%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : ALG267^1 : TPTP v8.1.2. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 04:13:29 EDT 2024
% Result : Theorem 2.05s 0.64s
% Output : Refutation 2.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 99
% Syntax : Number of formulae : 284 ( 221 unt; 57 typ; 0 def)
% Number of atoms : 6110 (1255 equ; 0 cnn)
% Maximal formula atoms : 37 ( 26 avg)
% Number of connectives : 27062 ( 216 ~; 0 |; 103 &;19774 @)
% ( 0 <=>;2970 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 2 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 : 4454 (4178 ^ 273 !; 2 ?;4454 :)
% ( 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 ) > 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: ( term > $o ) > term ).
thf(func_def_147,type,
sK6: ( term > $o ) > term ).
thf(func_def_148,type,
sK7: ( term > $o ) > term ).
thf(func_def_149,type,
sK8: ( term > $o ) > term ).
thf(func_def_150,type,
sK9: ( term > $o ) > subst > term ).
thf(func_def_151,type,
sK10: ( subst > term > term ) > term ).
thf(func_def_152,type,
sK11: ( subst > term > term ) > subst ).
thf(func_def_153,type,
sK12: ( subst > term > term ) > subst ).
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 ) > term ).
thf(func_def_158,type,
sK17: ( subst > term > subst > $o ) > subst ).
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 ) > term ).
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 ) > term ).
thf(func_def_165,type,
sK24: ( subst > term > subst > $o ) > subst ).
thf(func_def_166,type,
sK25: ( subst > term > subst > $o ) > term ).
thf(func_def_167,type,
sK26: ( subst > term > subst > $o ) > term ).
thf(func_def_168,type,
sK27: ( subst > term > subst > $o ) > subst ).
thf(func_def_169,type,
sK28: ( subst > term > subst > $o ) > subst ).
thf(func_def_170,type,
sK29: ( subst > term > subst > $o ) > term ).
thf(func_def_171,type,
sK30: ( subst > term > subst > $o ) > subst ).
thf(func_def_172,type,
sK31: ( subst > term > subst > $o ) > subst ).
thf(func_def_173,type,
sK32: term ).
thf(func_def_174,type,
sK33: ( subst > term > term ) > subst ).
thf(func_def_175,type,
sK34: ( subst > term > term ) > term ).
thf(func_def_176,type,
sK35: ( subst > term > term ) > subst ).
thf(func_def_177,type,
sK36: ( subst > term > term ) > subst ).
thf(func_def_178,type,
sK37: ( subst > term > term ) > subst ).
thf(func_def_179,type,
sK38: ( subst > term > term ) > term ).
thf(func_def_180,type,
ph39:
!>[X0: $tType] : X0 ).
thf(f1209,plain,
$false,
inference(equality_resolution,[],[f1199]) ).
thf(f1199,plain,
! [X1: subst > term > term] :
( ( X1 @ sh @ one )
!= sK32 ),
inference(forward_demodulation,[],[f1198,f474]) ).
thf(f474,plain,
! [X1: term] :
( ( sub @ X1 @ id )
= X1 ),
inference(equality_proxy_clausification,[],[f473]) ).
thf(f473,plain,
! [X1: term] :
( ( ( sub @ X1 @ id )
= X1 )
= $true ),
inference(beta_eta_normalization,[],[f472]) ).
thf(f472,plain,
! [X1: term] :
( $true
= ( ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 )
@ X1 ) ),
inference(pi_clausification,[],[f471]) ).
thf(f471,plain,
( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ),
inference(binary_proxy_clausification,[],[f468]) ).
thf(f468,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ ( lam @ Y1 ) @ Y0 )
= ( lam @ ( sub @ Y1 @ ( push @ one @ ( comp @ Y0 @ sh ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ 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 @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y0 ) @ Y1 )
= ( push @ ( sub @ Y2 @ Y1 ) @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y3 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ 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 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ Y0 ) ) ) )
=> ( ( Y1 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ ( push @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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 @ Y2 @ Y0 ) @ Y1 )
= ( comp @ Y2 @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) )
= ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 ) ) ) ) )
=> ( ( ( lam @ ( Y1 @ sh @ one ) )
= ( lam @ ( Y0 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y1 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y4 @ 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 @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ Y1 @ Y2 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f459]) ).
thf(f459,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ one @ ( push @ Y1 @ Y0 ) )
= Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ ( lam @ Y1 ) @ Y0 )
= ( lam @ ( sub @ Y1 @ ( push @ one @ ( comp @ Y0 @ sh ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ 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 @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y0 ) @ Y1 )
= ( push @ ( sub @ Y2 @ Y1 ) @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y3 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ 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 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ Y0 ) ) ) )
=> ( ( Y1 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ ( push @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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 @ Y2 @ Y0 ) @ Y1 )
= ( comp @ Y2 @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) )
= ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 ) ) ) ) )
=> ( ( ( lam @ ( Y1 @ sh @ one ) )
= ( lam @ ( Y0 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y1 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y4 @ 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 @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ Y1 @ Y2 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f458]) ).
thf(f458,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y0 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( ap @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ one @ ( push @ Y1 @ Y0 ) )
= Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ ( lam @ Y1 ) @ Y0 )
= ( lam @ ( sub @ Y1 @ ( push @ one @ ( comp @ Y0 @ sh ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ 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 @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y0 ) @ Y1 )
= ( push @ ( sub @ Y2 @ Y1 ) @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y3 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ 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 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ Y0 ) ) ) )
=> ( ( Y1 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ ( push @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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 @ Y2 @ Y0 ) @ Y1 )
= ( comp @ Y2 @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) )
= ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 ) ) ) ) )
=> ( ( ( lam @ ( Y1 @ sh @ one ) )
= ( lam @ ( Y0 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y1 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y4 @ 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 @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ Y1 @ Y2 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f457]) ).
thf(f457,plain,
( $true
= ( ~ ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y0 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( ap @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ one @ ( push @ Y1 @ Y0 ) )
= Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ ( lam @ Y1 ) @ Y0 )
= ( lam @ ( sub @ Y1 @ ( push @ one @ ( comp @ Y0 @ sh ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ 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 @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y0 ) @ Y1 )
= ( push @ ( sub @ Y2 @ Y1 ) @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y3 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ 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 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ Y0 ) ) ) )
=> ( ( Y1 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ ( push @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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 @ Y2 @ Y0 ) @ Y1 )
= ( comp @ Y2 @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) )
= ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 ) ) ) ) )
=> ( ( ( lam @ ( Y1 @ sh @ one ) )
= ( lam @ ( Y0 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y1 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y4 @ 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 @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ Y1 @ Y2 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f456]) ).
thf(f456,plain,
( $true
= ( ~ ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y0 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( ap @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ one @ ( push @ Y1 @ Y0 ) )
= Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ ( lam @ Y1 ) @ Y0 )
= ( lam @ ( sub @ Y1 @ ( push @ one @ ( comp @ Y0 @ sh ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ 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 @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y0 ) @ Y1 )
= ( push @ ( sub @ Y2 @ Y1 ) @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y3 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ 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 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ Y0 ) ) ) )
=> ( ( Y1 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ ( push @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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 @ Y2 @ Y0 ) @ Y1 )
= ( comp @ Y2 @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ 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
@ Y2
@ id
@ Y3 )
= ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y0
@ id
@ Y1 ) )
=> ( Y2 = 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
@ Y2
@ id
@ Y3 )
= ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y0
@ id
@ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) )
= ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 ) ) ) ) )
=> ( ( ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) )
= ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y0 @ Y2 @ Y3 ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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: term,Y5: subst,Y6: term] : ( ap @ ( sub @ Y4 @ Y5 ) @ Y6 )
@ id
@ Y2
@ id
@ Y1 )
!= ( ^ [Y3: subst,Y4: subst > term > term] : ( lam @ ( Y4 @ sh @ one ) )
@ id
@ ^ [Y3: subst,Y4: term] : ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ~ ( ^ [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
@ Y0
@ id
@ Y1 )
@ id ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y1 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y4 @ 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 @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ Y1 @ Y2 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f366,f444]) ).
thf(f444,plain,
( hoasinduction_lem3b_gthm
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y0 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( ap @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ one @ ( push @ Y1 @ Y0 ) )
= Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ ( lam @ Y1 ) @ Y0 )
= ( lam @ ( sub @ Y1 @ ( push @ one @ ( comp @ Y0 @ sh ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ 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 @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y0 ) @ Y1 )
= ( push @ ( sub @ Y2 @ Y1 ) @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y3 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ 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 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ Y0 ) ) ) )
=> ( ( Y1 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ ( push @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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 @ Y2 @ Y0 ) @ Y1 )
= ( comp @ Y2 @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ 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
@ Y2
@ id
@ Y3 )
= ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y0
@ id
@ Y1 ) )
=> ( Y2 = 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
@ Y2
@ id
@ Y3 )
= ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y0
@ id
@ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) )
= ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 ) ) ) ) )
=> ( ( ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) )
= ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y0 @ Y2 @ Y3 ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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: term,Y5: subst,Y6: term] : ( ap @ ( sub @ Y4 @ Y5 ) @ Y6 )
@ id
@ Y2
@ id
@ Y1 )
!= ( ^ [Y3: subst,Y4: subst > term > term] : ( lam @ ( Y4 @ sh @ one ) )
@ id
@ ^ [Y3: subst,Y4: term] : ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ~ ( ^ [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
@ Y0
@ id
@ Y1 )
@ id ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y1 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y4 @ 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 @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ Y1 @ Y2 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f358,f341,f348,f372,f355,f410,f338,f392,f373,f402,f357,f349,f365,f413,f397,f378,f340,f339,f384,f409,f354,f352,f383,f411,f337,f398,f362,f390,f359,f418,f417,f429,f435,f436,f434,f420,f421,f380]) ).
thf(f380,plain,
( hoasinduction_lem3b
= ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ),
inference(cnf_transformation,[],[f210]) ).
thf(f210,plain,
( hoasinduction_lem3b
= ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ),
inference(fool_elimination,[],[f209]) ).
thf(f209,plain,
( hoasinduction_lem3b
= ( ! [X0: term] :
? [X1: subst > term > term] :
( ( sub @ X0 @ ( push @ one @ sh ) )
= ( X1 @ sh @ one ) ) ) ),
inference(rectify,[],[f105]) ).
thf(f105,axiom,
( hoasinduction_lem3b
= ( ! [X1: term] :
? [X10: subst > term > term] :
( ( X10 @ sh @ one )
= ( sub @ X1 @ ( push @ one @ sh ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YlQgltIeMe/Vampire---4.8_1736',hoasinduction_lem3b) ).
thf(f421,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 @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y1 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y4 @ 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 @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ Y1 @ Y2 ) @ id ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f389,f405]) ).
thf(f405,plain,
( hoasap
= ( ^ [Y0: subst,Y1: term,Y2: subst,Y3: term] : ( ap @ ( sub @ Y1 @ Y2 ) @ Y3 ) ) ),
inference(cnf_transformation,[],[f189]) ).
