%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : ALG258^1 : 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/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n015.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 18:20:14 EDT 2024
% Result : Theorem 70.45s 9.25s
% Output : Refutation 70.45s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats ran out of CPU time)
% 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: subst > term > term ).
thf(func_def_144,type,
sK3: subst > term > term ).
thf(func_def_145,type,
sK4: subst ).
thf(func_def_146,type,
sK5: term ).
thf(f5204,plain,
$false,
inference(trivial_inequality_removal,[],[f5203]) ).
thf(f5203,plain,
$true = $false,
inference(boolean_simplification,[],[f5200]) ).
thf(f5200,plain,
( ( ( sub @ ( sK2 @ sK4 @ sK5 ) @ sh )
= ( sub @ ( sK2 @ sK4 @ sK5 ) @ sh ) )
= $false ),
inference(backward_demodulation,[],[f4772,f5180]) ).
thf(f5180,plain,
! [X0: term,X1: subst] :
( ( sK3 @ X1 @ X0 )
= ( sK2 @ X1 @ X0 ) ),
inference(forward_demodulation,[],[f5146,f677]) ).
thf(f677,plain,
! [X2: term,X1: subst] :
( ( comp @ sh @ ( push @ X2 @ X1 ) )
= X1 ),
inference(equality_proxy_clausification,[],[f676]) ).
thf(f676,plain,
! [X2: term,X1: subst] :
( $true
= ( ( comp @ sh @ ( push @ X2 @ X1 ) )
= X1 ) ),
inference(beta_eta_normalization,[],[f675]) ).
thf(f675,plain,
! [X2: term,X1: subst] :
( $true
= ( ^ [Y0: term] :
( ( comp @ sh @ ( push @ Y0 @ X1 ) )
= X1 )
@ X2 ) ),
inference(pi_clausification,[],[f664]) ).
thf(f664,plain,
! [X1: subst] :
( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( comp @ sh @ ( push @ Y0 @ X1 ) )
= X1 ) ) ),
inference(beta_eta_normalization,[],[f663]) ).
thf(f663,plain,
! [X1: subst] :
( $true
= ( ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) )
@ X1 ) ),
inference(pi_clausification,[],[f657]) ).
thf(f657,plain,
( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) ) ),
inference(binary_proxy_clausification,[],[f653]) ).
thf(f653,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y0 ) @ Y1 )
= ( push @ ( sub @ Y2 @ Y1 ) @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(boolean_simplification,[],[f652]) ).
thf(f652,plain,
( $false
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y0 ) @ Y1 )
= ( push @ ( sub @ Y2 @ Y1 ) @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& $true
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f650]) ).
thf(f650,plain,
( ( $true
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y0 ) @ Y1 )
= ( push @ ( sub @ Y2 @ Y1 ) @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& $true
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(backward_demodulation,[],[f639,f647]) ).
thf(f647,plain,
( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) ),
inference(binary_proxy_clausification,[],[f639]) ).
thf(f639,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y0 ) @ Y1 )
= ( push @ ( sub @ Y2 @ Y1 ) @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(boolean_simplification,[],[f638]) ).
thf(f638,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y0 ) @ Y1 )
= ( push @ ( sub @ Y2 @ Y1 ) @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) )
=> ( $true
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(boolean_simplification,[],[f636]) ).
thf(f636,plain,
( ( $true
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y0 ) @ Y1 )
= ( push @ ( sub @ Y2 @ Y1 ) @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) )
=> ( $true
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(backward_demodulation,[],[f595,f605]) ).
thf(f605,plain,
( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 )
= ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f595]) ).
thf(f595,plain,
( $false
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 )
= ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y0 ) @ Y1 )
= ( push @ ( sub @ Y2 @ Y1 ) @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 )
= ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f592]) ).
thf(f592,plain,
( $false
= ( $true
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 )
= ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y0 ) @ Y1 )
= ( push @ ( sub @ Y2 @ Y1 ) @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 )
= ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(backward_demodulation,[],[f551,f554]) ).
thf(f554,plain,
( $true
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( lam @ Y0 ) @ Y1 )
= ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f551]) ).
thf(f551,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( lam @ Y0 ) @ Y1 )
= ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 )
= ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y0 ) @ Y1 )
= ( push @ ( sub @ Y2 @ Y1 ) @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 )
= ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(boolean_simplification,[],[f550]) ).
thf(f550,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( lam @ Y0 ) @ Y1 )
= ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 )
= ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y0 ) @ Y1 )
= ( push @ ( sub @ Y2 @ Y1 ) @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) )
=> ( ( $true
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 )
= ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(boolean_simplification,[],[f548]) ).
thf(f548,plain,
( ( $true
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( lam @ Y0 ) @ Y1 )
= ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 )
= ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y0 ) @ Y1 )
= ( push @ ( sub @ Y2 @ Y1 ) @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) )
=> ( ( $true
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 )
= ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(backward_demodulation,[],[f545,f547]) ).
thf(f547,plain,
( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ),
inference(binary_proxy_clausification,[],[f545]) ).
thf(f545,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( lam @ Y0 ) @ Y1 )
= ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 )
= ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y0 ) @ Y1 )
= ( push @ ( sub @ Y2 @ Y1 ) @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 )
= ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(boolean_simplification,[],[f542]) ).
thf(f542,plain,
( $false
= ( $true
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( lam @ Y0 ) @ Y1 )
= ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 )
= ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y0 ) @ Y1 )
= ( push @ ( sub @ Y2 @ Y1 ) @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 )
= ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(backward_demodulation,[],[f536,f541]) ).
thf(f541,plain,
( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ one @ ( push @ Y1 @ Y0 ) )
= Y1 ) ) ) ),
inference(binary_proxy_clausification,[],[f536]) ).
thf(f536,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ one @ ( push @ Y1 @ Y0 ) )
= Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( lam @ Y0 ) @ Y1 )
= ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 )
= ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y0 ) @ Y1 )
= ( push @ ( sub @ Y2 @ Y1 ) @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 )
= ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(boolean_simplification,[],[f534]) ).
thf(f534,plain,
( ( $true
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ one @ ( push @ Y1 @ Y0 ) )
= Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( lam @ Y0 ) @ Y1 )
= ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 )
= ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y0 ) @ Y1 )
= ( push @ ( sub @ Y2 @ Y1 ) @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 )
= ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(backward_demodulation,[],[f529,f532]) ).
thf(f532,plain,
( $true
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( ap @ Y2 @ Y0 ) @ Y1 )
= ( ap @ ( sub @ Y2 @ Y1 ) @ ( sub @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f529]) ).
thf(f529,plain,
( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( ap @ Y2 @ Y0 ) @ Y1 )
= ( ap @ ( sub @ Y2 @ Y1 ) @ ( sub @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ one @ ( push @ Y1 @ Y0 ) )
= Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( lam @ Y0 ) @ Y1 )
= ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 )
= ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y0 ) @ Y1 )
= ( push @ ( sub @ Y2 @ Y1 ) @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 )
= ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f528]) ).
thf(f528,plain,
( $true
= ( ~ ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( ap @ Y2 @ Y0 ) @ Y1 )
= ( ap @ ( sub @ Y2 @ Y1 ) @ ( sub @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ one @ ( push @ Y1 @ Y0 ) )
= Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( lam @ Y0 ) @ Y1 )
= ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 )
= ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y0 ) @ Y1 )
= ( push @ ( sub @ Y2 @ Y1 ) @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 )
= ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f527]) ).
thf(f527,plain,
( $true
= ( ~ ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( ap @ Y2 @ Y0 ) @ Y1 )
= ( ap @ ( sub @ Y2 @ Y1 ) @ ( sub @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ one @ ( push @ Y1 @ Y0 ) )
= Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( lam @ Y0 ) @ Y1 )
= ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 )
= ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y0 ) @ Y1 )
= ( push @ ( sub @ Y2 @ Y1 ) @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 )
= ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y3
@ id
@ Y2 )
= ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y1
@ id
@ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y0
@ id
@ Y2 )
= ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y1
@ id
@ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y0 @ Y2 @ Y3 ) )
= ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f354,f511]) ).
thf(f511,plain,
( hoaslaminj_gthm
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( ap @ Y2 @ Y0 ) @ Y1 )
= ( ap @ ( sub @ Y2 @ Y1 ) @ ( sub @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ one @ ( push @ Y1 @ Y0 ) )
= Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( lam @ Y0 ) @ Y1 )
= ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 )
= ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y0 ) @ Y1 )
= ( push @ ( sub @ Y2 @ Y1 ) @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 )
= ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y3
@ id
@ Y2 )
= ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y1
@ id
@ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y0
@ id
@ Y2 )
= ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y1
@ id
@ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y0 @ Y2 @ Y3 ) )
= ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f449,f359,f388,f362,f374,f414,f410,f381,f386,f350,f369,f395,f356,f416,f348,f352,f383,f424,f373,f419,f396,f431,f353,f339,f389,f367,f394,f341,f423,f455,f456,f457]) ).
thf(f457,plain,
( hoaslaminj
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y0 @ Y2 @ Y3 ) )
= ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f392,f366,f366]) ).
thf(f366,plain,
( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( lam @ ( Y1 @ sh @ one ) ) ) ),
inference(cnf_transformation,[],[f237]) ).
thf(f237,plain,
( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( lam @ ( Y1 @ sh @ one ) ) ) ),
inference(fool_elimination,[],[f236]) ).
thf(f236,plain,
( hoaslam
= ( ^ [X0: subst,X1: subst > term > term] : ( lam @ ( X1 @ sh @ one ) ) ) ),
inference(rectify,[],[f56]) ).
thf(f56,axiom,
( hoaslam
= ( ^ [X2: subst,X10: subst > term > term] : ( lam @ ( X10 @ sh @ one ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoaslam) ).
thf(f392,plain,
( hoaslaminj
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y0 @ Y2 @ Y3 ) )
= ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f243]) ).
thf(f243,plain,
( hoaslaminj
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y0 @ Y2 @ Y3 ) )
= ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f242]) ).
thf(f242,plain,
! [X0: subst > term > term] :
( ( ! [X1: subst,X2: term,X3: subst] :
( ( sub @ ( X0 @ X1 @ X2 ) @ X3 )
= ( X0 @ ( comp @ X1 @ X3 ) @ ( sub @ X2 @ X3 ) ) )
=> ! [X4: subst > term > term] :
( ! [X5: subst,X6: term,X7: subst] :
( ( sub @ ( X4 @ X7 @ X6 ) @ X5 )
= ( X4 @ ( comp @ X7 @ X5 ) @ ( sub @ X6 @ X5 ) ) )
=> ( ( ( hoaslam @ id
@ ^ [X8: subst,X9: term] : ( X0 @ X8 @ X9 ) )
= ( hoaslam @ id
@ ^ [X10: subst,X11: term] : ( X4 @ X10 @ X11 ) ) )
=> ! [X12: term,X13: subst] :
( ( X0 @ X13 @ X12 )
= ( X4 @ X13 @ X12 ) ) ) ) )
= hoaslaminj ),
inference(rectify,[],[f64]) ).
thf(f64,axiom,
! [X10: subst > term > term] :
( ( ! [X2: subst,X0: term,X3: subst] :
( ( sub @ ( X10 @ X2 @ X0 ) @ X3 )
= ( X10 @ ( comp @ X2 @ X3 ) @ ( sub @ X0 @ X3 ) ) )
=> ! [X11: subst > term > term] :
( ! [X3: subst,X0: term,X2: subst] :
( ( sub @ ( X11 @ X2 @ X0 ) @ X3 )
= ( X11 @ ( comp @ X2 @ X3 ) @ ( sub @ X0 @ X3 ) ) )
=> ( ( ( hoaslam @ id
@ ^ [X2: subst,X0: term] : ( X10 @ X2 @ X0 ) )
= ( hoaslam @ id
@ ^ [X2: subst,X0: term] : ( X11 @ X2 @ X0 ) ) )
=> ! [X0: term,X2: subst] :
( ( X10 @ X2 @ X0 )
= ( X11 @ X2 @ X0 ) ) ) ) )
= hoaslaminj ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoaslaminj) ).
thf(f456,plain,
( hoasapinj2
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y0
@ id
@ Y2 )
= ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y1
@ id
@ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f409,f358,f358]) ).
thf(f358,plain,
( hoasap
= ( ^ [Y0: subst,Y1: term,Y2: subst,Y3: term] : ( ap @ ( sub @ Y1 @ Y2 ) @ Y3 ) ) ),
inference(cnf_transformation,[],[f149]) ).
thf(f149,plain,
( hoasap
= ( ^ [Y0: subst,Y1: term,Y2: subst,Y3: term] : ( ap @ ( sub @ Y1 @ Y2 ) @ Y3 ) ) ),
inference(fool_elimination,[],[f148]) ).
thf(f148,plain,
( ( ^ [X0: subst,X1: term,X2: subst,X3: term] : ( ap @ ( sub @ X1 @ X2 ) @ X3 ) )
= hoasap ),
inference(rectify,[],[f55]) ).
thf(f55,axiom,
( ( ^ [X2: subst,X0: term,X3: subst,X1: term] : ( ap @ ( sub @ X0 @ X3 ) @ X1 ) )
= hoasap ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasap) ).
thf(f409,plain,
( hoasapinj2
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( hoasap @ id @ Y0 @ id @ Y2 )
= ( hoasap @ id @ Y1 @ id @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f157]) ).
thf(f157,plain,
( hoasapinj2
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( hoasap @ id @ Y0 @ id @ Y2 )
= ( hoasap @ id @ Y1 @ id @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f156]) ).
thf(f156,plain,
! [X0: term,X1: term,X2: term,X3: term] :
( ( ( ( hoasap @ id @ X3 @ id @ X1 )
= ( hoasap @ id @ X2 @ id @ X0 ) )
=> ( X0 = X1 ) )
= hoasapinj2 ),
inference(rectify,[],[f61]) ).
thf(f61,axiom,
! [X7: term,X6: term,X1: term,X0: term] :
( ( ( ( hoasap @ id @ X0 @ id @ X6 )
= ( hoasap @ id @ X1 @ id @ X7 ) )
=> ( X6 = X7 ) )
= hoasapinj2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasapinj2) ).
thf(f455,plain,
( hoasapinj1
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y3
@ id
@ Y2 )
= ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y1
@ id
@ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f415,f358,f358]) ).
thf(f415,plain,
( hoasapinj1
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( hoasap @ id @ Y3 @ id @ Y2 )
= ( hoasap @ id @ Y1 @ id @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f181]) ).
thf(f181,plain,
( hoasapinj1
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( hoasap @ id @ Y3 @ id @ Y2 )
= ( hoasap @ id @ Y1 @ id @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f180]) ).
thf(f180,plain,
( hoasapinj1
= ( ! [X0: term,X1: term,X2: term,X3: term] :
( ( ( hoasap @ id @ X0 @ id @ X1 )
= ( hoasap @ id @ X2 @ id @ X3 ) )
=> ( X0 = X2 ) ) ) ),
inference(rectify,[],[f58]) ).
thf(f58,axiom,
( hoasapinj1
= ( ! [X1: term,X7: term,X0: term,X6: term] :
( ( ( hoasap @ id @ X0 @ id @ X6 )
= ( hoasap @ id @ X1 @ id @ X7 ) )
=> ( X0 = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasapinj1) ).
thf(f423,plain,
( termmset
= ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 )
= ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f300]) ).
thf(f300,plain,
( termmset
= ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 )
= ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f299]) ).
thf(f299,plain,
( ! [X0: term,X1: subst,X2: subst] :
( ( sub @ ( sub @ X0 @ X1 ) @ X2 )
= ( sub @ X0 @ ( comp @ X1 @ X2 ) ) )
& ! [X3: term] :
( ( ( sub @ X3 @ id )
= X3 )
= termmset ) ),
inference(rectify,[],[f52]) ).
thf(f52,axiom,
( ! [X0: term,X2: subst,X3: subst] :
( ( sub @ ( sub @ X0 @ X2 ) @ X3 )
= ( sub @ X0 @ ( comp @ X2 @ X3 ) ) )
& ! [X0: term] :
( ( ( sub @ X0 @ id )
= X0 )
= termmset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',termmset) ).
thf(f341,plain,
( substmonoid
= ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f239]) ).
thf(f239,plain,
( substmonoid
= ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f238]) ).
thf(f238,plain,
( ( substmonoid
= ( ! [X0: subst,X1: subst,X2: subst] :
( ( comp @ ( comp @ X1 @ X0 ) @ X2 )
= ( comp @ X1 @ ( comp @ X0 @ X2 ) ) ) ) )
& ! [X3: subst] :
( ( comp @ id @ X3 )
= X3 )
& ! [X4: subst] :
( ( comp @ X4 @ id )
= X4 ) ),
inference(rectify,[],[f49]) ).
thf(f49,axiom,
( ( substmonoid
= ( ! [X3: subst,X2: subst,X4: subst] :
( ( comp @ ( comp @ X2 @ X3 ) @ X4 )
= ( comp @ X2 @ ( comp @ X3 @ X4 ) ) ) ) )
& ! [X2: subst] :
( ( comp @ id @ X2 )
= X2 )
& ! [X2: subst] :
( ( comp @ X2 @ id )
= X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substmonoid) ).
thf(f394,plain,
( induction2
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f199]) ).
thf(f199,plain,
( induction2
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f198]) ).
thf(f198,plain,
( induction2
= ( ! [X0: term > $o] :
( ! [X1: term] :
( ( var @ X1 )
=> ( X0 @ X1 ) )
=> ( ! [X2: term,X3: term] :
( ( X0 @ X3 )
=> ( ( X0 @ X2 )
=> ( X0 @ ( ap @ X3 @ X2 ) ) ) )
=> ( ! [X4: term] :
( ! [X5: term] :
( ( X0 @ X5 )
=> ( X0 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X0 @ ( lam @ X4 ) ) )
=> ! [X6: term] : ( X0 @ X6 ) ) ) ) ) ),
inference(rectify,[],[f46]) ).
thf(f46,axiom,
( induction2
= ( ! [X5: term > $o] :
( ! [X0: term] :
( ( var @ X0 )
=> ( X5 @ X0 ) )
=> ( ! [X1: term,X0: term] :
( ( X5 @ X0 )
=> ( ( X5 @ X1 )
=> ( X5 @ ( ap @ X0 @ X1 ) ) ) )
=> ( ! [X0: term] :
( ! [X1: term] :
( ( X5 @ X1 )
=> ( X5 @ ( sub @ X0 @ ( push @ X1 @ id ) ) ) )
=> ( X5 @ ( lam @ X0 ) ) )
=> ! [X0: term] : ( X5 @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',induction2) ).
thf(f367,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,[],[f151]) ).
thf(f151,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,[],[f150]) ).
thf(f150,plain,
( induction2lem
= ( ! [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 ) ) ) ) ) ) ),
inference(rectify,[],[f43]) ).
thf(f43,axiom,
( induction2lem
= ( ! [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 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',induction2lem) ).
thf(f389,plain,
( pushprop
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f162]) ).
thf(f162,plain,
( pushprop
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f161]) ).
thf(f161,plain,
( pushprop
= ( ! [X0: term,X1: subst,X2: term > $o] :
( ! [X3: term] :
( ( var @ X3 )
=> ( X2 @ ( sub @ X3 @ X1 ) ) )
=> ( ( X2 @ X0 )
=> ! [X4: term] :
( ( var @ X4 )
=> ( X2 @ ( sub @ X4 @ ( push @ X0 @ X1 ) ) ) ) ) ) ) ),
inference(rectify,[],[f39]) ).
thf(f39,axiom,
( pushprop
= ( ! [X0: term,X2: subst,X5: term > $o] :
( ! [X1: term] :
( ( var @ X1 )
=> ( X5 @ ( sub @ X1 @ X2 ) ) )
=> ( ( X5 @ X0 )
=> ! [X1: term] :
( ( var @ X1 )
=> ( X5 @ ( sub @ X1 @ ( push @ X0 @ X2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pushprop) ).
thf(f339,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,[],[f283]) ).
thf(f283,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,[],[f282]) ).
thf(f282,plain,
( induction
= ( ! [X0: term > $o] :
( ! [X1: term] :
( ( var @ X1 )
=> ( X0 @ X1 ) )
=> ( ! [X2: term,X3: term] :
( ( X0 @ X3 )
=> ( ( X0 @ X2 )
=> ( X0 @ ( ap @ X3 @ X2 ) ) ) )
=> ( ! [X4: term] :
( ( X0 @ X4 )
=> ( X0 @ ( lam @ X4 ) ) )
=> ! [X5: term] : ( X0 @ X5 ) ) ) ) ) ),
inference(rectify,[],[f23]) ).
thf(f23,axiom,
( induction
= ( ! [X5: term > $o] :
( ! [X0: term] :
( ( var @ X0 )
=> ( X5 @ X0 ) )
=> ( ! [X1: term,X0: term] :
( ( X5 @ X0 )
=> ( ( X5 @ X1 )
=> ( X5 @ ( ap @ X0 @ X1 ) ) ) )
=> ( ! [X0: term] :
( ( X5 @ X0 )
=> ( X5 @ ( lam @ X0 ) ) )
=> ! [X0: term] : ( X5 @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',induction) ).
thf(f353,plain,
( lamnotvar
= ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f308]) ).
thf(f308,plain,
( lamnotvar
= ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) ) ),
inference(fool_elimination,[],[f307]) ).
thf(f307,plain,
! [X0: term] :
( ( ~ ( var @ ( lam @ X0 ) ) )
= lamnotvar ),
inference(rectify,[],[f22]) ).
thf(f22,axiom,
! [X0: term] :
( ( ~ ( var @ ( lam @ X0 ) ) )
= lamnotvar ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lamnotvar) ).
thf(f431,plain,
( apnotvar
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f277]) ).
thf(f277,plain,
( apnotvar
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f276]) ).
thf(f276,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/sandbox2/benchmark/theBenchmark.p',apnotvar) ).
thf(f396,plain,
( lamnotap
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f330]) ).
thf(f330,plain,
( lamnotap
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f329]) ).
thf(f329,plain,
! [X0: term,X1: term,X2: term] :
( ( ( lam @ X2 )
!= ( ap @ X1 @ X0 ) )
= lamnotap ),
inference(rectify,[],[f20]) ).
thf(f20,axiom,
! [X6: term,X1: term,X0: term] :
( ( ( lam @ X0 )
!= ( ap @ X1 @ X6 ) )
= lamnotap ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lamnotap) ).
thf(f419,plain,
( shinj
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f316]) ).
thf(f316,plain,
( shinj
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(fool_elimination,[],[f315]) ).
thf(f315,plain,
! [X0: term,X1: term] :
( ( ( ( sub @ X0 @ sh )
= ( sub @ X1 @ sh ) )
=> ( X0 = X1 ) )
= shinj ),
inference(rectify,[],[f19]) ).
thf(f19,axiom,
! [X1: term,X0: term] :
( ( ( ( sub @ X0 @ sh )
= ( sub @ X1 @ sh ) )
=> ( X0 = X1 ) )
= shinj ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',shinj) ).
thf(f373,plain,
( laminj
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f335]) ).
thf(f335,plain,
( laminj
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f18,axiom,
( laminj
= ( ! [X0: term,X1: term] :
( ( ( lam @ X0 )
= ( lam @ X1 ) )
=> ( X0 = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',laminj) ).
thf(f424,plain,
( apinj2
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f227]) ).
thf(f227,plain,
( apinj2
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f226]) ).
thf(f226,plain,
! [X0: term,X1: term,X2: term,X3: term] :
( ( ( ( ap @ X0 @ X2 )
= ( ap @ X3 @ X1 ) )
=> ( X1 = X2 ) )
= apinj2 ),
inference(rectify,[],[f17]) ).
thf(f17,axiom,
! [X1: term,X6: term,X7: term,X0: term] :
( ( ( ( ap @ X0 @ X6 )
= ( ap @ X1 @ X7 ) )
=> ( X6 = X7 ) )
= apinj2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apinj2) ).
thf(f383,plain,
( apinj1
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f191]) ).
thf(f191,plain,
( apinj1
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f190]) ).
thf(f190,plain,
( apinj1
= ( ! [X0: term,X1: term,X2: term,X3: term] :
( ( ( ap @ X0 @ X2 )
= ( ap @ X3 @ X1 ) )
=> ( X0 = X3 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f16,axiom,
( apinj1
= ( ! [X1: term,X6: term,X7: term,X0: term] :
( ( ( ap @ X0 @ X6 )
= ( ap @ X1 @ X7 ) )
=> ( X0 = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apinj1) ).
thf(f352,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,[],[f253]) ).
thf(f253,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,[],[f252]) ).
thf(f252,plain,
( ulamvarind
= ( ! [X0: term > $o] :
( ( X0 @ one )
=> ( ! [X1: term] :
( ( var @ X1 )
=> ( ( X0 @ X1 )
=> ( X0 @ ( sub @ X1 @ sh ) ) ) )
=> ! [X2: term] :
( ( var @ X2 )
=> ( X0 @ X2 ) ) ) ) ) ),
inference(rectify,[],[f15]) ).
thf(f15,axiom,
( ulamvarind
= ( ! [X5: term > $o] :
( ( X5 @ one )
=> ( ! [X0: term] :
( ( var @ X0 )
=> ( ( X5 @ X0 )
=> ( X5 @ ( sub @ X0 @ sh ) ) ) )
=> ! [X0: term] :
( ( var @ X0 )
=> ( X5 @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ulamvarind) ).
thf(f348,plain,
( ulamvarsh
= ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) ) ),
inference(cnf_transformation,[],[f318]) ).
thf(f318,plain,
( ulamvarsh
= ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) ) ),
inference(fool_elimination,[],[f317]) ).
thf(f317,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/sandbox2/benchmark/theBenchmark.p',ulamvarsh) ).
thf(f416,plain,
( ulamvar1
= ( var @ one ) ),
inference(cnf_transformation,[],[f261]) ).
thf(f261,plain,
( ulamvar1
= ( var @ one ) ),
inference(fool_elimination,[],[f13]) ).
thf(f13,axiom,
( ulamvar1
= ( var @ one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ulamvar1) ).
thf(f356,plain,
( axscons
= ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) ) ),
inference(cnf_transformation,[],[f185]) ).
thf(f185,plain,
( axscons
= ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) ) ),
inference(fool_elimination,[],[f184]) ).
thf(f184,plain,
( axscons
= ( ! [X0: subst] :
( ( push @ ( sub @ one @ X0 ) @ ( comp @ sh @ X0 ) )
= X0 ) ) ),
inference(rectify,[],[f12]) ).
