TSTP Solution File: ALG260^1 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : ALG260^1 : TPTP v8.2.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n028.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 18:20:26 EDT 2024
% Result : Theorem 1.91s 0.63s
% Output : Refutation 1.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 97
% Syntax : Number of formulae : 263 ( 198 unt; 59 typ; 0 def)
% Number of atoms : 4579 (1149 equ; 0 cnn)
% Maximal formula atoms : 33 ( 22 avg)
% Number of connectives : 17882 ( 173 ~; 0 |; 101 &;12835 @)
% ( 0 <=>;2033 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 1043 (1043 >; 0 *; 0 +; 0 <<)
% Number of symbols : 93 ( 89 usr; 40 con; 0-4 aty)
% (2740 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 3093 (2879 ^ 214 !; 0 ?;3093 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
term: $tType ).
thf(type_def_7,type,
subst: $tType ).
thf(func_def_0,type,
term: $tType ).
thf(func_def_1,type,
subst: $tType ).
thf(func_def_2,type,
one: term ).
thf(func_def_3,type,
ap: term > term > term ).
thf(func_def_4,type,
lam: term > term ).
thf(func_def_5,type,
sub: term > subst > term ).
thf(func_def_6,type,
id: subst ).
thf(func_def_7,type,
sh: subst ).
thf(func_def_8,type,
push: term > subst > subst ).
thf(func_def_9,type,
comp: subst > subst > subst ).
thf(func_def_10,type,
var: term > $o ).
thf(func_def_18,type,
hoasap: subst > term > subst > term > term ).
thf(func_def_73,type,
hoaslam: subst > ( subst > term > term ) > term ).
thf(func_def_86,type,
hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).
thf(func_def_107,type,
hoasvar: subst > term > subst > $o ).
thf(func_def_121,type,
pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).
thf(func_def_142,type,
sK1: ( term > $o ) > term ).
thf(func_def_143,type,
sK2: ( term > $o ) > term ).
thf(func_def_144,type,
sK3: ( term > $o ) > term ).
thf(func_def_145,type,
sK4: ( term > $o ) > term ).
thf(func_def_146,type,
sK5: ( term > $o ) > term ).
thf(func_def_147,type,
sK6: ( term > $o ) > term ).
thf(func_def_148,type,
sK7: ( term > $o ) > term ).
thf(func_def_149,type,
sK8: ( term > $o ) > term ).
thf(func_def_150,type,
sK9: ( term > $o ) > term ).
thf(func_def_151,type,
sK10: ( term > $o ) > subst > 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 ) > term ).
thf(func_def_155,type,
sK14: subst > ( term > $o ) > term ).
thf(func_def_156,type,
sK15: subst > ( term > $o ) > term ).
thf(func_def_157,type,
sK16: subst > ( term > $o ) > term ).
thf(func_def_158,type,
sK17: ( term > $o ) > subst > term ).
thf(func_def_159,type,
sK18: ( term > $o ) > term ).
thf(func_def_160,type,
sK19: ( term > $o ) > term ).
thf(func_def_161,type,
sK20: ( term > $o ) > term ).
thf(func_def_162,type,
sK21: ( term > $o ) > term ).
thf(func_def_163,type,
sK22: ( term > $o ) > term ).
thf(func_def_164,type,
sK23: ( term > $o ) > term ).
thf(func_def_165,type,
sK24: ( term > $o ) > term ).
thf(func_def_166,type,
sK25: ( term > $o ) > term ).
thf(func_def_167,type,
sK26: ( term > $o ) > term ).
thf(func_def_168,type,
sK27: ( term > $o ) > term ).
thf(func_def_169,type,
sK28: ( term > $o ) > term ).
thf(func_def_170,type,
sK29: ( term > $o ) > term ).
thf(func_def_171,type,
sK30: ( term > $o ) > term ).
thf(func_def_172,type,
sK31: ( term > $o ) > term ).
thf(func_def_173,type,
sK32: ( subst > term > term ) > subst ).
thf(func_def_174,type,
sK33: ( subst > term > term ) > subst ).
thf(func_def_175,type,
sK34: ( subst > term > term ) > term ).
thf(func_def_176,type,
sK35: ( subst > term > term ) > term ).
thf(func_def_177,type,
sK36: ( subst > term > term ) > subst ).
thf(func_def_178,type,
sK37: ( subst > term > term ) > subst ).
thf(func_def_179,type,
sK38: ( subst > term > term ) > subst ).
thf(func_def_180,type,
sK39: ( subst > term > term ) > term ).
thf(func_def_181,type,
sK40: ( subst > term > term ) > subst ).
thf(func_def_182,type,
sK41: subst > term > term ).
thf(f1018,plain,
$false,
inference(trivial_inequality_removal,[],[f1017]) ).
thf(f1017,plain,
$false = $true,
inference(backward_demodulation,[],[f1011,f691]) ).
thf(f691,plain,
! [X1: term] :
( $false
= ( var @ ( lam @ X1 ) ) ),
inference(not_proxy_clausification,[],[f690]) ).
thf(f690,plain,
! [X1: term] :
( ( ~ ( var @ ( lam @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[],[f689]) ).
thf(f689,plain,
! [X1: term] :
( ( ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[],[f688]) ).
thf(f688,plain,
( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f680]) ).
thf(f680,plain,
( $false
= ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y3 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y2 ) @ Y3 )
= ( Y1 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f670]) ).
thf(f670,plain,
( $false
= ( ( !! @ 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y3 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y2 ) @ Y3 )
= ( Y1 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f661]) ).
thf(f661,plain,
( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y3 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y2 ) @ Y3 )
= ( Y1 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f652]) ).
thf(f652,plain,
( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y3 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y2 ) @ Y3 )
= ( Y1 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f639]) ).
thf(f639,plain,
( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y3 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y2 ) @ Y3 )
= ( Y1 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f626]) ).
thf(f626,plain,
( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y3 )
= ( ap @ Y0 @ Y1 ) )
=> ( 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] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y3 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y2 ) @ Y3 )
= ( Y1 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f610]) ).
thf(f610,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y0 )
= ( ap @ Y1 @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y3 )
= ( ap @ Y0 @ Y1 ) )
=> ( 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] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y3 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y2 ) @ Y3 )
= ( Y1 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f605]) ).
thf(f605,plain,
( $false
= ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y0 )
= ( ap @ Y1 @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y3 )
= ( ap @ Y0 @ Y1 ) )
=> ( 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] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y3 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y2 ) @ Y3 )
= ( Y1 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f603]) ).
thf(f603,plain,
( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y0 )
= ( ap @ Y1 @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y3 )
= ( ap @ Y0 @ Y1 ) )
=> ( 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] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y3 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y2 ) @ Y3 )
= ( Y1 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f598]) ).
thf(f598,plain,
( $false
= ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y0 )
= ( ap @ Y1 @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y3 )
= ( ap @ Y0 @ Y1 ) )
=> ( 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] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y3 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y2 ) @ Y3 )
= ( Y1 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f595]) ).
thf(f595,plain,
( $false
= ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y0 )
= ( ap @ Y1 @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y3 )
= ( ap @ Y0 @ Y1 ) )
=> ( 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] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y3 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y2 ) @ Y3 )
= ( Y1 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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 @ Y3 @ Y0 )
= ( ap @ Y1 @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y3 )
= ( ap @ Y0 @ Y1 ) )
=> ( 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] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y3 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y2 ) @ Y3 )
= ( Y1 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ 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 @ Y3 @ Y0 )
= ( ap @ Y1 @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y3 )
= ( ap @ Y0 @ Y1 ) )
=> ( 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] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y3 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y2 ) @ Y3 )
= ( Y1 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f572]) ).
thf(f572,plain,
( $false
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y1 @ Y2 ) @ Y0 )
= ( push @ ( sub @ Y1 @ Y0 ) @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y0 )
= ( ap @ Y1 @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y3 )
= ( ap @ Y0 @ Y1 ) )
=> ( 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] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y3 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y2 ) @ Y3 )
= ( Y1 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f565]) ).
thf(f565,plain,
( $false
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y1 @ Y2 ) @ Y0 )
= ( push @ ( sub @ Y1 @ Y0 ) @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y0 )
= ( ap @ Y1 @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y3 )
= ( ap @ Y0 @ Y1 ) )
=> ( 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] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y3 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y2 ) @ Y3 )
= ( Y1 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f560]) ).
thf(f560,plain,
( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y1 @ Y2 ) @ Y0 )
= ( push @ ( sub @ Y1 @ Y0 ) @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y0 )
= ( ap @ Y1 @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y3 )
= ( ap @ Y0 @ Y1 ) )
=> ( 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] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y3 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y2 ) @ Y3 )
= ( Y1 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f551]) ).
thf(f551,plain,
( $false
= ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y1 @ Y2 ) @ Y0 )
= ( push @ ( sub @ Y1 @ Y0 ) @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y0 )
= ( ap @ Y1 @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y3 )
= ( ap @ Y0 @ Y1 ) )
=> ( 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] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y3 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y2 ) @ Y3 )
= ( Y1 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f544]) ).
