TSTP Solution File: ALG263^1 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : ALG263^1 : TPTP v8.2.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 18:20:28 EDT 2024
% Result : Theorem 1.50s 0.64s
% Output : Refutation 2.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 99
% Syntax : Number of formulae : 282 ( 214 unt; 59 typ; 0 def)
% Number of atoms : 5327 (1168 equ; 0 cnn)
% Maximal formula atoms : 3 ( 23 avg)
% Number of connectives : 21785 ( 208 ~; 3 |; 101 &;15761 @)
% ( 0 <=>;2431 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 1294 (1294 >; 0 *; 0 +; 0 <<)
% Number of symbols : 95 ( 91 usr; 43 con; 0-4 aty)
% (3281 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 3693 (3451 ^ 242 !; 0 ?;3693 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
term: $tType ).
thf(type_def_7,type,
subst: $tType ).
thf(func_def_0,type,
term: $tType ).
thf(func_def_1,type,
subst: $tType ).
thf(func_def_2,type,
one: term ).
thf(func_def_3,type,
ap: term > term > term ).
thf(func_def_4,type,
lam: term > term ).
thf(func_def_5,type,
sub: term > subst > term ).
thf(func_def_6,type,
id: subst ).
thf(func_def_7,type,
sh: subst ).
thf(func_def_8,type,
push: term > subst > subst ).
thf(func_def_9,type,
comp: subst > subst > subst ).
thf(func_def_10,type,
var: term > $o ).
thf(func_def_18,type,
hoasap: subst > term > subst > term > term ).
thf(func_def_73,type,
hoaslam: subst > ( subst > term > term ) > term ).
thf(func_def_86,type,
hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).
thf(func_def_107,type,
hoasvar: subst > term > subst > $o ).
thf(func_def_121,type,
pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).
thf(func_def_142,type,
sK1: ( term > $o ) > term ).
thf(func_def_143,type,
sK2: ( term > $o ) > term ).
thf(func_def_144,type,
sK3: ( term > $o ) > term ).
thf(func_def_145,type,
sK4: ( term > $o ) > term ).
thf(func_def_146,type,
sK5: ( term > $o ) > term ).
thf(func_def_147,type,
sK6: ( term > $o ) > term ).
thf(func_def_148,type,
sK7: ( term > $o ) > term ).
thf(func_def_149,type,
sK8: ( term > $o ) > term ).
thf(func_def_150,type,
sK9: ( term > $o ) > subst > term ).
thf(func_def_151,type,
sK10: ( 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 ) > subst > 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 ) > subst > term ).
thf(func_def_159,type,
sK18: ( term > $o ) > subst > term ).
thf(func_def_160,type,
sK19: ( term > $o ) > subst > term ).
thf(func_def_161,type,
sK20: ( term > $o ) > 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: ( subst > term > term ) > term ).
thf(func_def_170,type,
sK29: ( subst > term > term ) > subst ).
thf(func_def_171,type,
sK30: ( subst > term > term ) > subst ).
thf(func_def_172,type,
sK31: ( subst > term > term ) > subst ).
thf(func_def_173,type,
sK32: ( subst > term > term ) > term ).
thf(func_def_174,type,
sK33: ( subst > term > term ) > subst ).
thf(func_def_175,type,
sK34: ( subst > term > term ) > subst ).
thf(func_def_176,type,
sK35: ( subst > term > term ) > subst ).
thf(func_def_177,type,
sK36: ( subst > term > term ) > term ).
thf(func_def_178,type,
sK37: ( subst > term > term ) > subst ).
thf(func_def_179,type,
sK38: ( subst > term > term ) > subst ).
thf(func_def_180,type,
sK39: ( subst > term > term ) > term ).
thf(func_def_181,type,
sK40: subst > term > subst > $o ).
thf(func_def_182,type,
sK41: term ).
thf(f1102,plain,
$false,
inference(trivial_inequality_removal,[],[f1101]) ).
thf(f1101,plain,
$true = $false,
inference(backward_demodulation,[],[f1048,f1100]) ).
thf(f1100,plain,
( ( var @ sK41 )
= $false ),
inference(trivial_inequality_removal,[],[f1097]) ).
thf(f1097,plain,
( ( $true = $false )
| ( ( var @ sK41 )
= $false ) ),
inference(superposition,[],[f1053,f1047]) ).
thf(f1047,plain,
( ( sK40 @ id @ sK41 @ id )
= $false ),
inference(binary_proxy_clausification,[],[f1046]) ).
thf(f1046,plain,
( $false
= ( ( var @ sK41 )
=> ( sK40 @ id @ sK41 @ id ) ) ),
inference(beta_eta_normalization,[],[f1045]) ).
thf(f1045,plain,
( ( ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK40 @ id @ Y0 @ id ) )
@ sK41 )
= $false ),
inference(sigma_clausification,[],[f1040]) ).
thf(f1040,plain,
( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK40 @ id @ Y0 @ id ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f1029]) ).
thf(f1029,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ ( sub @ Y0 @ id ) )
=> ( sK40 @ id @ Y0 @ id ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK40 @ id @ Y0 @ id ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f1018]) ).
thf(f1018,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK40 @ ( comp @ Y2 @ Y0 ) @ ( sub @ Y1 @ Y0 ) @ Y3 )
=> ( sK40 @ Y2 @ Y1 @ ( comp @ Y0 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ ( sub @ Y0 @ id ) )
=> ( sK40 @ id @ Y0 @ id ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK40 @ id @ Y0 @ id ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f1017]) ).
thf(f1017,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK40 @ Y0 @ Y2 @ ( comp @ Y3 @ Y1 ) )
=> ( sK40 @ ( comp @ Y0 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK40 @ ( comp @ Y2 @ Y0 ) @ ( sub @ Y1 @ Y0 ) @ Y3 )
=> ( sK40 @ Y2 @ Y1 @ ( comp @ Y0 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ ( sub @ Y0 @ id ) )
=> ( sK40 @ id @ Y0 @ id ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK40 @ id @ Y0 @ id ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f1016]) ).
thf(f1016,plain,
( ( ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y4 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) )
@ sK40 )
= $false ),
inference(sigma_clausification,[],[f1009]) ).
thf(f1009,plain,
( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y4 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f996]) ).
thf(f996,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y4 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f978]) ).
thf(f978,plain,
( ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y4 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f949]) ).
thf(f949,plain,
( ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y4 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f936]) ).
thf(f936,plain,
( $false
= ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) )
= ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y4 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f923]) ).
thf(f923,plain,
( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) )
= ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y4 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f909]) ).
thf(f909,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) )
= ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y4 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f890]) ).
thf(f890,plain,
( $false
= ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( sub @ ( sub @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) )
= ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y4 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f830]) ).
thf(f830,plain,
( $false
= ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( comp @ ( comp @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( sub @ ( sub @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) )
= ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y4 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f755]) ).
thf(f755,plain,
( ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( comp @ ( comp @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( sub @ ( sub @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) )
= ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y4 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f737]) ).
thf(f737,plain,
( $false
= ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ 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 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( comp @ ( comp @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( sub @ ( sub @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) )
= ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y4 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f691]) ).
thf(f691,plain,
( ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( comp @ ( comp @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( sub @ ( sub @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) )
= ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y4 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f686]) ).
thf(f686,plain,
( ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( comp @ ( comp @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( sub @ ( sub @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) )
= ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y4 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f679]) ).
thf(f679,plain,
( $false
= ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( comp @ ( comp @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( sub @ ( sub @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) )
= ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y4 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f669]) ).
thf(f669,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( comp @ ( comp @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( sub @ ( sub @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) )
= ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y4 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f660]) ).
thf(f660,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( comp @ ( comp @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( sub @ ( sub @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) )
= ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y4 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f651]) ).
thf(f651,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( comp @ ( comp @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( sub @ ( sub @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) )
= ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y4 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f638]) ).
thf(f638,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] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( comp @ ( comp @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( sub @ ( sub @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) )
= ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y4 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f625]) ).
thf(f625,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y3 = 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] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( comp @ ( comp @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( sub @ ( sub @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) )
= ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y4 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f610]) ).
thf(f610,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y3 @ Y0 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y3 = 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] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( comp @ ( comp @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( sub @ ( sub @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) )
= ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y4 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f605]) ).
thf(f605,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 @ Y2 @ Y1 )
= ( ap @ Y3 @ Y0 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y3 = 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] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( comp @ ( comp @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( sub @ ( sub @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) )
= ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y4 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f603]) ).
thf(f603,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 @ Y2 @ Y1 )
= ( ap @ Y3 @ Y0 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y3 = 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] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( comp @ ( comp @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( sub @ ( sub @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) )
= ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y4 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f598]) ).
thf(f598,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 @ Y2 @ Y1 )
= ( ap @ Y3 @ Y0 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y3 = 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] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( comp @ ( comp @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( sub @ ( sub @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) )
= ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y4 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f595]) ).
thf(f595,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y3 @ Y0 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y3 = 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] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( comp @ ( comp @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( sub @ ( sub @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) )
= ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y4 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f590]) ).
thf(f590,plain,
( $false
= ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y3 @ Y0 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y3 = 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] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( comp @ ( comp @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( sub @ ( sub @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) )
= ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y4 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f581]) ).
thf(f581,plain,
( $false
= ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y3 @ Y0 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y3 = 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] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( comp @ ( comp @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( sub @ ( sub @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) )
= ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y4 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f572]) ).
thf(f572,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( push @ ( sub @ Y1 @ Y2 ) @ ( comp @ Y0 @ Y2 ) )
= ( comp @ ( push @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
=> ( ( !! @ 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 @ Y2 @ Y1 )
= ( ap @ Y3 @ Y0 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y3 = 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] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( comp @ ( comp @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( sub @ ( sub @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) )
= ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y4 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f565]) ).