thf(f12,axiom,
( axscons
= ( ! [X2: subst] :
( ( push @ ( sub @ one @ X2 ) @ ( comp @ sh @ X2 ) )
= X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axscons) ).
thf(f395,plain,
( axvarshift
= ( id
= ( push @ one @ sh ) ) ),
inference(cnf_transformation,[],[f208]) ).
thf(f208,plain,
( axvarshift
= ( id
= ( push @ one @ sh ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f11,axiom,
( ( id
= ( push @ one @ sh ) )
= axvarshift ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axvarshift) ).
thf(f369,plain,
( axidr
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) ),
inference(cnf_transformation,[],[f120]) ).
thf(f120,plain,
( axidr
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) ),
inference(fool_elimination,[],[f119]) ).
thf(f119,plain,
! [X0: subst] :
( ( ( comp @ X0 @ id )
= X0 )
= axidr ),
inference(rectify,[],[f10]) ).
thf(f10,axiom,
! [X2: subst] :
( ( ( comp @ X2 @ id )
= X2 )
= axidr ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axidr) ).
thf(f350,plain,
( axmap
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y0 ) @ Y1 )
= ( push @ ( sub @ Y2 @ Y1 ) @ ( comp @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f320]) ).
thf(f320,plain,
( axmap
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y0 ) @ Y1 )
= ( push @ ( sub @ Y2 @ Y1 ) @ ( comp @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f319]) ).
thf(f319,plain,
( axmap
= ( ! [X0: term,X1: subst,X2: subst] :
( ( comp @ ( push @ X0 @ X2 ) @ X1 )
= ( push @ ( sub @ X0 @ X1 ) @ ( comp @ X2 @ X1 ) ) ) ) ),
inference(rectify,[],[f9]) ).
thf(f9,axiom,
( axmap
= ( ! [X0: term,X3: subst,X2: subst] :
( ( comp @ ( push @ X0 @ X2 ) @ X3 )
= ( push @ ( sub @ X0 @ X3 ) @ ( comp @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axmap) ).
thf(f386,plain,
( axassoc
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f302]) ).
thf(f302,plain,
( axassoc
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f301]) ).
thf(f301,plain,
( axassoc
= ( ! [X0: subst,X1: subst,X2: subst] :
( ( comp @ ( comp @ X1 @ X0 ) @ X2 )
= ( comp @ X1 @ ( comp @ X0 @ X2 ) ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f8,axiom,
( axassoc
= ( ! [X3: subst,X2: subst,X4: subst] :
( ( comp @ ( comp @ X2 @ X3 ) @ X4 )
= ( comp @ X2 @ ( comp @ X3 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axassoc) ).
thf(f381,plain,
( axshiftcons
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) ) ),
inference(cnf_transformation,[],[f288]) ).
thf(f288,plain,
( axshiftcons
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) ) ),
inference(fool_elimination,[],[f287]) ).
thf(f287,plain,
! [X0: term,X1: subst] :
( ( ( comp @ sh @ ( push @ X0 @ X1 ) )
= X1 )
= axshiftcons ),
inference(rectify,[],[f7]) ).
thf(f7,axiom,
! [X0: term,X2: subst] :
( ( ( comp @ sh @ ( push @ X0 @ X2 ) )
= X2 )
= axshiftcons ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axshiftcons) ).
thf(f410,plain,
( axidl
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) ),
inference(cnf_transformation,[],[f147]) ).
thf(f147,plain,
( axidl
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) ),
inference(fool_elimination,[],[f146]) ).
thf(f146,plain,
( axidl
= ( ! [X0: subst] :
( ( comp @ id @ X0 )
= X0 ) ) ),
inference(rectify,[],[f6]) ).
thf(f6,axiom,
( axidl
= ( ! [X2: subst] :
( ( comp @ id @ X2 )
= X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axidl) ).
thf(f414,plain,
( axclos
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 )
= ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f143]) ).
thf(f143,plain,
( axclos
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 )
= ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f142]) ).
thf(f142,plain,
( axclos
= ( ! [X0: term,X1: subst,X2: subst] :
( ( sub @ ( sub @ X0 @ X1 ) @ X2 )
= ( sub @ X0 @ ( comp @ X1 @ X2 ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f5,axiom,
( axclos
= ( ! [X0: term,X2: subst,X3: subst] :
( ( sub @ ( sub @ X0 @ X2 ) @ X3 )
= ( sub @ X0 @ ( comp @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axclos) ).
thf(f374,plain,
( axabs
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( lam @ Y0 ) @ Y1 )
= ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f166]) ).
thf(f166,plain,
( axabs
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( lam @ Y0 ) @ Y1 )
= ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f165]) ).
thf(f165,plain,
( axabs
= ( ! [X0: subst,X1: term] :
( ( sub @ ( lam @ X1 ) @ X0 )
= ( lam @ ( sub @ X1 @ ( push @ one @ ( comp @ X0 @ sh ) ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f4,axiom,
( axabs
= ( ! [X2: subst,X0: term] :
( ( sub @ ( lam @ X0 ) @ X2 )
= ( lam @ ( sub @ X0 @ ( push @ one @ ( comp @ X2 @ sh ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axabs) ).
thf(f362,plain,
( axvarid
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ),
inference(cnf_transformation,[],[f225]) ).
thf(f225,plain,
( axvarid
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f3,axiom,
! [X0: term] :
( ( ( sub @ X0 @ id )
= X0 )
= axvarid ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axvarid) ).
thf(f388,plain,
( axvarcons
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ one @ ( push @ Y1 @ Y0 ) )
= Y1 ) ) ) ),
inference(cnf_transformation,[],[f159]) ).
thf(f159,plain,
( axvarcons
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ one @ ( push @ Y1 @ Y0 ) )
= Y1 ) ) ) ),
inference(fool_elimination,[],[f158]) ).
thf(f158,plain,
! [X0: term,X1: subst] :
( ( ( sub @ one @ ( push @ X0 @ X1 ) )
= X0 )
= axvarcons ),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
! [X0: term,X2: subst] :
( ( ( sub @ one @ ( push @ X0 @ X2 ) )
= X0 )
= axvarcons ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axvarcons) ).
thf(f359,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,[],[f197]) ).
thf(f197,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,[],[f196]) ).
thf(f196,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/sandbox2/benchmark/theBenchmark.p',axapp) ).
thf(f449,plain,
( hoaslaminj_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
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> hoaslaminj ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f267]) ).
thf(f267,plain,
( hoaslaminj_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
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> hoaslaminj ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f266]) ).
thf(f266,plain,
( ( hoaslaminj_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
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> hoaslaminj ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f65]) ).
thf(f65,axiom,
( ( hoaslaminj_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
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> hoaslaminj ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoaslaminj_gthm) ).
thf(f354,plain,
( ~ hoaslaminj_gthm = $true ),
inference(cnf_transformation,[],[f195]) ).
thf(f195,plain,
( ~ hoaslaminj_gthm = $true ),
inference(fool_elimination,[],[f194]) ).
thf(f194,plain,
~ hoaslaminj_gthm,
inference(rectify,[],[f115]) ).
thf(f115,negated_conjecture,
~ hoaslaminj_gthm,
inference(negated_conjecture,[],[f114]) ).
thf(f114,conjecture,
hoaslaminj_gthm,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(f5146,plain,
! [X0: term,X1: subst] :
( ( sK3 @ X1 @ X0 )
= ( sK2 @ ( comp @ sh @ ( push @ X0 @ X1 ) ) @ X0 ) ),
inference(superposition,[],[f2561,f5064]) ).
thf(f5064,plain,
! [X0: term,X1: subst] :
( ( sK3 @ X1 @ X0 )
= ( sub @ ( sK2 @ sh @ one ) @ ( push @ X0 @ X1 ) ) ),
inference(forward_demodulation,[],[f5039,f2214]) ).
thf(f2214,plain,
( ( sK2 @ sh @ one )
= ( sK3 @ sh @ one ) ),
inference(equality_proxy_clausification,[],[f2213]) ).
thf(f2213,plain,
( $true
= ( ( sK2 @ sh @ one )
= ( sK3 @ sh @ one ) ) ),
inference(trivial_inequality_removal,[],[f2212]) ).
thf(f2212,plain,
( ( $true = $false )
| ( $true
= ( ( sK2 @ sh @ one )
= ( sK3 @ sh @ one ) ) ) ),
inference(boolean_simplification,[],[f2211]) ).
thf(f2211,plain,
( ( $false
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sK3 @ Y0 @ Y1 ) @ Y2 )
= ( sK3 @ ( comp @ Y0 @ Y2 ) @ ( sub @ Y1 @ Y2 ) ) ) ) ) )
=> $true ) )
| ( $true
= ( ( sK2 @ sh @ one )
= ( sK3 @ sh @ one ) ) ) ),
inference(boolean_simplification,[],[f2210]) ).
thf(f2210,plain,
( ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sK3 @ Y0 @ Y1 ) @ Y2 )
= ( sK3 @ ( comp @ Y0 @ Y2 ) @ ( sub @ Y1 @ Y2 ) ) ) ) ) )
=> ( $false
=> ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ Y0 @ Y1 )
= ( sK3 @ Y0 @ Y1 ) ) ) ) ) )
= $false )
| ( $true
= ( ( sK2 @ sh @ one )
= ( sK3 @ sh @ one ) ) ) ),
inference(superposition,[],[f2205,f1375]) ).
thf(f1375,plain,
! [X2: term,X1: term] :
( ( $false
= ( ( lam @ X2 )
= ( lam @ X1 ) ) )
| ( $true
= ( X2 = X1 ) ) ),
inference(binary_proxy_clausification,[],[f1374]) ).
thf(f1374,plain,
! [X2: term,X1: term] :
( $true
= ( ( ( lam @ X2 )
= ( lam @ X1 ) )
=> ( X2 = X1 ) ) ),
inference(beta_eta_normalization,[],[f1373]) ).
thf(f1373,plain,
! [X2: term,X1: term] :
( $true
= ( ^ [Y0: term] :
( ( ( lam @ Y0 )
= ( lam @ X1 ) )
=> ( Y0 = X1 ) )
@ X2 ) ),
inference(pi_clausification,[],[f1333]) ).
thf(f1333,plain,
! [X1: term] :
( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( ( lam @ Y0 )
= ( lam @ X1 ) )
=> ( Y0 = X1 ) ) ) ),
inference(beta_eta_normalization,[],[f1331]) ).
thf(f1331,plain,
! [X1: term] :
( $true
= ( ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[],[f1312]) ).
thf(f1312,plain,
( $true
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f1289]) ).
thf(f1289,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] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f1287]) ).
thf(f1287,plain,
( $false
= ( $true
=> ( ( !! @ 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] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(backward_demodulation,[],[f1126,f1130]) ).
thf(f1130,plain,
( $true
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f1126]) ).
thf(f1126,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(boolean_simplification,[],[f1123]) ).
thf(f1123,plain,
( $false
= ( $true
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(backward_demodulation,[],[f1099,f1111]) ).
thf(f1111,plain,
( $true
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f1099]) ).
thf(f1099,plain,
( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f1097]) ).
thf(f1097,plain,
( $false
= ( $true
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(backward_demodulation,[],[f947,f966]) ).
thf(f966,plain,
( $true
= ( !! @ ( 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(binary_proxy_clausification,[],[f947]) ).
thf(f947,plain,
( ( ( !! @ ( 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 @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(boolean_simplification,[],[f945]) ).
thf(f945,plain,
( ( $true
=> ( ( !! @ ( 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 @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(backward_demodulation,[],[f925,f927]) ).
thf(f927,plain,
( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) ) ),
inference(binary_proxy_clausification,[],[f925]) ).
thf(f925,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 @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f924]) ).
thf(f924,plain,
( ( $true
=> ( ( !! @ 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 @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(backward_demodulation,[],[f901,f923]) ).
thf(f923,plain,
( ( var @ one )
= $true ),
inference(binary_proxy_clausification,[],[f901]) ).
thf(f901,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 @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(boolean_simplification,[],[f899]) ).
thf(f899,plain,
( ( $true
=> ( ( 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 @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(backward_demodulation,[],[f884,f886]) ).
thf(f886,plain,
( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
= $true ),
inference(binary_proxy_clausification,[],[f884]) ).
thf(f884,plain,
( $false
= ( ( !! @ 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 @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f882]) ).
thf(f882,plain,
( ( $true
=> ( ( !! @ 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 @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(backward_demodulation,[],[f866,f868]) ).
thf(f868,plain,
( $true
= ( id
= ( push @ one @ sh ) ) ),
inference(binary_proxy_clausification,[],[f866]) ).
thf(f866,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 @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(boolean_simplification,[],[f865]) ).
thf(f865,plain,
( $false
= ( ( 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 @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( $true
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f862]) ).
thf(f862,plain,
( ( $true
=> ( ( 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 @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( $true
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(backward_demodulation,[],[f855,f861]) ).
thf(f861,plain,
( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) ),
inference(binary_proxy_clausification,[],[f855]) ).
thf(f855,plain,
( $false
= ( ( !! @ 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 @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f853]) ).
thf(f853,plain,
( $false
= ( $true
=> ( ( !! @ 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 @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(backward_demodulation,[],[f793,f820]) ).
thf(f820,plain,
( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y0 ) @ Y1 )
= ( push @ ( sub @ Y2 @ Y1 ) @ ( comp @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f793]) ).
thf(f793,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y0 ) @ Y1 )
= ( push @ ( sub @ Y2 @ Y1 ) @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(boolean_simplification,[],[f792]) ).
thf(f792,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y0 ) @ Y1 )
= ( push @ ( sub @ Y2 @ Y1 ) @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& $true )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(boolean_simplification,[],[f790]) ).
thf(f790,plain,
( ( $true
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y0 ) @ Y1 )
= ( push @ ( sub @ Y2 @ Y1 ) @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& $true )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(backward_demodulation,[],[f665,f669]) ).
thf(f669,plain,
( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f665]) ).
thf(f665,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y0 ) @ Y1 )
= ( push @ ( sub @ Y2 @ Y1 ) @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(boolean_simplification,[],[f662]) ).
thf(f662,plain,
( $false
= ( $true
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y0 ) @ Y1 )
= ( push @ ( sub @ Y2 @ Y1 ) @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(backward_demodulation,[],[f653,f657]) ).
thf(f2205,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sK3 @ Y0 @ Y1 ) @ Y2 )
= ( sK3 @ ( comp @ Y0 @ Y2 ) @ ( sub @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( ( lam @ ( sK2 @ sh @ one ) )
= ( lam @ ( sK3 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ Y0 @ Y1 )
= ( sK3 @ Y0 @ Y1 ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f2204]) ).
thf(f2204,plain,
( ( ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( sK2 @ sh @ one ) )
= ( lam @ ( Y0 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sK2 @ Y1 @ Y2 )
= ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[],[f2200]) ).
thf(f2200,plain,
( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( sK2 @ sh @ one ) )
= ( lam @ ( Y0 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sK2 @ Y1 @ Y2 )
= ( Y0 @ Y1 @ Y2 ) ) ) ) ) ) )
= $false ),
inference(boolean_simplification,[],[f2198]) ).
thf(f2198,plain,
( $false
= ( $true
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( sK2 @ sh @ one ) )
= ( lam @ ( Y0 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sK2 @ Y1 @ Y2 )
= ( Y0 @ Y1 @ Y2 ) ) ) ) ) ) ) ) ),
inference(backward_demodulation,[],[f2191,f2195]) ).
thf(f2195,plain,
( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ ( comp @ Y2 @ Y0 ) @ ( sub @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f2191]) ).
thf(f2191,plain,
( $false
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ ( comp @ Y2 @ Y0 ) @ ( sub @ Y1 @ Y0 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( sK2 @ sh @ one ) )
= ( lam @ ( Y0 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sK2 @ Y1 @ Y2 )
= ( Y0 @ Y1 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f2190]) ).
thf(f2190,plain,
( ( ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[],[f2179]) ).
thf(f2179,plain,
( $false
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f2171]) ).
thf(f2171,plain,
( ( $true
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(backward_demodulation,[],[f2071,f2099]) ).
thf(f2099,plain,
( $true
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f2071]) ).
thf(f2071,plain,
( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f2068]) ).
thf(f2068,plain,
( $false
= ( $true
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(backward_demodulation,[],[f2029,f2059]) ).
thf(f2059,plain,
( $true
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f2029]) ).
thf(f2029,plain,
( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f2026]) ).
thf(f2026,plain,
( $false
= ( $true
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(backward_demodulation,[],[f1968,f1970]) ).
thf(f1970,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] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f1968]) ).
thf(f1968,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] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(boolean_simplification,[],[f1965]) ).
thf(f1965,plain,
( ( $true
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(backward_demodulation,[],[f1723,f1725]) ).
thf(f1725,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,[],[f1723]) ).
thf(f1723,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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(boolean_simplification,[],[f1720]) ).
thf(f1720,plain,
( $false
= ( $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 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(backward_demodulation,[],[f1716,f1719]) ).
thf(f1719,plain,
( $true
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f1716]) ).
thf(f1716,plain,
( $false
= ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f1714]) ).
thf(f1714,plain,
( ( $true
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(backward_demodulation,[],[f1499,f1511]) ).
thf(f1511,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 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f1499]) ).
thf(f1499,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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(boolean_simplification,[],[f1496]) ).
thf(f1496,plain,
( ( $true
=> ( ( !! @ ( 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(backward_demodulation,[],[f1487,f1493]) ).
thf(f1493,plain,
( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f1487]) ).
thf(f1487,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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f1485]) ).
thf(f1485,plain,
( ( $true
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(backward_demodulation,[],[f1388,f1482]) ).
thf(f1482,plain,
( $true
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f1388]) ).
thf(f1388,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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(boolean_simplification,[],[f1386]) ).
thf(f1386,plain,
( ( $true
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(backward_demodulation,[],[f1381,f1384]) ).
thf(f1384,plain,
( $true
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f1381]) ).
thf(f1381,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(boolean_simplification,[],[f1378]) ).
thf(f1378,plain,
( ( $true
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(backward_demodulation,[],[f1332,f1355]) ).
thf(f1355,plain,
( $true
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f1332]) ).
thf(f1332,plain,
( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f1330]) ).
thf(f1330,plain,
( $false
= ( $true
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 )
= ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(backward_demodulation,[],[f1289,f1312]) ).
thf(f5039,plain,
! [X0: term,X1: subst] :
( ( sK3 @ X1 @ X0 )
= ( sub @ ( sK3 @ sh @ one ) @ ( push @ X0 @ X1 ) ) ),
inference(superposition,[],[f2370,f677]) ).
thf(f2370,plain,
! [X2: subst,X0: term,X1: subst] :
( ( sub @ ( sK3 @ X2 @ one ) @ ( push @ X0 @ X1 ) )
= ( sK3 @ ( comp @ X2 @ ( push @ X0 @ X1 ) ) @ X0 ) ),
inference(superposition,[],[f2288,f560]) ).
thf(f560,plain,
! [X2: term,X1: subst] :
( ( sub @ one @ ( push @ X2 @ X1 ) )
= X2 ),
inference(equality_proxy_clausification,[],[f559]) ).
thf(f559,plain,
! [X2: term,X1: subst] :
( $true
= ( ( sub @ one @ ( push @ X2 @ X1 ) )
= X2 ) ),
inference(beta_eta_normalization,[],[f558]) ).
thf(f558,plain,
! [X2: term,X1: subst] :
( $true
= ( ^ [Y0: term] :
( ( sub @ one @ ( push @ Y0 @ X1 ) )
= Y0 )
@ X2 ) ),
inference(pi_clausification,[],[f544]) ).
thf(f544,plain,
! [X1: subst] :
( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ one @ ( push @ Y0 @ X1 ) )
= Y0 ) ) ),
inference(beta_eta_normalization,[],[f543]) ).
thf(f543,plain,
! [X1: subst] :
( $true
= ( ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ one @ ( push @ Y1 @ Y0 ) )
= Y1 ) )
@ X1 ) ),
inference(pi_clausification,[],[f541]) ).
thf(f2288,plain,
! [X2: term,X3: subst,X1: subst] :
( ( sub @ ( sK3 @ X1 @ X2 ) @ X3 )
= ( sK3 @ ( comp @ X1 @ X3 ) @ ( sub @ X2 @ X3 ) ) ),
inference(equality_proxy_clausification,[],[f2287]) ).
thf(f2287,plain,
! [X2: term,X3: subst,X1: subst] :
( ( ( sub @ ( sK3 @ X1 @ X2 ) @ X3 )
= ( sK3 @ ( comp @ X1 @ X3 ) @ ( sub @ X2 @ X3 ) ) )
= $true ),
inference(beta_eta_normalization,[],[f2286]) ).
thf(f2286,plain,
! [X2: term,X3: subst,X1: subst] :
( $true
= ( ^ [Y0: subst] :
( ( sub @ ( sK3 @ X1 @ X2 ) @ Y0 )
= ( sK3 @ ( comp @ X1 @ Y0 ) @ ( sub @ X2 @ Y0 ) ) )
@ X3 ) ),
inference(pi_clausification,[],[f2256]) ).
thf(f2256,plain,
! [X2: term,X1: subst] :
( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( ( sub @ ( sK3 @ X1 @ X2 ) @ Y0 )
= ( sK3 @ ( comp @ X1 @ Y0 ) @ ( sub @ X2 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[],[f2250]) ).
thf(f2250,plain,
! [X2: term,X1: subst] :
( $true
= ( ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( sK3 @ X1 @ Y0 ) @ Y1 )
= ( sK3 @ ( comp @ X1 @ Y1 ) @ ( sub @ Y0 @ Y1 ) ) ) )
@ X2 ) ),
inference(pi_clausification,[],[f2248]) ).
thf(f2248,plain,
! [X1: subst] :
( $true
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( sK3 @ X1 @ Y0 ) @ Y1 )
= ( sK3 @ ( comp @ X1 @ Y1 ) @ ( sub @ Y0 @ Y1 ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f2247]) ).
thf(f2247,plain,
! [X1: subst] :
( $true
= ( ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sK3 @ Y0 @ Y1 ) @ Y2 )
= ( sK3 @ ( comp @ Y0 @ Y2 ) @ ( sub @ Y1 @ Y2 ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[],[f2245]) ).
thf(f2245,plain,
( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sK3 @ Y0 @ Y1 ) @ Y2 )
= ( sK3 @ ( comp @ Y0 @ Y2 ) @ ( sub @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f2243]) ).
thf(f2243,plain,
( ( ~ ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sK3 @ Y0 @ Y1 ) @ Y2 )
= ( sK3 @ ( comp @ Y0 @ Y2 ) @ ( sub @ Y1 @ Y2 ) ) ) ) ) ) )
= $false ),
inference(boolean_simplification,[],[f2241]) ).
thf(f2241,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sK3 @ Y0 @ Y1 ) @ Y2 )
= ( sK3 @ ( comp @ Y0 @ Y2 ) @ ( sub @ Y1 @ Y2 ) ) ) ) ) )
=> $false )
= $false ),
inference(backward_demodulation,[],[f2236,f2237]) ).
thf(f2237,plain,
( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ Y0 @ Y1 )
= ( sK3 @ Y0 @ Y1 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f2236]) ).
thf(f2236,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sK3 @ Y0 @ Y1 ) @ Y2 )
= ( sK3 @ ( comp @ Y0 @ Y2 ) @ ( sub @ Y1 @ Y2 ) ) ) ) ) )
=> ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ Y0 @ Y1 )
= ( sK3 @ Y0 @ Y1 ) ) ) ) )
= $false ),
inference(boolean_simplification,[],[f2235]) ).
thf(f2235,plain,
( $false
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sK3 @ Y0 @ Y1 ) @ Y2 )
= ( sK3 @ ( comp @ Y0 @ Y2 ) @ ( sub @ Y1 @ Y2 ) ) ) ) ) )
=> ( $true
=> ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ Y0 @ Y1 )
= ( sK3 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f2233]) ).
thf(f2233,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sK3 @ Y0 @ Y1 ) @ Y2 )
= ( sK3 @ ( comp @ Y0 @ Y2 ) @ ( sub @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( ( lam @ ( sK2 @ sh @ one ) )
= ( lam @ ( sK2 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ Y0 @ Y1 )
= ( sK3 @ Y0 @ Y1 ) ) ) ) ) )
= $false ),
inference(backward_demodulation,[],[f2205,f2214]) ).
thf(f2561,plain,
! [X2: subst,X0: term,X1: subst] :
( ( sub @ ( sK2 @ X2 @ one ) @ ( push @ X0 @ X1 ) )
= ( sK2 @ ( comp @ X2 @ ( push @ X0 @ X1 ) ) @ X0 ) ),
inference(superposition,[],[f2475,f560]) ).
thf(f2475,plain,
! [X2: term,X3: subst,X1: subst] :
( ( sub @ ( sK2 @ X3 @ X2 ) @ X1 )
= ( sK2 @ ( comp @ X3 @ X1 ) @ ( sub @ X2 @ X1 ) ) ),
inference(equality_proxy_clausification,[],[f2469]) ).
thf(f2469,plain,
! [X2: term,X3: subst,X1: subst] :
( $true
= ( ( sub @ ( sK2 @ X3 @ X2 ) @ X1 )
= ( sK2 @ ( comp @ X3 @ X1 ) @ ( sub @ X2 @ X1 ) ) ) ),
inference(beta_eta_normalization,[],[f2468]) ).
thf(f2468,plain,
! [X2: term,X3: subst,X1: subst] :
( $true
= ( ^ [Y0: subst] :
( ( sub @ ( sK2 @ Y0 @ X2 ) @ X1 )
= ( sK2 @ ( comp @ Y0 @ X1 ) @ ( sub @ X2 @ X1 ) ) )
@ X3 ) ),
inference(pi_clausification,[],[f2231]) ).
thf(f2231,plain,
! [X2: term,X1: subst] :
( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( ( sub @ ( sK2 @ Y0 @ X2 ) @ X1 )
= ( sK2 @ ( comp @ Y0 @ X1 ) @ ( sub @ X2 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[],[f2225]) ).
thf(f2225,plain,
! [X2: term,X1: subst] :
( $true
= ( ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( sK2 @ Y1 @ Y0 ) @ X1 )
= ( sK2 @ ( comp @ Y1 @ X1 ) @ ( sub @ Y0 @ X1 ) ) ) )
@ X2 ) ),
inference(pi_clausification,[],[f2201]) ).
