%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : ALG267^1 : TPTP v8.2.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n021.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 18:20:31 EDT 2024
% Result : Theorem 2.12s 0.63s
% Output : Refutation 2.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 99
% Syntax : Number of formulae : 285 ( 222 unt; 57 typ; 0 def)
% Number of atoms : 6114 (1258 equ; 0 cnn)
% Maximal formula atoms : 3 ( 26 avg)
% Number of connectives : 27065 ( 216 ~; 0 |; 103 &;19776 @)
% ( 0 <=>;2971 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 1795 (1795 >; 0 *; 0 +; 0 <<)
% Number of symbols : 96 ( 91 usr; 46 con; 0-4 aty)
% (3955 !!; 44 ??; 0 @@+; 0 @@-)
% Number of variables : 4456 (4178 ^ 275 !; 2 ?;4456 :)
% ( 1 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
term: $tType ).
thf(type_def_7,type,
subst: $tType ).
thf(func_def_0,type,
term: $tType ).
thf(func_def_1,type,
subst: $tType ).
thf(func_def_2,type,
one: term ).
thf(func_def_3,type,
ap: term > term > term ).
thf(func_def_4,type,
lam: term > term ).
thf(func_def_5,type,
sub: term > subst > term ).
thf(func_def_6,type,
id: subst ).
thf(func_def_7,type,
sh: subst ).
thf(func_def_8,type,
push: term > subst > subst ).
thf(func_def_9,type,
comp: subst > subst > subst ).
thf(func_def_10,type,
var: term > $o ).
thf(func_def_18,type,
hoasap: subst > term > subst > term > term ).
thf(func_def_73,type,
hoaslam: subst > ( subst > term > term ) > term ).
thf(func_def_86,type,
hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).
thf(func_def_107,type,
hoasvar: subst > term > subst > $o ).
thf(func_def_121,type,
pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).
thf(func_def_142,type,
sK1: ( term > $o ) > subst > term ).
thf(func_def_143,type,
sK2: ( term > $o ) > term ).
thf(func_def_144,type,
sK3: ( term > $o ) > term ).
thf(func_def_145,type,
sK4: ( term > $o ) > term ).
thf(func_def_146,type,
sK5: ( subst > term > term ) > subst ).
thf(func_def_147,type,
sK6: ( subst > term > term ) > subst ).
thf(func_def_148,type,
sK7: ( subst > term > term ) > term ).
thf(func_def_149,type,
sK8: term ).
thf(func_def_150,type,
sK9: ( subst > term > subst > $o ) > term ).
thf(func_def_151,type,
sK10: ( subst > term > subst > $o ) > subst ).
thf(func_def_152,type,
sK11: ( subst > term > subst > $o ) > subst ).
thf(func_def_153,type,
sK12: ( subst > term > subst > $o ) > term ).
thf(func_def_154,type,
sK13: ( subst > term > subst > $o ) > subst ).
thf(func_def_155,type,
sK14: ( subst > term > subst > $o ) > subst ).
thf(func_def_156,type,
sK15: ( subst > term > subst > $o ) > term ).
thf(func_def_157,type,
sK16: ( subst > term > subst > $o ) > subst ).
thf(func_def_158,type,
sK17: ( subst > term > subst > $o ) > term ).
thf(func_def_159,type,
sK18: ( subst > term > subst > $o ) > subst ).
thf(func_def_160,type,
sK19: ( subst > term > subst > $o ) > subst ).
thf(func_def_161,type,
sK20: ( subst > term > subst > $o ) > subst ).
thf(func_def_162,type,
sK21: ( subst > term > subst > $o ) > subst ).
thf(func_def_163,type,
sK22: ( subst > term > subst > $o ) > subst ).
thf(func_def_164,type,
sK23: ( subst > term > subst > $o ) > subst ).
thf(func_def_165,type,
sK24: ( subst > term > subst > $o ) > term ).
thf(func_def_166,type,
sK25: ( subst > term > subst > $o ) > term ).
thf(func_def_167,type,
sK26: ( subst > term > subst > $o ) > subst ).
thf(func_def_168,type,
sK27: ( subst > term > subst > $o ) > term ).
thf(func_def_169,type,
sK28: ( subst > term > term ) > term ).
thf(func_def_170,type,
sK29: ( subst > term > term ) > subst ).
thf(func_def_171,type,
sK30: ( subst > term > term ) > subst ).
thf(func_def_172,type,
sK31: ( subst > term > term ) > subst ).
thf(func_def_173,type,
sK32: ( subst > term > term ) > term ).
thf(func_def_174,type,
sK33: ( subst > term > term ) > subst ).
thf(func_def_175,type,
sK34: ( term > $o ) > term ).
thf(func_def_176,type,
sK35: ( term > $o ) > term ).
thf(func_def_177,type,
sK36: ( term > $o ) > term ).
thf(func_def_178,type,
sK37: ( term > $o ) > term ).
thf(func_def_179,type,
sK38: ( term > $o ) > term ).
thf(func_def_180,type,
ph39:
!>[X0: $tType] : X0 ).
thf(f1185,plain,
$false,
inference(equality_resolution,[],[f1175]) ).
thf(f1175,plain,
! [X1: subst > term > term] :
( ( X1 @ sh @ one )
!= sK8 ),
inference(forward_demodulation,[],[f1174,f473]) ).
thf(f473,plain,
! [X1: term] :
( ( sub @ X1 @ id )
= X1 ),
inference(equality_proxy_clausification,[],[f472]) ).
thf(f472,plain,
! [X1: term] :
( $true
= ( ( sub @ X1 @ id )
= X1 ) ),
inference(beta_eta_normalization,[],[f471]) ).
thf(f471,plain,
! [X1: term] :
( $true
= ( ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 )
@ X1 ) ),
inference(pi_clausification,[],[f470]) ).
thf(f470,plain,
( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ),
inference(binary_proxy_clausification,[],[f462]) ).
thf(f462,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] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
=> ( ( !! @ 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 @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y0 @ Y2 ) @ Y1 )
= ( push @ ( sub @ Y0 @ Y1 ) @ ( comp @ Y2 @ 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 @ Y1 @ Y2 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y1 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y3 @ Y1 ) )
=> ( 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 @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 )
= ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y1 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) )
= ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y3 @ Y4 @ ( comp @ Y1 @ Y2 ) )
=> ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y4 )
=> ( Y0 @ Y1 @ Y3 @ ( comp @ Y2 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f460]) ).
thf(f460,plain,
( $false
= ( ( !! @ 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] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
=> ( ( !! @ 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 @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y0 @ Y2 ) @ Y1 )
= ( push @ ( sub @ Y0 @ Y1 ) @ ( comp @ Y2 @ 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 @ Y1 @ Y2 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y1 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y3 @ Y1 ) )
=> ( 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 @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 )
= ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y1 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) )
= ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y3 @ Y4 @ ( comp @ Y1 @ Y2 ) )
=> ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y4 )
=> ( Y0 @ Y1 @ Y3 @ ( comp @ Y2 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f459]) ).
thf(f459,plain,
( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( ap @ Y0 @ Y2 ) @ Y1 )
= ( ap @ ( sub @ Y0 @ Y1 ) @ ( sub @ Y2 @ 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] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
=> ( ( !! @ 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 @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y0 @ Y2 ) @ Y1 )
= ( push @ ( sub @ Y0 @ Y1 ) @ ( comp @ Y2 @ 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 @ Y1 @ Y2 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y1 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y3 @ Y1 ) )
=> ( 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 @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 )
= ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y1 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) )
= ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y3 @ Y4 @ ( comp @ Y1 @ Y2 ) )
=> ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y4 )
=> ( Y0 @ Y1 @ Y3 @ ( comp @ Y2 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f458]) ).
thf(f458,plain,
( $true
= ( ~ ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( ap @ Y0 @ Y2 ) @ Y1 )
= ( ap @ ( sub @ Y0 @ Y1 ) @ ( sub @ Y2 @ 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] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
=> ( ( !! @ 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 @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y0 @ Y2 ) @ Y1 )
= ( push @ ( sub @ Y0 @ Y1 ) @ ( comp @ Y2 @ 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 @ Y1 @ Y2 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y1 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y3 @ Y1 ) )
=> ( 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 @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 )
= ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y1 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) )
= ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y3 @ Y4 @ ( comp @ Y1 @ Y2 ) )
=> ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y4 )
=> ( Y0 @ Y1 @ Y3 @ ( comp @ Y2 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f457]) ).
thf(f457,plain,
( $true
= ( ~ ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( ap @ Y0 @ Y2 ) @ Y1 )
= ( ap @ ( sub @ Y0 @ Y1 ) @ ( sub @ Y2 @ 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] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
=> ( ( !! @ 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 @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y0 @ Y2 ) @ Y1 )
= ( push @ ( sub @ Y0 @ Y1 ) @ ( comp @ Y2 @ 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 @ Y1 @ Y2 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y1 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y3 @ Y1 ) )
=> ( 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 @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 )
= ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ 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
@ Y3
@ id
@ Y1 ) )
=> ( Y3 = 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
@ Y1
@ id
@ Y3 )
= ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y0
@ id
@ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) )
= ( sub @ ( Y1 @ Y2 @ 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 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ^ [Y3: subst,Y4: subst > term > term] : ( lam @ ( Y4 @ sh @ one ) )
@ id
@ ^ [Y3: subst,Y4: term] : ( Y0 @ Y3 @ Y4 ) )
!= ( ^ [Y3: subst,Y4: term,Y5: subst,Y6: term] : ( ap @ ( sub @ Y4 @ Y5 ) @ Y6 )
@ id
@ Y1
@ id
@ Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ~ ( ^ [Y1: subst,Y2: term,Y3: subst] : ( var @ ( sub @ Y2 @ Y3 ) )
@ id
@ ( ^ [Y1: subst,Y2: subst > term > term] : ( lam @ ( Y2 @ sh @ one ) )
@ id
@ ^ [Y1: subst,Y2: term] : ( Y0 @ Y1 @ Y2 ) )
@ id ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( ^ [Y2: subst,Y3: term,Y4: subst] : ( var @ ( sub @ Y3 @ Y4 ) )
@ id
@ ( ^ [Y2: subst,Y3: term,Y4: subst,Y5: term] : ( ap @ ( sub @ Y3 @ Y4 ) @ Y5 )
@ id
@ Y1
@ id
@ Y0 )
@ id ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y3 @ Y4 @ ( comp @ Y1 @ Y2 ) )
=> ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y4 )
=> ( Y0 @ Y1 @ Y3 @ ( comp @ Y2 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( ^ [Y2: subst,Y3: term,Y4: subst] : ( var @ ( sub @ Y3 @ Y4 ) )
@ id
@ Y1
@ id )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id
@ ( ^ [Y3: subst,Y4: term,Y5: subst,Y6: term] : ( ap @ ( sub @ Y4 @ Y5 ) @ Y6 )
@ id
@ Y1
@ id
@ Y2 )
@ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f391,f445]) ).
