%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : ALG264^3 : TPTP v8.2.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 18:20:29 EDT 2024
% Result : Theorem 21.52s 3.26s
% Output : Refutation 21.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 65
% Number of leaves : 83
% Syntax : Number of formulae : 288 ( 235 unt; 42 typ; 0 def)
% Number of atoms : 5802 (1281 equ; 0 cnn)
% Maximal formula atoms : 35 ( 23 avg)
% Number of connectives : 24156 ( 213 ~; 7 |; 103 &;17516 @)
% ( 2 <=>;2704 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 1402 (1402 >; 0 *; 0 +; 0 <<)
% Number of symbols : 78 ( 74 usr; 44 con; 0-4 aty)
% (3611 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 4068 (3800 ^ 267 !; 0 ?;4068 :)
% ( 1 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
term: $tType ).
thf(type_def_7,type,
subst: $tType ).
thf(func_def_0,type,
term: $tType ).
thf(func_def_1,type,
subst: $tType ).
thf(func_def_2,type,
one: term ).
thf(func_def_3,type,
ap: term > term > term ).
thf(func_def_4,type,
lam: term > term ).
thf(func_def_5,type,
sub: term > subst > term ).
thf(func_def_6,type,
id: subst ).
thf(func_def_7,type,
sh: subst ).
thf(func_def_8,type,
push: term > subst > subst ).
thf(func_def_9,type,
comp: subst > subst > subst ).
thf(func_def_10,type,
var: term > $o ).
thf(func_def_18,type,
hoasap: subst > term > subst > term > term ).
thf(func_def_73,type,
hoaslam: subst > ( subst > term > term ) > term ).
thf(func_def_86,type,
hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).
thf(func_def_107,type,
hoasvar: subst > term > subst > $o ).
thf(func_def_121,type,
pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).
thf(func_def_140,type,
sP0: $o > $o ).
thf(func_def_142,type,
ph2:
!>[X0: $tType] : X0 ).
thf(func_def_143,type,
sK3: ( term > $o ) > term ).
thf(func_def_144,type,
sK4: ( term > $o ) > subst > term ).
thf(func_def_145,type,
sK5: ( term > $o ) > term ).
thf(func_def_146,type,
sK6: ( term > $o ) > term ).
thf(func_def_147,type,
sK7: ( term > $o ) > term ).
thf(func_def_148,type,
sK8: ( term > $o ) > term ).
thf(func_def_149,type,
sK9: ( subst > term > term ) > subst ).
thf(func_def_150,type,
sK10: ( subst > term > term ) > subst ).
thf(func_def_151,type,
sK11: ( subst > term > term ) > term ).
thf(func_def_152,type,
sK12: ( subst > term > term ) > subst ).
thf(func_def_153,type,
sK13: ( subst > term > term ) > subst ).
thf(func_def_154,type,
sK14: ( subst > term > term ) > term ).
thf(func_def_155,type,
sK15: ( subst > term > term ) > subst ).
thf(func_def_156,type,
sK16: ( subst > term > term ) > term ).
thf(func_def_157,type,
sK17: ( subst > term > term ) > subst ).
thf(func_def_158,type,
sK18: term > $o ).
thf(func_def_159,type,
sK19: subst > term > subst > $o ).
thf(func_def_160,type,
sK20: term ).
thf(func_def_161,type,
sK21: term ).
thf(func_def_162,type,
sK22: ( term > $o ) > term ).
thf(func_def_163,type,
sK23: ( term > $o ) > term ).
thf(func_def_164,type,
sK24: ( term > $o ) > term ).
thf(f1115,plain,
$false,
inference(trivial_inequality_removal,[],[f1114]) ).
thf(f1114,plain,
$true = $false,
inference(backward_demodulation,[],[f857,f1113]) ).
thf(f1113,plain,
( $false
= ( sK18 @ sK21 ) ),
inference(trivial_inequality_removal,[],[f1112]) ).
thf(f1112,plain,
( ( $true = $false )
| ( $false
= ( sK18 @ sK21 ) ) ),
inference(forward_demodulation,[],[f1111,f859]) ).
thf(f859,plain,
( $true
= ( sK18 @ sK20 ) ),
inference(binary_proxy_clausification,[],[f856]) ).
thf(f856,plain,
( $false
= ( ( sK18 @ sK20 )
=> ( sK18 @ ( ap @ sK21 @ sK20 ) ) ) ),
inference(binary_proxy_clausification,[],[f855]) ).
thf(f855,plain,
( $false
= ( ( sK18 @ sK21 )
=> ( ( sK18 @ sK20 )
=> ( sK18 @ ( ap @ sK21 @ sK20 ) ) ) ) ),
inference(beta_eta_normalization,[],[f854]) ).
thf(f854,plain,
( $false
= ( ^ [Y0: term] :
( ( sK18 @ Y0 )
=> ( ( sK18 @ sK20 )
=> ( sK18 @ ( ap @ Y0 @ sK20 ) ) ) )
@ sK21 ) ),
inference(sigma_clausification,[],[f853]) ).
thf(f853,plain,
( $false
= ( !! @ term
@ ^ [Y0: term] :
( ( sK18 @ Y0 )
=> ( ( sK18 @ sK20 )
=> ( sK18 @ ( ap @ Y0 @ sK20 ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f852]) ).
thf(f852,plain,
( ( ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK18 @ Y1 )
=> ( ( sK18 @ Y0 )
=> ( sK18 @ ( ap @ Y1 @ Y0 ) ) ) ) )
@ sK20 )
= $false ),
inference(sigma_clausification,[],[f850]) ).
thf(f850,plain,
( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK18 @ Y1 )
=> ( ( sK18 @ Y0 )
=> ( sK18 @ ( ap @ Y1 @ Y0 ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f848]) ).
thf(f848,plain,
( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( ( sK19 @ id @ Y0 @ id )
= ( sK18 @ Y0 ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK18 @ Y1 )
=> ( ( sK18 @ Y0 )
=> ( sK18 @ ( ap @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f837]) ).
thf(f837,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK19 @ id @ Y1 @ id )
=> ( ( sK19 @ id @ Y0 @ id )
=> ( sK19 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sK19 @ id @ Y0 @ id )
= ( sK18 @ Y0 ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK18 @ Y1 )
=> ( ( sK18 @ Y0 )
=> ( sK18 @ ( ap @ Y1 @ Y0 ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f835]) ).