thf(f544,plain,
( $false
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sub @ Y2 @ Y0 ) @ Y1 )
= ( sub @ Y2 @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y1 @ Y2 ) @ Y0 )
= ( push @ ( sub @ Y1 @ Y0 ) @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y0 )
= ( ap @ Y1 @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y3 )
= ( ap @ Y0 @ Y1 ) )
=> ( 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] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y3 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y2 ) @ Y3 )
= ( Y1 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f539]) ).
thf(f539,plain,
( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( lam @ Y0 ) @ Y1 )
= ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sub @ Y2 @ Y0 ) @ Y1 )
= ( sub @ Y2 @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y1 @ Y2 ) @ Y0 )
= ( push @ ( sub @ Y1 @ Y0 ) @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y0 )
= ( ap @ Y1 @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y3 )
= ( ap @ Y0 @ Y1 ) )
=> ( 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] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y3 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y2 ) @ Y3 )
= ( Y1 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f532]) ).
thf(f532,plain,
( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( lam @ Y0 ) @ Y1 )
= ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sub @ Y2 @ Y0 ) @ Y1 )
= ( sub @ Y2 @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y1 @ Y2 ) @ Y0 )
= ( push @ ( sub @ Y1 @ Y0 ) @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y0 )
= ( ap @ Y1 @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y3 )
= ( ap @ Y0 @ Y1 ) )
=> ( 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] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y3 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y2 ) @ Y3 )
= ( Y1 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f523]) ).
thf(f523,plain,
( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( lam @ Y0 ) @ Y1 )
= ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sub @ Y2 @ Y0 ) @ Y1 )
= ( sub @ Y2 @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y1 @ Y2 ) @ Y0 )
= ( push @ ( sub @ Y1 @ Y0 ) @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y0 )
= ( ap @ Y1 @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y3 )
= ( ap @ Y0 @ Y1 ) )
=> ( 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] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y3 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y2 ) @ Y3 )
= ( Y1 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f522]) ).
thf(f522,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( ap @ Y2 @ Y1 ) @ Y0 )
= ( ap @ ( sub @ Y2 @ Y0 ) @ ( sub @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( lam @ Y0 ) @ Y1 )
= ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sub @ Y2 @ Y0 ) @ Y1 )
= ( sub @ Y2 @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y1 @ Y2 ) @ Y0 )
= ( push @ ( sub @ Y1 @ Y0 ) @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y0 )
= ( ap @ Y1 @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y3 )
= ( ap @ Y0 @ Y1 ) )
=> ( 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] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y3 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y2 ) @ Y3 )
= ( Y1 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
!= $true ),
inference(beta_eta_normalization,[],[f521]) ).
thf(f521,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( ap @ Y2 @ Y1 ) @ Y0 )
= ( ap @ ( sub @ Y2 @ Y0 ) @ ( sub @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( lam @ Y0 ) @ Y1 )
= ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sub @ Y2 @ Y0 ) @ Y1 )
= ( sub @ Y2 @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y1 @ Y2 ) @ Y0 )
= ( push @ ( sub @ Y1 @ Y0 ) @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y0 )
= ( ap @ Y1 @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y3 )
= ( ap @ Y0 @ Y1 ) )
=> ( 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] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
& ( !! @ 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
@ Y0 )
= ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y2
@ id
@ Y3 ) )
=> ( Y2 = 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
@ Y3
@ id
@ Y2 )
= ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y1
@ id
@ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y2 ) @ Y3 )
= ( Y1 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ 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] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ 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] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) )
= ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 ) ) ) ) )
=> ~ ( ^ [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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f410,f488]) ).
thf(f488,plain,
( hoaslamnotvar_gthm
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( ap @ Y2 @ Y1 ) @ Y0 )
= ( ap @ ( sub @ Y2 @ Y0 ) @ ( sub @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( lam @ Y0 ) @ Y1 )
= ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sub @ Y2 @ Y0 ) @ Y1 )
= ( sub @ Y2 @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y1 @ Y2 ) @ Y0 )
= ( push @ ( sub @ Y1 @ Y0 ) @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y0 )
= ( ap @ Y1 @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y3 )
= ( ap @ Y0 @ Y1 ) )
=> ( 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] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
& ( !! @ 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
@ Y0 )
= ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y2
@ id
@ Y3 ) )
=> ( Y2 = 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
@ Y3
@ id
@ Y2 )
= ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y1
@ id
@ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y2 ) @ Y3 )
= ( Y1 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ 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] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ 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] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) )
= ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 ) ) ) ) )
=> ~ ( ^ [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,[],[f336,f381,f370,f418,f429,f397,f344,f390,f408,f438,f331,f335,f415,f434,f378,f432,f402,f399,f384,f437,f365,f380,f383,f363,f367,f416,f435,f423,f386,f449,f450,f451,f452,f453]) ).
thf(f453,plain,
( hoaslamnotvar
= ( !! @ ( 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 ) ) ) ) )
=> ~ ( ^ [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,[],[f442,f340,f443]) ).
thf(f443,plain,
( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( lam @ ( Y1 @ sh @ one ) ) ) ),
inference(cnf_transformation,[],[f310]) ).
thf(f310,plain,
( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( lam @ ( Y1 @ sh @ one ) ) ) ),
inference(fool_elimination,[],[f309]) ).
thf(f309,plain,
( ( ^ [X0: subst,X1: subst > term > term] : ( lam @ ( X1 @ sh @ one ) ) )
= hoaslam ),
inference(rectify,[],[f56]) ).
thf(f56,axiom,
( ( ^ [X2: subst,X10: subst > term > term] : ( lam @ ( X10 @ sh @ one ) ) )
= hoaslam ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoaslam) ).
thf(f340,plain,
( hoasvar
= ( ^ [Y0: subst,Y1: term,Y2: subst] : ( var @ ( sub @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f270]) ).
thf(f270,plain,
( hoasvar
= ( ^ [Y0: subst,Y1: term,Y2: subst] : ( var @ ( sub @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f269]) ).
thf(f269,plain,
( hoasvar
= ( ^ [X0: subst,X1: term,X2: subst] : ( var @ ( sub @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f57]) ).
thf(f57,axiom,
( hoasvar
= ( ^ [X2: subst,X0: term,X3: subst] : ( var @ ( sub @ X0 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasvar) ).
thf(f442,plain,
( hoaslamnotvar
= ( !! @ ( 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 ) ) ) ) )
=> ~ ( hoasvar @ id
@ ( hoaslam @ id
@ ^ [Y1: subst,Y2: term] : ( Y0 @ Y1 @ Y2 ) )
@ id ) ) ) ),
inference(cnf_transformation,[],[f172]) ).
thf(f172,plain,
( hoaslamnotvar
= ( !! @ ( 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 ) ) ) ) )
=> ~ ( hoasvar @ id
@ ( hoaslam @ id
@ ^ [Y1: subst,Y2: term] : ( Y0 @ Y1 @ Y2 ) )
@ id ) ) ) ),
inference(fool_elimination,[],[f171]) ).
thf(f171,plain,
! [X0: subst > term > term] :
( ( ! [X1: subst,X2: subst,X3: term] :
( ( X0 @ ( comp @ X2 @ X1 ) @ ( sub @ X3 @ X1 ) )
= ( sub @ ( X0 @ X2 @ X3 ) @ X1 ) )
=> ~ ( hoasvar @ id
@ ( hoaslam @ id
@ ^ [X4: subst,X5: term] : ( X0 @ X4 @ X5 ) )
@ id ) )
= hoaslamnotvar ),
inference(rectify,[],[f70]) ).
thf(f70,axiom,
! [X10: subst > term > term] :
( ( ! [X3: subst,X2: subst,X0: term] :
( ( 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/sandbox/benchmark/theBenchmark.p',hoaslamnotvar) ).
thf(f452,plain,
( hoaslamnotap
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ 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,[],[f430,f366,f443]) ).
thf(f366,plain,
( hoasap
= ( ^ [Y0: subst,Y1: term,Y2: subst,Y3: term] : ( ap @ ( sub @ Y1 @ Y2 ) @ Y3 ) ) ),
inference(cnf_transformation,[],[f186]) ).
thf(f186,plain,
( hoasap
= ( ^ [Y0: subst,Y1: term,Y2: subst,Y3: term] : ( ap @ ( sub @ Y1 @ Y2 ) @ Y3 ) ) ),
inference(fool_elimination,[],[f185]) ).
thf(f185,plain,
( hoasap
= ( ^ [X0: subst,X1: term,X2: subst,X3: term] : ( ap @ ( sub @ X1 @ X2 ) @ X3 ) ) ),
inference(rectify,[],[f55]) ).
thf(f55,axiom,
( hoasap
= ( ^ [X2: subst,X0: term,X3: subst,X1: term] : ( ap @ ( sub @ X0 @ X3 ) @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasap) ).
thf(f430,plain,
( hoaslamnotap
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( hoasap @ id @ Y2 @ id @ Y1 )
!= ( hoaslam @ id
@ ^ [Y3: subst,Y4: term] : ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f296]) ).