thf(f189,plain,
( hoasap
= ( ^ [Y0: subst,Y1: term,Y2: subst,Y3: term] : ( ap @ ( sub @ Y1 @ Y2 ) @ Y3 ) ) ),
inference(fool_elimination,[],[f188]) ).
thf(f188,plain,
( hoasap
= ( ^ [X0: subst,X1: term,X2: subst,X3: term] : ( ap @ ( sub @ X1 @ X2 ) @ X3 ) ) ),
inference(rectify,[],[f55]) ).
thf(f55,axiom,
( hoasap
= ( ^ [X2: subst,X0: term,X3: subst,X1: term] : ( ap @ ( sub @ X0 @ X3 ) @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YlQgltIeMe/Vampire---4.8_1736',hoasap) ).
thf(f389,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 @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y1 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y4 @ 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 @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ Y1 @ Y2 ) @ id ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f195]) ).
thf(f195,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 @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y1 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y4 @ 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 @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ Y1 @ Y2 ) @ id ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f194]) ).
thf(f194,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 @ X6 @ X5 ) @ ( sub @ X7 @ X5 ) @ X8 )
=> ( X0 @ X6 @ X7 @ ( comp @ X5 @ 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 @ X12 @ id )
=> ( ( X0 @ id @ X11 @ id )
=> ( X0 @ id @ ( ap @ X12 @ X11 ) @ 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 ) )
=> ( ! [X4: subst,X2: 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 ) ) )
=> ! [X1: term,X0: term] :
( ( X5 @ id @ X0 @ id )
=> ( ( X5 @ id @ X1 @ id )
=> ( X5 @ id @ ( ap @ X0 @ X1 ) @ id ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YlQgltIeMe/Vampire---4.8_1736',hoasinduction_lem2) ).
thf(f420,plain,
( hoasinduction_lem1
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ 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,[],[f386,f374]) ).
thf(f374,plain,
( hoasvar
= ( ^ [Y0: subst,Y1: term,Y2: subst] : ( var @ ( sub @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f333]) ).
thf(f333,plain,
( hoasvar
= ( ^ [Y0: subst,Y1: term,Y2: subst] : ( var @ ( sub @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f332]) ).
thf(f332,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/tmp/tmp.YlQgltIeMe/Vampire---4.8_1736',hoasvar) ).
thf(f386,plain,
( hoasinduction_lem1
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( hoasvar @ id @ Y1 @ id )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f320]) ).
thf(f320,plain,
( hoasinduction_lem1
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( hoasvar @ id @ Y1 @ id )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f319]) ).
thf(f319,plain,
( hoasinduction_lem1
= ( ! [X0: subst > term > subst > $o] :
( ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( X0 @ X1 @ X2 @ ( comp @ X3 @ X4 ) )
=> ( X0 @ ( comp @ X1 @ X3 ) @ ( sub @ X2 @ X3 ) @ X4 ) )
=> ( ! [X5: subst,X6: subst,X7: subst,X8: term] :
( ( X0 @ ( comp @ X7 @ X5 ) @ ( sub @ X8 @ X5 ) @ X6 )
=> ( X0 @ X7 @ X8 @ ( comp @ X5 @ X6 ) ) )
=> ( ! [X9: term] :
( ( hoasvar @ id @ X9 @ id )
=> ( X0 @ id @ X9 @ id ) )
=> ! [X10: term] :
( ( var @ X10 )
=> ( X0 @ id @ X10 @ id ) ) ) ) ) ) ),
inference(rectify,[],[f90]) ).
thf(f90,axiom,
( hoasinduction_lem1
= ( ! [X5: subst > term > subst > $o] :
( ! [X2: subst,X0: term,X4: subst,X3: subst] :
( ( X5 @ X2 @ X0 @ ( comp @ X4 @ X3 ) )
=> ( X5 @ ( comp @ X2 @ X4 ) @ ( sub @ X0 @ X4 ) @ X3 ) )
=> ( ! [X4: subst,X3: subst,X2: subst,X0: term] :
( ( X5 @ ( comp @ X2 @ X4 ) @ ( sub @ X0 @ X4 ) @ X3 )
=> ( X5 @ X2 @ X0 @ ( comp @ X4 @ X3 ) ) )
=> ( ! [X0: term] :
( ( hoasvar @ id @ X0 @ id )
=> ( X5 @ id @ X0 @ id ) )
=> ! [X0: term] :
( ( var @ X0 )
=> ( X5 @ id @ X0 @ id ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YlQgltIeMe/Vampire---4.8_1736',hoasinduction_lem1) ).
thf(f434,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
@ Y0
@ id
@ Y1 )
@ id ) ) ) ),
inference(definition_unfolding,[],[f356,f374,f405]) ).
thf(f356,plain,
( hoasapnotvar
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( hoasvar @ id @ ( hoasap @ id @ Y0 @ id @ Y1 ) @ id ) ) ) ),
inference(cnf_transformation,[],[f160]) ).
thf(f160,plain,
( hoasapnotvar
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( hoasvar @ id @ ( hoasap @ id @ Y0 @ id @ Y1 ) @ id ) ) ) ),
inference(fool_elimination,[],[f159]) ).
thf(f159,plain,
! [X0: term,X1: term] :
( ( ~ ( hoasvar @ id @ ( hoasap @ id @ X1 @ id @ X0 ) @ id ) )
= hoasapnotvar ),
inference(rectify,[],[f73]) ).
thf(f73,axiom,
! [X1: term,X0: term] :
( ( ~ ( hoasvar @ id @ ( hoasap @ id @ X0 @ id @ X1 ) @ id ) )
= hoasapnotvar ),
file('/export/starexec/sandbox/tmp/tmp.YlQgltIeMe/Vampire---4.8_1736',hoasapnotvar) ).
thf(f436,plain,
( hoaslamnotvar
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ~ ( ^ [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,[],[f351,f374,f391]) ).
thf(f391,plain,
( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( lam @ ( Y1 @ sh @ one ) ) ) ),
inference(cnf_transformation,[],[f287]) ).
thf(f287,plain,
( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( lam @ ( Y1 @ sh @ one ) ) ) ),
inference(fool_elimination,[],[f286]) ).
thf(f286,plain,
( hoaslam
= ( ^ [X0: subst,X1: subst > term > term] : ( lam @ ( X1 @ sh @ one ) ) ) ),
inference(rectify,[],[f56]) ).
thf(f56,axiom,
( hoaslam
= ( ^ [X2: subst,X10: subst > term > term] : ( lam @ ( X10 @ sh @ one ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YlQgltIeMe/Vampire---4.8_1736',hoaslam) ).
thf(f351,plain,
( hoaslamnotvar
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ~ ( hoasvar @ id
@ ( hoaslam @ id
@ ^ [Y1: subst,Y2: term] : ( Y0 @ Y1 @ Y2 ) )
@ id ) ) ) ),
inference(cnf_transformation,[],[f139]) ).
thf(f139,plain,
( hoaslamnotvar
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ~ ( hoasvar @ id
@ ( hoaslam @ id
@ ^ [Y1: subst,Y2: term] : ( Y0 @ Y1 @ Y2 ) )
@ id ) ) ) ),
inference(fool_elimination,[],[f138]) ).
thf(f138,plain,
( hoaslamnotvar
= ( ! [X0: subst > term > term] :
( ! [X1: subst,X2: term,X3: subst] :
( ( X0 @ ( comp @ X1 @ X3 ) @ ( sub @ X2 @ X3 ) )
= ( sub @ ( X0 @ X1 @ X2 ) @ X3 ) )
=> ~ ( hoasvar @ id
@ ( hoaslam @ id
@ ^ [X4: subst,X5: term] : ( X0 @ X4 @ X5 ) )
@ id ) ) ) ),
inference(rectify,[],[f70]) ).
thf(f70,axiom,
( hoaslamnotvar
= ( ! [X10: subst > term > term] :
( ! [X2: subst,X0: term,X3: 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/tmp/tmp.YlQgltIeMe/Vampire---4.8_1736',hoaslamnotvar) ).
thf(f435,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: term,Y5: subst,Y6: term] : ( ap @ ( sub @ Y4 @ Y5 ) @ Y6 )
@ id
@ Y2
@ id
@ Y1 )
!= ( ^ [Y3: subst,Y4: subst > term > term] : ( lam @ ( Y4 @ sh @ one ) )
@ id
@ ^ [Y3: subst,Y4: term] : ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f394,f405,f391]) ).
thf(f394,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] :
( ( hoasap @ id @ Y2 @ id @ Y1 )
!= ( hoaslam @ id
@ ^ [Y3: subst,Y4: term] : ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f227]) ).
thf(f227,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] :
( ( hoasap @ id @ Y2 @ id @ Y1 )
!= ( hoaslam @ id
@ ^ [Y3: subst,Y4: term] : ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f226]) ).
thf(f226,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] :
( ( hoasap @ id @ X4 @ id @ X5 )
!= ( hoaslam @ id
@ ^ [X6: subst,X7: term] : ( X0 @ X6 @ X7 ) ) ) ) ) ),
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 ) ) )
=> ! [X0: term,X1: term] :
( ( hoasap @ id @ X0 @ id @ X1 )
!= ( hoaslam @ id
@ ^ [X2: subst,X6: term] : ( X10 @ X2 @ X6 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YlQgltIeMe/Vampire---4.8_1736',hoaslamnotap) ).
thf(f429,plain,
( hoaslaminj
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) )
= ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 ) ) ) ) )
=> ( ( ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) )
= ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y0 @ Y2 @ Y3 ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f350,f391,f391]) ).
thf(f350,plain,
( hoaslaminj
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) )
= ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 ) ) ) ) )
=> ( ( ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) )
= ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y0 @ Y2 @ Y3 ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f118]) ).
thf(f118,plain,
( hoaslaminj
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) )
= ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 ) ) ) ) )
=> ( ( ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) )
= ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y0 @ Y2 @ Y3 ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f117]) ).
thf(f117,plain,
( hoaslaminj
= ( ! [X0: subst > term > term] :
( ! [X1: subst,X2: term,X3: subst] :
( ( X0 @ ( comp @ X1 @ X3 ) @ ( sub @ X2 @ X3 ) )
= ( sub @ ( X0 @ X1 @ X2 ) @ X3 ) )
=> ! [X4: subst > term > term] :
( ! [X5: term,X6: subst,X7: subst] :
( ( X4 @ ( comp @ X7 @ X6 ) @ ( sub @ X5 @ X6 ) )
= ( sub @ ( X4 @ X7 @ X5 ) @ X6 ) )
=> ( ( ( hoaslam @ id
@ ^ [X8: subst,X9: term] : ( X4 @ X8 @ X9 ) )
= ( hoaslam @ id
@ ^ [X10: subst,X11: term] : ( X0 @ X10 @ X11 ) ) )
=> ! [X12: term,X13: subst] :
( ( X0 @ X13 @ X12 )
= ( X4 @ X13 @ X12 ) ) ) ) ) ) ),
inference(rectify,[],[f64]) ).
