%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : ALG261^1 : TPTP v8.1.2. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n002.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 04:13:25 EDT 2024
% Result : Theorem 0.21s 0.55s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 100
% Syntax : Number of formulae : 277 ( 210 unt; 61 typ; 0 def)
% Number of atoms : 4730 (1162 equ; 0 cnn)
% Maximal formula atoms : 3 ( 21 avg)
% Number of connectives : 18524 ( 217 ~; 0 |; 101 &;13318 @)
% ( 0 <=>;2071 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 1042 (1042 >; 0 *; 0 +; 0 <<)
% Number of symbols : 96 ( 92 usr; 43 con; 0-4 aty)
% (2817 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 3207 (2979 ^ 228 !; 0 ?;3207 :)
% 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 ) > term ).
thf(func_def_151,type,
sK10: ( term > $o ) > term ).
thf(func_def_152,type,
sK11: ( term > $o ) > term ).
thf(func_def_153,type,
sK12: ( term > $o ) > term ).
thf(func_def_154,type,
sK13: ( term > $o ) > subst > term ).
thf(func_def_155,type,
sK14: ( term > $o ) > term ).
thf(func_def_156,type,
sK15: ( term > $o ) > term ).
thf(func_def_157,type,
sK16: ( term > $o ) > subst > term ).
thf(func_def_158,type,
sK17: ( term > $o ) > term ).
thf(func_def_159,type,
sK18: ( term > $o ) > term ).
thf(func_def_160,type,
sK19: ( term > $o ) > term ).
thf(func_def_161,type,
sK20: ( term > $o ) > subst > term ).
thf(func_def_162,type,
sK21: ( term > $o ) > term ).
thf(func_def_163,type,
sK22: ( term > $o ) > term ).
thf(func_def_164,type,
sK23: ( term > $o ) > term ).
thf(func_def_165,type,
sK24: ( term > $o ) > term ).
thf(func_def_166,type,
sK25: ( term > $o ) > term ).
thf(func_def_167,type,
sK26: ( term > $o ) > term ).
thf(func_def_168,type,
sK27: ( term > $o ) > term ).
thf(func_def_169,type,
sK28: ( term > $o ) > term ).
thf(func_def_170,type,
sK29: ( term > $o ) > term ).
thf(func_def_171,type,
sK30: ( subst > term > term ) > term ).
thf(func_def_172,type,
sK31: ( subst > term > term ) > subst ).
thf(func_def_173,type,
sK32: ( subst > term > term ) > term ).
thf(func_def_174,type,
sK33: ( subst > term > term ) > subst ).
thf(func_def_175,type,
sK34: ( subst > term > term ) > subst ).
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,
sK39: ( subst > term > term ) > subst ).
thf(func_def_181,type,
sK40: ( subst > term > term ) > term ).
thf(func_def_182,type,
sK41: ( subst > term > term ) > subst ).
thf(func_def_183,type,
sK42: term ).
thf(func_def_184,type,
sK43: term ).
thf(f1022,plain,
$false,
inference(trivial_inequality_removal,[],[f1021]) ).
thf(f1021,plain,
$true = $false,
inference(backward_demodulation,[],[f1019,f688]) ).
thf(f688,plain,
! [X2: term,X1: term] :
( $false
= ( var @ ( ap @ X1 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f687]) ).
thf(f687,plain,
! [X2: term,X1: term] :
( $true
= ( ~ ( var @ ( ap @ X1 @ X2 ) ) ) ),
inference(beta_eta_normalization,[],[f686]) ).
thf(f686,plain,
! [X2: term,X1: term] :
( ( ^ [Y0: term] :
~ ( var @ ( ap @ X1 @ Y0 ) )
@ X2 )
= $true ),
inference(pi_clausification,[],[f685]) ).
thf(f685,plain,
! [X1: term] :
( $true
= ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( ap @ X1 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[],[f684]) ).
thf(f684,plain,
! [X1: term] :
( ( ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[],[f683]) ).
thf(f683,plain,
( $true
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f672]) ).
thf(f672,plain,
( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ ( term > $o )
@ ^ [Y2: term > $o] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y2 @ Y0 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ 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] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y2 @ id ) @ 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f663]) ).
thf(f663,plain,
( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ ( term > $o )
@ ^ [Y2: term > $o] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y2 @ Y0 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ 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] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y2 @ id ) @ 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f654]) ).
thf(f654,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ ( term > $o )
@ ^ [Y2: term > $o] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y2 @ Y0 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ 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] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y2 @ id ) @ 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f641]) ).
thf(f641,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ ( term > $o )
@ ^ [Y2: term > $o] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y2 @ Y0 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ 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] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y2 @ id ) @ 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f628]) ).
thf(f628,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y0 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ ( term > $o )
@ ^ [Y2: term > $o] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y2 @ Y0 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ 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] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y2 @ id ) @ 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f612]) ).
thf(f612,plain,
( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y2 )
= ( ap @ Y3 @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y0 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ ( term > $o )
@ ^ [Y2: term > $o] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y2 @ Y0 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ 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] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y2 @ id ) @ 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f607]) ).
thf(f607,plain,
( ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y2 )
= ( ap @ Y3 @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y0 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ ( term > $o )
@ ^ [Y2: term > $o] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y2 @ Y0 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ 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] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y2 @ id ) @ 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f605]) ).
thf(f605,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y2 )
= ( ap @ Y3 @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y0 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ ( term > $o )
@ ^ [Y2: term > $o] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y2 @ Y0 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ 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] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y2 @ id ) @ 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f600]) ).
thf(f600,plain,
( ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y2 )
= ( ap @ Y3 @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y0 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ ( term > $o )
@ ^ [Y2: term > $o] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y2 @ Y0 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ 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] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y2 @ id ) @ 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f597]) ).
thf(f597,plain,
( $false
= ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y2 )
= ( ap @ Y3 @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y0 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ ( term > $o )
@ ^ [Y2: term > $o] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y2 @ Y0 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ 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] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y2 @ id ) @ 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f592]) ).
thf(f592,plain,
( ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y2 )
= ( ap @ Y3 @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y0 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ ( term > $o )
@ ^ [Y2: term > $o] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y2 @ Y0 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ 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] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y2 @ id ) @ 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f583]) ).
thf(f583,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y2 )
= ( ap @ Y3 @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y0 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ ( term > $o )
@ ^ [Y2: term > $o] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y2 @ Y0 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ 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] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y2 @ id ) @ 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f574]) ).
thf(f574,plain,
( $false
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( push @ ( sub @ Y1 @ Y0 ) @ ( comp @ Y2 @ Y0 ) )
= ( comp @ ( push @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y2 )
= ( ap @ Y3 @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y0 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ ( term > $o )
@ ^ [Y2: term > $o] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y2 @ Y0 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ 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] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y2 @ id ) @ 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f567]) ).
thf(f567,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( push @ ( sub @ Y1 @ Y0 ) @ ( comp @ Y2 @ Y0 ) )
= ( comp @ ( push @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y2 )
= ( ap @ Y3 @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y0 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ ( term > $o )
@ ^ [Y2: term > $o] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y2 @ Y0 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ 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] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y2 @ id ) @ 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f562]) ).
thf(f562,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( push @ ( sub @ Y1 @ Y0 ) @ ( comp @ Y2 @ Y0 ) )
= ( comp @ ( push @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y2 )
= ( ap @ Y3 @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y0 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ ( term > $o )
@ ^ [Y2: term > $o] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y2 @ Y0 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ 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] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y2 @ id ) @ 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f553]) ).
thf(f553,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 @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( push @ ( sub @ Y1 @ Y0 ) @ ( comp @ Y2 @ Y0 ) )
= ( comp @ ( push @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y2 )
= ( ap @ Y3 @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y0 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ ( term > $o )
@ ^ [Y2: term > $o] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y2 @ Y0 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ 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] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y2 @ id ) @ 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f546]) ).
thf(f546,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( push @ ( sub @ Y1 @ Y0 ) @ ( comp @ Y2 @ Y0 ) )
= ( comp @ ( push @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y2 )
= ( ap @ Y3 @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y0 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ ( term > $o )
@ ^ [Y2: term > $o] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y2 @ Y0 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ 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] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y2 @ id ) @ 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f541]) ).
thf(f541,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( lam @ Y0 ) @ Y1 )
= ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( push @ ( sub @ Y1 @ Y0 ) @ ( comp @ Y2 @ Y0 ) )
= ( comp @ ( push @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y2 )
= ( ap @ Y3 @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y0 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ ( term > $o )
@ ^ [Y2: term > $o] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y2 @ Y0 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ 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] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y2 @ id ) @ 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f534]) ).
thf(f534,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( lam @ Y0 ) @ Y1 )
= ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( push @ ( sub @ Y1 @ Y0 ) @ ( comp @ Y2 @ Y0 ) )
= ( comp @ ( push @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y2 )
= ( ap @ Y3 @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y0 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ ( term > $o )
@ ^ [Y2: term > $o] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y2 @ Y0 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ 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] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y2 @ id ) @ 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f525]) ).