thf(f2201,plain,
! [X1: subst] :
( $true
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( sK2 @ Y1 @ Y0 ) @ X1 )
= ( sK2 @ ( comp @ Y1 @ X1 ) @ ( sub @ Y0 @ X1 ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f2199]) ).
thf(f2199,plain,
! [X1: subst] :
( $true
= ( ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sK2 @ Y2 @ Y1 ) @ Y0 )
= ( sK2 @ ( comp @ Y2 @ Y0 ) @ ( sub @ Y1 @ Y0 ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[],[f2195]) ).
thf(f4772,plain,
( ( ( sub @ ( sK2 @ sK4 @ sK5 ) @ sh )
= ( sub @ ( sK3 @ sK4 @ sK5 ) @ sh ) )
= $false ),
inference(not_proxy_clausification,[],[f2435]) ).
thf(f2435,plain,
( $true
= ( ( sub @ ( sK2 @ sK4 @ sK5 ) @ sh )
!= ( sub @ ( sK3 @ sK4 @ sK5 ) @ sh ) ) ),
inference(boolean_simplification,[],[f2428]) ).
thf(f2428,plain,
( $true
= ( ( ( sub @ ( sK2 @ sK4 @ sK5 ) @ sh )
= ( sub @ ( sK3 @ sK4 @ sK5 ) @ sh ) )
=> $false ) ),
inference(superposition,[],[f1598,f2425]) ).
thf(f2425,plain,
( ( ( sK2 @ sK4 @ sK5 )
= ( sK3 @ sK4 @ sK5 ) )
= $false ),
inference(beta_eta_normalization,[],[f2421]) ).
thf(f2421,plain,
( $false
= ( ^ [Y0: term] :
( ( sK2 @ sK4 @ Y0 )
= ( sK3 @ sK4 @ Y0 ) )
@ sK5 ) ),
inference(sigma_clausification,[],[f2244]) ).
thf(f2244,plain,
( $false
= ( !! @ term
@ ^ [Y0: term] :
( ( sK2 @ sK4 @ Y0 )
= ( sK3 @ sK4 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[],[f2242]) ).
thf(f2242,plain,
( ( ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ Y0 @ Y1 )
= ( sK3 @ Y0 @ Y1 ) ) )
@ sK4 )
= $false ),
inference(sigma_clausification,[],[f2237]) ).
thf(f1598,plain,
! [X2: term,X1: term] :
( $true
= ( ( ( sub @ X2 @ sh )
= ( sub @ X1 @ sh ) )
=> ( X2 = X1 ) ) ),
inference(beta_eta_normalization,[],[f1597]) ).
thf(f1597,plain,
! [X2: term,X1: term] :
( $true
= ( ^ [Y0: term] :
( ( ( sub @ Y0 @ sh )
= ( sub @ X1 @ sh ) )
=> ( Y0 = X1 ) )
@ X2 ) ),
inference(pi_clausification,[],[f1380]) ).
thf(f1380,plain,
! [X1: term] :
( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( ( sub @ Y0 @ sh )
= ( sub @ X1 @ sh ) )
=> ( Y0 = X1 ) ) ) ),
inference(beta_eta_normalization,[],[f1379]) ).
thf(f1379,plain,
! [X1: term] :
( $true
= ( ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[],[f1355]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ALG258^1 : 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/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.38 % Computer : n015.cluster.edu
% 0.15/0.38 % Model : x86_64 x86_64
% 0.15/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.38 % Memory : 8042.1875MB
% 0.15/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.38 % CPULimit : 300
% 0.15/0.38 % WCLimit : 300
% 0.15/0.38 % DateTime : Sat May 18 23:05:08 EDT 2024
% 0.15/0.38 % CPUTime :
% 0.15/0.38 This is a TH0_THM_EQU_NAR problem
% 0.15/0.38 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.24/0.41 % (15112)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)
% 0.24/0.41 % (15114)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)
% 0.24/0.41 % (15117)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)
% 0.24/0.41 % (15115)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)
% 0.24/0.41 % (15113)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.24/0.41 % (15110)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.24/0.41 % (15111)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)
% 0.24/0.41 % (15116)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.24/0.41 % (15113)Instruction limit reached!
% 0.24/0.41 % (15113)------------------------------
% 0.24/0.41 % (15113)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.41 % (15113)Termination reason: Unknown
% 0.24/0.41 % (15113)Termination phase: shuffling
% 0.24/0.41
% 0.24/0.41 % (15114)Instruction limit reached!
% 0.24/0.41 % (15114)------------------------------
% 0.24/0.41 % (15114)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.41 % (15114)Termination reason: Unknown
% 0.24/0.41 % (15114)Termination phase: shuffling
% 0.24/0.41
% 0.24/0.41 % (15114)Memory used [KB]: 1279
% 0.24/0.41 % (15114)Time elapsed: 0.004 s
% 0.24/0.41 % (15114)Instructions burned: 3 (million)
% 0.24/0.41 % (15114)------------------------------
% 0.24/0.41 % (15114)------------------------------
% 0.24/0.41 % (15113)Memory used [KB]: 1279
% 0.24/0.41 % (15113)Time elapsed: 0.004 s
% 0.24/0.41 % (15113)Instructions burned: 3 (million)
% 0.24/0.41 % (15113)------------------------------
% 0.24/0.41 % (15113)------------------------------
% 0.24/0.41 % (15117)Instruction limit reached!
% 0.24/0.41 % (15117)------------------------------
% 0.24/0.41 % (15117)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.41 % (15117)Termination reason: Unknown
% 0.24/0.41 % (15117)Termination phase: shuffling
% 0.24/0.41
% 0.24/0.41 % (15117)Memory used [KB]: 1279
% 0.24/0.41 % (15117)Time elapsed: 0.004 s
% 0.24/0.41 % (15117)Instructions burned: 4 (million)
% 0.24/0.41 % (15117)------------------------------
% 0.24/0.41 % (15117)------------------------------
% 0.24/0.41 % (15111)Instruction limit reached!
% 0.24/0.41 % (15111)------------------------------
% 0.24/0.41 % (15111)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.41 % (15111)Termination reason: Unknown
% 0.24/0.41 % (15111)Termination phase: shuffling
% 0.24/0.41
% 0.24/0.41 % (15111)Memory used [KB]: 1279
% 0.24/0.41 % (15111)Time elapsed: 0.004 s
% 0.24/0.41 % (15111)Instructions burned: 4 (million)
% 0.24/0.41 % (15111)------------------------------
% 0.24/0.41 % (15111)------------------------------
% 0.24/0.42 % (15116)Instruction limit reached!
% 0.24/0.42 % (15116)------------------------------
% 0.24/0.42 % (15116)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.42 % (15116)Termination reason: Unknown
% 0.24/0.42 % (15116)Termination phase: Property scanning
% 0.24/0.42
% 0.24/0.42 % (15116)Memory used [KB]: 1663
% 0.24/0.42 % (15116)Time elapsed: 0.013 s
% 0.24/0.42 % (15116)Instructions burned: 20 (million)
% 0.24/0.42 % (15116)------------------------------
% 0.24/0.42 % (15116)------------------------------
% 0.24/0.43 % (15112)Instruction limit reached!
% 0.24/0.43 % (15112)------------------------------
% 0.24/0.43 % (15112)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.43 % (15112)Termination reason: Unknown
% 0.24/0.43 % (15112)Termination phase: shuffling
% 0.24/0.43
% 0.24/0.43 % (15112)Memory used [KB]: 1791
% 0.24/0.43 % (15112)Time elapsed: 0.015 s
% 0.24/0.43 % (15112)Instructions burned: 27 (million)
% 0.24/0.43 % (15112)------------------------------
% 0.24/0.43 % (15112)------------------------------
% 0.24/0.43 % (15118)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)
% 0.24/0.43 % (15120)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)
% 0.24/0.43 % (15119)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)
% 0.24/0.43 % (15121)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)
% 0.24/0.43 % (15115)Refutation not found, incomplete strategy
% 0.24/0.43 % (15115)------------------------------
% 0.24/0.43 % (15115)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.43 % (15115)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.43
% 0.24/0.43
% 0.24/0.43 % (15115)Memory used [KB]: 6268
% 0.24/0.43 % (15115)Time elapsed: 0.020 s
% 0.24/0.43 % (15115)Instructions burned: 29 (million)
% 0.24/0.43 % (15115)------------------------------
% 0.24/0.43 % (15115)------------------------------
% 0.24/0.43 % (15120)Instruction limit reached!
% 0.24/0.43 % (15120)------------------------------
% 0.24/0.43 % (15120)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.43 % (15120)Termination reason: Unknown
% 0.24/0.43 % (15120)Termination phase: shuffling
% 0.24/0.43
% 0.24/0.43 % (15120)Memory used [KB]: 1279
% 0.24/0.43 % (15120)Time elapsed: 0.004 s
% 0.24/0.43 % (15120)Instructions burned: 4 (million)
% 0.24/0.43 % (15120)------------------------------
% 0.24/0.43 % (15120)------------------------------
% 0.24/0.44 % (15122)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.24/0.44 % (15119)Instruction limit reached!
% 0.24/0.44 % (15119)------------------------------
% 0.24/0.44 % (15119)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.44 % (15119)Termination reason: Unknown
% 0.24/0.44 % (15119)Termination phase: Property scanning
% 0.24/0.44
% 0.24/0.44 % (15119)Memory used [KB]: 1663
% 0.24/0.44 % (15119)Time elapsed: 0.011 s
% 0.24/0.44 % (15119)Instructions burned: 16 (million)
% 0.24/0.44 % (15119)------------------------------
% 0.24/0.44 % (15119)------------------------------
% 0.24/0.44 % (15123)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.24/0.44 % (15122)Instruction limit reached!
% 0.24/0.44 % (15122)------------------------------
% 0.24/0.44 % (15122)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.44 % (15122)Termination reason: Unknown
% 0.24/0.44 % (15122)Termination phase: shuffling
% 0.24/0.44
% 0.24/0.44 % (15122)Memory used [KB]: 1407
% 0.24/0.44 % (15122)Time elapsed: 0.006 s
% 0.24/0.44 % (15122)Instructions burned: 8 (million)
% 0.24/0.44 % (15122)------------------------------
% 0.24/0.44 % (15122)------------------------------
% 0.24/0.45 % (15124)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)
% 0.24/0.45 % (15125)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.24/0.45 % (15118)Instruction limit reached!
% 0.24/0.45 % (15118)------------------------------
% 0.24/0.45 % (15118)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.45 % (15118)Termination reason: Unknown
% 0.24/0.45 % (15118)Termination phase: Property scanning
% 0.24/0.45
% 0.24/0.45 % (15118)Memory used [KB]: 1791
% 0.24/0.45 % (15118)Time elapsed: 0.020 s
% 0.24/0.45 % (15118)Instructions burned: 38 (million)
% 0.24/0.45 % (15118)------------------------------
% 0.24/0.45 % (15118)------------------------------
% 0.24/0.45 % (15124)Instruction limit reached!
% 0.24/0.45 % (15124)------------------------------
% 0.24/0.45 % (15124)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.45 % (15124)Termination reason: Unknown
% 0.24/0.45 % (15124)Termination phase: shuffling
% 0.24/0.45
% 0.24/0.45 % (15124)Memory used [KB]: 1279
% 0.24/0.45 % (15124)Time elapsed: 0.004 s
% 0.24/0.45 % (15124)Instructions burned: 4 (million)
% 0.24/0.45 % (15124)------------------------------
% 0.24/0.45 % (15124)------------------------------
% 0.24/0.45 % (15125)Instruction limit reached!
% 0.24/0.45 % (15125)------------------------------
% 0.24/0.45 % (15125)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.45 % (15125)Termination reason: Unknown
% 0.24/0.45 % (15125)Termination phase: shuffling
% 0.24/0.45
% 0.24/0.45 % (15125)Memory used [KB]: 1279
% 0.24/0.45 % (15125)Time elapsed: 0.004 s
% 0.24/0.45 % (15125)Instructions burned: 4 (million)
% 0.24/0.45 % (15125)------------------------------
% 0.24/0.45 % (15125)------------------------------
% 0.24/0.45 % (15123)Instruction limit reached!
% 0.24/0.45 % (15123)------------------------------
% 0.24/0.45 % (15123)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.45 % (15123)Termination reason: Unknown
% 0.24/0.45 % (15123)Termination phase: shuffling
% 0.24/0.45
% 0.24/0.45 % (15123)Memory used [KB]: 1535
% 0.24/0.45 % (15123)Time elapsed: 0.010 s
% 0.24/0.45 % (15123)Instructions burned: 17 (million)
% 0.24/0.45 % (15123)------------------------------
% 0.24/0.45 % (15123)------------------------------
% 0.24/0.45 % (15126)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.24/0.46 % (15127)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.24/0.46 % (15126)Instruction limit reached!
% 0.24/0.46 % (15126)------------------------------
% 0.24/0.46 % (15126)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.46 % (15126)Termination reason: Unknown
% 0.24/0.46 % (15126)Termination phase: shuffling
% 0.24/0.46
% 0.24/0.46 % (15126)Memory used [KB]: 1407
% 0.24/0.46 % (15126)Time elapsed: 0.006 s
% 0.24/0.46 % (15126)Instructions burned: 8 (million)
% 0.24/0.46 % (15126)------------------------------
% 0.24/0.46 % (15126)------------------------------
% 0.24/0.46 % (15127)Instruction limit reached!
% 0.24/0.46 % (15127)------------------------------
% 0.24/0.46 % (15127)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.46 % (15127)Termination reason: Unknown
% 0.24/0.46 % (15127)Termination phase: shuffling
% 0.24/0.46
% 0.24/0.46 % (15127)Memory used [KB]: 1279
% 0.24/0.46 % (15127)Time elapsed: 0.004 s
% 0.24/0.46 % (15127)Instructions burned: 5 (million)
% 0.24/0.46 % (15127)------------------------------
% 0.24/0.46 % (15127)------------------------------
% 0.24/0.46 % (15128)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.24/0.46 % (15129)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)
% 0.24/0.46 % (15130)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.24/0.46 % (15131)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.24/0.46 % (15128)Instruction limit reached!
% 0.24/0.46 % (15128)------------------------------
% 0.24/0.46 % (15128)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.46 % (15128)Termination reason: Unknown
% 0.24/0.46 % (15128)Termination phase: shuffling
% 0.24/0.46
% 0.24/0.46 % (15128)Memory used [KB]: 1279
% 0.24/0.46 % (15128)Time elapsed: 0.004 s
% 0.24/0.46 % (15128)Instructions burned: 4 (million)
% 0.24/0.46 % (15128)------------------------------
% 0.24/0.46 % (15128)------------------------------
% 0.24/0.47 % (15131)Instruction limit reached!
% 0.24/0.47 % (15131)------------------------------
% 0.24/0.47 % (15131)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.47 % (15131)Termination reason: Unknown
% 0.24/0.47 % (15131)Termination phase: shuffling
% 0.24/0.47
% 0.24/0.47 % (15131)Memory used [KB]: 1279
% 0.24/0.47 % (15131)Time elapsed: 0.005 s
% 0.24/0.47 % (15131)Instructions burned: 7 (million)
% 0.24/0.47 % (15131)------------------------------
% 0.24/0.47 % (15131)------------------------------
% 0.24/0.47 % (15129)Instruction limit reached!
% 0.24/0.47 % (15129)------------------------------
% 0.24/0.47 % (15129)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.47 % (15129)Termination reason: Unknown
% 0.24/0.47 % (15129)Termination phase: shuffling
% 0.24/0.47
% 0.24/0.47 % (15129)Memory used [KB]: 1663
% 0.24/0.47 % (15129)Time elapsed: 0.011 s
% 0.24/0.47 % (15129)Instructions burned: 19 (million)
% 0.24/0.47 % (15129)------------------------------
% 0.24/0.47 % (15129)------------------------------
% 0.24/0.47 % (15132)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)
% 0.24/0.47 % (15133)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)
% 0.24/0.48 % (15134)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.24/0.48 % (15130)Refutation not found, incomplete strategy
% 0.24/0.48 % (15130)------------------------------
% 0.24/0.48 % (15130)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.48 % (15130)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.48
% 0.24/0.48
% 0.24/0.48 % (15130)Memory used [KB]: 6268
% 0.24/0.48 % (15130)Time elapsed: 0.018 s
% 0.24/0.48 % (15130)Instructions burned: 28 (million)
% 0.24/0.48 % (15130)------------------------------
% 0.24/0.48 % (15130)------------------------------
% 0.24/0.48 % (15135)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)
% 0.24/0.48 % (15134)Instruction limit reached!
% 0.24/0.48 % (15134)------------------------------
% 0.24/0.48 % (15134)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.48 % (15134)Termination reason: Unknown
% 0.24/0.48 % (15134)Termination phase: shuffling
% 0.24/0.48
% 0.24/0.48 % (15134)Memory used [KB]: 1279
% 0.24/0.48 % (15134)Time elapsed: 0.005 s
% 0.24/0.48 % (15134)Instructions burned: 6 (million)
% 0.24/0.48 % (15134)------------------------------
% 0.24/0.48 % (15134)------------------------------
% 0.24/0.48 % (15135)Instruction limit reached!
% 0.24/0.48 % (15135)------------------------------
% 0.24/0.48 % (15135)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.48 % (15135)Termination reason: Unknown
% 0.24/0.48 % (15135)Termination phase: shuffling
% 0.24/0.48
% 0.24/0.48 % (15135)Memory used [KB]: 1279
% 0.24/0.48 % (15135)Time elapsed: 0.005 s
% 0.24/0.48 % (15135)Instructions burned: 6 (million)
% 0.24/0.48 % (15135)------------------------------
% 0.24/0.48 % (15135)------------------------------
% 0.24/0.48 % (15133)Instruction limit reached!
% 0.24/0.48 % (15133)------------------------------
% 0.24/0.48 % (15133)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.48 % (15133)Termination reason: Unknown
% 0.24/0.48 % (15133)Termination phase: shuffling
% 0.24/0.48
% 0.24/0.48 % (15133)Memory used [KB]: 1663
% 0.24/0.48 % (15133)Time elapsed: 0.013 s
% 0.24/0.48 % (15133)Instructions burned: 22 (million)
% 0.24/0.48 % (15133)------------------------------
% 0.24/0.48 % (15133)------------------------------
% 0.24/0.49 % (15136)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2999ds/377Mi)
% 0.24/0.49 % (15137)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 (2998ds/779Mi)
% 0.24/0.50 % (15138)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 (2998ds/19Mi)
% 0.24/0.50 % (15139)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on theBenchmark for (2998ds/879Mi)
% 0.24/0.50 % (15140)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2998ds/17Mi)
% 0.24/0.50 % (15110)Instruction limit reached!
% 0.24/0.50 % (15110)------------------------------
% 0.24/0.50 % (15110)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.50 % (15110)Termination reason: Unknown
% 0.24/0.50 % (15110)Termination phase: Saturation
% 0.24/0.50
% 0.24/0.50 % (15110)Memory used [KB]: 6908
% 0.24/0.50 % (15110)Time elapsed: 0.089 s
% 0.24/0.50 % (15110)Instructions burned: 183 (million)
% 0.24/0.50 % (15110)------------------------------
% 0.24/0.50 % (15110)------------------------------
% 0.24/0.50 % (15138)Instruction limit reached!
% 0.24/0.50 % (15138)------------------------------
% 0.24/0.50 % (15138)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.50 % (15138)Termination reason: Unknown
% 0.24/0.50 % (15138)Termination phase: shuffling
% 0.24/0.50
% 0.24/0.50 % (15138)Memory used [KB]: 1663
% 0.24/0.50 % (15138)Time elapsed: 0.011 s
% 0.24/0.50 % (15138)Instructions burned: 19 (million)
% 0.24/0.50 % (15138)------------------------------
% 0.24/0.50 % (15138)------------------------------
% 0.24/0.51 % (15140)Instruction limit reached!
% 0.24/0.51 % (15140)------------------------------
% 0.24/0.51 % (15140)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.51 % (15140)Termination reason: Unknown
% 0.24/0.51 % (15140)Termination phase: shuffling
% 0.24/0.51
% 0.24/0.51 % (15140)Memory used [KB]: 1535
% 0.24/0.51 % (15140)Time elapsed: 0.011 s
% 0.24/0.51 % (15140)Instructions burned: 17 (million)
% 0.24/0.51 % (15140)------------------------------
% 0.24/0.51 % (15140)------------------------------
% 0.24/0.51 % (15141)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi)
% 0.24/0.52 % (15141)Instruction limit reached!
% 0.24/0.52 % (15141)------------------------------
% 0.24/0.52 % (15141)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.52 % (15141)Termination reason: Unknown
% 0.24/0.52 % (15141)Termination phase: shuffling
% 0.24/0.52
% 0.24/0.52 % (15141)Memory used [KB]: 1279
% 0.24/0.52 % (15141)Time elapsed: 0.004 s
% 0.24/0.52 % (15141)Instructions burned: 4 (million)
% 0.24/0.52 % (15141)------------------------------
% 0.24/0.52 % (15141)------------------------------
% 0.24/0.52 % (15142)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on theBenchmark for (2998ds/30Mi)
% 0.24/0.52 % (15143)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)
% 0.24/0.53 % (15139)Refutation not found, incomplete strategy
% 0.24/0.53 % (15139)------------------------------
% 0.24/0.53 % (15139)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.53 % (15139)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.53
% 0.24/0.53
% 0.24/0.53 % (15139)Memory used [KB]: 6268
% 0.24/0.53 % (15139)Time elapsed: 0.031 s
% 0.24/0.53 % (15139)Instructions burned: 60 (million)
% 0.24/0.53 % (15139)------------------------------
% 0.24/0.53 % (15139)------------------------------
% 1.13/0.53 % (15144)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)
% 1.13/0.53 % (15142)Instruction limit reached!
% 1.13/0.53 % (15142)------------------------------
% 1.13/0.53 % (15142)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.13/0.53 % (15142)Termination reason: Unknown
% 1.13/0.53 % (15142)Termination phase: Property scanning
% 1.13/0.53
% 1.13/0.53 % (15142)Memory used [KB]: 1791
% 1.13/0.53 % (15142)Time elapsed: 0.017 s
% 1.13/0.53 % (15142)Instructions burned: 30 (million)
% 1.13/0.53 % (15142)------------------------------
% 1.13/0.53 % (15142)------------------------------
% 1.13/0.54 % (15145)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)
% 1.13/0.55 % (15145)Instruction limit reached!
% 1.13/0.55 % (15145)------------------------------
% 1.13/0.55 % (15145)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.13/0.55 % (15145)Termination reason: Unknown
% 1.13/0.55 % (15145)Termination phase: shuffling
% 1.13/0.55
% 1.13/0.55 % (15145)Memory used [KB]: 1279
% 1.13/0.55 % (15145)Time elapsed: 0.004 s
% 1.13/0.55 % (15145)Instructions burned: 4 (million)
% 1.13/0.55 % (15145)------------------------------
% 1.13/0.55 % (15145)------------------------------
% 1.29/0.55 % (15146)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)
% 1.29/0.56 % (15146)Instruction limit reached!
% 1.29/0.56 % (15146)------------------------------
% 1.29/0.56 % (15146)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.29/0.56 % (15146)Termination reason: Unknown
% 1.29/0.56 % (15146)Termination phase: Property scanning
% 1.29/0.56
% 1.29/0.56 % (15146)Memory used [KB]: 1663
% 1.29/0.56 % (15146)Time elapsed: 0.013 s
% 1.29/0.56 % (15146)Instructions burned: 20 (million)
% 1.29/0.56 % (15147)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)
% 1.29/0.56 % (15146)------------------------------
% 1.29/0.56 % (15146)------------------------------
% 1.29/0.58 % (15148)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)
% 1.29/0.58 % (15144)Instruction limit reached!
% 1.29/0.58 % (15144)------------------------------
% 1.29/0.58 % (15144)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.29/0.58 % (15144)Termination reason: Unknown
% 1.29/0.58 % (15144)Termination phase: Saturation
% 1.29/0.58
% 1.29/0.58 % (15144)Memory used [KB]: 6524
% 1.29/0.58 % (15144)Time elapsed: 0.047 s
% 1.29/0.58 % (15144)Instructions burned: 101 (million)
% 1.29/0.58 % (15144)------------------------------
% 1.29/0.58 % (15144)------------------------------
% 1.29/0.58 % (15143)Instruction limit reached!
% 1.29/0.58 % (15143)------------------------------
% 1.29/0.58 % (15143)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.29/0.58 % (15143)Termination reason: Unknown
% 1.29/0.58 % (15143)Termination phase: Saturation
% 1.29/0.58
% 1.29/0.58 % (15143)Memory used [KB]: 6524
% 1.29/0.58 % (15143)Time elapsed: 0.059 s
% 1.29/0.58 % (15143)Instructions burned: 127 (million)
% 1.29/0.58 % (15143)------------------------------
% 1.29/0.58 % (15143)------------------------------
% 1.29/0.59 % (15149)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)
% 1.29/0.59 % (15150)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)
% 1.29/0.60 % (15147)Instruction limit reached!
% 1.29/0.60 % (15147)------------------------------
% 1.29/0.60 % (15147)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.29/0.60 % (15147)Termination reason: Unknown
% 1.29/0.60 % (15147)Termination phase: Property scanning
% 1.29/0.60
% 1.29/0.60 % (15147)Memory used [KB]: 2046
% 1.29/0.60 % (15147)Time elapsed: 0.039 s
% 1.29/0.60 % (15147)Instructions burned: 87 (million)
% 1.29/0.60 % (15147)------------------------------
% 1.29/0.60 % (15147)------------------------------
% 1.29/0.61 % (15149)Instruction limit reached!
% 1.29/0.61 % (15149)------------------------------
% 1.29/0.61 % (15149)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.29/0.61 % (15149)Termination reason: Unknown
% 1.29/0.61 % (15149)Termination phase: Property scanning
% 1.29/0.61
% 1.29/0.61 % (15149)Memory used [KB]: 1791
% 1.29/0.61 % (15149)Time elapsed: 0.020 s
% 1.29/0.61 % (15149)Instructions burned: 40 (million)
% 1.29/0.61 % (15149)------------------------------
% 1.29/0.61 % (15149)------------------------------
% 1.29/0.61 % (15151)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 (2997ds/46Mi)
% 1.29/0.61 % (15132)Refutation not found, incomplete strategy
% 1.29/0.61 % (15132)------------------------------
% 1.29/0.61 % (15132)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.29/0.61 % (15132)Termination reason: Refutation not found, incomplete strategy
% 1.29/0.61
% 1.29/0.61
% 1.29/0.61 % (15132)Memory used [KB]: 8187
% 1.29/0.61 % (15132)Time elapsed: 0.158 s
% 1.29/0.61 % (15132)Instructions burned: 232 (million)
% 1.29/0.61 % (15132)------------------------------
% 1.29/0.61 % (15132)------------------------------
% 1.29/0.62 % (15152)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 (2997ds/98Mi)
% 1.29/0.62 % (15148)Instruction limit reached!