thf(f565,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( push @ ( sub @ Y1 @ Y2 ) @ ( comp @ Y0 @ Y2 ) )
= ( comp @ ( push @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
=> ( ( !! @ 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 @ Y2 @ Y1 )
= ( ap @ Y3 @ Y0 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y3 = 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] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( comp @ ( comp @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( sub @ ( sub @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) )
= ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y4 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f560]) ).
thf(f560,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( push @ ( sub @ Y1 @ Y2 ) @ ( comp @ Y0 @ Y2 ) )
= ( comp @ ( push @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
=> ( ( !! @ 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 @ Y2 @ Y1 )
= ( ap @ Y3 @ Y0 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y3 = 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] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( comp @ ( comp @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( sub @ ( sub @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) )
= ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y4 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f551]) ).
thf(f551,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( push @ ( sub @ Y1 @ Y2 ) @ ( comp @ Y0 @ Y2 ) )
= ( comp @ ( push @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
=> ( ( !! @ 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 @ Y2 @ Y1 )
= ( ap @ Y3 @ Y0 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y3 = 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] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( comp @ ( comp @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( sub @ ( sub @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) )
= ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y4 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f544]) ).
thf(f544,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( push @ ( sub @ Y1 @ Y2 ) @ ( comp @ Y0 @ Y2 ) )
= ( comp @ ( push @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
=> ( ( !! @ 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 @ Y2 @ Y1 )
= ( ap @ Y3 @ Y0 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y3 = 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] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( comp @ ( comp @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( sub @ ( sub @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) )
= ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y4 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f539]) ).
thf(f539,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( lam @ Y0 ) @ Y1 )
= ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( push @ ( sub @ Y1 @ Y2 ) @ ( comp @ Y0 @ Y2 ) )
= ( comp @ ( push @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
=> ( ( !! @ 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 @ Y2 @ Y1 )
= ( ap @ Y3 @ Y0 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y3 = 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] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( comp @ ( comp @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( sub @ ( sub @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) )
= ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y4 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f532]) ).
thf(f532,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 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( push @ ( sub @ Y1 @ Y2 ) @ ( comp @ Y0 @ Y2 ) )
= ( comp @ ( push @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
=> ( ( !! @ 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 @ Y2 @ Y1 )
= ( ap @ Y3 @ Y0 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y3 = 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] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( comp @ ( comp @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( sub @ ( sub @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) )
= ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y4 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f523]) ).
thf(f523,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 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( push @ ( sub @ Y1 @ Y2 ) @ ( comp @ Y0 @ Y2 ) )
= ( comp @ ( push @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
=> ( ( !! @ 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 @ Y2 @ Y1 )
= ( ap @ Y3 @ Y0 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y3 = 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] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( comp @ ( comp @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( sub @ ( sub @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) )
= ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y4 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f522]) ).
thf(f522,plain,
( $true
!= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( ap @ ( sub @ Y0 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( ap @ Y0 @ Y1 ) @ 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 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( push @ ( sub @ Y1 @ Y2 ) @ ( comp @ Y0 @ Y2 ) )
= ( comp @ ( push @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
=> ( ( !! @ 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 @ Y2 @ Y1 )
= ( ap @ Y3 @ Y0 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y3 = 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] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( comp @ ( comp @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( sub @ ( sub @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y2 )
= ( ap @ ( sub @ Y3 @ id ) @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y3 )
= ( ap @ ( sub @ Y0 @ id ) @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) )
= ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y4 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f521]) ).
thf(f521,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( ap @ ( sub @ Y0 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( ap @ Y0 @ Y1 ) @ 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 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( push @ ( sub @ Y1 @ Y2 ) @ ( comp @ Y0 @ Y2 ) )
= ( comp @ ( push @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
=> ( ( !! @ 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 @ Y2 @ Y1 )
= ( ap @ Y3 @ Y0 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y3 = 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] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( comp @ ( comp @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( sub @ ( sub @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ 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
@ Y1
@ id
@ Y2 )
= ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y3
@ id
@ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y2
@ id
@ Y3 )
= ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y0
@ id
@ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) )
= ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y0 @ Y2 @ Y3 ) )
= ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ^ [Y3: subst,Y4: term,Y5: subst,Y6: term] : ( ap @ ( sub @ Y4 @ Y5 ) @ Y6 )
@ id
@ Y2
@ id
@ Y1 )
!= ( ^ [Y3: subst,Y4: subst > term > term] : ( lam @ ( Y4 @ sh @ one ) )
@ id
@ ^ [Y3: subst,Y4: term] : ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ~ ( ^ [Y1: subst,Y2: term,Y3: subst] : ( var @ ( sub @ Y2 @ Y3 ) )
@ id
@ ( ^ [Y1: subst,Y2: subst > term > term] : ( lam @ ( Y2 @ sh @ one ) )
@ id
@ ^ [Y1: subst,Y2: term] : ( Y0 @ Y1 @ Y2 ) )
@ id ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( ^ [Y2: subst,Y3: term,Y4: subst] : ( var @ ( sub @ Y3 @ Y4 ) )
@ id
@ ( ^ [Y2: subst,Y3: term,Y4: subst,Y5: term] : ( ap @ ( sub @ Y3 @ Y4 ) @ Y5 )
@ id
@ Y1
@ id
@ Y0 )
@ id ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y4 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( ^ [Y2: subst,Y3: term,Y4: subst] : ( var @ ( sub @ Y3 @ Y4 ) )
@ id
@ Y1
@ id )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f435,f511]) ).
thf(f511,plain,
( hoasinduction_lem1_gthm
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( ap @ ( sub @ Y0 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( ap @ Y0 @ Y1 ) @ 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 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( push @ ( sub @ Y1 @ Y2 ) @ ( comp @ Y0 @ Y2 ) )
= ( comp @ ( push @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
=> ( ( !! @ 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 @ Y2 @ Y1 )
= ( ap @ Y3 @ Y0 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y3 = 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] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( comp @ ( comp @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( sub @ ( sub @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ 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
@ Y1
@ id
@ Y2 )
= ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y3
@ id
@ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y2
@ id
@ Y3 )
= ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y0
@ id
@ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) )
= ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y0 @ Y2 @ Y3 ) )
= ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ^ [Y3: subst,Y4: term,Y5: subst,Y6: term] : ( ap @ ( sub @ Y4 @ Y5 ) @ Y6 )
@ id
@ Y2
@ id
@ Y1 )
!= ( ^ [Y3: subst,Y4: subst > term > term] : ( lam @ ( Y4 @ sh @ one ) )
@ id
@ ^ [Y3: subst,Y4: term] : ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ~ ( ^ [Y1: subst,Y2: term,Y3: subst] : ( var @ ( sub @ Y2 @ Y3 ) )
@ id
@ ( ^ [Y1: subst,Y2: subst > term > term] : ( lam @ ( Y2 @ sh @ one ) )
@ id
@ ^ [Y1: subst,Y2: term] : ( Y0 @ Y1 @ Y2 ) )
@ id ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( ^ [Y2: subst,Y3: term,Y4: subst] : ( var @ ( sub @ Y3 @ Y4 ) )
@ id
@ ( ^ [Y2: subst,Y3: term,Y4: subst,Y5: term] : ( ap @ ( sub @ Y3 @ Y4 ) @ Y5 )
@ id
@ Y1
@ id
@ Y0 )
@ id ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y4 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( ^ [Y2: subst,Y3: term,Y4: subst] : ( var @ ( sub @ Y3 @ Y4 ) )
@ id
@ Y1
@ id )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f413,f441,f396,f439,f350,f384,f349,f334,f411,f394,f362,f403,f443,f333,f366,f357,f428,f426,f346,f383,f338,f348,f422,f408,f344,f386,f364,f430,f376,f449,f450,f451,f452,f453,f454,f462]) ).
thf(f462,plain,
( hoasinduction_lem1
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y4 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( ^ [Y2: subst,Y3: term,Y4: subst] : ( var @ ( sub @ Y3 @ Y4 ) )
@ id
@ Y1
@ id )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f385,f416]) ).
thf(f416,plain,
( hoasvar
= ( ^ [Y0: subst,Y1: term,Y2: subst] : ( var @ ( sub @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f273]) ).
thf(f273,plain,
( hoasvar
= ( ^ [Y0: subst,Y1: term,Y2: subst] : ( var @ ( sub @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f272]) ).
thf(f272,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/benchmark/theBenchmark.p',hoasvar) ).
thf(f385,plain,
( hoasinduction_lem1
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y4 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( hoasvar @ id @ Y1 @ id )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f181]) ).
thf(f181,plain,
( hoasinduction_lem1
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y4 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y1 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( hoasvar @ id @ Y1 @ id )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f180]) ).
thf(f180,plain,
! [X0: subst > term > subst > $o] :
( ( ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( X0 @ X4 @ X2 @ ( comp @ X1 @ X3 ) )
=> ( X0 @ ( comp @ X4 @ X1 ) @ ( sub @ X2 @ X1 ) @ X3 ) )
=> ( ! [X5: subst,X6: subst,X7: term,X8: subst] :
( ( X0 @ ( comp @ X6 @ X8 ) @ ( sub @ X7 @ X8 ) @ X5 )
=> ( X0 @ X6 @ X7 @ ( comp @ X8 @ X5 ) ) )
=> ( ! [X9: term] :
( ( hoasvar @ id @ X9 @ id )
=> ( X0 @ id @ X9 @ id ) )
=> ! [X10: term] :
( ( var @ X10 )
=> ( X0 @ id @ X10 @ id ) ) ) ) )
= hoasinduction_lem1 ),
inference(rectify,[],[f90]) ).