thf(f525,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( lam @ Y0 ) @ Y1 )
= ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( push @ ( sub @ Y1 @ Y0 ) @ ( comp @ Y2 @ Y0 ) )
= ( comp @ ( push @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y2 )
= ( ap @ Y3 @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y0 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ ( term > $o )
@ ^ [Y2: term > $o] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y2 @ Y0 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ 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] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y2 @ id ) @ 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f524]) ).
thf(f524,plain,
( $true
!= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( ap @ Y1 @ Y0 ) @ Y2 )
= ( ap @ ( sub @ Y1 @ Y2 ) @ ( sub @ Y0 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( lam @ Y0 ) @ Y1 )
= ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( push @ ( sub @ Y1 @ Y0 ) @ ( comp @ Y2 @ Y0 ) )
= ( comp @ ( push @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y2 )
= ( ap @ Y3 @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y0 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ ( term > $o )
@ ^ [Y2: term > $o] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y2 @ Y0 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ 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] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y2 @ id ) @ 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f523]) ).
thf(f523,plain,
( $true
!= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( ap @ Y1 @ Y0 ) @ Y2 )
= ( ap @ ( sub @ Y1 @ Y2 ) @ ( sub @ Y0 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( lam @ Y0 ) @ Y1 )
= ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( push @ ( sub @ Y1 @ Y0 ) @ ( comp @ Y2 @ Y0 ) )
= ( comp @ ( push @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y2 )
= ( ap @ Y3 @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y0 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ ( term > $o )
@ ^ [Y2: term > $o] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y2 @ Y0 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y3
@ id
@ Y0 )
= ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y1
@ id
@ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y1
@ id
@ Y3 )
= ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y0
@ id
@ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ 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] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y0 @ Y2 @ Y3 ) )
= ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ^ [Y3: subst,Y4: subst > term > term] : ( lam @ ( Y4 @ sh @ one ) )
@ id
@ ^ [Y3: subst,Y4: term] : ( Y0 @ Y3 @ Y4 ) )
!= ( ^ [Y3: subst,Y4: term,Y5: subst,Y6: term] : ( ap @ ( sub @ Y4 @ Y5 ) @ Y6 )
@ id
@ Y2
@ id
@ 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 ) ) ) ) )
=> ~ ( ^ [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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f393,f458]) ).
thf(f458,plain,
( hoasapnotvar_gthm
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( ap @ Y1 @ Y0 ) @ Y2 )
= ( ap @ ( sub @ Y1 @ Y2 ) @ ( sub @ Y0 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( lam @ Y0 ) @ Y1 )
= ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( push @ ( sub @ Y1 @ Y0 ) @ ( comp @ Y2 @ Y0 ) )
= ( comp @ ( push @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y2 )
= ( ap @ Y3 @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y0 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ ( term > $o )
@ ^ [Y2: term > $o] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y2 @ Y0 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y3
@ id
@ Y0 )
= ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y1
@ id
@ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y1
@ id
@ Y3 )
= ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y0
@ id
@ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ 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] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y0 @ Y2 @ Y3 ) )
= ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ^ [Y3: subst,Y4: subst > term > term] : ( lam @ ( Y4 @ sh @ one ) )
@ id
@ ^ [Y3: subst,Y4: term] : ( Y0 @ Y3 @ Y4 ) )
!= ( ^ [Y3: subst,Y4: term,Y5: subst,Y6: term] : ( ap @ ( sub @ Y4 @ Y5 ) @ Y6 )
@ id
@ Y2
@ id
@ 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 ) ) ) ) )
=> ~ ( ^ [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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f433,f336,f382,f422,f361,f351,f379,f360,f420,f427,f343,f428,f437,f344,f397,f431,f339,f358,f429,f348,f406,f412,f371,f333,f338,f340,f381,f405,f445,f451,f452,f453,f454,f455,f456]) ).
thf(f456,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,[],[f411,f404,f407]) ).
thf(f407,plain,
( hoasap
= ( ^ [Y0: subst,Y1: term,Y2: subst,Y3: term] : ( ap @ ( sub @ Y1 @ Y2 ) @ Y3 ) ) ),
inference(cnf_transformation,[],[f142]) ).
thf(f142,plain,
( hoasap
= ( ^ [Y0: subst,Y1: term,Y2: subst,Y3: term] : ( ap @ ( sub @ Y1 @ Y2 ) @ Y3 ) ) ),
inference(fool_elimination,[],[f141]) ).
thf(f141,plain,
( ( ^ [X0: subst,X1: term,X2: subst,X3: term] : ( ap @ ( sub @ X1 @ X2 ) @ X3 ) )
= hoasap ),
inference(rectify,[],[f55]) ).
thf(f55,axiom,
( ( ^ [X2: subst,X0: term,X3: subst,X1: term] : ( ap @ ( sub @ X0 @ X3 ) @ X1 ) )
= hoasap ),
file('/export/starexec/sandbox2/tmp/tmp.Heur3guCZx/Vampire---4.8_27630',hoasap) ).
thf(f404,plain,
( hoasvar
= ( ^ [Y0: subst,Y1: term,Y2: subst] : ( var @ ( sub @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f138]) ).
thf(f138,plain,
( hoasvar
= ( ^ [Y0: subst,Y1: term,Y2: subst] : ( var @ ( sub @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f137]) ).
thf(f137,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/sandbox2/tmp/tmp.Heur3guCZx/Vampire---4.8_27630',hoasvar) ).
thf(f411,plain,
( hoasapnotvar
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( hoasvar @ id @ ( hoasap @ id @ Y0 @ id @ Y1 ) @ id ) ) ) ),
inference(cnf_transformation,[],[f330]) ).
thf(f330,plain,
( hoasapnotvar
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( hoasvar @ id @ ( hoasap @ id @ Y0 @ id @ Y1 ) @ id ) ) ) ),
inference(fool_elimination,[],[f329]) ).
thf(f329,plain,
( hoasapnotvar
= ( ! [X0: term,X1: term] :
~ ( hoasvar @ id @ ( hoasap @ id @ X1 @ id @ X0 ) @ id ) ) ),
inference(rectify,[],[f73]) ).
thf(f73,axiom,
( hoasapnotvar
= ( ! [X1: term,X0: term] :
~ ( hoasvar @ id @ ( hoasap @ id @ X0 @ id @ X1 ) @ id ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Heur3guCZx/Vampire---4.8_27630',hoasapnotvar) ).
thf(f455,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,[],[f416,f404,f421]) ).
thf(f421,plain,
( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( lam @ ( Y1 @ sh @ one ) ) ) ),
inference(cnf_transformation,[],[f158]) ).
thf(f158,plain,
( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( lam @ ( Y1 @ sh @ one ) ) ) ),
inference(fool_elimination,[],[f157]) ).
thf(f157,plain,
( hoaslam
= ( ^ [X0: subst,X1: subst > term > term] : ( lam @ ( X1 @ sh @ one ) ) ) ),
inference(rectify,[],[f56]) ).
thf(f56,axiom,
( hoaslam
= ( ^ [X2: subst,X10: subst > term > term] : ( lam @ ( X10 @ sh @ one ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Heur3guCZx/Vampire---4.8_27630',hoaslam) ).
thf(f416,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,[],[f176]) ).
thf(f176,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,[],[f175]) ).
thf(f175,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/sandbox2/tmp/tmp.Heur3guCZx/Vampire---4.8_27630',hoaslamnotvar) ).
thf(f454,plain,
( hoaslamnotap
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ^ [Y3: subst,Y4: subst > term > term] : ( lam @ ( Y4 @ sh @ one ) )
@ id
@ ^ [Y3: subst,Y4: term] : ( Y0 @ Y3 @ Y4 ) )
!= ( ^ [Y3: subst,Y4: term,Y5: subst,Y6: term] : ( ap @ ( sub @ Y4 @ Y5 ) @ Y6 )
@ id
@ Y2
@ id
@ Y1 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f402,f421,f407]) ).
thf(f402,plain,
( hoaslamnotap
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( hoaslam @ id
@ ^ [Y3: subst,Y4: term] : ( Y0 @ Y3 @ Y4 ) )
!= ( hoasap @ id @ Y2 @ id @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f213]) ).
thf(f213,plain,
( hoaslamnotap
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( hoaslam @ id
@ ^ [Y3: subst,Y4: term] : ( Y0 @ Y3 @ Y4 ) )
!= ( hoasap @ id @ Y2 @ id @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f212]) ).
thf(f212,plain,
( hoaslamnotap
= ( ! [X0: subst > term > term] :
( ! [X1: term,X2: subst,X3: subst] :
( ( X0 @ ( comp @ X2 @ X3 ) @ ( sub @ X1 @ X3 ) )
= ( sub @ ( X0 @ X2 @ X1 ) @ X3 ) )
=> ! [X4: term,X5: term] :
( ( hoaslam @ id
@ ^ [X6: subst,X7: term] : ( X0 @ X6 @ X7 ) )
!= ( hoasap @ id @ X4 @ id @ X5 ) ) ) ) ),
inference(rectify,[],[f67]) ).
thf(f67,axiom,
( hoaslamnotap
= ( ! [X10: subst > term > term] :
( ! [X0: term,X2: subst,X3: subst] :
( ( sub @ ( X10 @ X2 @ X0 ) @ X3 )
= ( X10 @ ( comp @ X2 @ X3 ) @ ( sub @ X0 @ X3 ) ) )
=> ! [X0: term,X1: term] :
( ( hoaslam @ id
@ ^ [X2: subst,X6: term] : ( X10 @ X2 @ X6 ) )
!= ( hoasap @ id @ X0 @ id @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Heur3guCZx/Vampire---4.8_27630',hoaslamnotap) ).