thf(f296,plain,
( hoaslamnotap
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( hoasap @ id @ Y2 @ id @ Y1 )
!= ( hoaslam @ id
@ ^ [Y3: subst,Y4: term] : ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f295]) ).
thf(f295,plain,
! [X0: subst > term > term] :
( ( ! [X1: subst,X2: term,X3: subst] :
( ( sub @ ( X0 @ X3 @ X2 ) @ X1 )
= ( X0 @ ( comp @ X3 @ X1 ) @ ( sub @ X2 @ X1 ) ) )
=> ! [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] :
( ( ! [X3: subst,X0: term,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/sandbox/benchmark/theBenchmark.p',hoaslamnotap) ).
thf(f451,plain,
( hoaslaminj
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y2 ) @ Y3 )
= ( Y1 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ 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] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f420,f443,f443]) ).
thf(f420,plain,
( hoaslaminj
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y2 ) @ Y3 )
= ( Y1 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ 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] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f231]) ).
thf(f231,plain,
( hoaslaminj
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y2 ) @ Y3 )
= ( Y1 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ 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] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f230]) ).
thf(f230,plain,
! [X0: subst > term > term] :
( ( ! [X1: term,X2: subst,X3: subst] :
( ( X0 @ ( comp @ X2 @ X3 ) @ ( sub @ X1 @ X3 ) )
= ( sub @ ( X0 @ X2 @ X1 ) @ X3 ) )
=> ! [X4: subst > term > term] :
( ! [X5: subst,X6: subst,X7: term] :
( ( sub @ ( X4 @ X5 @ X7 ) @ X6 )
= ( X4 @ ( comp @ X5 @ X6 ) @ ( sub @ X7 @ X6 ) ) )
=> ( ( ( hoaslam @ id
@ ^ [X8: subst,X9: term] : ( X0 @ X8 @ X9 ) )
= ( hoaslam @ id
@ ^ [X10: subst,X11: term] : ( X4 @ X10 @ X11 ) ) )
=> ! [X12: subst,X13: term] :
( ( X0 @ X12 @ X13 )
= ( X4 @ X12 @ X13 ) ) ) ) )
= hoaslaminj ),
inference(rectify,[],[f64]) ).
thf(f64,axiom,
! [X10: subst > term > term] :
( ( ! [X0: term,X2: subst,X3: subst] :
( ( sub @ ( X10 @ X2 @ X0 ) @ X3 )
= ( X10 @ ( comp @ X2 @ X3 ) @ ( sub @ X0 @ X3 ) ) )
=> ! [X11: subst > term > term] :
( ! [X2: subst,X3: subst,X0: term] :
( ( sub @ ( X11 @ X2 @ X0 ) @ X3 )
= ( X11 @ ( comp @ X2 @ X3 ) @ ( sub @ X0 @ X3 ) ) )
=> ( ( ( hoaslam @ id
@ ^ [X2: subst,X0: term] : ( X10 @ X2 @ X0 ) )
= ( hoaslam @ id
@ ^ [X2: subst,X0: term] : ( X11 @ X2 @ X0 ) ) )
=> ! [X2: subst,X0: term] :
( ( X10 @ X2 @ X0 )
= ( X11 @ X2 @ X0 ) ) ) ) )
= hoaslaminj ),
file('/export/starexec/sandbox/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
@ Y3
@ id
@ Y2 )
= ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y1
@ id
@ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f350,f366,f366]) ).
thf(f350,plain,
( hoasapinj2
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( hoasap @ id @ Y3 @ id @ Y2 )
= ( hoasap @ id @ Y1 @ id @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f118]) ).
thf(f118,plain,
( hoasapinj2
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( hoasap @ id @ Y3 @ id @ Y2 )
= ( hoasap @ id @ Y1 @ id @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f117]) ).
thf(f117,plain,
( hoasapinj2
= ( ! [X0: term,X1: term,X2: term,X3: term] :
( ( ( hoasap @ id @ X0 @ id @ X1 )
= ( hoasap @ id @ X2 @ id @ X3 ) )
=> ( X1 = X3 ) ) ) ),
inference(rectify,[],[f61]) ).
thf(f61,axiom,
( hoasapinj2
= ( ! [X0: term,X6: term,X1: term,X7: term] :
( ( ( hoasap @ id @ X0 @ id @ X6 )
= ( hoasap @ id @ X1 @ id @ X7 ) )
=> ( X6 = X7 ) ) ) ),
file('/export/starexec/sandbox/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
@ Y0 )
= ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y2
@ id
@ Y3 ) )
=> ( Y2 = Y1 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f369,f366,f366]) ).
thf(f369,plain,
( hoasapinj1
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( hoasap @ id @ Y1 @ id @ Y0 )
= ( hoasap @ id @ Y2 @ id @ Y3 ) )
=> ( Y2 = Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f282]) ).
thf(f282,plain,
( hoasapinj1
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( hoasap @ id @ Y1 @ id @ Y0 )
= ( hoasap @ id @ Y2 @ id @ Y3 ) )
=> ( Y2 = Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f281]) ).
thf(f281,plain,
! [X0: term,X1: term,X2: term,X3: term] :
( ( ( ( hoasap @ id @ X2 @ id @ X3 )
= ( hoasap @ id @ X1 @ id @ X0 ) )
=> ( X1 = X2 ) )
= hoasapinj1 ),
inference(rectify,[],[f58]) ).
thf(f58,axiom,
! [X6: term,X0: term,X1: term,X7: term] :
( ( ( ( hoasap @ id @ X0 @ id @ X6 )
= ( hoasap @ id @ X1 @ id @ X7 ) )
=> ( X0 = X1 ) )
= hoasapinj1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasapinj1) ).
thf(f386,plain,
( termmset
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ) ),
inference(cnf_transformation,[],[f155]) ).
thf(f155,plain,
( termmset
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ) ),
inference(fool_elimination,[],[f154]) ).
thf(f154,plain,
( ( termmset
= ( ! [X0: term] :
( ( sub @ X0 @ id )
= X0 ) ) )
& ! [X1: subst,X2: subst,X3: term] :
( ( sub @ X3 @ ( comp @ X2 @ X1 ) )
= ( sub @ ( sub @ X3 @ X2 ) @ X1 ) ) ),
inference(rectify,[],[f52]) ).
thf(f52,axiom,
( ( termmset
= ( ! [X0: term] :
( ( sub @ X0 @ id )
= X0 ) ) )
& ! [X3: subst,X2: subst,X0: term] :
( ( sub @ ( sub @ X0 @ X2 ) @ X3 )
= ( sub @ X0 @ ( comp @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',termmset) ).
thf(f423,plain,
( substmonoid
= ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f207]) ).
thf(f207,plain,
( substmonoid
= ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f206]) ).
thf(f206,plain,
( ! [X0: subst,X1: subst,X2: subst] :
( ( comp @ X2 @ ( comp @ X1 @ X0 ) )
= ( comp @ ( comp @ X2 @ X1 ) @ X0 ) )
& ! [X3: subst] :
( ( comp @ X3 @ id )
= X3 )
& ! [X4: subst] :
( ( ( comp @ id @ X4 )
= X4 )
= substmonoid ) ),
inference(rectify,[],[f49]) ).
thf(f49,axiom,
( ! [X4: subst,X3: subst,X2: subst] :
( ( comp @ ( comp @ X2 @ X3 ) @ X4 )
= ( comp @ X2 @ ( comp @ X3 @ X4 ) ) )
& ! [X2: subst] :
( ( comp @ X2 @ id )
= X2 )
& ! [X2: subst] :
( ( ( comp @ id @ X2 )
= X2 )
= substmonoid ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',substmonoid) ).
thf(f435,plain,
( induction2
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f128]) ).
thf(f128,plain,
( induction2
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f127]) ).
thf(f127,plain,
! [X0: term > $o] :
( ( ! [X1: term] :
( ( var @ X1 )
=> ( X0 @ X1 ) )
=> ( ! [X2: term,X3: term] :
( ( X0 @ X3 )
=> ( ( X0 @ X2 )
=> ( X0 @ ( ap @ X3 @ X2 ) ) ) )
=> ( ! [X4: term] :
( ! [X5: term] :
( ( X0 @ X5 )
=> ( X0 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X0 @ ( lam @ X4 ) ) )
=> ! [X6: term] : ( X0 @ X6 ) ) ) )
= induction2 ),
inference(rectify,[],[f46]) ).
thf(f46,axiom,
! [X5: term > $o] :
( ( ! [X0: term] :
( ( var @ X0 )
=> ( X5 @ X0 ) )
=> ( ! [X1: term,X0: term] :
( ( X5 @ X0 )
=> ( ( X5 @ X1 )
=> ( X5 @ ( ap @ X0 @ X1 ) ) ) )
=> ( ! [X0: term] :
( ! [X1: term] :
( ( X5 @ X1 )
=> ( X5 @ ( sub @ X0 @ ( push @ X1 @ id ) ) ) )
=> ( X5 @ ( lam @ X0 ) ) )
=> ! [X0: term] : ( X5 @ X0 ) ) ) )
= induction2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',induction2) ).