thf(f445,plain,
( hoasinduction_lem3b_gthm
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( ap @ Y0 @ Y2 ) @ Y1 )
= ( ap @ ( sub @ Y0 @ Y1 ) @ ( sub @ Y2 @ 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] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
=> ( ( !! @ 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 @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y0 @ Y2 ) @ Y1 )
= ( push @ ( sub @ Y0 @ Y1 ) @ ( comp @ Y2 @ 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 @ Y1 @ Y2 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y1 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y3 @ Y1 ) )
=> ( 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 @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 )
= ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ 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
@ Y3
@ id
@ Y1 ) )
=> ( Y3 = 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
@ Y1
@ id
@ Y3 )
= ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y0
@ id
@ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) )
= ( sub @ ( Y1 @ Y2 @ 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 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ^ [Y3: subst,Y4: subst > term > term] : ( lam @ ( Y4 @ sh @ one ) )
@ id
@ ^ [Y3: subst,Y4: term] : ( Y0 @ Y3 @ Y4 ) )
!= ( ^ [Y3: subst,Y4: term,Y5: subst,Y6: term] : ( ap @ ( sub @ Y4 @ Y5 ) @ Y6 )
@ id
@ Y1
@ id
@ Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ~ ( ^ [Y1: subst,Y2: term,Y3: subst] : ( var @ ( sub @ Y2 @ Y3 ) )
@ id
@ ( ^ [Y1: subst,Y2: subst > term > term] : ( lam @ ( Y2 @ sh @ one ) )
@ id
@ ^ [Y1: subst,Y2: term] : ( Y0 @ Y1 @ Y2 ) )
@ id ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( ^ [Y2: subst,Y3: term,Y4: subst] : ( var @ ( sub @ Y3 @ Y4 ) )
@ id
@ ( ^ [Y2: subst,Y3: term,Y4: subst,Y5: term] : ( ap @ ( sub @ Y3 @ Y4 ) @ Y5 )
@ id
@ Y1
@ id
@ Y0 )
@ id ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y3 @ Y4 @ ( comp @ Y1 @ Y2 ) )
=> ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y4 )
=> ( Y0 @ Y1 @ Y3 @ ( comp @ Y2 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( ^ [Y2: subst,Y3: term,Y4: subst] : ( var @ ( sub @ Y3 @ Y4 ) )
@ id
@ Y1
@ id )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id
@ ( ^ [Y3: subst,Y4: term,Y5: subst,Y6: term] : ( ap @ ( sub @ Y4 @ Y5 ) @ Y6 )
@ id
@ Y1
@ id
@ Y2 )
@ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f386,f340,f370,f382,f410,f406,f397,f399,f339,f381,f412,f358,f376,f378,f360,f379,f346,f383,f409,f357,f364,f388,f353,f342,f402,f351,f384,f359,f380,f419,f418,f430,f436,f437,f435,f421,f422,f414]) ).
thf(f414,plain,
( hoasinduction_lem3b
= ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ),
inference(cnf_transformation,[],[f181]) ).
thf(f181,plain,
( hoasinduction_lem3b
= ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ),
inference(fool_elimination,[],[f180]) ).
thf(f180,plain,
! [X0: term] :
? [X1: subst > term > term] :
( ( ( sub @ X0 @ ( push @ one @ sh ) )
= ( X1 @ sh @ one ) )
= hoasinduction_lem3b ),
inference(rectify,[],[f105]) ).
thf(f105,axiom,
! [X1: term] :
? [X10: subst > term > term] :
( ( ( X10 @ sh @ one )
= ( sub @ X1 @ ( push @ one @ sh ) ) )
= hoasinduction_lem3b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3b) ).
thf(f422,plain,
( hoasinduction_lem2
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id
@ ( ^ [Y3: subst,Y4: term,Y5: subst,Y6: term] : ( ap @ ( sub @ Y4 @ Y5 ) @ Y6 )
@ id
@ Y1
@ id
@ Y2 )
@ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f347,f394]) ).
thf(f394,plain,
( hoasap
= ( ^ [Y0: subst,Y1: term,Y2: subst,Y3: term] : ( ap @ ( sub @ Y1 @ Y2 ) @ Y3 ) ) ),
inference(cnf_transformation,[],[f299]) ).
thf(f299,plain,
( hoasap
= ( ^ [Y0: subst,Y1: term,Y2: subst,Y3: term] : ( ap @ ( sub @ Y1 @ Y2 ) @ Y3 ) ) ),
inference(fool_elimination,[],[f298]) ).
thf(f298,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/sandbox/benchmark/theBenchmark.p',hoasap) ).
thf(f347,plain,
( hoasinduction_lem2
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( hoasap @ id @ Y1 @ id @ Y2 ) @ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f148]) ).
thf(f148,plain,
( hoasinduction_lem2
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( hoasap @ id @ Y1 @ id @ Y2 ) @ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f147]) ).
thf(f147,plain,
( hoasinduction_lem2
= ( ! [X0: subst > term > subst > $o] :
( ! [X1: subst,X2: subst,X3: subst,X4: term] :
( ( X0 @ X3 @ X4 @ ( comp @ X1 @ X2 ) )
=> ( X0 @ ( comp @ X3 @ X1 ) @ ( sub @ X4 @ X1 ) @ X2 ) )
=> ( ! [X5: subst,X6: subst,X7: term,X8: subst] :
( ( X0 @ ( comp @ X5 @ X6 ) @ ( sub @ X7 @ X6 ) @ X8 )
=> ( X0 @ X5 @ X7 @ ( comp @ X6 @ X8 ) ) )
=> ( ! [X9: term,X10: term] :
( ( X0 @ id @ X10 @ id )
=> ( ( X0 @ id @ X9 @ id )
=> ( X0 @ id @ ( hoasap @ id @ X10 @ id @ X9 ) @ id ) ) )
=> ! [X11: term,X12: term] :
( ( X0 @ id @ X11 @ id )
=> ( ( X0 @ id @ X12 @ id )
=> ( X0 @ id @ ( ap @ X11 @ X12 ) @ id ) ) ) ) ) ) ) ),
inference(rectify,[],[f93]) ).
thf(f93,axiom,
( hoasinduction_lem2
= ( ! [X5: subst > term > subst > $o] :
( ! [X4: subst,X3: subst,X2: subst,X0: term] :
( ( X5 @ X2 @ X0 @ ( comp @ X4 @ X3 ) )
=> ( X5 @ ( comp @ X2 @ X4 ) @ ( sub @ X0 @ X4 ) @ X3 ) )
=> ( ! [X2: subst,X4: subst,X0: term,X3: subst] :
( ( X5 @ ( comp @ X2 @ X4 ) @ ( sub @ X0 @ X4 ) @ X3 )
=> ( X5 @ X2 @ X0 @ ( comp @ X4 @ X3 ) ) )
=> ( ! [X1: term,X0: term] :
( ( X5 @ id @ X0 @ id )
=> ( ( X5 @ id @ X1 @ id )
=> ( X5 @ id @ ( hoasap @ id @ X0 @ id @ X1 ) @ id ) ) )
=> ! [X0: term,X1: term] :
( ( X5 @ id @ X0 @ id )
=> ( ( X5 @ id @ X1 @ id )
=> ( X5 @ id @ ( ap @ X0 @ X1 ) @ id ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem2) ).
thf(f421,plain,
( hoasinduction_lem1
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y3 @ Y4 @ ( comp @ Y1 @ Y2 ) )
=> ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y4 )
=> ( Y0 @ Y1 @ Y3 @ ( comp @ Y2 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( ^ [Y2: subst,Y3: term,Y4: subst] : ( var @ ( sub @ Y3 @ Y4 ) )
@ id
@ Y1
@ id )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f392,f375]) ).
thf(f375,plain,
( hoasvar
= ( ^ [Y0: subst,Y1: term,Y2: subst] : ( var @ ( sub @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f231]) ).
thf(f231,plain,
( hoasvar
= ( ^ [Y0: subst,Y1: term,Y2: subst] : ( var @ ( sub @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f230]) ).
thf(f230,plain,
( ( ^ [X0: subst,X1: term,X2: subst] : ( var @ ( sub @ X1 @ X2 ) ) )
= hoasvar ),
inference(rectify,[],[f57]) ).
thf(f57,axiom,
( ( ^ [X2: subst,X0: term,X3: subst] : ( var @ ( sub @ X0 @ X3 ) ) )
= hoasvar ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasvar) ).
thf(f392,plain,
( hoasinduction_lem1
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y3 @ Y4 @ ( comp @ Y1 @ Y2 ) )
=> ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y4 )
=> ( Y0 @ Y1 @ Y3 @ ( comp @ Y2 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( hoasvar @ id @ Y1 @ id )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f177]) ).
thf(f177,plain,
( hoasinduction_lem1
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y3 @ Y4 @ ( comp @ Y1 @ Y2 ) )
=> ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y4 )
=> ( Y0 @ Y1 @ Y3 @ ( comp @ Y2 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( hoasvar @ id @ Y1 @ id )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f176]) ).
thf(f176,plain,
! [X0: subst > term > subst > $o] :
( ( ! [X1: term,X2: subst,X3: subst,X4: subst] :
( ( X0 @ X2 @ X1 @ ( comp @ X4 @ X3 ) )
=> ( X0 @ ( comp @ X2 @ X4 ) @ ( sub @ X1 @ X4 ) @ X3 ) )
=> ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( X0 @ ( comp @ X8 @ X7 ) @ ( sub @ X6 @ X7 ) @ X5 )
=> ( X0 @ X8 @ X6 @ ( comp @ X7 @ X5 ) ) )
=> ( ! [X9: term] :
( ( hoasvar @ id @ X9 @ id )
=> ( X0 @ id @ X9 @ id ) )
=> ! [X10: term] :
( ( var @ X10 )
=> ( X0 @ id @ X10 @ id ) ) ) ) )
= hoasinduction_lem1 ),
inference(rectify,[],[f90]) ).
thf(f90,axiom,
! [X5: subst > term > subst > $o] :
( ( ! [X0: term,X2: subst,X3: subst,X4: subst] :
( ( X5 @ X2 @ X0 @ ( comp @ X4 @ X3 ) )
=> ( X5 @ ( comp @ X2 @ X4 ) @ ( sub @ X0 @ X4 ) @ X3 ) )
=> ( ! [X3: subst,X0: term,X4: subst,X2: subst] :
( ( X5 @ ( comp @ X2 @ X4 ) @ ( sub @ X0 @ X4 ) @ X3 )
=> ( X5 @ X2 @ X0 @ ( comp @ X4 @ X3 ) ) )
=> ( ! [X0: term] :
( ( hoasvar @ id @ X0 @ id )
=> ( X5 @ id @ X0 @ id ) )
=> ! [X0: term] :
( ( var @ X0 )
=> ( X5 @ id @ X0 @ id ) ) ) ) )
= hoasinduction_lem1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem1) ).
thf(f435,plain,
( hoasapnotvar
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( ^ [Y2: subst,Y3: term,Y4: subst] : ( var @ ( sub @ Y3 @ Y4 ) )
@ id
@ ( ^ [Y2: subst,Y3: term,Y4: subst,Y5: term] : ( ap @ ( sub @ Y3 @ Y4 ) @ Y5 )
@ id
@ Y1
@ id
@ Y0 )
@ id ) ) ) ),
inference(definition_unfolding,[],[f355,f375,f394]) ).
thf(f355,plain,
( hoasapnotvar
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( hoasvar @ id @ ( hoasap @ id @ Y1 @ id @ Y0 ) @ id ) ) ) ),
inference(cnf_transformation,[],[f229]) ).
thf(f229,plain,
( hoasapnotvar
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( hoasvar @ id @ ( hoasap @ id @ Y1 @ id @ Y0 ) @ id ) ) ) ),
inference(fool_elimination,[],[f228]) ).
thf(f228,plain,
! [X0: term,X1: term] :
( ( ~ ( hoasvar @ id @ ( hoasap @ id @ X0 @ id @ X1 ) @ id ) )
= hoasapnotvar ),
inference(rectify,[],[f73]) ).
thf(f73,axiom,
! [X0: term,X1: term] :
( ( ~ ( hoasvar @ id @ ( hoasap @ id @ X0 @ id @ X1 ) @ id ) )
= hoasapnotvar ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasapnotvar) ).
thf(f437,plain,
( hoaslamnotvar
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ~ ( ^ [Y1: subst,Y2: term,Y3: subst] : ( var @ ( sub @ Y2 @ Y3 ) )
@ id
@ ( ^ [Y1: subst,Y2: subst > term > term] : ( lam @ ( Y2 @ sh @ one ) )
@ id
@ ^ [Y1: subst,Y2: term] : ( Y0 @ Y1 @ Y2 ) )
@ id ) ) ) ),
inference(definition_unfolding,[],[f377,f375,f369]) ).
thf(f369,plain,
( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( lam @ ( Y1 @ sh @ one ) ) ) ),
inference(cnf_transformation,[],[f199]) ).