thf(f64,axiom,
( hoaslaminj
= ( ! [X10: subst > term > term] :
( ! [X2: subst,X0: term,X3: subst] :
( ( sub @ ( X10 @ X2 @ X0 ) @ X3 )
= ( X10 @ ( comp @ X2 @ X3 ) @ ( sub @ X0 @ X3 ) ) )
=> ! [X11: subst > term > term] :
( ! [X0: term,X3: subst,X2: subst] :
( ( sub @ ( X11 @ X2 @ X0 ) @ X3 )
= ( X11 @ ( comp @ X2 @ X3 ) @ ( sub @ X0 @ X3 ) ) )
=> ( ( ( hoaslam @ id
@ ^ [X2: subst,X0: term] : ( X11 @ X2 @ X0 ) )
= ( hoaslam @ id
@ ^ [X2: subst,X0: term] : ( X10 @ X2 @ X0 ) ) )
=> ! [X0: term,X2: subst] :
( ( X10 @ X2 @ X0 )
= ( X11 @ X2 @ X0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YlQgltIeMe/Vampire---4.8_1736',hoaslaminj) ).
thf(f417,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
@ Y2
@ id
@ Y3 )
= ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y0
@ id
@ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f381,f405,f405]) ).
thf(f381,plain,
( hoasapinj2
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( hoasap @ id @ Y2 @ id @ Y3 )
= ( hoasap @ id @ Y0 @ id @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f312]) ).
thf(f312,plain,
( hoasapinj2
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( hoasap @ id @ Y2 @ id @ Y3 )
= ( hoasap @ id @ Y0 @ id @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f311]) ).
thf(f311,plain,
( hoasapinj2
= ( ! [X0: term,X1: term,X2: term,X3: term] :
( ( ( hoasap @ id @ X1 @ id @ X0 )
= ( hoasap @ id @ X3 @ id @ X2 ) )
=> ( X0 = X2 ) ) ) ),
inference(rectify,[],[f61]) ).
thf(f61,axiom,
( hoasapinj2
= ( ! [X7: term,X1: term,X6: term,X0: term] :
( ( ( hoasap @ id @ X0 @ id @ X6 )
= ( hoasap @ id @ X1 @ id @ X7 ) )
=> ( X6 = X7 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YlQgltIeMe/Vampire---4.8_1736',hoasapinj2) ).
thf(f418,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
@ Y2
@ id
@ Y3 )
= ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y0
@ id
@ Y1 ) )
=> ( Y2 = Y0 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f387,f405,f405]) ).
thf(f387,plain,
( hoasapinj1
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( hoasap @ id @ Y2 @ id @ Y3 )
= ( hoasap @ id @ Y0 @ id @ Y1 ) )
=> ( Y2 = Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f322]) ).
thf(f322,plain,
( hoasapinj1
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( hoasap @ id @ Y2 @ id @ Y3 )
= ( hoasap @ id @ Y0 @ id @ Y1 ) )
=> ( Y2 = Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f321]) ).
thf(f321,plain,
! [X0: term,X1: term,X2: term,X3: term] :
( ( ( ( hoasap @ id @ X1 @ id @ X0 )
= ( hoasap @ id @ X3 @ id @ X2 ) )
=> ( X1 = X3 ) )
= hoasapinj1 ),
inference(rectify,[],[f58]) ).
thf(f58,axiom,
! [X7: term,X1: term,X6: term,X0: term] :
( ( ( ( hoasap @ id @ X0 @ id @ X6 )
= ( hoasap @ id @ X1 @ id @ X7 ) )
=> ( X0 = X1 ) )
= hoasapinj1 ),
file('/export/starexec/sandbox/tmp/tmp.YlQgltIeMe/Vampire---4.8_1736',hoasapinj1) ).
thf(f359,plain,
( termmset
= ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f217]) ).
thf(f217,plain,
( termmset
= ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f216]) ).
thf(f216,plain,
( ! [X0: subst,X1: term,X2: subst] :
( ( sub @ X1 @ ( comp @ X2 @ X0 ) )
= ( sub @ ( sub @ X1 @ X2 ) @ X0 ) )
& ! [X3: term] :
( ( ( sub @ X3 @ id )
= X3 )
= termmset ) ),
inference(rectify,[],[f52]) ).
thf(f52,axiom,
( ! [X3: subst,X0: term,X2: subst] :
( ( sub @ ( sub @ X0 @ X2 ) @ X3 )
= ( sub @ X0 @ ( comp @ X2 @ X3 ) ) )
& ! [X0: term] :
( ( ( sub @ X0 @ id )
= X0 )
= termmset ) ),
file('/export/starexec/sandbox/tmp/tmp.YlQgltIeMe/Vampire---4.8_1736',termmset) ).
thf(f390,plain,
( substmonoid
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y0 ) @ Y1 )
= ( comp @ Y2 @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) ) ),
inference(cnf_transformation,[],[f171]) ).
thf(f171,plain,
( substmonoid
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y0 ) @ Y1 )
= ( comp @ Y2 @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) ) ),
inference(fool_elimination,[],[f170]) ).
thf(f170,plain,
( ! [X0: subst] :
( ( comp @ id @ X0 )
= X0 )
& ! [X1: subst] :
( ( comp @ X1 @ id )
= X1 )
& ! [X2: subst,X3: subst,X4: subst] :
( ( ( comp @ ( comp @ X2 @ X4 ) @ X3 )
= ( comp @ X2 @ ( comp @ X4 @ X3 ) ) )
= substmonoid ) ),
inference(rectify,[],[f49]) ).
thf(f49,axiom,
( ! [X2: subst] :
( ( comp @ id @ X2 )
= X2 )
& ! [X2: subst] :
( ( comp @ X2 @ id )
= X2 )
& ! [X2: subst,X4: subst,X3: subst] :
( ( ( comp @ ( comp @ X2 @ X3 ) @ X4 )
= ( comp @ X2 @ ( comp @ X3 @ X4 ) ) )
= substmonoid ) ),
file('/export/starexec/sandbox/tmp/tmp.YlQgltIeMe/Vampire---4.8_1736',substmonoid) ).
thf(f362,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,[],[f310]) ).
thf(f310,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,[],[f309]) ).
thf(f309,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/tmp/tmp.YlQgltIeMe/Vampire---4.8_1736',induction2) ).
thf(f398,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 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f158]) ).
thf(f158,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 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f157]) ).
thf(f157,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: term,X6: subst] :
( ! [X7: term] :
( ( var @ X7 )
=> ( X0 @ ( sub @ X7 @ X6 ) ) )
=> ( X0 @ ( sub @ X5 @ X6 ) ) ) ) ) ) ),
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 ) ) )
=> ! [X0: term,X2: subst] :
( ! [X1: term] :
( ( var @ X1 )
=> ( X5 @ ( sub @ X1 @ X2 ) ) )
=> ( X5 @ ( sub @ X0 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YlQgltIeMe/Vampire---4.8_1736',induction2lem) ).
thf(f337,plain,
( pushprop
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ Y0 ) ) ) )
=> ( ( Y1 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ ( push @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f177]) ).
thf(f177,plain,
( pushprop
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ Y0 ) ) ) )
=> ( ( Y1 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ ( push @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f176]) ).
thf(f176,plain,
( pushprop
= ( ! [X0: term,X1: term > $o,X2: subst] :
( ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ ( sub @ X3 @ X2 ) ) )
=> ( ( X1 @ X0 )
=> ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ ( push @ X0 @ X2 ) ) ) ) ) ) ) ),
inference(rectify,[],[f39]) ).
thf(f39,axiom,
( pushprop
= ( ! [X0: term,X5: term > $o,X2: subst] :
( ! [X1: term] :
( ( var @ X1 )
=> ( X5 @ ( sub @ X1 @ X2 ) ) )
=> ( ( X5 @ X0 )
=> ! [X1: term] :
( ( var @ X1 )
=> ( X5 @ ( sub @ X1 @ ( push @ X0 @ X2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YlQgltIeMe/Vampire---4.8_1736',pushprop) ).
thf(f411,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,[],[f199]) ).
thf(f199,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,[],[f198]) ).
thf(f198,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/tmp/tmp.YlQgltIeMe/Vampire---4.8_1736',induction) ).
thf(f383,plain,
( lamnotvar
= ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f235]) ).
thf(f235,plain,
( lamnotvar
= ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) ) ),
inference(fool_elimination,[],[f234]) ).
thf(f234,plain,
! [X0: term] :
( ( ~ ( var @ ( lam @ X0 ) ) )
= lamnotvar ),
inference(rectify,[],[f22]) ).
thf(f22,axiom,
! [X0: term] :
( ( ~ ( var @ ( lam @ X0 ) ) )
= lamnotvar ),
file('/export/starexec/sandbox/tmp/tmp.YlQgltIeMe/Vampire---4.8_1736',lamnotvar) ).
thf(f352,plain,
( apnotvar
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f155]) ).
thf(f155,plain,
( apnotvar
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f154]) ).
thf(f154,plain,
( apnotvar
= ( ! [X0: term,X1: term] :
~ ( var @ ( ap @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f21]) ).
thf(f21,axiom,
( apnotvar
= ( ! [X0: term,X1: term] :
~ ( var @ ( ap @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YlQgltIeMe/Vampire---4.8_1736',apnotvar) ).
thf(f354,plain,
( lamnotap
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f137]) ).
thf(f137,plain,
( lamnotap
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f136]) ).
thf(f136,plain,
( lamnotap
= ( ! [X0: term,X1: term,X2: term] :
( ( lam @ X0 )
!= ( ap @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f20]) ).
thf(f20,axiom,
( lamnotap
= ( ! [X0: term,X6: term,X1: term] :
( ( lam @ X0 )
!= ( ap @ X1 @ X6 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YlQgltIeMe/Vampire---4.8_1736',lamnotap) ).
thf(f409,plain,
( shinj
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f335]) ).
thf(f335,plain,
( shinj
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(fool_elimination,[],[f334]) ).
thf(f334,plain,
! [X0: term,X1: term] :
( ( ( ( sub @ X0 @ sh )
= ( sub @ X1 @ sh ) )
=> ( X0 = X1 ) )
= shinj ),
inference(rectify,[],[f19]) ).
thf(f19,axiom,
! [X1: term,X0: term] :
( ( ( ( sub @ X0 @ sh )
= ( sub @ X1 @ sh ) )
=> ( X0 = X1 ) )
= shinj ),
file('/export/starexec/sandbox/tmp/tmp.YlQgltIeMe/Vampire---4.8_1736',shinj) ).
thf(f384,plain,
( laminj
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f298]) ).
thf(f298,plain,
( laminj
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f18,axiom,
! [X0: term,X1: term] :
( ( ( ( lam @ X0 )
= ( lam @ X1 ) )
=> ( X0 = X1 ) )
= laminj ),
file('/export/starexec/sandbox/tmp/tmp.YlQgltIeMe/Vampire---4.8_1736',laminj) ).
thf(f339,plain,
( apinj2
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y3 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f273]) ).