thf(f416,plain,
( induction2lem
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f174]) ).
thf(f174,plain,
( induction2lem
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f173]) ).
thf(f173,plain,
( induction2lem
= ( ! [X0: term > $o] :
( ! [X1: term,X2: term] :
( ( X0 @ X2 )
=> ( ( X0 @ X1 )
=> ( X0 @ ( ap @ X2 @ X1 ) ) ) )
=> ( ! [X3: term] :
( ! [X4: term] :
( ( X0 @ X4 )
=> ( X0 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X0 @ ( lam @ X3 ) ) )
=> ! [X5: term,X6: subst] :
( ! [X7: term] :
( ( var @ X7 )
=> ( X0 @ ( sub @ X7 @ X6 ) ) )
=> ( X0 @ ( sub @ X5 @ X6 ) ) ) ) ) ) ),
inference(rectify,[],[f43]) ).
thf(f43,axiom,
( induction2lem
= ( ! [X5: term > $o] :
( ! [X1: term,X0: term] :
( ( X5 @ X0 )
=> ( ( X5 @ X1 )
=> ( X5 @ ( ap @ X0 @ X1 ) ) ) )
=> ( ! [X0: term] :
( ! [X1: term] :
( ( X5 @ X1 )
=> ( X5 @ ( sub @ X0 @ ( push @ X1 @ id ) ) ) )
=> ( X5 @ ( lam @ X0 ) ) )
=> ! [X0: term,X2: subst] :
( ! [X1: term] :
( ( var @ X1 )
=> ( X5 @ ( sub @ X1 @ X2 ) ) )
=> ( X5 @ ( sub @ X0 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',induction2lem) ).
thf(f367,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,[],[f130]) ).
thf(f130,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,[],[f129]) ).
thf(f129,plain,
! [X0: term,X1: subst,X2: term > $o] :
( ( ! [X3: term] :
( ( var @ X3 )
=> ( X2 @ ( sub @ X3 @ X1 ) ) )
=> ( ( X2 @ X0 )
=> ! [X4: term] :
( ( var @ X4 )
=> ( X2 @ ( sub @ X4 @ ( push @ X0 @ X1 ) ) ) ) ) )
= pushprop ),
inference(rectify,[],[f39]) ).
thf(f39,axiom,
! [X0: term,X2: subst,X5: term > $o] :
( ( ! [X1: term] :
( ( var @ X1 )
=> ( X5 @ ( sub @ X1 @ X2 ) ) )
=> ( ( X5 @ X0 )
=> ! [X1: term] :
( ( var @ X1 )
=> ( X5 @ ( sub @ X1 @ ( push @ X0 @ X2 ) ) ) ) ) )
= pushprop ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop) ).
thf(f363,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,[],[f286]) ).
thf(f286,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,[],[f285]) ).
thf(f285,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/sandbox/benchmark/theBenchmark.p',induction) ).
thf(f383,plain,
( lamnotvar
= ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f258]) ).
thf(f258,plain,
( lamnotvar
= ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) ) ),
inference(fool_elimination,[],[f257]) ).
thf(f257,plain,
( lamnotvar
= ( ! [X0: term] :
~ ( var @ ( lam @ X0 ) ) ) ),
inference(rectify,[],[f22]) ).
thf(f22,axiom,
( lamnotvar
= ( ! [X0: term] :
~ ( var @ ( lam @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamnotvar) ).
thf(f380,plain,
( apnotvar
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f136]) ).
thf(f136,plain,
( apnotvar
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f135]) ).
thf(f135,plain,
! [X0: term,X1: term] :
( ( ~ ( var @ ( ap @ X0 @ X1 ) ) )
= apnotvar ),
inference(rectify,[],[f21]) ).
thf(f21,axiom,
! [X0: term,X1: term] :
( ( ~ ( var @ ( ap @ X0 @ X1 ) ) )
= apnotvar ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apnotvar) ).
thf(f365,plain,
( lamnotap
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f300]) ).
thf(f300,plain,
( lamnotap
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f299]) ).
thf(f299,plain,
( lamnotap
= ( ! [X0: term,X1: term,X2: term] :
( ( lam @ X0 )
!= ( ap @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f20]) ).
thf(f20,axiom,
( lamnotap
= ( ! [X0: term,X6: term,X1: term] :
( ( lam @ X0 )
!= ( ap @ X1 @ X6 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamnotap) ).
thf(f437,plain,
( shinj
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f156]) ).
thf(f156,plain,
( shinj
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f19,axiom,
( shinj
= ( ! [X0: term,X1: term] :
( ( ( sub @ X0 @ sh )
= ( sub @ X1 @ sh ) )
=> ( X0 = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',shinj) ).
thf(f384,plain,
( laminj
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f213]) ).
thf(f213,plain,
( laminj
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(fool_elimination,[],[f212]) ).
thf(f212,plain,
( laminj
= ( ! [X0: term,X1: term] :
( ( ( lam @ X0 )
= ( lam @ X1 ) )
=> ( X0 = X1 ) ) ) ),
inference(rectify,[],[f18]) ).
thf(f18,axiom,
( laminj
= ( ! [X1: term,X0: term] :
( ( ( lam @ X0 )
= ( lam @ X1 ) )
=> ( X0 = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',laminj) ).
thf(f399,plain,
( apinj2
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y3 )
= ( ap @ Y0 @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f288]) ).
thf(f288,plain,
( apinj2
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y3 )
= ( ap @ Y0 @ Y1 ) )
=> ( Y3 = Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f287]) ).
thf(f287,plain,
( apinj2
= ( ! [X0: term,X1: term,X2: term,X3: term] :
( ( ( ap @ X1 @ X0 )
= ( ap @ X3 @ X2 ) )
=> ( X0 = X2 ) ) ) ),
inference(rectify,[],[f17]) ).
thf(f17,axiom,
( apinj2
= ( ! [X6: term,X0: term,X7: term,X1: term] :
( ( ( ap @ X0 @ X6 )
= ( ap @ X1 @ X7 ) )
=> ( X6 = X7 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apinj2) ).
thf(f402,plain,
( apinj1
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y0 )
= ( ap @ Y1 @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f134]) ).
thf(f134,plain,
( apinj1
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y0 )
= ( ap @ Y1 @ Y2 ) )
=> ( Y3 = Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f133]) ).
thf(f133,plain,
! [X0: term,X1: term,X2: term,X3: term] :
( ( ( ( ap @ X0 @ X3 )
= ( ap @ X2 @ X1 ) )
=> ( X0 = X2 ) )
= apinj1 ),
inference(rectify,[],[f16]) ).
thf(f16,axiom,
! [X1: term,X6: term,X0: term,X7: term] :
( ( ( ( ap @ X0 @ X6 )
= ( ap @ X1 @ X7 ) )
=> ( X0 = X1 ) )
= apinj1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apinj1) ).
thf(f432,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,[],[f245]) ).
thf(f245,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,[],[f244]) ).
thf(f244,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/sandbox/benchmark/theBenchmark.p',ulamvarind) ).
thf(f378,plain,
( ulamvarsh
= ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) ) ),
inference(cnf_transformation,[],[f201]) ).
thf(f201,plain,
( ulamvarsh
= ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) ) ),
inference(fool_elimination,[],[f200]) ).
thf(f200,plain,
! [X0: term] :
( ( ( var @ X0 )
=> ( var @ ( sub @ X0 @ sh ) ) )
= ulamvarsh ),
inference(rectify,[],[f14]) ).
thf(f14,axiom,
! [X0: term] :
( ( ( var @ X0 )
=> ( var @ ( sub @ X0 @ sh ) ) )
= ulamvarsh ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ulamvarsh) ).
thf(f434,plain,
( ulamvar1
= ( var @ one ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f13,axiom,
( ulamvar1
= ( var @ one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ulamvar1) ).
thf(f415,plain,
( axscons
= ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) ) ),
inference(cnf_transformation,[],[f243]) ).
thf(f243,plain,
( axscons
= ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) ) ),
inference(fool_elimination,[],[f242]) ).
thf(f242,plain,
! [X0: subst] :
( ( ( push @ ( sub @ one @ X0 ) @ ( comp @ sh @ X0 ) )
= X0 )
= axscons ),
inference(rectify,[],[f12]) ).
thf(f12,axiom,
! [X2: subst] :
( ( ( push @ ( sub @ one @ X2 ) @ ( comp @ sh @ X2 ) )
= X2 )
= axscons ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axscons) ).
thf(f335,plain,
( axvarshift
= ( id
= ( push @ one @ sh ) ) ),
inference(cnf_transformation,[],[f197]) ).
thf(f197,plain,
( axvarshift
= ( id
= ( push @ one @ sh ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f11,axiom,
( ( id
= ( push @ one @ sh ) )
= axvarshift ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axvarshift) ).
thf(f331,plain,
( axidr
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) ),
inference(cnf_transformation,[],[f227]) ).