thf(f199,plain,
( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( lam @ ( Y1 @ sh @ one ) ) ) ),
inference(fool_elimination,[],[f198]) ).
thf(f198,plain,
( ( ^ [X0: subst,X1: subst > term > term] : ( lam @ ( X1 @ sh @ one ) ) )
= hoaslam ),
inference(rectify,[],[f56]) ).
thf(f56,axiom,
( ( ^ [X2: subst,X10: subst > term > term] : ( lam @ ( X10 @ sh @ one ) ) )
= hoaslam ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoaslam) ).
thf(f377,plain,
( hoaslamnotvar
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ~ ( hoasvar @ id
@ ( hoaslam @ id
@ ^ [Y1: subst,Y2: term] : ( Y0 @ Y1 @ Y2 ) )
@ id ) ) ) ),
inference(cnf_transformation,[],[f332]) ).
thf(f332,plain,
( hoaslamnotvar
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ~ ( hoasvar @ id
@ ( hoaslam @ id
@ ^ [Y1: subst,Y2: term] : ( Y0 @ Y1 @ Y2 ) )
@ id ) ) ) ),
inference(fool_elimination,[],[f331]) ).
thf(f331,plain,
( hoaslamnotvar
= ( ! [X0: subst > term > term] :
( ! [X1: term,X2: subst,X3: subst] :
( ( sub @ ( X0 @ X3 @ X1 ) @ X2 )
= ( X0 @ ( comp @ X3 @ X2 ) @ ( sub @ X1 @ X2 ) ) )
=> ~ ( hoasvar @ id
@ ( hoaslam @ id
@ ^ [X4: subst,X5: term] : ( X0 @ X4 @ X5 ) )
@ id ) ) ) ),
inference(rectify,[],[f70]) ).
thf(f70,axiom,
( hoaslamnotvar
= ( ! [X10: subst > term > term] :
( ! [X0: term,X3: subst,X2: subst] :
( ( sub @ ( X10 @ X2 @ X0 ) @ X3 )
= ( X10 @ ( comp @ X2 @ X3 ) @ ( sub @ X0 @ X3 ) ) )
=> ~ ( hoasvar @ id
@ ( hoaslam @ id
@ ^ [X2: subst,X0: term] : ( X10 @ X2 @ X0 ) )
@ id ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoaslamnotvar) ).
thf(f436,plain,
( hoaslamnotap
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ^ [Y3: subst,Y4: subst > term > term] : ( lam @ ( Y4 @ sh @ one ) )
@ id
@ ^ [Y3: subst,Y4: term] : ( Y0 @ Y3 @ Y4 ) )
!= ( ^ [Y3: subst,Y4: term,Y5: subst,Y6: term] : ( ap @ ( sub @ Y4 @ Y5 ) @ Y6 )
@ id
@ Y1
@ id
@ Y2 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f350,f369,f394]) ).
thf(f350,plain,
( hoaslamnotap
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( hoaslam @ id
@ ^ [Y3: subst,Y4: term] : ( Y0 @ Y3 @ Y4 ) )
!= ( hoasap @ id @ Y1 @ id @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f146]) ).
thf(f146,plain,
( hoaslamnotap
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( hoaslam @ id
@ ^ [Y3: subst,Y4: term] : ( Y0 @ Y3 @ Y4 ) )
!= ( hoasap @ id @ Y1 @ id @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f145]) ).
thf(f145,plain,
( hoaslamnotap
= ( ! [X0: subst > term > term] :
( ! [X1: subst,X2: subst,X3: term] :
( ( X0 @ ( comp @ X1 @ X2 ) @ ( sub @ X3 @ X2 ) )
= ( sub @ ( X0 @ X1 @ X3 ) @ X2 ) )
=> ! [X4: term,X5: term] :
( ( hoaslam @ id
@ ^ [X6: subst,X7: term] : ( X0 @ X6 @ X7 ) )
!= ( hoasap @ id @ X5 @ id @ X4 ) ) ) ) ),
inference(rectify,[],[f67]) ).
thf(f67,axiom,
( hoaslamnotap
= ( ! [X10: subst > term > term] :
( ! [X2: subst,X3: subst,X0: term] :
( ( sub @ ( X10 @ X2 @ X0 ) @ X3 )
= ( X10 @ ( comp @ X2 @ X3 ) @ ( sub @ X0 @ X3 ) ) )
=> ! [X1: term,X0: term] :
( ( hoaslam @ id
@ ^ [X2: subst,X6: term] : ( X10 @ X2 @ X6 ) )
!= ( hoasap @ id @ X0 @ id @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoaslamnotap) ).
thf(f430,plain,
( hoaslaminj
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) )
= ( sub @ ( Y1 @ Y2 @ 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 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f367,f369,f369]) ).
thf(f367,plain,
( hoaslaminj
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) )
= ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 ) ) ) ) )
=> ( ( ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y0 @ Y2 @ Y3 ) )
= ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f243]) ).
thf(f243,plain,
( hoaslaminj
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) )
= ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 ) ) ) ) )
=> ( ( ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y0 @ Y2 @ Y3 ) )
= ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f242]) ).
thf(f242,plain,
( hoaslaminj
= ( ! [X0: subst > term > term] :
( ! [X1: subst,X2: subst,X3: term] :
( ( X0 @ ( comp @ X1 @ X2 ) @ ( sub @ X3 @ X2 ) )
= ( sub @ ( X0 @ X1 @ X3 ) @ X2 ) )
=> ! [X4: subst > term > term] :
( ! [X5: subst,X6: term,X7: subst] :
( ( X4 @ ( comp @ X7 @ X5 ) @ ( sub @ X6 @ X5 ) )
= ( sub @ ( X4 @ X7 @ X6 ) @ X5 ) )
=> ( ( ( hoaslam @ id
@ ^ [X8: subst,X9: term] : ( X0 @ X8 @ X9 ) )
= ( hoaslam @ id
@ ^ [X10: subst,X11: term] : ( X4 @ X10 @ X11 ) ) )
=> ! [X12: subst,X13: term] :
( ( X0 @ X12 @ X13 )
= ( X4 @ X12 @ X13 ) ) ) ) ) ) ),
inference(rectify,[],[f64]) ).
thf(f64,axiom,
( hoaslaminj
= ( ! [X10: subst > term > term] :
( ! [X2: subst,X3: subst,X0: term] :
( ( 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 ) ) )
=> ! [X2: subst,X0: term] :
( ( X10 @ X2 @ X0 )
= ( X11 @ X2 @ X0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoaslaminj) ).
thf(f418,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
@ Y1
@ id
@ Y3 )
= ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y0
@ id
@ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f354,f394,f394]) ).
thf(f354,plain,
( hoasapinj2
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( hoasap @ id @ Y1 @ id @ Y3 )
= ( hoasap @ id @ Y0 @ id @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f122]) ).
thf(f122,plain,
( hoasapinj2
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( hoasap @ id @ Y1 @ id @ Y3 )
= ( hoasap @ id @ Y0 @ id @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f121]) ).
thf(f121,plain,
! [X0: term,X1: term,X2: term,X3: term] :
( ( ( ( hoasap @ id @ X2 @ id @ X0 )
= ( hoasap @ id @ X3 @ id @ X1 ) )
=> ( 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/sandbox/benchmark/theBenchmark.p',hoasapinj2) ).
thf(f419,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
@ Y0
@ id
@ Y2 )
= ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y3
@ id
@ Y1 ) )
=> ( Y3 = Y0 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f403,f394,f394]) ).
thf(f403,plain,
( hoasapinj1
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( hoasap @ id @ Y0 @ id @ Y2 )
= ( hoasap @ id @ Y3 @ id @ Y1 ) )
=> ( Y3 = Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f279]) ).
thf(f279,plain,
( hoasapinj1
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( hoasap @ id @ Y0 @ id @ Y2 )
= ( hoasap @ id @ Y3 @ id @ Y1 ) )
=> ( Y3 = Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f278]) ).
thf(f278,plain,
( hoasapinj1
= ( ! [X0: term,X1: term,X2: term,X3: term] :
( ( ( hoasap @ id @ X3 @ id @ X1 )
= ( hoasap @ id @ X0 @ id @ X2 ) )
=> ( X0 = X3 ) ) ) ),
inference(rectify,[],[f58]) ).
thf(f58,axiom,
( hoasapinj1
= ( ! [X1: term,X6: term,X7: term,X0: term] :
( ( ( hoasap @ id @ X0 @ id @ X6 )
= ( hoasap @ id @ X1 @ id @ X7 ) )
=> ( X0 = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasapinj1) ).
thf(f380,plain,
( termmset
= ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 )
= ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f225]) ).
thf(f225,plain,
( termmset
= ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 )
= ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f224]) ).
thf(f224,plain,
( ! [X0: subst,X1: subst,X2: term] :
( ( sub @ ( sub @ X2 @ X1 ) @ X0 )
= ( sub @ X2 @ ( comp @ X1 @ X0 ) ) )
& ! [X3: term] :
( ( ( sub @ X3 @ id )
= X3 )
= termmset ) ),
inference(rectify,[],[f52]) ).
thf(f52,axiom,
( ! [X3: subst,X2: subst,X0: term] :
( ( sub @ ( sub @ X0 @ X2 ) @ X3 )
= ( sub @ X0 @ ( comp @ X2 @ X3 ) ) )
& ! [X0: term] :
( ( ( sub @ X0 @ id )
= X0 )
= termmset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',termmset) ).
thf(f359,plain,
( substmonoid
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) ) ),
inference(cnf_transformation,[],[f239]) ).
thf(f239,plain,
( substmonoid
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) ) ),
inference(fool_elimination,[],[f238]) ).
thf(f238,plain,
( ! [X0: subst] :
( ( comp @ id @ X0 )
= X0 )
& ! [X1: subst] :
( ( comp @ X1 @ id )
= X1 )
& ! [X2: subst,X3: subst,X4: subst] :
( ( ( comp @ ( comp @ X4 @ X3 ) @ X2 )
= ( comp @ X4 @ ( comp @ X3 @ X2 ) ) )
= substmonoid ) ),
inference(rectify,[],[f49]) ).
thf(f49,axiom,
( ! [X2: subst] :
( ( comp @ id @ X2 )
= X2 )
& ! [X2: subst] :
( ( comp @ X2 @ id )
= X2 )
& ! [X4: subst,X3: subst,X2: subst] :
( ( ( comp @ ( comp @ X2 @ X3 ) @ X4 )
= ( comp @ X2 @ ( comp @ X3 @ X4 ) ) )
= substmonoid ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',substmonoid) ).
thf(f384,plain,
( induction2
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f150]) ).
thf(f150,plain,
( induction2
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f149]) ).
thf(f149,plain,
! [X0: term > $o] :
( ( ! [X1: term] :
( ( var @ X1 )
=> ( X0 @ X1 ) )
=> ( ! [X2: term,X3: term] :
( ( X0 @ X2 )
=> ( ( X0 @ X3 )
=> ( X0 @ ( ap @ X2 @ X3 ) ) ) )
=> ( ! [X4: term] :
( ! [X5: term] :
( ( X0 @ X5 )
=> ( X0 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X0 @ ( lam @ X4 ) ) )
=> ! [X6: term] : ( X0 @ X6 ) ) ) )
= induction2 ),
inference(rectify,[],[f46]) ).
thf(f46,axiom,
! [X5: term > $o] :
( ( ! [X0: term] :
( ( var @ X0 )
=> ( X5 @ X0 ) )
=> ( ! [X0: term,X1: term] :
( ( X5 @ X0 )
=> ( ( X5 @ X1 )
=> ( X5 @ ( ap @ X0 @ X1 ) ) ) )
=> ( ! [X0: term] :
( ! [X1: term] :
( ( X5 @ X1 )
=> ( X5 @ ( sub @ X0 @ ( push @ X1 @ id ) ) ) )
=> ( X5 @ ( lam @ X0 ) ) )
=> ! [X0: term] : ( X5 @ X0 ) ) ) )
= induction2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',induction2) ).