thf(f835,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK19 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) @ Y0 )
=> ( sK19 @ Y2 @ Y1 @ ( comp @ Y3 @ Y0 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK19 @ id @ Y1 @ id )
=> ( ( sK19 @ id @ Y0 @ id )
=> ( sK19 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sK19 @ id @ Y0 @ id )
= ( sK18 @ Y0 ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK18 @ Y1 )
=> ( ( sK18 @ Y0 )
=> ( sK18 @ ( ap @ Y1 @ Y0 ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f834]) ).
thf(f834,plain,
( $false
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK19 @ Y0 @ Y2 @ ( comp @ Y3 @ Y1 ) )
=> ( sK19 @ ( comp @ Y0 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK19 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) @ Y0 )
=> ( sK19 @ Y2 @ Y1 @ ( comp @ Y3 @ Y0 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK19 @ id @ Y1 @ id )
=> ( ( sK19 @ id @ Y0 @ id )
=> ( sK19 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sK19 @ id @ Y0 @ id )
= ( sK18 @ Y0 ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK18 @ Y1 )
=> ( ( sK18 @ Y0 )
=> ( sK18 @ ( ap @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f833]) ).
thf(f833,plain,
( $false
= ( ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y1 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y4 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y2 @ id ) @ Y1 ) @ id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ id @ Y1 @ id )
= ( sK18 @ Y1 ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( sK18 @ Y2 )
=> ( ( sK18 @ Y1 )
=> ( sK18 @ ( ap @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
@ sK19 ) ),
inference(sigma_clausification,[],[f832]) ).
thf(f832,plain,
( $false
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) @ Y1 )
=> ( Y0 @ Y3 @ Y2 @ ( comp @ Y4 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y2 @ id ) @ Y1 ) @ id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ id @ Y1 @ id )
= ( sK18 @ Y1 ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( sK18 @ Y2 )
=> ( ( sK18 @ Y1 )
=> ( sK18 @ ( ap @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f831]) ).
thf(f831,plain,
( ( ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y4 @ ( comp @ Y5 @ Y3 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y2 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y5 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( ( Y1 @ id @ Y2 @ id )
=> ( Y1 @ id @ ( ap @ ( sub @ Y3 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ id @ Y2 @ id )
= ( Y0 @ Y2 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) )
@ sK18 )
= $false ),
inference(sigma_clausification,[],[f829]) ).
thf(f829,plain,
( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y4 @ ( comp @ Y5 @ Y3 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y2 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y5 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( ( Y1 @ id @ Y2 @ id )
=> ( Y1 @ id @ ( ap @ ( sub @ Y3 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ id @ Y2 @ id )
= ( Y0 @ Y2 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f827]) ).
thf(f827,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y4 @ ( comp @ Y5 @ Y3 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y2 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y5 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( ( Y1 @ id @ Y2 @ id )
=> ( Y1 @ id @ ( ap @ ( sub @ Y3 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ id @ Y2 @ id )
= ( Y0 @ Y2 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f810]) ).
thf(f810,plain,
( ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y4 @ ( comp @ Y5 @ Y3 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y2 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y5 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( ( Y1 @ id @ Y2 @ id )
=> ( Y1 @ id @ ( ap @ ( sub @ Y3 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ id @ Y2 @ id )
= ( Y0 @ Y2 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f781]) ).
thf(f781,plain,
( ( ( !! @ ( 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 @ Y1 @ id ) @ Y2 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y4 @ ( comp @ Y5 @ Y3 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y2 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y5 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( ( Y1 @ id @ Y2 @ id )
=> ( Y1 @ id @ ( ap @ ( sub @ Y3 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ id @ Y2 @ id )
= ( Y0 @ Y2 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f779]) ).
thf(f779,plain,
( $false
= ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ 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 @ Y1 @ id ) @ Y2 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y4 @ ( comp @ Y5 @ Y3 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y2 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y5 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( ( Y1 @ id @ Y2 @ id )
=> ( Y1 @ id @ ( ap @ ( sub @ Y3 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ id @ Y2 @ id )
= ( Y0 @ Y2 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f764]) ).
thf(f764,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ 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 @ Y1 @ id ) @ Y2 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y4 @ ( comp @ Y5 @ Y3 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y2 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y5 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( ( Y1 @ id @ Y2 @ id )
=> ( Y1 @ id @ ( ap @ ( sub @ Y3 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ id @ Y2 @ id )
= ( Y0 @ Y2 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f762]) ).
thf(f762,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y1 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ 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 @ Y1 @ id ) @ Y2 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y4 @ ( comp @ Y5 @ Y3 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y2 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y5 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( ( Y1 @ id @ Y2 @ id )
=> ( Y1 @ id @ ( ap @ ( sub @ Y3 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ id @ Y2 @ id )
= ( Y0 @ Y2 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f760]) ).
thf(f760,plain,
( ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y1 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ 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 @ Y1 @ id ) @ Y2 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y4 @ ( comp @ Y5 @ Y3 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y2 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y5 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( ( Y1 @ id @ Y2 @ id )
=> ( Y1 @ id @ ( ap @ ( sub @ Y3 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ id @ Y2 @ id )
= ( Y0 @ Y2 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f702]) ).
thf(f702,plain,
( $false
= ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( comp @ ( comp @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y1 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ 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 @ Y1 @ id ) @ Y2 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y4 @ ( comp @ Y5 @ Y3 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y2 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y5 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( ( Y1 @ id @ Y2 @ id )
=> ( Y1 @ id @ ( ap @ ( sub @ Y3 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ id @ Y2 @ id )
= ( Y0 @ Y2 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f700]) ).
thf(f700,plain,
( ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( comp @ ( comp @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y1 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ 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 @ Y1 @ id ) @ Y2 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y4 @ ( comp @ Y5 @ Y3 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y2 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y5 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( ( Y1 @ id @ Y2 @ id )
=> ( Y1 @ id @ ( ap @ ( sub @ Y3 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ id @ Y2 @ id )
= ( Y0 @ Y2 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f679]) ).
thf(f679,plain,
( ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( comp @ ( comp @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y1 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ 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 @ Y1 @ id ) @ Y2 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y4 @ ( comp @ Y5 @ Y3 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y2 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y5 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( ( Y1 @ id @ Y2 @ id )
=> ( Y1 @ id @ ( ap @ ( sub @ Y3 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ id @ Y2 @ id )
= ( Y0 @ Y2 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f677]) ).
thf(f677,plain,
( ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( comp @ ( comp @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y1 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ 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 @ Y1 @ id ) @ Y2 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y4 @ ( comp @ Y5 @ Y3 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y2 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y5 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( ( Y1 @ id @ Y2 @ id )
=> ( Y1 @ id @ ( ap @ ( sub @ Y3 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ id @ Y2 @ id )
= ( Y0 @ Y2 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f673]) ).
