27781)Termination phase: Property scanning
% 0.22/0.52
% 0.22/0.52 % (27781)Memory used [KB]: 1663
% 0.22/0.52 % (27781)Time elapsed: 0.008 s
% 0.22/0.52 % (27781)Instructions burned: 21 (million)
% 0.22/0.52 % (27781)------------------------------
% 0.22/0.52 % (27781)------------------------------
% 0.22/0.52 % (27779)Instruction limit reached!
% 0.22/0.52 % (27779)------------------------------
% 0.22/0.52 % (27779)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.52 % (27779)Termination reason: Unknown
% 0.22/0.52 % (27779)Termination phase: Saturation
% 0.22/0.52
% 0.22/0.52 % (27779)Memory used [KB]: 6524
% 0.22/0.52 % (27779)Time elapsed: 0.027 s
% 0.22/0.52 % (27779)Instructions burned: 103 (million)
% 0.22/0.52 % (27779)------------------------------
% 0.22/0.52 % (27779)------------------------------
% 1.40/0.53 % (27778)Instruction limit reached!
% 1.40/0.53 % (27778)------------------------------
% 1.40/0.53 % (27778)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.40/0.53 % (27778)Termination reason: Unknown
% 1.40/0.53 % (27778)Termination phase: Saturation
% 1.40/0.53
% 1.40/0.53 % (27778)Memory used [KB]: 6652
% 1.40/0.53 % (27778)Time elapsed: 0.036 s
% 1.40/0.53 % (27778)Instructions burned: 128 (million)
% 1.40/0.53 % (27778)------------------------------
% 1.40/0.53 % (27778)------------------------------
% 1.40/0.53 % (27784)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 theBenchmark for (2998ds/39Mi)
% 1.40/0.53 % (27783)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 theBenchmark for (2998ds/107Mi)
% 1.40/0.53 % (27785)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 theBenchmark for (2998ds/448Mi)
% 1.40/0.54 % (27782)Instruction limit reached!
% 1.40/0.54 % (27782)------------------------------
% 1.40/0.54 % (27782)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.40/0.54 % (27782)Termination reason: Unknown
% 1.40/0.54 % (27782)Termination phase: Saturation
% 1.40/0.54
% 1.40/0.54 % (27782)Memory used [KB]: 6524
% 1.40/0.54 % (27782)Time elapsed: 0.024 s
% 1.40/0.54 % (27782)Instructions burned: 88 (million)
% 1.40/0.54 % (27782)------------------------------
% 1.40/0.54 % (27782)------------------------------
% 1.50/0.54 % (27784)Instruction limit reached!
% 1.50/0.54 % (27784)------------------------------
% 1.50/0.54 % (27784)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.50/0.54 % (27784)Termination reason: Unknown
% 1.50/0.54 % (27784)Termination phase: Property scanning
% 1.50/0.54
% 1.50/0.54 % (27784)Memory used [KB]: 1791
% 1.50/0.54 % (27784)Time elapsed: 0.012 s
% 1.50/0.54 % (27784)Instructions burned: 40 (million)
% 1.50/0.54 % (27784)------------------------------
% 1.50/0.54 % (27784)------------------------------
% 1.50/0.54 % (27786)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 theBenchmark for (2998ds/46Mi)
% 1.50/0.55 % (27787)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 theBenchmark for (2998ds/98Mi)
% 1.50/0.56 % (27786)Instruction limit reached!
% 1.50/0.56 % (27786)------------------------------
% 1.50/0.56 % (27786)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.50/0.56 % (27786)Termination reason: Unknown
% 1.50/0.56 % (27786)Termination phase: SInE selection
% 1.50/0.56
% 1.50/0.56 % (27786)Memory used [KB]: 1791
% 1.50/0.56 % (27786)Time elapsed: 0.014 s
% 1.50/0.56 % (27786)Instructions burned: 47 (million)
% 1.50/0.56 % (27786)------------------------------
% 1.50/0.56 % (27786)------------------------------
% 1.50/0.56 % (27783)Instruction limit reached!
% 1.50/0.56 % (27783)------------------------------
% 1.50/0.56 % (27783)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.50/0.56 % (27783)Termination reason: Unknown
% 1.50/0.56 % (27783)Termination phase: Saturation
% 1.50/0.56
% 1.50/0.56 % (27783)Memory used [KB]: 6524
% 1.50/0.56 % (27783)Time elapsed: 0.031 s
% 1.50/0.56 % (27783)Instructions burned: 108 (million)
% 1.50/0.56 % (27783)------------------------------
% 1.50/0.56 % (27783)------------------------------
% 1.50/0.57 % (27788)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 theBenchmark for (2998ds/507Mi)
% 1.50/0.57 % (27789)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 theBenchmark for (2998ds/149Mi)
% 1.50/0.58 % (27787)Instruction limit reached!
% 1.50/0.58 % (27787)------------------------------
% 1.50/0.58 % (27787)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.50/0.58 % (27787)Termination reason: Unknown
% 1.50/0.58 % (27787)Termination phase: Saturation
% 1.50/0.58
% 1.50/0.58 % (27787)Memory used [KB]: 2046
% 1.50/0.58 % (27787)Time elapsed: 0.027 s
% 1.50/0.58 % (27787)Instructions burned: 101 (million)
% 1.50/0.58 % (27787)------------------------------
% 1.50/0.58 % (27787)------------------------------
% 1.50/0.59 % (27790)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on theBenchmark for (2997ds/39Mi)
% 1.50/0.60 % (27790)Instruction limit reached!
% 1.50/0.60 % (27790)------------------------------
% 1.50/0.60 % (27790)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.50/0.60 % (27790)Termination reason: Unknown
% 1.50/0.60 % (27790)Termination phase: Property scanning
% 1.50/0.60
% 1.50/0.60 % (27790)Memory used [KB]: 1791
% 1.50/0.60 % (27790)Time elapsed: 0.012 s
% 1.50/0.60 % (27790)Instructions burned: 39 (million)
% 1.50/0.60 % (27790)------------------------------
% 1.50/0.60 % (27790)------------------------------
% 1.50/0.60 % (27771)Instruction limit reached!
% 1.50/0.60 % (27771)------------------------------
% 1.50/0.60 % (27771)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.50/0.60 % (27771)Termination reason: Unknown
% 1.50/0.60 % (27771)Termination phase: Saturation
% 1.50/0.60
% 1.50/0.60 % (27771)Memory used [KB]: 7547
% 1.50/0.60 % (27771)Time elapsed: 0.167 s
% 1.50/0.60 % (27771)Instructions burned: 379 (million)
% 1.50/0.60 % (27771)------------------------------
% 1.50/0.60 % (27771)------------------------------
% 1.50/0.60 % (27791)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 theBenchmark for (2997ds/6Mi)
% 1.50/0.61 % (27791)Instruction limit reached!