% 1.29/0.62 % (15148)------------------------------
% 1.29/0.62 % (15148)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.29/0.62 % (15148)Termination reason: Unknown
% 1.29/0.62 % (15148)Termination phase: Saturation
% 1.29/0.62
% 1.29/0.62 % (15148)Memory used [KB]: 6524
% 1.29/0.62 % (15148)Time elapsed: 0.050 s
% 1.29/0.62 % (15148)Instructions burned: 107 (million)
% 1.29/0.62 % (15148)------------------------------
% 1.29/0.62 % (15148)------------------------------
% 1.29/0.63 % (15153)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 (2997ds/507Mi)
% 1.29/0.63 % (15151)Instruction limit reached!
% 1.29/0.63 % (15151)------------------------------
% 1.29/0.63 % (15151)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.29/0.63 % (15151)Termination reason: Unknown
% 1.29/0.63 % (15151)Termination phase: SInE selection
% 1.29/0.63
% 1.29/0.63 % (15151)Memory used [KB]: 1791
% 1.29/0.63 % (15151)Time elapsed: 0.022 s
% 1.29/0.63 % (15151)Instructions burned: 46 (million)
% 1.29/0.63 % (15151)------------------------------
% 1.29/0.63 % (15151)------------------------------
% 1.29/0.64 % (15154)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 (2997ds/149Mi)
% 1.98/0.64 % (15155)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on theBenchmark for (2997ds/39Mi)
% 1.98/0.66 % (15152)Instruction limit reached!
% 1.98/0.66 % (15152)------------------------------
% 1.98/0.66 % (15152)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.98/0.66 % (15152)Termination reason: Unknown
% 1.98/0.66 % (15152)Termination phase: Saturation
% 1.98/0.66
% 1.98/0.66 % (15152)Memory used [KB]: 2046
% 1.98/0.66 % (15152)Time elapsed: 0.041 s
% 1.98/0.66 % (15152)Instructions burned: 98 (million)
% 1.98/0.66 % (15152)------------------------------
% 1.98/0.66 % (15152)------------------------------
% 1.98/0.66 % (15155)Instruction limit reached!
% 1.98/0.66 % (15155)------------------------------
% 1.98/0.66 % (15155)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.98/0.66 % (15155)Termination reason: Unknown
% 1.98/0.66 % (15155)Termination phase: Property scanning
% 1.98/0.66
% 1.98/0.66 % (15155)Memory used [KB]: 1791
% 1.98/0.66 % (15155)Time elapsed: 0.020 s
% 1.98/0.66 % (15155)Instructions burned: 41 (million)
% 1.98/0.66 % (15155)------------------------------
% 1.98/0.66 % (15155)------------------------------
% 1.98/0.68 % (15156)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)
% 1.98/0.68 % (15157)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)
% 1.98/0.68 % (15156)Instruction limit reached!
% 1.98/0.68 % (15156)------------------------------
% 1.98/0.68 % (15156)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.98/0.68 % (15156)Termination reason: Unknown
% 1.98/0.68 % (15156)Termination phase: shuffling
% 1.98/0.68
% 1.98/0.68 % (15156)Memory used [KB]: 1279
% 1.98/0.68 % (15156)Time elapsed: 0.005 s
% 1.98/0.68 % (15156)Instructions burned: 7 (million)
% 1.98/0.68 % (15156)------------------------------
% 1.98/0.68 % (15156)------------------------------
% 1.98/0.68 % (15136)Instruction limit reached!
% 1.98/0.68 % (15136)------------------------------
% 1.98/0.68 % (15136)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.98/0.68 % (15136)Termination reason: Unknown
% 1.98/0.68 % (15136)Termination phase: Saturation
% 1.98/0.68
% 1.98/0.68 % (15136)Memory used [KB]: 7291
% 1.98/0.68 % (15136)Time elapsed: 0.199 s
% 1.98/0.68 % (15136)Instructions burned: 377 (million)
% 1.98/0.68 % (15136)------------------------------
% 1.98/0.68 % (15136)------------------------------
% 1.98/0.69 % (15157)Refutation not found, incomplete strategy
% 1.98/0.69 % (15157)------------------------------
% 1.98/0.69 % (15157)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.23/0.69 % (15157)Termination reason: Refutation not found, incomplete strategy
% 2.23/0.69
% 2.23/0.69
% 2.23/0.69 % (15157)Memory used [KB]: 6268
% 2.23/0.69 % (15157)Time elapsed: 0.017 s
% 2.23/0.69 % (15157)Instructions burned: 30 (million)
% 2.23/0.69 % (15157)------------------------------
% 2.23/0.69 % (15157)------------------------------
% 2.23/0.69 % (15158)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on theBenchmark for (2997ds/47Mi)
% 2.23/0.70 % (15159)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)
% 2.23/0.71 % (15160)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)
% 2.23/0.71 % (15154)Instruction limit reached!
% 2.23/0.71 % (15154)------------------------------
% 2.23/0.71 % (15154)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.23/0.71 % (15154)Termination reason: Unknown
% 2.23/0.71 % (15154)Termination phase: Saturation
% 2.23/0.71
% 2.23/0.71 % (15154)Memory used [KB]: 6908
% 2.23/0.71 % (15154)Time elapsed: 0.071 s
% 2.23/0.71 % (15154)Instructions burned: 149 (million)
% 2.23/0.71 % (15154)------------------------------
% 2.23/0.71 % (15154)------------------------------
% 2.23/0.71 % (15158)Instruction limit reached!
% 2.23/0.71 % (15158)------------------------------
% 2.23/0.71 % (15158)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.23/0.71 % (15158)Termination reason: Unknown
% 2.23/0.71 % (15158)Termination phase: Property scanning
% 2.23/0.71
% 2.23/0.71 % (15158)Memory used [KB]: 1791
% 2.23/0.71 % (15158)Time elapsed: 0.023 s
% 2.23/0.71 % (15158)Instructions burned: 48 (million)
% 2.23/0.71 % (15158)------------------------------
% 2.23/0.71 % (15158)------------------------------
% 2.23/0.72 % (15159)Instruction limit reached!
% 2.23/0.72 % (15159)------------------------------
% 2.23/0.72 % (15159)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.23/0.72 % (15159)Termination reason: Unknown
% 2.23/0.72 % (15159)Termination phase: Property scanning
% 2.23/0.72
% 2.23/0.72 % (15159)Memory used [KB]: 1791
% 2.23/0.72 % (15159)Time elapsed: 0.021 s
% 2.23/0.72 % (15159)Instructions burned: 44 (million)
% 2.23/0.72 % (15159)------------------------------
% 2.23/0.72 % (15159)------------------------------
% 2.23/0.72 % (15161)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on theBenchmark for (2996ds/62Mi)
% 2.23/0.73 % (15162)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 (2996ds/31Mi)
% 2.23/0.73 % (15163)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on theBenchmark for (2996ds/96Mi)
% 2.23/0.74 % (15162)Instruction limit reached!
% 2.23/0.74 % (15162)------------------------------
% 2.23/0.74 % (15162)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.23/0.74 % (15162)Termination reason: Unknown
% 2.23/0.74 % (15162)Termination phase: Property scanning
% 2.23/0.74
% 2.23/0.74 % (15162)Memory used [KB]: 1791
% 2.23/0.74 % (15162)Time elapsed: 0.016 s
% 2.23/0.74 % (15162)Instructions burned: 32 (million)
% 2.23/0.74 % (15162)------------------------------
% 2.23/0.74 % (15162)------------------------------
% 2.55/0.75 % (15161)Instruction limit reached!
% 2.55/0.75 % (15161)------------------------------
% 2.55/0.75 % (15161)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.55/0.75 % (15161)Termination reason: Unknown
% 2.55/0.75 % (15161)Termination phase: Property scanning
% 2.55/0.75
% 2.55/0.75 % (15161)Memory used [KB]: 1791
% 2.55/0.75 % (15161)Time elapsed: 0.028 s
% 2.55/0.75 % (15161)Instructions burned: 62 (million)
% 2.55/0.75 % (15161)------------------------------
% 2.55/0.75 % (15161)------------------------------
% 2.61/0.76 % (15164)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 (2996ds/453Mi)
% 2.61/0.76 % (15165)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)
% 2.61/0.77 % (15163)Instruction limit reached!
% 2.61/0.77 % (15163)------------------------------
% 2.61/0.77 % (15163)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.61/0.77 % (15163)Termination reason: Unknown
% 2.61/0.77 % (15163)Termination phase: Saturation
% 2.61/0.77
% 2.61/0.77 % (15163)Memory used [KB]: 6524
% 2.61/0.77 % (15163)Time elapsed: 0.042 s
% 2.61/0.77 % (15163)Instructions burned: 98 (million)
% 2.61/0.77 % (15163)------------------------------
% 2.61/0.77 % (15163)------------------------------
% 2.61/0.78 % (15166)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)
% 2.61/0.79 % (15165)Instruction limit reached!
% 2.61/0.79 % (15165)------------------------------
% 2.61/0.79 % (15165)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.61/0.79 % (15165)Termination reason: Unknown
% 2.61/0.79 % (15165)Termination phase: Function definition elimination
% 2.61/0.79
% 2.61/0.79 % (15165)Memory used [KB]: 1918
% 2.61/0.79 % (15165)Time elapsed: 0.033 s
% 2.61/0.79 % (15165)Instructions burned: 73 (million)
% 2.61/0.79 % (15165)------------------------------
% 2.61/0.79 % (15165)------------------------------
% 2.80/0.80 % (15167)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)
% 2.80/0.81 % (15167)Instruction limit reached!
% 2.80/0.81 % (15167)------------------------------
% 2.80/0.81 % (15167)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.80/0.81 % (15167)Termination reason: Unknown
% 2.80/0.81 % (15167)Termination phase: shuffling
% 2.80/0.81
% 2.80/0.81 % (15167)Memory used [KB]: 1407
% 2.80/0.81 % (15167)Time elapsed: 0.007 s
% 2.80/0.81 % (15167)Instructions burned: 11 (million)
% 2.80/0.81 % (15167)------------------------------
% 2.80/0.81 % (15167)------------------------------
% 2.80/0.81 % (15150)Instruction limit reached!
% 2.80/0.81 % (15150)------------------------------
% 2.80/0.81 % (15150)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.80/0.81 % (15150)Termination reason: Unknown
% 2.80/0.81 % (15150)Termination phase: Saturation
% 2.80/0.81
% 2.80/0.81 % (15150)Memory used [KB]: 7164
% 2.80/0.81 % (15150)Time elapsed: 0.218 s
% 2.80/0.81 % (15150)Instructions burned: 449 (million)
% 2.80/0.81 % (15150)------------------------------
% 2.80/0.81 % (15150)------------------------------
% 2.80/0.81 % (15166)Refutation not found, incomplete strategy
% 2.80/0.81 % (15166)------------------------------
% 2.80/0.81 % (15166)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.80/0.81 % (15166)Termination reason: Refutation not found, incomplete strategy
% 2.80/0.81
% 2.80/0.81
% 2.80/0.81 % (15166)Memory used [KB]: 6268
% 2.80/0.81 % (15166)Time elapsed: 0.030 s
% 2.80/0.81 % (15166)Instructions burned: 59 (million)
% 2.80/0.81 % (15166)------------------------------
% 2.80/0.81 % (15166)------------------------------
% 2.80/0.82 % (15168)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 (2995ds/41Mi)
% 2.80/0.82 % (15169)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2995ds/6Mi)
% 2.80/0.83 % (15170)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on theBenchmark for (2995ds/150Mi)
% 2.80/0.83 % (15169)Instruction limit reached!
% 2.80/0.83 % (15169)------------------------------
% 2.80/0.83 % (15169)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.80/0.83 % (15169)Termination reason: Unknown
% 2.80/0.83 % (15169)Termination phase: shuffling
% 2.80/0.83
% 2.80/0.83 % (15169)Memory used [KB]: 1279
% 2.80/0.83 % (15169)Time elapsed: 0.005 s
% 2.80/0.83 % (15169)Instructions burned: 7 (million)
% 2.80/0.83 % (15169)------------------------------
% 2.80/0.83 % (15169)------------------------------
% 2.80/0.84 % (15171)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 (2995ds/343Mi)
% 2.80/0.84 % (15168)Instruction limit reached!
% 2.80/0.84 % (15168)------------------------------
% 2.80/0.84 % (15168)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.80/0.84 % (15168)Termination reason: Unknown
% 2.80/0.84 % (15168)Termination phase: Property scanning
% 2.80/0.84
% 2.80/0.84 % (15168)Memory used [KB]: 1791
% 2.80/0.84 % (15168)Time elapsed: 0.020 s
% 2.80/0.84 % (15168)Instructions burned: 41 (million)
% 2.80/0.84 % (15168)------------------------------
% 2.80/0.84 % (15168)------------------------------
% 2.80/0.84 % (15153)Instruction limit reached!
% 2.80/0.84 % (15153)------------------------------
% 2.80/0.84 % (15153)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.80/0.84 % (15153)Termination reason: Unknown
% 2.80/0.84 % (15153)Termination phase: Saturation
% 2.80/0.84
% 2.80/0.84 % (15153)Memory used [KB]: 6780
% 2.80/0.84 % (15153)Time elapsed: 0.216 s
% 2.80/0.84 % (15153)Instructions burned: 509 (million)
% 2.80/0.84 % (15153)------------------------------
% 2.80/0.84 % (15153)------------------------------
% 3.45/0.86 % (15172)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 (2995ds/109Mi)
% 3.45/0.86 % (15173)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 (2995ds/253Mi)
% 3.45/0.88 % (15137)Instruction limit reached!
% 3.45/0.88 % (15137)------------------------------
% 3.45/0.88 % (15137)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.45/0.88 % (15137)Termination reason: Unknown
% 3.45/0.88 % (15137)Termination phase: Saturation
% 3.45/0.88
% 3.45/0.88 % (15137)Memory used [KB]: 7803
% 3.45/0.88 % (15137)Time elapsed: 0.388 s
% 3.45/0.88 % (15137)Instructions burned: 780 (million)
% 3.45/0.88 % (15137)------------------------------
% 3.45/0.88 % (15137)------------------------------
% 3.45/0.89 % (15160)Instruction limit reached!
% 3.45/0.89 % (15160)------------------------------
% 3.45/0.89 % (15160)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.45/0.89 % (15160)Termination reason: Unknown
% 3.45/0.89 % (15160)Termination phase: Saturation
% 3.45/0.89
% 3.45/0.89 % (15160)Memory used [KB]: 2814
% 3.45/0.89 % (15160)Time elapsed: 0.184 s
% 3.45/0.89 % (15160)Instructions burned: 432 (million)
% 3.45/0.89 % (15160)------------------------------
% 3.45/0.89 % (15160)------------------------------
% 3.45/0.89 % (15170)Instruction limit reached!
% 3.45/0.89 % (15170)------------------------------
% 3.45/0.89 % (15170)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.45/0.89 % (15170)Termination reason: Unknown
% 3.45/0.89 % (15170)Termination phase: Property scanning
% 3.45/0.89
% 3.45/0.89 % (15170)Memory used [KB]: 2942
% 3.45/0.89 % (15170)Time elapsed: 0.067 s
% 3.45/0.89 % (15170)Instructions burned: 150 (million)
% 3.45/0.89 % (15170)------------------------------
% 3.45/0.89 % (15170)------------------------------
% 3.45/0.89 % (15174)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on theBenchmark for (2994ds/140Mi)
% 3.45/0.90 % (15172)Instruction limit reached!
% 3.45/0.90 % (15172)------------------------------
% 3.45/0.90 % (15172)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.45/0.90 % (15172)Termination reason: Unknown
% 3.45/0.90 % (15172)Termination phase: Saturation
% 3.45/0.90
% 3.45/0.90 % (15172)Memory used [KB]: 6524
% 3.45/0.90 % (15172)Time elapsed: 0.047 s
% 3.45/0.90 % (15172)Instructions burned: 110 (million)
% 3.45/0.90 % (15172)------------------------------
% 3.45/0.90 % (15172)------------------------------
% 3.45/0.90 % (15175)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 (2994ds/614Mi)
% 3.45/0.90 % (15176)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 (2994ds/202Mi)
% 3.45/0.91 % (15177)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 (2994ds/339Mi)
% 3.45/0.92 % (15174)Refutation not found, incomplete strategy
% 3.45/0.92 % (15174)------------------------------
% 3.45/0.92 % (15174)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.45/0.92 % (15174)Termination reason: Refutation not found, incomplete strategy
% 3.45/0.92
% 3.45/0.92
% 3.45/0.92 % (15174)Memory used [KB]: 6268
% 3.45/0.92 % (15174)Time elapsed: 0.025 s
% 3.45/0.92 % (15174)Instructions burned: 52 (million)
% 3.45/0.92 % (15174)------------------------------
% 3.45/0.92 % (15174)------------------------------
% 3.45/0.92 % (15176)Refutation not found, incomplete strategy
% 3.45/0.92 % (15176)------------------------------
% 3.45/0.92 % (15176)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.45/0.92 % (15176)Termination reason: Refutation not found, incomplete strategy
% 3.45/0.92
% 3.45/0.92
% 3.45/0.92 % (15176)Memory used [KB]: 6140
% 3.45/0.92 % (15176)Time elapsed: 0.017 s
% 3.45/0.92 % (15176)Instructions burned: 30 (million)
% 3.45/0.92 % (15176)------------------------------
% 3.45/0.92 % (15176)------------------------------
% 3.45/0.93 % (15178)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 (2994ds/283Mi)
% 3.45/0.93 % (15121)Instruction limit reached!
% 3.45/0.93 % (15121)------------------------------
% 3.45/0.93 % (15121)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.45/0.93 % (15121)Termination reason: Unknown
% 3.45/0.93 % (15121)Termination phase: Saturation
% 3.45/0.93
% 3.45/0.93 % (15121)Memory used [KB]: 9594
% 3.45/0.93 % (15121)Time elapsed: 0.505 s
% 3.45/0.93 % (15121)Instructions burned: 1041 (million)
% 3.45/0.93 % (15121)------------------------------
% 3.45/0.93 % (15121)------------------------------
% 3.45/0.93 % (15179)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 (2994ds/134Mi)
% 4.00/0.95 % (15180)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on theBenchmark for (2994ds/298Mi)
% 4.00/0.97 % (15164)Instruction limit reached!
% 4.00/0.97 % (15164)------------------------------
% 4.00/0.97 % (15164)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.00/0.97 % (15164)Termination reason: Unknown
% 4.00/0.97 % (15164)Termination phase: Saturation
% 4.00/0.97
% 4.00/0.97 % (15164)Memory used [KB]: 7419
% 4.00/0.97 % (15164)Time elapsed: 0.216 s
% 4.00/0.97 % (15164)Instructions burned: 454 (million)
% 4.00/0.97 % (15164)------------------------------
% 4.00/0.97 % (15164)------------------------------
% 4.00/0.98 % (15173)Instruction limit reached!
% 4.00/0.98 % (15173)------------------------------
% 4.00/0.98 % (15173)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.00/0.98 % (15173)Termination reason: Unknown
% 4.00/0.98 % (15173)Termination phase: Saturation
% 4.00/0.98
% 4.00/0.98 % (15173)Memory used [KB]: 6908
% 4.00/0.98 % (15173)Time elapsed: 0.121 s
% 4.00/0.98 % (15173)Instructions burned: 253 (million)
% 4.00/0.98 % (15173)------------------------------
% 4.00/0.98 % (15173)------------------------------
% 4.00/0.98 % (15181)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on theBenchmark for (2994ds/192Mi)
% 4.00/0.99 % (15179)Instruction limit reached!
% 4.00/0.99 % (15179)------------------------------
% 4.00/0.99 % (15179)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.00/0.99 % (15179)Termination reason: Unknown
% 4.00/0.99 % (15179)Termination phase: Saturation
% 4.00/0.99
% 4.00/0.99 % (15179)Memory used [KB]: 6652
% 4.00/0.99 % (15179)Time elapsed: 0.057 s
% 4.00/0.99 % (15179)Instructions burned: 136 (million)
% 4.00/0.99 % (15179)------------------------------
% 4.00/0.99 % (15179)------------------------------
% 4.00/0.99 % (15182)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 (2994ds/258Mi)
% 4.43/1.00 % (15183)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 (2993ds/90Mi)
% 4.43/1.01 % (15171)Instruction limit reached!
% 4.43/1.01 % (15171)------------------------------
% 4.43/1.01 % (15171)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.43/1.01 % (15171)Termination reason: Unknown
% 4.43/1.01 % (15171)Termination phase: Saturation
% 4.43/1.01
% 4.43/1.01 % (15171)Memory used [KB]: 7675
% 4.43/1.01 % (15171)Time elapsed: 0.169 s
% 4.43/1.01 % (15171)Instructions burned: 344 (million)
% 4.43/1.01 % (15171)------------------------------
% 4.43/1.01 % (15171)------------------------------
% 4.43/1.02 % (15184)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 (2993ds/231Mi)
% 4.43/1.03 % (15177)Instruction limit reached!
% 4.43/1.03 % (15177)------------------------------
% 4.43/1.03 % (15177)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.43/1.03 % (15177)Termination reason: Unknown
% 4.43/1.03 % (15177)Termination phase: Saturation
% 4.43/1.03
% 4.43/1.03 % (15177)Memory used [KB]: 6908
% 4.43/1.03 % (15177)Time elapsed: 0.119 s
% 4.43/1.03 % (15177)Instructions burned: 339 (million)
% 4.43/1.03 % (15177)------------------------------
% 4.43/1.03 % (15177)------------------------------
% 4.43/1.04 % (15183)Instruction limit reached!
% 4.43/1.04 % (15183)------------------------------
% 4.43/1.04 % (15183)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.43/1.04 % (15183)Termination reason: Unknown
% 4.43/1.04 % (15183)Termination phase: Property scanning
% 4.43/1.04
% 4.43/1.04 % (15183)Memory used [KB]: 2174
% 4.43/1.04 % (15183)Time elapsed: 0.039 s
% 4.43/1.04 % (15183)Instructions burned: 90 (million)
% 4.43/1.04 % (15183)------------------------------
% 4.43/1.04 % (15183)------------------------------
% 4.79/1.04 % (15185)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 (2993ds/458Mi)
% 4.79/1.05 % (15178)Instruction limit reached!
% 4.79/1.05 % (15178)------------------------------
% 4.79/1.05 % (15178)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.79/1.05 % (15178)Termination reason: Unknown
% 4.79/1.05 % (15178)Termination phase: Saturation
% 4.79/1.05
% 4.79/1.05 % (15178)Memory used [KB]: 6908
% 4.79/1.05 % (15178)Time elapsed: 0.119 s
% 4.79/1.05 % (15178)Instructions burned: 283 (million)
% 4.79/1.05 % (15178)------------------------------
% 4.79/1.05 % (15178)------------------------------
% 4.79/1.05 % (15186)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 (2993ds/31Mi)
% 4.79/1.06 % (15187)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 (2993ds/297Mi)
% 4.79/1.07 % (15181)Instruction limit reached!
% 4.79/1.07 % (15181)------------------------------
% 4.79/1.07 % (15181)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.79/1.07 % (15181)Termination reason: Unknown
% 4.79/1.07 % (15181)Termination phase: Saturation
% 4.79/1.07
% 4.79/1.07 % (15181)Memory used [KB]: 6908
% 4.79/1.07 % (15181)Time elapsed: 0.086 s
% 4.79/1.07 % (15181)Instructions burned: 193 (million)
% 4.79/1.07 % (15181)------------------------------
% 4.79/1.07 % (15181)------------------------------
% 4.79/1.07 % (15186)Instruction limit reached!
% 4.79/1.07 % (15186)------------------------------
% 4.79/1.07 % (15186)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.79/1.07 % (15186)Termination reason: Unknown
% 4.79/1.07 % (15186)Termination phase: Property scanning
% 4.79/1.07
% 4.79/1.07 % (15186)Memory used [KB]: 1791
% 4.79/1.07 % (15186)Time elapsed: 0.016 s
% 4.79/1.07 % (15186)Instructions burned: 31 (million)
% 4.79/1.07 % (15186)------------------------------
% 4.79/1.07 % (15186)------------------------------
% 5.49/1.08 % (15188)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 (2993ds/987Mi)
% 5.49/1.08 % (15189)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 (2993ds/182Mi)
% 5.49/1.09 % (15180)Instruction limit reached!
% 5.49/1.09 % (15180)------------------------------
% 5.49/1.09 % (15180)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 5.49/1.09 % (15180)Termination reason: Unknown
% 5.49/1.09 % (15180)Termination phase: Saturation
% 5.49/1.09
% 5.49/1.09 % (15180)Memory used [KB]: 7291
% 5.49/1.09 % (15180)Time elapsed: 0.144 s
% 5.49/1.09 % (15180)Instructions burned: 298 (million)
% 5.49/1.09 % (15180)------------------------------
% 5.49/1.09 % (15180)------------------------------
% 5.49/1.10 % (15190)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 (2993ds/182Mi)
% 5.80/1.13 % (15182)Instruction limit reached!
% 5.80/1.13 % (15182)------------------------------
% 5.80/1.13 % (15182)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 5.80/1.13 % (15182)Termination reason: Unknown
% 5.80/1.13 % (15182)Termination phase: Saturation
% 5.80/1.13
% 5.80/1.13 % (15182)Memory used [KB]: 6908
% 5.80/1.13 % (15182)Time elapsed: 0.151 s
% 5.80/1.13 % (15182)Instructions burned: 259 (million)
% 5.80/1.13 % (15182)------------------------------
% 5.80/1.13 % (15182)------------------------------
% 5.80/1.15 % (15191)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 (2992ds/154Mi)
% 5.80/1.15 % (15184)Instruction limit reached!