thf(f273,plain,
( apinj2
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y3 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f272]) ).
thf(f272,plain,
! [X0: term,X1: term,X2: term,X3: term] :
( ( ( ( ap @ X2 @ X0 )
= ( ap @ X3 @ X1 ) )
=> ( X0 = X1 ) )
= apinj2 ),
inference(rectify,[],[f17]) ).
thf(f17,axiom,
! [X7: term,X6: term,X1: term,X0: term] :
( ( ( ( ap @ X0 @ X6 )
= ( ap @ X1 @ X7 ) )
=> ( X6 = X7 ) )
= apinj2 ),
file('/export/starexec/sandbox/tmp/tmp.YlQgltIeMe/Vampire---4.8_1736',apinj2) ).
thf(f340,plain,
( apinj1
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f173]) ).
thf(f173,plain,
( apinj1
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f172]) ).
thf(f172,plain,
! [X0: term,X1: term,X2: term,X3: term] :
( ( ( ( ap @ X0 @ X2 )
= ( ap @ X3 @ X1 ) )
=> ( X0 = X3 ) )
= apinj1 ),
inference(rectify,[],[f16]) ).
thf(f16,axiom,
! [X0: term,X7: term,X6: term,X1: term] :
( ( ( ( ap @ X0 @ X6 )
= ( ap @ X1 @ X7 ) )
=> ( X0 = X1 ) )
= apinj1 ),
file('/export/starexec/sandbox/tmp/tmp.YlQgltIeMe/Vampire---4.8_1736',apinj1) ).
thf(f378,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,[],[f295]) ).
thf(f295,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,[],[f294]) ).
thf(f294,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/tmp/tmp.YlQgltIeMe/Vampire---4.8_1736',ulamvarind) ).
thf(f397,plain,
( ulamvarsh
= ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) ) ),
inference(cnf_transformation,[],[f193]) ).
thf(f193,plain,
( ulamvarsh
= ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) ) ),
inference(fool_elimination,[],[f192]) ).
thf(f192,plain,
! [X0: term] :
( ( ( var @ X0 )
=> ( var @ ( sub @ X0 @ sh ) ) )
= ulamvarsh ),
inference(rectify,[],[f14]) ).
thf(f14,axiom,
! [X0: term] :
( ( ( var @ X0 )
=> ( var @ ( sub @ X0 @ sh ) ) )
= ulamvarsh ),
file('/export/starexec/sandbox/tmp/tmp.YlQgltIeMe/Vampire---4.8_1736',ulamvarsh) ).
thf(f413,plain,
( ulamvar1
= ( var @ one ) ),
inference(cnf_transformation,[],[f156]) ).
thf(f156,plain,
( ulamvar1
= ( var @ one ) ),
inference(fool_elimination,[],[f13]) ).
thf(f13,axiom,
( ulamvar1
= ( var @ one ) ),
file('/export/starexec/sandbox/tmp/tmp.YlQgltIeMe/Vampire---4.8_1736',ulamvar1) ).
thf(f365,plain,
( axscons
= ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) ) ),
inference(cnf_transformation,[],[f255]) ).
thf(f255,plain,
( axscons
= ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) ) ),
inference(fool_elimination,[],[f254]) ).
thf(f254,plain,
( axscons
= ( ! [X0: subst] :
( ( push @ ( sub @ one @ X0 ) @ ( comp @ sh @ X0 ) )
= X0 ) ) ),
inference(rectify,[],[f12]) ).
thf(f12,axiom,
( axscons
= ( ! [X2: subst] :
( ( push @ ( sub @ one @ X2 ) @ ( comp @ sh @ X2 ) )
= X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YlQgltIeMe/Vampire---4.8_1736',axscons) ).
thf(f349,plain,
( axvarshift
= ( id
= ( push @ one @ sh ) ) ),
inference(cnf_transformation,[],[f206]) ).
thf(f206,plain,
( axvarshift
= ( id
= ( push @ one @ sh ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f11,axiom,
( ( id
= ( push @ one @ sh ) )
= axvarshift ),
file('/export/starexec/sandbox/tmp/tmp.YlQgltIeMe/Vampire---4.8_1736',axvarshift) ).
thf(f357,plain,
( axidr
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) ),
inference(cnf_transformation,[],[f153]) ).
thf(f153,plain,
( axidr
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) ),
inference(fool_elimination,[],[f152]) ).
thf(f152,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/tmp/tmp.YlQgltIeMe/Vampire---4.8_1736',axidr) ).
thf(f402,plain,
( axmap
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y0 ) @ Y1 )
= ( push @ ( sub @ Y2 @ Y1 ) @ ( comp @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f135]) ).
thf(f135,plain,
( axmap
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y0 ) @ Y1 )
= ( push @ ( sub @ Y2 @ Y1 ) @ ( comp @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f134]) ).
thf(f134,plain,
! [X0: term,X1: subst,X2: subst] :
( ( ( comp @ ( push @ X0 @ X2 ) @ X1 )
= ( push @ ( sub @ X0 @ X1 ) @ ( comp @ X2 @ X1 ) ) )
= axmap ),
inference(rectify,[],[f9]) ).
thf(f9,axiom,
! [X0: term,X3: subst,X2: subst] :
( ( ( comp @ ( push @ X0 @ X2 ) @ X3 )
= ( push @ ( sub @ X0 @ X3 ) @ ( comp @ X2 @ X3 ) ) )
= axmap ),
file('/export/starexec/sandbox/tmp/tmp.YlQgltIeMe/Vampire---4.8_1736',axmap) ).
thf(f373,plain,
( axassoc
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f257]) ).
thf(f257,plain,
( axassoc
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f256]) ).
thf(f256,plain,
( axassoc
= ( ! [X0: subst,X1: subst,X2: subst] :
( ( comp @ ( comp @ X1 @ X0 ) @ X2 )
= ( comp @ X1 @ ( comp @ X0 @ X2 ) ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f8,axiom,
( axassoc
= ( ! [X3: subst,X2: subst,X4: subst] :
( ( comp @ ( comp @ X2 @ X3 ) @ X4 )
= ( comp @ X2 @ ( comp @ X3 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YlQgltIeMe/Vampire---4.8_1736',axassoc) ).
thf(f392,plain,
( axshiftcons
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) ) ),
inference(cnf_transformation,[],[f302]) ).
thf(f302,plain,
( axshiftcons
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) ) ),
inference(fool_elimination,[],[f301]) ).
thf(f301,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/tmp/tmp.YlQgltIeMe/Vampire---4.8_1736',axshiftcons) ).
thf(f338,plain,
( axidl
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) ),
inference(cnf_transformation,[],[f308]) ).
thf(f308,plain,
( axidl
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) ),
inference(fool_elimination,[],[f307]) ).
thf(f307,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/tmp/tmp.YlQgltIeMe/Vampire---4.8_1736',axidl) ).
thf(f410,plain,
( axclos
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f281]) ).
thf(f281,plain,
( axclos
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f280]) ).
thf(f280,plain,
( axclos
= ( ! [X0: subst,X1: subst,X2: term] :
( ( sub @ X2 @ ( comp @ X1 @ X0 ) )
= ( sub @ ( sub @ X2 @ X1 ) @ X0 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f5,axiom,
( axclos
= ( ! [X3: subst,X2: subst,X0: term] :
( ( sub @ ( sub @ X0 @ X2 ) @ X3 )
= ( sub @ X0 @ ( comp @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YlQgltIeMe/Vampire---4.8_1736',axclos) ).
thf(f355,plain,
( axabs
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ ( lam @ Y1 ) @ Y0 )
= ( lam @ ( sub @ Y1 @ ( push @ one @ ( comp @ Y0 @ sh ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f237]) ).
thf(f237,plain,
( axabs
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ ( lam @ Y1 ) @ Y0 )
= ( lam @ ( sub @ Y1 @ ( push @ one @ ( comp @ Y0 @ sh ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f236]) ).
thf(f236,plain,
( axabs
= ( ! [X0: term,X1: subst] :
( ( sub @ ( lam @ X0 ) @ X1 )
= ( lam @ ( sub @ X0 @ ( push @ one @ ( comp @ X1 @ sh ) ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f4,axiom,
( axabs
= ( ! [X0: term,X2: subst] :
( ( sub @ ( lam @ X0 ) @ X2 )
= ( lam @ ( sub @ X0 @ ( push @ one @ ( comp @ X2 @ sh ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YlQgltIeMe/Vampire---4.8_1736',axabs) ).
thf(f372,plain,
( axvarid
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ),
inference(cnf_transformation,[],[f133]) ).
thf(f133,plain,
( axvarid
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f3,axiom,
( axvarid
= ( ! [X0: term] :
( ( sub @ X0 @ id )
= X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YlQgltIeMe/Vampire---4.8_1736',axvarid) ).
thf(f348,plain,
( axvarcons
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ one @ ( push @ Y1 @ Y0 ) )
= Y1 ) ) ) ),
inference(cnf_transformation,[],[f149]) ).
thf(f149,plain,
( axvarcons
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ one @ ( push @ Y1 @ Y0 ) )
= Y1 ) ) ) ),
inference(fool_elimination,[],[f148]) ).
thf(f148,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/tmp/tmp.YlQgltIeMe/Vampire---4.8_1736',axvarcons) ).
thf(f341,plain,
( axapp
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y0 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( ap @ Y0 @ Y2 ) @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f277]) ).
thf(f277,plain,
( axapp
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y0 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( ap @ Y0 @ Y2 ) @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f276]) ).
thf(f276,plain,
( axapp
= ( ! [X0: term,X1: subst,X2: term] :
( ( ap @ ( sub @ X2 @ X1 ) @ ( sub @ X0 @ X1 ) )
= ( sub @ ( ap @ X2 @ 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/tmp/tmp.YlQgltIeMe/Vampire---4.8_1736',axapp) ).
thf(f358,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,[],[f225]) ).
thf(f225,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,[],[f224]) ).
thf(f224,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(rectify,[],[f106]) ).
thf(f106,axiom,
( ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YlQgltIeMe/Vampire---4.8_1736',hoasinduction_lem3b_gthm) ).
thf(f366,plain,
( $true = ~ hoasinduction_lem3b_gthm ),
inference(cnf_transformation,[],[f306]) ).
thf(f306,plain,
( $true = ~ hoasinduction_lem3b_gthm ),
inference(fool_elimination,[],[f305]) ).
thf(f305,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/tmp/tmp.YlQgltIeMe/Vampire---4.8_1736',thm) ).
thf(f1198,plain,
! [X1: subst > term > term] :
( ( X1 @ sh @ one )
!= ( sub @ sK32 @ id ) ),
inference(forward_demodulation,[],[f941,f1071]) ).
thf(f1071,plain,
( id
= ( push @ one @ sh ) ),
inference(equality_proxy_clausification,[],[f507]) ).
thf(f507,plain,
( ( id
= ( push @ one @ sh ) )
= $true ),
inference(binary_proxy_clausification,[],[f501]) ).