thf(f90,axiom,
! [X5: subst > term > subst > $o] :
( ( ! [X4: subst,X0: term,X3: subst,X2: subst] :
( ( X5 @ X2 @ X0 @ ( comp @ X4 @ X3 ) )
=> ( X5 @ ( comp @ X2 @ X4 ) @ ( sub @ X0 @ X4 ) @ X3 ) )
=> ( ! [X3: subst,X2: subst,X0: term,X4: subst] :
( ( X5 @ ( comp @ X2 @ X4 ) @ ( sub @ X0 @ X4 ) @ X3 )
=> ( X5 @ X2 @ X0 @ ( comp @ X4 @ X3 ) ) )
=> ( ! [X0: term] :
( ( hoasvar @ id @ X0 @ id )
=> ( X5 @ id @ X0 @ id ) )
=> ! [X0: term] :
( ( var @ X0 )
=> ( X5 @ id @ X0 @ id ) ) ) ) )
= hoasinduction_lem1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem1) ).
thf(f454,plain,
( hoasapnotvar
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( ^ [Y2: subst,Y3: term,Y4: subst] : ( var @ ( sub @ Y3 @ Y4 ) )
@ id
@ ( ^ [Y2: subst,Y3: term,Y4: subst,Y5: term] : ( ap @ ( sub @ Y3 @ Y4 ) @ Y5 )
@ id
@ Y1
@ id
@ Y0 )
@ id ) ) ) ),
inference(definition_unfolding,[],[f431,f416,f440]) ).
thf(f440,plain,
( hoasap
= ( ^ [Y0: subst,Y1: term,Y2: subst,Y3: term] : ( ap @ ( sub @ Y1 @ Y2 ) @ Y3 ) ) ),
inference(cnf_transformation,[],[f239]) ).
thf(f239,plain,
( hoasap
= ( ^ [Y0: subst,Y1: term,Y2: subst,Y3: term] : ( ap @ ( sub @ Y1 @ Y2 ) @ Y3 ) ) ),
inference(fool_elimination,[],[f238]) ).
thf(f238,plain,
( ( ^ [X0: subst,X1: term,X2: subst,X3: term] : ( ap @ ( sub @ X1 @ X2 ) @ X3 ) )
= hoasap ),
inference(rectify,[],[f55]) ).
thf(f55,axiom,
( ( ^ [X2: subst,X0: term,X3: subst,X1: term] : ( ap @ ( sub @ X0 @ X3 ) @ X1 ) )
= hoasap ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasap) ).
thf(f431,plain,
( hoasapnotvar
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( hoasvar @ id @ ( hoasap @ id @ Y1 @ id @ Y0 ) @ id ) ) ) ),
inference(cnf_transformation,[],[f207]) ).
thf(f207,plain,
( hoasapnotvar
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( hoasvar @ id @ ( hoasap @ id @ Y1 @ id @ Y0 ) @ id ) ) ) ),
inference(fool_elimination,[],[f206]) ).
thf(f206,plain,
! [X0: term,X1: term] :
( ( ~ ( hoasvar @ id @ ( hoasap @ id @ X0 @ id @ X1 ) @ id ) )
= hoasapnotvar ),
inference(rectify,[],[f73]) ).
thf(f73,axiom,
! [X0: term,X1: term] :
( ( ~ ( hoasvar @ id @ ( hoasap @ id @ X0 @ id @ X1 ) @ id ) )
= hoasapnotvar ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasapnotvar) ).
thf(f453,plain,
( hoaslamnotvar
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ~ ( ^ [Y1: subst,Y2: term,Y3: subst] : ( var @ ( sub @ Y2 @ Y3 ) )
@ id
@ ( ^ [Y1: subst,Y2: subst > term > term] : ( lam @ ( Y2 @ sh @ one ) )
@ id
@ ^ [Y1: subst,Y2: term] : ( Y0 @ Y1 @ Y2 ) )
@ id ) ) ) ),
inference(definition_unfolding,[],[f392,f416,f381]) ).
thf(f381,plain,
( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( lam @ ( Y1 @ sh @ one ) ) ) ),
inference(cnf_transformation,[],[f193]) ).
thf(f193,plain,
( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( lam @ ( Y1 @ sh @ one ) ) ) ),
inference(fool_elimination,[],[f192]) ).
thf(f192,plain,
( hoaslam
= ( ^ [X0: subst,X1: subst > term > term] : ( lam @ ( X1 @ sh @ one ) ) ) ),
inference(rectify,[],[f56]) ).
thf(f56,axiom,
( hoaslam
= ( ^ [X2: subst,X10: subst > term > term] : ( lam @ ( X10 @ sh @ one ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoaslam) ).
thf(f392,plain,
( hoaslamnotvar
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ~ ( hoasvar @ id
@ ( hoaslam @ id
@ ^ [Y1: subst,Y2: term] : ( Y0 @ Y1 @ Y2 ) )
@ id ) ) ) ),
inference(cnf_transformation,[],[f122]) ).
thf(f122,plain,
( hoaslamnotvar
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ~ ( hoasvar @ id
@ ( hoaslam @ id
@ ^ [Y1: subst,Y2: term] : ( Y0 @ Y1 @ Y2 ) )
@ id ) ) ) ),
inference(fool_elimination,[],[f121]) ).
thf(f121,plain,
! [X0: subst > term > term] :
( ( ! [X1: term,X2: subst,X3: subst] :
( ( X0 @ ( comp @ X3 @ X2 ) @ ( sub @ X1 @ X2 ) )
= ( sub @ ( X0 @ X3 @ X1 ) @ X2 ) )
=> ~ ( hoasvar @ id
@ ( hoaslam @ id
@ ^ [X4: subst,X5: term] : ( X0 @ X4 @ X5 ) )
@ id ) )
= hoaslamnotvar ),
inference(rectify,[],[f70]) ).
thf(f70,axiom,
! [X10: subst > term > term] :
( ( ! [X0: term,X3: subst,X2: subst] :
( ( sub @ ( X10 @ X2 @ X0 ) @ X3 )
= ( X10 @ ( comp @ X2 @ X3 ) @ ( sub @ X0 @ X3 ) ) )
=> ~ ( hoasvar @ id
@ ( hoaslam @ id
@ ^ [X2: subst,X0: term] : ( X10 @ X2 @ X0 ) )
@ id ) )
= hoaslamnotvar ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoaslamnotvar) ).
thf(f452,plain,
( hoaslamnotap
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ^ [Y3: subst,Y4: term,Y5: subst,Y6: term] : ( ap @ ( sub @ Y4 @ Y5 ) @ Y6 )
@ id
@ Y2
@ id
@ Y1 )
!= ( ^ [Y3: subst,Y4: subst > term > term] : ( lam @ ( Y4 @ sh @ one ) )
@ id
@ ^ [Y3: subst,Y4: term] : ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f404,f440,f381]) ).
thf(f404,plain,
( hoaslamnotap
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( hoasap @ id @ Y2 @ id @ Y1 )
!= ( hoaslam @ id
@ ^ [Y3: subst,Y4: term] : ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f179]) ).
thf(f179,plain,
( hoaslamnotap
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( hoasap @ id @ Y2 @ id @ Y1 )
!= ( hoaslam @ id
@ ^ [Y3: subst,Y4: term] : ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f178]) ).
thf(f178,plain,
! [X0: subst > term > term] :
( ( ! [X1: term,X2: subst,X3: subst] :
( ( X0 @ ( comp @ X3 @ X2 ) @ ( sub @ X1 @ X2 ) )
= ( sub @ ( X0 @ X3 @ X1 ) @ X2 ) )
=> ! [X4: term,X5: term] :
( ( hoasap @ id @ X4 @ id @ X5 )
!= ( hoaslam @ id
@ ^ [X6: subst,X7: term] : ( X0 @ X6 @ X7 ) ) ) )
= hoaslamnotap ),
inference(rectify,[],[f67]) ).
thf(f67,axiom,
! [X10: subst > term > term] :
( ( ! [X0: term,X3: subst,X2: subst] :
( ( sub @ ( X10 @ X2 @ X0 ) @ X3 )
= ( X10 @ ( comp @ X2 @ X3 ) @ ( sub @ X0 @ X3 ) ) )
=> ! [X0: term,X1: term] :
( ( hoasap @ id @ X0 @ id @ X1 )
!= ( hoaslam @ id
@ ^ [X2: subst,X6: term] : ( X10 @ X2 @ X6 ) ) ) )
= hoaslamnotap ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoaslamnotap) ).
thf(f451,plain,
( hoaslaminj
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) )
= ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y0 @ Y2 @ Y3 ) )
= ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f412,f381,f381]) ).
thf(f412,plain,
( hoaslaminj
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) )
= ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y0 @ Y2 @ Y3 ) )
= ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f281]) ).
thf(f281,plain,
( hoaslaminj
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) )
= ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y0 @ Y2 @ Y3 ) )
= ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f280]) ).
thf(f280,plain,
! [X0: subst > term > term] :
( ( ! [X1: subst,X2: subst,X3: term] :
( ( X0 @ ( comp @ X2 @ X1 ) @ ( sub @ X3 @ X1 ) )
= ( sub @ ( X0 @ X2 @ X3 ) @ X1 ) )
=> ! [X4: subst > term > term] :
( ! [X5: term,X6: subst,X7: subst] :
( ( sub @ ( X4 @ X7 @ X5 ) @ X6 )
= ( X4 @ ( comp @ X7 @ X6 ) @ ( sub @ X5 @ X6 ) ) )
=> ( ( ( hoaslam @ id
@ ^ [X8: subst,X9: term] : ( X0 @ X8 @ X9 ) )
= ( hoaslam @ id
@ ^ [X10: subst,X11: term] : ( X4 @ X10 @ X11 ) ) )
=> ! [X12: subst,X13: term] :
( ( X4 @ X12 @ X13 )
= ( X0 @ X12 @ X13 ) ) ) ) )
= hoaslaminj ),
inference(rectify,[],[f64]) ).