% 5.80/1.15 % (15184)------------------------------
% 5.80/1.15 % (15184)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 5.80/1.15 % (15184)Termination reason: Unknown
% 5.80/1.15 % (15184)Termination phase: Saturation
% 5.80/1.15
% 5.80/1.15 % (15184)Memory used [KB]: 7931
% 5.80/1.15 % (15184)Time elapsed: 0.128 s
% 5.80/1.15 % (15184)Instructions burned: 232 (million)
% 5.80/1.15 % (15184)------------------------------
% 5.80/1.15 % (15184)------------------------------
% 5.80/1.16 % (15189)Instruction limit reached!
% 5.80/1.16 % (15189)------------------------------
% 5.80/1.16 % (15189)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 5.80/1.16 % (15189)Termination reason: Unknown
% 5.80/1.16 % (15189)Termination phase: Saturation
% 5.80/1.16
% 5.80/1.16 % (15189)Memory used [KB]: 6780
% 5.80/1.16 % (15189)Time elapsed: 0.081 s
% 5.80/1.16 % (15189)Instructions burned: 183 (million)
% 5.80/1.16 % (15189)------------------------------
% 5.80/1.16 % (15189)------------------------------
% 5.80/1.16 % (15192)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 (2992ds/79Mi)
% 6.08/1.17 % (15193)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 (2992ds/216Mi)
% 6.08/1.19 % (15187)Instruction limit reached!
% 6.08/1.19 % (15187)------------------------------
% 6.08/1.19 % (15187)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.08/1.19 % (15187)Termination reason: Unknown
% 6.08/1.19 % (15187)Termination phase: Saturation
% 6.08/1.19
% 6.08/1.19 % (15187)Memory used [KB]: 6652
% 6.08/1.19 % (15187)Time elapsed: 0.127 s
% 6.08/1.19 % (15187)Instructions burned: 298 (million)
% 6.08/1.19 % (15187)------------------------------
% 6.08/1.19 % (15187)------------------------------
% 6.08/1.19 % (15175)Instruction limit reached!
% 6.08/1.19 % (15175)------------------------------
% 6.08/1.19 % (15175)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.08/1.19 % (15175)Termination reason: Unknown
% 6.08/1.19 % (15175)Termination phase: Saturation
% 6.08/1.19
% 6.08/1.19 % (15175)Memory used [KB]: 7675
% 6.08/1.19 % (15175)Time elapsed: 0.291 s
% 6.08/1.19 % (15175)Instructions burned: 614 (million)
% 6.08/1.19 % (15175)------------------------------
% 6.08/1.19 % (15175)------------------------------
% 6.08/1.20 % (15192)Instruction limit reached!
% 6.08/1.20 % (15192)------------------------------
% 6.08/1.20 % (15192)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.08/1.20 % (15192)Termination reason: Unknown
% 6.08/1.20 % (15192)Termination phase: Function definition elimination
% 6.08/1.20
% 6.08/1.20 % (15192)Memory used [KB]: 2046
% 6.08/1.20 % (15192)Time elapsed: 0.034 s
% 6.08/1.20 % (15192)Instructions burned: 79 (million)
% 6.08/1.20 % (15192)------------------------------
% 6.08/1.20 % (15192)------------------------------
% 6.08/1.20 % (15190)Instruction limit reached!
% 6.08/1.20 % (15190)------------------------------
% 6.08/1.20 % (15190)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.08/1.20 % (15190)Termination reason: Unknown
% 6.08/1.20 % (15190)Termination phase: Saturation
% 6.08/1.20
% 6.08/1.20 % (15190)Memory used [KB]: 9466
% 6.08/1.20 % (15190)Time elapsed: 0.094 s
% 6.08/1.20 % (15190)Instructions burned: 182 (million)
% 6.08/1.20 % (15190)------------------------------
% 6.08/1.20 % (15190)------------------------------
% 6.08/1.20 % (15194)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 (2992ds/114Mi)
% 6.08/1.21 % (15195)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 (2992ds/922Mi)
% 6.08/1.21 % (15191)Instruction limit reached!
% 6.08/1.21 % (15191)------------------------------
% 6.08/1.21 % (15191)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.08/1.21 % (15191)Termination reason: Unknown
% 6.08/1.21 % (15191)Termination phase: Saturation
% 6.08/1.21
% 6.08/1.21 % (15191)Memory used [KB]: 6524
% 6.08/1.21 % (15191)Time elapsed: 0.064 s
% 6.08/1.21 % (15191)Instructions burned: 155 (million)
% 6.08/1.21 % (15191)------------------------------
% 6.08/1.21 % (15191)------------------------------
% 6.08/1.21 % (15196)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 (2991ds/182Mi)
% 6.08/1.21 % (15197)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 (2991ds/164Mi)
% 6.08/1.22 % (15198)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 (2991ds/50Mi)
% 6.08/1.23 % (15195)Refutation not found, incomplete strategy
% 6.08/1.23 % (15195)------------------------------
% 6.08/1.23 % (15195)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.08/1.23 % (15195)Termination reason: Refutation not found, incomplete strategy
% 6.08/1.23
% 6.08/1.23
% 6.08/1.23 % (15195)Memory used [KB]: 6396
% 6.08/1.23 % (15195)Time elapsed: 0.024 s
% 6.08/1.23 % (15195)Instructions burned: 40 (million)
% 6.08/1.23 % (15195)------------------------------
% 6.08/1.23 % (15195)------------------------------
% 6.08/1.24 % (15197)Refutation not found, incomplete strategy
% 6.08/1.24 % (15197)------------------------------
% 6.08/1.24 % (15197)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.08/1.24 % (15197)Termination reason: Refutation not found, incomplete strategy
% 6.08/1.24
% 6.08/1.24
% 6.08/1.24 % (15197)Memory used [KB]: 1791
% 6.08/1.24 % (15197)Time elapsed: 0.030 s
% 6.08/1.24 % (15197)Instructions burned: 63 (million)
% 6.08/1.24 % (15197)------------------------------
% 6.08/1.24 % (15197)------------------------------
% 6.08/1.24 % (15199)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 (2991ds/368Mi)
% 6.51/1.24 % (15198)Instruction limit reached!
% 6.51/1.24 % (15198)------------------------------
% 6.51/1.24 % (15198)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.51/1.24 % (15198)Termination reason: Unknown
% 6.51/1.24 % (15198)Termination phase: Property scanning
% 6.51/1.24
% 6.51/1.24 % (15198)Memory used [KB]: 1791
% 6.51/1.24 % (15198)Time elapsed: 0.025 s
% 6.51/1.24 % (15198)Instructions burned: 52 (million)
% 6.51/1.24 % (15198)------------------------------
% 6.51/1.24 % (15198)------------------------------
% 6.51/1.25 % (15194)Refutation not found, incomplete strategy
% 6.51/1.25 % (15194)------------------------------
% 6.51/1.25 % (15194)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.51/1.25 % (15194)Termination reason: Refutation not found, incomplete strategy
% 6.51/1.25
% 6.51/1.25
% 6.51/1.25 % (15194)Memory used [KB]: 6780
% 6.51/1.25 % (15194)Time elapsed: 0.048 s
% 6.51/1.25 % (15194)Instructions burned: 110 (million)
% 6.51/1.25 % (15194)------------------------------
% 6.51/1.25 % (15194)------------------------------
% 6.51/1.25 % (15200)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 (2991ds/1021Mi)
% 6.51/1.26 % (15201)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 (2991ds/267Mi)
% 6.51/1.26 % (15202)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 (2991ds/204Mi)
% 6.51/1.26 % (15193)Instruction limit reached!
% 6.51/1.26 % (15193)------------------------------
% 6.51/1.26 % (15193)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.51/1.26 % (15193)Termination reason: Unknown
% 6.51/1.26 % (15193)Termination phase: Saturation
% 6.51/1.26
% 6.51/1.26 % (15193)Memory used [KB]: 6652
% 6.51/1.26 % (15193)Time elapsed: 0.090 s
% 6.51/1.26 % (15193)Instructions burned: 216 (million)
% 6.51/1.26 % (15193)------------------------------
% 6.51/1.26 % (15193)------------------------------
% 6.51/1.26 % (15185)Instruction limit reached!
% 6.51/1.26 % (15185)------------------------------
% 6.51/1.26 % (15185)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.51/1.26 % (15185)Termination reason: Unknown
% 6.51/1.26 % (15185)Termination phase: Saturation
% 6.51/1.26
% 6.51/1.26 % (15185)Memory used [KB]: 7931
% 6.51/1.26 % (15185)Time elapsed: 0.222 s
% 6.51/1.27 % (15185)Instructions burned: 458 (million)
% 6.51/1.27 % (15185)------------------------------
% 6.51/1.27 % (15185)------------------------------
% 6.74/1.28 % (15203)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 (2991ds/26Mi)
% 6.74/1.28 % (15204)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 (2991ds/53Mi)
% 6.74/1.28 % (15196)Instruction limit reached!
% 6.74/1.28 % (15196)------------------------------
% 6.74/1.28 % (15196)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.74/1.28 % (15196)Termination reason: Unknown
% 6.74/1.28 % (15196)Termination phase: Saturation
% 6.74/1.28
% 6.74/1.28 % (15196)Memory used [KB]: 6652
% 6.74/1.28 % (15196)Time elapsed: 0.076 s
% 6.74/1.28 % (15196)Instructions burned: 182 (million)
% 6.74/1.28 % (15196)------------------------------
% 6.74/1.28 % (15196)------------------------------
% 6.74/1.29 % (15203)Instruction limit reached!
% 6.74/1.29 % (15203)------------------------------
% 6.74/1.29 % (15203)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.74/1.29 % (15203)Termination reason: Unknown
% 6.74/1.29 % (15203)Termination phase: Property scanning
% 6.74/1.29
% 6.74/1.29 % (15203)Memory used [KB]: 1791
% 6.74/1.29 % (15203)Time elapsed: 0.014 s
% 6.74/1.29 % (15203)Instructions burned: 27 (million)
% 6.74/1.29 % (15203)------------------------------
% 6.74/1.29 % (15203)------------------------------
% 6.74/1.30 % (15205)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 (2991ds/4436Mi)
% 6.74/1.30 % (15204)Instruction limit reached!
% 6.74/1.30 % (15204)------------------------------
% 6.74/1.30 % (15204)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.74/1.30 % (15204)Termination reason: Unknown
% 6.74/1.30 % (15204)Termination phase: Property scanning
% 6.74/1.30
% 6.74/1.30 % (15204)Memory used [KB]: 1791
% 6.74/1.30 % (15204)Time elapsed: 0.025 s
% 6.74/1.30 % (15204)Instructions burned: 54 (million)
% 6.74/1.30 % (15204)------------------------------
% 6.74/1.30 % (15204)------------------------------
% 6.74/1.30 % (15206)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 (2991ds/1539Mi)
% 6.74/1.31 % (15205)Refutation not found, incomplete strategy
% 6.74/1.31 % (15205)------------------------------
% 6.74/1.31 % (15205)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.74/1.31 % (15205)Termination reason: Refutation not found, incomplete strategy
% 6.74/1.31
% 6.74/1.31
% 6.74/1.31 % (15205)Memory used [KB]: 6268
% 6.74/1.31 % (15205)Time elapsed: 0.017 s
% 6.74/1.31 % (15205)Instructions burned: 29 (million)
% 6.74/1.31 % (15205)------------------------------
% 6.74/1.31 % (15205)------------------------------
% 6.74/1.32 % (15207)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 (2990ds/408Mi)
% 6.93/1.33 % (15208)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 (2990ds/5205Mi)
% 6.93/1.35 % (15202)Instruction limit reached!
% 6.93/1.35 % (15202)------------------------------
% 6.93/1.35 % (15202)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.93/1.35 % (15202)Termination reason: Unknown
% 6.93/1.35 % (15202)Termination phase: Saturation
% 6.93/1.35
% 6.93/1.35 % (15202)Memory used [KB]: 6780
% 6.93/1.35 % (15202)Time elapsed: 0.093 s
% 6.93/1.35 % (15202)Instructions burned: 205 (million)
% 6.93/1.35 % (15202)------------------------------
% 6.93/1.35 % (15202)------------------------------
% 6.93/1.37 % (15209)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 (2990ds/1913Mi)
% 6.93/1.37 % (15201)Instruction limit reached!
% 6.93/1.37 % (15201)------------------------------
% 6.93/1.37 % (15201)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.93/1.37 % (15201)Termination reason: Unknown
% 6.93/1.37 % (15201)Termination phase: Saturation
% 6.93/1.37
% 6.93/1.37 % (15201)Memory used [KB]: 6908
% 6.93/1.37 % (15201)Time elapsed: 0.114 s
% 6.93/1.37 % (15201)Instructions burned: 269 (million)
% 6.93/1.37 % (15201)------------------------------
% 6.93/1.37 % (15201)------------------------------
% 6.93/1.38 % (15210)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 (2990ds/4350Mi)
% 6.93/1.40 % (15199)Instruction limit reached!
% 6.93/1.40 % (15199)------------------------------
% 6.93/1.40 % (15199)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.93/1.40 % (15199)Termination reason: Unknown
% 6.93/1.40 % (15199)Termination phase: Saturation
% 6.93/1.40
% 6.93/1.40 % (15199)Memory used [KB]: 6908
% 6.93/1.40 % (15199)Time elapsed: 0.156 s
% 6.93/1.40 % (15199)Instructions burned: 369 (million)
% 6.93/1.40 % (15199)------------------------------
% 6.93/1.40 % (15199)------------------------------
% 6.93/1.41 % (15210)Refutation not found, incomplete strategy
% 6.93/1.41 % (15210)------------------------------
% 6.93/1.41 % (15210)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.93/1.41 % (15210)Termination reason: Refutation not found, incomplete strategy
% 6.93/1.41
% 6.93/1.41
% 6.93/1.41 % (15210)Memory used [KB]: 6268
% 6.93/1.41 % (15210)Time elapsed: 0.049 s
% 6.93/1.41 % (15210)Instructions burned: 55 (million)
% 6.93/1.41 % (15210)------------------------------
% 6.93/1.41 % (15210)------------------------------
% 6.93/1.41 % (15211)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 (2989ds/68Mi)
% 7.36/1.44 % (15211)Instruction limit reached!
% 7.36/1.44 % (15211)------------------------------
% 7.36/1.44 % (15211)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.36/1.44 % (15211)Termination reason: Unknown
% 7.36/1.44 % (15211)Termination phase: Property scanning
% 7.36/1.44
% 7.36/1.44 % (15211)Memory used [KB]: 1791
% 7.36/1.44 % (15211)Time elapsed: 0.031 s
% 7.36/1.44 % (15211)Instructions burned: 68 (million)
% 7.36/1.44 % (15211)------------------------------
% 7.36/1.44 % (15211)------------------------------
% 7.36/1.45 % (15212)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 (2989ds/358Mi)
% 7.36/1.45 % (15213)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 (2989ds/31Mi)
% 7.36/1.47 % (15213)Instruction limit reached!
% 7.36/1.47 % (15213)------------------------------
% 7.36/1.47 % (15213)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.36/1.47 % (15213)Termination reason: Unknown
% 7.36/1.47 % (15213)Termination phase: Property scanning
% 7.36/1.47
% 7.36/1.47 % (15213)Memory used [KB]: 1791
% 7.36/1.47 % (15213)Time elapsed: 0.017 s
% 7.36/1.47 % (15213)Instructions burned: 32 (million)
% 7.36/1.47 % (15213)------------------------------
% 7.36/1.47 % (15213)------------------------------
% 7.44/1.48 % (15214)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on theBenchmark for (2989ds/279Mi)
% 7.44/1.52 % (15188)Instruction limit reached!
% 7.44/1.52 % (15188)------------------------------
% 7.44/1.52 % (15188)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.44/1.52 % (15188)Termination reason: Unknown
% 7.44/1.52 % (15188)Termination phase: Saturation
% 7.44/1.52
% 7.44/1.52 % (15188)Memory used [KB]: 7675
% 7.44/1.52 % (15188)Time elapsed: 0.447 s
% 7.44/1.52 % (15188)Instructions burned: 988 (million)
% 7.44/1.52 % (15188)------------------------------
% 7.44/1.52 % (15188)------------------------------
% 7.44/1.54 % (15215)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on theBenchmark for (2988ds/258Mi)
% 7.87/1.56 % (15207)Instruction limit reached!
% 7.87/1.56 % (15207)------------------------------
% 7.87/1.56 % (15207)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.87/1.56 % (15207)Termination reason: Unknown
% 7.87/1.56 % (15207)Termination phase: Saturation
% 7.87/1.56
% 7.87/1.56 % (15207)Memory used [KB]: 9466
% 7.87/1.56 % (15207)Time elapsed: 0.267 s
% 7.87/1.56 % (15207)Instructions burned: 408 (million)
% 7.87/1.56 % (15207)------------------------------
% 7.87/1.56 % (15207)------------------------------
% 8.09/1.58 % (15216)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 (2988ds/26Mi)
% 8.09/1.59 % (15216)Instruction limit reached!
% 8.09/1.59 % (15216)------------------------------
% 8.09/1.59 % (15216)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 8.09/1.59 % (15216)Termination reason: Unknown
% 8.09/1.59 % (15216)Termination phase: Property scanning
% 8.09/1.59
% 8.09/1.59 % (15216)Memory used [KB]: 1791
% 8.09/1.59 % (15216)Time elapsed: 0.014 s
% 8.09/1.59 % (15216)Instructions burned: 26 (million)
% 8.09/1.59 % (15216)------------------------------
% 8.09/1.59 % (15216)------------------------------
% 8.09/1.60 % (15217)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 (2987ds/995Mi)
% 8.09/1.61 % (15214)Instruction limit reached!
% 8.09/1.61 % (15214)------------------------------
% 8.09/1.61 % (15214)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 8.09/1.61 % (15214)Termination reason: Unknown
% 8.09/1.61 % (15214)Termination phase: Saturation
% 8.09/1.61
% 8.09/1.61 % (15214)Memory used [KB]: 6908
% 8.09/1.61 % (15214)Time elapsed: 0.132 s
% 8.09/1.61 % (15214)Instructions burned: 280 (million)
% 8.09/1.61 % (15214)------------------------------
% 8.09/1.61 % (15214)------------------------------
% 8.09/1.62 % (15212)Instruction limit reached!
% 8.09/1.62 % (15212)------------------------------
% 8.09/1.62 % (15212)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 8.09/1.62 % (15212)Termination reason: Unknown
% 8.09/1.62 % (15212)Termination phase: Saturation
% 8.09/1.62
% 8.09/1.62 % (15212)Memory used [KB]: 7291
% 8.09/1.62 % (15212)Time elapsed: 0.199 s
% 8.09/1.62 % (15212)Instructions burned: 358 (million)
% 8.09/1.62 % (15212)------------------------------
% 8.09/1.62 % (15212)------------------------------
% 8.09/1.63 % (15218)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 (2987ds/373Mi)
% 8.09/1.63 % (15219)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 (2987ds/253Mi)
% 9.97/1.65 % (15215)Instruction limit reached!
% 9.97/1.65 % (15215)------------------------------
% 9.97/1.65 % (15215)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 9.97/1.65 % (15215)Termination reason: Unknown
% 9.97/1.65 % (15215)Termination phase: Saturation
% 9.97/1.65
% 9.97/1.65 % (15215)Memory used [KB]: 7291
% 9.97/1.65 % (15215)Time elapsed: 0.113 s
% 9.97/1.65 % (15215)Instructions burned: 258 (million)
% 9.97/1.65 % (15215)------------------------------
% 9.97/1.65 % (15215)------------------------------
% 9.97/1.66 % (15220)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 (2987ds/832Mi)
% 10.18/1.72 % (15200)Instruction limit reached!
% 10.18/1.72 % (15200)------------------------------
% 10.18/1.72 % (15200)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 10.18/1.72 % (15200)Termination reason: Unknown
% 10.18/1.72 % (15200)Termination phase: Saturation
% 10.18/1.72
% 10.18/1.72 % (15200)Memory used [KB]: 11257
% 10.18/1.72 % (15200)Time elapsed: 0.473 s
% 10.18/1.72 % (15200)Instructions burned: 1023 (million)
% 10.18/1.72 % (15200)------------------------------
% 10.18/1.72 % (15200)------------------------------
% 10.18/1.74 % (15221)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on theBenchmark for (2986ds/668Mi)
% 10.18/1.74 % (15219)Instruction limit reached!
% 10.18/1.74 % (15219)------------------------------
% 10.18/1.74 % (15219)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 10.18/1.75 % (15219)Termination reason: Unknown
% 10.18/1.75 % (15219)Termination phase: Saturation
% 10.18/1.75
% 10.18/1.75 % (15219)Memory used [KB]: 6908
% 10.18/1.75 % (15219)Time elapsed: 0.115 s
% 10.18/1.75 % (15219)Instructions burned: 253 (million)
% 10.18/1.75 % (15219)------------------------------
% 10.18/1.75 % (15219)------------------------------
% 10.70/1.76 % (15222)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=40:si=on:rtra=on_0 on theBenchmark for (2986ds/40Mi)
% 10.70/1.77 % (15220)Refutation not found, incomplete strategy
% 10.70/1.77 % (15220)------------------------------
% 10.70/1.77 % (15220)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 10.70/1.77 % (15220)Termination reason: Refutation not found, incomplete strategy
% 10.70/1.77
% 10.70/1.77
% 10.70/1.77 % (15220)Memory used [KB]: 8315
% 10.70/1.77 % (15220)Time elapsed: 0.104 s
% 10.70/1.77 % (15220)Instructions burned: 200 (million)
% 10.70/1.77 % (15220)------------------------------
% 10.70/1.77 % (15220)------------------------------
% 10.92/1.78 % (15222)Instruction limit reached!
% 10.92/1.78 % (15222)------------------------------
% 10.92/1.78 % (15222)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 10.92/1.78 % (15222)Termination reason: Unknown
% 10.92/1.78 % (15222)Termination phase: Property scanning
% 10.92/1.78
% 10.92/1.78 % (15222)Memory used [KB]: 1791
% 10.92/1.78 % (15222)Time elapsed: 0.020 s
% 10.92/1.78 % (15222)Instructions burned: 40 (million)
% 10.92/1.78 % (15222)------------------------------
% 10.92/1.78 % (15222)------------------------------
% 10.92/1.78 % (15223)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on theBenchmark for (2986ds/294Mi)
% 10.92/1.79 % (15224)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on theBenchmark for (2986ds/187Mi)
% 10.92/1.80 % (15218)Instruction limit reached!
% 10.92/1.80 % (15218)------------------------------
% 10.92/1.80 % (15218)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 10.92/1.80 % (15218)Termination reason: Unknown
% 10.92/1.80 % (15218)Termination phase: Saturation
% 10.92/1.80
% 10.92/1.80 % (15218)Memory used [KB]: 7419
% 10.92/1.80 % (15218)Time elapsed: 0.177 s
% 10.92/1.80 % (15218)Instructions burned: 373 (million)
% 10.92/1.80 % (15218)------------------------------
% 10.92/1.80 % (15218)------------------------------
% 10.92/1.81 % (15223)Refutation not found, incomplete strategy
% 10.92/1.81 % (15223)------------------------------
% 10.92/1.81 % (15223)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 10.92/1.81 % (15223)Termination reason: Refutation not found, incomplete strategy
% 10.92/1.81
% 10.92/1.81
% 10.92/1.81 % (15223)Memory used [KB]: 6396
% 10.92/1.81 % (15223)Time elapsed: 0.031 s
% 10.92/1.81 % (15223)Instructions burned: 63 (million)
% 10.92/1.81 % (15223)------------------------------
% 10.92/1.81 % (15223)------------------------------
% 10.92/1.82 % (15225)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on theBenchmark for (2985ds/371Mi)
% 11.24/1.82 % (15226)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on theBenchmark for (2985ds/1827Mi)
% 11.34/1.87 % (15224)Instruction limit reached!
% 11.34/1.87 % (15224)------------------------------
% 11.34/1.87 % (15224)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 11.34/1.87 % (15224)Termination reason: Unknown
% 11.34/1.87 % (15224)Termination phase: Saturation
% 11.34/1.87
% 11.34/1.87 % (15224)Memory used [KB]: 6780
% 11.34/1.87 % (15224)Time elapsed: 0.082 s
% 11.34/1.87 % (15224)Instructions burned: 188 (million)
% 11.34/1.87 % (15224)------------------------------
% 11.34/1.87 % (15224)------------------------------
% 11.34/1.89 % (15227)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on theBenchmark for (2985ds/70Mi)
% 11.34/1.91 % (15227)Instruction limit reached!
% 11.34/1.91 % (15227)------------------------------
% 11.34/1.91 % (15227)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 11.34/1.92 % (15227)Termination reason: Unknown
% 11.34/1.92 % (15227)Termination phase: Function definition elimination
% 11.34/1.92
% 11.34/1.92 % (15227)Memory used [KB]: 1791
% 11.34/1.92 % (15227)Time elapsed: 0.032 s
% 11.34/1.92 % (15227)Instructions burned: 70 (million)
% 11.34/1.92 % (15227)------------------------------
% 11.34/1.92 % (15227)------------------------------
% 11.78/1.93 % (15228)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on theBenchmark for (2984ds/316Mi)
% 11.99/2.00 % (15225)Instruction limit reached!
% 11.99/2.00 % (15225)------------------------------
% 11.99/2.00 % (15225)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 11.99/2.00 % (15225)Termination reason: Unknown
% 11.99/2.00 % (15225)Termination phase: Saturation
% 11.99/2.00
% 11.99/2.00 % (15225)Memory used [KB]: 7547
% 11.99/2.00 % (15225)Time elapsed: 0.183 s
% 11.99/2.00 % (15225)Instructions burned: 372 (million)
% 11.99/2.00 % (15225)------------------------------
% 11.99/2.00 % (15225)------------------------------
% 11.99/2.01 % (15229)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on theBenchmark for (2983ds/932Mi)
% 11.99/2.04 % (15221)Instruction limit reached!
% 11.99/2.04 % (15221)------------------------------
% 11.99/2.04 % (15221)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 11.99/2.04 % (15221)Termination reason: Unknown
% 11.99/2.04 % (15221)Termination phase: Saturation
% 11.99/2.04
% 11.99/2.04 % (15221)Memory used [KB]: 12281
% 11.99/2.04 % (15221)Time elapsed: 0.304 s
% 11.99/2.04 % (15221)Instructions burned: 669 (million)
% 11.99/2.04 % (15221)------------------------------
% 11.99/2.04 % (15221)------------------------------
% 12.78/2.06 % (15230)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on theBenchmark for (2983ds/4714Mi)
% 12.78/2.07 % (15228)Instruction limit reached!