thf(f673,plain,
( ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( comp @ ( comp @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y1 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ 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 @ Y1 @ id ) @ Y2 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y4 @ ( comp @ Y5 @ Y3 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y2 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y5 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( ( Y1 @ id @ Y2 @ id )
=> ( Y1 @ id @ ( ap @ ( sub @ Y3 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ id @ Y2 @ id )
= ( Y0 @ Y2 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f671]) ).
thf(f671,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( comp @ ( comp @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y1 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ 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 @ Y1 @ id ) @ Y2 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y4 @ ( comp @ Y5 @ Y3 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y2 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y5 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( ( Y1 @ id @ Y2 @ id )
=> ( Y1 @ id @ ( ap @ ( sub @ Y3 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ id @ Y2 @ id )
= ( Y0 @ Y2 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f663]) ).
thf(f663,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 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( comp @ ( comp @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y1 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ 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 @ Y1 @ id ) @ Y2 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y4 @ ( comp @ Y5 @ Y3 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y2 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y5 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( ( Y1 @ id @ Y2 @ id )
=> ( Y1 @ id @ ( ap @ ( sub @ Y3 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ id @ Y2 @ id )
= ( Y0 @ Y2 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f661]) ).
thf(f661,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( comp @ ( comp @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y1 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ 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 @ Y1 @ id ) @ Y2 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y4 @ ( comp @ Y5 @ Y3 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y2 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y5 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( ( Y1 @ id @ Y2 @ id )
=> ( Y1 @ id @ ( ap @ ( sub @ Y3 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ id @ Y2 @ id )
= ( Y0 @ Y2 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
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 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( comp @ ( comp @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y1 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ 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 @ Y1 @ id ) @ Y2 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y4 @ ( comp @ Y5 @ Y3 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y2 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y5 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( ( Y1 @ id @ Y2 @ id )
=> ( Y1 @ id @ ( ap @ ( sub @ Y3 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ id @ Y2 @ id )
= ( Y0 @ Y2 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f639]) ).
thf(f639,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( comp @ ( comp @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y1 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ 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 @ Y1 @ id ) @ Y2 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y4 @ ( comp @ Y5 @ Y3 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y2 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y5 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( ( Y1 @ id @ Y2 @ id )
=> ( Y1 @ id @ ( ap @ ( sub @ Y3 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ id @ Y2 @ id )
= ( Y0 @ Y2 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f626]) ).
thf(f626,plain,
( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y0 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( comp @ ( comp @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y1 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ 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 @ Y1 @ id ) @ Y2 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y4 @ ( comp @ Y5 @ Y3 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y2 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y5 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( ( Y1 @ id @ Y2 @ id )
=> ( Y1 @ id @ ( ap @ ( sub @ Y3 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ id @ Y2 @ id )
= ( Y0 @ Y2 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f605]) ).
thf(f605,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y1 )
= ( ap @ Y2 @ Y3 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y0 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( comp @ ( comp @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y1 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ 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 @ Y1 @ id ) @ Y2 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y4 @ ( comp @ Y5 @ Y3 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y2 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y5 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( ( Y1 @ id @ Y2 @ id )
=> ( Y1 @ id @ ( ap @ ( sub @ Y3 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ id @ Y2 @ id )
= ( Y0 @ Y2 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f603]) ).
thf(f603,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 @ Y0 @ Y1 )
= ( ap @ Y2 @ Y3 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y0 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( comp @ ( comp @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y1 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ 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 @ Y1 @ id ) @ Y2 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y4 @ ( comp @ Y5 @ Y3 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y2 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y5 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( ( Y1 @ id @ Y2 @ id )
=> ( Y1 @ id @ ( ap @ ( sub @ Y3 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ id @ Y2 @ id )
= ( Y0 @ Y2 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f601]) ).
thf(f601,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 @ Y0 @ Y1 )
= ( ap @ Y2 @ Y3 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y0 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( comp @ ( comp @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y1 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ 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 @ Y1 @ id ) @ Y2 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y4 @ ( comp @ Y5 @ Y3 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y2 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y5 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( ( Y1 @ id @ Y2 @ id )
=> ( Y1 @ id @ ( ap @ ( sub @ Y3 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ id @ Y2 @ id )
= ( Y0 @ Y2 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f599]) ).
thf(f599,plain,
( ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y1 )
= ( ap @ Y2 @ Y3 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y0 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( comp @ ( comp @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y1 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ 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 @ Y1 @ id ) @ Y2 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y4 @ ( comp @ Y5 @ Y3 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y2 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y5 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( ( Y1 @ id @ Y2 @ id )
=> ( Y1 @ id @ ( ap @ ( sub @ Y3 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ id @ Y2 @ id )
= ( Y0 @ Y2 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f597]) ).
thf(f597,plain,
( $false
= ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y1 )
= ( ap @ Y2 @ Y3 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y0 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( comp @ ( comp @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y1 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ 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 @ Y1 @ id ) @ Y2 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y4 @ ( comp @ Y5 @ Y3 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y2 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y5 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( ( Y1 @ id @ Y2 @ id )
=> ( Y1 @ id @ ( ap @ ( sub @ Y3 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ id @ Y2 @ id )
= ( Y0 @ Y2 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f595]) ).
thf(f595,plain,
( ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y1 )
= ( ap @ Y2 @ Y3 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y0 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( comp @ ( comp @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y1 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ 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 @ Y1 @ id ) @ Y2 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y4 @ ( comp @ Y5 @ Y3 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y2 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y5 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( ( Y1 @ id @ Y2 @ id )
=> ( Y1 @ id @ ( ap @ ( sub @ Y3 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ id @ Y2 @ id )
= ( Y0 @ Y2 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f586]) ).
thf(f586,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( id
= ( push @ one @ sh ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y1 )
= ( ap @ Y2 @ Y3 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y0 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( comp @ ( comp @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y1 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ 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 @ Y1 @ id ) @ Y2 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y4 @ ( comp @ Y5 @ Y3 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y2 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y5 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( ( Y1 @ id @ Y2 @ id )
=> ( Y1 @ id @ ( ap @ ( sub @ Y3 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ id @ Y2 @ id )
= ( Y0 @ Y2 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f577]) ).
thf(f577,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y1 ) @ Y0 )
= ( push @ ( sub @ Y2 @ Y0 ) @ ( comp @ Y1 @ 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 @ Y0 @ Y1 )
= ( ap @ Y2 @ Y3 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y0 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( comp @ ( comp @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y1 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ 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 @ Y1 @ id ) @ Y2 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y4 @ ( comp @ Y5 @ Y3 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y2 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y5 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( ( Y1 @ id @ Y2 @ id )
=> ( Y1 @ id @ ( ap @ ( sub @ Y3 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ id @ Y2 @ id )
= ( Y0 @ Y2 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f575]) ).