thf(f453,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] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y0 @ Y2 @ Y3 ) )
= ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f389,f421,f421]) ).
thf(f389,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] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y0 @ Y2 @ Y3 ) )
= ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f233]) ).
thf(f233,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] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y0 @ Y2 @ Y3 ) )
= ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f232]) ).
thf(f232,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: subst,X6: subst,X7: term] :
( ( X4 @ ( comp @ X6 @ X5 ) @ ( sub @ X7 @ X5 ) )
= ( sub @ ( X4 @ X6 @ X7 ) @ X5 ) )
=> ( ( ( hoaslam @ id
@ ^ [X8: subst,X9: term] : ( X0 @ X8 @ X9 ) )
= ( hoaslam @ id
@ ^ [X10: subst,X11: term] : ( X4 @ X10 @ X11 ) ) )
=> ! [X12: term,X13: subst] :
( ( X0 @ X13 @ X12 )
= ( X4 @ X13 @ X12 ) ) ) ) ) ) ),
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] :
( ! [X3: subst,X2: subst,X0: term] :
( ( sub @ ( X11 @ X2 @ X0 ) @ X3 )
= ( X11 @ ( comp @ X2 @ X3 ) @ ( sub @ X0 @ X3 ) ) )
=> ( ( ( hoaslam @ id
@ ^ [X2: subst,X0: term] : ( X10 @ X2 @ X0 ) )
= ( hoaslam @ id
@ ^ [X2: subst,X0: term] : ( X11 @ X2 @ X0 ) ) )
=> ! [X0: term,X2: subst] :
( ( X10 @ X2 @ X0 )
= ( X11 @ X2 @ X0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Heur3guCZx/Vampire---4.8_27630',hoaslaminj) ).
thf(f452,plain,
( hoasapinj2
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y1
@ id
@ Y3 )
= ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y0
@ id
@ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f365,f407,f407]) ).
thf(f365,plain,
( hoasapinj2
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( hoasap @ id @ Y1 @ id @ Y3 )
= ( hoasap @ id @ Y0 @ id @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f286]) ).
thf(f286,plain,
( hoasapinj2
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( hoasap @ id @ Y1 @ id @ Y3 )
= ( hoasap @ id @ Y0 @ id @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f285]) ).
thf(f285,plain,
! [X0: term,X1: term,X2: term,X3: term] :
( ( ( ( hoasap @ id @ X2 @ id @ X0 )
= ( hoasap @ id @ X3 @ id @ X1 ) )
=> ( X0 = X1 ) )
= hoasapinj2 ),
inference(rectify,[],[f61]) ).
thf(f61,axiom,
! [X6: term,X7: term,X0: term,X1: term] :
( ( ( ( hoasap @ id @ X0 @ id @ X6 )
= ( hoasap @ id @ X1 @ id @ X7 ) )
=> ( X6 = X7 ) )
= hoasapinj2 ),
file('/export/starexec/sandbox2/tmp/tmp.Heur3guCZx/Vampire---4.8_27630',hoasapinj2) ).
thf(f451,plain,
( hoasapinj1
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y3
@ id
@ Y0 )
= ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y1
@ id
@ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f376,f407,f407]) ).
thf(f376,plain,
( hoasapinj1
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( hoasap @ id @ Y3 @ id @ Y0 )
= ( hoasap @ id @ Y1 @ id @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f126]) ).
thf(f126,plain,
( hoasapinj1
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( hoasap @ id @ Y3 @ id @ Y0 )
= ( hoasap @ id @ Y1 @ id @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f125]) ).
thf(f125,plain,
! [X0: term,X1: term,X2: term,X3: term] :
( ( ( ( hoasap @ id @ X0 @ id @ X3 )
= ( hoasap @ id @ X2 @ id @ X1 ) )
=> ( X0 = X2 ) )
= hoasapinj1 ),
inference(rectify,[],[f58]) ).
thf(f58,axiom,
! [X0: term,X7: term,X1: term,X6: term] :
( ( ( ( hoasap @ id @ X0 @ id @ X6 )
= ( hoasap @ id @ X1 @ id @ X7 ) )
=> ( X0 = X1 ) )
= hoasapinj1 ),
file('/export/starexec/sandbox2/tmp/tmp.Heur3guCZx/Vampire---4.8_27630',hoasapinj1) ).
thf(f445,plain,
( termmset
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ) ),
inference(cnf_transformation,[],[f318]) ).
thf(f318,plain,
( termmset
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ) ),
inference(fool_elimination,[],[f317]) ).
thf(f317,plain,
( ( termmset
= ( ! [X0: term] :
( ( sub @ X0 @ id )
= X0 ) ) )
& ! [X1: term,X2: subst,X3: subst] :
( ( sub @ X1 @ ( comp @ X2 @ X3 ) )
= ( sub @ ( sub @ X1 @ X2 ) @ X3 ) ) ),
inference(rectify,[],[f52]) ).
thf(f52,axiom,
( ( termmset
= ( ! [X0: term] :
( ( sub @ X0 @ id )
= X0 ) ) )
& ! [X0: term,X2: subst,X3: subst] :
( ( sub @ ( sub @ X0 @ X2 ) @ X3 )
= ( sub @ X0 @ ( comp @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Heur3guCZx/Vampire---4.8_27630',termmset) ).
thf(f405,plain,
( substmonoid
= ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f202]) ).
thf(f202,plain,
( substmonoid
= ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f201]) ).
thf(f201,plain,
( ( substmonoid
= ( ! [X0: subst,X1: subst,X2: subst] :
( ( comp @ ( comp @ X0 @ X1 ) @ X2 )
= ( comp @ X0 @ ( comp @ X1 @ X2 ) ) ) ) )
& ! [X3: subst] :
( ( comp @ X3 @ id )
= X3 )
& ! [X4: subst] :
( ( comp @ id @ X4 )
= X4 ) ),
inference(rectify,[],[f49]) ).
thf(f49,axiom,
( ( substmonoid
= ( ! [X2: subst,X3: subst,X4: subst] :
( ( comp @ ( comp @ X2 @ X3 ) @ X4 )
= ( comp @ X2 @ ( comp @ X3 @ X4 ) ) ) ) )
& ! [X2: subst] :
( ( comp @ X2 @ id )
= X2 )
& ! [X2: subst] :
( ( comp @ id @ X2 )
= X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.Heur3guCZx/Vampire---4.8_27630',substmonoid) ).
thf(f381,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,[],[f257]) ).
thf(f257,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,[],[f256]) ).
thf(f256,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/sandbox2/tmp/tmp.Heur3guCZx/Vampire---4.8_27630',induction2) ).
thf(f340,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,[],[f249]) ).
thf(f249,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,[],[f248]) ).
thf(f248,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/sandbox2/tmp/tmp.Heur3guCZx/Vampire---4.8_27630',induction2lem) ).
thf(f338,plain,
( pushprop
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ ( term > $o )
@ ^ [Y2: term > $o] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y2 @ Y0 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f184]) ).
thf(f184,plain,
( pushprop
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ ( term > $o )
@ ^ [Y2: term > $o] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y2 @ Y0 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f183]) ).
thf(f183,plain,
( pushprop
= ( ! [X0: term > $o,X1: subst,X2: term] :
( ! [X3: term] :
( ( var @ X3 )
=> ( X0 @ ( sub @ X3 @ X1 ) ) )
=> ( ( X0 @ X2 )
=> ! [X4: term] :
( ( var @ X4 )
=> ( X0 @ ( sub @ X4 @ ( push @ X2 @ X1 ) ) ) ) ) ) ) ),
inference(rectify,[],[f39]) ).
thf(f39,axiom,
( pushprop
= ( ! [X5: term > $o,X2: subst,X0: term] :
( ! [X1: term] :
( ( var @ X1 )
=> ( X5 @ ( sub @ X1 @ X2 ) ) )
=> ( ( X5 @ X0 )
=> ! [X1: term] :
( ( var @ X1 )
=> ( X5 @ ( sub @ X1 @ ( push @ X0 @ X2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Heur3guCZx/Vampire---4.8_27630',pushprop) ).
thf(f333,plain,
( induction
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f300]) ).
thf(f300,plain,
( induction
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f299]) ).
thf(f299,plain,
! [X0: term > $o] :
( ( ! [X1: term] :
( ( var @ X1 )
=> ( X0 @ X1 ) )
=> ( ! [X2: term,X3: term] :
( ( X0 @ X3 )
=> ( ( X0 @ X2 )
=> ( X0 @ ( ap @ X3 @ X2 ) ) ) )
=> ( ! [X4: term] :
( ( X0 @ X4 )
=> ( X0 @ ( lam @ X4 ) ) )
=> ! [X5: term] : ( X0 @ X5 ) ) ) )
= induction ),
inference(rectify,[],[f23]) ).