% 12.78/2.07 % (15228)------------------------------
% 12.78/2.07 % (15228)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 12.78/2.07 % (15228)Termination reason: Unknown
% 12.78/2.07 % (15228)Termination phase: Saturation
% 12.78/2.07
% 12.78/2.07 % (15228)Memory used [KB]: 6908
% 12.78/2.07 % (15228)Time elapsed: 0.142 s
% 12.78/2.07 % (15228)Instructions burned: 317 (million)
% 12.78/2.07 % (15228)------------------------------
% 12.78/2.07 % (15228)------------------------------
% 13.04/2.07 % (15206)Instruction limit reached!
% 13.04/2.07 % (15206)------------------------------
% 13.04/2.07 % (15206)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 13.04/2.07 % (15206)Termination reason: Unknown
% 13.04/2.07 % (15206)Termination phase: Saturation
% 13.04/2.07
% 13.04/2.07 % (15206)Memory used [KB]: 9083
% 13.04/2.07 % (15206)Time elapsed: 0.793 s
% 13.04/2.07 % (15206)Instructions burned: 1539 (million)
% 13.04/2.07 % (15206)------------------------------
% 13.04/2.07 % (15206)------------------------------
% 13.04/2.08 % (15231)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on theBenchmark for (2983ds/8250Mi)
% 13.04/2.09 % (15217)Instruction limit reached!
% 13.04/2.09 % (15217)------------------------------
% 13.04/2.09 % (15217)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 13.04/2.09 % (15217)Termination reason: Unknown
% 13.04/2.09 % (15217)Termination phase: Saturation
% 13.04/2.09 % (15232)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on theBenchmark for (2983ds/770Mi)
% 13.04/2.09
% 13.04/2.09 % (15217)Memory used [KB]: 8187
% 13.04/2.09 % (15217)Time elapsed: 0.470 s
% 13.04/2.09 % (15217)Instructions burned: 996 (million)
% 13.04/2.09 % (15217)------------------------------
% 13.04/2.09 % (15217)------------------------------
% 13.04/2.10 % (15233)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on theBenchmark for (2983ds/794Mi)
% 13.18/2.17 % (15233)Refutation not found, incomplete strategy
% 13.18/2.17 % (15233)------------------------------
% 13.18/2.17 % (15233)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 13.18/2.17 % (15233)Termination reason: Refutation not found, incomplete strategy
% 13.18/2.17
% 13.18/2.17
% 13.18/2.17 % (15233)Memory used [KB]: 2302
% 14.10/2.17 % (15233)Time elapsed: 0.083 s
% 14.10/2.17 % (15233)Instructions burned: 111 (million)
% 14.10/2.17 % (15233)------------------------------
% 14.10/2.17 % (15233)------------------------------
% 14.10/2.18 % (15234)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on theBenchmark for (2982ds/464Mi)
% 14.10/2.24 % (15232)Refutation not found, incomplete strategy
% 14.10/2.24 % (15232)------------------------------
% 14.10/2.24 % (15232)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 14.10/2.24 % (15232)Termination reason: Refutation not found, incomplete strategy
% 14.10/2.24
% 14.10/2.24
% 14.10/2.24 % (15232)Memory used [KB]: 7419
% 14.10/2.24 % (15232)Time elapsed: 0.149 s
% 14.10/2.24 % (15232)Instructions burned: 302 (million)
% 14.10/2.24 % (15232)------------------------------
% 14.10/2.24 % (15232)------------------------------
% 14.68/2.25 % (15235)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on theBenchmark for (2981ds/1376Mi)
% 14.99/2.32 % (15209)Instruction limit reached!
% 14.99/2.32 % (15209)------------------------------
% 14.99/2.32 % (15209)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 14.99/2.32 % (15209)Termination reason: Unknown
% 14.99/2.32 % (15209)Termination phase: Saturation
% 14.99/2.32
% 14.99/2.32 % (15209)Memory used [KB]: 4605
% 14.99/2.32 % (15209)Time elapsed: 0.977 s
% 14.99/2.32 % (15209)Instructions burned: 1913 (million)
% 14.99/2.32 % (15209)------------------------------
% 14.99/2.32 % (15209)------------------------------
% 14.99/2.33 % (15236)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on theBenchmark for (2980ds/906Mi)
% 15.29/2.40 % (15234)Instruction limit reached!
% 15.29/2.40 % (15234)------------------------------
% 15.29/2.40 % (15234)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 15.29/2.40 % (15234)Termination reason: Unknown
% 15.29/2.40 % (15234)Termination phase: Saturation
% 15.29/2.40
% 15.29/2.40 % (15234)Memory used [KB]: 7419
% 15.29/2.40 % (15234)Time elapsed: 0.221 s
% 15.29/2.40 % (15234)Instructions burned: 464 (million)
% 15.29/2.40 % (15234)------------------------------
% 15.29/2.40 % (15234)------------------------------
% 15.29/2.42 % (15237)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on theBenchmark for (2979ds/434Mi)
% 15.29/2.43 % (15237)Refutation not found, incomplete strategy
% 15.29/2.43 % (15237)------------------------------
% 15.29/2.43 % (15237)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 15.29/2.43 % (15237)Termination reason: Refutation not found, incomplete strategy
% 15.29/2.43
% 15.29/2.43
% 15.29/2.43 % (15237)Memory used [KB]: 6268
% 15.29/2.43 % (15237)Time elapsed: 0.018 s
% 15.29/2.43 % (15237)Instructions burned: 31 (million)
% 15.29/2.43 % (15237)------------------------------
% 15.29/2.43 % (15237)------------------------------
% 16.02/2.45 % (15238)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on theBenchmark for (2979ds/865Mi)
% 16.02/2.47 % (15229)Instruction limit reached!
% 16.02/2.47 % (15229)------------------------------
% 16.02/2.47 % (15229)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 16.02/2.47 % (15229)Termination reason: Unknown
% 16.02/2.47 % (15229)Termination phase: Saturation
% 16.02/2.47
% 16.02/2.47 % (15229)Memory used [KB]: 8571
% 16.02/2.47 % (15229)Time elapsed: 0.457 s
% 16.02/2.47 % (15229)Instructions burned: 933 (million)
% 16.02/2.47 % (15229)------------------------------
% 16.02/2.47 % (15229)------------------------------
% 16.02/2.48 % (15238)Refutation not found, incomplete strategy
% 16.02/2.48 % (15238)------------------------------
% 16.02/2.48 % (15238)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 16.02/2.48 % (15238)Termination reason: Refutation not found, incomplete strategy
% 16.02/2.48
% 16.02/2.48
% 16.02/2.48 % (15238)Memory used [KB]: 6268
% 16.02/2.48 % (15238)Time elapsed: 0.028 s
% 16.02/2.48 % (15238)Instructions burned: 57 (million)
% 16.02/2.48 % (15238)------------------------------
% 16.02/2.48 % (15238)------------------------------
% 16.02/2.48 % (15239)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on theBenchmark for (2979ds/593Mi)
% 16.02/2.49 % (15240)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on theBenchmark for (2979ds/443Mi)
% 16.89/2.71 % (15240)Instruction limit reached!
% 16.89/2.71 % (15240)------------------------------
% 16.89/2.71 % (15240)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 16.89/2.71 % (15240)Termination reason: Unknown
% 16.89/2.71 % (15240)Termination phase: Saturation
% 16.89/2.71
% 16.89/2.71 % (15240)Memory used [KB]: 7291
% 16.89/2.71 % (15240)Time elapsed: 0.219 s
% 16.89/2.71 % (15240)Instructions burned: 443 (million)
% 16.89/2.71 % (15240)------------------------------
% 16.89/2.71 % (15240)------------------------------
% 16.89/2.72 % (15241)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on theBenchmark for (2976ds/594Mi)
% 16.89/2.74 % (15226)Instruction limit reached!
% 16.89/2.74 % (15226)------------------------------
% 16.89/2.74 % (15226)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 16.89/2.74 % (15226)Termination reason: Unknown
% 16.89/2.74 % (15226)Termination phase: Saturation
% 16.89/2.74
% 16.89/2.74 % (15226)Memory used [KB]: 14839
% 16.89/2.74 % (15226)Time elapsed: 0.917 s
% 16.89/2.74 % (15226)Instructions burned: 1827 (million)
% 16.89/2.74 % (15226)------------------------------
% 16.89/2.74 % (15226)------------------------------
% 17.52/2.76 % (15242)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on theBenchmark for (2976ds/327Mi)
% 17.52/2.76 % (15239)Instruction limit reached!
% 17.52/2.76 % (15239)------------------------------
% 17.52/2.76 % (15239)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 17.52/2.76 % (15239)Termination reason: Unknown
% 17.52/2.76 % (15239)Termination phase: Saturation
% 17.52/2.76
% 17.52/2.76 % (15239)Memory used [KB]: 7547
% 17.52/2.76 % (15239)Time elapsed: 0.283 s
% 17.52/2.76 % (15239)Instructions burned: 593 (million)
% 17.52/2.76 % (15239)------------------------------
% 17.52/2.76 % (15239)------------------------------
% 17.52/2.77 % (15236)Instruction limit reached!
% 17.52/2.77 % (15236)------------------------------
% 17.52/2.77 % (15236)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 17.52/2.77 % (15236)Termination reason: Unknown
% 17.52/2.77 % (15236)Termination phase: Saturation
% 17.52/2.77
% 17.52/2.77 % (15236)Memory used [KB]: 8443
% 17.52/2.77 % (15236)Time elapsed: 0.443 s
% 17.52/2.77 % (15236)Instructions burned: 906 (million)
% 17.52/2.77 % (15236)------------------------------
% 17.52/2.77 % (15236)------------------------------
% 17.52/2.78 % (15243)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on theBenchmark for (2976ds/5411Mi)
% 17.52/2.79 % (15244)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on theBenchmark for (2976ds/1762Mi)
% 17.52/2.79 % (15243)Refutation not found, incomplete strategy
% 17.52/2.79 % (15243)------------------------------
% 17.52/2.79 % (15243)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 17.52/2.79 % (15243)Termination reason: Refutation not found, incomplete strategy
% 17.52/2.79
% 17.52/2.79
% 17.52/2.79 % (15243)Memory used [KB]: 6140
% 17.52/2.79 % (15243)Time elapsed: 0.018 s
% 17.52/2.79 % (15243)Instructions burned: 30 (million)
% 17.52/2.79 % (15243)------------------------------
% 17.52/2.79 % (15243)------------------------------
% 17.52/2.81 % (15245)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on theBenchmark for (2975ds/96Mi)
% 19.26/2.85 % (15245)Instruction limit reached!
% 19.26/2.85 % (15245)------------------------------
% 19.26/2.85 % (15245)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 19.26/2.85 % (15245)Termination reason: Unknown
% 19.26/2.85 % (15245)Termination phase: Saturation
% 19.26/2.85
% 19.26/2.85 % (15245)Memory used [KB]: 6524
% 19.26/2.85 % (15245)Time elapsed: 0.043 s
% 19.26/2.85 % (15245)Instructions burned: 96 (million)
% 19.26/2.85 % (15245)------------------------------
% 19.26/2.85 % (15245)------------------------------
% 19.26/2.86 % (15246)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on theBenchmark for (2975ds/503Mi)
% 19.72/2.89 % (15246)Refutation not found, incomplete strategy
% 19.72/2.89 % (15246)------------------------------
% 19.72/2.89 % (15246)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 19.72/2.89 % (15246)Termination reason: Refutation not found, incomplete strategy
% 19.72/2.89
% 19.72/2.89
% 19.72/2.89 % (15246)Memory used [KB]: 6268
% 19.72/2.89 % (15246)Time elapsed: 0.027 s
% 19.72/2.89 % (15246)Instructions burned: 55 (million)
% 19.72/2.89 % (15246)------------------------------
% 19.72/2.89 % (15246)------------------------------
% 19.91/2.90 % (15247)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 (2974ds/90Mi)
% 20.05/2.92 % (15235)Instruction limit reached!
% 20.05/2.92 % (15235)------------------------------
% 20.05/2.92 % (15235)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 20.05/2.92 % (15235)Termination reason: Unknown
% 20.05/2.92 % (15235)Termination phase: Saturation
% 20.05/2.92
% 20.05/2.92 % (15235)Memory used [KB]: 9722
% 20.05/2.92 % (15235)Time elapsed: 0.667 s
% 20.05/2.92 % (15235)Instructions burned: 1376 (million)
% 20.05/2.92 % (15235)------------------------------
% 20.05/2.92 % (15235)------------------------------
% 20.05/2.93 % (15242)Instruction limit reached!
% 20.05/2.93 % (15242)------------------------------
% 20.05/2.93 % (15242)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 20.05/2.93 % (15242)Termination reason: Unknown
% 20.05/2.93 % (15242)Termination phase: Saturation
% 20.05/2.93
% 20.05/2.93 % (15242)Memory used [KB]: 9978
% 20.05/2.93 % (15242)Time elapsed: 0.173 s
% 20.05/2.93 % (15242)Instructions burned: 328 (million)
% 20.05/2.93 % (15242)------------------------------
% 20.05/2.93 % (15242)------------------------------
% 20.05/2.93 % (15248)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on theBenchmark for (2974ds/593Mi)
% 20.05/2.94 % (15247)Instruction limit reached!
% 20.05/2.94 % (15247)------------------------------
% 20.05/2.94 % (15247)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 20.05/2.94 % (15247)Termination reason: Unknown
% 20.05/2.94 % (15247)Termination phase: Property scanning
% 20.05/2.94
% 20.05/2.94 % (15247)Memory used [KB]: 2174
% 20.05/2.94 % (15247)Time elapsed: 0.039 s
% 20.05/2.94 % (15247)Instructions burned: 90 (million)
% 20.05/2.94 % (15247)------------------------------
% 20.05/2.94 % (15247)------------------------------
% 20.05/2.94 % (15249)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on theBenchmark for (2974ds/1512Mi)
% 20.05/2.95 % (15250)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on theBenchmark for (2974ds/569Mi)
% 20.64/3.03 % (15241)Instruction limit reached!
% 20.64/3.03 % (15241)------------------------------
% 20.64/3.03 % (15241)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 20.64/3.03 % (15241)Termination reason: Unknown
% 20.64/3.03 % (15241)Termination phase: Saturation
% 20.64/3.03
% 20.64/3.03 % (15241)Memory used [KB]: 7419
% 20.64/3.03 % (15241)Time elapsed: 0.321 s
% 20.64/3.03 % (15241)Instructions burned: 595 (million)
% 20.64/3.03 % (15241)------------------------------
% 20.64/3.03 % (15241)------------------------------
% 20.64/3.05 % (15251)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on theBenchmark for (2973ds/501Mi)
% 20.64/3.05 % (15249)Refutation not found, incomplete strategy
% 20.64/3.05 % (15249)------------------------------
% 20.64/3.05 % (15249)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 20.64/3.05 % (15249)Termination reason: Refutation not found, incomplete strategy
% 20.64/3.05
% 20.64/3.05
% 20.64/3.05 % (15249)Memory used [KB]: 8315
% 20.64/3.05 % (15249)Time elapsed: 0.111 s
% 20.64/3.05 % (15249)Instructions burned: 225 (million)
% 20.64/3.05 % (15249)------------------------------
% 20.64/3.05 % (15249)------------------------------
% 20.64/3.07 % (15252)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on theBenchmark for (2973ds/562Mi)
% 20.64/3.09 % (15252)Refutation not found, incomplete strategy
% 20.64/3.09 % (15252)------------------------------
% 20.64/3.09 % (15252)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 20.64/3.09 % (15252)Termination reason: Refutation not found, incomplete strategy
% 20.64/3.09
% 20.64/3.09
% 20.64/3.09 % (15252)Memory used [KB]: 6268
% 20.64/3.09 % (15252)Time elapsed: 0.029 s
% 20.64/3.09 % (15252)Instructions burned: 58 (million)
% 20.64/3.09 % (15252)------------------------------
% 20.64/3.09 % (15252)------------------------------
% 21.15/3.11 % (15253)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on theBenchmark for (2972ds/406Mi)
% 21.15/3.17 % (15253)Refutation not found, incomplete strategy
% 21.15/3.17 % (15253)------------------------------
% 21.15/3.17 % (15253)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 21.15/3.17 % (15253)Termination reason: Refutation not found, incomplete strategy
% 21.15/3.17
% 21.15/3.17
% 21.15/3.17 % (15253)Memory used [KB]: 6652
% 21.15/3.17 % (15253)Time elapsed: 0.060 s
% 21.15/3.17 % (15253)Instructions burned: 120 (million)
% 21.15/3.17 % (15253)------------------------------
% 21.15/3.17 % (15253)------------------------------
% 21.55/3.18 % (15254)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on theBenchmark for (2972ds/582Mi)
% 21.71/3.22 % (15250)Instruction limit reached!
% 21.71/3.22 % (15250)------------------------------
% 21.71/3.22 % (15250)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 21.71/3.22 % (15250)Termination reason: Unknown
% 21.71/3.22 % (15250)Termination phase: Saturation
% 21.71/3.22
% 21.71/3.22 % (15250)Memory used [KB]: 7547
% 21.71/3.22 % (15250)Time elapsed: 0.272 s
% 21.71/3.22 % (15250)Instructions burned: 569 (million)
% 21.71/3.22 % (15250)------------------------------
% 21.71/3.22 % (15250)------------------------------
% 21.71/3.24 % (15248)Instruction limit reached!
% 21.71/3.24 % (15248)------------------------------
% 21.71/3.24 % (15248)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 21.71/3.24 % (15248)Termination reason: Unknown
% 21.71/3.24 % (15248)Termination phase: Saturation
% 21.71/3.24
% 21.71/3.24 % (15248)Memory used [KB]: 7803
% 21.71/3.24 % (15248)Time elapsed: 0.306 s
% 21.71/3.24 % (15248)Instructions burned: 594 (million)
% 21.71/3.24 % (15248)------------------------------
% 21.71/3.24 % (15248)------------------------------
% 21.71/3.24 % (15255)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on theBenchmark for (2971ds/456Mi)
% 21.71/3.25 % (15256)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on theBenchmark for (2971ds/393Mi)
% 21.71/3.29 % (15251)Instruction limit reached!
% 21.71/3.29 % (15251)------------------------------
% 21.71/3.29 % (15251)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 21.71/3.29 % (15251)Termination reason: Unknown
% 21.71/3.29 % (15251)Termination phase: Saturation
% 21.71/3.29
% 21.71/3.29 % (15251)Memory used [KB]: 9850
% 21.71/3.29 % (15251)Time elapsed: 0.245 s
% 21.71/3.29 % (15251)Instructions burned: 502 (million)
% 21.71/3.29 % (15251)------------------------------
% 21.71/3.29 % (15251)------------------------------
% 21.71/3.31 % (15257)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on theBenchmark for (2971ds/1335Mi)
% 24.08/3.46 % (15256)Instruction limit reached!
% 24.08/3.46 % (15256)------------------------------
% 24.08/3.46 % (15256)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 24.08/3.46 % (15256)Termination reason: Unknown
% 24.08/3.46 % (15256)Termination phase: Saturation
% 24.08/3.46
% 24.08/3.46 % (15256)Memory used [KB]: 8059
% 24.08/3.46 % (15256)Time elapsed: 0.212 s
% 24.08/3.46 % (15256)Instructions burned: 394 (million)
% 24.08/3.46 % (15256)------------------------------
% 24.08/3.46 % (15256)------------------------------
% 24.08/3.46 % (15255)Instruction limit reached!
% 24.08/3.46 % (15255)------------------------------
% 24.08/3.46 % (15255)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 24.08/3.46 % (15255)Termination reason: Unknown
% 24.08/3.46 % (15255)Termination phase: Saturation
% 24.08/3.46
% 24.08/3.46 % (15255)Memory used [KB]: 7291
% 24.08/3.46 % (15255)Time elapsed: 0.226 s
% 24.08/3.46 % (15255)Instructions burned: 457 (million)
% 24.08/3.46 % (15255)------------------------------
% 24.08/3.46 % (15255)------------------------------
% 24.08/3.47 % (15258)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on theBenchmark for (2969ds/3373Mi)
% 24.08/3.48 % (15259)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on theBenchmark for (2969ds/474Mi)
% 24.08/3.49 % (15254)Instruction limit reached!
% 24.08/3.49 % (15254)------------------------------
% 24.08/3.49 % (15254)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 24.08/3.49 % (15254)Termination reason: Unknown
% 24.08/3.49 % (15254)Termination phase: Saturation
% 24.08/3.49
% 24.08/3.49 % (15254)Memory used [KB]: 8955
% 24.08/3.49 % (15254)Time elapsed: 0.314 s
% 24.08/3.49 % (15254)Instructions burned: 582 (million)
% 24.08/3.49 % (15254)------------------------------
% 24.08/3.49 % (15254)------------------------------
% 24.08/3.50 % (15244)Instruction limit reached!
% 24.08/3.50 % (15244)------------------------------
% 24.08/3.50 % (15244)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 24.08/3.50 % (15244)Termination reason: Unknown
% 24.08/3.50 % (15244)Termination phase: Saturation
% 24.08/3.50
% 24.08/3.50 % (15244)Memory used [KB]: 7803
% 24.08/3.50 % (15244)Time elapsed: 0.709 s
% 24.08/3.50 % (15244)Instructions burned: 1762 (million)
% 24.08/3.50 % (15244)------------------------------
% 24.08/3.50 % (15244)------------------------------
% 24.68/3.51 % (15260)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on theBenchmark for (2969ds/157Mi)
% 24.68/3.51 % (15261)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on theBenchmark for (2968ds/590Mi)
% 24.68/3.57 % (15260)Instruction limit reached!
% 24.68/3.57 % (15260)------------------------------
% 24.68/3.57 % (15260)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 24.68/3.57 % (15260)Termination reason: Unknown
% 24.68/3.57 % (15260)Termination phase: Saturation
% 24.68/3.57
% 24.68/3.57 % (15260)Memory used [KB]: 6524
% 24.68/3.57 % (15260)Time elapsed: 0.065 s
% 24.68/3.57 % (15260)Instructions burned: 158 (million)
% 24.68/3.57 % (15260)------------------------------
% 24.68/3.57 % (15260)------------------------------
% 25.08/3.58 % (15262)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on theBenchmark for (2968ds/104Mi)
% 25.08/3.63 % (15262)Instruction limit reached!
% 25.08/3.63 % (15262)------------------------------
% 25.08/3.63 % (15262)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 25.08/3.63 % (15262)Termination reason: Unknown
% 25.08/3.63 % (15262)Termination phase: Saturation
% 25.08/3.63
% 25.08/3.63 % (15262)Memory used [KB]: 6524
% 25.08/3.63 % (15262)Time elapsed: 0.046 s
% 25.08/3.63 % (15262)Instructions burned: 105 (million)
% 25.08/3.63 % (15262)------------------------------
% 25.08/3.63 % (15262)------------------------------
% 25.08/3.64 % (15263)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on theBenchmark for (2967ds/414Mi)
% 25.58/3.70 % (15259)Instruction limit reached!
% 25.58/3.70 % (15259)------------------------------
% 25.58/3.70 % (15259)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 25.58/3.70 % (15259)Termination reason: Unknown
% 25.58/3.70 % (15259)Termination phase: Saturation
% 25.58/3.70
% 25.58/3.70 % (15259)Memory used [KB]: 7291
% 25.58/3.70 % (15259)Time elapsed: 0.244 s
% 25.58/3.70 % (15259)Instructions burned: 474 (million)
% 25.58/3.70 % (15259)------------------------------
% 25.58/3.70 % (15259)------------------------------
% 25.58/3.71 % (15264)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on theBenchmark for (2966ds/715Mi)
% 25.58/3.71 % (15261)Instruction limit reached!
% 25.58/3.71 % (15261)------------------------------
% 25.58/3.71 % (15261)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 25.58/3.71 % (15261)Termination reason: Unknown
% 25.58/3.71 % (15261)Termination phase: Saturation
% 25.58/3.71
% 25.58/3.71 % (15261)Memory used [KB]: 7419
% 25.58/3.71 % (15261)Time elapsed: 0.205 s
% 25.58/3.71 % (15261)Instructions burned: 590 (million)
% 25.58/3.71 % (15261)------------------------------
% 25.58/3.71 % (15261)------------------------------
% 26.14/3.73 % (15265)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on theBenchmark for (2966ds/961Mi)
% 26.46/3.84 % (15263)Instruction limit reached!
% 26.46/3.84 % (15263)------------------------------
% 26.46/3.84 % (15263)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 26.46/3.84 % (15263)Termination reason: Unknown
% 26.46/3.84 % (15263)Termination phase: Saturation
% 26.46/3.84
% 26.46/3.84 % (15263)Memory used [KB]: 7164
% 26.46/3.84 % (15263)Time elapsed: 0.195 s
% 26.46/3.84 % (15263)Instructions burned: 414 (million)
% 26.46/3.84 % (15263)------------------------------
% 26.46/3.84 % (15263)------------------------------
% 26.46/3.85 % (15266)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on theBenchmark for (2965ds/1213Mi)
% 26.97/3.97 % (15208)Instruction limit reached!
% 26.97/3.97 % (15208)------------------------------
% 26.97/3.97 % (15208)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 26.97/3.97 % (15208)Termination reason: Unknown
% 26.97/3.97 % (15208)Termination phase: Saturation
% 26.97/3.97
% 26.97/3.97 % (15208)Memory used [KB]: 21620
% 26.97/3.97 % (15208)Time elapsed: 2.669 s
% 26.97/3.97 % (15208)Instructions burned: 5205 (million)
% 26.97/3.97 % (15208)------------------------------
% 26.97/3.97 % (15208)------------------------------
% 27.36/3.99 % (15267)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on theBenchmark for (2964ds/1979Mi)
% 28.80/4.03 % (15257)Instruction limit reached!
% 28.80/4.03 % (15257)------------------------------
% 28.80/4.03 % (15257)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 28.80/4.03 % (15257)Termination reason: Unknown
% 28.80/4.03 % (15257)Termination phase: Saturation
% 28.80/4.03
% 28.80/4.03 % (15257)Memory used [KB]: 9083
% 28.80/4.03 % (15257)Time elapsed: 0.718 s
% 28.80/4.03 % (15257)Instructions burned: 1336 (million)
% 28.80/4.03 % (15257)------------------------------
% 28.80/4.03 % (15257)------------------------------
% 29.00/4.04 % (15268)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on theBenchmark for (2963ds/481Mi)
% 29.04/4.05 % (15264)Instruction limit reached!