thf(f575,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) )
= ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y1 ) @ Y0 )
= ( push @ ( sub @ Y2 @ Y0 ) @ ( comp @ Y1 @ 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 @ Y0 @ Y1 )
= ( ap @ Y2 @ Y3 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y0 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( comp @ ( comp @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y1 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ 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 @ Y1 @ id ) @ Y2 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y4 @ ( comp @ Y5 @ Y3 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y2 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y5 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( ( Y1 @ id @ Y2 @ id )
=> ( Y1 @ id @ ( ap @ ( sub @ Y3 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ id @ Y2 @ id )
= ( Y0 @ Y2 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f570]) ).
thf(f570,plain,
( $false
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) )
= ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y1 ) @ Y0 )
= ( push @ ( sub @ Y2 @ Y0 ) @ ( comp @ Y1 @ 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 @ Y0 @ Y1 )
= ( ap @ Y2 @ Y3 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y0 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( comp @ ( comp @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y1 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ 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 @ Y1 @ id ) @ Y2 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y4 @ ( comp @ Y5 @ Y3 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y2 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y5 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( ( Y1 @ id @ Y2 @ id )
=> ( Y1 @ id @ ( ap @ ( sub @ Y3 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ id @ Y2 @ id )
= ( Y0 @ Y2 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f561]) ).
thf(f561,plain,
( $false
= ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) )
= ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y1 ) @ Y0 )
= ( push @ ( sub @ Y2 @ Y0 ) @ ( comp @ Y1 @ 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 @ Y0 @ Y1 )
= ( ap @ Y2 @ Y3 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y0 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( comp @ ( comp @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y1 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ 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 @ Y1 @ id ) @ Y2 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y4 @ ( comp @ Y5 @ Y3 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y2 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y5 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( ( Y1 @ id @ Y2 @ id )
=> ( Y1 @ id @ ( ap @ ( sub @ Y3 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ id @ Y2 @ id )
= ( Y0 @ Y2 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f554]) ).
thf(f554,plain,
( $false
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) )
= ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y1 ) @ Y0 )
= ( push @ ( sub @ Y2 @ Y0 ) @ ( comp @ Y1 @ 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 @ Y0 @ Y1 )
= ( ap @ Y2 @ Y3 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y0 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( comp @ ( comp @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y1 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ 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 @ Y1 @ id ) @ Y2 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y4 @ ( comp @ Y5 @ Y3 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y2 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y5 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( ( Y1 @ id @ Y2 @ id )
=> ( Y1 @ id @ ( ap @ ( sub @ Y3 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ id @ Y2 @ id )
= ( Y0 @ Y2 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f549]) ).
thf(f549,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) )
= ( sub @ ( lam @ Y0 ) @ Y1 ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) )
= ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y1 ) @ Y0 )
= ( push @ ( sub @ Y2 @ Y0 ) @ ( comp @ Y1 @ 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 @ Y0 @ Y1 )
= ( ap @ Y2 @ Y3 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y0 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( comp @ ( comp @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y1 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ 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 @ Y1 @ id ) @ Y2 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y4 @ ( comp @ Y5 @ Y3 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y2 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y5 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( ( Y1 @ id @ Y2 @ id )
=> ( Y1 @ id @ ( ap @ ( sub @ Y3 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ id @ Y2 @ id )
= ( Y0 @ Y2 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f542]) ).
thf(f542,plain,
( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) )
= ( sub @ ( lam @ Y0 ) @ Y1 ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) )
= ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y1 ) @ Y0 )
= ( push @ ( sub @ Y2 @ Y0 ) @ ( comp @ Y1 @ 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 @ Y0 @ Y1 )
= ( ap @ Y2 @ Y3 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y0 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( comp @ ( comp @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y1 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ 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 @ Y1 @ id ) @ Y2 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y4 @ ( comp @ Y5 @ Y3 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y2 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y5 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( ( Y1 @ id @ Y2 @ id )
=> ( Y1 @ id @ ( ap @ ( sub @ Y3 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ id @ Y2 @ id )
= ( Y0 @ Y2 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f533]) ).
thf(f533,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) )
= ( sub @ ( lam @ Y0 ) @ Y1 ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) )
= ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y1 ) @ Y0 )
= ( push @ ( sub @ Y2 @ Y0 ) @ ( comp @ Y1 @ 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 @ Y0 @ Y1 )
= ( ap @ Y2 @ Y3 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y0 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( comp @ ( comp @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y1 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ 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 @ Y1 @ id ) @ Y2 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y4 @ ( comp @ Y5 @ Y3 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y2 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y5 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( ( Y1 @ id @ Y2 @ id )
=> ( Y1 @ id @ ( ap @ ( sub @ Y3 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ id @ Y2 @ id )
= ( Y0 @ Y2 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f532]) ).
thf(f532,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( ap @ ( sub @ Y0 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( ap @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) )
= ( sub @ ( lam @ Y0 ) @ Y1 ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) )
= ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y1 ) @ Y0 )
= ( push @ ( sub @ Y2 @ Y0 ) @ ( comp @ Y1 @ 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 @ Y0 @ Y1 )
= ( ap @ Y2 @ Y3 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y0 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( comp @ ( comp @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y1 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ 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 @ Y1 @ id ) @ Y2 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y4 @ ( comp @ Y5 @ Y3 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y2 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y5 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( ( Y1 @ id @ Y2 @ id )
=> ( Y1 @ id @ ( ap @ ( sub @ Y3 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ id @ Y2 @ id )
= ( Y0 @ Y2 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f529]) ).
thf(f529,plain,
( $true
= ( ~ ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( ap @ ( sub @ Y0 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( ap @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) )
= ( sub @ ( lam @ Y0 ) @ Y1 ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) )
= ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y1 ) @ Y0 )
= ( push @ ( sub @ Y2 @ Y0 ) @ ( comp @ Y1 @ 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 @ Y0 @ Y1 )
= ( ap @ Y2 @ Y3 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y0 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( comp @ ( comp @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y3 @ id ) @ Y0 )
= ( ap @ ( sub @ Y2 @ id ) @ Y1 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ Y3 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( lam @ ( Y0 @ sh @ one ) )
= ( lam @ ( Y1 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ 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 @ Y1 @ id ) @ Y2 )
!= ( lam @ ( Y0 @ sh @ one ) ) ) ) ) ) )
=> ( ( !! @ ( 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 ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y4 @ ( comp @ Y5 @ Y3 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y2 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y5 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( ( Y1 @ id @ Y2 @ id )
=> ( Y1 @ id @ ( ap @ ( sub @ Y3 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ id @ Y2 @ id )
= ( Y0 @ Y2 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f526]) ).