% 1.50/0.61 % (27791)------------------------------
% 1.50/0.61 % (27791)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.50/0.61 % (27791)Termination reason: Unknown
% 1.50/0.61 % (27791)Termination phase: shuffling
% 1.50/0.61
% 1.50/0.61 % (27791)Memory used [KB]: 1407
% 1.50/0.61 % (27791)Time elapsed: 0.003 s
% 1.50/0.61 % (27791)Instructions burned: 7 (million)
% 1.50/0.61 % (27791)------------------------------
% 1.50/0.61 % (27791)------------------------------
% 1.50/0.61 % (27792)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 theBenchmark for (2997ds/1087Mi)
% 1.50/0.61 % (27789)Instruction limit reached!
% 1.50/0.61 % (27789)------------------------------
% 1.50/0.61 % (27789)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.50/0.61 % (27789)Termination reason: Unknown
% 1.50/0.61 % (27789)Termination phase: Saturation
% 1.50/0.61
% 1.50/0.61 % (27789)Memory used [KB]: 6908
% 1.50/0.61 % (27789)Time elapsed: 0.046 s
% 1.50/0.61 % (27789)Instructions burned: 150 (million)
% 1.50/0.61 % (27789)------------------------------
% 1.50/0.61 % (27789)------------------------------
% 1.50/0.62 % (27793)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on theBenchmark for (2997ds/47Mi)
% 1.50/0.62 % (27792)Refutation not found, incomplete strategy
% 1.50/0.62 % (27792)------------------------------
% 1.50/0.62 % (27792)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.50/0.62 % (27792)Termination reason: Refutation not found, incomplete strategy
% 1.50/0.62
% 1.50/0.62
% 1.50/0.62 % (27792)Memory used [KB]: 6268
% 1.50/0.62 % (27792)Time elapsed: 0.011 s
% 1.50/0.62 % (27792)Instructions burned: 27 (million)
% 1.50/0.62 % (27792)------------------------------
% 1.50/0.62 % (27792)------------------------------
% 1.50/0.62 % (27794)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 theBenchmark for (2997ds/44Mi)
% 2.04/0.63 % (27795)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 theBenchmark for (2997ds/432Mi)
% 2.04/0.63 % (27793)Instruction limit reached!
% 2.04/0.63 % (27793)------------------------------
% 2.04/0.63 % (27793)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.04/0.63 % (27793)Termination reason: Unknown
% 2.04/0.63 % (27793)Termination phase: Property scanning
% 2.04/0.63
% 2.04/0.63 % (27793)Memory used [KB]: 1791
% 2.04/0.63 % (27793)Time elapsed: 0.014 s
% 2.04/0.63 % (27793)Instructions burned: 48 (million)
% 2.04/0.63 % (27793)------------------------------
% 2.04/0.63 % (27793)------------------------------
% 2.04/0.64 % (27794)Instruction limit reached!
% 2.04/0.64 % (27794)------------------------------
% 2.04/0.64 % (27794)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.04/0.64 % (27794)Termination reason: Unknown
% 2.04/0.64 % (27794)Termination phase: Property scanning
% 2.04/0.64
% 2.04/0.64 % (27794)Memory used [KB]: 1791
% 2.04/0.64 % (27794)Time elapsed: 0.013 s
% 2.04/0.64 % (27794)Instructions burned: 44 (million)
% 2.04/0.64 % (27794)------------------------------
% 2.04/0.64 % (27794)------------------------------
% 2.04/0.64 % (27796)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on theBenchmark for (2997ds/62Mi)
% 2.04/0.64 % (27797)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 theBenchmark for (2997ds/31Mi)
% 2.04/0.65 % (27796)Instruction limit reached!
% 2.04/0.65 % (27796)------------------------------
% 2.04/0.65 % (27796)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.04/0.65 % (27796)Termination reason: Unknown
% 2.04/0.65 % (27796)Termination phase: Property scanning
% 2.04/0.65
% 2.04/0.65 % (27796)Memory used [KB]: 1791
% 2.04/0.65 % (27796)Time elapsed: 0.017 s
% 2.04/0.65 % (27796)Instructions burned: 62 (million)
% 2.04/0.65 % (27796)------------------------------
% 2.04/0.65 % (27796)------------------------------
% 2.04/0.65 % (27797)Instruction limit reached!
% 2.04/0.65 % (27797)------------------------------
% 2.04/0.65 % (27797)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.04/0.65 % (27797)Termination reason: Unknown
% 2.04/0.65 % (27797)Termination phase: Property scanning
% 2.04/0.65
% 2.04/0.65 % (27797)Memory used [KB]: 1791
% 2.04/0.65 % (27797)Time elapsed: 0.010 s
% 2.04/0.65 % (27797)Instructions burned: 32 (million)
% 2.04/0.65 % (27797)------------------------------
% 2.04/0.65 % (27797)------------------------------
% 2.04/0.66 % (27798)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on theBenchmark for (2997ds/96Mi)
% 2.04/0.66 % (27799)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 theBenchmark for (2997ds/453Mi)
% 2.04/0.68 % (27785)Instruction limit reached!
% 2.04/0.68 % (27785)------------------------------
% 2.04/0.68 % (27785)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.04/0.68 % (27785)Termination reason: Unknown
% 2.04/0.68 % (27785)Termination phase: Saturation
% 2.04/0.68
% 2.04/0.68 % (27785)Memory used [KB]: 7291
% 2.04/0.68 % (27785)Time elapsed: 0.144 s
% 2.04/0.68 % (27785)Instructions burned: 449 (million)
% 2.04/0.68 % (27785)------------------------------
% 2.04/0.68 % (27785)------------------------------
% 2.43/0.68 % (27798)Instruction limit reached!
% 2.43/0.68 % (27798)------------------------------
% 2.43/0.68 % (27798)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.43/0.68 % (27798)Termination reason: Unknown
% 2.43/0.68 % (27798)Termination phase: Saturation
% 2.43/0.68
% 2.43/0.68 % (27798)Memory used [KB]: 6524
% 2.43/0.68 % (27798)Time elapsed: 0.024 s
% 2.43/0.68 % (27798)Instructions burned: 98 (million)
% 2.43/0.68 % (27798)------------------------------
% 2.43/0.68 % (27798)------------------------------
% 2.43/0.69 % (27800)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on theBenchmark for (2996ds/71Mi)
% 2.43/0.69 % (27801)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on theBenchmark for (2996ds/83Mi)
% 2.43/0.70 % (27800)Instruction limit reached!