thf(f501,plain,
( ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y3 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ 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 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ Y0 ) ) ) )
=> ( ( Y1 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ ( push @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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 @ Y2 @ Y0 ) @ Y1 )
= ( comp @ Y2 @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) )
= ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 ) ) ) ) )
=> ( ( ( lam @ ( Y1 @ sh @ one ) )
= ( lam @ ( Y0 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y1 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y4 @ 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 @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ Y1 @ Y2 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f499]) ).
thf(f499,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 @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y3 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ 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 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ Y0 ) ) ) )
=> ( ( Y1 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ ( push @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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 @ Y2 @ Y0 ) @ Y1 )
= ( comp @ Y2 @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) )
= ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 ) ) ) ) )
=> ( ( ( lam @ ( Y1 @ sh @ one ) )
= ( lam @ ( Y0 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y1 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y4 @ 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 @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ Y1 @ Y2 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f490]) ).
thf(f490,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y0 ) @ Y1 )
= ( push @ ( sub @ Y2 @ Y1 ) @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y3 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ 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 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ Y0 ) ) ) )
=> ( ( Y1 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ ( push @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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 @ Y2 @ Y0 ) @ Y1 )
= ( comp @ Y2 @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) )
= ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 ) ) ) ) )
=> ( ( ( lam @ ( Y1 @ sh @ one ) )
= ( lam @ ( Y0 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y1 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y4 @ 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 @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ Y1 @ Y2 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f488]) ).
thf(f488,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y0 ) @ Y1 )
= ( push @ ( sub @ Y2 @ Y1 ) @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y3 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ 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 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ Y0 ) ) ) )
=> ( ( Y1 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ ( push @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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 @ Y2 @ Y0 ) @ Y1 )
= ( comp @ Y2 @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) )
= ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 ) ) ) ) )
=> ( ( ( lam @ ( Y1 @ sh @ one ) )
= ( lam @ ( Y0 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y1 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y4 @ 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 @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ Y1 @ Y2 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f486]) ).
thf(f486,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y0 ) @ Y1 )
= ( push @ ( sub @ Y2 @ Y1 ) @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y3 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ 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 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ Y0 ) ) ) )
=> ( ( Y1 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ ( push @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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 @ Y2 @ Y0 ) @ Y1 )
= ( comp @ Y2 @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) )
= ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 ) ) ) ) )
=> ( ( ( lam @ ( Y1 @ sh @ one ) )
= ( lam @ ( Y0 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y1 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y4 @ 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 @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ Y1 @ Y2 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f477]) ).
thf(f477,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y0 ) @ Y1 )
= ( push @ ( sub @ Y2 @ Y1 ) @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y3 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ 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 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ Y0 ) ) ) )
=> ( ( Y1 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ ( push @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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 @ Y2 @ Y0 ) @ Y1 )
= ( comp @ Y2 @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) )
= ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 ) ) ) ) )
=> ( ( ( lam @ ( Y1 @ sh @ one ) )
= ( lam @ ( Y0 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y1 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y4 @ 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 @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ Y1 @ Y2 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f475]) ).
thf(f475,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ 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 @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y0 ) @ Y1 )
= ( push @ ( sub @ Y2 @ Y1 ) @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y3 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ 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 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ Y0 ) ) ) )
=> ( ( Y1 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ ( push @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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 @ Y2 @ Y0 ) @ Y1 )
= ( comp @ Y2 @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) )
= ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 ) ) ) ) )
=> ( ( ( lam @ ( Y1 @ sh @ one ) )
= ( lam @ ( Y0 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y1 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y4 @ 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 @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ Y1 @ Y2 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f470]) ).
thf(f470,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ ( lam @ Y1 ) @ Y0 )
= ( lam @ ( sub @ Y1 @ ( push @ one @ ( comp @ Y0 @ sh ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ 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 @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y0 ) @ Y1 )
= ( push @ ( sub @ Y2 @ Y1 ) @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y3 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ 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 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ Y0 ) ) ) )
=> ( ( Y1 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ ( push @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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 @ Y2 @ Y0 ) @ Y1 )
= ( comp @ Y2 @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) )
= ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 ) ) ) ) )
=> ( ( ( lam @ ( Y1 @ sh @ one ) )
= ( lam @ ( Y0 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y1 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y4 @ 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 @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ Y1 @ Y2 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f468]) ).
thf(f941,plain,
! [X1: subst > term > term] :
( ( X1 @ sh @ one )
!= ( sub @ sK32 @ ( push @ one @ sh ) ) ),
inference(equality_proxy_clausification,[],[f940]) ).
thf(f940,plain,
! [X1: subst > term > term] :
( ( ( sub @ sK32 @ ( push @ one @ sh ) )
= ( X1 @ sh @ one ) )
= $false ),
inference(beta_eta_normalization,[],[f939]) ).
thf(f939,plain,
! [X1: subst > term > term] :
( ( ^ [Y0: subst > term > term] :
( ( sub @ sK32 @ ( push @ one @ sh ) )
= ( Y0 @ sh @ one ) )
@ X1 )
= $false ),
inference(pi_clausification,[],[f938]) ).
thf(f938,plain,
( ( ?? @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( sub @ sK32 @ ( push @ one @ sh ) )
= ( Y0 @ sh @ one ) ) )
= $false ),
inference(beta_eta_normalization,[],[f937]) ).
thf(f937,plain,
( ( ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) )
@ sK32 )
= $false ),
inference(sigma_clausification,[],[f822]) ).
thf(f822,plain,
( ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f771]) ).
thf(f771,plain,
( ( ( !! @ ( 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 @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y1 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y4 @ 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 @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ Y1 @ Y2 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f769]) ).
thf(f769,plain,
( ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y1 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y4 @ 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 @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ Y1 @ Y2 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f767]) ).
thf(f767,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y1 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y4 @ 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 @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ Y1 @ Y2 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f749]) ).
thf(f749,plain,
( ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y1 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y4 @ 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 @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ Y1 @ Y2 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f747]) ).
thf(f747,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] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y1 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y4 @ 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 @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ Y1 @ Y2 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f734]) ).
thf(f734,plain,
( ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) )
= ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 ) ) ) ) )
=> ( ( ( lam @ ( Y1 @ sh @ one ) )
= ( lam @ ( Y0 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y1 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y4 @ 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 @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ Y1 @ Y2 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f721]) ).
thf(f721,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) )
= ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 ) ) ) ) )
=> ( ( ( lam @ ( Y1 @ sh @ one ) )
= ( lam @ ( Y0 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y1 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y4 @ 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 @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ Y1 @ Y2 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f707]) ).
thf(f707,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) )
= ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 ) ) ) ) )
=> ( ( ( lam @ ( Y1 @ sh @ one ) )
= ( lam @ ( Y0 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y1 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y4 @ 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 @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ Y1 @ Y2 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f688]) ).
thf(f688,plain,
( ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) )
= ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 ) ) ) ) )
=> ( ( ( lam @ ( Y1 @ sh @ one ) )
= ( lam @ ( Y0 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y1 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y4 @ 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 @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ Y1 @ Y2 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f686]) ).
thf(f686,plain,
( ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y0 ) @ Y1 )
= ( comp @ Y2 @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) )
= ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 ) ) ) ) )
=> ( ( ( lam @ ( Y1 @ sh @ one ) )
= ( lam @ ( Y0 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y1 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y4 @ 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 @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ Y1 @ Y2 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f625]) ).
thf(f625,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 @ Y2 @ Y0 ) @ Y1 )
= ( comp @ Y2 @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) )
= ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 ) ) ) ) )
=> ( ( ( lam @ ( Y1 @ sh @ one ) )
= ( lam @ ( Y0 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y1 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y4 @ 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 @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ Y1 @ Y2 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f623]) ).
thf(f623,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 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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 @ Y2 @ Y0 ) @ Y1 )
= ( comp @ Y2 @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) )
= ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 ) ) ) ) )
=> ( ( ( lam @ ( Y1 @ sh @ one ) )
= ( lam @ ( Y0 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y1 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y4 @ 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 @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ Y1 @ Y2 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f577]) ).
thf(f577,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ Y0 ) ) ) )
=> ( ( Y1 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ ( push @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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 @ Y2 @ Y0 ) @ Y1 )
= ( comp @ Y2 @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) )
= ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 ) ) ) ) )
=> ( ( ( lam @ ( Y1 @ sh @ one ) )
= ( lam @ ( Y0 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y1 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y4 @ 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 @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ Y1 @ Y2 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f575]) ).
thf(f575,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] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ Y0 ) ) ) )
=> ( ( Y1 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ ( push @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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 @ Y2 @ Y0 ) @ Y1 )
= ( comp @ Y2 @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) )
= ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 ) ) ) ) )
=> ( ( ( lam @ ( Y1 @ sh @ one ) )
= ( lam @ ( Y0 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y1 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y4 @ 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 @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ Y1 @ Y2 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f573]) ).
thf(f573,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 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ Y0 ) ) ) )
=> ( ( Y1 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ ( push @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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 @ Y2 @ Y0 ) @ Y1 )
= ( comp @ Y2 @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) )
= ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 ) ) ) ) )
=> ( ( ( lam @ ( Y1 @ sh @ one ) )
= ( lam @ ( Y0 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y1 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y4 @ 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 @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ Y1 @ Y2 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f571]) ).
thf(f571,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 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ Y0 ) ) ) )
=> ( ( Y1 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ ( push @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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 @ Y2 @ Y0 ) @ Y1 )
= ( comp @ Y2 @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) )
= ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 ) ) ) ) )
=> ( ( ( lam @ ( Y1 @ sh @ one ) )
= ( lam @ ( Y0 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y1 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y4 @ 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 @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ Y1 @ Y2 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f562]) ).
thf(f562,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ 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 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ Y0 ) ) ) )
=> ( ( Y1 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ ( push @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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 @ Y2 @ Y0 ) @ Y1 )
= ( comp @ Y2 @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) )
= ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 ) ) ) ) )
=> ( ( ( lam @ ( Y1 @ sh @ one ) )
= ( lam @ ( Y0 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y1 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y4 @ 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 @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ Y1 @ Y2 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f560]) ).
thf(f560,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 @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ 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 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ Y0 ) ) ) )
=> ( ( Y1 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ ( push @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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 @ Y2 @ Y0 ) @ Y1 )
= ( comp @ Y2 @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) )
= ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 ) ) ) ) )
=> ( ( ( lam @ ( Y1 @ sh @ one ) )
= ( lam @ ( Y0 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y1 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y4 @ 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 @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ Y1 @ Y2 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f547]) ).
thf(f547,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 @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ 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 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ Y0 ) ) ) )
=> ( ( Y1 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ ( push @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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 @ Y2 @ Y0 ) @ Y1 )
= ( comp @ Y2 @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) )
= ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 ) ) ) ) )
=> ( ( ( lam @ ( Y1 @ sh @ one ) )
= ( lam @ ( Y0 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y1 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y4 @ 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 @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ Y1 @ Y2 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f534]) ).