thf(f23,axiom,
! [X5: term > $o] :
( ( ! [X0: term] :
( ( var @ X0 )
=> ( X5 @ X0 ) )
=> ( ! [X1: term,X0: term] :
( ( X5 @ X0 )
=> ( ( X5 @ X1 )
=> ( X5 @ ( ap @ X0 @ X1 ) ) ) )
=> ( ! [X0: term] :
( ( X5 @ X0 )
=> ( X5 @ ( lam @ X0 ) ) )
=> ! [X0: term] : ( X5 @ X0 ) ) ) )
= induction ),
file('/export/starexec/sandbox2/tmp/tmp.Heur3guCZx/Vampire---4.8_27630',induction) ).
thf(f371,plain,
( lamnotvar
= ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f198]) ).
thf(f198,plain,
( lamnotvar
= ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) ) ),
inference(fool_elimination,[],[f197]) ).
thf(f197,plain,
! [X0: term] :
( ( ~ ( var @ ( lam @ X0 ) ) )
= lamnotvar ),
inference(rectify,[],[f22]) ).
thf(f22,axiom,
! [X0: term] :
( ( ~ ( var @ ( lam @ X0 ) ) )
= lamnotvar ),
file('/export/starexec/sandbox2/tmp/tmp.Heur3guCZx/Vampire---4.8_27630',lamnotvar) ).
thf(f412,plain,
( apnotvar
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f298]) ).
thf(f298,plain,
( apnotvar
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f297]) ).
thf(f297,plain,
( apnotvar
= ( ! [X0: term,X1: term] :
~ ( var @ ( ap @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f21]) ).
thf(f21,axiom,
( apnotvar
= ( ! [X1: term,X0: term] :
~ ( var @ ( ap @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Heur3guCZx/Vampire---4.8_27630',apnotvar) ).
thf(f406,plain,
( lamnotap
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f272]) ).
thf(f272,plain,
( lamnotap
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f271]) ).
thf(f271,plain,
! [X0: term,X1: term,X2: term] :
( ( ( lam @ X1 )
!= ( ap @ X2 @ X0 ) )
= lamnotap ),
inference(rectify,[],[f20]) ).
thf(f20,axiom,
! [X6: term,X0: term,X1: term] :
( ( ( lam @ X0 )
!= ( ap @ X1 @ X6 ) )
= lamnotap ),
file('/export/starexec/sandbox2/tmp/tmp.Heur3guCZx/Vampire---4.8_27630',lamnotap) ).
thf(f348,plain,
( shinj
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f243]) ).
thf(f243,plain,
( shinj
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(fool_elimination,[],[f242]) ).
thf(f242,plain,
( shinj
= ( ! [X0: term,X1: term] :
( ( ( sub @ X0 @ sh )
= ( sub @ X1 @ sh ) )
=> ( X0 = X1 ) ) ) ),
inference(rectify,[],[f19]) ).
thf(f19,axiom,
( shinj
= ( ! [X1: term,X0: term] :
( ( ( sub @ X0 @ sh )
= ( sub @ X1 @ sh ) )
=> ( X0 = X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Heur3guCZx/Vampire---4.8_27630',shinj) ).
thf(f429,plain,
( laminj
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f255]) ).
thf(f255,plain,
( laminj
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(fool_elimination,[],[f254]) ).
thf(f254,plain,
! [X0: term,X1: term] :
( ( ( ( lam @ X0 )
= ( lam @ X1 ) )
=> ( X0 = X1 ) )
= laminj ),
inference(rectify,[],[f18]) ).
thf(f18,axiom,
! [X1: term,X0: term] :
( ( ( ( lam @ X0 )
= ( lam @ X1 ) )
=> ( X0 = X1 ) )
= laminj ),
file('/export/starexec/sandbox2/tmp/tmp.Heur3guCZx/Vampire---4.8_27630',laminj) ).
thf(f358,plain,
( apinj2
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y0 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f308]) ).
thf(f308,plain,
( apinj2
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y0 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f307]) ).
thf(f307,plain,
( apinj2
= ( ! [X0: term,X1: term,X2: term,X3: term] :
( ( ( ap @ X0 @ X1 )
= ( ap @ X3 @ X2 ) )
=> ( X1 = X2 ) ) ) ),
inference(rectify,[],[f17]) ).
thf(f17,axiom,
( apinj2
= ( ! [X0: term,X6: term,X7: term,X1: term] :
( ( ( ap @ X0 @ X6 )
= ( ap @ X1 @ X7 ) )
=> ( X6 = X7 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Heur3guCZx/Vampire---4.8_27630',apinj2) ).
thf(f339,plain,
( apinj1
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y2 )
= ( ap @ Y3 @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f194]) ).
thf(f194,plain,
( apinj1
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y1 @ Y2 )
= ( ap @ Y3 @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f193]) ).
thf(f193,plain,
( apinj1
= ( ! [X0: term,X1: term,X2: term,X3: term] :
( ( ( ap @ X2 @ X1 )
= ( ap @ X0 @ X3 ) )
=> ( X0 = X2 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f16,axiom,
( apinj1
= ( ! [X1: term,X6: term,X0: term,X7: term] :
( ( ( ap @ X0 @ X6 )
= ( ap @ X1 @ X7 ) )
=> ( X0 = X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Heur3guCZx/Vampire---4.8_27630',apinj1) ).
thf(f431,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,[],[f227]) ).
thf(f227,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,[],[f226]) ).
thf(f226,plain,
( ulamvarind
= ( ! [X0: term > $o] :
( ( X0 @ one )
=> ( ! [X1: term] :
( ( var @ X1 )
=> ( ( X0 @ X1 )
=> ( X0 @ ( sub @ X1 @ sh ) ) ) )
=> ! [X2: term] :
( ( var @ X2 )
=> ( X0 @ X2 ) ) ) ) ) ),
inference(rectify,[],[f15]) ).
thf(f15,axiom,
( ulamvarind
= ( ! [X5: term > $o] :
( ( X5 @ one )
=> ( ! [X0: term] :
( ( var @ X0 )
=> ( ( X5 @ X0 )
=> ( X5 @ ( sub @ X0 @ sh ) ) ) )
=> ! [X0: term] :
( ( var @ X0 )
=> ( X5 @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Heur3guCZx/Vampire---4.8_27630',ulamvarind) ).
thf(f397,plain,
( ulamvarsh
= ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) ) ),
inference(cnf_transformation,[],[f219]) ).
thf(f219,plain,
( ulamvarsh
= ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) ) ),
inference(fool_elimination,[],[f218]) ).
thf(f218,plain,
( ulamvarsh
= ( ! [X0: term] :
( ( var @ X0 )
=> ( var @ ( sub @ X0 @ sh ) ) ) ) ),
inference(rectify,[],[f14]) ).
thf(f14,axiom,
( ulamvarsh
= ( ! [X0: term] :
( ( var @ X0 )
=> ( var @ ( sub @ X0 @ sh ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Heur3guCZx/Vampire---4.8_27630',ulamvarsh) ).
thf(f344,plain,
( ulamvar1
= ( var @ one ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f13,axiom,
( ulamvar1
= ( var @ one ) ),
file('/export/starexec/sandbox2/tmp/tmp.Heur3guCZx/Vampire---4.8_27630',ulamvar1) ).
thf(f437,plain,
( axscons
= ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) ) ),
inference(cnf_transformation,[],[f136]) ).
thf(f136,plain,
( axscons
= ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) ) ),
inference(fool_elimination,[],[f135]) ).
thf(f135,plain,
( axscons
= ( ! [X0: subst] :
( ( push @ ( sub @ one @ X0 ) @ ( comp @ sh @ X0 ) )
= X0 ) ) ),
inference(rectify,[],[f12]) ).
thf(f12,axiom,
( axscons
= ( ! [X2: subst] :
( ( push @ ( sub @ one @ X2 ) @ ( comp @ sh @ X2 ) )
= X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Heur3guCZx/Vampire---4.8_27630',axscons) ).
thf(f428,plain,
( axvarshift
= ( id
= ( push @ one @ sh ) ) ),
inference(cnf_transformation,[],[f209]) ).
thf(f209,plain,
( axvarshift
= ( id
= ( push @ one @ sh ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f11,axiom,
( axvarshift
= ( id
= ( push @ one @ sh ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Heur3guCZx/Vampire---4.8_27630',axvarshift) ).
thf(f343,plain,
( axidr
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) ),
inference(cnf_transformation,[],[f316]) ).
thf(f316,plain,
( axidr
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) ),
inference(fool_elimination,[],[f315]) ).
thf(f315,plain,
! [X0: subst] :
( ( ( comp @ X0 @ id )
= X0 )
= axidr ),
inference(rectify,[],[f10]) ).
thf(f10,axiom,
! [X2: subst] :
( ( ( comp @ X2 @ id )
= X2 )
= axidr ),
file('/export/starexec/sandbox2/tmp/tmp.Heur3guCZx/Vampire---4.8_27630',axidr) ).
thf(f427,plain,
( axmap
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( push @ ( sub @ Y1 @ Y0 ) @ ( comp @ Y2 @ Y0 ) )
= ( comp @ ( push @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f225]) ).
thf(f225,plain,
( axmap
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( push @ ( sub @ Y1 @ Y0 ) @ ( comp @ Y2 @ Y0 ) )
= ( comp @ ( push @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f224]) ).