% 29.04/4.05 % (15264)------------------------------
% 29.04/4.05 % (15264)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 29.04/4.05 % (15264)Termination reason: Unknown
% 29.04/4.05 % (15264)Termination phase: Saturation
% 29.04/4.05
% 29.04/4.05 % (15264)Memory used [KB]: 4221
% 29.04/4.05 % (15264)Time elapsed: 0.343 s
% 29.04/4.05 % (15264)Instructions burned: 715 (million)
% 29.04/4.05 % (15264)------------------------------
% 29.04/4.05 % (15264)------------------------------
% 29.04/4.07 % (15269)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on theBenchmark for (2963ds/783Mi)
% 29.72/4.21 % (15265)Instruction limit reached!
% 29.72/4.21 % (15265)------------------------------
% 29.72/4.21 % (15265)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 29.72/4.21 % (15265)Termination reason: Unknown
% 29.72/4.21 % (15265)Termination phase: Saturation
% 29.72/4.21
% 29.72/4.21 % (15265)Memory used [KB]: 8059
% 29.72/4.21 % (15265)Time elapsed: 0.480 s
% 29.72/4.21 % (15265)Instructions burned: 961 (million)
% 29.72/4.21 % (15265)------------------------------
% 29.72/4.21 % (15265)------------------------------
% 29.72/4.22 % (15270)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on theBenchmark for (2961ds/432Mi)
% 29.72/4.25 % (15270)Refutation not found, incomplete strategy
% 29.72/4.25 % (15270)------------------------------
% 29.72/4.25 % (15270)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 29.72/4.25 % (15270)Termination reason: Refutation not found, incomplete strategy
% 29.72/4.25
% 29.72/4.25
% 29.72/4.25 % (15270)Memory used [KB]: 6268
% 29.72/4.25 % (15270)Time elapsed: 0.027 s
% 29.72/4.25 % (15270)Instructions burned: 55 (million)
% 29.72/4.25 % (15270)------------------------------
% 29.72/4.25 % (15270)------------------------------
% 30.30/4.25 % (15268)Instruction limit reached!
% 30.30/4.25 % (15268)------------------------------
% 30.30/4.25 % (15268)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 30.30/4.25 % (15268)Termination reason: Unknown
% 30.30/4.25 % (15268)Termination phase: Saturation
% 30.30/4.25
% 30.30/4.25 % (15268)Memory used [KB]: 7036
% 30.30/4.25 % (15268)Time elapsed: 0.212 s
% 30.30/4.25 % (15268)Instructions burned: 482 (million)
% 30.30/4.25 % (15268)------------------------------
% 30.30/4.25 % (15268)------------------------------
% 30.30/4.26 % (15271)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on theBenchmark for (2961ds/1670Mi)
% 30.30/4.26 % (15272)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on theBenchmark for (2961ds/90Mi)
% 30.73/4.30 % (15272)Instruction limit reached!
% 30.73/4.30 % (15272)------------------------------
% 30.73/4.30 % (15272)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 30.73/4.30 % (15272)Termination reason: Unknown
% 30.73/4.30 % (15272)Termination phase: Saturation
% 30.73/4.30
% 30.73/4.30 % (15272)Memory used [KB]: 6524
% 30.73/4.30 % (15272)Time elapsed: 0.040 s
% 30.73/4.30 % (15272)Instructions burned: 91 (million)
% 30.73/4.30 % (15272)------------------------------
% 30.73/4.30 % (15272)------------------------------
% 30.73/4.32 % (15273)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on theBenchmark for (2960ds/346Mi)
% 30.73/4.33 % (15230)Instruction limit reached!
% 30.73/4.33 % (15230)------------------------------
% 30.73/4.33 % (15230)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 30.73/4.33 % (15230)Termination reason: Unknown
% 30.73/4.33 % (15230)Termination phase: Saturation
% 30.73/4.33
% 30.73/4.33 % (15230)Memory used [KB]: 17654
% 30.73/4.33 % (15230)Time elapsed: 2.274 s
% 30.73/4.33 % (15230)Instructions burned: 4715 (million)
% 30.73/4.33 % (15230)------------------------------
% 30.73/4.33 % (15230)------------------------------
% 31.02/4.34 % (15274)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on theBenchmark for (2960ds/401Mi)
% 31.02/4.37 % (15266)Refutation not found, non-redundant clauses discarded% (15266)------------------------------
% 31.02/4.37 % (15266)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 31.02/4.37 % (15266)Termination reason: Refutation not found, non-redundant clauses discarded
% 31.02/4.37
% 31.02/4.37 % (15266)Memory used [KB]: 11897
% 31.02/4.37 % (15266)Time elapsed: 0.526 s
% 31.02/4.37 % (15266)Instructions burned: 1029 (million)
% 31.02/4.38 % (15266)------------------------------
% 31.02/4.38 % (15266)------------------------------
% 31.02/4.39 % (15275)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on theBenchmark for (2960ds/6454Mi)
% 31.26/4.42 % (15275)Refutation not found, incomplete strategy
% 31.26/4.42 % (15275)------------------------------
% 31.26/4.42 % (15275)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 31.26/4.42 % (15275)Termination reason: Refutation not found, incomplete strategy
% 31.26/4.42
% 31.26/4.42
% 31.26/4.42 % (15275)Memory used [KB]: 6268
% 31.26/4.42 % (15275)Time elapsed: 0.030 s
% 31.26/4.42 % (15275)Instructions burned: 60 (million)
% 31.26/4.42 % (15275)------------------------------
% 31.26/4.42 % (15275)------------------------------
% 31.26/4.42 % (15269)Instruction limit reached!
% 31.26/4.42 % (15269)------------------------------
% 31.26/4.42 % (15269)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 31.26/4.42 % (15269)Termination reason: Unknown
% 31.26/4.42 % (15269)Termination phase: Saturation
% 31.26/4.42
% 31.26/4.42 % (15269)Memory used [KB]: 8699
% 31.26/4.42 % (15269)Time elapsed: 0.360 s
% 31.26/4.42 % (15269)Instructions burned: 785 (million)
% 31.26/4.42 % (15269)------------------------------
% 31.26/4.42 % (15269)------------------------------
% 31.26/4.43 % (15276)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on theBenchmark for (2959ds/283Mi)
% 31.26/4.44 % (15277)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on theBenchmark for (2959ds/865Mi)
% 31.82/4.46 % (15273)Instruction limit reached!
% 31.82/4.46 % (15273)------------------------------
% 31.82/4.46 % (15273)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 31.82/4.46 % (15273)Termination reason: Unknown
% 31.82/4.46 % (15273)Termination phase: Saturation
% 31.82/4.46
% 31.82/4.46 % (15273)Memory used [KB]: 6908
% 31.82/4.46 % (15273)Time elapsed: 0.150 s
% 31.82/4.46 % (15273)Instructions burned: 347 (million)
% 31.82/4.46 % (15273)------------------------------
% 31.82/4.46 % (15273)------------------------------
% 31.82/4.48 % (15278)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on theBenchmark for (2959ds/4528Mi)
% 31.82/4.50 % (15278)Refutation not found, incomplete strategy
% 31.82/4.50 % (15278)------------------------------
% 31.82/4.50 % (15278)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 31.82/4.50 % (15278)Termination reason: Refutation not found, incomplete strategy
% 31.82/4.50
% 31.82/4.50
% 31.82/4.50 % (15278)Memory used [KB]: 1791
% 31.82/4.50 % (15278)Time elapsed: 0.025 s
% 31.82/4.50 % (15278)Instructions burned: 52 (million)
% 31.82/4.50 % (15278)------------------------------
% 31.82/4.50 % (15278)------------------------------
% 31.82/4.52 % (15279)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on theBenchmark for (2958ds/1001Mi)
% 31.82/4.53 % (15274)Instruction limit reached!
% 31.82/4.53 % (15274)------------------------------
% 31.82/4.53 % (15274)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 31.82/4.53 % (15274)Termination reason: Unknown
% 31.82/4.53 % (15274)Termination phase: Saturation
% 31.82/4.53
% 31.82/4.53 % (15274)Memory used [KB]: 7291
% 31.82/4.53 % (15274)Time elapsed: 0.186 s
% 31.82/4.53 % (15274)Instructions burned: 402 (million)
% 31.82/4.53 % (15274)------------------------------
% 31.82/4.53 % (15274)------------------------------
% 31.82/4.54 % (15280)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on theBenchmark for (2958ds/102Mi)
% 31.82/4.56 % (15276)Instruction limit reached!
% 31.82/4.56 % (15276)------------------------------
% 31.82/4.56 % (15276)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 31.82/4.56 % (15276)Termination reason: Unknown
% 31.82/4.56 % (15276)Termination phase: Saturation
% 31.82/4.56
% 31.82/4.56 % (15276)Memory used [KB]: 7164
% 31.82/4.56 % (15276)Time elapsed: 0.131 s
% 31.82/4.56 % (15276)Instructions burned: 283 (million)
% 31.82/4.56 % (15276)------------------------------
% 31.82/4.56 % (15276)------------------------------
% 31.82/4.58 % (15281)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on theBenchmark for (2958ds/952Mi)
% 33.21/4.58 % (15280)Instruction limit reached!
% 33.21/4.58 % (15280)------------------------------
% 33.21/4.58 % (15280)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 33.21/4.58 % (15280)Termination reason: Unknown
% 33.21/4.58 % (15280)Termination phase: Saturation
% 33.21/4.58
% 33.21/4.58 % (15280)Memory used [KB]: 6524
% 33.21/4.58 % (15280)Time elapsed: 0.044 s
% 33.21/4.58 % (15280)Instructions burned: 103 (million)
% 33.21/4.58 % (15280)------------------------------
% 33.21/4.58 % (15280)------------------------------
% 33.21/4.60 % (15282)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on theBenchmark for (2958ds/578Mi)
% 34.46/4.79 % (15277)Instruction limit reached!
% 34.46/4.79 % (15277)------------------------------
% 34.46/4.79 % (15277)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 34.46/4.79 % (15277)Termination reason: Unknown
% 34.46/4.79 % (15277)Termination phase: Saturation
% 34.46/4.79
% 34.46/4.79 % (15277)Memory used [KB]: 7164
% 34.46/4.79 % (15277)Time elapsed: 0.356 s
% 34.46/4.79 % (15277)Instructions burned: 866 (million)
% 34.46/4.79 % (15277)------------------------------
% 34.46/4.79 % (15277)------------------------------
% 34.46/4.81 % (15283)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on theBenchmark for (2956ds/643Mi)
% 34.88/4.89 % (15282)Instruction limit reached!
% 34.88/4.89 % (15282)------------------------------
% 34.88/4.89 % (15282)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 34.88/4.89 % (15282)Termination reason: Unknown
% 34.88/4.89 % (15282)Termination phase: Saturation
% 34.88/4.89
% 34.88/4.89 % (15282)Memory used [KB]: 8059
% 34.88/4.89 % (15282)Time elapsed: 0.294 s
% 34.88/4.89 % (15282)Instructions burned: 579 (million)
% 34.88/4.89 % (15282)------------------------------
% 34.88/4.89 % (15282)------------------------------
% 34.88/4.91 % (15284)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on theBenchmark for (2955ds/865Mi)
% 35.52/4.95 % (15284)Refutation not found, incomplete strategy
% 35.52/4.95 % (15284)------------------------------
% 35.52/4.95 % (15284)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 35.52/4.95 % (15284)Termination reason: Refutation not found, incomplete strategy
% 35.52/4.95
% 35.52/4.95
% 35.52/4.95 % (15284)Memory used [KB]: 6652
% 35.52/4.95 % (15284)Time elapsed: 0.045 s
% 35.52/4.95 % (15284)Instructions burned: 105 (million)
% 35.52/4.95 % (15284)------------------------------
% 35.52/4.95 % (15284)------------------------------
% 35.52/4.96 % (15285)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on theBenchmark for (2954ds/1174Mi)
% 35.81/4.99 % (15279)Instruction limit reached!
% 35.81/4.99 % (15279)------------------------------
% 35.81/4.99 % (15279)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 35.81/4.99 % (15279)Termination reason: Unknown
% 35.81/4.99 % (15279)Termination phase: Saturation
% 35.81/4.99
% 35.81/4.99 % (15279)Memory used [KB]: 8955
% 35.81/4.99 % (15279)Time elapsed: 0.483 s
% 35.81/4.99 % (15279)Instructions burned: 1002 (million)
% 35.81/4.99 % (15279)------------------------------
% 35.81/4.99 % (15279)------------------------------
% 35.81/5.00 % (15286)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on theBenchmark for (2954ds/644Mi)
% 35.81/5.00 % (15267)Instruction limit reached!
% 35.81/5.00 % (15267)------------------------------
% 35.81/5.00 % (15267)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 35.81/5.00 % (15267)Termination reason: Unknown
% 35.81/5.00 % (15267)Termination phase: Saturation
% 35.81/5.00
% 35.81/5.00 % (15267)Memory used [KB]: 8827
% 35.81/5.00 % (15267)Time elapsed: 1.016 s
% 35.81/5.00 % (15267)Instructions burned: 1980 (million)
% 35.81/5.00 % (15267)------------------------------
% 35.81/5.00 % (15267)------------------------------
% 35.81/5.02 % (15287)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on theBenchmark for (2953ds/1201Mi)
% 35.81/5.04 % (15271)Instruction limit reached!
% 35.81/5.04 % (15271)------------------------------
% 35.81/5.04 % (15271)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 35.81/5.04 % (15271)Termination reason: Unknown
% 35.81/5.04 % (15271)Termination phase: Saturation
% 35.81/5.04
% 35.81/5.04 % (15271)Memory used [KB]: 8827
% 35.81/5.04 % (15271)Time elapsed: 0.779 s
% 35.81/5.04 % (15271)Instructions burned: 1671 (million)
% 35.81/5.04 % (15271)------------------------------
% 35.81/5.04 % (15271)------------------------------
% 36.14/5.05 % (15288)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on theBenchmark for (2953ds/1046Mi)
% 36.14/5.05 % (15281)Instruction limit reached!
% 36.14/5.05 % (15281)------------------------------
% 36.14/5.05 % (15281)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 36.14/5.05 % (15281)Termination reason: Unknown
% 36.14/5.05 % (15281)Termination phase: Saturation
% 36.14/5.05
% 36.14/5.05 % (15281)Memory used [KB]: 8955
% 36.14/5.05 % (15281)Time elapsed: 0.479 s
% 36.14/5.05 % (15281)Instructions burned: 953 (million)
% 36.14/5.05 % (15281)------------------------------
% 36.14/5.05 % (15281)------------------------------
% 36.14/5.07 % (15289)lrs+1010_1:1_c=on:cnfonf=lazy_simp:fsr=off:hud=5:kws=arity:nm=32:plsq=on:plsqc=1:plsqr=642,29:prag=on:i=222:si=on:rtra=on_0 on theBenchmark for (2953ds/222Mi)
% 36.69/5.10 % (15283)Instruction limit reached!
% 36.69/5.10 % (15283)------------------------------
% 36.69/5.10 % (15283)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 36.69/5.10 % (15283)Termination reason: Unknown
% 36.69/5.10 % (15283)Termination phase: Saturation
% 36.69/5.10
% 36.69/5.10 % (15283)Memory used [KB]: 7547
% 36.69/5.10 % (15283)Time elapsed: 0.290 s
% 36.69/5.10 % (15283)Instructions burned: 644 (million)
% 36.69/5.10 % (15283)------------------------------
% 36.69/5.10 % (15283)------------------------------
% 36.69/5.11 % (15290)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 (2952ds/68Mi)
% 36.69/5.14 % (15258)Instruction limit reached!
% 36.69/5.14 % (15258)------------------------------
% 36.69/5.14 % (15258)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 36.69/5.14 % (15258)Termination reason: Unknown
% 36.69/5.14 % (15258)Termination phase: Saturation
% 36.69/5.14
% 36.69/5.14 % (15258)Memory used [KB]: 11641
% 36.69/5.14 % (15258)Time elapsed: 1.683 s
% 36.69/5.14 % (15258)Instructions burned: 3374 (million)
% 36.69/5.14 % (15258)------------------------------
% 36.69/5.14 % (15258)------------------------------
% 36.69/5.14 % (15290)Instruction limit reached!
% 36.69/5.14 % (15290)------------------------------
% 36.69/5.14 % (15290)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 36.69/5.14 % (15290)Termination reason: Unknown
% 36.69/5.14 % (15290)Termination phase: Property scanning
% 36.69/5.14
% 36.69/5.14 % (15290)Memory used [KB]: 1791
% 36.69/5.14 % (15290)Time elapsed: 0.031 s
% 36.69/5.14 % (15290)Instructions burned: 68 (million)
% 36.69/5.14 % (15290)------------------------------
% 36.69/5.14 % (15290)------------------------------
% 37.83/5.15 % (15291)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on theBenchmark for (2952ds/454Mi)
% 37.83/5.15 % (15292)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on theBenchmark for (2952ds/360Mi)
% 37.83/5.16 % (15289)Instruction limit reached!
% 37.83/5.16 % (15289)------------------------------
% 37.83/5.16 % (15289)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 37.83/5.16 % (15289)Termination reason: Unknown
% 37.83/5.16 % (15289)Termination phase: Saturation
% 37.83/5.16
% 37.83/5.16 % (15289)Memory used [KB]: 6652
% 37.83/5.16 % (15289)Time elapsed: 0.093 s
% 37.83/5.16 % (15289)Instructions burned: 222 (million)
% 37.83/5.16 % (15289)------------------------------
% 37.83/5.16 % (15289)------------------------------
% 37.98/5.17 % (15293)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on theBenchmark for (2952ds/157Mi)
% 37.98/5.24 % (15293)Instruction limit reached!
% 37.98/5.24 % (15293)------------------------------
% 37.98/5.24 % (15293)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 37.98/5.24 % (15293)Termination reason: Unknown
% 37.98/5.24 % (15293)Termination phase: Saturation
% 37.98/5.24
% 37.98/5.24 % (15293)Memory used [KB]: 6524
% 37.98/5.24 % (15293)Time elapsed: 0.067 s
% 37.98/5.24 % (15293)Instructions burned: 157 (million)
% 37.98/5.24 % (15293)------------------------------
% 37.98/5.24 % (15293)------------------------------
% 38.42/5.25 % (15294)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=5061:si=on:rtra=on_0 on theBenchmark for (2951ds/5061Mi)
% 38.54/5.29 % (15286)Instruction limit reached!
% 38.54/5.29 % (15286)------------------------------
% 38.54/5.29 % (15286)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 38.54/5.29 % (15286)Termination reason: Unknown
% 38.54/5.29 % (15286)Termination phase: Saturation
% 38.54/5.29
% 38.54/5.29 % (15286)Memory used [KB]: 7419
% 38.54/5.29 % (15286)Time elapsed: 0.304 s
% 38.54/5.29 % (15286)Instructions burned: 644 (million)
% 38.54/5.29 % (15286)------------------------------
% 38.54/5.29 % (15286)------------------------------
% 38.54/5.30 % (15295)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on theBenchmark for (2950ds/2401Mi)
% 38.54/5.31 % (15292)Instruction limit reached!
% 38.54/5.31 % (15292)------------------------------
% 38.54/5.31 % (15292)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 38.54/5.32 % (15292)Termination reason: Unknown
% 38.54/5.32 % (15292)Termination phase: Saturation
% 38.54/5.32
% 38.54/5.32 % (15292)Memory used [KB]: 7164
% 38.54/5.32 % (15292)Time elapsed: 0.164 s
% 38.54/5.32 % (15292)Instructions burned: 361 (million)
% 38.54/5.32 % (15292)------------------------------
% 38.54/5.32 % (15292)------------------------------
% 38.94/5.33 % (15296)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on theBenchmark for (2950ds/5798Mi)
% 39.06/5.35 % (15291)Instruction limit reached!
% 39.06/5.35 % (15291)------------------------------
% 39.06/5.35 % (15291)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 39.06/5.35 % (15291)Termination reason: Unknown
% 39.06/5.35 % (15291)Termination phase: Saturation
% 39.06/5.35
% 39.06/5.35 % (15291)Memory used [KB]: 11897
% 39.06/5.35 % (15291)Time elapsed: 0.202 s
% 39.06/5.35 % (15291)Instructions burned: 454 (million)
% 39.06/5.35 % (15291)------------------------------
% 39.06/5.35 % (15291)------------------------------
% 39.06/5.36 % (15297)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on theBenchmark for (2950ds/346Mi)
% 39.77/5.51 % (15287)Refutation not found, non-redundant clauses discarded% (15287)------------------------------
% 39.77/5.51 % (15287)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 39.77/5.51 % (15287)Termination reason: Refutation not found, non-redundant clauses discarded
% 39.77/5.51
% 39.77/5.51 % (15287)Memory used [KB]: 8827
% 39.77/5.51 % (15287)Time elapsed: 0.517 s
% 39.77/5.51 % (15287)Instructions burned: 1072 (million)
% 39.77/5.51 % (15287)------------------------------
% 39.77/5.51 % (15287)------------------------------
% 39.77/5.51 % (15297)Instruction limit reached!
% 39.77/5.51 % (15297)------------------------------
% 39.77/5.51 % (15297)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 39.77/5.51 % (15297)Termination reason: Unknown
% 39.77/5.51 % (15297)Termination phase: Saturation
% 39.77/5.51
% 39.77/5.51 % (15297)Memory used [KB]: 6908
% 39.77/5.51 % (15297)Time elapsed: 0.152 s
% 39.77/5.51 % (15297)Instructions burned: 347 (million)
% 39.77/5.51 % (15297)------------------------------
% 39.77/5.51 % (15297)------------------------------
% 39.77/5.53 % (15298)lrs+1002_1:1_av=off:bd=off:bet=on:e2e=on:fde=unused:fe=off:plsq=on:prag=on:sos=on:i=1321:si=on:rtra=on_0 on theBenchmark for (2948ds/1321Mi)
% 39.77/5.53 % (15299)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on theBenchmark for (2948ds/1312Mi)
% 40.18/5.54 % (15285)Instruction limit reached!
% 40.18/5.54 % (15285)------------------------------
% 40.18/5.54 % (15285)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 40.18/5.54 % (15285)Termination reason: Unknown
% 40.18/5.54 % (15285)Termination phase: Saturation
% 40.18/5.54
% 40.18/5.54 % (15285)Memory used [KB]: 8699
% 40.18/5.54 % (15285)Time elapsed: 0.581 s
% 40.18/5.54 % (15285)Instructions burned: 1174 (million)
% 40.18/5.54 % (15285)------------------------------
% 40.18/5.54 % (15285)------------------------------
% 40.18/5.56 % (15300)ott+2_8:1_add=large:c=on:cnfonf=off:e2e=on:er=filter:hud=5:plsq=on:plsqr=1,1:ss=axioms:i=672:si=on:rtra=on_0 on theBenchmark for (2948ds/672Mi)
% 40.24/5.59 % (15288)Instruction limit reached!
% 40.24/5.59 % (15288)------------------------------
% 40.24/5.59 % (15288)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 40.24/5.59 % (15288)Termination reason: Unknown
% 40.24/5.59 % (15288)Termination phase: Saturation
% 40.24/5.59
% 40.24/5.59 % (15288)Memory used [KB]: 8315
% 40.24/5.59 % (15288)Time elapsed: 0.566 s
% 40.24/5.59 % (15288)Instructions burned: 1047 (million)
% 40.24/5.59 % (15288)------------------------------
% 40.24/5.59 % (15288)------------------------------
% 40.24/5.61 % (15301)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=1897:si=on:rtra=on_0 on theBenchmark for (2947ds/1897Mi)
% 43.36/5.87 % (15300)Instruction limit reached!
% 43.36/5.87 % (15300)------------------------------
% 43.36/5.87 % (15300)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 43.36/5.87 % (15300)Termination reason: Unknown
% 43.36/5.87 % (15300)Termination phase: Saturation
% 43.36/5.87
% 43.36/5.87 % (15300)Memory used [KB]: 7931
% 43.36/5.87 % (15300)Time elapsed: 0.311 s
% 43.36/5.87 % (15300)Instructions burned: 673 (million)
% 43.36/5.87 % (15300)------------------------------
% 43.36/5.87 % (15300)------------------------------
% 43.36/5.88 % (15302)lrs+10_1:40_av=off:fde=unused:ntd=on:plsq=on:plsqc=2:plsqr=411915,1048576:sp=unary_frequency:tgt=full:i=1202:si=on:rtra=on_0 on theBenchmark for (2945ds/1202Mi)
% 44.86/6.08 % (15299)Instruction limit reached!
% 44.86/6.08 % (15299)------------------------------
% 44.86/6.08 % (15299)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 44.86/6.08 % (15299)Termination reason: Unknown
% 44.86/6.08 % (15299)Termination phase: Saturation
% 44.86/6.08
% 44.86/6.08 % (15299)Memory used [KB]: 7547
% 44.86/6.08 % (15299)Time elapsed: 0.553 s
% 44.86/6.08 % (15299)Instructions burned: 1313 (million)
% 44.86/6.08 % (15299)------------------------------
% 44.86/6.08 % (15299)------------------------------
% 44.86/6.09 % (15303)dis+21_1:1_au=on:cnfonf=lazy_pi_sigma_gen:hfsq=on:hfsqc=40:hfsqr=8,1:ntd=on:sos=on:sp=occurrence:ss=axioms:i=1493:si=on:rtra=on_0 on theBenchmark for (2943ds/1493Mi)
% 45.44/6.17 % (15298)Instruction limit reached!