thf(f534,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y3 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ 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 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ Y0 ) ) ) )
=> ( ( Y1 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ ( push @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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 @ Y2 @ Y0 ) @ Y1 )
= ( comp @ Y2 @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) )
= ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 ) ) ) ) )
=> ( ( ( lam @ ( Y1 @ sh @ one ) )
= ( lam @ ( Y0 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y1 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y4 @ 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 @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ Y1 @ Y2 ) @ 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 @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y3 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ 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 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ Y0 ) ) ) )
=> ( ( Y1 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ ( push @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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 @ Y2 @ Y0 ) @ Y1 )
= ( comp @ Y2 @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) )
= ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 ) ) ) ) )
=> ( ( ( lam @ ( Y1 @ sh @ one ) )
= ( lam @ ( Y0 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y1 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y4 @ 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 @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ Y1 @ Y2 ) @ 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 > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y3 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ 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 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ Y0 ) ) ) )
=> ( ( Y1 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ ( push @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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 @ Y2 @ Y0 ) @ Y1 )
= ( comp @ Y2 @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) )
= ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 ) ) ) ) )
=> ( ( ( lam @ ( Y1 @ sh @ one ) )
= ( lam @ ( Y0 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y1 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y4 @ 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 @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ Y1 @ Y2 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f513]) ).
thf(f513,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 @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y3 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ 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 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ Y0 ) ) ) )
=> ( ( Y1 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ ( push @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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 @ Y2 @ Y0 ) @ Y1 )
= ( comp @ Y2 @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) )
= ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 ) ) ) ) )
=> ( ( ( lam @ ( Y1 @ sh @ one ) )
= ( lam @ ( Y0 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y1 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y4 @ 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 @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ Y1 @ Y2 ) @ 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,
( ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y3 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ 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 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ Y0 ) ) ) )
=> ( ( Y1 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ ( push @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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 @ Y2 @ Y0 ) @ Y1 )
= ( comp @ Y2 @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) )
= ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 ) ) ) ) )
=> ( ( ( lam @ ( Y1 @ sh @ one ) )
= ( lam @ ( Y0 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y1 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y4 @ 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 @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ Y1 @ Y2 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f506]) ).
thf(f506,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 @ Y3 @ Y1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y3 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ 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 @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ 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 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ Y0 ) ) ) )
=> ( ( Y1 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ ( push @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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 @ Y2 @ Y0 ) @ Y1 )
= ( comp @ Y2 @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) )
= ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 ) ) ) ) )
=> ( ( ( lam @ ( Y1 @ sh @ one ) )
= ( lam @ ( Y0 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( 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] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y3 )
=> ( Y0 @ Y2 @ Y1 @ ( comp @ Y4 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ 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 @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y1 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y4 @ 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 @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ Y1 @ Y2 ) @ id ) ) ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( sub @ Y0 @ ( push @ one @ sh ) )
= ( Y1 @ sh @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f501]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : ALG267^1 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.08/0.15 % 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
% 0.15/0.36 % Computer : n011.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 3 20:01:38 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 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/tmp/tmp.YlQgltIeMe/Vampire---4.8_1736
% 0.15/0.39 % (1997)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on Vampire---4 for (2999ds/183Mi)
% 0.15/0.39 % (1999)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on Vampire---4 for (2999ds/27Mi)
% 0.15/0.39 % (2000)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.15/0.39 % (1998)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on Vampire---4 for (2999ds/4Mi)
% 0.15/0.39 % (2001)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.15/0.39 % (2002)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on Vampire---4 for (2999ds/275Mi)
% 0.15/0.39 % (2003)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.15/0.39 % (2004)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.15/0.40 % (2000)Instruction limit reached!
% 0.15/0.40 % (2000)------------------------------
% 0.15/0.40 % (2000)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (2001)Instruction limit reached!
% 0.15/0.40 % (2001)------------------------------
% 0.15/0.40 % (2001)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (2000)Termination reason: Unknown
% 0.15/0.40 % (2000)Termination phase: shuffling
% 0.15/0.40
% 0.15/0.40 % (2000)Memory used [KB]: 1279
% 0.15/0.40 % (2000)Time elapsed: 0.004 s
% 0.15/0.40 % (2000)Instructions burned: 3 (million)
% 0.15/0.40 % (2000)------------------------------
% 0.15/0.40 % (2000)------------------------------
% 0.15/0.40 % (2001)Termination reason: Unknown
% 0.15/0.40 % (2001)Termination phase: shuffling
% 0.15/0.40
% 0.15/0.40 % (2001)Memory used [KB]: 1279
% 0.15/0.40 % (2001)Time elapsed: 0.004 s
% 0.15/0.40 % (2001)Instructions burned: 3 (million)
% 0.15/0.40 % (2001)------------------------------
% 0.15/0.40 % (2001)------------------------------
% 0.15/0.40 % (1998)Instruction limit reached!
% 0.15/0.40 % (1998)------------------------------
% 0.15/0.40 % (1998)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (1998)Termination reason: Unknown
% 0.15/0.40 % (1998)Termination phase: shuffling
% 0.15/0.40
% 0.15/0.40 % (1998)Memory used [KB]: 1279
% 0.15/0.40 % (1998)Time elapsed: 0.004 s
% 0.15/0.40 % (1998)Instructions burned: 4 (million)
% 0.15/0.40 % (1998)------------------------------
% 0.15/0.40 % (1998)------------------------------
% 0.15/0.40 % (2004)Instruction limit reached!
% 0.15/0.40 % (2004)------------------------------
% 0.15/0.40 % (2004)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (2004)Termination reason: Unknown
% 0.15/0.40 % (2004)Termination phase: shuffling
% 0.15/0.40
% 0.15/0.40 % (2004)Memory used [KB]: 1279
% 0.15/0.40 % (2004)Time elapsed: 0.004 s
% 0.15/0.40 % (2004)Instructions burned: 4 (million)
% 0.15/0.40 % (2004)------------------------------
% 0.15/0.40 % (2004)------------------------------
% 0.22/0.41 % (2003)Instruction limit reached!
% 0.22/0.41 % (2003)------------------------------
% 0.22/0.41 % (2003)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.41 % (2003)Termination reason: Unknown
% 0.22/0.41 % (2003)Termination phase: Property scanning
% 0.22/0.41
% 0.22/0.41 % (2003)Memory used [KB]: 1663
% 0.22/0.41 % (2003)Time elapsed: 0.014 s
% 0.22/0.41 % (2003)Instructions burned: 20 (million)
% 0.22/0.41 % (2003)------------------------------
% 0.22/0.41 % (2003)------------------------------
% 0.22/0.41 % (1999)Instruction limit reached!
% 0.22/0.41 % (1999)------------------------------
% 0.22/0.41 % (1999)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.41 % (1999)Termination reason: Unknown
% 0.22/0.41 % (1999)Termination phase: shuffling
% 0.22/0.41
% 0.22/0.41 % (1999)Memory used [KB]: 1791
% 0.22/0.41 % (1999)Time elapsed: 0.016 s
% 0.22/0.41 % (1999)Instructions burned: 27 (million)
% 0.22/0.41 % (1999)------------------------------
% 0.22/0.41 % (1999)------------------------------
% 0.22/0.41 % (2005)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on Vampire---4 for (2999ds/37Mi)
% 0.22/0.41 % (2006)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on Vampire---4 for (2999ds/15Mi)
% 0.22/0.41 % (2007)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.22/0.41 % (2008)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on Vampire---4 for (2999ds/1041Mi)
% 0.22/0.41 % (2007)Instruction limit reached!
% 0.22/0.41 % (2007)------------------------------
% 0.22/0.41 % (2007)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.41 % (2007)Termination reason: Unknown
% 0.22/0.41 % (2007)Termination phase: shuffling
% 0.22/0.41
% 0.22/0.41 % (2007)Memory used [KB]: 1279
% 0.22/0.41 % (2007)Time elapsed: 0.004 s
% 0.22/0.41 % (2007)Instructions burned: 3 (million)
% 0.22/0.41 % (2007)------------------------------
% 0.22/0.41 % (2007)------------------------------
% 0.22/0.42 % (2002)Refutation not found, incomplete strategy
% 0.22/0.42 % (2002)------------------------------
% 0.22/0.42 % (2002)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (2002)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.42
% 0.22/0.42
% 0.22/0.42 % (2002)Memory used [KB]: 6268
% 0.22/0.42 % (2002)Time elapsed: 0.024 s
% 0.22/0.42 % (2002)Instructions burned: 36 (million)
% 0.22/0.42 % (2002)------------------------------
% 0.22/0.42 % (2002)------------------------------
% 0.22/0.42 % (2006)Instruction limit reached!
% 0.22/0.42 % (2006)------------------------------
% 0.22/0.42 % (2006)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (2006)Termination reason: Unknown
% 0.22/0.42 % (2006)Termination phase: Property scanning
% 0.22/0.42
% 0.22/0.42 % (2006)Memory used [KB]: 1663
% 0.22/0.42 % (2006)Time elapsed: 0.012 s
% 0.22/0.42 % (2006)Instructions burned: 16 (million)
% 0.22/0.42 % (2006)------------------------------
% 0.22/0.42 % (2006)------------------------------
% 0.22/0.42 % (2009)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on Vampire---4 for (2999ds/7Mi)
% 0.22/0.42 % (2010)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on Vampire---4 for (2999ds/16Mi)
% 0.22/0.42 % (2009)Instruction limit reached!
% 0.22/0.42 % (2009)------------------------------
% 0.22/0.42 % (2009)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.43 % (2009)Termination reason: Unknown
% 0.22/0.43 % (2009)Termination phase: shuffling
% 0.22/0.43
% 0.22/0.43 % (2009)Memory used [KB]: 1407
% 0.22/0.43 % (2009)Time elapsed: 0.006 s
% 0.22/0.43 % (2009)Instructions burned: 7 (million)
% 0.22/0.43 % (2009)------------------------------
% 0.22/0.43 % (2009)------------------------------
% 0.22/0.43 % (2011)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.22/0.43 % (2005)Instruction limit reached!
% 0.22/0.43 % (2005)------------------------------
% 0.22/0.43 % (2005)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.43 % (2005)Termination reason: Unknown
% 0.22/0.43 % (2005)Termination phase: Property scanning
% 0.22/0.43
% 0.22/0.43 % (2005)Memory used [KB]: 1791
% 0.22/0.43 % (2005)Time elapsed: 0.020 s
% 0.22/0.43 % (2005)Instructions burned: 38 (million)
% 0.22/0.43 % (2005)------------------------------
% 0.22/0.43 % (2005)------------------------------
% 0.22/0.43 % (2011)Instruction limit reached!
% 0.22/0.43 % (2011)------------------------------
% 0.22/0.43 % (2011)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.43 % (2011)Termination reason: Unknown
% 0.22/0.43 % (2011)Termination phase: shuffling
% 0.22/0.43
% 0.22/0.43 % (2011)Memory used [KB]: 1279
% 0.22/0.43 % (2011)Time elapsed: 0.004 s
% 0.22/0.43 % (2011)Instructions burned: 3 (million)
% 0.22/0.43 % (2011)------------------------------
% 0.22/0.43 % (2011)------------------------------
% 0.22/0.43 % (2010)Instruction limit reached!