% 2.43/0.70 % (27800)------------------------------
% 2.43/0.70 % (27800)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.43/0.70 % (27800)Termination reason: Unknown
% 2.43/0.70 % (27800)Termination phase: Function definition elimination
% 2.43/0.70
% 2.43/0.70 % (27800)Memory used [KB]: 1791
% 2.43/0.70 % (27800)Time elapsed: 0.018 s
% 2.43/0.70 % (27800)Instructions burned: 71 (million)
% 2.43/0.70 % (27800)------------------------------
% 2.43/0.70 % (27800)------------------------------
% 2.43/0.71 % (27801)Refutation not found, incomplete strategy
% 2.43/0.71 % (27801)------------------------------
% 2.43/0.71 % (27801)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.43/0.71 % (27801)Termination reason: Refutation not found, incomplete strategy
% 2.43/0.71
% 2.43/0.71
% 2.43/0.71 % (27801)Memory used [KB]: 6268
% 2.43/0.71 % (27801)Time elapsed: 0.016 s
% 2.43/0.71 % (27801)Instructions burned: 58 (million)
% 2.43/0.71 % (27801)------------------------------
% 2.43/0.71 % (27801)------------------------------
% 2.43/0.71 % (27788)Instruction limit reached!
% 2.43/0.71 % (27788)------------------------------
% 2.43/0.71 % (27788)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.43/0.71 % (27788)Termination reason: Unknown
% 2.43/0.71 % (27788)Termination phase: Saturation
% 2.43/0.71
% 2.43/0.71 % (27788)Memory used [KB]: 7164
% 2.43/0.71 % (27788)Time elapsed: 0.144 s
% 2.43/0.71 % (27788)Instructions burned: 507 (million)
% 2.43/0.71 % (27788)------------------------------
% 2.43/0.71 % (27788)------------------------------
% 2.43/0.71 % (27802)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on theBenchmark for (2996ds/11Mi)
% 2.43/0.71 % (27802)Instruction limit reached!
% 2.43/0.71 % (27802)------------------------------
% 2.43/0.71 % (27802)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.43/0.71 % (27802)Termination reason: Unknown
% 2.43/0.71 % (27802)Termination phase: shuffling
% 2.43/0.71
% 2.43/0.71 % (27802)Memory used [KB]: 1535
% 2.43/0.71 % (27802)Time elapsed: 0.005 s
% 2.43/0.71 % (27802)Instructions burned: 14 (million)
% 2.43/0.71 % (27802)------------------------------
% 2.43/0.71 % (27802)------------------------------
% 2.43/0.71 % (27803)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 theBenchmark for (2996ds/41Mi)
% 2.43/0.72 % (27804)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2996ds/6Mi)
% 2.43/0.72 % (27767)Instruction limit reached!
% 2.43/0.72 % (27767)------------------------------
% 2.43/0.72 % (27767)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.43/0.72 % (27767)Termination reason: Unknown
% 2.43/0.72 % (27767)Termination phase: Saturation
% 2.43/0.72
% 2.43/0.72 % (27767)Memory used [KB]: 8699
% 2.43/0.72 % (27767)Time elapsed: 0.307 s
% 2.43/0.72 % (27767)Instructions burned: 903 (million)
% 2.43/0.72 % (27767)------------------------------
% 2.43/0.72 % (27767)------------------------------
% 2.43/0.72 % (27804)Instruction limit reached!
% 2.43/0.72 % (27804)------------------------------
% 2.43/0.72 % (27804)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.43/0.72 % (27804)Termination reason: Unknown
% 2.43/0.72 % (27804)Termination phase: shuffling
% 2.43/0.72
% 2.43/0.72 % (27804)Memory used [KB]: 1279
% 2.43/0.72 % (27804)Time elapsed: 0.003 s
% 2.43/0.72 % (27804)Instructions burned: 6 (million)
% 2.43/0.72 % (27804)------------------------------
% 2.43/0.72 % (27804)------------------------------
% 2.43/0.72 % (27805)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on theBenchmark for (2996ds/150Mi)
% 2.43/0.73 % (27803)Instruction limit reached!
% 2.43/0.73 % (27803)------------------------------
% 2.43/0.73 % (27803)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.43/0.73 % (27803)Termination reason: Unknown
% 2.43/0.73 % (27803)Termination phase: Property scanning
% 2.43/0.73
% 2.43/0.73 % (27803)Memory used [KB]: 1791
% 2.43/0.73 % (27803)Time elapsed: 0.012 s
% 2.43/0.73 % (27803)Instructions burned: 44 (million)
% 2.43/0.73 % (27803)------------------------------
% 2.43/0.73 % (27803)------------------------------
% 2.43/0.73 % (27806)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on theBenchmark for (2996ds/343Mi)
% 2.43/0.73 % (27807)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 theBenchmark for (2996ds/109Mi)
% 2.43/0.73 % (27772)Instruction limit reached!
% 2.43/0.73 % (27772)------------------------------
% 2.43/0.73 % (27772)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.43/0.73 % (27772)Termination reason: Unknown
% 2.43/0.73 % (27772)Termination phase: Saturation
% 2.43/0.73
% 2.43/0.73 % (27772)Memory used [KB]: 7931
% 2.43/0.73 % (27772)Time elapsed: 0.270 s
% 2.43/0.73 % (27772)Instructions burned: 780 (million)
% 2.43/0.73 % (27772)------------------------------
% 2.43/0.73 % (27772)------------------------------
% 2.43/0.73 % (27808)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 theBenchmark for (2996ds/253Mi)
% 2.43/0.74 % (27809)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on theBenchmark for (2996ds/140Mi)
% 2.43/0.74 % (27808)Refutation not found, incomplete strategy
% 2.43/0.74 % (27808)------------------------------
% 2.43/0.74 % (27808)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.43/0.74 % (27808)Termination reason: Refutation not found, incomplete strategy
% 2.43/0.74
% 2.43/0.74
% 2.43/0.74 % (27808)Memory used [KB]: 6140
% 2.43/0.74 % (27808)Time elapsed: 0.010 s
% 2.43/0.74 % (27808)Instructions burned: 28 (million)
% 2.43/0.74 % (27808)------------------------------
% 2.43/0.74 % (27808)------------------------------
% 2.43/0.74 % (27795)Instruction limit reached!