thf(f351,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,[],[f168]) ).
thf(f168,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,[],[f167]) ).
thf(f167,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/sandbox/benchmark/theBenchmark.p',induction2lem) ).
thf(f402,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,[],[f315]) ).
thf(f315,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,[],[f314]) ).
thf(f314,plain,
! [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 ) ) ) ) ) )
= pushprop ),
inference(rectify,[],[f39]) ).
thf(f39,axiom,
! [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 ) ) ) ) ) )
= pushprop ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop) ).
thf(f342,plain,
( induction
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f124]) ).
thf(f124,plain,
( induction
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f123]) ).
thf(f123,plain,
! [X0: term > $o] :
( ( ! [X1: term] :
( ( var @ X1 )
=> ( X0 @ X1 ) )
=> ( ! [X2: term,X3: term] :
( ( X0 @ X2 )
=> ( ( X0 @ X3 )
=> ( X0 @ ( ap @ X2 @ X3 ) ) ) )
=> ( ! [X4: term] :
( ( X0 @ X4 )
=> ( X0 @ ( lam @ X4 ) ) )
=> ! [X5: term] : ( X0 @ X5 ) ) ) )
= induction ),
inference(rectify,[],[f23]) ).
thf(f23,axiom,
! [X5: term > $o] :
( ( ! [X0: term] :
( ( var @ X0 )
=> ( X5 @ X0 ) )
=> ( ! [X0: term,X1: term] :
( ( X5 @ X0 )
=> ( ( X5 @ X1 )
=> ( X5 @ ( ap @ X0 @ X1 ) ) ) )
=> ( ! [X0: term] :
( ( X5 @ X0 )
=> ( X5 @ ( lam @ X0 ) ) )
=> ! [X0: term] : ( X5 @ X0 ) ) ) )
= induction ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',induction) ).
thf(f353,plain,
( lamnotvar
= ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f248]) ).
thf(f248,plain,
( lamnotvar
= ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) ) ),
inference(fool_elimination,[],[f247]) ).
thf(f247,plain,
( lamnotvar
= ( ! [X0: term] :
~ ( var @ ( lam @ X0 ) ) ) ),
inference(rectify,[],[f22]) ).
thf(f22,axiom,
( lamnotvar
= ( ! [X0: term] :
~ ( var @ ( lam @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamnotvar) ).
thf(f388,plain,
( apnotvar
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f220]) ).
thf(f220,plain,
( apnotvar
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f219]) ).
thf(f219,plain,
! [X0: term,X1: term] :
( ( ~ ( var @ ( ap @ X0 @ X1 ) ) )
= apnotvar ),
inference(rectify,[],[f21]) ).
thf(f21,axiom,
! [X0: term,X1: term] :
( ( ~ ( var @ ( ap @ X0 @ X1 ) ) )
= apnotvar ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apnotvar) ).
thf(f364,plain,
( lamnotap
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f227]) ).
thf(f227,plain,
( lamnotap
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f226]) ).
thf(f226,plain,
( lamnotap
= ( ! [X0: term,X1: term,X2: term] :
( ( lam @ X1 )
!= ( ap @ X2 @ X0 ) ) ) ),
inference(rectify,[],[f20]) ).
thf(f20,axiom,
( lamnotap
= ( ! [X6: term,X0: term,X1: term] :
( ( lam @ X0 )
!= ( ap @ X1 @ X6 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamnotap) ).
thf(f357,plain,
( shinj
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f321]) ).
thf(f321,plain,
( shinj
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(fool_elimination,[],[f320]) ).
thf(f320,plain,
( shinj
= ( ! [X0: term,X1: term] :
( ( ( sub @ X0 @ sh )
= ( sub @ X1 @ sh ) )
=> ( X0 = X1 ) ) ) ),
inference(rectify,[],[f19]) ).
thf(f19,axiom,
( shinj
= ( ! [X1: term,X0: term] :
( ( ( sub @ X0 @ sh )
= ( sub @ X1 @ sh ) )
=> ( X0 = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',shinj) ).
thf(f409,plain,
( laminj
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f317]) ).
thf(f317,plain,
( laminj
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(fool_elimination,[],[f316]) ).
thf(f316,plain,
! [X0: term,X1: term] :
( ( ( ( lam @ X0 )
= ( lam @ X1 ) )
=> ( X0 = X1 ) )
= laminj ),
inference(rectify,[],[f18]) ).
thf(f18,axiom,
! [X1: term,X0: term] :
( ( ( ( lam @ X0 )
= ( lam @ X1 ) )
=> ( X0 = X1 ) )
= laminj ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',laminj) ).
thf(f383,plain,
( apinj2
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y3 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f270]) ).
thf(f270,plain,
( apinj2
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y3 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f269]) ).
thf(f269,plain,
( apinj2
= ( ! [X0: term,X1: term,X2: term,X3: term] :
( ( ( ap @ X3 @ X1 )
= ( ap @ X0 @ X2 ) )
=> ( X1 = X2 ) ) ) ),
inference(rectify,[],[f17]) ).
thf(f17,axiom,
( apinj2
= ( ! [X0: term,X7: term,X6: term,X1: term] :
( ( ( ap @ X0 @ X6 )
= ( ap @ X1 @ X7 ) )
=> ( X6 = X7 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apinj2) ).
thf(f346,plain,
( apinj1
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y2 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y1 = Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f237]) ).
thf(f237,plain,
( apinj1
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y2 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y1 = Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f236]) ).
thf(f236,plain,
! [X0: term,X1: term,X2: term,X3: term] :
( ( ( ( ap @ X2 @ X1 )
= ( ap @ X3 @ X0 ) )
=> ( X2 = X3 ) )
= apinj1 ),
inference(rectify,[],[f16]) ).
thf(f16,axiom,
! [X6: term,X7: term,X1: term,X0: term] :
( ( ( ( ap @ X0 @ X6 )
= ( ap @ X1 @ X7 ) )
=> ( X0 = X1 ) )
= apinj1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apinj1) ).
thf(f379,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,[],[f283]) ).
thf(f283,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,[],[f282]) ).
thf(f282,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/sandbox/benchmark/theBenchmark.p',ulamvarind) ).
thf(f360,plain,
( ulamvarsh
= ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) ) ),
inference(cnf_transformation,[],[f274]) ).
thf(f274,plain,
( ulamvarsh
= ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) ) ),
inference(fool_elimination,[],[f273]) ).
thf(f273,plain,
( ulamvarsh
= ( ! [X0: term] :
( ( var @ X0 )
=> ( var @ ( sub @ X0 @ sh ) ) ) ) ),
inference(rectify,[],[f14]) ).
thf(f14,axiom,
( ulamvarsh
= ( ! [X0: term] :
( ( var @ X0 )
=> ( var @ ( sub @ X0 @ sh ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ulamvarsh) ).
thf(f378,plain,
( ulamvar1
= ( var @ one ) ),
inference(cnf_transformation,[],[f223]) ).
thf(f223,plain,
( ulamvar1
= ( var @ one ) ),
inference(fool_elimination,[],[f13]) ).
thf(f13,axiom,
( ulamvar1
= ( var @ one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ulamvar1) ).
thf(f376,plain,
( axscons
= ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) ) ),
inference(cnf_transformation,[],[f187]) ).
thf(f187,plain,
( axscons
= ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) ) ),
inference(fool_elimination,[],[f186]) ).
thf(f186,plain,
! [X0: subst] :
( ( ( push @ ( sub @ one @ X0 ) @ ( comp @ sh @ X0 ) )
= X0 )
= axscons ),
inference(rectify,[],[f12]) ).
thf(f12,axiom,
! [X2: subst] :
( ( ( push @ ( sub @ one @ X2 ) @ ( comp @ sh @ X2 ) )
= X2 )
= axscons ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axscons) ).
thf(f358,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/sandbox/benchmark/theBenchmark.p',axvarshift) ).
thf(f412,plain,
( axidr
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) ),
inference(cnf_transformation,[],[f266]) ).
thf(f266,plain,
( axidr
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) ),
inference(fool_elimination,[],[f265]) ).
thf(f265,plain,
! [X0: subst] :
( ( ( comp @ X0 @ id )
= X0 )
= axidr ),
inference(rectify,[],[f10]) ).
thf(f10,axiom,
! [X2: subst] :
( ( ( comp @ X2 @ id )
= X2 )
= axidr ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axidr) ).
thf(f381,plain,
( axmap
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y0 @ Y2 ) @ Y1 )
= ( push @ ( sub @ Y0 @ Y1 ) @ ( comp @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f268]) ).
thf(f268,plain,
( axmap
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y0 @ Y2 ) @ Y1 )
= ( push @ ( sub @ Y0 @ Y1 ) @ ( comp @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f267]) ).
thf(f267,plain,
( axmap
= ( ! [X0: subst,X1: subst,X2: term] :
( ( comp @ ( push @ X2 @ X0 ) @ X1 )
= ( push @ ( sub @ X2 @ X1 ) @ ( comp @ X0 @ X1 ) ) ) ) ),
inference(rectify,[],[f9]) ).
thf(f9,axiom,
( axmap
= ( ! [X2: subst,X3: subst,X0: term] :
( ( comp @ ( push @ X0 @ X2 ) @ X3 )
= ( push @ ( sub @ X0 @ X3 ) @ ( comp @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axmap) ).
thf(f339,plain,
( axassoc
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f144]) ).
thf(f144,plain,
( axassoc
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f143]) ).
thf(f143,plain,
( axassoc
= ( ! [X0: subst,X1: subst,X2: subst] :
( ( comp @ X0 @ ( comp @ X1 @ X2 ) )
= ( comp @ ( comp @ X0 @ X1 ) @ X2 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f8,axiom,
( axassoc
= ( ! [X2: subst,X3: subst,X4: subst] :
( ( comp @ ( comp @ X2 @ X3 ) @ X4 )
= ( comp @ X2 @ ( comp @ X3 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axassoc) ).
thf(f399,plain,
( axshiftcons
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) ) ),
inference(cnf_transformation,[],[f291]) ).
thf(f291,plain,
( axshiftcons
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) ) ),
inference(fool_elimination,[],[f290]) ).
thf(f290,plain,
( axshiftcons
= ( ! [X0: term,X1: subst] :
( ( comp @ sh @ ( push @ X0 @ X1 ) )
= X1 ) ) ),
inference(rectify,[],[f7]) ).
thf(f7,axiom,
( axshiftcons
= ( ! [X0: term,X2: subst] :
( ( comp @ sh @ ( push @ X0 @ X2 ) )
= X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axshiftcons) ).
thf(f397,plain,
( axidl
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) ),
inference(cnf_transformation,[],[f214]) ).
thf(f214,plain,
( axidl
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) ),
inference(fool_elimination,[],[f213]) ).
thf(f213,plain,
! [X0: subst] :
( ( ( comp @ id @ X0 )
= X0 )
= axidl ),
inference(rectify,[],[f6]) ).
thf(f6,axiom,
! [X2: subst] :
( ( ( comp @ id @ X2 )
= X2 )
= axidl ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axidl) ).
thf(f406,plain,
( axclos
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f134]) ).
thf(f134,plain,
( axclos
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f133]) ).
thf(f133,plain,
! [X0: subst,X1: term,X2: subst] :
( ( ( sub @ X1 @ ( comp @ X2 @ X0 ) )
= ( sub @ ( sub @ X1 @ X2 ) @ X0 ) )
= axclos ),
inference(rectify,[],[f5]) ).
thf(f5,axiom,
! [X3: subst,X0: term,X2: subst] :
( ( ( sub @ ( sub @ X0 @ X2 ) @ X3 )
= ( sub @ X0 @ ( comp @ X2 @ X3 ) ) )
= axclos ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axclos) ).
thf(f410,plain,
( axabs
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( lam @ Y0 ) @ Y1 )
= ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f128]) ).