thf(f227,plain,
( axidr
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) ),
inference(fool_elimination,[],[f226]) ).
thf(f226,plain,
( axidr
= ( ! [X0: subst] :
( ( comp @ X0 @ id )
= X0 ) ) ),
inference(rectify,[],[f10]) ).
thf(f10,axiom,
( axidr
= ( ! [X2: subst] :
( ( comp @ X2 @ id )
= X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axidr) ).
thf(f438,plain,
( axmap
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y1 @ Y2 ) @ Y0 )
= ( push @ ( sub @ Y1 @ Y0 ) @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f196]) ).
thf(f196,plain,
( axmap
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y1 @ Y2 ) @ Y0 )
= ( push @ ( sub @ Y1 @ Y0 ) @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f195]) ).
thf(f195,plain,
( axmap
= ( ! [X0: subst,X1: term,X2: subst] :
( ( comp @ ( push @ X1 @ X0 ) @ X2 )
= ( push @ ( sub @ X1 @ X2 ) @ ( comp @ X0 @ X2 ) ) ) ) ),
inference(rectify,[],[f9]) ).
thf(f9,axiom,
( axmap
= ( ! [X2: subst,X0: term,X3: subst] :
( ( comp @ ( push @ X0 @ X2 ) @ X3 )
= ( push @ ( sub @ X0 @ X3 ) @ ( comp @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axmap) ).
thf(f408,plain,
( axassoc
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f292]) ).
thf(f292,plain,
( axassoc
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y2 @ Y1 ) @ Y0 )
= ( comp @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f291]) ).
thf(f291,plain,
! [X0: subst,X1: subst,X2: subst] :
( ( ( comp @ ( comp @ X0 @ X1 ) @ X2 )
= ( comp @ X0 @ ( comp @ X1 @ X2 ) ) )
= axassoc ),
inference(rectify,[],[f8]) ).
thf(f8,axiom,
! [X2: subst,X3: subst,X4: subst] :
( ( ( comp @ ( comp @ X2 @ X3 ) @ X4 )
= ( comp @ X2 @ ( comp @ X3 @ X4 ) ) )
= axassoc ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axassoc) ).
thf(f390,plain,
( axshiftcons
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) ) ),
inference(cnf_transformation,[],[f188]) ).
thf(f188,plain,
( axshiftcons
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) ) ),
inference(fool_elimination,[],[f187]) ).
thf(f187,plain,
( axshiftcons
= ( ! [X0: subst,X1: term] :
( ( comp @ sh @ ( push @ X1 @ X0 ) )
= X0 ) ) ),
inference(rectify,[],[f7]) ).
thf(f7,axiom,
( axshiftcons
= ( ! [X2: subst,X0: term] :
( ( comp @ sh @ ( push @ X0 @ X2 ) )
= X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axshiftcons) ).
thf(f344,plain,
( axidl
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) ),
inference(cnf_transformation,[],[f147]) ).
thf(f147,plain,
( axidl
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) ),
inference(fool_elimination,[],[f146]) ).
thf(f146,plain,
( axidl
= ( ! [X0: subst] :
( ( comp @ id @ X0 )
= X0 ) ) ),
inference(rectify,[],[f6]) ).
thf(f6,axiom,
( axidl
= ( ! [X2: subst] :
( ( comp @ id @ X2 )
= X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axidl) ).
thf(f397,plain,
( axclos
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sub @ Y2 @ Y0 ) @ Y1 )
= ( sub @ Y2 @ ( comp @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f272]) ).
thf(f272,plain,
( axclos
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sub @ Y2 @ Y0 ) @ Y1 )
= ( sub @ Y2 @ ( comp @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f271]) ).
thf(f271,plain,
( axclos
= ( ! [X0: term,X1: subst,X2: subst] :
( ( sub @ ( sub @ X0 @ X2 ) @ X1 )
= ( sub @ X0 @ ( comp @ X2 @ X1 ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f5,axiom,
( axclos
= ( ! [X0: term,X3: subst,X2: subst] :
( ( sub @ ( sub @ X0 @ X2 ) @ X3 )
= ( sub @ X0 @ ( comp @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axclos) ).
thf(f429,plain,
( axabs
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( lam @ Y0 ) @ Y1 )
= ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f149]) ).
thf(f149,plain,
( axabs
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( lam @ Y0 ) @ Y1 )
= ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f148]) ).
thf(f148,plain,
! [X0: subst,X1: term] :
( ( ( sub @ ( lam @ X1 ) @ X0 )
= ( lam @ ( sub @ X1 @ ( push @ one @ ( comp @ X0 @ sh ) ) ) ) )
= axabs ),
inference(rectify,[],[f4]) ).
thf(f4,axiom,
! [X2: subst,X0: term] :
( ( ( sub @ ( lam @ X0 ) @ X2 )
= ( lam @ ( sub @ X0 @ ( push @ one @ ( comp @ X2 @ sh ) ) ) ) )
= axabs ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axabs) ).
thf(f418,plain,
( axvarid
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ),
inference(cnf_transformation,[],[f254]) ).
thf(f254,plain,
( axvarid
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f3,axiom,
( axvarid
= ( ! [X0: term] :
( ( sub @ X0 @ id )
= X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axvarid) ).
thf(f370,plain,
( axvarcons
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) ) ),
inference(cnf_transformation,[],[f239]) ).
thf(f239,plain,
( axvarcons
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) ) ),
inference(fool_elimination,[],[f238]) ).
thf(f238,plain,
( axvarcons
= ( ! [X0: subst,X1: term] :
( ( sub @ one @ ( push @ X1 @ X0 ) )
= X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
( axvarcons
= ( ! [X2: subst,X0: term] :
( ( sub @ one @ ( push @ X0 @ X2 ) )
= X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axvarcons) ).
thf(f381,plain,
( axapp
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( ap @ Y2 @ Y1 ) @ Y0 )
= ( ap @ ( sub @ Y2 @ Y0 ) @ ( sub @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f139]) ).
thf(f139,plain,
( axapp
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( ap @ Y2 @ Y1 ) @ Y0 )
= ( ap @ ( sub @ Y2 @ Y0 ) @ ( sub @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f1,axiom,
( axapp
= ( ! [X0: term,X1: term,X2: subst] :
( ( sub @ ( ap @ X0 @ X1 ) @ X2 )
= ( ap @ ( sub @ X0 @ X2 ) @ ( sub @ X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axapp) ).
thf(f336,plain,
( hoaslamnotvar_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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f314]) ).
thf(f314,plain,
( hoaslamnotvar_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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f313]) ).
thf(f313,plain,
( ( hoaslamnotvar_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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f71]) ).
thf(f71,axiom,
( ( hoaslamnotvar_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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoaslamnotvar_gthm) ).
thf(f410,plain,
hoaslamnotvar_gthm != $true,
inference(cnf_transformation,[],[f329]) ).
thf(f329,plain,
hoaslamnotvar_gthm != $true,
inference(flattening,[],[f320]) ).
thf(f320,plain,
hoaslamnotvar_gthm != $true,
inference(fool_elimination,[],[f319]) ).
thf(f319,plain,
~ hoaslamnotvar_gthm,
inference(rectify,[],[f115]) ).
thf(f115,negated_conjecture,
~ hoaslamnotvar_gthm,
inference(negated_conjecture,[],[f114]) ).
thf(f114,conjecture,
hoaslamnotvar_gthm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f1011,plain,
( $true
= ( var @ ( lam @ ( sK41 @ sh @ one ) ) ) ),
inference(backward_demodulation,[],[f1010,f925]) ).
thf(f925,plain,
! [X1: term] :
( ( sub @ X1 @ id )
= X1 ),
inference(equality_proxy_clausification,[],[f924]) ).
thf(f924,plain,
! [X1: term] :
( $true
= ( ( sub @ X1 @ id )
= X1 ) ),
inference(beta_eta_normalization,[],[f923]) ).
thf(f923,plain,
! [X1: term] :
( ( ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 )
@ X1 )
= $true ),
inference(pi_clausification,[],[f914]) ).
thf(f914,plain,
( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
= $true ),
inference(binary_proxy_clausification,[],[f913]) ).
thf(f913,plain,
( $true
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ) ),
inference(binary_proxy_clausification,[],[f893]) ).
thf(f893,plain,
( $false
= ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y3 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y2 ) @ Y3 )
= ( Y1 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f835]) ).
thf(f835,plain,
( $false
= ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y3 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y2 ) @ Y3 )
= ( Y1 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f762]) ).
thf(f762,plain,
( $false
= ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y3 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y2 ) @ Y3 )
= ( Y1 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f742]) ).
thf(f742,plain,
( $false
= ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y3 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y2 ) @ Y3 )
= ( Y1 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f692]) ).
thf(f692,plain,
( $false
= ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y3 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y2 ) @ Y3 )
= ( Y1 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f687]) ).
thf(f687,plain,
( $false
= ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ 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 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) )
= ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
& ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y3 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y2 ) @ Y3 )
= ( Y1 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f680]) ).