% 0.22/0.43 % (2010)------------------------------
% 0.22/0.43 % (2010)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.43 % (2010)Termination reason: Unknown
% 0.22/0.43 % (2010)Termination phase: shuffling
% 0.22/0.43
% 0.22/0.43 % (2010)Memory used [KB]: 1535
% 0.22/0.43 % (2010)Time elapsed: 0.011 s
% 0.22/0.43 % (2010)Instructions burned: 17 (million)
% 0.22/0.43 % (2010)------------------------------
% 0.22/0.43 % (2010)------------------------------
% 0.22/0.43 % (2012)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.22/0.43 % (2012)Instruction limit reached!
% 0.22/0.43 % (2012)------------------------------
% 0.22/0.43 % (2012)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.43 % (2012)Termination reason: Unknown
% 0.22/0.43 % (2012)Termination phase: shuffling
% 0.22/0.43
% 0.22/0.43 % (2012)Memory used [KB]: 1279
% 0.22/0.43 % (2012)Time elapsed: 0.004 s
% 0.22/0.43 % (2012)Instructions burned: 3 (million)
% 0.22/0.43 % (2012)------------------------------
% 0.22/0.43 % (2012)------------------------------
% 0.22/0.44 % (2013)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on Vampire---4 for (2999ds/7Mi)
% 0.22/0.44 % (2013)Instruction limit reached!
% 0.22/0.44 % (2013)------------------------------
% 0.22/0.44 % (2013)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.44 % (2013)Termination reason: Unknown
% 0.22/0.44 % (2013)Termination phase: shuffling
% 0.22/0.44
% 0.22/0.44 % (2013)Memory used [KB]: 1407
% 0.22/0.44 % (2013)Time elapsed: 0.006 s
% 0.22/0.44 % (2013)Instructions burned: 7 (million)
% 0.22/0.44 % (2013)------------------------------
% 0.22/0.44 % (2013)------------------------------
% 0.22/0.44 % (2014)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.22/0.44 % (2014)Instruction limit reached!
% 0.22/0.44 % (2014)------------------------------
% 0.22/0.44 % (2014)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.44 % (2014)Termination reason: Unknown
% 0.22/0.44 % (2014)Termination phase: shuffling
% 0.22/0.44
% 0.22/0.44 % (2014)Memory used [KB]: 1279
% 0.22/0.44 % (2014)Time elapsed: 0.004 s
% 0.22/0.44 % (2014)Instructions burned: 3 (million)
% 0.22/0.44 % (2014)------------------------------
% 0.22/0.44 % (2014)------------------------------
% 0.22/0.45 % (2016)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.22/0.45 % (2015)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on Vampire---4 for (2999ds/4Mi)
% 0.22/0.45 % (2017)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on Vampire---4 for (2999ds/710Mi)
% 0.22/0.45 % (2015)Instruction limit reached!
% 0.22/0.45 % (2015)------------------------------
% 0.22/0.45 % (2015)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.45 % (2015)Termination reason: Unknown
% 0.22/0.45 % (2015)Termination phase: shuffling
% 0.22/0.45
% 0.22/0.45 % (2015)Memory used [KB]: 1279
% 0.22/0.45 % (2015)Time elapsed: 0.004 s
% 0.22/0.45 % (2015)Instructions burned: 4 (million)
% 0.22/0.45 % (2015)------------------------------
% 0.22/0.45 % (2015)------------------------------
% 0.22/0.45 % (2018)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on Vampire---4 for (2999ds/6Mi)
% 0.22/0.45 % (2018)Instruction limit reached!
% 0.22/0.45 % (2018)------------------------------
% 0.22/0.45 % (2018)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.45 % (2018)Termination reason: Unknown
% 0.22/0.45 % (2018)Termination phase: shuffling
% 0.22/0.45
% 0.22/0.45 % (2018)Memory used [KB]: 1279
% 0.22/0.45 % (2018)Time elapsed: 0.005 s
% 0.22/0.45 % (2018)Instructions burned: 6 (million)
% 0.22/0.45 % (2018)------------------------------
% 0.22/0.45 % (2018)------------------------------
% 0.22/0.45 % (2016)Instruction limit reached!
% 0.22/0.45 % (2016)------------------------------
% 0.22/0.45 % (2016)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.45 % (2016)Termination reason: Unknown
% 0.22/0.45 % (2016)Termination phase: shuffling
% 0.22/0.45
% 0.22/0.45 % (2016)Memory used [KB]: 1535
% 0.22/0.45 % (2016)Time elapsed: 0.011 s
% 0.22/0.45 % (2016)Instructions burned: 18 (million)
% 0.22/0.45 % (2016)------------------------------
% 0.22/0.45 % (2016)------------------------------
% 0.22/0.45 % (2019)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on Vampire---4 for (2999ds/902Mi)
% 0.22/0.46 % (2021)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on Vampire---4 for (2999ds/21Mi)
% 0.22/0.46 % (2023)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on Vampire---4 for (2999ds/5Mi)
% 0.22/0.47 % (2017)Refutation not found, incomplete strategy
% 0.22/0.47 % (2017)------------------------------
% 0.22/0.47 % (2017)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.47 % (2017)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.47
% 0.22/0.47
% 0.22/0.47 % (2017)Memory used [KB]: 6268
% 0.22/0.47 % (2017)Time elapsed: 0.043 s
% 0.22/0.47 % (2017)Instructions burned: 29 (million)
% 0.22/0.47 % (2017)------------------------------
% 0.22/0.47 % (2017)------------------------------
% 0.22/0.47 % (2023)Instruction limit reached!
% 0.22/0.47 % (2023)------------------------------
% 0.22/0.47 % (2023)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.47 % (2023)Termination reason: Unknown
% 0.22/0.47 % (2023)Termination phase: shuffling
% 0.22/0.47
% 0.22/0.47 % (2023)Memory used [KB]: 1279
% 0.22/0.47 % (2023)Time elapsed: 0.006 s
% 0.22/0.47 % (2023)Instructions burned: 5 (million)
% 0.22/0.47 % (2023)------------------------------
% 0.22/0.47 % (2023)------------------------------
% 0.22/0.47 % (2024)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on Vampire---4 for (2999ds/6Mi)
% 0.22/0.47 % (2021)Instruction limit reached!
% 0.22/0.47 % (2021)------------------------------
% 0.22/0.47 % (2021)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.47 % (2021)Termination reason: Unknown
% 0.22/0.47 % (2021)Termination phase: shuffling
% 0.22/0.47
% 0.22/0.47 % (2021)Memory used [KB]: 1663
% 0.22/0.47 % (2021)Time elapsed: 0.015 s
% 0.22/0.47 % (2021)Instructions burned: 21 (million)
% 0.22/0.47 % (2021)------------------------------
% 0.22/0.47 % (2021)------------------------------
% 0.22/0.47 % (2025)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on Vampire---4 for (2999ds/377Mi)
% 0.22/0.48 % (2024)Instruction limit reached!
% 0.22/0.48 % (2024)------------------------------
% 0.22/0.48 % (2024)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.48 % (2024)Termination reason: Unknown
% 0.22/0.48 % (2024)Termination phase: shuffling
% 0.22/0.48
% 0.22/0.48 % (2024)Memory used [KB]: 1279
% 0.22/0.48 % (2024)Time elapsed: 0.008 s
% 0.22/0.48 % (2024)Instructions burned: 6 (million)
% 0.22/0.48 % (2024)------------------------------
% 0.22/0.48 % (2024)------------------------------
% 0.22/0.49 % (1997)Instruction limit reached!
% 0.22/0.49 % (1997)------------------------------
% 0.22/0.49 % (1997)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.49 % (1997)Termination reason: Unknown
% 0.22/0.49 % (1997)Termination phase: Saturation
% 0.22/0.49
% 0.22/0.49 % (1997)Memory used [KB]: 6652
% 0.22/0.49 % (1997)Time elapsed: 0.095 s
% 0.22/0.49 % (1997)Instructions burned: 184 (million)
% 0.22/0.49 % (1997)------------------------------
% 0.22/0.49 % (1997)------------------------------
% 0.22/0.49 % (2034)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on Vampire---4 for (2999ds/19Mi)
% 0.22/0.49 % (2033)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on Vampire---4 for (2999ds/779Mi)
% 0.22/0.50 % (2036)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on Vampire---4 for (2999ds/879Mi)
% 0.22/0.50 % (2038)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2998ds/3Mi)
% 0.22/0.50 % (2037)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on Vampire---4 for (2998ds/17Mi)
% 0.22/0.51 % (2038)Instruction limit reached!
% 0.22/0.51 % (2038)------------------------------
% 0.22/0.51 % (2038)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.51 % (2038)Termination reason: Unknown
% 0.22/0.51 % (2038)Termination phase: shuffling
% 0.22/0.51
% 0.22/0.51 % (2038)Memory used [KB]: 1279
% 0.22/0.51 % (2038)Time elapsed: 0.004 s
% 0.22/0.51 % (2038)Instructions burned: 4 (million)
% 0.22/0.51 % (2038)------------------------------
% 0.22/0.51 % (2038)------------------------------
% 0.22/0.51 % (2034)Instruction limit reached!
% 0.22/0.51 % (2034)------------------------------
% 0.22/0.51 % (2034)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.51 % (2034)Termination reason: Unknown
% 0.22/0.51 % (2034)Termination phase: shuffling
% 0.22/0.51
% 0.22/0.51 % (2034)Memory used [KB]: 1663
% 0.22/0.51 % (2034)Time elapsed: 0.017 s
% 0.22/0.51 % (2034)Instructions burned: 19 (million)
% 0.22/0.51 % (2034)------------------------------
% 0.22/0.51 % (2034)------------------------------
% 0.22/0.52 % (2037)Instruction limit reached!
% 0.22/0.52 % (2037)------------------------------
% 0.22/0.52 % (2037)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.52 % (2037)Termination reason: Unknown
% 0.22/0.52 % (2037)Termination phase: shuffling
% 0.22/0.52
% 0.22/0.52 % (2037)Memory used [KB]: 1663
% 0.22/0.52 % (2037)Time elapsed: 0.015 s
% 0.22/0.52 % (2037)Instructions burned: 18 (million)
% 0.22/0.52 % (2037)------------------------------
% 0.22/0.52 % (2037)------------------------------
% 0.22/0.52 % (2039)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on Vampire---4 for (2998ds/30Mi)
% 0.22/0.53 % (2039)Instruction limit reached!