thf(f526,plain,
( ( ~ ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( ap @ ( sub @ Y0 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( ap @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) )
= ( sub @ ( lam @ Y0 ) @ Y1 ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) )
= ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y1 ) @ Y0 )
= ( push @ ( sub @ Y2 @ Y0 ) @ ( comp @ Y1 @ 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 @ Y0 @ Y1 )
= ( ap @ Y2 @ Y3 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y0 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( comp @ ( comp @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y3
@ id
@ Y0 )
= ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y2
@ id
@ Y1 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y2
@ id
@ Y0 )
= ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y1
@ id
@ Y3 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y0 @ Y2 @ Y3 ) )
= ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ 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
@ Y1
@ id
@ Y2 )
!= ( ^ [Y3: subst,Y4: subst > term > term] : ( lam @ ( Y4 @ sh @ one ) )
@ id
@ ^ [Y3: subst,Y4: term] : ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ~ ( ^ [Y1: subst,Y2: term,Y3: subst] : ( var @ ( sub @ Y2 @ Y3 ) )
@ id
@ ( ^ [Y1: subst,Y2: subst > term > term] : ( lam @ ( Y2 @ sh @ one ) )
@ id
@ ^ [Y1: subst,Y2: term] : ( Y0 @ Y1 @ Y2 ) )
@ id ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( ^ [Y2: subst,Y3: term,Y4: subst] : ( var @ ( sub @ Y3 @ Y4 ) )
@ id
@ ( ^ [Y2: subst,Y3: term,Y4: subst,Y5: term] : ( ap @ ( sub @ Y3 @ Y4 ) @ Y5 )
@ id
@ Y1
@ id
@ Y0 )
@ id ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y4 @ ( comp @ Y5 @ Y3 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y2 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y5 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( ( Y1 @ id @ Y2 @ id )
=> ( Y1 @ id
@ ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y3
@ id
@ Y2 )
@ id ) ) ) ) )
=> ( ( ^ [Y2: subst > term > subst > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y2 @ id @ Y4 @ id )
= ( Y3 @ Y4 ) ) )
@ Y1
@ Y0 )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f396,f502]) ).
thf(f502,plain,
( hoasinduction_lem2v2_gthm
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( ap @ ( sub @ Y0 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( ap @ Y0 @ Y1 ) @ Y2 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) )
= ( sub @ ( lam @ Y0 ) @ Y1 ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) )
= ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y1 ) @ Y0 )
= ( push @ ( sub @ Y2 @ Y0 ) @ ( comp @ Y1 @ 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 @ Y0 @ Y1 )
= ( ap @ Y2 @ Y3 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y0 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( ( Y0 @ Y2 )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) )
=> ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ 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] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( comp @ ( comp @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) )
=> ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y3
@ id
@ Y0 )
= ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y2
@ id
@ Y1 ) )
=> ( Y3 = Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y2
@ id
@ Y0 )
= ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y1
@ id
@ Y3 ) )
=> ( Y3 = Y0 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y0 @ Y2 @ Y3 ) )
= ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ 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
@ Y1
@ id
@ Y2 )
!= ( ^ [Y3: subst,Y4: subst > term > term] : ( lam @ ( Y4 @ sh @ one ) )
@ id
@ ^ [Y3: subst,Y4: term] : ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ~ ( ^ [Y1: subst,Y2: term,Y3: subst] : ( var @ ( sub @ Y2 @ Y3 ) )
@ id
@ ( ^ [Y1: subst,Y2: subst > term > term] : ( lam @ ( Y2 @ sh @ one ) )
@ id
@ ^ [Y1: subst,Y2: term] : ( Y0 @ Y1 @ Y2 ) )
@ id ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( ^ [Y2: subst,Y3: term,Y4: subst] : ( var @ ( sub @ Y3 @ Y4 ) )
@ id
@ ( ^ [Y2: subst,Y3: term,Y4: subst,Y5: term] : ( ap @ ( sub @ Y3 @ Y4 ) @ Y5 )
@ id
@ Y1
@ id
@ Y0 )
@ id ) ) )
=> ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y4 @ ( comp @ Y5 @ Y3 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y2 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y5 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( ( Y1 @ id @ Y2 @ id )
=> ( Y1 @ id
@ ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y3
@ id
@ Y2 )
@ id ) ) ) ) )
=> ( ( ^ [Y2: subst > term > subst > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y2 @ id @ Y4 @ id )
= ( Y3 @ Y4 ) ) )
@ Y1
@ Y0 )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f401,f439,f357,f391,f416,f354,f374,f405,f392,f400,f434,f381,f395,f435,f425,f426,f404,f419,f346,f372,f371,f347,f385,f366,f355,f420,f343,f365,f440,f454,f455,f456,f457,f458,f459,f497]) ).
thf(f497,plain,
( hoasinduction_lem2v2
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y4 @ ( comp @ Y5 @ Y3 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y2 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y5 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( ( Y1 @ id @ Y2 @ id )
=> ( Y1 @ id
@ ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y3
@ id
@ Y2 )
@ id ) ) ) ) )
=> ( ( ^ [Y2: subst > term > subst > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y2 @ id @ Y4 @ id )
= ( Y3 @ Y4 ) ) )
@ Y1
@ Y0 )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f412,f336,f421]) ).
thf(f421,plain,
( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
= ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f306]) ).
thf(f306,plain,
( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
= ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f305]) ).
thf(f305,plain,
( hoasinduction_p_and_p_prime
= ( ^ [X0: subst > term > subst > $o,X1: term > $o] :
! [X2: term] :
( ( X0 @ id @ X2 @ id )
<=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f76]) ).
thf(f76,axiom,
( hoasinduction_p_and_p_prime
= ( ^ [X5: subst > term > subst > $o,X8: term > $o] :
! [X9: term] :
( ( X5 @ id @ X9 @ id )
<=> ( X8 @ X9 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_p_and_p_prime) ).
thf(f336,plain,
( hoasap
= ( ^ [Y0: subst,Y1: term,Y2: subst,Y3: term] : ( ap @ ( sub @ Y1 @ Y2 ) @ Y3 ) ) ),
inference(cnf_transformation,[],[f181]) ).