thf(f1010,plain,
( ( var @ ( sub @ ( lam @ ( sK41 @ sh @ one ) ) @ id ) )
= $true ),
inference(not_proxy_clausification,[],[f1001]) ).
thf(f1001,plain,
( $false
= ( ~ ( var @ ( sub @ ( lam @ ( sK41 @ sh @ one ) ) @ id ) ) ) ),
inference(binary_proxy_clausification,[],[f1000]) ).
thf(f1000,plain,
( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sK41 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y0 @ Y2 ) )
= ( sub @ ( sK41 @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( sK41 @ sh @ one ) ) @ id ) ) ) ),
inference(beta_eta_normalization,[],[f999]) ).
thf(f999,plain,
( $false
= ( ^ [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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) )
@ sK41 ) ),
inference(sigma_clausification,[],[f981]) ).
thf(f981,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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) ) ),
inference(binary_proxy_clausification,[],[f952]) ).
thf(f952,plain,
( $false
= ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f939]) ).
thf(f939,plain,
( $false
= ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y2 ) @ Y3 )
= ( Y1 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f926]) ).
thf(f926,plain,
( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y2 ) @ Y3 )
= ( Y1 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f912]) ).
thf(f912,plain,
( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y3 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y2 )
= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y2 ) @ Y3 )
= ( Y1 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f893]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : ALG260^1 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.10/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.35 % Computer : n028.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sat May 18 23:42:08 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a TH0_THM_EQU_NAR problem
% 0.15/0.36 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.41 % (17755)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.22/0.41 % (17759)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)
% 0.22/0.41 % (17759)Instruction limit reached!
% 0.22/0.41 % (17759)------------------------------
% 0.22/0.41 % (17759)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.41 % (17759)Termination reason: Unknown
% 0.22/0.41 % (17759)Termination phase: shuffling
% 0.22/0.41
% 0.22/0.41 % (17759)Memory used [KB]: 1279
% 0.22/0.41 % (17759)Time elapsed: 0.003 s
% 0.22/0.41 % (17759)Instructions burned: 2 (million)
% 0.22/0.41 % (17759)------------------------------
% 0.22/0.41 % (17759)------------------------------
% 0.22/0.41 % (17757)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)
% 0.22/0.41 % (17760)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)
% 0.22/0.41 % (17756)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)
% 0.22/0.41 % (17758)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.22/0.41 % (17761)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.22/0.41 % (17758)Instruction limit reached!
% 0.22/0.41 % (17758)------------------------------
% 0.22/0.41 % (17758)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.41 % (17758)Termination reason: Unknown
% 0.22/0.41 % (17758)Termination phase: shuffling
% 0.22/0.41
% 0.22/0.41 % (17758)Memory used [KB]: 1151
% 0.22/0.41 % (17758)Time elapsed: 0.004 s
% 0.22/0.41 % (17758)Instructions burned: 2 (million)
% 0.22/0.41 % (17758)------------------------------
% 0.22/0.41 % (17758)------------------------------
% 0.22/0.41 % (17762)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)
% 0.22/0.41 % (17756)Instruction limit reached!
% 0.22/0.41 % (17756)------------------------------
% 0.22/0.41 % (17756)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.41 % (17756)Termination reason: Unknown
% 0.22/0.41 % (17756)Termination phase: shuffling
% 0.22/0.41
% 0.22/0.41 % (17756)Memory used [KB]: 1279
% 0.22/0.41 % (17756)Time elapsed: 0.006 s
% 0.22/0.41 % (17756)Instructions burned: 4 (million)
% 0.22/0.41 % (17756)------------------------------
% 0.22/0.41 % (17756)------------------------------
% 0.22/0.42 % (17762)Instruction limit reached!
% 0.22/0.42 % (17762)------------------------------
% 0.22/0.42 % (17762)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (17762)Termination reason: Unknown
% 0.22/0.42 % (17762)Termination phase: shuffling
% 0.22/0.42
% 0.22/0.42 % (17762)Memory used [KB]: 1279
% 0.22/0.42 % (17762)Time elapsed: 0.005 s
% 0.22/0.42 % (17762)Instructions burned: 3 (million)
% 0.22/0.42 % (17762)------------------------------
% 0.22/0.42 % (17762)------------------------------
% 0.22/0.43 % (17761)Instruction limit reached!
% 0.22/0.43 % (17761)------------------------------
% 0.22/0.43 % (17761)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.43 % (17763)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)
% 0.22/0.43 % (17761)Termination reason: Unknown
% 0.22/0.43 % (17761)Termination phase: Property scanning
% 0.22/0.43
% 0.22/0.43 % (17761)Memory used [KB]: 1663
% 0.22/0.43 % (17761)Time elapsed: 0.017 s
% 0.22/0.43 % (17761)Instructions burned: 18 (million)
% 0.22/0.43 % (17761)------------------------------
% 0.22/0.43 % (17761)------------------------------
% 0.22/0.43 % (17757)Instruction limit reached!
% 0.22/0.43 % (17757)------------------------------
% 0.22/0.43 % (17757)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.43 % (17757)Termination reason: Unknown
% 0.22/0.43 % (17757)Termination phase: shuffling
% 0.22/0.43
% 0.22/0.43 % (17757)Memory used [KB]: 1791
% 0.22/0.43 % (17757)Time elapsed: 0.019 s
% 0.22/0.43 % (17757)Instructions burned: 27 (million)
% 0.22/0.43 % (17757)------------------------------
% 0.22/0.43 % (17757)------------------------------
% 0.22/0.43 % (17760)Refutation not found, incomplete strategy
% 0.22/0.43 % (17760)------------------------------
% 0.22/0.43 % (17760)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.43 % (17760)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.43
% 0.22/0.43
% 0.22/0.43 % (17760)Memory used [KB]: 6140
% 0.22/0.43 % (17760)Time elapsed: 0.019 s
% 0.22/0.43 % (17760)Instructions burned: 28 (million)
% 0.22/0.43 % (17760)------------------------------
% 0.22/0.43 % (17760)------------------------------
% 0.22/0.43 % (17765)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)
% 0.22/0.43 % (17764)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)
% 0.22/0.43 % (17765)Instruction limit reached!
% 0.22/0.43 % (17765)------------------------------
% 0.22/0.43 % (17765)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.43 % (17765)Termination reason: Unknown
% 0.22/0.43 % (17765)Termination phase: shuffling
% 0.22/0.43
% 0.22/0.43 % (17765)Memory used [KB]: 1279
% 0.22/0.43 % (17765)Time elapsed: 0.003 s
% 0.22/0.43 % (17765)Instructions burned: 3 (million)
% 0.22/0.43 % (17765)------------------------------
% 0.22/0.43 % (17765)------------------------------
% 0.22/0.44 % (17766)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)
% 0.22/0.44 % (17767)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.22/0.44 % (17764)Instruction limit reached!
% 0.22/0.44 % (17764)------------------------------
% 0.22/0.44 % (17764)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.44 % (17764)Termination reason: Unknown
% 0.22/0.44 % (17764)Termination phase: Property scanning
% 0.22/0.44
% 0.22/0.44 % (17764)Memory used [KB]: 1663
% 0.22/0.44 % (17764)Time elapsed: 0.011 s
% 0.22/0.44 % (17764)Instructions burned: 16 (million)
% 0.22/0.44 % (17764)------------------------------
% 0.22/0.44 % (17764)------------------------------
% 0.22/0.44 % (17768)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.22/0.44 % (17763)Instruction limit reached!
% 0.22/0.44 % (17763)------------------------------
% 0.22/0.44 % (17763)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.44 % (17763)Termination reason: Unknown
% 0.22/0.44 % (17763)Termination phase: Property scanning
% 0.22/0.44
% 0.22/0.44 % (17763)Memory used [KB]: 1791
% 0.22/0.44 % (17763)Time elapsed: 0.020 s
% 0.22/0.44 % (17763)Instructions burned: 37 (million)
% 0.22/0.44 % (17763)------------------------------
% 0.22/0.44 % (17763)------------------------------
% 0.22/0.44 % (17769)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.22/0.45 % (17767)Instruction limit reached!
% 0.22/0.45 % (17767)------------------------------
% 0.22/0.45 % (17767)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.45 % (17767)Termination reason: Unknown
% 0.22/0.45 % (17767)Termination phase: shuffling
% 0.22/0.45
% 0.22/0.45 % (17767)Memory used [KB]: 1407
% 0.22/0.45 % (17767)Time elapsed: 0.005 s
% 0.22/0.45 % (17767)Instructions burned: 7 (million)
% 0.22/0.45 % (17767)------------------------------
% 0.22/0.45 % (17767)------------------------------
% 0.22/0.45 % (17769)Instruction limit reached!
% 0.22/0.45 % (17769)------------------------------
% 0.22/0.45 % (17769)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.45 % (17769)Termination reason: Unknown
% 0.22/0.45 % (17769)Termination phase: shuffling
% 0.22/0.45
% 0.22/0.45 % (17769)Memory used [KB]: 1279
% 0.22/0.45 % (17769)Time elapsed: 0.004 s
% 0.22/0.45 % (17769)Instructions burned: 4 (million)
% 0.22/0.45 % (17769)------------------------------
% 0.22/0.45 % (17769)------------------------------
% 0.22/0.45 % (17770)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.22/0.45 % (17768)Instruction limit reached!