thf(f64,axiom,
! [X10: subst > term > term] :
( ( ! [X3: subst,X2: subst,X0: term] :
( ( sub @ ( X10 @ X2 @ X0 ) @ X3 )
= ( X10 @ ( comp @ X2 @ X3 ) @ ( sub @ X0 @ X3 ) ) )
=> ! [X11: subst > term > term] :
( ! [X0: term,X3: subst,X2: subst] :
( ( sub @ ( X11 @ X2 @ X0 ) @ X3 )
= ( X11 @ ( comp @ X2 @ X3 ) @ ( sub @ X0 @ X3 ) ) )
=> ( ( ( hoaslam @ id
@ ^ [X2: subst,X0: term] : ( X10 @ X2 @ X0 ) )
= ( hoaslam @ id
@ ^ [X2: subst,X0: term] : ( X11 @ X2 @ X0 ) ) )
=> ! [X2: subst,X0: term] :
( ( X10 @ X2 @ X0 )
= ( X11 @ X2 @ X0 ) ) ) ) )
= hoaslaminj ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoaslaminj) ).
thf(f450,plain,
( hoasapinj2
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y2
@ id
@ Y3 )
= ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y0
@ id
@ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f391,f440,f440]) ).
thf(f391,plain,
( hoasapinj2
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( hoasap @ id @ Y2 @ id @ Y3 )
= ( hoasap @ id @ Y0 @ id @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f177]) ).
thf(f177,plain,
( hoasapinj2
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( hoasap @ id @ Y2 @ id @ Y3 )
= ( hoasap @ id @ Y0 @ id @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f176]) ).
thf(f176,plain,
! [X0: term,X1: term,X2: term,X3: term] :
( ( ( ( hoasap @ id @ X1 @ id @ X0 )
= ( hoasap @ id @ X3 @ id @ X2 ) )
=> ( X0 = X2 ) )
= hoasapinj2 ),
inference(rectify,[],[f61]) ).
thf(f61,axiom,
! [X7: term,X1: term,X6: term,X0: term] :
( ( ( ( hoasap @ id @ X0 @ id @ X6 )
= ( hoasap @ id @ X1 @ id @ X7 ) )
=> ( X6 = X7 ) )
= hoasapinj2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasapinj2) ).
thf(f449,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
@ Y1
@ id
@ Y2 )
= ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y3
@ id
@ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f399,f440,f440]) ).
thf(f399,plain,
( hoasapinj1
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( hoasap @ id @ Y1 @ id @ Y2 )
= ( hoasap @ id @ Y3 @ id @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f219]) ).
thf(f219,plain,
( hoasapinj1
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( hoasap @ id @ Y1 @ id @ Y2 )
= ( hoasap @ id @ Y3 @ id @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f218]) ).
thf(f218,plain,
( hoasapinj1
= ( ! [X0: term,X1: term,X2: term,X3: term] :
( ( ( hoasap @ id @ X2 @ id @ X1 )
= ( hoasap @ id @ X0 @ id @ X3 ) )
=> ( X0 = X2 ) ) ) ),
inference(rectify,[],[f58]) ).
thf(f58,axiom,
( hoasapinj1
= ( ! [X1: term,X6: term,X0: term,X7: term] :
( ( ( hoasap @ id @ X0 @ id @ X6 )
= ( hoasap @ id @ X1 @ id @ X7 ) )
=> ( X0 = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasapinj1) ).
thf(f376,plain,
( termmset
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( sub @ ( sub @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ) ),
inference(cnf_transformation,[],[f132]) ).
thf(f132,plain,
( termmset
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( sub @ ( sub @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ) ),
inference(fool_elimination,[],[f131]) ).
thf(f131,plain,
( ( termmset
= ( ! [X0: term] :
( ( sub @ X0 @ id )
= X0 ) ) )
& ! [X1: subst,X2: subst,X3: term] :
( ( sub @ X3 @ ( comp @ X1 @ X2 ) )
= ( sub @ ( sub @ X3 @ X1 ) @ X2 ) ) ),
inference(rectify,[],[f52]) ).
thf(f52,axiom,
( ( termmset
= ( ! [X0: term] :
( ( sub @ X0 @ id )
= X0 ) ) )
& ! [X2: subst,X3: subst,X0: term] :
( ( sub @ ( sub @ X0 @ X2 ) @ X3 )
= ( sub @ X0 @ ( comp @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',termmset) ).
thf(f430,plain,
( substmonoid
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( comp @ ( comp @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) ) ),
inference(cnf_transformation,[],[f225]) ).
thf(f225,plain,
( substmonoid
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y0 @ Y2 ) )
= ( comp @ ( comp @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) ) ),
inference(fool_elimination,[],[f224]) ).
thf(f224,plain,
( ( substmonoid
= ( ! [X0: subst] :
( ( comp @ X0 @ id )
= X0 ) ) )
& ! [X1: subst] :
( ( comp @ id @ X1 )
= X1 )
& ! [X2: subst,X3: subst,X4: subst] :
( ( comp @ X3 @ ( comp @ X4 @ X2 ) )
= ( comp @ ( comp @ X3 @ X4 ) @ X2 ) ) ),
inference(rectify,[],[f49]) ).
thf(f49,axiom,
( ( substmonoid
= ( ! [X2: subst] :
( ( comp @ X2 @ id )
= X2 ) ) )
& ! [X2: subst] :
( ( comp @ id @ X2 )
= X2 )
& ! [X4: subst,X2: subst,X3: subst] :
( ( comp @ ( comp @ X2 @ X3 ) @ X4 )
= ( comp @ X2 @ ( comp @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substmonoid) ).
thf(f364,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,[],[f267]) ).
thf(f267,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,[],[f266]) ).
thf(f266,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/benchmark/theBenchmark.p',induction2) ).
thf(f386,plain,
( induction2lem
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ 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 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f277]) ).
thf(f277,plain,
( induction2lem
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ 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 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f276]) ).
thf(f276,plain,
! [X0: term > $o] :
( ( ! [X1: term,X2: term] :
( ( X0 @ X1 )
=> ( ( X0 @ X2 )
=> ( X0 @ ( ap @ X1 @ X2 ) ) ) )
=> ( ! [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 ) ) ) ) )
= induction2lem ),
inference(rectify,[],[f43]) ).
thf(f43,axiom,
! [X5: term > $o] :
( ( ! [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,X2: subst] :
( ! [X1: term] :
( ( var @ X1 )
=> ( X5 @ ( sub @ X1 @ X2 ) ) )
=> ( X5 @ ( sub @ X0 @ X2 ) ) ) ) )
= induction2lem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',induction2lem) ).
thf(f344,plain,
( pushprop
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f169]) ).
thf(f169,plain,
( pushprop
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f168]) ).
thf(f168,plain,
! [X0: term,X1: subst,X2: term > $o] :
( ( ! [X3: term] :
( ( var @ X3 )
=> ( X2 @ ( sub @ X3 @ X1 ) ) )
=> ( ( X2 @ X0 )
=> ! [X4: term] :
( ( var @ X4 )
=> ( X2 @ ( sub @ X4 @ ( push @ X0 @ X1 ) ) ) ) ) )
= pushprop ),
inference(rectify,[],[f39]) ).
thf(f39,axiom,
! [X0: term,X2: subst,X5: term > $o] :
( ( ! [X1: term] :
( ( var @ X1 )
=> ( X5 @ ( sub @ X1 @ X2 ) ) )
=> ( ( X5 @ X0 )
=> ! [X1: term] :
( ( var @ X1 )
=> ( X5 @ ( sub @ X1 @ ( push @ X0 @ X2 ) ) ) ) ) )
= pushprop ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pushprop) ).
thf(f408,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,[],[f124]) ).
thf(f124,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,[],[f123]) ).
thf(f123,plain,
( induction
= ( ! [X0: term > $o] :
( ! [X1: term] :
( ( var @ X1 )
=> ( X0 @ X1 ) )
=> ( ! [X2: term,X3: term] :
( ( X0 @ X3 )
=> ( ( X0 @ X2 )
=> ( X0 @ ( ap @ X3 @ X2 ) ) ) )
=> ( ! [X4: term] :
( ( X0 @ X4 )
=> ( X0 @ ( lam @ X4 ) ) )
=> ! [X5: term] : ( X0 @ X5 ) ) ) ) ) ),
inference(rectify,[],[f23]) ).
thf(f23,axiom,
( induction
= ( ! [X5: term > $o] :
( ! [X0: term] :
( ( var @ X0 )
=> ( X5 @ X0 ) )
=> ( ! [X1: term,X0: term] :
( ( X5 @ X0 )
=> ( ( X5 @ X1 )
=> ( X5 @ ( ap @ X0 @ X1 ) ) ) )
=> ( ! [X0: term] :
( ( X5 @ X0 )
=> ( X5 @ ( lam @ X0 ) ) )
=> ! [X0: term] : ( X5 @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',induction) ).
thf(f422,plain,
( lamnotvar
= ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f141]) ).
thf(f141,plain,
( lamnotvar
= ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) ) ),
inference(fool_elimination,[],[f140]) ).
thf(f140,plain,
( lamnotvar
= ( ! [X0: term] :
~ ( var @ ( lam @ X0 ) ) ) ),
inference(rectify,[],[f22]) ).
thf(f22,axiom,
( lamnotvar
= ( ! [X0: term] :
~ ( var @ ( lam @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lamnotvar) ).
thf(f348,plain,
( apnotvar
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f213]) ).
thf(f213,plain,
( apnotvar
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f212]) ).
thf(f212,plain,
( apnotvar
= ( ! [X0: term,X1: term] :
~ ( var @ ( ap @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f21]) ).
thf(f21,axiom,
( apnotvar
= ( ! [X0: term,X1: term] :
~ ( var @ ( ap @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apnotvar) ).
thf(f338,plain,
( lamnotap
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f271]) ).