thf(f128,plain,
( axabs
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( lam @ Y0 ) @ Y1 )
= ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f127]) ).
thf(f127,plain,
! [X0: subst,X1: term] :
( ( ( sub @ ( lam @ X1 ) @ X0 )
= ( lam @ ( sub @ X1 @ ( push @ one @ ( comp @ X0 @ sh ) ) ) ) )
= axabs ),
inference(rectify,[],[f4]) ).
thf(f4,axiom,
! [X2: subst,X0: term] :
( ( ( sub @ ( lam @ X0 ) @ X2 )
= ( lam @ ( sub @ X0 @ ( push @ one @ ( comp @ X2 @ sh ) ) ) ) )
= axabs ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axabs) ).
thf(f382,plain,
( axvarid
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ),
inference(cnf_transformation,[],[f306]) ).
thf(f306,plain,
( axvarid
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f3,axiom,
! [X0: term] :
( ( ( sub @ X0 @ id )
= X0 )
= axvarid ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axvarid) ).
thf(f370,plain,
( axvarcons
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ one @ ( push @ Y1 @ Y0 ) )
= Y1 ) ) ) ),
inference(cnf_transformation,[],[f195]) ).
thf(f195,plain,
( axvarcons
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ one @ ( push @ Y1 @ Y0 ) )
= Y1 ) ) ) ),
inference(fool_elimination,[],[f194]) ).
thf(f194,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/sandbox/benchmark/theBenchmark.p',axvarcons) ).
thf(f340,plain,
( axapp
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( ap @ Y0 @ Y2 ) @ Y1 )
= ( ap @ ( sub @ Y0 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f164]) ).
thf(f164,plain,
( axapp
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( ap @ Y0 @ Y2 ) @ Y1 )
= ( ap @ ( sub @ Y0 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f163]) ).
thf(f163,plain,
( axapp
= ( ! [X0: term,X1: subst,X2: term] :
( ( sub @ ( ap @ X2 @ X0 ) @ X1 )
= ( ap @ ( sub @ X2 @ X1 ) @ ( sub @ X0 @ X1 ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
( axapp
= ( ! [X1: term,X2: subst,X0: term] :
( ( sub @ ( ap @ X0 @ X1 ) @ X2 )
= ( ap @ ( sub @ X0 @ X2 ) @ ( sub @ X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axapp) ).
thf(f386,plain,
( hoasinduction_lem3b_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
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f175]) ).
thf(f175,plain,
( hoasinduction_lem3b_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
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f174]) ).
thf(f174,plain,
( axapp
=> ( ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= hoasinduction_lem3b_gthm ) ),
inference(rectify,[],[f106]) ).
thf(f106,axiom,
( axapp
=> ( ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= hoasinduction_lem3b_gthm ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3b_gthm) ).
thf(f391,plain,
( $true = ~ hoasinduction_lem3b_gthm ),
inference(cnf_transformation,[],[f126]) ).
thf(f126,plain,
( $true = ~ hoasinduction_lem3b_gthm ),
inference(fool_elimination,[],[f125]) ).
thf(f125,plain,
~ hoasinduction_lem3b_gthm,
inference(rectify,[],[f115]) ).
thf(f115,negated_conjecture,
~ hoasinduction_lem3b_gthm,
inference(negated_conjecture,[],[f114]) ).
thf(f114,conjecture,
hoasinduction_lem3b_gthm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f1174,plain,
! [X1: subst > term > term] :
( ( X1 @ sh @ one )
!= ( sub @ sK8 @ id ) ),
inference(forward_demodulation,[],[f698,f502]) ).
thf(f502,plain,
( id
= ( push @ one @ sh ) ),
inference(equality_proxy_clausification,[],[f501]) ).
thf(f501,plain,
( $true
= ( id
= ( push @ one @ sh ) ) ),
inference(binary_proxy_clausification,[],[f498]) ).
thf(f498,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 @ Y1 @ Y2 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y1 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y3 @ Y1 ) )
=> ( 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 @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 )
= ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y1 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) )
= ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y3 @ Y4 @ ( comp @ Y1 @ Y2 ) )
=> ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y4 )
=> ( Y0 @ Y1 @ Y3 @ ( comp @ Y2 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f489]) ).
thf(f489,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y2 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y1 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y3 @ Y1 ) )
=> ( 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 @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 )
= ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y1 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) )
= ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y3 @ Y4 @ ( comp @ Y1 @ Y2 ) )
=> ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y4 )
=> ( Y0 @ Y1 @ Y3 @ ( comp @ Y2 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f487]) ).
thf(f487,plain,
( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y0 @ Y2 ) @ Y1 )
= ( push @ ( sub @ Y0 @ Y1 ) @ ( comp @ Y2 @ 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 @ Y1 @ Y2 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y1 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y3 @ Y1 ) )
=> ( 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 @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 )
= ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y1 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) )
= ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y3 @ Y4 @ ( comp @ Y1 @ Y2 ) )
=> ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y4 )
=> ( Y0 @ Y1 @ Y3 @ ( comp @ Y2 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f480]) ).
thf(f480,plain,
( $false
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y0 @ Y2 ) @ Y1 )
= ( push @ ( sub @ Y0 @ Y1 ) @ ( comp @ Y2 @ 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 @ Y1 @ Y2 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y1 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y3 @ Y1 ) )
=> ( 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 @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 )
= ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y1 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) )
= ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y3 @ Y4 @ ( comp @ Y1 @ Y2 ) )
=> ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y4 )
=> ( Y0 @ Y1 @ Y3 @ ( comp @ Y2 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f478]) ).
thf(f478,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y0 @ Y2 ) @ Y1 )
= ( push @ ( sub @ Y0 @ Y1 ) @ ( comp @ Y2 @ 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 @ Y1 @ Y2 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y1 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y3 @ Y1 ) )
=> ( 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 @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 )
= ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y1 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) )
= ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y3 @ Y4 @ ( comp @ Y1 @ Y2 ) )
=> ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y4 )
=> ( Y0 @ Y1 @ Y3 @ ( comp @ Y2 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f476]) ).
thf(f476,plain,
( $false
= ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y0 @ Y2 ) @ Y1 )
= ( push @ ( sub @ Y0 @ Y1 ) @ ( comp @ Y2 @ 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 @ Y1 @ Y2 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y1 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y3 @ Y1 ) )
=> ( 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 @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 )
= ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y1 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) )
= ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y3 @ Y4 @ ( comp @ Y1 @ Y2 ) )
=> ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y4 )
=> ( Y0 @ Y1 @ Y3 @ ( comp @ Y2 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f474]) ).
thf(f474,plain,
( $false
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y0 @ Y2 ) @ Y1 )
= ( push @ ( sub @ Y0 @ Y1 ) @ ( comp @ Y2 @ 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 @ Y1 @ Y2 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y1 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y3 @ Y1 ) )
=> ( 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 @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 )
= ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y1 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) )
= ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y3 @ Y4 @ ( comp @ Y1 @ Y2 ) )
=> ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y4 )
=> ( Y0 @ Y1 @ Y3 @ ( comp @ Y2 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f469]) ).
thf(f469,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( lam @ Y0 ) @ Y1 )
= ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y0 @ Y2 ) @ Y1 )
= ( push @ ( sub @ Y0 @ Y1 ) @ ( comp @ Y2 @ 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 @ Y1 @ Y2 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y1 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y3 @ Y1 ) )
=> ( 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 @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 )
= ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y1 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) )
= ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y3 @ Y4 @ ( comp @ Y1 @ Y2 ) )
=> ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y4 )
=> ( Y0 @ Y1 @ Y3 @ ( comp @ Y2 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f462]) ).
thf(f698,plain,
! [X1: subst > term > term] :
( ( X1 @ sh @ one )
!= ( sub @ sK8 @ ( push @ one @ sh ) ) ),
inference(equality_proxy_clausification,[],[f697]) ).
thf(f697,plain,
! [X1: subst > term > term] :
( $false
= ( ( sub @ sK8 @ ( push @ one @ sh ) )
= ( X1 @ sh @ one ) ) ),
inference(beta_eta_normalization,[],[f696]) ).
thf(f696,plain,
! [X1: subst > term > term] :
( ( ^ [Y0: subst > term > term] :
( ( sub @ sK8 @ ( push @ one @ sh ) )
= ( Y0 @ sh @ one ) )
@ X1 )
= $false ),
inference(pi_clausification,[],[f695]) ).
thf(f695,plain,
( $false
= ( ?? @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( sub @ sK8 @ ( push @ one @ sh ) )
= ( Y0 @ sh @ one ) ) ) ),
inference(beta_eta_normalization,[],[f694]) ).
thf(f694,plain,
( ( ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) )
@ sK8 )
= $false ),
inference(sigma_clausification,[],[f692]) ).
thf(f692,plain,
( $false
= ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ),
inference(binary_proxy_clausification,[],[f690]) ).
thf(f690,plain,
( $false
= ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f688]) ).
thf(f688,plain,
( $false
= ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y3 @ Y4 @ ( comp @ Y1 @ Y2 ) )
=> ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y4 )
=> ( Y0 @ Y1 @ Y3 @ ( comp @ Y2 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f675]) ).
thf(f675,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y3 @ Y4 @ ( comp @ Y1 @ Y2 ) )
=> ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y4 )
=> ( Y0 @ Y1 @ Y3 @ ( comp @ Y2 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f673]) ).
thf(f673,plain,
( $false
= ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y3 @ Y4 @ ( comp @ Y1 @ Y2 ) )
=> ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y4 )
=> ( Y0 @ Y1 @ Y3 @ ( comp @ Y2 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f671]) ).
thf(f671,plain,
( ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y3 @ Y4 @ ( comp @ Y1 @ Y2 ) )
=> ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y4 )
=> ( Y0 @ Y1 @ Y3 @ ( comp @ Y2 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f658]) ).
thf(f658,plain,
( ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) )
= ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y3 @ Y4 @ ( comp @ Y1 @ Y2 ) )
=> ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y4 )
=> ( Y0 @ Y1 @ Y3 @ ( comp @ Y2 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f656]) ).
thf(f656,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) )
= ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y3 @ Y4 @ ( comp @ Y1 @ Y2 ) )
=> ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y4 )
=> ( Y0 @ Y1 @ Y3 @ ( comp @ Y2 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f642]) ).
thf(f642,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y1 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) )
= ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y3 @ Y4 @ ( comp @ Y1 @ Y2 ) )
=> ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y4 )
=> ( Y0 @ Y1 @ Y3 @ ( comp @ Y2 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f640]) ).
thf(f640,plain,
( ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 )
= ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y1 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) )
= ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y3 @ Y4 @ ( comp @ Y1 @ Y2 ) )
=> ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y4 )
=> ( Y0 @ Y1 @ Y3 @ ( comp @ Y2 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f638]) ).
thf(f638,plain,
( $false
= ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 )
= ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y1 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) )
= ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y3 @ Y4 @ ( comp @ Y1 @ Y2 ) )
=> ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y4 )
=> ( Y0 @ Y1 @ Y3 @ ( comp @ Y2 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f571]) ).
thf(f571,plain,
( ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 )
= ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y1 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) )
= ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y3 @ Y4 @ ( comp @ Y1 @ Y2 ) )
=> ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y4 )
=> ( Y0 @ Y1 @ Y3 @ ( comp @ Y2 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f553]) ).
thf(f553,plain,
( ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( Y0 @ ( sub @ Y1 @ Y2 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 )
= ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y1 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) )
= ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y3 @ Y4 @ ( comp @ Y1 @ Y2 ) )
=> ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y4 )
=> ( Y0 @ Y1 @ Y3 @ ( comp @ Y2 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f551]) ).
thf(f551,plain,
( ( ( !! @ ( 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 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 )
= ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y1 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) )
= ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y3 @ Y4 @ ( comp @ Y1 @ Y2 ) )
=> ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y4 )
=> ( Y0 @ Y1 @ Y3 @ ( comp @ Y2 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f549]) ).