thf(f181,plain,
( hoasap
= ( ^ [Y0: subst,Y1: term,Y2: subst,Y3: term] : ( ap @ ( sub @ Y1 @ Y2 ) @ Y3 ) ) ),
inference(fool_elimination,[],[f180]) ).
thf(f180,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/sandbox2/benchmark/theBenchmark.p',hoasap) ).
thf(f412,plain,
( hoasinduction_lem2v2
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y4 @ ( comp @ Y5 @ Y3 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y2 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y5 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( ( Y1 @ id @ Y2 @ id )
=> ( Y1 @ id @ ( hoasap @ id @ Y3 @ id @ Y2 ) @ id ) ) ) ) )
=> ( ( hoasinduction_p_and_p_prime @ Y1 @ Y0 )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f137]) ).
thf(f137,plain,
( hoasinduction_lem2v2
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ Y2 @ Y4 @ ( comp @ Y5 @ Y3 ) )
=> ( Y1 @ ( comp @ Y2 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y1 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y3 @ Y5 ) @ Y2 )
=> ( Y1 @ Y4 @ Y3 @ ( comp @ Y5 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( ( Y1 @ id @ Y2 @ id )
=> ( Y1 @ id @ ( hoasap @ id @ Y3 @ id @ Y2 ) @ id ) ) ) ) )
=> ( ( hoasinduction_p_and_p_prime @ Y1 @ Y0 )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f136]) ).
thf(f136,plain,
( hoasinduction_lem2v2
= ( ! [X0: subst > term > subst > $o,X1: term > $o] :
( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( X0 @ X5 @ X3 @ ( comp @ X2 @ X4 ) )
=> ( X0 @ ( comp @ X5 @ X2 ) @ ( sub @ X3 @ X2 ) @ X4 ) )
=> ( ! [X6: subst,X7: subst,X8: term,X9: subst] :
( ( X0 @ ( comp @ X7 @ X6 ) @ ( sub @ X8 @ X6 ) @ X9 )
=> ( X0 @ X7 @ X8 @ ( comp @ X6 @ X9 ) ) )
=> ( ! [X10: term,X11: term] :
( ( X0 @ id @ X10 @ id )
=> ( ( X0 @ id @ X11 @ id )
=> ( X0 @ id @ ( hoasap @ id @ X10 @ id @ X11 ) @ id ) ) )
=> ( ( hoasinduction_p_and_p_prime @ X0 @ X1 )
=> ! [X12: term,X13: term] :
( ( X1 @ X12 )
=> ( ( X1 @ X13 )
=> ( X1 @ ( ap @ X12 @ X13 ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f81]) ).
thf(f81,axiom,
( hoasinduction_lem2v2
= ( ! [X5: subst > term > subst > $o,X8: term > $o] :
( ! [X4: subst,X0: term,X3: subst,X2: subst] :
( ( X5 @ X2 @ X0 @ ( comp @ X4 @ X3 ) )
=> ( X5 @ ( comp @ X2 @ X4 ) @ ( sub @ X0 @ X4 ) @ X3 ) )
=> ( ! [X4: subst,X2: subst,X0: term,X3: subst] :
( ( X5 @ ( comp @ X2 @ X4 ) @ ( sub @ X0 @ X4 ) @ X3 )
=> ( X5 @ X2 @ X0 @ ( comp @ X4 @ X3 ) ) )
=> ( ! [X0: term,X1: term] :
( ( X5 @ id @ X0 @ id )
=> ( ( X5 @ id @ X1 @ id )
=> ( X5 @ id @ ( hoasap @ id @ X0 @ id @ X1 ) @ id ) ) )
=> ( ( hoasinduction_p_and_p_prime @ X5 @ X8 )
=> ! [X0: term,X1: term] :
( ( X8 @ X0 )
=> ( ( X8 @ X1 )
=> ( X8 @ ( ap @ X0 @ X1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem2v2) ).
thf(f459,plain,
( hoasapnotvar
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( ^ [Y2: subst,Y3: term,Y4: subst] : ( var @ ( sub @ Y3 @ Y4 ) )
@ id
@ ( ^ [Y2: subst,Y3: term,Y4: subst,Y5: term] : ( ap @ ( sub @ Y3 @ Y4 ) @ Y5 )
@ id
@ Y1
@ id
@ Y0 )
@ id ) ) ) ),
inference(definition_unfolding,[],[f403,f444,f336]) ).
thf(f444,plain,
( hoasvar
= ( ^ [Y0: subst,Y1: term,Y2: subst] : ( var @ ( sub @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f283]) ).
thf(f283,plain,
( hoasvar
= ( ^ [Y0: subst,Y1: term,Y2: subst] : ( var @ ( sub @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f282]) ).
thf(f282,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/sandbox2/benchmark/theBenchmark.p',hoasvar) ).
thf(f403,plain,
( hoasapnotvar
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( hoasvar @ id @ ( hoasap @ id @ Y1 @ id @ Y0 ) @ id ) ) ) ),
inference(cnf_transformation,[],[f211]) ).
thf(f211,plain,
( hoasapnotvar
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( hoasvar @ id @ ( hoasap @ id @ Y1 @ id @ Y0 ) @ id ) ) ) ),
inference(fool_elimination,[],[f210]) ).
thf(f210,plain,
( hoasapnotvar
= ( ! [X0: term,X1: term] :
~ ( hoasvar @ id @ ( hoasap @ id @ X0 @ id @ X1 ) @ id ) ) ),
inference(rectify,[],[f73]) ).
thf(f73,axiom,
( hoasapnotvar
= ( ! [X0: term,X1: term] :
~ ( hoasvar @ id @ ( hoasap @ id @ X0 @ id @ X1 ) @ id ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasapnotvar) ).
thf(f458,plain,
( hoaslamnotvar
= ( !! @ ( 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 ) ) ) ) )
=> ~ ( ^ [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,[],[f417,f444,f389]) ).
thf(f389,plain,
( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( lam @ ( Y1 @ sh @ one ) ) ) ),
inference(cnf_transformation,[],[f135]) ).
thf(f135,plain,
( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( lam @ ( Y1 @ sh @ one ) ) ) ),
inference(fool_elimination,[],[f134]) ).
thf(f134,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/sandbox2/benchmark/theBenchmark.p',hoaslam) ).
thf(f417,plain,
( hoaslamnotvar
= ( !! @ ( 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 ) ) ) ) )
=> ~ ( hoasvar @ id
@ ( hoaslam @ id
@ ^ [Y1: subst,Y2: term] : ( Y0 @ Y1 @ Y2 ) )
@ id ) ) ) ),
inference(cnf_transformation,[],[f122]) ).