thf(f271,plain,
( lamnotap
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ Y1 @ Y2 )
!= ( lam @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f270]) ).
thf(f270,plain,
( lamnotap
= ( ! [X0: term,X1: term,X2: term] :
( ( ap @ X1 @ X0 )
!= ( lam @ X2 ) ) ) ),
inference(rectify,[],[f20]) ).
thf(f20,axiom,
( lamnotap
= ( ! [X6: term,X1: term,X0: term] :
( ( lam @ X0 )
!= ( ap @ X1 @ X6 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lamnotap) ).
thf(f383,plain,
( shinj
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f165]) ).
thf(f165,plain,
( shinj
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f19,axiom,
! [X0: term,X1: term] :
( ( ( ( sub @ X0 @ sh )
= ( sub @ X1 @ sh ) )
=> ( X0 = X1 ) )
= shinj ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',shinj) ).
thf(f346,plain,
( laminj
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f154]) ).
thf(f154,plain,
( laminj
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f18,axiom,
! [X0: term,X1: term] :
( ( ( ( lam @ X0 )
= ( lam @ X1 ) )
=> ( X0 = X1 ) )
= laminj ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',laminj) ).
thf(f426,plain,
( apinj2
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y3 = Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f233]) ).
thf(f233,plain,
( apinj2
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y0 @ Y3 ) )
=> ( Y3 = Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f232]) ).
thf(f232,plain,
( apinj2
= ( ! [X0: term,X1: term,X2: term,X3: term] :
( ( ( ap @ X1 @ X2 )
= ( ap @ X3 @ X0 ) )
=> ( X0 = X2 ) ) ) ),
inference(rectify,[],[f17]) ).
thf(f17,axiom,
( apinj2
= ( ! [X7: term,X0: term,X6: term,X1: term] :
( ( ( ap @ X0 @ X6 )
= ( ap @ X1 @ X7 ) )
=> ( X6 = X7 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apinj2) ).
thf(f428,plain,
( apinj1
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y3 @ Y0 ) )
=> ( Y3 = Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f296]) ).
thf(f296,plain,
( apinj1
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y1 )
= ( ap @ Y3 @ Y0 ) )
=> ( Y3 = Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f295]) ).
thf(f295,plain,
! [X0: term,X1: term,X2: term,X3: term] :
( ( ( ( ap @ X1 @ X2 )
= ( ap @ X0 @ X3 ) )
=> ( X0 = X1 ) )
= apinj1 ),
inference(rectify,[],[f16]) ).
thf(f16,axiom,
! [X0: term,X1: term,X7: term,X6: term] :
( ( ( ( ap @ X0 @ X6 )
= ( ap @ X1 @ X7 ) )
=> ( X0 = X1 ) )
= apinj1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apinj1) ).
thf(f357,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,[],[f231]) ).
thf(f231,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,[],[f230]) ).
thf(f230,plain,
! [X0: term > $o] :
( ( ( X0 @ one )
=> ( ! [X1: term] :
( ( var @ X1 )
=> ( ( X0 @ X1 )
=> ( X0 @ ( sub @ X1 @ sh ) ) ) )
=> ! [X2: term] :
( ( var @ X2 )
=> ( X0 @ X2 ) ) ) )
= ulamvarind ),
inference(rectify,[],[f15]) ).
thf(f15,axiom,
! [X5: term > $o] :
( ( ( X5 @ one )
=> ( ! [X0: term] :
( ( var @ X0 )
=> ( ( X5 @ X0 )
=> ( X5 @ ( sub @ X0 @ sh ) ) ) )
=> ! [X0: term] :
( ( var @ X0 )
=> ( X5 @ X0 ) ) ) )
= ulamvarind ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ulamvarind) ).
thf(f366,plain,
( ulamvarsh
= ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) ) ),
inference(cnf_transformation,[],[f139]) ).
thf(f139,plain,
( ulamvarsh
= ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) ) ),
inference(fool_elimination,[],[f138]) ).
thf(f138,plain,
! [X0: term] :
( ( ( var @ X0 )
=> ( var @ ( sub @ X0 @ sh ) ) )
= ulamvarsh ),
inference(rectify,[],[f14]) ).
thf(f14,axiom,
! [X0: term] :
( ( ( var @ X0 )
=> ( var @ ( sub @ X0 @ sh ) ) )
= ulamvarsh ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ulamvarsh) ).
thf(f333,plain,
( ulamvar1
= ( var @ one ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f13,axiom,
( ulamvar1
= ( var @ one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ulamvar1) ).
thf(f443,plain,
( axscons
= ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) ) ),
inference(cnf_transformation,[],[f326]) ).
thf(f326,plain,
( axscons
= ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) ) ),
inference(fool_elimination,[],[f325]) ).
thf(f325,plain,
! [X0: subst] :
( ( ( push @ ( sub @ one @ X0 ) @ ( comp @ sh @ X0 ) )
= X0 )
= axscons ),
inference(rectify,[],[f12]) ).
thf(f12,axiom,
! [X2: subst] :
( ( ( push @ ( sub @ one @ X2 ) @ ( comp @ sh @ X2 ) )
= X2 )
= axscons ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axscons) ).
thf(f403,plain,
( axvarshift
= ( id
= ( push @ one @ sh ) ) ),
inference(cnf_transformation,[],[f133]) ).
thf(f133,plain,
( axvarshift
= ( id
= ( push @ one @ sh ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f11,axiom,
( ( id
= ( push @ one @ sh ) )
= axvarshift ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axvarshift) ).
thf(f362,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/benchmark/theBenchmark.p',axidr) ).
thf(f394,plain,
( axmap
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( push @ ( sub @ Y1 @ Y2 ) @ ( comp @ Y0 @ Y2 ) )
= ( comp @ ( push @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f251]) ).
thf(f251,plain,
( axmap
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( push @ ( sub @ Y1 @ Y2 ) @ ( comp @ Y0 @ Y2 ) )
= ( comp @ ( push @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f250]) ).
thf(f250,plain,
( axmap
= ( ! [X0: subst,X1: term,X2: subst] :
( ( push @ ( sub @ X1 @ X0 ) @ ( comp @ X2 @ X0 ) )
= ( comp @ ( push @ X1 @ X2 ) @ X0 ) ) ) ),
inference(rectify,[],[f9]) ).
thf(f9,axiom,
( axmap
= ( ! [X3: subst,X0: term,X2: subst] :
( ( comp @ ( push @ X0 @ X2 ) @ X3 )
= ( push @ ( sub @ X0 @ X3 ) @ ( comp @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axmap) ).
thf(f411,plain,
( axassoc
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f130]) ).
thf(f130,plain,
( axassoc
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 )
= ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f129]) ).
thf(f129,plain,
( axassoc
= ( ! [X0: subst,X1: subst,X2: subst] :
( ( comp @ ( comp @ X1 @ X0 ) @ X2 )
= ( comp @ X1 @ ( comp @ X0 @ X2 ) ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f8,axiom,
( axassoc
= ( ! [X3: subst,X2: subst,X4: subst] :
( ( comp @ ( comp @ X2 @ X3 ) @ X4 )
= ( comp @ X2 @ ( comp @ X3 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axassoc) ).
thf(f334,plain,
( axshiftcons
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) ) ),
inference(cnf_transformation,[],[f312]) ).
thf(f312,plain,
( axshiftcons
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) ) ),
inference(fool_elimination,[],[f311]) ).
thf(f311,plain,
! [X0: term,X1: subst] :
( ( ( comp @ sh @ ( push @ X0 @ X1 ) )
= X1 )
= axshiftcons ),
inference(rectify,[],[f7]) ).
thf(f7,axiom,
! [X0: term,X2: subst] :
( ( ( comp @ sh @ ( push @ X0 @ X2 ) )
= X2 )
= axshiftcons ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axshiftcons) ).
thf(f349,plain,
( axidl
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) ),
inference(cnf_transformation,[],[f147]) ).
thf(f147,plain,
( axidl
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) ),
inference(fool_elimination,[],[f146]) ).
thf(f146,plain,
! [X0: subst] :
( ( ( comp @ id @ X0 )
= X0 )
= axidl ),
inference(rectify,[],[f6]) ).
thf(f6,axiom,
! [X2: subst] :
( ( ( comp @ id @ X2 )
= X2 )
= axidl ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axidl) ).
thf(f384,plain,
( axclos
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f289]) ).
thf(f289,plain,
( axclos
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f288]) ).
thf(f288,plain,
( axclos
= ( ! [X0: subst,X1: subst,X2: term] :
( ( sub @ X2 @ ( comp @ X1 @ X0 ) )
= ( sub @ ( sub @ X2 @ X1 ) @ X0 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f5,axiom,
( axclos
= ( ! [X3: subst,X2: subst,X0: term] :
( ( sub @ ( sub @ X0 @ X2 ) @ X3 )
= ( sub @ X0 @ ( comp @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axclos) ).
thf(f350,plain,
( axabs
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( lam @ Y0 ) @ Y1 )
= ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f215]) ).
thf(f215,plain,
( axabs
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( lam @ Y0 ) @ Y1 )
= ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f214]) ).
thf(f214,plain,
! [X0: subst,X1: term] :
( ( ( sub @ ( lam @ X1 ) @ X0 )
= ( lam @ ( sub @ X1 @ ( push @ one @ ( comp @ X0 @ sh ) ) ) ) )
= axabs ),
inference(rectify,[],[f4]) ).
thf(f4,axiom,
! [X2: subst,X0: term] :
( ( ( sub @ ( lam @ X0 ) @ X2 )
= ( lam @ ( sub @ X0 @ ( push @ one @ ( comp @ X2 @ sh ) ) ) ) )
= axabs ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axabs) ).
thf(f439,plain,
( axvarid
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ),
inference(cnf_transformation,[],[f292]) ).