% 45.44/6.17 % (15298)------------------------------
% 45.44/6.17 % (15298)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 45.44/6.17 % (15298)Termination reason: Unknown
% 45.44/6.17 % (15298)Termination phase: Saturation
% 45.44/6.17
% 45.44/6.17 % (15298)Memory used [KB]: 8059
% 45.44/6.17 % (15298)Time elapsed: 0.644 s
% 45.44/6.17 % (15298)Instructions burned: 1322 (million)
% 45.44/6.17 % (15298)------------------------------
% 45.44/6.17 % (15298)------------------------------
% 45.44/6.18 % (15304)dis+1010_3:1_av=off:fde=unused:hud=10:nwc=10.0:s2a=on:ss=axioms:i=7679:si=on:rtra=on_0 on theBenchmark for (2942ds/7679Mi)
% 45.96/6.25 % (15304)Refutation not found, incomplete strategy
% 45.96/6.25 % (15304)------------------------------
% 45.96/6.25 % (15304)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 45.96/6.25 % (15304)Termination reason: Refutation not found, incomplete strategy
% 45.96/6.25
% 45.96/6.25
% 45.96/6.25 % (15304)Memory used [KB]: 1918
% 45.96/6.25 % (15304)Time elapsed: 0.068 s
% 45.96/6.25 % (15304)Instructions burned: 134 (million)
% 45.96/6.25 % (15304)------------------------------
% 45.96/6.25 % (15304)------------------------------
% 45.96/6.27 % (15305)lrs+2_1:1024_anc=all:cnfonf=off:cs=on:e2e=on:nm=20:s2at=1.5:slsq=on:slsqr=1,2:spb=goal:i=340:si=on:rtra=on_0 on theBenchmark for (2941ds/340Mi)
% 47.08/6.31 % (15231)Instruction limit reached!
% 47.08/6.31 % (15231)------------------------------
% 47.08/6.31 % (15231)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 47.08/6.31 % (15231)Termination reason: Unknown
% 47.08/6.31 % (15231)Termination phase: Saturation
% 47.08/6.31
% 47.08/6.31 % (15231)Memory used [KB]: 26225
% 47.08/6.31 % (15231)Time elapsed: 4.229 s
% 47.08/6.31 % (15231)Instructions burned: 8251 (million)
% 47.08/6.31 % (15231)------------------------------
% 47.08/6.31 % (15231)------------------------------
% 47.08/6.33 % (15306)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=3672:si=on:rtra=on_0 on theBenchmark for (2940ds/3672Mi)
% 47.91/6.44 % (15305)Instruction limit reached!
% 47.91/6.44 % (15305)------------------------------
% 47.91/6.44 % (15305)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 47.91/6.44 % (15305)Termination reason: Unknown
% 47.91/6.44 % (15305)Termination phase: Saturation
% 47.91/6.44
% 47.91/6.44 % (15305)Memory used [KB]: 10106
% 47.91/6.44 % (15305)Time elapsed: 0.172 s
% 47.91/6.44 % (15305)Instructions burned: 340 (million)
% 47.91/6.44 % (15305)------------------------------
% 47.91/6.44 % (15305)------------------------------
% 47.91/6.45 % (15307)dis-1002_3:1_acc=model:bd=off:bsd=on:bsdmm=1:cnfonf=lazy_not_be_gen:fd=off:fe=off:ntd=on:nwc=10.0:piset=equals:plsq=on:plsqc=1:plsqr=32,1:sp=const_max:uhcvi=on:i=1535:si=on:rtra=on_0 on theBenchmark for (2939ds/1535Mi)
% 47.91/6.46 % (15301)Instruction limit reached!
% 47.91/6.46 % (15301)------------------------------
% 47.91/6.46 % (15301)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 47.91/6.46 % (15301)Termination reason: Unknown
% 47.91/6.46 % (15301)Termination phase: Saturation
% 47.91/6.46
% 47.91/6.46 % (15301)Memory used [KB]: 10618
% 47.91/6.46 % (15301)Time elapsed: 0.851 s
% 47.91/6.46 % (15301)Instructions burned: 1897 (million)
% 47.91/6.46 % (15301)------------------------------
% 47.91/6.46 % (15301)------------------------------
% 47.91/6.47 % (15308)dis+10_16:1_hud=1:plsq=on:plsqc=1:plsqr=32,1:prag=on:sd=1:sgt=64:ss=axioms:i=4637:si=on:rtra=on_0 on theBenchmark for (2939ds/4637Mi)
% 47.91/6.50 % (15302)Instruction limit reached!
% 47.91/6.50 % (15302)------------------------------
% 47.91/6.50 % (15302)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 47.91/6.50 % (15302)Termination reason: Unknown
% 47.91/6.50 % (15302)Termination phase: Saturation
% 47.91/6.50
% 47.91/6.50 % (15302)Memory used [KB]: 3965
% 47.91/6.50 % (15302)Time elapsed: 0.616 s
% 47.91/6.50 % (15302)Instructions burned: 1203 (million)
% 47.91/6.50 % (15302)------------------------------
% 47.91/6.50 % (15302)------------------------------
% 47.91/6.50 % (15308)Refutation not found, incomplete strategy
% 47.91/6.50 % (15308)------------------------------
% 47.91/6.50 % (15308)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 47.91/6.50 % (15308)Termination reason: Refutation not found, incomplete strategy
% 47.91/6.50
% 47.91/6.50
% 47.91/6.50 % (15308)Memory used [KB]: 6268
% 47.91/6.50 % (15308)Time elapsed: 0.028 s
% 47.91/6.50 % (15308)Instructions burned: 56 (million)
% 47.91/6.50 % (15308)------------------------------
% 47.91/6.50 % (15308)------------------------------
% 47.91/6.51 % (15309)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on theBenchmark for (2938ds/3174Mi)
% 47.91/6.51 % (15310)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on theBenchmark for (2938ds/307Mi)
% 48.48/6.57 % (15295)Instruction limit reached!
% 48.48/6.57 % (15295)------------------------------
% 48.48/6.57 % (15295)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 48.48/6.57 % (15295)Termination reason: Unknown
% 48.48/6.57 % (15295)Termination phase: Saturation
% 48.48/6.57
% 48.48/6.57 % (15295)Memory used [KB]: 12665
% 48.48/6.57 % (15295)Time elapsed: 1.274 s
% 48.48/6.57 % (15295)Instructions burned: 2401 (million)
% 48.48/6.57 % (15295)------------------------------
% 48.48/6.57 % (15295)------------------------------
% 48.75/6.59 % (15311)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=3619:si=on:rtra=on_0 on theBenchmark for (2938ds/3619Mi)
% 48.75/6.65 % (15310)Instruction limit reached!
% 48.75/6.65 % (15310)------------------------------
% 48.75/6.65 % (15310)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 48.75/6.65 % (15310)Termination reason: Unknown
% 48.75/6.65 % (15310)Termination phase: Saturation
% 48.75/6.65
% 48.75/6.65 % (15310)Memory used [KB]: 7164
% 48.75/6.65 % (15310)Time elapsed: 0.141 s
% 48.75/6.65 % (15310)Instructions burned: 308 (million)
% 48.75/6.65 % (15310)------------------------------
% 48.75/6.65 % (15310)------------------------------
% 49.13/6.67 % (15312)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on theBenchmark for (2937ds/2325Mi)
% 49.23/6.71 % (15311)Refutation not found, incomplete strategy
% 49.23/6.71 % (15311)------------------------------
% 49.23/6.71 % (15311)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 49.23/6.71 % (15311)Termination reason: Refutation not found, incomplete strategy
% 49.23/6.71
% 49.23/6.71
% 49.23/6.71 % (15311)Memory used [KB]: 8187
% 49.23/6.71 % (15311)Time elapsed: 0.123 s
% 49.23/6.71 % (15311)Instructions burned: 244 (million)
% 49.23/6.71 % (15311)------------------------------
% 49.23/6.71 % (15311)------------------------------
% 49.43/6.73 % (15313)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2341:si=on:rtra=on_0 on theBenchmark for (2936ds/2341Mi)
% 49.43/6.82 % (15303)Instruction limit reached!
% 49.43/6.82 % (15303)------------------------------
% 49.43/6.82 % (15303)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 49.43/6.82 % (15303)Termination reason: Unknown
% 49.43/6.82 % (15303)Termination phase: Saturation
% 49.43/6.82
% 49.43/6.82 % (15303)Memory used [KB]: 9466
% 49.43/6.82 % (15303)Time elapsed: 0.726 s
% 49.43/6.82 % (15303)Instructions burned: 1493 (million)
% 49.43/6.82 % (15303)------------------------------
% 49.43/6.82 % (15303)------------------------------
% 49.43/6.83 % (15314)lrs+1010_1:16_apa=on:bsd=on:cnfonf=off:hud=10:sac=on:sos=on:ss=axioms:i=7257:si=on:rtra=on_0 on theBenchmark for (2935ds/7257Mi)
% 51.86/6.94 % (15314)Refutation not found, incomplete strategy
% 51.86/6.94 % (15314)------------------------------
% 51.86/6.94 % (15314)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 51.86/6.94 % (15314)Termination reason: Refutation not found, incomplete strategy
% 51.86/6.94
% 51.86/6.94
% 51.86/6.94 % (15314)Memory used [KB]: 7164
% 51.86/6.94 % (15314)Time elapsed: 0.111 s
% 51.86/6.94 % (15314)Instructions burned: 217 (million)
% 51.86/6.94 % (15314)------------------------------
% 51.86/6.94 % (15314)------------------------------
% 51.86/6.96 % (15315)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=3710:si=on:rtra=on_0 on theBenchmark for (2934ds/3710Mi)
% 53.09/7.09 % (15307)Instruction limit reached!
% 53.09/7.09 % (15307)------------------------------
% 53.09/7.09 % (15307)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 53.09/7.09 % (15307)Termination reason: Unknown
% 53.09/7.09 % (15307)Termination phase: Saturation
% 53.09/7.09
% 53.09/7.09 % (15307)Memory used [KB]: 10234
% 53.09/7.09 % (15307)Time elapsed: 0.641 s
% 53.09/7.09 % (15307)Instructions burned: 1535 (million)
% 53.09/7.09 % (15307)------------------------------
% 53.09/7.09 % (15307)------------------------------
% 53.26/7.11 % (15316)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=326:si=on:rtra=on_0 on theBenchmark for (2933ds/326Mi)
% 53.33/7.13 % (15316)Refutation not found, incomplete strategy
% 53.33/7.13 % (15316)------------------------------
% 53.33/7.13 % (15316)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 53.33/7.13 % (15316)Termination reason: Refutation not found, incomplete strategy
% 53.33/7.13
% 53.33/7.13
% 53.33/7.13 % (15316)Memory used [KB]: 6268
% 53.33/7.13 % (15316)Time elapsed: 0.027 s
% 53.33/7.13 % (15316)Instructions burned: 54 (million)
% 53.33/7.13 % (15316)------------------------------
% 53.33/7.13 % (15316)------------------------------
% 53.33/7.15 % (15317)lrs+1010_1:64_au=on:c=on:e2e=on:flr=on:hfsq=on:hfsql=off:hfsqr=4,1:ins=1:ntd=on:sp=occurrence:i=1100:si=on:rtra=on_0 on theBenchmark for (2932ds/1100Mi)
% 58.47/7.77 % (15317)Instruction limit reached!
% 58.47/7.77 % (15317)------------------------------
% 58.47/7.77 % (15317)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 58.47/7.77 % (15317)Termination reason: Unknown
% 58.47/7.77 % (15317)Termination phase: Saturation
% 58.47/7.77
% 58.47/7.77 % (15317)Memory used [KB]: 17142
% 58.47/7.77 % (15317)Time elapsed: 0.622 s
% 58.47/7.77 % (15317)Instructions burned: 1100 (million)
% 58.47/7.77 % (15317)------------------------------
% 58.47/7.77 % (15317)------------------------------
% 58.47/7.78 % (15318)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on theBenchmark for (2926ds/406Mi)
% 59.15/7.84 % (15318)Refutation not found, incomplete strategy
% 59.15/7.84 % (15318)------------------------------
% 59.15/7.84 % (15318)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 59.15/7.84 % (15318)Termination reason: Refutation not found, incomplete strategy
% 59.15/7.84
% 59.15/7.84
% 59.15/7.84 % (15318)Memory used [KB]: 6652
% 59.15/7.84 % (15318)Time elapsed: 0.060 s
% 59.15/7.84 % (15318)Instructions burned: 122 (million)
% 59.15/7.84 % (15318)------------------------------
% 59.15/7.84 % (15318)------------------------------
% 59.15/7.86 % (15319)dis+1010_1:1_aac=none:bd=preordered:e2e=on:fde=none:fe=axiom:nm=16:nwc=10.0:prag=on:i=1871:si=on:rtra=on_0 on theBenchmark for (2925ds/1871Mi)
% 59.15/7.87 % (15294)Instruction limit reached!
% 59.15/7.87 % (15294)------------------------------
% 59.15/7.87 % (15294)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 59.15/7.87 % (15294)Termination reason: Unknown
% 59.15/7.87 % (15294)Termination phase: Saturation
% 59.15/7.87
% 59.15/7.87 % (15294)Memory used [KB]: 17014
% 59.15/7.87 % (15294)Time elapsed: 2.620 s
% 59.15/7.87 % (15294)Instructions burned: 5061 (million)
% 59.15/7.87 % (15294)------------------------------
% 59.15/7.87 % (15294)------------------------------
% 59.15/7.88 % (15312)Instruction limit reached!
% 59.15/7.88 % (15312)------------------------------
% 59.15/7.88 % (15312)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 59.15/7.88 % (15312)Termination reason: Unknown
% 59.15/7.88 % (15312)Termination phase: Saturation
% 59.15/7.88
% 59.15/7.88 % (15312)Memory used [KB]: 14456
% 59.15/7.88 % (15312)Time elapsed: 1.212 s
% 59.15/7.88 % (15312)Instructions burned: 2326 (million)
% 59.15/7.88 % (15312)------------------------------
% 59.15/7.88 % (15312)------------------------------
% 59.15/7.89 % (15320)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1194:si=on:rtra=on_0 on theBenchmark for (2925ds/1194Mi)
% 59.60/7.89 % (15321)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on theBenchmark for (2925ds/474Mi)
% 59.60/7.94 % (15313)Instruction limit reached!
% 59.60/7.94 % (15313)------------------------------
% 59.60/7.94 % (15313)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 59.60/7.94 % (15313)Termination reason: Unknown
% 59.60/7.94 % (15313)Termination phase: Saturation
% 59.60/7.94
% 59.60/7.94 % (15313)Memory used [KB]: 9466
% 59.60/7.94 % (15313)Time elapsed: 1.230 s
% 59.60/7.94 % (15313)Instructions burned: 2341 (million)
% 59.60/7.94 % (15313)------------------------------
% 59.60/7.94 % (15313)------------------------------
% 59.91/7.97 % (15322)dis+1010_1:1_au=on:cnfonf=lazy_gen:ins=3:plsq=on:plsqc=1:plsqr=15142123,262144:sp=reverse_arity:i=3115:si=on:rtra=on_0 on theBenchmark for (2924ds/3115Mi)
% 61.07/8.11 % (15321)Instruction limit reached!
% 61.07/8.11 % (15321)------------------------------
% 61.07/8.11 % (15321)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 61.07/8.11 % (15321)Termination reason: Unknown
% 61.07/8.11 % (15321)Termination phase: Saturation
% 61.07/8.11
% 61.07/8.11 % (15321)Memory used [KB]: 7291
% 61.07/8.11 % (15321)Time elapsed: 0.222 s
% 61.07/8.11 % (15321)Instructions burned: 474 (million)
% 61.07/8.11 % (15321)------------------------------
% 61.07/8.11 % (15321)------------------------------
% 61.07/8.13 % (15323)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=831:si=on:rtra=on_0 on theBenchmark for (2922ds/831Mi)
% 61.60/8.16 % (15309)Instruction limit reached!
% 61.60/8.16 % (15309)------------------------------
% 61.60/8.16 % (15309)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 61.60/8.16 % (15309)Termination reason: Unknown
% 61.60/8.16 % (15309)Termination phase: Saturation
% 61.60/8.16
% 61.60/8.16 % (15309)Memory used [KB]: 12537
% 61.60/8.16 % (15309)Time elapsed: 1.650 s
% 61.60/8.16 % (15309)Instructions burned: 3174 (million)
% 61.60/8.16 % (15309)------------------------------
% 61.60/8.16 % (15309)------------------------------
% 61.80/8.17 % (15324)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on theBenchmark for (2922ds/1188Mi)
% 61.80/8.17 % (15306)Instruction limit reached!
% 61.80/8.17 % (15306)------------------------------
% 61.80/8.17 % (15306)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 61.80/8.17 % (15306)Termination reason: Unknown
% 61.80/8.17 % (15306)Termination phase: Saturation
% 61.80/8.17
% 61.80/8.17 % (15306)Memory used [KB]: 12025
% 61.80/8.17 % (15306)Time elapsed: 1.848 s
% 61.80/8.17 % (15306)Instructions burned: 3673 (million)
% 61.80/8.17 % (15306)------------------------------
% 61.80/8.17 % (15306)------------------------------
% 61.80/8.19 % (15325)ott+1010_1:20_cnfonf=lazy_pi_sigma_gen:fe=axiom:plsq=on:plsqc=2:plsqr=32,1:sac=on:sos=all:i=2868:si=on:rtra=on_0 on theBenchmark for (2922ds/2868Mi)
% 61.80/8.21 % (15296)Instruction limit reached!
% 61.80/8.21 % (15296)------------------------------
% 61.80/8.21 % (15296)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 61.80/8.21 % (15296)Termination reason: Unknown
% 61.80/8.21 % (15296)Termination phase: Saturation
% 61.80/8.21
% 61.80/8.21 % (15296)Memory used [KB]: 18933
% 61.80/8.21 % (15296)Time elapsed: 2.885 s
% 61.80/8.21 % (15296)Instructions burned: 5799 (million)
% 61.80/8.21 % (15296)------------------------------
% 61.80/8.21 % (15296)------------------------------
% 62.13/8.23 % (15326)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1516:si=on:rtra=on_0 on theBenchmark for (2921ds/1516Mi)
% 62.13/8.24 % (15326)Refutation not found, incomplete strategy
% 62.13/8.24 % (15326)------------------------------
% 62.13/8.24 % (15326)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 62.13/8.24 % (15326)Termination reason: Refutation not found, incomplete strategy
% 62.13/8.24
% 62.13/8.24
% 62.13/8.24 % (15326)Memory used [KB]: 6268
% 62.13/8.24 % (15326)Time elapsed: 0.017 s
% 62.13/8.24 % (15326)Instructions burned: 28 (million)
% 62.13/8.24 % (15326)------------------------------
% 62.13/8.24 % (15326)------------------------------
% 62.28/8.26 % (15327)lrs+1002_1:20_afp=1000:au=on:bsd=on:cnfonf=lazy_not_gen_be_off:sos=all:sp=const_max:i=2321:si=on:rtra=on_0 on theBenchmark for (2921ds/2321Mi)
% 63.00/8.44 % (15320)Instruction limit reached!
% 63.00/8.44 % (15320)------------------------------
% 63.00/8.44 % (15320)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 63.00/8.44 % (15320)Termination reason: Unknown
% 63.00/8.44 % (15320)Termination phase: Saturation
% 63.00/8.44
% 63.00/8.44 % (15320)Memory used [KB]: 11385
% 63.00/8.44 % (15320)Time elapsed: 0.557 s
% 63.00/8.44 % (15320)Instructions burned: 1194 (million)
% 63.00/8.44 % (15320)------------------------------
% 63.00/8.44 % (15320)------------------------------
% 63.00/8.46 % (15328)dis+1010_1:1_au=on:bd=off:bsd=on:ixr=off:sp=const_max:i=2812:si=on:rtra=on_0 on theBenchmark for (2919ds/2812Mi)
% 63.11/8.53 % (15323)Instruction limit reached!
% 63.11/8.53 % (15323)------------------------------
% 63.11/8.53 % (15323)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 63.11/8.53 % (15323)Termination reason: Unknown
% 63.11/8.53 % (15323)Termination phase: Saturation
% 63.11/8.53
% 63.11/8.53 % (15323)Memory used [KB]: 7803
% 63.11/8.53 % (15323)Time elapsed: 0.408 s
% 63.11/8.53 % (15323)Instructions burned: 832 (million)
% 63.11/8.53 % (15323)------------------------------
% 63.11/8.53 % (15323)------------------------------
% 64.85/8.55 % (15329)dis+1002_8:1_bd=off:sd=1:sgt=16:ss=axioms:i=4604:si=on:rtra=on_0 on theBenchmark for (2918ds/4604Mi)
% 64.85/8.57 % (15329)Refutation not found, incomplete strategy
% 64.85/8.57 % (15329)------------------------------
% 64.85/8.57 % (15329)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 64.85/8.57 % (15329)Termination reason: Refutation not found, incomplete strategy
% 64.85/8.57
% 64.85/8.57
% 64.85/8.57 % (15329)Memory used [KB]: 6268
% 64.85/8.57 % (15329)Time elapsed: 0.027 s
% 64.85/8.57 % (15329)Instructions burned: 55 (million)
% 64.85/8.57 % (15329)------------------------------
% 64.85/8.57 % (15329)------------------------------
% 65.12/8.59 % (15330)ott+1002_1:4_c=on:chr=on:cnfonf=lazy_not_be_gen:hud=10:nm=10:piset=all_but_not_eq:rp=on:spb=goal:uhcvi=on:i=2678:si=on:rtra=on_0 on theBenchmark for (2918ds/2678Mi)
% 65.76/8.70 % (15324)Instruction limit reached!
% 65.76/8.70 % (15324)------------------------------
% 65.76/8.70 % (15324)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 65.76/8.70 % (15324)Termination reason: Unknown
% 65.76/8.70 % (15324)Termination phase: Saturation
% 65.76/8.70
% 65.76/8.70 % (15324)Memory used [KB]: 8699
% 65.76/8.70 % (15324)Time elapsed: 0.530 s
% 65.76/8.70 % (15324)Instructions burned: 1188 (million)
% 65.76/8.70 % (15324)------------------------------
% 65.76/8.70 % (15324)------------------------------
% 66.10/8.72 % (15331)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on theBenchmark for (2916ds/643Mi)
% 66.26/8.81 % (15319)Instruction limit reached!
% 66.26/8.81 % (15319)------------------------------
% 66.26/8.81 % (15319)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 66.26/8.81 % (15319)Termination reason: Unknown
% 66.26/8.81 % (15319)Termination phase: Saturation
% 66.26/8.81
% 66.26/8.81 % (15319)Memory used [KB]: 18293
% 66.26/8.81 % (15319)Time elapsed: 0.962 s
% 66.26/8.81 % (15319)Instructions burned: 1872 (million)
% 66.26/8.81 % (15319)------------------------------
% 66.26/8.81 % (15319)------------------------------
% 66.74/8.83 % (15332)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=458:si=on:rtra=on_0 on theBenchmark for (2915ds/458Mi)
% 67.01/8.90 % (15315)Instruction limit reached!
% 67.01/8.90 % (15315)------------------------------
% 67.01/8.90 % (15315)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 67.01/8.90 % (15315)Termination reason: Unknown
% 67.01/8.90 % (15315)Termination phase: Saturation
% 67.01/8.90
% 67.01/8.90 % (15315)Memory used [KB]: 16758
% 67.01/8.90 % (15315)Time elapsed: 1.948 s
% 67.01/8.90 % (15315)Instructions burned: 3710 (million)
% 67.01/8.90 % (15315)------------------------------
% 67.01/8.90 % (15315)------------------------------
% 67.01/8.92 % (15333)lrs+1010_1:1_anc=all_dependent:apa=on:au=on:bd=off:c=on:cnfonf=off:ntd=on:i=2546:si=on:rtra=on_0 on theBenchmark for (2914ds/2546Mi)
% 67.41/9.00 % (15331)Instruction limit reached!
% 67.41/9.00 % (15331)------------------------------
% 67.41/9.00 % (15331)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 67.41/9.00 % (15331)Termination reason: Unknown
% 67.41/9.00 % (15331)Termination phase: Saturation
% 67.41/9.00
% 67.41/9.00 % (15331)Memory used [KB]: 7547
% 67.41/9.00 % (15331)Time elapsed: 0.289 s
% 67.41/9.00 % (15331)Instructions burned: 644 (million)
% 67.41/9.00 % (15331)------------------------------
% 67.41/9.00 % (15331)------------------------------
% 67.90/9.02 % (15334)dis+21_1:1_acc=model:au=on:cnfonf=lazy_gen:ins=2:plsq=on:plsqc=1:plsqr=32,1:i=1432:si=on:rtra=on_0 on theBenchmark for (2913ds/1432Mi)
% 67.90/9.02 % (15332)Instruction limit reached!
% 67.90/9.02 % (15332)------------------------------
% 67.90/9.02 % (15332)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 67.90/9.02 % (15332)Termination reason: Unknown
% 67.90/9.02 % (15332)Termination phase: Saturation
% 67.90/9.02
% 67.90/9.02 % (15332)Memory used [KB]: 7036
% 67.90/9.02 % (15332)Time elapsed: 0.195 s
% 67.90/9.02 % (15332)Instructions burned: 458 (million)
% 67.90/9.02 % (15332)------------------------------
% 67.90/9.02 % (15332)------------------------------
% 67.90/9.04 % (15335)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=386:si=on:rtra=on_0 on theBenchmark for (2913ds/386Mi)
% 69.64/9.19 % (15322)First to succeed.
% 70.04/9.22 % (15335)Instruction limit reached!
% 70.04/9.22 % (15335)------------------------------
% 70.04/9.22 % (15335)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 70.04/9.22 % (15335)Termination reason: Unknown
% 70.04/9.22 % (15335)Termination phase: Saturation
% 70.04/9.22
% 70.04/9.22 % (15335)Memory used [KB]: 7291
% 70.04/9.22 % (15335)Time elapsed: 0.183 s
% 70.04/9.22 % (15335)Instructions burned: 387 (million)
% 70.04/9.22 % (15335)------------------------------
% 70.04/9.22 % (15335)------------------------------
% 70.04/9.23 % (15336)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on theBenchmark for (2911ds/360Mi)
% 70.45/9.25 % (15322)Refutation found. Thanks to Tanya!
% 70.45/9.25 % SZS status Theorem for theBenchmark
% 70.45/9.25 % SZS output start Proof for theBenchmark
% See solution above
% 70.45/9.26 % (15322)------------------------------
% 70.45/9.26 % (15322)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 70.45/9.26 % (15322)Termination reason: Refutation
% 70.45/9.26
% 70.45/9.26 % (15322)Memory used [KB]: 13560
% 70.45/9.26 % (15322)Time elapsed: 1.301 s
% 70.45/9.26 % (15322)Instructions burned: 2573 (million)
% 70.45/9.26 % (15322)------------------------------
% 70.45/9.26 % (15322)------------------------------
% 70.45/9.26 % (15109)Success in time 8.867 s
% 70.45/9.26 % Vampire---4.8 exiting
%------------------------------------------------------------------------------