thf(f549,plain,
( $false
= ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( 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 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 )
= ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y1 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) )
= ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y3 @ Y4 @ ( comp @ Y1 @ Y2 ) )
=> ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y4 )
=> ( Y0 @ Y1 @ Y3 @ ( comp @ Y2 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f542]) ).
thf(f542,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 )
= ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y1 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) )
= ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y3 @ Y4 @ ( comp @ Y1 @ Y2 ) )
=> ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y4 )
=> ( Y0 @ Y1 @ Y3 @ ( comp @ Y2 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f532]) ).
thf(f532,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 )
= ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y1 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) )
= ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y3 @ Y4 @ ( comp @ Y1 @ Y2 ) )
=> ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y4 )
=> ( Y0 @ Y1 @ Y3 @ ( comp @ Y2 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f523]) ).
thf(f523,plain,
( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 )
= ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y1 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) )
= ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y3 @ Y4 @ ( comp @ Y1 @ Y2 ) )
=> ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y4 )
=> ( Y0 @ Y1 @ Y3 @ ( comp @ Y2 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f521]) ).
thf(f521,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 )
= ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y1 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) )
= ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y3 @ Y4 @ ( comp @ Y1 @ Y2 ) )
=> ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y4 )
=> ( Y0 @ Y1 @ Y3 @ ( comp @ Y2 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f519]) ).
thf(f519,plain,
( ( ( !! @ 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 @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 )
= ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y1 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) )
= ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y3 @ Y4 @ ( comp @ Y1 @ Y2 ) )
=> ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y4 )
=> ( Y0 @ Y1 @ Y3 @ ( comp @ Y2 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f517]) ).
thf(f517,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y3 @ Y1 ) )
=> ( 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 @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 )
= ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y1 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) )
= ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y3 @ Y4 @ ( comp @ Y1 @ Y2 ) )
=> ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y4 )
=> ( Y0 @ Y1 @ Y3 @ ( comp @ Y2 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f515]) ).
thf(f515,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y2 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y1 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y3 @ Y1 ) )
=> ( 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 @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 )
= ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y1 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) )
= ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y3 @ Y4 @ ( comp @ Y1 @ Y2 ) )
=> ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y4 )
=> ( Y0 @ Y1 @ Y3 @ ( comp @ Y2 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f510]) ).
thf(f510,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 @ Y1 @ Y2 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y1 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y3 @ Y1 ) )
=> ( 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 @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 )
= ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y1 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) )
= ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y3 @ Y4 @ ( comp @ Y1 @ Y2 ) )
=> ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y4 )
=> ( Y0 @ Y1 @ Y3 @ ( comp @ Y2 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f508]) ).
thf(f508,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y2 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y1 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y3 @ Y1 ) )
=> ( 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 @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 )
= ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y1 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) )
= ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y3 @ Y4 @ ( comp @ Y1 @ Y2 ) )
=> ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y4 )
=> ( Y0 @ Y1 @ Y3 @ ( comp @ Y2 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f503]) ).
thf(f503,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 @ Y1 @ Y2 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y1 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y3 @ Y1 ) )
=> ( 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 @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 )
= ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y1 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) )
= ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y3 @ Y4 @ ( comp @ Y1 @ Y2 ) )
=> ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y4 )
=> ( Y0 @ Y1 @ Y3 @ ( comp @ Y2 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f500]) ).
thf(f500,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y2 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y1 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y3 @ Y1 ) )
=> ( 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 @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 )
= ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y1 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) )
= ( sub @ ( Y1 @ Y2 @ Y3 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( Y0 @ Y3 @ Y1 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y3 @ Y4 @ ( comp @ Y1 @ Y2 ) )
=> ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y4 )
=> ( Y0 @ Y1 @ Y3 @ ( comp @ Y2 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) )
=> ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f498]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : ALG267^1 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.10/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.35 % Computer : n021.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sat May 18 23:33:23 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.35 This is a TH0_THM_EQU_NAR problem
% 0.15/0.36 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.39 % (9143)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.15/0.39 % (9139)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.15/0.39 % (9144)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.15/0.39 % (9138)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.39 % (9145)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.15/0.39 % (9139)Instruction limit reached!
% 0.15/0.39 % (9139)------------------------------
% 0.15/0.39 % (9139)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (9139)Termination reason: Unknown
% 0.15/0.39 % (9139)Termination phase: shuffling
% 0.15/0.39
% 0.15/0.39 % (9139)Memory used [KB]: 1279
% 0.15/0.39 % (9139)Time elapsed: 0.004 s
% 0.15/0.39 % (9139)Instructions burned: 4 (million)
% 0.15/0.39 % (9139)------------------------------
% 0.15/0.39 % (9139)------------------------------
% 0.15/0.39 % (9145)Instruction limit reached!
% 0.15/0.39 % (9145)------------------------------
% 0.15/0.39 % (9145)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (9145)Termination reason: Unknown
% 0.15/0.39 % (9145)Termination phase: shuffling
% 0.15/0.39
% 0.15/0.39 % (9145)Memory used [KB]: 1279
% 0.15/0.39 % (9145)Time elapsed: 0.004 s
% 0.15/0.39 % (9145)Instructions burned: 3 (million)
% 0.15/0.39 % (9142)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.39 % (9145)------------------------------
% 0.15/0.39 % (9145)------------------------------
% 0.15/0.39 % (9142)Instruction limit reached!
% 0.15/0.39 % (9142)------------------------------
% 0.15/0.39 % (9142)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (9142)Termination reason: Unknown
% 0.15/0.39 % (9142)Termination phase: shuffling
% 0.15/0.39
% 0.15/0.39 % (9142)Memory used [KB]: 1279
% 0.15/0.39 % (9142)Time elapsed: 0.005 s
% 0.15/0.39 % (9142)Instructions burned: 2 (million)
% 0.15/0.39 % (9142)------------------------------
% 0.15/0.39 % (9142)------------------------------
% 0.15/0.39 % (9140)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.15/0.39 % (9141)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.39 % (9141)Instruction limit reached!
% 0.15/0.39 % (9141)------------------------------
% 0.15/0.39 % (9141)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (9141)Termination reason: Unknown
% 0.15/0.39 % (9141)Termination phase: shuffling
% 0.15/0.39
% 0.15/0.39 % (9141)Memory used [KB]: 1279
% 0.15/0.39 % (9141)Time elapsed: 0.003 s
% 0.15/0.39 % (9141)Instructions burned: 3 (million)
% 0.15/0.39 % (9141)------------------------------
% 0.15/0.39 % (9141)------------------------------
% 0.15/0.40 % (9144)Instruction limit reached!
% 0.15/0.40 % (9144)------------------------------
% 0.15/0.40 % (9144)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (9144)Termination reason: Unknown
% 0.15/0.40 % (9144)Termination phase: Property scanning
% 0.15/0.40
% 0.15/0.40 % (9144)Memory used [KB]: 1663
% 0.15/0.40 % (9144)Time elapsed: 0.013 s
% 0.15/0.40 % (9144)Instructions burned: 18 (million)
% 0.15/0.40 % (9144)------------------------------
% 0.15/0.40 % (9144)------------------------------
% 0.15/0.40 % (9140)Instruction limit reached!
% 0.15/0.40 % (9140)------------------------------
% 0.15/0.40 % (9140)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (9140)Termination reason: Unknown
% 0.15/0.40 % (9140)Termination phase: Property scanning
% 0.15/0.40
% 0.15/0.40 % (9140)Memory used [KB]: 1791
% 0.15/0.40 % (9140)Time elapsed: 0.016 s
% 0.15/0.40 % (9140)Instructions burned: 27 (million)
% 0.15/0.40 % (9140)------------------------------
% 0.15/0.40 % (9140)------------------------------
% 0.15/0.40 % (9146)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.15/0.40 % (9148)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.15/0.41 % (9148)Instruction limit reached!
% 0.15/0.41 % (9148)------------------------------
% 0.15/0.41 % (9148)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.41 % (9148)Termination reason: Unknown
% 0.15/0.41 % (9148)Termination phase: shuffling
% 0.15/0.41
% 0.15/0.41 % (9148)Memory used [KB]: 1279
% 0.15/0.41 % (9148)Time elapsed: 0.004 s
% 0.15/0.41 % (9148)Instructions burned: 3 (million)
% 0.15/0.41 % (9148)------------------------------
% 0.15/0.41 % (9148)------------------------------
% 0.15/0.41 % (9143)Refutation not found, incomplete strategy
% 0.15/0.41 % (9143)------------------------------
% 0.15/0.41 % (9143)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.41 % (9143)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.41
% 0.15/0.41
% 0.15/0.41 % (9143)Memory used [KB]: 6268
% 0.15/0.41 % (9143)Time elapsed: 0.024 s
% 0.15/0.41 % (9143)Instructions burned: 36 (million)
% 0.15/0.41 % (9143)------------------------------
% 0.15/0.41 % (9143)------------------------------
% 0.15/0.41 % (9147)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.15/0.41 % (9149)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.15/0.41 % (9150)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.22/0.41 % (9150)Instruction limit reached!
% 0.22/0.41 % (9150)------------------------------
% 0.22/0.41 % (9150)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (9150)Termination reason: Unknown
% 0.22/0.42 % (9150)Termination phase: shuffling
% 0.22/0.42
% 0.22/0.42 % (9150)Memory used [KB]: 1407
% 0.22/0.42 % (9150)Time elapsed: 0.006 s
% 0.22/0.42 % (9150)Instructions burned: 7 (million)
% 0.22/0.42 % (9150)------------------------------
% 0.22/0.42 % (9150)------------------------------
% 0.22/0.42 % (9147)Instruction limit reached!
% 0.22/0.42 % (9147)------------------------------
% 0.22/0.42 % (9147)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (9147)Termination reason: Unknown
% 0.22/0.42 % (9147)Termination phase: Property scanning
% 0.22/0.42
% 0.22/0.42 % (9147)Memory used [KB]: 1663
% 0.22/0.42 % (9147)Time elapsed: 0.012 s
% 0.22/0.42 % (9147)Instructions burned: 16 (million)
% 0.22/0.42 % (9147)------------------------------
% 0.22/0.42 % (9147)------------------------------
% 0.22/0.42 % (9151)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.22/0.42 % (9152)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.22/0.42 % (9146)Instruction limit reached!
% 0.22/0.42 % (9146)------------------------------
% 0.22/0.42 % (9146)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (9146)Termination reason: Unknown
% 0.22/0.42 % (9146)Termination phase: Property scanning
% 0.22/0.42
% 0.22/0.42 % (9146)Memory used [KB]: 1791
% 0.22/0.42 % (9146)Time elapsed: 0.020 s
% 0.22/0.42 % (9146)Instructions burned: 37 (million)
% 0.22/0.42 % (9146)------------------------------
% 0.22/0.42 % (9146)------------------------------
% 0.22/0.42 % (9153)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.22/0.42 % (9152)Instruction limit reached!
% 0.22/0.42 % (9152)------------------------------
% 0.22/0.42 % (9152)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (9152)Termination reason: Unknown
% 0.22/0.42 % (9152)Termination phase: shuffling
% 0.22/0.42
% 0.22/0.42 % (9152)Memory used [KB]: 1279
% 0.22/0.42 % (9152)Time elapsed: 0.004 s
% 0.22/0.42 % (9152)Instructions burned: 3 (million)
% 0.22/0.42 % (9152)------------------------------
% 0.22/0.42 % (9152)------------------------------
% 0.22/0.42 % (9153)Instruction limit reached!
% 0.22/0.42 % (9153)------------------------------
% 0.22/0.42 % (9153)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (9153)Termination reason: Unknown
% 0.22/0.42 % (9153)Termination phase: shuffling
% 0.22/0.42
% 0.22/0.42 % (9153)Memory used [KB]: 1279
% 0.22/0.42 % (9153)Time elapsed: 0.004 s
% 0.22/0.42 % (9153)Instructions burned: 3 (million)
% 0.22/0.42 % (9153)------------------------------
% 0.22/0.42 % (9153)------------------------------
% 0.22/0.43 % (9151)Instruction limit reached!