% 0.22/0.45 % (17768)------------------------------
% 0.22/0.45 % (17768)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.45 % (17768)Termination reason: Unknown
% 0.22/0.45 % (17768)Termination phase: shuffling
% 0.22/0.45
% 0.22/0.45 % (17768)Memory used [KB]: 1535
% 0.22/0.45 % (17768)Time elapsed: 0.010 s
% 0.22/0.45 % (17768)Instructions burned: 16 (million)
% 0.22/0.45 % (17768)------------------------------
% 0.22/0.45 % (17768)------------------------------
% 0.22/0.45 % (17770)Instruction limit reached!
% 0.22/0.45 % (17770)------------------------------
% 0.22/0.45 % (17770)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.45 % (17770)Termination reason: Unknown
% 0.22/0.45 % (17770)Termination phase: shuffling
% 0.22/0.45
% 0.22/0.45 % (17770)Memory used [KB]: 1279
% 0.22/0.45 % (17770)Time elapsed: 0.004 s
% 0.22/0.45 % (17770)Instructions burned: 4 (million)
% 0.22/0.45 % (17770)------------------------------
% 0.22/0.45 % (17770)------------------------------
% 0.22/0.46 % (17771)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.22/0.46 % (17772)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.22/0.46 % (17773)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.22/0.46 % (17771)Instruction limit reached!
% 0.22/0.46 % (17771)------------------------------
% 0.22/0.46 % (17771)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.46 % (17771)Termination reason: Unknown
% 0.22/0.46 % (17771)Termination phase: shuffling
% 0.22/0.46
% 0.22/0.46 % (17771)Memory used [KB]: 1407
% 0.22/0.46 % (17771)Time elapsed: 0.006 s
% 0.22/0.46 % (17771)Instructions burned: 8 (million)
% 0.22/0.46 % (17771)------------------------------
% 0.22/0.46 % (17771)------------------------------
% 0.22/0.46 % (17772)Instruction limit reached!
% 0.22/0.46 % (17772)------------------------------
% 0.22/0.46 % (17772)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.46 % (17772)Termination reason: Unknown
% 0.22/0.46 % (17772)Termination phase: shuffling
% 0.22/0.46
% 0.22/0.46 % (17772)Memory used [KB]: 1279
% 0.22/0.46 % (17772)Time elapsed: 0.004 s
% 0.22/0.46 % (17772)Instructions burned: 4 (million)
% 0.22/0.46 % (17772)------------------------------
% 0.22/0.46 % (17772)------------------------------
% 0.22/0.46 % (17774)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.22/0.46 % (17773)Instruction limit reached!
% 0.22/0.46 % (17773)------------------------------
% 0.22/0.46 % (17773)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.46 % (17773)Termination reason: Unknown
% 0.22/0.46 % (17773)Termination phase: shuffling
% 0.22/0.46
% 0.22/0.46 % (17773)Memory used [KB]: 1279
% 0.22/0.46 % (17773)Time elapsed: 0.004 s
% 0.22/0.46 % (17773)Instructions burned: 4 (million)
% 0.22/0.46 % (17773)------------------------------
% 0.22/0.46 % (17773)------------------------------
% 0.22/0.47 % (17775)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.22/0.47 % (17776)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.22/0.47 % (17776)Instruction limit reached!
% 0.22/0.47 % (17776)------------------------------
% 0.22/0.47 % (17776)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.47 % (17776)Termination reason: Unknown
% 0.22/0.47 % (17776)Termination phase: shuffling
% 0.22/0.47
% 0.22/0.47 % (17776)Memory used [KB]: 1279
% 0.22/0.47 % (17776)Time elapsed: 0.005 s
% 0.22/0.47 % (17776)Instructions burned: 6 (million)
% 0.22/0.47 % (17776)------------------------------
% 0.22/0.47 % (17776)------------------------------
% 0.22/0.47 % (17774)Instruction limit reached!
% 0.22/0.47 % (17774)------------------------------
% 0.22/0.47 % (17774)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.47 % (17774)Termination reason: Unknown
% 0.22/0.47 % (17774)Termination phase: shuffling
% 0.22/0.47
% 0.22/0.47 % (17774)Memory used [KB]: 1663
% 0.22/0.47 % (17774)Time elapsed: 0.011 s
% 0.22/0.47 % (17774)Instructions burned: 18 (million)
% 0.22/0.47 % (17774)------------------------------
% 0.22/0.47 % (17774)------------------------------
% 0.22/0.48 % (17777)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on theBenchmark for (2999ds/902Mi)
% 0.22/0.48 % (17778)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on theBenchmark for (2999ds/21Mi)
% 0.22/0.48 % (17779)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.22/0.48 % (17779)Instruction limit reached!
% 0.22/0.48 % (17779)------------------------------
% 0.22/0.48 % (17779)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.48 % (17779)Termination reason: Unknown
% 0.22/0.48 % (17779)Termination phase: shuffling
% 0.22/0.48
% 0.22/0.48 % (17779)Memory used [KB]: 1279
% 0.22/0.48 % (17779)Time elapsed: 0.005 s
% 0.22/0.48 % (17779)Instructions burned: 6 (million)
% 0.22/0.48 % (17779)------------------------------
% 0.22/0.48 % (17779)------------------------------
% 0.22/0.48 % (17775)Refutation not found, incomplete strategy
% 0.22/0.48 % (17775)------------------------------
% 0.22/0.48 % (17775)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.48 % (17775)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.48
% 0.22/0.48
% 0.22/0.48 % (17775)Memory used [KB]: 6268
% 0.22/0.48 % (17775)Time elapsed: 0.018 s
% 0.22/0.48 % (17775)Instructions burned: 29 (million)
% 0.22/0.48 % (17775)------------------------------
% 0.22/0.48 % (17775)------------------------------
% 0.22/0.48 % (17780)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.22/0.48 % (17781)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2999ds/377Mi)
% 0.22/0.49 % (17778)Instruction limit reached!
% 0.22/0.49 % (17778)------------------------------
% 0.22/0.49 % (17778)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.49 % (17778)Termination reason: Unknown
% 0.22/0.49 % (17778)Termination phase: shuffling
% 0.22/0.49
% 0.22/0.49 % (17778)Memory used [KB]: 1663
% 0.22/0.49 % (17778)Time elapsed: 0.013 s
% 0.22/0.49 % (17780)Instruction limit reached!
% 0.22/0.49 % (17780)------------------------------
% 0.22/0.49 % (17780)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.49 % (17780)Termination reason: Unknown
% 0.22/0.49 % (17780)Termination phase: shuffling
% 0.22/0.49
% 0.22/0.49 % (17780)Memory used [KB]: 1279
% 0.22/0.49 % (17780)Time elapsed: 0.005 s
% 0.22/0.49 % (17780)Instructions burned: 6 (million)
% 0.22/0.49 % (17780)------------------------------
% 0.22/0.49 % (17780)------------------------------
% 0.22/0.49 % (17778)Instructions burned: 22 (million)
% 0.22/0.49 % (17778)------------------------------
% 0.22/0.49 % (17778)------------------------------
% 0.22/0.49 % (17755)Instruction limit reached!
% 0.22/0.49 % (17755)------------------------------
% 0.22/0.49 % (17755)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.49 % (17755)Termination reason: Unknown
% 0.22/0.49 % (17755)Termination phase: Saturation
% 0.22/0.49
% 0.22/0.49 % (17755)Memory used [KB]: 6780
% 0.22/0.49 % (17755)Time elapsed: 0.091 s
% 0.22/0.49 % (17755)Instructions burned: 183 (million)
% 0.22/0.49 % (17755)------------------------------
% 0.22/0.49 % (17755)------------------------------
% 0.22/0.49 % (17782)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on theBenchmark for (2998ds/779Mi)
% 0.22/0.50 % (17783)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on theBenchmark for (2998ds/19Mi)
% 0.22/0.50 % (17784)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)
% 0.22/0.50 % (17785)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2998ds/17Mi)
% 0.22/0.51 % (17783)Instruction limit reached!
% 0.22/0.51 % (17783)------------------------------
% 0.22/0.51 % (17783)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.51 % (17783)Termination reason: Unknown
% 0.22/0.51 % (17783)Termination phase: shuffling
% 0.22/0.51
% 0.22/0.51 % (17783)Memory used [KB]: 1663
% 0.22/0.51 % (17783)Time elapsed: 0.012 s
% 0.22/0.51 % (17783)Instructions burned: 20 (million)
% 0.22/0.51 % (17783)------------------------------
% 0.22/0.51 % (17783)------------------------------
% 0.22/0.51 % (17786)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi)
% 0.22/0.51 % (17785)Instruction limit reached!