% 2.43/0.74 % (27795)------------------------------
% 2.43/0.74 % (27795)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.43/0.74 % (27795)Termination reason: Unknown
% 2.43/0.74 % (27795)Termination phase: Saturation
% 2.43/0.74
% 2.43/0.74 % (27795)Memory used [KB]: 2942
% 2.43/0.74 % (27795)Time elapsed: 0.119 s
% 2.43/0.74 % (27795)Instructions burned: 434 (million)
% 2.43/0.75 % (27795)------------------------------
% 2.43/0.75 % (27795)------------------------------
% 3.03/0.75 % (27809)Refutation not found, incomplete strategy
% 3.03/0.75 % (27809)------------------------------
% 3.03/0.75 % (27809)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.03/0.75 % (27809)Termination reason: Refutation not found, incomplete strategy
% 3.03/0.75
% 3.03/0.75
% 3.03/0.75 % (27809)Memory used [KB]: 6268
% 3.03/0.75 % (27809)Time elapsed: 0.014 s
% 3.03/0.75 % (27809)Instructions burned: 51 (million)
% 3.03/0.75 % (27809)------------------------------
% 3.03/0.75 % (27809)------------------------------
% 3.03/0.75 % (27810)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 theBenchmark for (2996ds/614Mi)
% 3.03/0.75 % (27807)Instruction limit reached!
% 3.03/0.75 % (27807)------------------------------
% 3.03/0.75 % (27807)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.03/0.75 % (27807)Termination reason: Unknown
% 3.03/0.75 % (27807)Termination phase: Saturation
% 3.03/0.75
% 3.03/0.75 % (27807)Memory used [KB]: 6524
% 3.03/0.75 % (27807)Time elapsed: 0.027 s
% 3.03/0.75 % (27807)Instructions burned: 109 (million)
% 3.03/0.75 % (27807)------------------------------
% 3.03/0.75 % (27807)------------------------------
% 3.03/0.75 % (27811)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 theBenchmark for (2996ds/202Mi)
% 3.03/0.76 % (27812)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 theBenchmark for (2996ds/339Mi)
% 3.03/0.76 % (27805)Instruction limit reached!
% 3.03/0.76 % (27805)------------------------------
% 3.03/0.76 % (27805)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.03/0.76 % (27805)Termination reason: Unknown
% 3.03/0.76 % (27805)Termination phase: Property scanning
% 3.03/0.76
% 3.03/0.76 % (27805)Memory used [KB]: 2942
% 3.03/0.76 % (27805)Time elapsed: 0.039 s
% 3.03/0.76 % (27805)Instructions burned: 150 (million)
% 3.03/0.76 % (27805)------------------------------
% 3.03/0.76 % (27805)------------------------------
% 3.03/0.76 % (27813)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 theBenchmark for (2996ds/283Mi)
% 3.03/0.76 % (27811)Refutation not found, incomplete strategy
% 3.03/0.76 % (27811)------------------------------
% 3.03/0.76 % (27811)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.03/0.76 % (27811)Termination reason: Refutation not found, incomplete strategy
% 3.03/0.76
% 3.03/0.76
% 3.03/0.76 % (27811)Memory used [KB]: 6140
% 3.03/0.76 % (27811)Time elapsed: 0.010 s
% 3.03/0.76 % (27811)Instructions burned: 29 (million)
% 3.03/0.76 % (27811)------------------------------
% 3.03/0.76 % (27811)------------------------------
% 3.16/0.77 % (27814)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on theBenchmark for (2996ds/134Mi)
% 3.16/0.77 % (27816)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on theBenchmark for (2996ds/298Mi)
% 3.16/0.78 % (27756)Instruction limit reached!
% 3.16/0.78 % (27756)------------------------------
% 3.16/0.78 % (27756)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.16/0.78 % (27756)Termination reason: Unknown
% 3.16/0.78 % (27756)Termination phase: Saturation
% 3.16/0.78
% 3.16/0.78 % (27756)Memory used [KB]: 9594
% 3.16/0.78 % (27756)Time elapsed: 0.381 s
% 3.16/0.78 % (27756)Instructions burned: 1042 (million)
% 3.16/0.78 % (27756)------------------------------
% 3.16/0.78 % (27756)------------------------------
% 3.16/0.79 % (27817)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on theBenchmark for (2995ds/192Mi)
% 3.16/0.80 % (27814)Instruction limit reached!
% 3.16/0.80 % (27814)------------------------------
% 3.16/0.80 % (27814)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.16/0.80 % (27814)Termination reason: Unknown
% 3.16/0.80 % (27814)Termination phase: Saturation
% 3.16/0.80
% 3.16/0.80 % (27814)Memory used [KB]: 6652
% 3.16/0.80 % (27814)Time elapsed: 0.056 s
% 3.16/0.80 % (27814)Instructions burned: 136 (million)
% 3.16/0.80 % (27814)------------------------------
% 3.16/0.80 % (27814)------------------------------
% 3.16/0.81 % (27818)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 theBenchmark for (2995ds/258Mi)
% 3.16/0.81 % (27799)Instruction limit reached!
% 3.16/0.81 % (27799)------------------------------
% 3.16/0.81 % (27799)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.16/0.81 % (27799)Termination reason: Unknown
% 3.16/0.81 % (27799)Termination phase: Saturation
% 3.16/0.81
% 3.16/0.81 % (27799)Memory used [KB]: 7419
% 3.16/0.81 % (27799)Time elapsed: 0.147 s
% 3.16/0.81 % (27799)Instructions burned: 455 (million)
% 3.16/0.81 % (27799)------------------------------
% 3.16/0.81 % (27799)------------------------------
% 3.37/0.82 % (27819)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 theBenchmark for (2995ds/90Mi)
% 3.37/0.83 % (27812)Instruction limit reached!
% 3.37/0.83 % (27812)------------------------------
% 3.37/0.83 % (27812)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.37/0.83 % (27812)Termination reason: Unknown
% 3.37/0.83 % (27812)Termination phase: Saturation
% 3.37/0.83
% 3.37/0.83 % (27812)Memory used [KB]: 7036
% 3.37/0.83 % (27812)Time elapsed: 0.074 s
% 3.37/0.83 % (27812)Instructions burned: 341 (million)
% 3.37/0.83 % (27812)------------------------------
% 3.37/0.83 % (27812)------------------------------
% 3.37/0.83 % (27806)Instruction limit reached!