thf(f224,plain,
! [X0: subst,X1: term,X2: subst] :
( ( ( push @ ( sub @ X1 @ X2 ) @ ( comp @ X0 @ X2 ) )
= ( comp @ ( push @ X1 @ X0 ) @ X2 ) )
= axmap ),
inference(rectify,[],[f9]) ).
thf(f9,axiom,
! [X2: subst,X0: term,X3: subst] :
( ( ( comp @ ( push @ X0 @ X2 ) @ X3 )
= ( push @ ( sub @ X0 @ X3 ) @ ( comp @ X2 @ X3 ) ) )
= axmap ),
file('/export/starexec/sandbox2/tmp/tmp.Heur3guCZx/Vampire---4.8_27630',axmap) ).
thf(f420,plain,
( axassoc
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f178]) ).
thf(f178,plain,
( axassoc
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f177]) ).
thf(f177,plain,
( axassoc
= ( ! [X0: subst,X1: subst,X2: subst] :
( ( comp @ ( comp @ X0 @ X1 ) @ X2 )
= ( comp @ X0 @ ( comp @ X1 @ X2 ) ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f8,axiom,
( axassoc
= ( ! [X2: subst,X3: subst,X4: subst] :
( ( comp @ ( comp @ X2 @ X3 ) @ X4 )
= ( comp @ X2 @ ( comp @ X3 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Heur3guCZx/Vampire---4.8_27630',axassoc) ).
thf(f360,plain,
( axshiftcons
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) ) ),
inference(cnf_transformation,[],[f310]) ).
thf(f310,plain,
( axshiftcons
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) ) ),
inference(fool_elimination,[],[f309]) ).
thf(f309,plain,
! [X0: term,X1: subst] :
( ( ( comp @ sh @ ( push @ X0 @ X1 ) )
= X1 )
= axshiftcons ),
inference(rectify,[],[f7]) ).
thf(f7,axiom,
! [X0: term,X2: subst] :
( ( ( comp @ sh @ ( push @ X0 @ X2 ) )
= X2 )
= axshiftcons ),
file('/export/starexec/sandbox2/tmp/tmp.Heur3guCZx/Vampire---4.8_27630',axshiftcons) ).
thf(f379,plain,
( axidl
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) ),
inference(cnf_transformation,[],[f118]) ).
thf(f118,plain,
( axidl
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) ),
inference(fool_elimination,[],[f117]) ).
thf(f117,plain,
( axidl
= ( ! [X0: subst] :
( ( comp @ id @ X0 )
= X0 ) ) ),
inference(rectify,[],[f6]) ).
thf(f6,axiom,
( axidl
= ( ! [X2: subst] :
( ( comp @ id @ X2 )
= X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Heur3guCZx/Vampire---4.8_27630',axidl) ).
thf(f351,plain,
( axclos
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f124]) ).
thf(f124,plain,
( axclos
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f123]) ).
thf(f123,plain,
! [X0: subst,X1: term,X2: subst] :
( ( ( sub @ X1 @ ( comp @ X2 @ X0 ) )
= ( sub @ ( sub @ X1 @ X2 ) @ X0 ) )
= axclos ),
inference(rectify,[],[f5]) ).
thf(f5,axiom,
! [X3: subst,X0: term,X2: subst] :
( ( ( sub @ ( sub @ X0 @ X2 ) @ X3 )
= ( sub @ X0 @ ( comp @ X2 @ X3 ) ) )
= axclos ),
file('/export/starexec/sandbox2/tmp/tmp.Heur3guCZx/Vampire---4.8_27630',axclos) ).
thf(f361,plain,
( axabs
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( lam @ Y0 ) @ Y1 )
= ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f156]) ).
thf(f156,plain,
( axabs
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( lam @ Y0 ) @ Y1 )
= ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f155]) ).
thf(f155,plain,
( axabs
= ( ! [X0: subst,X1: term] :
( ( sub @ ( lam @ X1 ) @ X0 )
= ( lam @ ( sub @ X1 @ ( push @ one @ ( comp @ X0 @ sh ) ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f4,axiom,
( axabs
= ( ! [X2: subst,X0: term] :
( ( sub @ ( lam @ X0 ) @ X2 )
= ( lam @ ( sub @ X0 @ ( push @ one @ ( comp @ X2 @ sh ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Heur3guCZx/Vampire---4.8_27630',axabs) ).
thf(f422,plain,
( axvarid
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ),
inference(cnf_transformation,[],[f268]) ).
thf(f268,plain,
( axvarid
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f3,axiom,
! [X0: term] :
( ( ( sub @ X0 @ id )
= X0 )
= axvarid ),
file('/export/starexec/sandbox2/tmp/tmp.Heur3guCZx/Vampire---4.8_27630',axvarid) ).
thf(f382,plain,
( axvarcons
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) ) ),
inference(cnf_transformation,[],[f292]) ).
thf(f292,plain,
( axvarcons
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) ) ),
inference(fool_elimination,[],[f291]) ).
thf(f291,plain,
( axvarcons
= ( ! [X0: subst,X1: term] :
( ( sub @ one @ ( push @ X1 @ X0 ) )
= X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
( axvarcons
= ( ! [X2: subst,X0: term] :
( ( sub @ one @ ( push @ X0 @ X2 ) )
= X0 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Heur3guCZx/Vampire---4.8_27630',axvarcons) ).
thf(f336,plain,
( axapp
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( ap @ Y1 @ Y0 ) @ Y2 )
= ( ap @ ( sub @ Y1 @ Y2 ) @ ( sub @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f168]) ).
thf(f168,plain,
( axapp
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( ap @ Y1 @ Y0 ) @ Y2 )
= ( ap @ ( sub @ Y1 @ Y2 ) @ ( sub @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f167]) ).
thf(f167,plain,
! [X0: subst,X1: term,X2: term] :
( ( ( sub @ ( ap @ X1 @ X2 ) @ X0 )
= ( ap @ ( sub @ X1 @ X0 ) @ ( sub @ X2 @ X0 ) ) )
= axapp ),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
! [X2: subst,X0: term,X1: term] :
( ( ( sub @ ( ap @ X0 @ X1 ) @ X2 )
= ( ap @ ( sub @ X0 @ X2 ) @ ( sub @ X1 @ X2 ) ) )
= axapp ),
file('/export/starexec/sandbox2/tmp/tmp.Heur3guCZx/Vampire---4.8_27630',axapp) ).
thf(f433,plain,
( hoasapnotvar_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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f140]) ).
thf(f140,plain,
( hoasapnotvar_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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f139]) ).
thf(f139,plain,
( axapp
=> ( ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> hoasapnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= hoasapnotvar_gthm ) ),
inference(rectify,[],[f74]) ).
thf(f74,axiom,
( axapp
=> ( ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> hoasapnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= hoasapnotvar_gthm ) ),
file('/export/starexec/sandbox2/tmp/tmp.Heur3guCZx/Vampire---4.8_27630',hoasapnotvar_gthm) ).
thf(f393,plain,
hoasapnotvar_gthm != $true,
inference(cnf_transformation,[],[f331]) ).
thf(f331,plain,
hoasapnotvar_gthm != $true,
inference(flattening,[],[f245]) ).
thf(f245,plain,
hoasapnotvar_gthm != $true,
inference(fool_elimination,[],[f244]) ).
thf(f244,plain,
~ hoasapnotvar_gthm,
inference(rectify,[],[f115]) ).
thf(f115,negated_conjecture,
~ hoasapnotvar_gthm,
inference(negated_conjecture,[],[f114]) ).
thf(f114,conjecture,
hoasapnotvar_gthm,
file('/export/starexec/sandbox2/tmp/tmp.Heur3guCZx/Vampire---4.8_27630',thm) ).
thf(f1019,plain,
( $true
= ( var @ ( ap @ sK42 @ sK43 ) ) ),
inference(forward_demodulation,[],[f1014,f921]) ).
thf(f921,plain,
! [X1: term] :
( ( sub @ X1 @ id )
= X1 ),
inference(equality_proxy_clausification,[],[f920]) ).
thf(f920,plain,
! [X1: term] :
( $true
= ( ( sub @ X1 @ id )
= X1 ) ),
inference(beta_eta_normalization,[],[f919]) ).
thf(f919,plain,
! [X1: term] :
( $true
= ( ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 )
@ X1 ) ),
inference(pi_clausification,[],[f910]) ).
thf(f910,plain,
( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
= $true ),
inference(binary_proxy_clausification,[],[f909]) ).
thf(f909,plain,
( $true
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ) ),
inference(binary_proxy_clausification,[],[f889]) ).
thf(f889,plain,
( ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ 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] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y2 @ id ) @ 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f824]) ).
thf(f824,plain,
( ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ 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] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y2 @ id ) @ 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f771]) ).
thf(f771,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] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ 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] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y2 @ id ) @ 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f751]) ).
thf(f751,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] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ 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] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y2 @ id ) @ 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f694]) ).
thf(f694,plain,
( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ ( term > $o )
@ ^ [Y2: term > $o] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y2 @ Y0 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ 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] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y2 @ id ) @ 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f689]) ).