thf(f292,plain,
( axvarid
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f3,axiom,
( axvarid
= ( ! [X0: term] :
( ( sub @ X0 @ id )
= X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axvarid) ).
thf(f396,plain,
( axvarcons
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) ) ),
inference(cnf_transformation,[],[f304]) ).
thf(f304,plain,
( axvarcons
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) ) ),
inference(fool_elimination,[],[f303]) ).
thf(f303,plain,
! [X0: subst,X1: term] :
( ( ( sub @ one @ ( push @ X1 @ X0 ) )
= X1 )
= axvarcons ),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
! [X2: subst,X0: term] :
( ( ( sub @ one @ ( push @ X0 @ X2 ) )
= X0 )
= axvarcons ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axvarcons) ).
thf(f441,plain,
( axapp
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( ap @ ( sub @ Y0 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( ap @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f237]) ).
thf(f237,plain,
( axapp
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( ap @ ( sub @ Y0 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( ap @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f236]) ).
thf(f236,plain,
( axapp
= ( ! [X0: subst,X1: term,X2: term] :
( ( ap @ ( sub @ X2 @ X0 ) @ ( sub @ X1 @ X0 ) )
= ( sub @ ( ap @ X2 @ X1 ) @ X0 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
( axapp
= ( ! [X2: subst,X1: term,X0: term] :
( ( sub @ ( ap @ X0 @ X1 ) @ X2 )
= ( ap @ ( sub @ X0 @ X2 ) @ ( sub @ X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axapp) ).
thf(f413,plain,
( hoasinduction_lem1_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f118]) ).
thf(f118,plain,
( hoasinduction_lem1_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f117]) ).
thf(f117,plain,
( axapp
=> ( ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= hoasinduction_lem1_gthm ) ),
inference(rectify,[],[f91]) ).
thf(f91,axiom,
( axapp
=> ( ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= hoasinduction_lem1_gthm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem1_gthm) ).
thf(f435,plain,
hoasinduction_lem1_gthm != $true,
inference(cnf_transformation,[],[f329]) ).
thf(f329,plain,
hoasinduction_lem1_gthm != $true,
inference(flattening,[],[f160]) ).
thf(f160,plain,
hoasinduction_lem1_gthm != $true,
inference(fool_elimination,[],[f159]) ).
thf(f159,plain,
~ hoasinduction_lem1_gthm,
inference(rectify,[],[f115]) ).
thf(f115,negated_conjecture,
~ hoasinduction_lem1_gthm,
inference(negated_conjecture,[],[f114]) ).
thf(f114,conjecture,
hoasinduction_lem1_gthm,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(f1053,plain,
! [X1: term] :
( ( ( sK40 @ id @ X1 @ id )
= $true )
| ( ( var @ X1 )
= $false ) ),
inference(backward_demodulation,[],[f1044,f922]) ).
thf(f922,plain,
! [X1: term] :
( ( sub @ X1 @ id )
= X1 ),
inference(equality_proxy_clausification,[],[f921]) ).
thf(f921,plain,
! [X1: term] :
( ( ( sub @ X1 @ id )
= X1 )
= $true ),
inference(beta_eta_normalization,[],[f920]) ).
thf(f920,plain,
! [X1: term] :
( $true
= ( ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 )
@ X1 ) ),
inference(pi_clausification,[],[f911]) ).
thf(f911,plain,
( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ),
inference(binary_proxy_clausification,[],[f910]) ).
thf(f910,plain,
( $true
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( sub @ ( sub @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ) ),
inference(binary_proxy_clausification,[],[f890]) ).
thf(f1044,plain,
! [X1: term] :
( ( ( sK40 @ id @ X1 @ id )
= $true )
| ( ( var @ ( sub @ X1 @ id ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f1043]) ).
thf(f1043,plain,
! [X1: term] :
( $true
= ( ( var @ ( sub @ X1 @ id ) )
=> ( sK40 @ id @ X1 @ id ) ) ),
inference(beta_eta_normalization,[],[f1042]) ).
thf(f1042,plain,
! [X1: term] :
( ( ^ [Y0: term] :
( ( var @ ( sub @ Y0 @ id ) )
=> ( sK40 @ id @ Y0 @ id ) )
@ X1 )
= $true ),
inference(pi_clausification,[],[f1041]) ).
thf(f1041,plain,
( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( var @ ( sub @ Y0 @ id ) )
=> ( sK40 @ id @ Y0 @ id ) ) ) ),
inference(binary_proxy_clausification,[],[f1029]) ).
thf(f1048,plain,
( ( var @ sK41 )
= $true ),
inference(binary_proxy_clausification,[],[f1046]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : ALG263^1 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.04/0.15 % 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
% 0.15/0.36 % Computer : n006.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sat May 18 23:29:38 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a TH0_THM_EQU_NAR problem
% 0.15/0.37 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.40 % (2284)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.21/0.40 % (2283)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.21/0.40 % (2285)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.21/0.40 % (2288)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.21/0.40 % (2286)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.21/0.40 % (2282)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.21/0.40 % (2287)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.21/0.40 % (2289)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.40 % (2285)Instruction limit reached!
% 0.21/0.40 % (2285)------------------------------
% 0.21/0.40 % (2285)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (2285)Termination reason: Unknown
% 0.21/0.40 % (2286)Instruction limit reached!
% 0.21/0.40 % (2286)------------------------------
% 0.21/0.40 % (2286)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (2286)Termination reason: Unknown
% 0.21/0.40 % (2286)Termination phase: shuffling
% 0.21/0.40
% 0.21/0.40 % (2286)Memory used [KB]: 1279
% 0.21/0.40 % (2286)Time elapsed: 0.004 s
% 0.21/0.40 % (2286)Instructions burned: 3 (million)
% 0.21/0.40 % (2286)------------------------------
% 0.21/0.40 % (2286)------------------------------
% 0.21/0.40 % (2285)Termination phase: shuffling
% 0.21/0.40
% 0.21/0.40 % (2285)Memory used [KB]: 1279
% 0.21/0.40 % (2285)Time elapsed: 0.003 s
% 0.21/0.40 % (2285)Instructions burned: 3 (million)
% 0.21/0.40 % (2285)------------------------------
% 0.21/0.40 % (2285)------------------------------
% 0.21/0.40 % (2289)Instruction limit reached!
% 0.21/0.40 % (2289)------------------------------
% 0.21/0.40 % (2289)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (2289)Termination reason: Unknown
% 0.21/0.40 % (2289)Termination phase: shuffling
% 0.21/0.40
% 0.21/0.40 % (2289)Memory used [KB]: 1279
% 0.21/0.40 % (2289)Time elapsed: 0.003 s
% 0.21/0.40 % (2289)Instructions burned: 3 (million)
% 0.21/0.40 % (2289)------------------------------
% 0.21/0.40 % (2289)------------------------------
% 0.21/0.40 % (2283)Instruction limit reached!
% 0.21/0.40 % (2283)------------------------------
% 0.21/0.40 % (2283)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (2283)Termination reason: Unknown
% 0.21/0.40 % (2283)Termination phase: shuffling
% 0.21/0.40
% 0.21/0.40 % (2283)Memory used [KB]: 1279
% 0.21/0.40 % (2283)Time elapsed: 0.004 s
% 0.21/0.40 % (2283)Instructions burned: 5 (million)
% 0.21/0.40 % (2283)------------------------------
% 0.21/0.40 % (2283)------------------------------
% 0.21/0.41 % (2288)Instruction limit reached!
% 0.21/0.41 % (2288)------------------------------
% 0.21/0.41 % (2288)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (2288)Termination reason: Unknown
% 0.21/0.41 % (2288)Termination phase: Property scanning
% 0.21/0.41
% 0.21/0.41 % (2288)Memory used [KB]: 1663
% 0.21/0.41 % (2288)Time elapsed: 0.013 s
% 0.21/0.41 % (2288)Instructions burned: 19 (million)
% 0.21/0.41 % (2288)------------------------------
% 0.21/0.41 % (2288)------------------------------
% 0.21/0.41 % (2284)Instruction limit reached!
% 0.21/0.41 % (2284)------------------------------
% 0.21/0.41 % (2284)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (2284)Termination reason: Unknown
% 0.21/0.41 % (2284)Termination phase: Property scanning
% 0.21/0.41
% 0.21/0.41 % (2284)Memory used [KB]: 1791
% 0.21/0.41 % (2284)Time elapsed: 0.016 s
% 0.21/0.41 % (2284)Instructions burned: 28 (million)
% 0.21/0.41 % (2284)------------------------------
% 0.21/0.41 % (2284)------------------------------
% 0.21/0.42 % (2290)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.21/0.42 % (2291)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.21/0.42 % (2292)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.42 % (2293)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.21/0.42 % (2292)Instruction limit reached!
% 0.21/0.42 % (2292)------------------------------
% 0.21/0.42 % (2292)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (2292)Termination reason: Unknown
% 0.21/0.42 % (2292)Termination phase: shuffling
% 0.21/0.42
% 0.21/0.42 % (2292)Memory used [KB]: 1279
% 0.21/0.42 % (2292)Time elapsed: 0.003 s
% 0.21/0.42 % (2292)Instructions burned: 3 (million)
% 0.21/0.42 % (2292)------------------------------
% 0.21/0.42 % (2292)------------------------------
% 0.21/0.42 % (2287)Refutation not found, incomplete strategy
% 0.21/0.42 % (2287)------------------------------
% 0.21/0.42 % (2287)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (2287)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.42
% 0.21/0.42
% 0.21/0.42 % (2287)Memory used [KB]: 6268
% 0.21/0.42 % (2287)Time elapsed: 0.020 s
% 0.21/0.42 % (2287)Instructions burned: 31 (million)
% 0.21/0.42 % (2287)------------------------------
% 0.21/0.42 % (2287)------------------------------
% 0.21/0.42 % (2291)Instruction limit reached!