% 3.37/0.83 % (27806)------------------------------
% 3.37/0.83 % (27806)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.37/0.83 % (27806)Termination reason: Unknown
% 3.37/0.83 % (27806)Termination phase: Saturation
% 3.37/0.83
% 3.37/0.83 % (27806)Memory used [KB]: 7675
% 3.37/0.83 % (27806)Time elapsed: 0.106 s
% 3.37/0.83 % (27806)Instructions burned: 345 (million)
% 3.37/0.83 % (27806)------------------------------
% 3.37/0.83 % (27806)------------------------------
% 3.37/0.83 % (27813)Instruction limit reached!
% 3.37/0.83 % (27813)------------------------------
% 3.37/0.83 % (27813)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.37/0.83 % (27813)Termination reason: Unknown
% 3.37/0.83 % (27813)Termination phase: Saturation
% 3.37/0.83
% 3.37/0.83 % (27813)Memory used [KB]: 6908
% 3.37/0.83 % (27813)Time elapsed: 0.096 s
% 3.37/0.83 % (27813)Instructions burned: 283 (million)
% 3.37/0.83 % (27813)------------------------------
% 3.37/0.83 % (27813)------------------------------
% 3.37/0.84 % (27820)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 theBenchmark for (2995ds/231Mi)
% 3.37/0.84 % (27821)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 theBenchmark for (2995ds/458Mi)
% 3.37/0.84 % (27819)Instruction limit reached!
% 3.37/0.84 % (27819)------------------------------
% 3.37/0.84 % (27819)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.37/0.84 % (27819)Termination reason: Unknown
% 3.37/0.84 % (27819)Termination phase: Property scanning
% 3.37/0.84
% 3.37/0.84 % (27819)Memory used [KB]: 2174
% 3.37/0.84 % (27819)Time elapsed: 0.024 s
% 3.37/0.84 % (27819)Instructions burned: 90 (million)
% 3.37/0.84 % (27819)------------------------------
% 3.37/0.84 % (27819)------------------------------
% 3.37/0.84 % (27822)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 theBenchmark for (2995ds/31Mi)
% 3.37/0.84 % (27817)Instruction limit reached!
% 3.37/0.84 % (27817)------------------------------
% 3.37/0.84 % (27817)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.37/0.84 % (27817)Termination reason: Unknown
% 3.37/0.84 % (27817)Termination phase: Saturation
% 3.37/0.84
% 3.37/0.84 % (27817)Memory used [KB]: 7036
% 3.37/0.84 % (27817)Time elapsed: 0.079 s
% 3.37/0.84 % (27817)Instructions burned: 194 (million)
% 3.37/0.84 % (27817)------------------------------
% 3.37/0.84 % (27817)------------------------------
% 3.74/0.85 % (27824)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 theBenchmark for (2995ds/987Mi)
% 3.74/0.85 % (27823)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 theBenchmark for (2995ds/297Mi)
% 3.74/0.85 % (27822)Instruction limit reached!
% 3.74/0.85 % (27822)------------------------------
% 3.74/0.85 % (27822)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.74/0.85 % (27822)Termination reason: Unknown
% 3.74/0.85 % (27822)Termination phase: Property scanning
% 3.74/0.85
% 3.74/0.85 % (27822)Memory used [KB]: 1791
% 3.74/0.85 % (27822)Time elapsed: 0.010 s
% 3.74/0.85 % (27822)Instructions burned: 34 (million)
% 3.74/0.85 % (27822)------------------------------
% 3.74/0.85 % (27822)------------------------------
% 3.74/0.86 % (27825)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 theBenchmark for (2995ds/182Mi)
% 3.74/0.86 % (27816)Instruction limit reached!
% 3.74/0.86 % (27816)------------------------------
% 3.74/0.86 % (27816)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.74/0.86 % (27816)Termination reason: Unknown
% 3.74/0.86 % (27816)Termination phase: Saturation
% 3.74/0.86
% 3.74/0.86 % (27816)Memory used [KB]: 7291
% 3.74/0.86 % (27816)Time elapsed: 0.112 s
% 3.74/0.86 % (27816)Instructions burned: 301 (million)
% 3.74/0.86 % (27816)------------------------------
% 3.74/0.86 % (27816)------------------------------
% 3.74/0.86 % (27826)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 theBenchmark for (2995ds/182Mi)
% 3.74/0.88 % (27818)Instruction limit reached!
% 3.74/0.88 % (27818)------------------------------
% 3.74/0.88 % (27818)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.74/0.88 % (27818)Termination reason: Unknown
% 3.74/0.88 % (27818)Termination phase: Saturation
% 3.74/0.88
% 3.74/0.88 % (27818)Memory used [KB]: 7164
% 3.74/0.88 % (27818)Time elapsed: 0.074 s
% 3.74/0.88 % (27818)Instructions burned: 258 (million)
% 3.74/0.88 % (27818)------------------------------
% 3.74/0.88 % (27818)------------------------------
% 3.74/0.89 % (27827)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 theBenchmark for (2994ds/154Mi)
% 3.74/0.90 % (27825)Instruction limit reached!
% 3.74/0.90 % (27825)------------------------------
% 3.74/0.90 % (27825)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.74/0.90 % (27825)Termination reason: Unknown
% 3.74/0.90 % (27825)Termination phase: Saturation
% 3.74/0.90
% 3.74/0.90 % (27825)Memory used [KB]: 7164
% 3.74/0.90 % (27825)Time elapsed: 0.048 s
% 3.74/0.90 % (27825)Instructions burned: 182 (million)
% 3.74/0.90 % (27825)------------------------------
% 3.74/0.90 % (27825)------------------------------
% 3.74/0.91 % (27828)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 theBenchmark for (2994ds/79Mi)
% 3.74/0.91 % (27820)Instruction limit reached!
% 3.74/0.91 % (27820)------------------------------
% 3.74/0.91 % (27820)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.74/0.91 % (27820)Termination reason: Unknown
% 3.74/0.91 % (27820)Termination phase: Saturation
% 3.74/0.91
% 3.74/0.91 % (27820)Memory used [KB]: 7803
% 3.74/0.91 % (27820)Time elapsed: 0.074 s
% 3.74/0.91 % (27820)Instructions burned: 231 (million)
% 3.74/0.91 % (27820)------------------------------
% 3.74/0.91 % (27820)------------------------------
% 3.74/0.92 % (27826)Instruction limit reached!
% 3.74/0.92 % (27826)------------------------------
% 3.74/0.92 % (27826)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.74/0.92 % (27826)Termination reason: Unknown
% 3.74/0.92 % (27826)Termination phase: Saturation
% 3.74/0.92
% 3.74/0.92 % (27826)Memory used [KB]: 9466
% 3.74/0.92 % (27826)Time elapsed: 0.056 s
% 3.74/0.92 % (27826)Instructions burned: 183 (million)
% 3.74/0.92 % (27826)------------------------------
% 3.74/0.92 % (27826)------------------------------
% 3.74/0.92 % (27829)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 theBenchmark for (2994ds/216Mi)
% 3.74/0.92 % (27823)Instruction limit reached!