% 0.22/0.43 % (9151)------------------------------
% 0.22/0.43 % (9151)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.43 % (9151)Termination reason: Unknown
% 0.22/0.43 % (9151)Termination phase: shuffling
% 0.22/0.43
% 0.22/0.43 % (9151)Memory used [KB]: 1535
% 0.22/0.43 % (9151)Time elapsed: 0.010 s
% 0.22/0.43 % (9151)Instructions burned: 16 (million)
% 0.22/0.43 % (9151)------------------------------
% 0.22/0.43 % (9151)------------------------------
% 0.22/0.43 % (9154)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.22/0.43 % (9155)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.22/0.43 % (9154)Instruction limit reached!
% 0.22/0.43 % (9154)------------------------------
% 0.22/0.43 % (9154)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.43 % (9154)Termination reason: Unknown
% 0.22/0.43 % (9154)Termination phase: shuffling
% 0.22/0.43
% 0.22/0.43 % (9154)Memory used [KB]: 1407
% 0.22/0.43 % (9154)Time elapsed: 0.006 s
% 0.22/0.43 % (9154)Instructions burned: 8 (million)
% 0.22/0.43 % (9154)------------------------------
% 0.22/0.43 % (9154)------------------------------
% 0.22/0.43 % (9155)Instruction limit reached!
% 0.22/0.43 % (9155)------------------------------
% 0.22/0.43 % (9155)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.44 % (9155)Termination reason: Unknown
% 0.22/0.44 % (9155)Termination phase: shuffling
% 0.22/0.44
% 0.22/0.44 % (9155)Memory used [KB]: 1279
% 0.22/0.44 % (9155)Time elapsed: 0.003 s
% 0.22/0.44 % (9155)Instructions burned: 3 (million)
% 0.22/0.44 % (9155)------------------------------
% 0.22/0.44 % (9155)------------------------------
% 0.22/0.44 % (9156)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.22/0.44 % (9157)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.22/0.44 % (9156)Instruction limit reached!
% 0.22/0.44 % (9156)------------------------------
% 0.22/0.44 % (9156)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.44 % (9156)Termination reason: Unknown
% 0.22/0.44 % (9156)Termination phase: shuffling
% 0.22/0.44
% 0.22/0.44 % (9156)Memory used [KB]: 1279
% 0.22/0.44 % (9156)Time elapsed: 0.004 s
% 0.22/0.44 % (9156)Instructions burned: 4 (million)
% 0.22/0.44 % (9156)------------------------------
% 0.22/0.44 % (9156)------------------------------
% 0.22/0.44 % (9158)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.22/0.44 % (9159)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.22/0.44 % (9159)Instruction limit reached!
% 0.22/0.44 % (9159)------------------------------
% 0.22/0.44 % (9159)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.44 % (9159)Termination reason: Unknown
% 0.22/0.44 % (9159)Termination phase: shuffling
% 0.22/0.44
% 0.22/0.44 % (9159)Memory used [KB]: 1279
% 0.22/0.44 % (9159)Time elapsed: 0.005 s
% 0.22/0.44 % (9159)Instructions burned: 6 (million)
% 0.22/0.44 % (9159)------------------------------
% 0.22/0.44 % (9159)------------------------------
% 0.22/0.45 % (9157)Instruction limit reached!
% 0.22/0.45 % (9157)------------------------------
% 0.22/0.45 % (9157)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.45 % (9157)Termination reason: Unknown
% 0.22/0.45 % (9157)Termination phase: shuffling
% 0.22/0.45
% 0.22/0.45 % (9157)Memory used [KB]: 1663
% 0.22/0.45 % (9157)Time elapsed: 0.011 s
% 0.22/0.45 % (9157)Instructions burned: 18 (million)
% 0.22/0.45 % (9157)------------------------------
% 0.22/0.45 % (9157)------------------------------
% 0.22/0.45 % (9160)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on theBenchmark for (2999ds/902Mi)
% 0.22/0.45 % (9161)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on theBenchmark for (2999ds/21Mi)
% 0.22/0.45 % (9162)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.22/0.46 % (9162)Instruction limit reached!
% 0.22/0.46 % (9162)------------------------------
% 0.22/0.46 % (9162)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.46 % (9162)Termination reason: Unknown
% 0.22/0.46 % (9162)Termination phase: shuffling
% 0.22/0.46
% 0.22/0.46 % (9162)Memory used [KB]: 1279
% 0.22/0.46 % (9162)Time elapsed: 0.005 s
% 0.22/0.46 % (9162)Instructions burned: 6 (million)
% 0.22/0.46 % (9162)------------------------------
% 0.22/0.46 % (9162)------------------------------
% 0.22/0.46 % (9158)Refutation not found, incomplete strategy
% 0.22/0.46 % (9158)------------------------------
% 0.22/0.46 % (9158)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.46 % (9158)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.46
% 0.22/0.46
% 0.22/0.46 % (9158)Memory used [KB]: 6268
% 0.22/0.46 % (9158)Time elapsed: 0.044 s
% 0.22/0.46 % (9158)Instructions burned: 29 (million)
% 0.22/0.46 % (9158)------------------------------
% 0.22/0.46 % (9158)------------------------------
% 0.22/0.46 % (9163)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.22/0.46 % (9161)Instruction limit reached!
% 0.22/0.46 % (9161)------------------------------
% 0.22/0.46 % (9161)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.46 % (9161)Termination reason: Unknown
% 0.22/0.46 % (9161)Termination phase: shuffling
% 0.22/0.46
% 0.22/0.46 % (9161)Memory used [KB]: 1663
% 0.22/0.46 % (9161)Time elapsed: 0.013 s
% 0.22/0.46 % (9161)Instructions burned: 22 (million)
% 0.22/0.46 % (9161)------------------------------
% 0.22/0.46 % (9161)------------------------------
% 0.22/0.46 % (9163)Instruction limit reached!
% 0.22/0.46 % (9163)------------------------------
% 0.22/0.46 % (9163)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.46 % (9164)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2999ds/377Mi)
% 0.22/0.46 % (9163)Termination reason: Unknown
% 0.22/0.46 % (9163)Termination phase: shuffling
% 0.22/0.46
% 0.22/0.46 % (9163)Memory used [KB]: 1279
% 0.22/0.46 % (9163)Time elapsed: 0.005 s
% 0.22/0.46 % (9163)Instructions burned: 6 (million)
% 0.22/0.46 % (9163)------------------------------
% 0.22/0.46 % (9163)------------------------------
% 0.22/0.47 % (9138)Instruction limit reached!
% 0.22/0.47 % (9138)------------------------------
% 0.22/0.47 % (9138)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.47 % (9138)Termination reason: Unknown
% 0.22/0.47 % (9138)Termination phase: Saturation
% 0.22/0.47
% 0.22/0.47 % (9138)Memory used [KB]: 6652
% 0.22/0.47 % (9138)Time elapsed: 0.085 s
% 0.22/0.47 % (9138)Instructions burned: 184 (million)
% 0.22/0.47 % (9138)------------------------------
% 0.22/0.47 % (9138)------------------------------
% 0.22/0.47 % (9165)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on theBenchmark for (2999ds/779Mi)
% 0.22/0.48 % (9167)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on theBenchmark for (2999ds/879Mi)
% 0.22/0.48 % (9168)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2999ds/17Mi)
% 0.22/0.48 % (9166)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on theBenchmark for (2999ds/19Mi)
% 0.22/0.48 % (9169)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi)
% 0.22/0.49 % (9166)Instruction limit reached!
% 0.22/0.49 % (9166)------------------------------
% 0.22/0.49 % (9166)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.49 % (9166)Termination reason: Unknown
% 0.22/0.49 % (9166)Termination phase: shuffling
% 0.22/0.49
% 0.22/0.49 % (9166)Memory used [KB]: 1663
% 0.22/0.49 % (9166)Time elapsed: 0.009 s
% 0.22/0.49 % (9166)Instructions burned: 21 (million)
% 0.22/0.49 % (9166)------------------------------
% 0.22/0.49 % (9166)------------------------------
% 0.22/0.49 % (9169)Instruction limit reached!
% 0.22/0.49 % (9169)------------------------------
% 0.22/0.49 % (9169)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.49 % (9169)Termination reason: Unknown
% 0.22/0.49 % (9169)Termination phase: shuffling
% 0.22/0.49
% 0.22/0.49 % (9169)Memory used [KB]: 1279
% 0.22/0.49 % (9169)Time elapsed: 0.004 s
% 0.22/0.49 % (9169)Instructions burned: 3 (million)
% 0.22/0.49 % (9169)------------------------------
% 0.22/0.49 % (9169)------------------------------
% 0.22/0.49 % (9168)Instruction limit reached!
% 0.22/0.49 % (9168)------------------------------
% 0.22/0.49 % (9168)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.49 % (9168)Termination reason: Unknown
% 0.22/0.49 % (9168)Termination phase: shuffling
% 0.22/0.49
% 0.22/0.49 % (9168)Memory used [KB]: 1535
% 0.22/0.49 % (9168)Time elapsed: 0.013 s
% 0.22/0.49 % (9168)Instructions burned: 17 (million)
% 0.22/0.49 % (9168)------------------------------
% 0.22/0.49 % (9168)------------------------------
% 0.22/0.50 % (9170)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on theBenchmark for (2998ds/30Mi)
% 0.22/0.50 % (9171)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on theBenchmark for (2998ds/127Mi)
% 0.22/0.50 % (9172)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on theBenchmark for (2998ds/100Mi)
% 0.22/0.50 % (9167)Refutation not found, incomplete strategy
% 0.22/0.50 % (9167)------------------------------
% 0.22/0.50 % (9167)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.50 % (9167)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.50
% 0.22/0.50
% 0.22/0.50 % (9167)Memory used [KB]: 6268
% 0.22/0.50 % (9167)Time elapsed: 0.030 s
% 0.22/0.50 % (9167)Instructions burned: 60 (million)
% 0.22/0.50 % (9167)------------------------------
% 0.22/0.50 % (9167)------------------------------
% 0.22/0.51 % (9170)Instruction limit reached!
% 0.22/0.51 % (9170)------------------------------
% 0.22/0.51 % (9170)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.51 % (9170)Termination reason: Unknown
% 0.22/0.51 % (9170)Termination phase: Property scanning
% 0.22/0.51
% 0.22/0.51 % (9170)Memory used [KB]: 1791
% 0.22/0.51 % (9170)Time elapsed: 0.017 s
% 0.22/0.51 % (9170)Instructions burned: 33 (million)
% 0.22/0.51 % (9170)------------------------------
% 0.22/0.51 % (9170)------------------------------
% 0.22/0.51 % (9173)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi)
% 0.22/0.52 % (9173)Instruction limit reached!
% 0.22/0.52 % (9173)------------------------------
% 0.22/0.52 % (9173)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.52 % (9173)Termination reason: Unknown
% 0.22/0.52 % (9173)Termination phase: shuffling
% 0.22/0.52
% 0.22/0.52 % (9173)Memory used [KB]: 1279
% 0.22/0.52 % (9173)Time elapsed: 0.003 s
% 0.22/0.52 % (9173)Instructions burned: 6 (million)
% 0.22/0.52 % (9173)------------------------------
% 0.22/0.52 % (9173)------------------------------
% 0.22/0.52 % (9174)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on theBenchmark for (2998ds/20Mi)
% 0.22/0.52 % (9160)Refutation not found, incomplete strategy
% 0.22/0.52 % (9160)------------------------------
% 0.22/0.52 % (9160)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.52 % (9160)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.52
% 0.22/0.52
% 0.22/0.52 % (9160)Memory used [KB]: 8059
% 0.22/0.52 % (9160)Time elapsed: 0.076 s
% 0.22/0.52 % (9160)Instructions burned: 198 (million)
% 0.22/0.52 % (9160)------------------------------
% 0.22/0.52 % (9160)------------------------------
% 0.22/0.52 % (9175)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on theBenchmark for (2998ds/86Mi)
% 0.22/0.52 % (9172)Instruction limit reached!