thf(f689,plain,
( ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ ( term > $o )
@ ^ [Y2: term > $o] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y2 @ Y0 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ 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] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y2 @ id ) @ 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f682]) ).
thf(f682,plain,
( $false
= ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ ( term > $o )
@ ^ [Y2: term > $o] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y2 @ Y0 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ 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] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y2 @ id ) @ 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f672]) ).
thf(f1014,plain,
( ( var @ ( ap @ ( sub @ sK42 @ id ) @ sK43 ) )
= $true ),
inference(backward_demodulation,[],[f1012,f921]) ).
thf(f1012,plain,
( $true
= ( var @ ( sub @ ( ap @ ( sub @ sK42 @ id ) @ sK43 ) @ id ) ) ),
inference(not_proxy_clausification,[],[f1011]) ).
thf(f1011,plain,
( $false
= ( ~ ( var @ ( sub @ ( ap @ ( sub @ sK42 @ id ) @ sK43 ) @ id ) ) ) ),
inference(beta_eta_normalization,[],[f1010]) ).
thf(f1010,plain,
( ( ^ [Y0: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ sK42 @ id ) @ Y0 ) @ id ) )
@ sK43 )
= $false ),
inference(sigma_clausification,[],[f1009]) ).
thf(f1009,plain,
( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ sK42 @ id ) @ Y0 ) @ id ) ) )
= $false ),
inference(beta_eta_normalization,[],[f1008]) ).
thf(f1008,plain,
( ( ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) )
@ sK42 )
= $false ),
inference(sigma_clausification,[],[f995]) ).
thf(f995,plain,
( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f977]) ).
thf(f977,plain,
( $false
= ( ( !! @ ( 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 ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f948]) ).
thf(f948,plain,
( ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y2 @ id ) @ 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f935]) ).
thf(f935,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] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y2 @ id ) @ 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f922]) ).
thf(f922,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ 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] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y2 @ id ) @ 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f908]) ).
thf(f908,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y2 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ 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] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y2 @ Y3 )
= ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ ( Y0 @ sh @ one ) )
!= ( ap @ ( sub @ Y2 @ id ) @ 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f889]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG261^1 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.07/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.35 % Computer : n002.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 3 19:57:53 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.35 This is a TH0_THM_EQU_NAR problem
% 0.15/0.35 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/tmp/tmp.Heur3guCZx/Vampire---4.8_27630
% 0.15/0.38 % (27747)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)
% 0.15/0.38 % (27741)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)
% 0.15/0.38 % (27740)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)
% 0.15/0.38 % (27743)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.15/0.38 % (27744)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)
% 0.15/0.38 % (27742)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)
% 0.15/0.38 % (27745)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)
% 0.15/0.38 % (27743)Instruction limit reached!
% 0.15/0.38 % (27743)------------------------------
% 0.15/0.38 % (27743)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (27743)Termination reason: Unknown
% 0.15/0.38 % (27743)Termination phase: shuffling
% 0.15/0.38
% 0.15/0.38 % (27743)Memory used [KB]: 1151
% 0.15/0.38 % (27743)Time elapsed: 0.003 s
% 0.15/0.38 % (27743)Instructions burned: 2 (million)
% 0.15/0.38 % (27743)------------------------------
% 0.15/0.38 % (27743)------------------------------
% 0.15/0.38 % (27744)Instruction limit reached!
% 0.15/0.38 % (27744)------------------------------
% 0.15/0.38 % (27744)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (27744)Termination reason: Unknown
% 0.15/0.38 % (27744)Termination phase: shuffling
% 0.15/0.38
% 0.15/0.38 % (27744)Memory used [KB]: 1151
% 0.15/0.38 % (27744)Time elapsed: 0.003 s
% 0.15/0.38 % (27744)Instructions burned: 2 (million)
% 0.15/0.38 % (27744)------------------------------
% 0.15/0.38 % (27744)------------------------------
% 0.15/0.38 % (27747)Instruction limit reached!
% 0.15/0.38 % (27747)------------------------------
% 0.15/0.38 % (27747)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (27747)Termination reason: Unknown
% 0.15/0.38 % (27747)Termination phase: shuffling
% 0.15/0.38
% 0.15/0.38 % (27747)Memory used [KB]: 1279
% 0.15/0.38 % (27747)Time elapsed: 0.004 s
% 0.15/0.38 % (27747)Instructions burned: 4 (million)
% 0.15/0.38 % (27747)------------------------------
% 0.15/0.38 % (27747)------------------------------
% 0.15/0.39 % (27741)Instruction limit reached!
% 0.15/0.39 % (27741)------------------------------
% 0.15/0.39 % (27741)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (27741)Termination reason: Unknown
% 0.15/0.39 % (27741)Termination phase: shuffling
% 0.15/0.39
% 0.15/0.39 % (27741)Memory used [KB]: 1279
% 0.15/0.39 % (27741)Time elapsed: 0.005 s
% 0.15/0.39 % (27741)Instructions burned: 5 (million)
% 0.15/0.39 % (27741)------------------------------
% 0.15/0.39 % (27741)------------------------------
% 0.15/0.39 % (27746)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.15/0.40 % (27748)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)
% 0.15/0.40 % (27750)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)
% 0.15/0.40 % (27745)Refutation not found, incomplete strategy
% 0.15/0.40 % (27745)------------------------------
% 0.15/0.40 % (27745)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (27745)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.40
% 0.15/0.40 % (27751)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)
% 0.15/0.40
% 0.15/0.40 % (27745)Memory used [KB]: 6140
% 0.15/0.40 % (27745)Time elapsed: 0.019 s
% 0.15/0.40 % (27745)Instructions burned: 29 (million)
% 0.15/0.40 % (27745)------------------------------
% 0.15/0.40 % (27745)------------------------------
% 0.15/0.40 % (27742)Instruction limit reached!
% 0.15/0.40 % (27742)------------------------------
% 0.15/0.40 % (27742)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (27742)Termination reason: Unknown
% 0.15/0.40 % (27742)Termination phase: Property scanning
% 0.15/0.40
% 0.15/0.40 % (27742)Memory used [KB]: 1791
% 0.15/0.40 % (27742)Time elapsed: 0.017 s
% 0.15/0.40 % (27742)Instructions burned: 29 (million)
% 0.15/0.40 % (27742)------------------------------
% 0.15/0.40 % (27742)------------------------------
% 0.15/0.40 % (27750)Instruction limit reached!
% 0.15/0.40 % (27750)------------------------------
% 0.15/0.40 % (27750)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (27750)Termination reason: Unknown
% 0.15/0.40 % (27750)Termination phase: shuffling
% 0.15/0.40
% 0.15/0.40 % (27750)Memory used [KB]: 1279
% 0.15/0.40 % (27750)Time elapsed: 0.004 s
% 0.15/0.40 % (27750)Instructions burned: 4 (million)
% 0.15/0.40 % (27750)------------------------------
% 0.15/0.40 % (27750)------------------------------
% 0.15/0.40 % (27749)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)
% 0.15/0.40 % (27746)Instruction limit reached!
% 0.15/0.40 % (27746)------------------------------
% 0.15/0.40 % (27746)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.41 % (27746)Termination reason: Unknown
% 0.15/0.41 % (27746)Termination phase: Property scanning
% 0.15/0.41
% 0.15/0.41 % (27746)Memory used [KB]: 1663
% 0.15/0.41 % (27746)Time elapsed: 0.013 s
% 0.15/0.41 % (27746)Instructions burned: 20 (million)
% 0.15/0.41 % (27746)------------------------------
% 0.15/0.41 % (27746)------------------------------
% 0.21/0.41 % (27749)Instruction limit reached!
% 0.21/0.41 % (27749)------------------------------
% 0.21/0.41 % (27749)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (27749)Termination reason: Unknown
% 0.21/0.41 % (27749)Termination phase: Property scanning
% 0.21/0.41
% 0.21/0.41 % (27749)Memory used [KB]: 1663
% 0.21/0.41 % (27749)Time elapsed: 0.012 s
% 0.21/0.41 % (27749)Instructions burned: 16 (million)
% 0.21/0.41 % (27749)------------------------------
% 0.21/0.41 % (27749)------------------------------
% 0.21/0.41 % (27752)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on Vampire---4 for (2999ds/7Mi)
% 0.21/0.42 % (27753)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on Vampire---4 for (2999ds/16Mi)
% 0.21/0.42 % (27754)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.21/0.42 % (27748)Instruction limit reached!
% 0.21/0.42 % (27748)------------------------------
% 0.21/0.42 % (27748)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (27748)Termination reason: Unknown
% 0.21/0.42 % (27748)Termination phase: Property scanning
% 0.21/0.42
% 0.21/0.42 % (27748)Memory used [KB]: 1791
% 0.21/0.42 % (27748)Time elapsed: 0.020 s
% 0.21/0.42 % (27748)Instructions burned: 38 (million)
% 0.21/0.42 % (27748)------------------------------
% 0.21/0.42 % (27748)------------------------------
% 0.21/0.42 % (27752)Instruction limit reached!