% 3.74/0.92 % (27823)------------------------------
% 3.74/0.92 % (27823)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.74/0.92 % (27823)Termination reason: Unknown
% 3.74/0.92 % (27823)Termination phase: Saturation
% 3.74/0.92
% 3.74/0.92 % (27823)Memory used [KB]: 6652
% 3.74/0.92 % (27823)Time elapsed: 0.078 s
% 3.74/0.92 % (27823)Instructions burned: 299 (million)
% 3.74/0.92 % (27823)------------------------------
% 3.74/0.92 % (27823)------------------------------
% 3.74/0.92 % (27827)Instruction limit reached!
% 3.74/0.92 % (27827)------------------------------
% 3.74/0.92 % (27827)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.74/0.93 % (27827)Termination reason: Unknown
% 3.74/0.93 % (27827)Termination phase: Saturation
% 3.74/0.93
% 3.74/0.93 % (27827)Memory used [KB]: 6652
% 3.74/0.93 % (27827)Time elapsed: 0.039 s
% 3.74/0.93 % (27827)Instructions burned: 156 (million)
% 3.74/0.93 % (27827)------------------------------
% 3.74/0.93 % (27827)------------------------------
% 4.25/0.93 % (27830)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on theBenchmark for (2994ds/114Mi)
% 4.25/0.93 % (27828)Instruction limit reached!
% 4.25/0.93 % (27828)------------------------------
% 4.25/0.93 % (27828)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.25/0.93 % (27828)Termination reason: Unknown
% 4.25/0.93 % (27828)Termination phase: Function definition elimination
% 4.25/0.93
% 4.25/0.93 % (27828)Memory used [KB]: 2046
% 4.25/0.93 % (27828)Time elapsed: 0.020 s
% 4.25/0.93 % (27828)Instructions burned: 81 (million)
% 4.25/0.93 % (27828)------------------------------
% 4.25/0.93 % (27828)------------------------------
% 4.25/0.93 % (27810)Instruction limit reached!
% 4.25/0.93 % (27810)------------------------------
% 4.25/0.93 % (27810)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.25/0.93 % (27810)Termination reason: Unknown
% 4.25/0.93 % (27810)Termination phase: Saturation
% 4.25/0.93
% 4.25/0.93 % (27810)Memory used [KB]: 7675
% 4.25/0.93 % (27810)Time elapsed: 0.202 s
% 4.25/0.93 % (27810)Instructions burned: 616 (million)
% 4.25/0.93 % (27810)------------------------------
% 4.25/0.93 % (27810)------------------------------
% 4.25/0.93 % (27831)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on theBenchmark for (2994ds/922Mi)
% 4.25/0.93 % (27832)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 theBenchmark for (2994ds/182Mi)
% 4.25/0.94 % (27833)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 theBenchmark for (2994ds/164Mi)
% 4.25/0.94 % (27834)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 theBenchmark for (2994ds/50Mi)
% 4.25/0.94 % (27831)Refutation not found, incomplete strategy
% 4.25/0.94 % (27831)------------------------------
% 4.25/0.94 % (27831)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.25/0.94 % (27831)Termination reason: Refutation not found, incomplete strategy
% 4.25/0.94
% 4.25/0.94
% 4.25/0.94 % (27831)Memory used [KB]: 6268
% 4.25/0.94 % (27831)Time elapsed: 0.010 s
% 4.25/0.94 % (27831)Instructions burned: 28 (million)
% 4.25/0.94 % (27831)------------------------------
% 4.25/0.94 % (27831)------------------------------
% 4.25/0.95 % (27835)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on theBenchmark for (2994ds/368Mi)
% 4.25/0.95 % (27834)Instruction limit reached!
% 4.25/0.95 % (27834)------------------------------
% 4.25/0.95 % (27834)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.25/0.95 % (27834)Termination reason: Unknown
% 4.25/0.95 % (27834)Termination phase: Property scanning
% 4.25/0.95
% 4.25/0.95 % (27834)Memory used [KB]: 1791
% 4.25/0.95 % (27834)Time elapsed: 0.014 s
% 4.25/0.95 % (27834)Instructions burned: 52 (million)
% 4.25/0.95 % (27834)------------------------------
% 4.25/0.95 % (27834)------------------------------
% 4.25/0.95 % (27830)Refutation not found, incomplete strategy
% 4.25/0.95 % (27830)------------------------------
% 4.25/0.95 % (27830)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.25/0.95 % (27830)Termination reason: Refutation not found, incomplete strategy
% 4.25/0.95
% 4.25/0.95
% 4.25/0.95 % (27830)Memory used [KB]: 6652
% 4.25/0.95 % (27830)Time elapsed: 0.025 s
% 4.25/0.95 % (27830)Instructions burned: 102 (million)
% 4.25/0.95 % (27830)------------------------------
% 4.25/0.95 % (27830)------------------------------
% 4.25/0.95 % (27833)Refutation not found, incomplete strategy
% 4.25/0.95 % (27833)------------------------------
% 4.25/0.95 % (27833)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.25/0.95 % (27833)Termination reason: Refutation not found, incomplete strategy
% 4.25/0.95
% 4.25/0.95
% 4.25/0.95 % (27833)Memory used [KB]: 1791
% 4.25/0.95 % (27833)Time elapsed: 0.016 s
% 4.25/0.95 % (27833)Instructions burned: 59 (million)
% 4.25/0.95 % (27833)------------------------------
% 4.25/0.95 % (27833)------------------------------
% 4.25/0.96 % (27836)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 theBenchmark for (2994ds/1021Mi)
% 4.25/0.96 % (27837)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 theBenchmark for (2994ds/267Mi)
% 4.25/0.96 % (27838)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 theBenchmark for (2994ds/204Mi)
% 4.25/0.97 % (27829)Instruction limit reached!
% 4.25/0.97 % (27829)------------------------------
% 4.25/0.97 % (27829)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.25/0.97 % (27829)Termination reason: Unknown
% 4.25/0.97 % (27829)Termination phase: Saturation
% 4.25/0.97
% 4.25/0.97 % (27829)Memory used [KB]: 6524
% 4.25/0.97 % (27829)Time elapsed: 0.052 s
% 4.25/0.97 % (27829)Instructions burned: 218 (million)
% 4.25/0.97 % (27829)------------------------------
% 4.25/0.97 % (27829)------------------------------
% 4.25/0.98 % (27821)Instruction limit reached!