% 0.22/0.52 % (9172)------------------------------
% 0.22/0.52 % (9172)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.52 % (9172)Termination reason: Unknown
% 0.22/0.52 % (9172)Termination phase: Saturation
% 0.22/0.52
% 0.22/0.52 % (9172)Memory used [KB]: 6524
% 0.22/0.52 % (9172)Time elapsed: 0.027 s
% 0.22/0.52 % (9172)Instructions burned: 100 (million)
% 0.22/0.52 % (9172)------------------------------
% 0.22/0.52 % (9172)------------------------------
% 0.22/0.53 % (9174)Instruction limit reached!
% 0.22/0.53 % (9174)------------------------------
% 0.22/0.53 % (9174)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.53 % (9174)Termination reason: Unknown
% 0.22/0.53 % (9174)Termination phase: Property scanning
% 0.22/0.53
% 0.22/0.53 % (9174)Memory used [KB]: 1663
% 0.22/0.53 % (9174)Time elapsed: 0.008 s
% 0.22/0.53 % (9174)Instructions burned: 21 (million)
% 0.22/0.53 % (9174)------------------------------
% 0.22/0.53 % (9174)------------------------------
% 0.22/0.53 % (9176)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)
% 0.22/0.53 % (9171)Instruction limit reached!
% 0.22/0.53 % (9171)------------------------------
% 0.22/0.53 % (9171)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.53 % (9171)Termination reason: Unknown
% 0.22/0.53 % (9171)Termination phase: Saturation
% 0.22/0.53
% 0.22/0.53 % (9171)Memory used [KB]: 6524
% 0.22/0.53 % (9171)Time elapsed: 0.035 s
% 0.22/0.53 % (9171)Instructions burned: 129 (million)
% 0.22/0.53 % (9171)------------------------------
% 0.22/0.53 % (9171)------------------------------
% 0.22/0.53 % (9177)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)
% 0.22/0.54 % (9178)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)
% 0.22/0.54 % (9179)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on theBenchmark for (2998ds/46Mi)
% 0.22/0.54 % (9177)Instruction limit reached!
% 0.22/0.54 % (9177)------------------------------
% 0.22/0.54 % (9177)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.54 % (9177)Termination reason: Unknown
% 0.22/0.54 % (9177)Termination phase: Property scanning
% 0.22/0.54
% 0.22/0.54 % (9177)Memory used [KB]: 1791
% 0.22/0.54 % (9177)Time elapsed: 0.012 s
% 0.22/0.54 % (9177)Instructions burned: 40 (million)
% 0.22/0.54 % (9177)------------------------------
% 0.22/0.54 % (9177)------------------------------
% 0.22/0.55 % (9175)Instruction limit reached!
% 0.22/0.55 % (9175)------------------------------
% 0.22/0.55 % (9175)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.55 % (9175)Termination reason: Unknown
% 0.22/0.55 % (9175)Termination phase: Property scanning
% 0.22/0.55
% 0.22/0.55 % (9175)Memory used [KB]: 2046
% 0.22/0.55 % (9175)Time elapsed: 0.024 s
% 0.22/0.55 % (9175)Instructions burned: 88 (million)
% 0.22/0.55 % (9175)------------------------------
% 0.22/0.55 % (9175)------------------------------
% 0.22/0.55 % (9180)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on theBenchmark for (2998ds/98Mi)
% 0.22/0.55 % (9179)Instruction limit reached!
% 0.22/0.55 % (9179)------------------------------
% 0.22/0.55 % (9179)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.55 % (9179)Termination reason: Unknown
% 0.22/0.55 % (9179)Termination phase: SInE selection
% 0.22/0.55
% 0.22/0.55 % (9179)Memory used [KB]: 1791
% 0.22/0.55 % (9179)Time elapsed: 0.014 s
% 0.22/0.55 % (9179)Instructions burned: 47 (million)
% 0.22/0.55 % (9179)------------------------------
% 0.22/0.55 % (9179)------------------------------
% 0.22/0.56 % (9181)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on theBenchmark for (2998ds/507Mi)
% 0.22/0.56 % (9176)Instruction limit reached!
% 0.22/0.56 % (9176)------------------------------
% 0.22/0.56 % (9176)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.56 % (9176)Termination reason: Unknown
% 0.22/0.56 % (9176)Termination phase: Saturation
% 0.22/0.56
% 0.22/0.56 % (9176)Memory used [KB]: 6396
% 0.22/0.56 % (9176)Time elapsed: 0.030 s
% 0.22/0.56 % (9176)Instructions burned: 108 (million)
% 0.22/0.56 % (9176)------------------------------
% 0.22/0.56 % (9176)------------------------------
% 0.22/0.56 % (9182)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on theBenchmark for (2998ds/149Mi)
% 1.71/0.57 % (9183)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on theBenchmark for (2998ds/39Mi)
% 1.71/0.58 % (9180)Instruction limit reached!
% 1.71/0.58 % (9180)------------------------------
% 1.71/0.58 % (9180)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.71/0.58 % (9180)Termination reason: Unknown
% 1.71/0.58 % (9180)Termination phase: Saturation
% 1.71/0.58
% 1.71/0.58 % (9180)Memory used [KB]: 2046
% 1.71/0.58 % (9180)Time elapsed: 0.026 s
% 1.71/0.58 % (9180)Instructions burned: 99 (million)
% 1.71/0.58 % (9180)------------------------------
% 1.71/0.58 % (9180)------------------------------
% 1.71/0.58 % (9183)Instruction limit reached!
% 1.71/0.58 % (9183)------------------------------
% 1.71/0.58 % (9183)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.71/0.58 % (9183)Termination reason: Unknown
% 1.71/0.58 % (9183)Termination phase: Property scanning
% 1.71/0.58
% 1.71/0.58 % (9183)Memory used [KB]: 1791
% 1.71/0.58 % (9183)Time elapsed: 0.014 s
% 1.71/0.58 % (9183)Instructions burned: 42 (million)
% 1.71/0.58 % (9183)------------------------------
% 1.71/0.58 % (9183)------------------------------
% 1.71/0.59 % (9184)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)
% 1.71/0.59 % (9184)Instruction limit reached!
% 1.71/0.59 % (9184)------------------------------
% 1.71/0.59 % (9184)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.71/0.59 % (9184)Termination reason: Unknown
% 1.71/0.59 % (9184)Termination phase: shuffling
% 1.71/0.59
% 1.71/0.59 % (9184)Memory used [KB]: 1279
% 1.71/0.59 % (9184)Time elapsed: 0.003 s
% 1.71/0.59 % (9184)Instructions burned: 7 (million)
% 1.71/0.59 % (9184)------------------------------
% 1.71/0.59 % (9184)------------------------------
% 1.86/0.59 % (9165)First to succeed.
% 1.86/0.59 % (9164)Refutation not found, non-redundant clauses discarded% (9164)------------------------------
% 1.86/0.59 % (9164)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.86/0.59 % (9164)Termination reason: Refutation not found, non-redundant clauses discarded
% 1.86/0.59
% 1.86/0.59 % (9164)Memory used [KB]: 7547
% 1.86/0.59 % (9164)Time elapsed: 0.132 s
% 1.86/0.59 % (9164)Instructions burned: 371 (million)
% 1.86/0.59 % (9164)------------------------------
% 1.86/0.59 % (9164)------------------------------
% 1.86/0.59 % (9185)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)
% 1.86/0.60 % (9186)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on theBenchmark for (2997ds/47Mi)
% 1.86/0.60 % (9187)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)
% 1.86/0.60 % (9185)Refutation not found, incomplete strategy
% 1.86/0.60 % (9185)------------------------------
% 1.86/0.60 % (9185)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.86/0.60 % (9185)Termination reason: Refutation not found, incomplete strategy
% 1.86/0.60
% 1.86/0.60
% 1.86/0.60 % (9185)Memory used [KB]: 6268
% 1.86/0.60 % (9185)Time elapsed: 0.011 s
% 1.86/0.60 % (9185)Instructions burned: 29 (million)
% 1.86/0.60 % (9185)------------------------------
% 1.86/0.60 % (9185)------------------------------
% 1.86/0.61 % (9182)Instruction limit reached!
% 1.86/0.61 % (9182)------------------------------
% 1.86/0.61 % (9182)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.86/0.61 % (9182)Termination reason: Unknown
% 1.86/0.61 % (9182)Termination phase: Saturation
% 1.86/0.61
% 1.86/0.61 % (9182)Memory used [KB]: 6908
% 1.86/0.61 % (9182)Time elapsed: 0.045 s
% 1.86/0.61 % (9182)Instructions burned: 149 (million)
% 1.86/0.61 % (9182)------------------------------
% 1.86/0.61 % (9182)------------------------------
% 1.86/0.61 % (9186)Instruction limit reached!
% 1.86/0.61 % (9186)------------------------------
% 1.86/0.61 % (9186)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.86/0.61 % (9186)Termination reason: Unknown
% 1.86/0.61 % (9186)Termination phase: Property scanning
% 1.86/0.61
% 1.86/0.61 % (9186)Memory used [KB]: 1791
% 1.86/0.61 % (9186)Time elapsed: 0.015 s
% 1.86/0.61 % (9186)Instructions burned: 49 (million)
% 1.86/0.61 % (9186)------------------------------
% 1.86/0.61 % (9186)------------------------------
% 1.86/0.61 % (9187)Instruction limit reached!
% 1.86/0.61 % (9187)------------------------------
% 1.86/0.61 % (9187)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.86/0.61 % (9187)Termination reason: Unknown
% 1.86/0.61 % (9187)Termination phase: Property scanning
% 1.86/0.61
% 1.86/0.61 % (9187)Memory used [KB]: 1791
% 1.86/0.61 % (9187)Time elapsed: 0.013 s
% 1.86/0.61 % (9187)Instructions burned: 44 (million)
% 1.86/0.61 % (9187)------------------------------
% 1.86/0.61 % (9187)------------------------------
% 1.86/0.62 % (9189)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on theBenchmark for (2997ds/62Mi)
% 1.86/0.62 % (9188)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)
% 1.86/0.62 % (9190)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on theBenchmark for (2997ds/31Mi)
% 1.86/0.62 % (9191)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on theBenchmark for (2997ds/96Mi)
% 2.12/0.63 % (9190)Instruction limit reached!
% 2.12/0.63 % (9190)------------------------------
% 2.12/0.63 % (9190)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.12/0.63 % (9190)Termination reason: Unknown
% 2.12/0.63 % (9190)Termination phase: Property scanning
% 2.12/0.63
% 2.12/0.63 % (9190)Memory used [KB]: 1791
% 2.12/0.63 % (9190)Time elapsed: 0.010 s
% 2.12/0.63 % (9190)Instructions burned: 32 (million)
% 2.12/0.63 % (9190)------------------------------
% 2.12/0.63 % (9190)------------------------------
% 2.12/0.63 % (9165)Refutation found. Thanks to Tanya!
% 2.12/0.63 % SZS status Theorem for theBenchmark
% 2.12/0.63 % SZS output start Proof for theBenchmark
% See solution above
% 2.12/0.63 % (9165)------------------------------
% 2.12/0.63 % (9165)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.12/0.63 % (9165)Termination reason: Refutation
% 2.12/0.63
% 2.12/0.63 % (9165)Memory used [KB]: 10362
% 2.12/0.63 % (9165)Time elapsed: 0.149 s
% 2.12/0.63 % (9165)Instructions burned: 298 (million)
% 2.12/0.63 % (9165)------------------------------
% 2.12/0.63 % (9165)------------------------------
% 2.12/0.63 % (9137)Success in time 0.254 s
% 2.15/0.63 % Vampire---4.8 exiting
%------------------------------------------------------------------------------