% 0.21/0.42 % (2291)------------------------------
% 0.21/0.42 % (2291)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (2291)Termination reason: Unknown
% 0.21/0.42 % (2291)Termination phase: Property scanning
% 0.21/0.42
% 0.21/0.42 % (2291)Memory used [KB]: 1663
% 0.21/0.42 % (2291)Time elapsed: 0.010 s
% 0.21/0.42 % (2291)Instructions burned: 15 (million)
% 0.21/0.42 % (2291)------------------------------
% 0.21/0.42 % (2291)------------------------------
% 0.21/0.43 % (2294)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.43 % (2295)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.21/0.43 % (2294)Instruction limit reached!
% 0.21/0.43 % (2294)------------------------------
% 0.21/0.43 % (2294)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43 % (2294)Termination reason: Unknown
% 0.21/0.43 % (2294)Termination phase: shuffling
% 0.21/0.43
% 0.21/0.43 % (2294)Memory used [KB]: 1407
% 0.21/0.43 % (2294)Time elapsed: 0.006 s
% 0.21/0.43 % (2294)Instructions burned: 8 (million)
% 0.21/0.43 % (2294)------------------------------
% 0.21/0.43 % (2294)------------------------------
% 0.21/0.43 % (2296)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.43 % (2290)Instruction limit reached!
% 0.21/0.43 % (2290)------------------------------
% 0.21/0.43 % (2290)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43 % (2297)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.43 % (2290)Termination reason: Unknown
% 0.21/0.43 % (2290)Termination phase: Property scanning
% 0.21/0.43
% 0.21/0.43 % (2290)Memory used [KB]: 1791
% 0.21/0.43 % (2290)Time elapsed: 0.020 s
% 0.21/0.43 % (2290)Instructions burned: 37 (million)
% 0.21/0.43 % (2290)------------------------------
% 0.21/0.43 % (2290)------------------------------
% 0.21/0.43 % (2296)Instruction limit reached!
% 0.21/0.43 % (2296)------------------------------
% 0.21/0.43 % (2296)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43 % (2296)Termination reason: Unknown
% 0.21/0.43 % (2296)Termination phase: shuffling
% 0.21/0.43
% 0.21/0.43 % (2296)Memory used [KB]: 1279
% 0.21/0.43 % (2296)Time elapsed: 0.004 s
% 0.21/0.43 % (2296)Instructions burned: 5 (million)
% 0.21/0.43 % (2296)------------------------------
% 0.21/0.43 % (2296)------------------------------
% 0.21/0.44 % (2297)Instruction limit reached!
% 0.21/0.44 % (2297)------------------------------
% 0.21/0.44 % (2297)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.44 % (2297)Termination reason: Unknown
% 0.21/0.44 % (2297)Termination phase: shuffling
% 0.21/0.44
% 0.21/0.44 % (2297)Memory used [KB]: 1279
% 0.21/0.44 % (2297)Time elapsed: 0.004 s
% 0.21/0.44 % (2297)Instructions burned: 4 (million)
% 0.21/0.44 % (2297)------------------------------
% 0.21/0.44 % (2297)------------------------------
% 0.21/0.44 % (2295)Instruction limit reached!
% 0.21/0.44 % (2295)------------------------------
% 0.21/0.44 % (2295)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.44 % (2295)Termination reason: Unknown
% 0.21/0.44 % (2295)Termination phase: shuffling
% 0.21/0.44
% 0.21/0.44 % (2295)Memory used [KB]: 1535
% 0.21/0.44 % (2295)Time elapsed: 0.010 s
% 0.21/0.44 % (2295)Instructions burned: 16 (million)
% 0.21/0.44 % (2295)------------------------------
% 0.21/0.44 % (2295)------------------------------
% 0.21/0.44 % (2298)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.44 % (2298)Instruction limit reached!
% 0.21/0.44 % (2298)------------------------------
% 0.21/0.44 % (2298)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.44 % (2298)Termination reason: Unknown
% 0.21/0.44 % (2298)Termination phase: shuffling
% 0.21/0.44
% 0.21/0.44 % (2298)Memory used [KB]: 1407
% 0.21/0.44 % (2298)Time elapsed: 0.006 s
% 0.21/0.44 % (2298)Instructions burned: 8 (million)
% 0.21/0.44 % (2298)------------------------------
% 0.21/0.44 % (2298)------------------------------
% 0.21/0.44 % (2299)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.45 % (2299)Instruction limit reached!
% 0.21/0.45 % (2299)------------------------------
% 0.21/0.45 % (2299)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.45 % (2299)Termination reason: Unknown
% 0.21/0.45 % (2299)Termination phase: shuffling
% 0.21/0.45
% 0.21/0.45 % (2299)Memory used [KB]: 1279
% 0.21/0.45 % (2299)Time elapsed: 0.003 s
% 0.21/0.45 % (2299)Instructions burned: 3 (million)
% 0.21/0.45 % (2299)------------------------------
% 0.21/0.45 % (2299)------------------------------
% 0.21/0.45 % (2301)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.21/0.45 % (2300)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.21/0.45 % (2302)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.21/0.45 % (2300)Instruction limit reached!
% 0.21/0.45 % (2300)------------------------------
% 0.21/0.45 % (2300)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.45 % (2300)Termination reason: Unknown
% 0.21/0.45 % (2303)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.21/0.45 % (2300)Termination phase: shuffling
% 0.21/0.45
% 0.21/0.45 % (2300)Memory used [KB]: 1279
% 0.21/0.45 % (2300)Time elapsed: 0.004 s
% 0.21/0.45 % (2300)Instructions burned: 4 (million)
% 0.21/0.45 % (2300)------------------------------
% 0.21/0.45 % (2300)------------------------------
% 0.21/0.45 % (2303)Instruction limit reached!
% 0.21/0.45 % (2303)------------------------------
% 0.21/0.45 % (2303)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.45 % (2303)Termination reason: Unknown
% 0.21/0.45 % (2303)Termination phase: shuffling
% 0.21/0.45
% 0.21/0.45 % (2303)Memory used [KB]: 1279
% 0.21/0.45 % (2303)Time elapsed: 0.005 s
% 0.21/0.45 % (2303)Instructions burned: 6 (million)
% 0.21/0.45 % (2303)------------------------------
% 0.21/0.45 % (2303)------------------------------
% 0.21/0.46 % (2301)Instruction limit reached!
% 0.21/0.46 % (2301)------------------------------
% 0.21/0.46 % (2301)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.46 % (2301)Termination reason: Unknown
% 0.21/0.46 % (2301)Termination phase: shuffling
% 0.21/0.46
% 0.21/0.46 % (2301)Memory used [KB]: 1663
% 0.21/0.46 % (2301)Time elapsed: 0.012 s
% 0.21/0.46 % (2301)Instructions burned: 19 (million)
% 0.21/0.46 % (2301)------------------------------
% 0.21/0.46 % (2301)------------------------------
% 0.21/0.46 % (2304)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on theBenchmark for (2999ds/902Mi)
% 0.21/0.46 % (2305)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on theBenchmark for (2999ds/21Mi)
% 0.21/0.47 % (2306)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.21/0.47 % (2302)Refutation not found, incomplete strategy
% 0.21/0.47 % (2302)------------------------------
% 0.21/0.47 % (2302)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.47 % (2302)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.47
% 0.21/0.47
% 0.21/0.47 % (2302)Memory used [KB]: 6268
% 0.21/0.47 % (2302)Time elapsed: 0.019 s
% 0.21/0.47 % (2302)Instructions burned: 28 (million)
% 0.21/0.47 % (2302)------------------------------
% 0.21/0.47 % (2302)------------------------------
% 0.21/0.47 % (2306)Instruction limit reached!
% 0.21/0.47 % (2306)------------------------------
% 0.21/0.47 % (2306)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.47 % (2307)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.21/0.47 % (2306)Termination reason: Unknown
% 0.21/0.47 % (2306)Termination phase: shuffling
% 0.21/0.47
% 0.21/0.47 % (2306)Memory used [KB]: 1279
% 0.21/0.47 % (2306)Time elapsed: 0.005 s
% 0.21/0.47 % (2306)Instructions burned: 5 (million)
% 0.21/0.47 % (2306)------------------------------
% 0.21/0.47 % (2306)------------------------------
% 0.21/0.47 % (2305)Instruction limit reached!
% 0.21/0.47 % (2305)------------------------------
% 0.21/0.47 % (2305)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.47 % (2305)Termination reason: Unknown
% 0.21/0.47 % (2305)Termination phase: shuffling
% 0.21/0.47
% 0.21/0.47 % (2305)Memory used [KB]: 1663
% 0.21/0.47 % (2305)Time elapsed: 0.013 s
% 0.21/0.47 % (2305)Instructions burned: 22 (million)
% 0.21/0.47 % (2305)------------------------------
% 0.21/0.47 % (2305)------------------------------
% 0.21/0.47 % (2307)Instruction limit reached!
% 0.21/0.47 % (2307)------------------------------
% 0.21/0.47 % (2307)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.47 % (2307)Termination reason: Unknown
% 0.21/0.47 % (2307)Termination phase: shuffling
% 0.21/0.47
% 0.21/0.47 % (2307)Memory used [KB]: 1279
% 0.21/0.47 % (2307)Time elapsed: 0.005 s
% 0.21/0.47 % (2307)Instructions burned: 7 (million)
% 0.21/0.47 % (2307)------------------------------
% 0.21/0.47 % (2307)------------------------------
% 0.21/0.48 % (2308)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2999ds/377Mi)
% 0.21/0.48 % (2309)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on theBenchmark for (2999ds/779Mi)
% 0.21/0.49 % (2310)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on theBenchmark for (2999ds/19Mi)
% 0.21/0.49 % (2311)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on theBenchmark for (2998ds/879Mi)
% 0.21/0.49 % (2312)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2998ds/17Mi)
% 0.21/0.49 % (2282)Instruction limit reached!