% 0.21/0.42 % (27752)------------------------------
% 0.21/0.42 % (27752)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (27752)Termination reason: Unknown
% 0.21/0.42 % (27752)Termination phase: shuffling
% 0.21/0.42
% 0.21/0.42 % (27752)Memory used [KB]: 1407
% 0.21/0.42 % (27752)Time elapsed: 0.005 s
% 0.21/0.42 % (27752)Instructions burned: 8 (million)
% 0.21/0.42 % (27752)------------------------------
% 0.21/0.42 % (27752)------------------------------
% 0.21/0.42 % (27754)Instruction limit reached!
% 0.21/0.42 % (27754)------------------------------
% 0.21/0.42 % (27754)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (27754)Termination reason: Unknown
% 0.21/0.42 % (27754)Termination phase: shuffling
% 0.21/0.42
% 0.21/0.42 % (27754)Memory used [KB]: 1279
% 0.21/0.42 % (27754)Time elapsed: 0.004 s
% 0.21/0.42 % (27754)Instructions burned: 4 (million)
% 0.21/0.42 % (27754)------------------------------
% 0.21/0.42 % (27754)------------------------------
% 0.21/0.42 % (27755)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.21/0.42 % (27755)Instruction limit reached!
% 0.21/0.42 % (27755)------------------------------
% 0.21/0.42 % (27755)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (27755)Termination reason: Unknown
% 0.21/0.42 % (27755)Termination phase: shuffling
% 0.21/0.42
% 0.21/0.42 % (27755)Memory used [KB]: 1279
% 0.21/0.42 % (27755)Time elapsed: 0.004 s
% 0.21/0.42 % (27755)Instructions burned: 3 (million)
% 0.21/0.42 % (27755)------------------------------
% 0.21/0.42 % (27755)------------------------------
% 0.21/0.42 % (27753)Instruction limit reached!
% 0.21/0.42 % (27753)------------------------------
% 0.21/0.42 % (27753)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (27753)Termination reason: Unknown
% 0.21/0.42 % (27753)Termination phase: shuffling
% 0.21/0.42
% 0.21/0.42 % (27753)Memory used [KB]: 1535
% 0.21/0.42 % (27753)Time elapsed: 0.010 s
% 0.21/0.42 % (27753)Instructions burned: 16 (million)
% 0.21/0.42 % (27753)------------------------------
% 0.21/0.42 % (27753)------------------------------
% 0.21/0.43 % (27756)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on Vampire---4 for (2999ds/7Mi)
% 0.21/0.43 % (27759)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on Vampire---4 for (2999ds/4Mi)
% 0.21/0.43 % (27757)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.21/0.43 % (27756)Instruction limit reached!
% 0.21/0.43 % (27756)------------------------------
% 0.21/0.43 % (27756)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43 % (27756)Termination reason: Unknown
% 0.21/0.43 % (27756)Termination phase: shuffling
% 0.21/0.43
% 0.21/0.43 % (27756)Memory used [KB]: 1407
% 0.21/0.43 % (27756)Time elapsed: 0.006 s
% 0.21/0.43 % (27756)Instructions burned: 7 (million)
% 0.21/0.43 % (27756)------------------------------
% 0.21/0.43 % (27756)------------------------------
% 0.21/0.43 % (27760)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.21/0.43 % (27759)Instruction limit reached!
% 0.21/0.43 % (27759)------------------------------
% 0.21/0.43 % (27759)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43 % (27759)Termination reason: Unknown
% 0.21/0.43 % (27759)Termination phase: shuffling
% 0.21/0.43
% 0.21/0.43 % (27759)Memory used [KB]: 1279
% 0.21/0.43 % (27759)Time elapsed: 0.004 s
% 0.21/0.43 % (27759)Instructions burned: 6 (million)
% 0.21/0.43 % (27759)------------------------------
% 0.21/0.43 % (27759)------------------------------
% 0.21/0.43 % (27757)Instruction limit reached!
% 0.21/0.43 % (27757)------------------------------
% 0.21/0.43 % (27757)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43 % (27757)Termination reason: Unknown
% 0.21/0.43 % (27757)Termination phase: shuffling
% 0.21/0.43
% 0.21/0.43 % (27757)Memory used [KB]: 1279
% 0.21/0.43 % (27757)Time elapsed: 0.004 s
% 0.21/0.43 % (27757)Instructions burned: 4 (million)
% 0.21/0.43 % (27757)------------------------------
% 0.21/0.43 % (27757)------------------------------
% 0.21/0.44 % (27761)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on Vampire---4 for (2999ds/710Mi)
% 0.21/0.44 % (27762)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on Vampire---4 for (2999ds/6Mi)
% 0.21/0.44 % (27762)Instruction limit reached!
% 0.21/0.44 % (27762)------------------------------
% 0.21/0.44 % (27762)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.44 % (27762)Termination reason: Unknown
% 0.21/0.44 % (27762)Termination phase: shuffling
% 0.21/0.44
% 0.21/0.44 % (27762)Memory used [KB]: 1279
% 0.21/0.44 % (27762)Time elapsed: 0.005 s
% 0.21/0.44 % (27762)Instructions burned: 6 (million)
% 0.21/0.44 % (27762)------------------------------
% 0.21/0.44 % (27762)------------------------------
% 0.21/0.44 % (27760)Instruction limit reached!
% 0.21/0.44 % (27760)------------------------------
% 0.21/0.44 % (27760)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.44 % (27760)Termination reason: Unknown
% 0.21/0.44 % (27760)Termination phase: shuffling
% 0.21/0.44
% 0.21/0.44 % (27760)Memory used [KB]: 1663
% 0.21/0.44 % (27760)Time elapsed: 0.011 s
% 0.21/0.44 % (27760)Instructions burned: 18 (million)
% 0.21/0.44 % (27760)------------------------------
% 0.21/0.44 % (27760)------------------------------
% 0.21/0.45 % (27764)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on Vampire---4 for (2999ds/21Mi)
% 0.21/0.45 % (27763)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on Vampire---4 for (2999ds/902Mi)
% 0.21/0.45 % (27765)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on Vampire---4 for (2999ds/5Mi)
% 0.21/0.45 % (27765)Instruction limit reached!
% 0.21/0.45 % (27765)------------------------------
% 0.21/0.45 % (27765)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.45 % (27765)Termination reason: Unknown
% 0.21/0.45 % (27765)Termination phase: shuffling
% 0.21/0.45
% 0.21/0.45 % (27765)Memory used [KB]: 1279
% 0.21/0.45 % (27765)Time elapsed: 0.005 s
% 0.21/0.45 % (27765)Instructions burned: 6 (million)
% 0.21/0.45 % (27765)------------------------------
% 0.21/0.45 % (27765)------------------------------
% 0.21/0.45 % (27761)Refutation not found, incomplete strategy
% 0.21/0.45 % (27761)------------------------------
% 0.21/0.45 % (27761)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.45 % (27761)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.45
% 0.21/0.45
% 0.21/0.45 % (27761)Memory used [KB]: 6268
% 0.21/0.45 % (27761)Time elapsed: 0.018 s
% 0.21/0.45 % (27761)Instructions burned: 28 (million)
% 0.21/0.45 % (27761)------------------------------
% 0.21/0.45 % (27761)------------------------------
% 0.21/0.46 % (27764)Instruction limit reached!
% 0.21/0.46 % (27764)------------------------------
% 0.21/0.46 % (27764)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.46 % (27764)Termination reason: Unknown
% 0.21/0.46 % (27764)Termination phase: shuffling
% 0.21/0.46
% 0.21/0.46 % (27764)Memory used [KB]: 1663
% 0.21/0.46 % (27764)Time elapsed: 0.011 s
% 0.21/0.46 % (27764)Instructions burned: 22 (million)
% 0.21/0.46 % (27764)------------------------------
% 0.21/0.46 % (27764)------------------------------
% 0.21/0.46 % (27766)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on Vampire---4 for (2999ds/6Mi)
% 0.21/0.46 % (27767)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on Vampire---4 for (2999ds/377Mi)
% 0.21/0.46 % (27766)Instruction limit reached!
% 0.21/0.46 % (27766)------------------------------
% 0.21/0.46 % (27766)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.46 % (27766)Termination reason: Unknown
% 0.21/0.46 % (27766)Termination phase: shuffling
% 0.21/0.46
% 0.21/0.46 % (27766)Memory used [KB]: 1279
% 0.21/0.46 % (27766)Time elapsed: 0.005 s
% 0.21/0.46 % (27766)Instructions burned: 6 (million)
% 0.21/0.46 % (27766)------------------------------
% 0.21/0.46 % (27766)------------------------------
% 0.21/0.46 % (27770)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on Vampire---4 for (2998ds/879Mi)
% 0.21/0.47 % (27768)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on Vampire---4 for (2999ds/779Mi)
% 0.21/0.47 % (27740)Instruction limit reached!