thf(f122,plain,
( hoaslamnotvar
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) )
= ( sub @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
=> ~ ( hoasvar @ id
@ ( hoaslam @ id
@ ^ [Y1: subst,Y2: term] : ( Y0 @ Y1 @ Y2 ) )
@ id ) ) ) ),
inference(fool_elimination,[],[f121]) ).
thf(f121,plain,
( hoaslamnotvar
= ( ! [X0: subst > term > term] :
( ! [X1: term,X2: subst,X3: subst] :
( ( X0 @ ( comp @ X2 @ X3 ) @ ( sub @ X1 @ X3 ) )
= ( sub @ ( X0 @ X2 @ X1 ) @ X3 ) )
=> ~ ( hoasvar @ id
@ ( hoaslam @ id
@ ^ [X4: subst,X5: term] : ( X0 @ X4 @ X5 ) )
@ id ) ) ) ),
inference(rectify,[],[f70]) ).
thf(f70,axiom,
( hoaslamnotvar
= ( ! [X10: subst > term > term] :
( ! [X0: term,X2: subst,X3: subst] :
( ( sub @ ( X10 @ X2 @ X0 ) @ X3 )
= ( X10 @ ( comp @ X2 @ X3 ) @ ( sub @ X0 @ X3 ) ) )
=> ~ ( hoasvar @ id
@ ( hoaslam @ id
@ ^ [X2: subst,X0: term] : ( X10 @ X2 @ X0 ) )
@ id ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoaslamnotvar) ).
thf(f457,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
@ Y1
@ id
@ Y2 )
!= ( ^ [Y3: subst,Y4: subst > term > term] : ( lam @ ( Y4 @ sh @ one ) )
@ id
@ ^ [Y3: subst,Y4: term] : ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f350,f336,f389]) ).
thf(f350,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 @ Y1 @ id @ Y2 )
!= ( hoaslam @ id
@ ^ [Y3: subst,Y4: term] : ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f183]) ).
thf(f183,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 @ Y1 @ id @ Y2 )
!= ( hoaslam @ id
@ ^ [Y3: subst,Y4: term] : ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f182]) ).
thf(f182,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 @ X5 @ id @ X4 )
!= ( 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 ) ) )
=> ! [X1: term,X0: term] :
( ( hoasap @ id @ X0 @ id @ X1 )
!= ( hoaslam @ id
@ ^ [X2: subst,X6: term] : ( X10 @ X2 @ X6 ) ) ) )
= hoaslamnotap ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoaslamnotap) ).
thf(f456,plain,
( hoaslaminj
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y0 @ Y2 @ Y3 ) )
= ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f370,f389,f389]) ).
thf(f370,plain,
( hoaslaminj
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y0 @ Y2 @ Y3 ) )
= ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f167]) ).
thf(f167,plain,
( hoaslaminj
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y1 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y2 @ Y4 ) )
= ( sub @ ( Y1 @ Y3 @ Y2 ) @ Y4 ) ) ) ) )
=> ( ( ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y0 @ Y2 @ Y3 ) )
= ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f166]) ).
thf(f166,plain,
! [X0: subst > term > term] :
( ( ! [X1: term,X2: subst,X3: subst] :
( ( X0 @ ( comp @ X3 @ X2 ) @ ( sub @ X1 @ X2 ) )
= ( sub @ ( X0 @ X3 @ X1 ) @ X2 ) )
=> ! [X4: subst > term > term] :
( ! [X5: subst,X6: subst,X7: term] :
( ( X4 @ ( comp @ X6 @ X5 ) @ ( sub @ X7 @ X5 ) )
= ( sub @ ( X4 @ X6 @ X7 ) @ X5 ) )
=> ( ( ( hoaslam @ id
@ ^ [X8: subst,X9: term] : ( X0 @ X8 @ X9 ) )
= ( hoaslam @ id
@ ^ [X10: subst,X11: term] : ( X4 @ X10 @ X11 ) ) )
=> ! [X12: subst,X13: term] :
( ( X4 @ X12 @ X13 )
= ( X0 @ X12 @ X13 ) ) ) ) )
= hoaslaminj ),
inference(rectify,[],[f64]) ).
thf(f64,axiom,
! [X10: subst > term > term] :
( ( ! [X0: term,X3: subst,X2: subst] :
( ( sub @ ( X10 @ X2 @ X0 ) @ X3 )
= ( X10 @ ( comp @ X2 @ X3 ) @ ( sub @ X0 @ X3 ) ) )
=> ! [X11: subst > term > term] :
( ! [X3: subst,X2: subst,X0: term] :
( ( sub @ ( X11 @ X2 @ X0 ) @ X3 )
= ( X11 @ ( comp @ X2 @ X3 ) @ ( sub @ X0 @ X3 ) ) )
=> ( ( ( hoaslam @ id
@ ^ [X2: subst,X0: term] : ( X10 @ X2 @ X0 ) )
= ( hoaslam @ id
@ ^ [X2: subst,X0: term] : ( X11 @ X2 @ X0 ) ) )
=> ! [X2: subst,X0: term] :
( ( X10 @ X2 @ X0 )
= ( X11 @ X2 @ X0 ) ) ) ) )
= hoaslaminj ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoaslaminj) ).
thf(f455,plain,
( hoasapinj2
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y2
@ id
@ Y0 )
= ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y1
@ id
@ Y3 ) )
=> ( Y3 = Y0 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f418,f336,f336]) ).
thf(f418,plain,
( hoasapinj2
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( hoasap @ id @ Y2 @ id @ Y0 )
= ( hoasap @ id @ Y1 @ id @ Y3 ) )
=> ( Y3 = Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f195]) ).
thf(f195,plain,
( hoasapinj2
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( hoasap @ id @ Y2 @ id @ Y0 )
= ( hoasap @ id @ Y1 @ id @ Y3 ) )
=> ( Y3 = Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f194]) ).
thf(f194,plain,
( hoasapinj2
= ( ! [X0: term,X1: term,X2: term,X3: term] :
( ( ( hoasap @ id @ X1 @ id @ X3 )
= ( hoasap @ id @ X2 @ id @ X0 ) )
=> ( X0 = X3 ) ) ) ),
inference(rectify,[],[f61]) ).
thf(f61,axiom,
( hoasapinj2
= ( ! [X7: term,X0: term,X1: term,X6: term] :
( ( ( hoasap @ id @ X0 @ id @ X6 )
= ( hoasap @ id @ X1 @ id @ X7 ) )
=> ( X6 = X7 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasapinj2) ).