% 0.22/0.51 % (17785)------------------------------
% 0.22/0.51 % (17785)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.51 % (17785)Termination reason: Unknown
% 0.22/0.51 % (17785)Termination phase: shuffling
% 0.22/0.51
% 0.22/0.51 % (17785)Memory used [KB]: 1663
% 0.22/0.51 % (17785)Time elapsed: 0.011 s
% 0.22/0.51 % (17785)Instructions burned: 18 (million)
% 0.22/0.51 % (17785)------------------------------
% 0.22/0.51 % (17785)------------------------------
% 0.22/0.51 % (17786)Instruction limit reached!
% 0.22/0.51 % (17786)------------------------------
% 0.22/0.51 % (17786)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.51 % (17786)Termination reason: Unknown
% 0.22/0.51 % (17786)Termination phase: shuffling
% 0.22/0.51
% 0.22/0.51 % (17786)Memory used [KB]: 1279
% 0.22/0.51 % (17786)Time elapsed: 0.003 s
% 0.22/0.51 % (17786)Instructions burned: 3 (million)
% 0.22/0.51 % (17786)------------------------------
% 0.22/0.51 % (17786)------------------------------
% 0.22/0.52 % (17787)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on theBenchmark for (2998ds/30Mi)
% 0.22/0.52 % (17788)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on theBenchmark for (2998ds/127Mi)
% 0.22/0.53 % (17789)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on theBenchmark for (2998ds/100Mi)
% 0.22/0.53 % (17784)Refutation not found, incomplete strategy
% 0.22/0.53 % (17784)------------------------------
% 0.22/0.53 % (17784)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.53 % (17784)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.53
% 0.22/0.53
% 0.22/0.53 % (17784)Memory used [KB]: 6268
% 0.22/0.53 % (17784)Time elapsed: 0.032 s
% 0.22/0.53 % (17784)Instructions burned: 61 (million)
% 0.22/0.53 % (17784)------------------------------
% 0.22/0.53 % (17784)------------------------------
% 0.22/0.54 % (17787)Instruction limit reached!
% 0.22/0.54 % (17787)------------------------------
% 0.22/0.54 % (17787)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.54 % (17787)Termination reason: Unknown
% 0.22/0.54 % (17787)Termination phase: Property scanning
% 0.22/0.54
% 0.22/0.54 % (17787)Memory used [KB]: 1791
% 0.22/0.54 % (17787)Time elapsed: 0.017 s
% 0.22/0.54 % (17787)Instructions burned: 30 (million)
% 0.22/0.54 % (17787)------------------------------
% 0.22/0.54 % (17787)------------------------------
% 0.22/0.55 % (17790)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi)
% 0.22/0.55 % (17790)Instruction limit reached!
% 0.22/0.55 % (17790)------------------------------
% 0.22/0.55 % (17790)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.55 % (17790)Termination reason: Unknown
% 0.22/0.55 % (17790)Termination phase: shuffling
% 0.22/0.55
% 0.22/0.55 % (17790)Memory used [KB]: 1279
% 0.22/0.55 % (17790)Time elapsed: 0.003 s
% 0.22/0.55 % (17790)Instructions burned: 3 (million)
% 0.22/0.55 % (17790)------------------------------
% 0.22/0.55 % (17790)------------------------------
% 0.22/0.55 % (17791)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on theBenchmark for (2998ds/20Mi)
% 0.22/0.56 % (17791)Instruction limit reached!
% 0.22/0.56 % (17791)------------------------------
% 0.22/0.56 % (17791)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.56 % (17791)Termination reason: Unknown
% 0.22/0.56 % (17791)Termination phase: Property scanning
% 0.22/0.56
% 0.22/0.56 % (17791)Memory used [KB]: 1663
% 0.22/0.56 % (17791)Time elapsed: 0.013 s
% 0.22/0.56 % (17791)Instructions burned: 22 (million)
% 0.22/0.56 % (17791)------------------------------
% 0.22/0.56 % (17791)------------------------------
% 0.22/0.56 % (17792)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on theBenchmark for (2998ds/86Mi)
% 0.22/0.57 % (17789)Instruction limit reached!
% 0.22/0.57 % (17789)------------------------------
% 0.22/0.57 % (17789)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.57 % (17789)Termination reason: Unknown
% 0.22/0.57 % (17789)Termination phase: Saturation
% 0.22/0.57
% 0.22/0.57 % (17789)Memory used [KB]: 6524
% 0.22/0.57 % (17789)Time elapsed: 0.047 s
% 0.22/0.57 % (17789)Instructions burned: 102 (million)
% 0.22/0.57 % (17789)------------------------------
% 0.22/0.57 % (17789)------------------------------
% 0.22/0.58 % (17793)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on theBenchmark for (2998ds/107Mi)
% 0.22/0.58 % (17788)Instruction limit reached!
% 0.22/0.58 % (17788)------------------------------
% 0.22/0.58 % (17788)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.58 % (17788)Termination reason: Unknown
% 0.22/0.58 % (17788)Termination phase: Saturation
% 0.22/0.58
% 0.22/0.58 % (17788)Memory used [KB]: 6524
% 0.22/0.58 % (17788)Time elapsed: 0.059 s
% 0.22/0.58 % (17788)Instructions burned: 128 (million)
% 0.22/0.58 % (17788)------------------------------
% 0.22/0.58 % (17788)------------------------------
% 0.22/0.59 % (17794)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)
% 1.75/0.59 % (17781)First to succeed.
% 1.75/0.60 % (17795)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)
% 1.75/0.60 % (17792)Instruction limit reached!
% 1.75/0.60 % (17792)------------------------------
% 1.75/0.60 % (17792)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.75/0.60 % (17792)Termination reason: Unknown
% 1.75/0.60 % (17792)Termination phase: Property scanning
% 1.75/0.60
% 1.75/0.60 % (17792)Memory used [KB]: 2046
% 1.75/0.60 % (17792)Time elapsed: 0.041 s
% 1.75/0.60 % (17792)Instructions burned: 87 (million)
% 1.75/0.60 % (17792)------------------------------
% 1.75/0.60 % (17792)------------------------------
% 1.75/0.60 % (17794)Instruction limit reached!
% 1.75/0.60 % (17794)------------------------------
% 1.75/0.60 % (17794)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.75/0.60 % (17794)Termination reason: Unknown
% 1.75/0.60 % (17794)Termination phase: Property scanning
% 1.75/0.60
% 1.75/0.60 % (17794)Memory used [KB]: 1791
% 1.75/0.60 % (17794)Time elapsed: 0.020 s
% 1.75/0.60 % (17794)Instructions burned: 39 (million)
% 1.75/0.60 % (17794)------------------------------
% 1.75/0.60 % (17794)------------------------------
% 1.75/0.61 % (17777)Refutation not found, incomplete strategy
% 1.75/0.61 % (17777)------------------------------
% 1.75/0.61 % (17777)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.75/0.61 % (17777)Termination reason: Refutation not found, incomplete strategy
% 1.75/0.61
% 1.75/0.61
% 1.75/0.61 % (17777)Memory used [KB]: 8187
% 1.75/0.61 % (17777)Time elapsed: 0.135 s
% 1.75/0.61 % (17777)Instructions burned: 255 (million)
% 1.75/0.61 % (17777)------------------------------
% 1.75/0.61 % (17777)------------------------------
% 1.91/0.62 % (17796)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)
% 1.91/0.62 % (17797)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)
% 1.91/0.62 % (17798)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on theBenchmark for (2997ds/507Mi)
% 1.91/0.63 % (17793)Instruction limit reached!
% 1.91/0.63 % (17793)------------------------------
% 1.91/0.63 % (17793)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.91/0.63 % (17793)Termination reason: Unknown
% 1.91/0.63 % (17793)Termination phase: Saturation
% 1.91/0.63
% 1.91/0.63 % (17793)Memory used [KB]: 6524
% 1.91/0.63 % (17793)Time elapsed: 0.052 s
% 1.91/0.63 % (17793)Instructions burned: 107 (million)
% 1.91/0.63 % (17793)------------------------------
% 1.91/0.63 % (17793)------------------------------
% 1.91/0.63 % (17782)Also succeeded, but the first one will report.
% 1.91/0.63 % (17781)Refutation found. Thanks to Tanya!
% 1.91/0.63 % SZS status Theorem for theBenchmark
% 1.91/0.63 % SZS output start Proof for theBenchmark
% See solution above
% 1.91/0.64 % (17781)------------------------------
% 1.91/0.64 % (17781)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.91/0.64 % (17781)Termination reason: Refutation
% 1.91/0.64
% 1.91/0.64 % (17781)Memory used [KB]: 8955
% 1.91/0.64 % (17781)Time elapsed: 0.132 s
% 1.91/0.64 % (17781)Instructions burned: 185 (million)
% 1.91/0.64 % (17781)------------------------------
% 1.91/0.64 % (17781)------------------------------
% 1.91/0.64 % (17754)Success in time 0.271 s
% 1.91/0.64 % Vampire---4.8 exiting
%------------------------------------------------------------------------------