% 0.21/0.47 % (27740)------------------------------
% 0.21/0.47 % (27740)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.47 % (27740)Termination reason: Unknown
% 0.21/0.47 % (27740)Termination phase: Saturation
% 0.21/0.47
% 0.21/0.47 % (27740)Memory used [KB]: 6780
% 0.21/0.47 % (27740)Time elapsed: 0.089 s
% 0.21/0.47 % (27740)Instructions burned: 183 (million)
% 0.21/0.47 % (27740)------------------------------
% 0.21/0.47 % (27740)------------------------------
% 0.21/0.47 % (27771)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on Vampire---4 for (2998ds/17Mi)
% 0.21/0.48 % (27769)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 (2998ds/19Mi)
% 0.21/0.48 % (27770)Refutation not found, incomplete strategy
% 0.21/0.48 % (27770)------------------------------
% 0.21/0.48 % (27770)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.48 % (27770)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.48
% 0.21/0.48
% 0.21/0.48 % (27770)Memory used [KB]: 6268
% 0.21/0.48 % (27770)Time elapsed: 0.016 s
% 0.21/0.48 % (27770)Instructions burned: 60 (million)
% 0.21/0.48 % (27770)------------------------------
% 0.21/0.48 % (27770)------------------------------
% 0.21/0.48 % (27771)Instruction limit reached!
% 0.21/0.48 % (27771)------------------------------
% 0.21/0.48 % (27771)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.48 % (27771)Termination reason: Unknown
% 0.21/0.48 % (27771)Termination phase: shuffling
% 0.21/0.48
% 0.21/0.48 % (27771)Memory used [KB]: 1663
% 0.21/0.48 % (27771)Time elapsed: 0.010 s
% 0.21/0.48 % (27771)Instructions burned: 18 (million)
% 0.21/0.48 % (27771)------------------------------
% 0.21/0.48 % (27771)------------------------------
% 0.21/0.49 % (27772)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2998ds/3Mi)
% 0.21/0.49 % (27769)Instruction limit reached!
% 0.21/0.49 % (27769)------------------------------
% 0.21/0.49 % (27769)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.49 % (27769)Termination reason: Unknown
% 0.21/0.49 % (27769)Termination phase: shuffling
% 0.21/0.49
% 0.21/0.49 % (27769)Memory used [KB]: 1663
% 0.21/0.49 % (27769)Time elapsed: 0.013 s
% 0.21/0.49 % (27769)Instructions burned: 19 (million)
% 0.21/0.49 % (27769)------------------------------
% 0.21/0.49 % (27769)------------------------------
% 0.21/0.49 % (27772)Instruction limit reached!
% 0.21/0.49 % (27772)------------------------------
% 0.21/0.49 % (27772)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.49 % (27772)Termination reason: Unknown
% 0.21/0.49 % (27772)Termination phase: shuffling
% 0.21/0.49
% 0.21/0.49 % (27772)Memory used [KB]: 1279
% 0.21/0.49 % (27772)Time elapsed: 0.004 s
% 0.21/0.49 % (27772)Instructions burned: 3 (million)
% 0.21/0.49 % (27772)------------------------------
% 0.21/0.49 % (27772)------------------------------
% 0.21/0.49 % (27773)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on Vampire---4 for (2998ds/30Mi)
% 0.21/0.49 % (27774)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on Vampire---4 for (2998ds/127Mi)
% 0.21/0.50 % (27773)Instruction limit reached!
% 0.21/0.50 % (27773)------------------------------
% 0.21/0.50 % (27773)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.50 % (27773)Termination reason: Unknown
% 0.21/0.50 % (27773)Termination phase: Property scanning
% 0.21/0.50
% 0.21/0.50 % (27773)Memory used [KB]: 1791
% 0.21/0.50 % (27773)Time elapsed: 0.009 s
% 0.21/0.50 % (27773)Instructions burned: 31 (million)
% 0.21/0.50 % (27773)------------------------------
% 0.21/0.50 % (27773)------------------------------
% 0.21/0.50 % (27775)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on Vampire---4 for (2998ds/100Mi)
% 0.21/0.50 % (27776)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2998ds/3Mi)
% 0.21/0.50 % (27776)Instruction limit reached!
% 0.21/0.50 % (27776)------------------------------
% 0.21/0.50 % (27776)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.50 % (27776)Termination reason: Unknown
% 0.21/0.50 % (27776)Termination phase: shuffling
% 0.21/0.50
% 0.21/0.50 % (27776)Memory used [KB]: 1279
% 0.21/0.50 % (27776)Time elapsed: 0.003 s
% 0.21/0.50 % (27776)Instructions burned: 5 (million)
% 0.21/0.50 % (27776)------------------------------
% 0.21/0.50 % (27776)------------------------------
% 0.21/0.51 % (27777)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on Vampire---4 for (2998ds/20Mi)
% 0.21/0.51 % (27778)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on Vampire---4 for (2998ds/86Mi)
% 0.21/0.52 % (27777)Instruction limit reached!
% 0.21/0.52 % (27777)------------------------------
% 0.21/0.52 % (27777)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.52 % (27777)Termination reason: Unknown
% 0.21/0.52 % (27777)Termination phase: Property scanning
% 0.21/0.52
% 0.21/0.52 % (27777)Memory used [KB]: 1663
% 0.21/0.52 % (27777)Time elapsed: 0.011 s
% 0.21/0.52 % (27777)Instructions burned: 20 (million)
% 0.21/0.52 % (27777)------------------------------
% 0.21/0.52 % (27777)------------------------------
% 0.21/0.52 % (27767)First to succeed.
% 0.21/0.52 % (27775)Instruction limit reached!
% 0.21/0.52 % (27775)------------------------------
% 0.21/0.52 % (27775)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.52 % (27775)Termination reason: Unknown
% 0.21/0.52 % (27775)Termination phase: Saturation
% 0.21/0.52
% 0.21/0.52 % (27775)Memory used [KB]: 6524
% 0.21/0.52 % (27775)Time elapsed: 0.027 s
% 0.21/0.52 % (27775)Instructions burned: 102 (million)
% 0.21/0.52 % (27775)------------------------------
% 0.21/0.52 % (27775)------------------------------
% 0.21/0.52 % (27763)Refutation not found, incomplete strategy
% 0.21/0.52 % (27763)------------------------------
% 0.21/0.52 % (27763)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.52 % (27763)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.52
% 0.21/0.52
% 0.21/0.52 % (27763)Memory used [KB]: 8187
% 0.21/0.52 % (27763)Time elapsed: 0.078 s
% 0.21/0.52 % (27763)Instructions burned: 167 (million)
% 0.21/0.52 % (27763)------------------------------
% 0.21/0.52 % (27763)------------------------------
% 0.21/0.52 % (27774)Instruction limit reached!
% 0.21/0.52 % (27774)------------------------------
% 0.21/0.52 % (27774)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.52 % (27774)Termination reason: Unknown
% 0.21/0.52 % (27774)Termination phase: Saturation
% 0.21/0.52
% 0.21/0.52 % (27774)Memory used [KB]: 6524
% 0.21/0.52 % (27774)Time elapsed: 0.034 s
% 0.21/0.52 % (27774)Instructions burned: 128 (million)
% 0.21/0.52 % (27774)------------------------------
% 0.21/0.52 % (27774)------------------------------
% 0.21/0.53 % (27779)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on Vampire---4 for (2998ds/107Mi)
% 0.21/0.53 % (27780)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on Vampire---4 for (2998ds/39Mi)
% 0.21/0.53 % (27781)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on Vampire---4 for (2998ds/448Mi)
% 0.21/0.53 % (27778)Instruction limit reached!
% 0.21/0.53 % (27778)------------------------------
% 0.21/0.53 % (27778)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.53 % (27778)Termination reason: Unknown
% 0.21/0.53 % (27778)Termination phase: Property scanning
% 0.21/0.53
% 0.21/0.53 % (27778)Memory used [KB]: 2046
% 0.21/0.53 % (27778)Time elapsed: 0.023 s
% 0.21/0.53 % (27778)Instructions burned: 87 (million)
% 0.21/0.53 % (27778)------------------------------
% 0.21/0.53 % (27778)------------------------------
% 0.21/0.54 % (27782)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)
% 0.21/0.54 % (27780)Instruction limit reached!
% 0.21/0.54 % (27780)------------------------------
% 0.21/0.54 % (27780)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.54 % (27780)Termination reason: Unknown
% 0.21/0.54 % (27780)Termination phase: Property scanning
% 0.21/0.54
% 0.21/0.54 % (27780)Memory used [KB]: 1791
% 0.21/0.54 % (27780)Time elapsed: 0.012 s
% 0.21/0.54 % (27780)Instructions burned: 41 (million)
% 0.21/0.54 % (27783)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)
% 0.21/0.54 % (27780)------------------------------
% 0.21/0.54 % (27780)------------------------------
% 0.21/0.55 % (27767)Refutation found. Thanks to Tanya!
% 0.21/0.55 % SZS status Theorem for Vampire---4
% 0.21/0.55 % SZS output start Proof for Vampire---4
% See solution above
% 0.21/0.55 % (27767)------------------------------
% 0.21/0.55 % (27767)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.55 % (27767)Termination reason: Refutation
% 0.21/0.55
% 0.21/0.55 % (27767)Memory used [KB]: 9083
% 0.21/0.55 % (27767)Time elapsed: 0.092 s
% 0.21/0.55 % (27767)Instructions burned: 182 (million)
% 0.21/0.55 % (27767)------------------------------
% 0.21/0.55 % (27767)------------------------------
% 0.21/0.55 % (27739)Success in time 0.188 s
% 0.21/0.55 % Vampire---4.8 exiting
%------------------------------------------------------------------------------