% 4.25/0.98 % (27821)------------------------------
% 4.25/0.98 % (27821)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.25/0.98 % (27821)Termination reason: Unknown
% 4.25/0.98 % (27821)Termination phase: Saturation
% 4.25/0.98
% 4.25/0.98 % (27821)Memory used [KB]: 7931
% 4.25/0.98 % (27821)Time elapsed: 0.139 s
% 4.25/0.98 % (27821)Instructions burned: 460 (million)
% 4.25/0.98 % (27821)------------------------------
% 4.25/0.98 % (27821)------------------------------
% 4.25/0.98 % (27839)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 theBenchmark for (2994ds/26Mi)
% 4.25/0.98 % (27832)Instruction limit reached!
% 4.25/0.98 % (27832)------------------------------
% 4.25/0.98 % (27832)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.25/0.98 % (27832)Termination reason: Unknown
% 4.25/0.98 % (27832)Termination phase: Saturation
% 4.25/0.98
% 4.25/0.98 % (27832)Memory used [KB]: 6652
% 4.25/0.98 % (27832)Time elapsed: 0.046 s
% 4.25/0.98 % (27832)Instructions burned: 182 (million)
% 4.25/0.98 % (27832)------------------------------
% 4.25/0.98 % (27832)------------------------------
% 4.82/0.98 % (27839)Instruction limit reached!
% 4.82/0.98 % (27839)------------------------------
% 4.82/0.98 % (27839)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.82/0.98 % (27839)Termination reason: Unknown
% 4.82/0.98 % (27839)Termination phase: shuffling
% 4.82/0.98
% 4.82/0.98 % (27839)Memory used [KB]: 1791
% 4.82/0.98 % (27839)Time elapsed: 0.008 s
% 4.82/0.98 % (27839)Instructions burned: 26 (million)
% 4.82/0.98 % (27839)------------------------------
% 4.82/0.98 % (27839)------------------------------
% 4.82/0.98 % (27840)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 theBenchmark for (2993ds/53Mi)
% 4.82/0.99 % (27841)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 theBenchmark for (2993ds/4436Mi)
% 4.82/0.99 % (27842)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on theBenchmark for (2993ds/1539Mi)
% 4.82/0.99 % (27841)Refutation not found, incomplete strategy
% 4.82/0.99 % (27841)------------------------------
% 4.82/0.99 % (27841)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.82/0.99 % (27841)Termination reason: Refutation not found, incomplete strategy
% 4.82/0.99
% 4.82/0.99
% 4.82/0.99 % (27841)Memory used [KB]: 6268
% 4.82/0.99 % (27841)Time elapsed: 0.010 s
% 4.82/0.99 % (27841)Instructions burned: 28 (million)
% 4.82/0.99 % (27841)------------------------------
% 4.82/0.99 % (27841)------------------------------
% 4.82/1.00 % (27840)Instruction limit reached!
% 4.82/1.00 % (27840)------------------------------
% 4.82/1.00 % (27840)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.82/1.00 % (27840)Termination reason: Unknown
% 4.82/1.00 % (27840)Termination phase: Property scanning
% 4.82/1.00
% 4.82/1.00 % (27840)Memory used [KB]: 1791
% 4.82/1.00 % (27840)Time elapsed: 0.015 s
% 4.82/1.00 % (27840)Instructions burned: 57 (million)
% 4.82/1.00 % (27840)------------------------------
% 4.82/1.00 % (27840)------------------------------
% 4.82/1.00 % (27843)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 theBenchmark for (2993ds/408Mi)
% 4.82/1.01 % (27844)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 theBenchmark for (2993ds/5205Mi)
% 4.82/1.02 % (27838)Instruction limit reached!
% 4.82/1.02 % (27838)------------------------------
% 4.82/1.02 % (27838)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.82/1.02 % (27838)Termination reason: Unknown
% 4.82/1.02 % (27838)Termination phase: Saturation
% 4.82/1.02
% 4.82/1.02 % (27838)Memory used [KB]: 6908
% 4.82/1.02 % (27838)Time elapsed: 0.058 s
% 4.82/1.02 % (27838)Instructions burned: 206 (million)
% 4.82/1.02 % (27838)------------------------------
% 4.82/1.02 % (27838)------------------------------
% 4.82/1.02 % (27845)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 theBenchmark for (2993ds/1913Mi)
% 4.82/1.03 % (27837)Instruction limit reached!
% 4.82/1.03 % (27837)------------------------------
% 4.82/1.03 % (27837)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.82/1.03 % (27837)Termination reason: Unknown
% 4.82/1.03 % (27837)Termination phase: Saturation
% 4.82/1.03
% 4.82/1.03 % (27837)Memory used [KB]: 6908
% 4.82/1.03 % (27837)Time elapsed: 0.070 s
% 4.82/1.03 % (27837)Instructions burned: 269 (million)
% 4.82/1.03 % (27837)------------------------------
% 4.82/1.03 % (27837)------------------------------
% 4.82/1.04 % (27846)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 theBenchmark for (2993ds/4350Mi)
% 4.82/1.04 % (27835)Instruction limit reached!
% 4.82/1.04 % (27835)------------------------------
% 4.82/1.04 % (27835)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.82/1.04 % (27835)Termination reason: Unknown
% 4.82/1.04 % (27835)Termination phase: Saturation
% 4.82/1.04
% 4.82/1.04 % (27835)Memory used [KB]: 6908
% 4.82/1.04 % (27835)Time elapsed: 0.094 s
% 4.82/1.04 % (27835)Instructions burned: 369 (million)
% 4.82/1.04 % (27835)------------------------------
% 4.82/1.04 % (27835)------------------------------
% 4.82/1.05 % (27846)Refutation not found, incomplete strategy
% 4.82/1.05 % (27846)------------------------------
% 4.82/1.05 % (27846)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.82/1.05 % (27846)Termination reason: Refutation not found, incomplete strategy
% 4.82/1.05
% 4.82/1.05
% 4.82/1.05 % (27846)Memory used [KB]: 6268
% 4.82/1.05 % (27846)Time elapsed: 0.015 s
% 4.82/1.05 % (27846)Instructions burned: 53 (million)
% 4.82/1.05 % (27846)------------------------------
% 4.82/1.05 % (27846)------------------------------
% 5.11/1.05 % (27847)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 theBenchmark for (2993ds/68Mi)
% 5.11/1.06 % (27848)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 theBenchmark for (2993ds/358Mi)
% 5.78/1.08 % (27847)Instruction limit reached!