% 0.22/0.53 % (2039)------------------------------
% 0.22/0.53 % (2039)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.53 % (2039)Termination reason: Unknown
% 0.22/0.53 % (2039)Termination phase: Property scanning
% 0.22/0.53
% 0.22/0.53 % (2039)Memory used [KB]: 1791
% 0.22/0.53 % (2039)Time elapsed: 0.010 s
% 0.22/0.53 % (2039)Instructions burned: 30 (million)
% 0.22/0.53 % (2039)------------------------------
% 0.22/0.53 % (2039)------------------------------
% 0.22/0.53 % (2040)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on Vampire---4 for (2998ds/127Mi)
% 0.22/0.53 % (2041)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on Vampire---4 for (2998ds/100Mi)
% 0.22/0.54 % (2036)Refutation not found, incomplete strategy
% 0.22/0.54 % (2036)------------------------------
% 0.22/0.54 % (2036)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.54 % (2036)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.54
% 0.22/0.54
% 0.22/0.54 % (2036)Memory used [KB]: 6268
% 0.22/0.54 % (2036)Time elapsed: 0.040 s
% 0.22/0.54 % (2036)Instructions burned: 61 (million)
% 0.22/0.54 % (2036)------------------------------
% 0.22/0.54 % (2036)------------------------------
% 0.22/0.54 % (2043)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2998ds/3Mi)
% 0.22/0.54 % (2043)Instruction limit reached!
% 0.22/0.54 % (2043)------------------------------
% 0.22/0.54 % (2043)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.54 % (2043)Termination reason: Unknown
% 0.22/0.54 % (2043)Termination phase: shuffling
% 0.22/0.54
% 0.22/0.54 % (2043)Memory used [KB]: 1279
% 0.22/0.54 % (2043)Time elapsed: 0.003 s
% 0.22/0.54 % (2043)Instructions burned: 3 (million)
% 0.22/0.54 % (2043)------------------------------
% 0.22/0.54 % (2043)------------------------------
% 0.22/0.55 % (2045)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on Vampire---4 for (2998ds/20Mi)
% 0.22/0.55 % (2046)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on Vampire---4 for (2998ds/86Mi)
% 0.22/0.55 % (2045)Instruction limit reached!
% 0.22/0.55 % (2045)------------------------------
% 0.22/0.55 % (2045)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.55 % (2045)Termination reason: Unknown
% 0.22/0.55 % (2045)Termination phase: Property scanning
% 0.22/0.55
% 0.22/0.55 % (2045)Memory used [KB]: 1663
% 0.22/0.55 % (2045)Time elapsed: 0.009 s
% 0.22/0.55 % (2045)Instructions burned: 22 (million)
% 0.22/0.55 % (2045)------------------------------
% 0.22/0.55 % (2045)------------------------------
% 0.22/0.56 % (2041)Instruction limit reached!
% 0.22/0.56 % (2041)------------------------------
% 0.22/0.56 % (2041)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.56 % (2041)Termination reason: Unknown
% 0.22/0.56 % (2041)Termination phase: Saturation
% 0.22/0.56
% 0.22/0.56 % (2041)Memory used [KB]: 6524
% 0.22/0.56 % (2041)Time elapsed: 0.031 s
% 0.22/0.56 % (2041)Instructions burned: 102 (million)
% 0.22/0.56 % (2041)------------------------------
% 0.22/0.56 % (2041)------------------------------
% 0.22/0.56 % (2048)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on Vampire---4 for (2998ds/107Mi)
% 0.22/0.57 % (2046)Instruction limit reached!
% 0.22/0.57 % (2046)------------------------------
% 0.22/0.57 % (2046)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.57 % (2046)Termination reason: Unknown
% 0.22/0.57 % (2046)Termination phase: Property scanning
% 0.22/0.57
% 0.22/0.57 % (2046)Memory used [KB]: 2046
% 0.22/0.57 % (2046)Time elapsed: 0.024 s
% 0.22/0.57 % (2046)Instructions burned: 88 (million)
% 0.22/0.57 % (2046)------------------------------
% 0.22/0.57 % (2046)------------------------------
% 0.22/0.57 % (2040)Instruction limit reached!
% 0.22/0.57 % (2040)------------------------------
% 0.22/0.57 % (2040)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.57 % (2040)Termination reason: Unknown
% 0.22/0.57 % (2040)Termination phase: Saturation
% 0.22/0.57
% 0.22/0.57 % (2040)Memory used [KB]: 6524
% 0.22/0.57 % (2040)Time elapsed: 0.041 s
% 0.22/0.57 % (2040)Instructions burned: 127 (million)
% 0.22/0.57 % (2040)------------------------------
% 0.22/0.57 % (2040)------------------------------
% 0.22/0.57 % (2049)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on Vampire---4 for (2998ds/39Mi)
% 0.22/0.57 % (2019)Refutation not found, incomplete strategy
% 0.22/0.57 % (2019)------------------------------
% 0.22/0.57 % (2019)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.57 % (2019)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.57
% 0.22/0.57
% 0.22/0.57 % (2019)Memory used [KB]: 8187
% 0.22/0.57 % (2019)Time elapsed: 0.145 s
% 0.22/0.57 % (2019)Instructions burned: 214 (million)
% 0.22/0.57 % (2019)------------------------------
% 0.22/0.57 % (2019)------------------------------
% 0.22/0.58 % (2050)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on Vampire---4 for (2998ds/448Mi)
% 0.22/0.58 % (2051)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on Vampire---4 for (2998ds/46Mi)
% 0.22/0.58 % (2049)Instruction limit reached!
% 0.22/0.58 % (2049)------------------------------
% 0.22/0.58 % (2049)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.58 % (2049)Termination reason: Unknown
% 0.22/0.58 % (2049)Termination phase: Property scanning
% 0.22/0.58
% 0.22/0.58 % (2049)Memory used [KB]: 1791
% 0.22/0.58 % (2049)Time elapsed: 0.012 s
% 0.22/0.58 % (2049)Instructions burned: 40 (million)
% 0.22/0.58 % (2049)------------------------------
% 0.22/0.58 % (2049)------------------------------
% 0.22/0.58 % (2054)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on Vampire---4 for (2998ds/98Mi)
% 1.71/0.59 % (2057)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on Vampire---4 for (2997ds/507Mi)
% 1.71/0.59 % (2051)Instruction limit reached!
% 1.71/0.59 % (2051)------------------------------
% 1.71/0.59 % (2051)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.71/0.59 % (2051)Termination reason: Unknown
% 1.71/0.59 % (2051)Termination phase: SInE selection
% 1.71/0.59
% 1.71/0.59 % (2051)Memory used [KB]: 1791
% 1.71/0.59 % (2051)Time elapsed: 0.014 s
% 1.71/0.59 % (2051)Instructions burned: 46 (million)
% 1.71/0.59 % (2051)------------------------------
% 1.71/0.59 % (2051)------------------------------
% 1.71/0.59 % (2048)Instruction limit reached!
% 1.71/0.59 % (2048)------------------------------
% 1.71/0.59 % (2048)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.71/0.59 % (2048)Termination reason: Unknown
% 1.71/0.59 % (2048)Termination phase: Saturation
% 1.71/0.59
% 1.71/0.59 % (2048)Memory used [KB]: 6396
% 1.71/0.59 % (2048)Time elapsed: 0.030 s
% 1.71/0.59 % (2048)Instructions burned: 107 (million)
% 1.71/0.59 % (2048)------------------------------
% 1.71/0.59 % (2048)------------------------------
% 1.71/0.60 % (2063)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on Vampire---4 for (2997ds/149Mi)
% 1.71/0.60 % (2064)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on Vampire---4 for (2997ds/39Mi)
% 1.71/0.60 % (2033)First to succeed.
% 1.88/0.61 % (2054)Instruction limit reached!
% 1.88/0.61 % (2054)------------------------------
% 1.88/0.61 % (2054)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.88/0.61 % (2054)Termination reason: Unknown
% 1.88/0.61 % (2054)Termination phase: Saturation
% 1.88/0.61
% 1.88/0.61 % (2054)Memory used [KB]: 2046
% 1.88/0.61 % (2054)Time elapsed: 0.026 s
% 1.88/0.61 % (2054)Instructions burned: 99 (million)
% 1.88/0.61 % (2054)------------------------------
% 1.88/0.61 % (2054)------------------------------
% 1.88/0.61 % (2064)Instruction limit reached!
% 1.88/0.61 % (2064)------------------------------
% 1.88/0.61 % (2064)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.88/0.61 % (2064)Termination reason: Unknown
% 1.88/0.61 % (2064)Termination phase: Property scanning
% 1.88/0.61
% 1.88/0.61 % (2064)Memory used [KB]: 1791
% 1.88/0.61 % (2064)Time elapsed: 0.012 s
% 1.88/0.61 % (2064)Instructions burned: 39 (million)
% 1.88/0.61 % (2064)------------------------------
% 1.88/0.61 % (2064)------------------------------
% 1.88/0.62 % (2073)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on Vampire---4 for (2997ds/6Mi)
% 1.88/0.62 % (2073)Instruction limit reached!
% 1.88/0.62 % (2073)------------------------------
% 1.88/0.62 % (2073)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.88/0.62 % (2073)Termination reason: Unknown
% 1.88/0.62 % (2073)Termination phase: shuffling
% 1.88/0.62
% 1.88/0.62 % (2073)Memory used [KB]: 1407
% 1.88/0.62 % (2073)Time elapsed: 0.003 s
% 1.88/0.62 % (2073)Instructions burned: 7 (million)
% 1.88/0.62 % (2073)------------------------------
% 1.88/0.62 % (2073)------------------------------
% 1.88/0.62 % (2075)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on Vampire---4 for (2997ds/1087Mi)
% 1.88/0.63 % (2079)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on Vampire---4 for (2997ds/47Mi)
% 1.88/0.63 % (2075)Refutation not found, incomplete strategy
% 1.88/0.63 % (2075)------------------------------
% 1.88/0.63 % (2075)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.88/0.63 % (2075)Termination reason: Refutation not found, incomplete strategy
% 1.88/0.63
% 1.88/0.63
% 1.88/0.63 % (2075)Memory used [KB]: 6268
% 1.88/0.63 % (2075)Time elapsed: 0.011 s
% 1.88/0.63 % (2075)Instructions burned: 29 (million)
% 1.88/0.63 % (2075)------------------------------
% 1.88/0.63 % (2075)------------------------------
% 2.05/0.64 % (2085)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on Vampire---4 for (2997ds/44Mi)
% 2.05/0.64 % (2033)Refutation found. Thanks to Tanya!
% 2.05/0.64 % SZS status Theorem for Vampire---4
% 2.05/0.64 % SZS output start Proof for Vampire---4
% See solution above
% 2.05/0.64 % (2033)------------------------------
% 2.05/0.64 % (2033)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.05/0.64 % (2033)Termination reason: Refutation
% 2.05/0.64
% 2.05/0.64 % (2033)Memory used [KB]: 10490
% 2.05/0.64 % (2033)Time elapsed: 0.146 s
% 2.05/0.64 % (2033)Instructions burned: 298 (million)
% 2.05/0.64 % (2033)------------------------------
% 2.05/0.64 % (2033)------------------------------
% 2.05/0.64 % (1996)Success in time 0.257 s
% 2.05/0.64 % Vampire---4.8 exiting
%------------------------------------------------------------------------------