% 0.21/0.49 % (2282)------------------------------
% 0.21/0.49 % (2282)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.49 % (2282)Termination reason: Unknown
% 0.21/0.49 % (2282)Termination phase: Saturation
% 0.21/0.49
% 0.21/0.49 % (2282)Memory used [KB]: 6780
% 0.21/0.49 % (2282)Time elapsed: 0.093 s
% 0.21/0.49 % (2282)Instructions burned: 184 (million)
% 0.21/0.49 % (2282)------------------------------
% 0.21/0.49 % (2282)------------------------------
% 0.21/0.50 % (2310)Instruction limit reached!
% 0.21/0.50 % (2310)------------------------------
% 0.21/0.50 % (2310)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.50 % (2310)Termination reason: Unknown
% 0.21/0.50 % (2310)Termination phase: shuffling
% 0.21/0.50
% 0.21/0.50 % (2310)Memory used [KB]: 1663
% 0.21/0.50 % (2310)Time elapsed: 0.012 s
% 0.21/0.50 % (2310)Instructions burned: 20 (million)
% 0.21/0.50 % (2310)------------------------------
% 0.21/0.50 % (2310)------------------------------
% 0.21/0.50 % (2312)Instruction limit reached!
% 0.21/0.50 % (2312)------------------------------
% 0.21/0.50 % (2312)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.50 % (2312)Termination reason: Unknown
% 0.21/0.50 % (2312)Termination phase: shuffling
% 0.21/0.50
% 0.21/0.50 % (2312)Memory used [KB]: 1535
% 0.21/0.50 % (2312)Time elapsed: 0.011 s
% 0.21/0.50 % (2312)Instructions burned: 18 (million)
% 0.21/0.50 % (2312)------------------------------
% 0.21/0.50 % (2312)------------------------------
% 0.21/0.51 % (2313)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi)
% 0.21/0.51 % (2313)Instruction limit reached!
% 0.21/0.51 % (2313)------------------------------
% 0.21/0.51 % (2313)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.51 % (2313)Termination reason: Unknown
% 0.21/0.51 % (2313)Termination phase: shuffling
% 0.21/0.51
% 0.21/0.51 % (2313)Memory used [KB]: 1279
% 0.21/0.51 % (2313)Time elapsed: 0.004 s
% 0.21/0.51 % (2313)Instructions burned: 3 (million)
% 0.21/0.51 % (2313)------------------------------
% 0.21/0.51 % (2313)------------------------------
% 0.21/0.51 % (2314)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on theBenchmark for (2998ds/30Mi)
% 0.21/0.51 % (2315)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on theBenchmark for (2998ds/127Mi)
% 0.21/0.52 % (2311)Refutation not found, incomplete strategy
% 0.21/0.52 % (2311)------------------------------
% 0.21/0.52 % (2311)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.52 % (2311)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.52
% 0.21/0.52
% 0.21/0.52 % (2311)Memory used [KB]: 6268
% 0.21/0.52 % (2311)Time elapsed: 0.035 s
% 0.21/0.52 % (2311)Instructions burned: 61 (million)
% 0.21/0.52 % (2311)------------------------------
% 0.21/0.52 % (2311)------------------------------
% 0.21/0.52 % (2316)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on theBenchmark for (2998ds/100Mi)
% 0.21/0.53 % (2314)Instruction limit reached!
% 0.21/0.53 % (2314)------------------------------
% 0.21/0.53 % (2314)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.53 % (2314)Termination reason: Unknown
% 0.21/0.53 % (2314)Termination phase: Property scanning
% 0.21/0.53
% 0.21/0.53 % (2314)Memory used [KB]: 1791
% 0.21/0.53 % (2314)Time elapsed: 0.017 s
% 0.21/0.53 % (2314)Instructions burned: 30 (million)
% 0.21/0.53 % (2314)------------------------------
% 0.21/0.53 % (2314)------------------------------
% 0.21/0.54 % (2317)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi)
% 0.21/0.54 % (2317)Instruction limit reached!
% 0.21/0.54 % (2317)------------------------------
% 0.21/0.54 % (2317)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.54 % (2317)Termination reason: Unknown
% 0.21/0.54 % (2317)Termination phase: shuffling
% 0.21/0.54
% 0.21/0.54 % (2317)Memory used [KB]: 1279
% 0.21/0.54 % (2317)Time elapsed: 0.004 s
% 0.21/0.54 % (2317)Instructions burned: 3 (million)
% 0.21/0.54 % (2317)------------------------------
% 0.21/0.54 % (2317)------------------------------
% 1.32/0.54 % (2318)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on theBenchmark for (2998ds/20Mi)
% 1.32/0.55 % (2318)Instruction limit reached!
% 1.32/0.55 % (2318)------------------------------
% 1.32/0.55 % (2318)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.32/0.55 % (2318)Termination reason: Unknown
% 1.32/0.55 % (2318)Termination phase: Property scanning
% 1.32/0.55
% 1.32/0.55 % (2318)Memory used [KB]: 1663
% 1.32/0.55 % (2318)Time elapsed: 0.013 s
% 1.32/0.55 % (2318)Instructions burned: 20 (million)
% 1.32/0.55 % (2318)------------------------------
% 1.32/0.55 % (2318)------------------------------
% 1.32/0.56 % (2319)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on theBenchmark for (2998ds/86Mi)
% 1.50/0.57 % (2320)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on theBenchmark for (2998ds/107Mi)
% 1.50/0.57 % (2316)Instruction limit reached!
% 1.50/0.57 % (2316)------------------------------
% 1.50/0.57 % (2316)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.50/0.57 % (2316)Termination reason: Unknown
% 1.50/0.57 % (2316)Termination phase: Saturation
% 1.50/0.57
% 1.50/0.57 % (2316)Memory used [KB]: 6524
% 1.50/0.57 % (2316)Time elapsed: 0.051 s
% 1.50/0.57 % (2316)Instructions burned: 100 (million)
% 1.50/0.57 % (2316)------------------------------
% 1.50/0.57 % (2316)------------------------------
% 1.50/0.58 % (2308)First to succeed.
% 1.50/0.59 % (2321)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on theBenchmark for (2997ds/39Mi)
% 1.50/0.60 % (2315)Instruction limit reached!
% 1.50/0.60 % (2315)------------------------------
% 1.50/0.60 % (2315)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.50/0.60 % (2315)Termination reason: Unknown
% 1.50/0.60 % (2315)Termination phase: Saturation
% 1.50/0.60
% 1.50/0.60 % (2315)Memory used [KB]: 6524
% 1.50/0.60 % (2315)Time elapsed: 0.070 s
% 1.50/0.60 % (2315)Instructions burned: 127 (million)
% 1.50/0.60 % (2315)------------------------------
% 1.50/0.60 % (2315)------------------------------
% 1.50/0.60 % (2319)Instruction limit reached!
% 1.50/0.60 % (2319)------------------------------
% 1.50/0.60 % (2319)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.50/0.60 % (2319)Termination reason: Unknown
% 1.50/0.60 % (2319)Termination phase: Property scanning
% 1.50/0.60
% 1.50/0.60 % (2319)Memory used [KB]: 2046
% 1.50/0.60 % (2319)Time elapsed: 0.044 s
% 1.50/0.60 % (2319)Instructions burned: 86 (million)
% 1.50/0.60 % (2319)------------------------------
% 1.50/0.60 % (2319)------------------------------
% 1.50/0.61 % (2321)Instruction limit reached!
% 1.50/0.61 % (2321)------------------------------
% 1.50/0.61 % (2321)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.50/0.61 % (2321)Termination reason: Unknown
% 1.50/0.61 % (2321)Termination phase: Property scanning
% 1.50/0.61
% 1.50/0.61 % (2321)Memory used [KB]: 1791
% 1.50/0.61 % (2321)Time elapsed: 0.022 s
% 1.50/0.61 % (2321)Instructions burned: 40 (million)
% 1.50/0.61 % (2321)------------------------------
% 1.50/0.61 % (2321)------------------------------
% 1.50/0.61 % (2322)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on theBenchmark for (2997ds/448Mi)
% 1.50/0.61 % (2323)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on theBenchmark for (2997ds/46Mi)
% 1.50/0.63 % (2320)Instruction limit reached!
% 1.50/0.63 % (2320)------------------------------
% 1.50/0.63 % (2320)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.50/0.63 % (2320)Termination reason: Unknown
% 1.50/0.63 % (2320)Termination phase: Saturation
% 1.50/0.63
% 1.50/0.63 % (2320)Memory used [KB]: 6524
% 1.50/0.63 % (2320)Time elapsed: 0.057 s
% 1.50/0.63 % (2320)Instructions burned: 108 (million)
% 1.50/0.63 % (2320)------------------------------
% 1.50/0.63 % (2320)------------------------------
% 1.50/0.63 % (2324)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on theBenchmark for (2997ds/98Mi)
% 1.50/0.64 % (2308)Refutation found. Thanks to Tanya!
% 1.50/0.64 % SZS status Theorem for theBenchmark
% 1.50/0.64 % SZS output start Proof for theBenchmark
% See solution above
% 2.06/0.64 % (2308)------------------------------
% 2.06/0.64 % (2308)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.06/0.64 % (2308)Termination reason: Refutation
% 2.06/0.64
% 2.06/0.64 % (2308)Memory used [KB]: 9722
% 2.06/0.64 % (2308)Time elapsed: 0.161 s
% 2.06/0.64 % (2308)Instructions burned: 213 (million)
% 2.06/0.64 % (2308)------------------------------
% 2.06/0.64 % (2308)------------------------------
% 2.06/0.64 % (2281)Success in time 0.267 s
% 2.06/0.64 % Vampire---4.8 exiting
%------------------------------------------------------------------------------