% 5.78/1.08 % (27847)------------------------------
% 5.78/1.08 % (27847)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 5.78/1.08 % (27847)Termination reason: Unknown
% 5.78/1.08 % (27847)Termination phase: Function definition elimination
% 5.78/1.08
% 5.78/1.08 % (27847)Memory used [KB]: 1791
% 5.78/1.08 % (27847)Time elapsed: 0.020 s
% 5.78/1.08 % (27847)Instructions burned: 70 (million)
% 5.78/1.08 % (27847)------------------------------
% 5.78/1.08 % (27847)------------------------------
% 5.78/1.08 % (27849)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 theBenchmark for (2992ds/31Mi)
% 5.78/1.09 % (27849)Instruction limit reached!
% 5.78/1.09 % (27849)------------------------------
% 5.78/1.09 % (27849)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 5.78/1.09 % (27849)Termination reason: Unknown
% 5.78/1.09 % (27849)Termination phase: Property scanning
% 5.78/1.09
% 5.78/1.09 % (27849)Memory used [KB]: 1791
% 5.78/1.09 % (27849)Time elapsed: 0.010 s
% 5.78/1.09 % (27849)Instructions burned: 33 (million)
% 5.78/1.09 % (27849)------------------------------
% 5.78/1.09 % (27849)------------------------------
% 5.78/1.10 % (27850)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on theBenchmark for (2992ds/279Mi)
% 6.15/1.13 % (27843)Instruction limit reached!
% 6.15/1.13 % (27843)------------------------------
% 6.15/1.13 % (27843)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.15/1.13 % (27843)Termination reason: Unknown
% 6.15/1.13 % (27843)Termination phase: Saturation
% 6.15/1.13
% 6.15/1.13 % (27843)Memory used [KB]: 9338
% 6.15/1.13 % (27843)Time elapsed: 0.146 s
% 6.15/1.13 % (27843)Instructions burned: 408 (million)
% 6.15/1.13 % (27843)------------------------------
% 6.15/1.13 % (27843)------------------------------
% 6.15/1.13 % (27824)Instruction limit reached!
% 6.15/1.13 % (27824)------------------------------
% 6.15/1.13 % (27824)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.15/1.13 % (27824)Termination reason: Unknown
% 6.15/1.13 % (27824)Termination phase: Saturation
% 6.15/1.13
% 6.15/1.13 % (27824)Memory used [KB]: 9083
% 6.15/1.13 % (27824)Time elapsed: 0.283 s
% 6.15/1.13 % (27824)Instructions burned: 990 (million)
% 6.15/1.13 % (27824)------------------------------
% 6.15/1.13 % (27824)------------------------------
% 6.15/1.13 % (27851)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on theBenchmark for (2992ds/258Mi)
% 6.15/1.14 % (27852)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 theBenchmark for (2992ds/26Mi)
% 6.15/1.15 % (27852)Instruction limit reached!
% 6.15/1.15 % (27852)------------------------------
% 6.15/1.15 % (27852)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.15/1.15 % (27852)Termination reason: Unknown
% 6.15/1.15 % (27852)Termination phase: Property scanning
% 6.15/1.15
% 6.15/1.15 % (27852)Memory used [KB]: 1791
% 6.15/1.15 % (27852)Time elapsed: 0.009 s
% 6.15/1.15 % (27852)Instructions burned: 29 (million)
% 6.15/1.15 % (27852)------------------------------
% 6.15/1.15 % (27852)------------------------------
% 6.34/1.15 % (27853)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 theBenchmark for (2992ds/995Mi)
% 6.34/1.16 % (27848)Instruction limit reached!
% 6.34/1.16 % (27848)------------------------------
% 6.34/1.16 % (27848)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.34/1.16 % (27848)Termination reason: Unknown
% 6.34/1.16 % (27848)Termination phase: Saturation
% 6.34/1.16
% 6.34/1.16 % (27848)Memory used [KB]: 7164
% 6.34/1.16 % (27848)Time elapsed: 0.128 s
% 6.34/1.16 % (27848)Instructions burned: 359 (million)
% 6.34/1.16 % (27848)------------------------------
% 6.34/1.16 % (27848)------------------------------
% 6.34/1.17 % (27854)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 theBenchmark for (2991ds/373Mi)
% 6.34/1.18 % (27850)Instruction limit reached!
% 6.34/1.18 % (27850)------------------------------
% 6.34/1.18 % (27850)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.34/1.18 % (27850)Termination reason: Unknown
% 6.34/1.18 % (27850)Termination phase: Saturation
% 6.34/1.18
% 6.34/1.18 % (27850)Memory used [KB]: 7164
% 6.34/1.18 % (27850)Time elapsed: 0.080 s
% 6.34/1.18 % (27850)Instructions burned: 279 (million)
% 6.34/1.18 % (27850)------------------------------
% 6.34/1.18 % (27850)------------------------------
% 6.34/1.19 % (27855)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 theBenchmark for (2991ds/253Mi)
% 6.34/1.20 % (27851)Instruction limit reached!
% 6.34/1.20 % (27851)------------------------------
% 6.34/1.20 % (27851)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.34/1.20 % (27851)Termination reason: Unknown
% 6.34/1.20 % (27851)Termination phase: Saturation
% 6.34/1.20
% 6.34/1.20 % (27851)Memory used [KB]: 7547
% 6.34/1.20 % (27851)Time elapsed: 0.066 s
% 6.34/1.20 % (27851)Instructions burned: 258 (million)
% 6.34/1.20 % (27851)------------------------------
% 6.34/1.20 % (27851)------------------------------
% 6.34/1.21 % (27856)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on theBenchmark for (2991ds/832Mi)
% 6.79/1.24 % (27855)First to succeed.
% 6.79/1.25 % (27855)Refutation found. Thanks to Tanya!
% 6.79/1.25 % SZS status Theorem for theBenchmark
% 6.79/1.25 % SZS output start Proof for theBenchmark
% See solution above
% 6.79/1.26 % (27855)------------------------------
% 6.79/1.26 % (27855)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.79/1.26 % (27855)Termination reason: Refutation
% 6.79/1.26
% 6.79/1.26 % (27855)Memory used [KB]: 7931
% 6.79/1.26 % (27855)Time elapsed: 0.067 s
% 6.79/1.26 % (27855)Instructions burned: 195 (million)
% 6.79/1.26 % (27855)------------------------------
% 6.79/1.26 % (27855)------------------------------
% 6.79/1.26 % (27744)Success in time 0.894 s
% 6.79/1.26 % Vampire---4.8 exiting
%------------------------------------------------------------------------------