thf(f454,plain,
( hoasapinj1
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y3
@ id
@ Y0 )
= ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y2
@ id
@ Y1 ) )
=> ( Y3 = Y2 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f358,f336,f336]) ).
thf(f358,plain,
( hoasapinj1
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( hoasap @ id @ Y3 @ id @ Y0 )
= ( hoasap @ id @ Y2 @ id @ Y1 ) )
=> ( Y3 = Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f233]) ).
thf(f233,plain,
( hoasapinj1
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( hoasap @ id @ Y3 @ id @ Y0 )
= ( hoasap @ id @ Y2 @ id @ Y1 ) )
=> ( Y3 = Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f232]) ).
thf(f232,plain,
! [X0: term,X1: term,X2: term,X3: term] :
( ( ( ( hoasap @ id @ X0 @ id @ X3 )
= ( hoasap @ id @ X1 @ id @ X2 ) )
=> ( X0 = X1 ) )
= hoasapinj1 ),
inference(rectify,[],[f58]) ).
thf(f58,axiom,
! [X1: term,X0: term,X6: term,X7: term] :
( ( ( ( hoasap @ id @ X0 @ id @ X6 )
= ( hoasap @ id @ X1 @ id @ X7 ) )
=> ( X0 = X1 ) )
= hoasapinj1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasapinj1) ).
thf(f440,plain,
( termmset
= ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f118]) ).
thf(f118,plain,
( termmset
= ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f117]) ).
thf(f117,plain,
( ( termmset
= ( ! [X0: term,X1: subst,X2: subst] :
( ( sub @ X0 @ ( comp @ X1 @ X2 ) )
= ( sub @ ( sub @ X0 @ X1 ) @ X2 ) ) ) )
& ! [X3: term] :
( ( sub @ X3 @ id )
= X3 ) ),
inference(rectify,[],[f52]) ).
thf(f52,axiom,
( ( termmset
= ( ! [X0: term,X2: subst,X3: subst] :
( ( sub @ ( sub @ X0 @ X2 ) @ X3 )
= ( sub @ X0 @ ( comp @ X2 @ X3 ) ) ) ) )
& ! [X0: term] :
( ( sub @ X0 @ id )
= X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',termmset) ).
thf(f365,plain,
( substmonoid
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( comp @ ( comp @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) ) ),
inference(cnf_transformation,[],[f273]) ).
thf(f273,plain,
( substmonoid
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y0 @ ( comp @ Y2 @ Y1 ) )
= ( comp @ ( comp @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
& ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) ) ),
inference(fool_elimination,[],[f272]) ).
thf(f272,plain,
( ( substmonoid
= ( ! [X0: subst] :
( ( comp @ X0 @ id )
= X0 ) ) )
& ! [X1: subst] :
( ( comp @ id @ X1 )
= X1 )
& ! [X2: subst,X3: subst,X4: subst] :
( ( comp @ X4 @ ( comp @ X2 @ X3 ) )
= ( comp @ ( comp @ X4 @ X2 ) @ X3 ) ) ),
inference(rectify,[],[f49]) ).
thf(f49,axiom,
( ( substmonoid
= ( ! [X2: subst] :
( ( comp @ X2 @ id )
= X2 ) ) )
& ! [X2: subst] :
( ( comp @ id @ X2 )
= X2 )
& ! [X3: subst,X4: subst,X2: subst] :
( ( comp @ ( comp @ X2 @ X3 ) @ X4 )
= ( comp @ X2 @ ( comp @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substmonoid) ).
thf(f343,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,[],[f278]) ).
thf(f278,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,[],[f277]) ).
thf(f277,plain,
( induction2
= ( ! [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 ) ) ) ) ) ),
inference(rectify,[],[f46]) ).
thf(f46,axiom,
( induction2
= ( ! [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 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',induction2) ).
thf(f420,plain,
( induction2lem
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f308]) ).
thf(f308,plain,
( induction2lem
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y1 ) ) ) )
=> ( Y0 @ ( sub @ Y2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f307]) ).
thf(f307,plain,
! [X0: term > $o] :
( ( ! [X1: term,X2: term] :
( ( X0 @ X1 )
=> ( ( X0 @ X2 )
=> ( X0 @ ( ap @ X1 @ X2 ) ) ) )
=> ( ! [X3: term] :
( ! [X4: term] :
( ( X0 @ X4 )
=> ( X0 @ ( sub @ X3 @ ( push @ X4 @ id ) ) ) )
=> ( X0 @ ( lam @ X3 ) ) )
=> ! [X5: term,X6: subst] :
( ! [X7: term] :
( ( var @ X7 )
=> ( X0 @ ( sub @ X7 @ X6 ) ) )
=> ( X0 @ ( sub @ X5 @ X6 ) ) ) ) )
= induction2lem ),
inference(rectify,[],[f43]) ).
thf(f43,axiom,
! [X5: term > $o] :
( ( ! [X0: term,X1: term] :
( ( X5 @ X0 )
=> ( ( X5 @ X1 )
=> ( X5 @ ( ap @ X0 @ X1 ) ) ) )
=> ( ! [X0: term] :
( ! [X1: term] :
( ( X5 @ X1 )
=> ( X5 @ ( sub @ X0 @ ( push @ X1 @ id ) ) ) )
=> ( X5 @ ( lam @ X0 ) ) )
=> ! [X0: term,X2: subst] :
( ! [X1: term] :
( ( var @ X1 )
=> ( X5 @ ( sub @ X1 @ X2 ) ) )
=> ( X5 @ ( sub @ X0 @ X2 ) ) ) ) )
= induction2lem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',induction2lem) ).
thf(f355,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,[],[f145]) ).
thf(f145,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,[],[f144]) ).
thf(f144,plain,
( pushprop
= ( ! [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 ) ) ) ) ) ) ) ),
inference(rectify,[],[f39]) ).
thf(f39,axiom,
( pushprop
= ( ! [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 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pushprop) ).
thf(f366,plain,
( induction
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f151]) ).
thf(f151,plain,
( induction
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f150]) ).
thf(f150,plain,
( induction
= ( ! [X0: term > $o] :
( ! [X1: term] :
( ( var @ X1 )
=> ( X0 @ X1 ) )
=> ( ! [X2: term,X3: term] :
( ( X0 @ X2 )
=> ( ( X0 @ X3 )
=> ( X0 @ ( ap @ X2 @ X3 ) ) ) )
=> ( ! [X4: term] :
( ( X0 @ X4 )
=> ( X0 @ ( lam @ X4 ) ) )
=> ! [X5: term] : ( X0 @ X5 ) ) ) ) ) ),
inference(rectify,[],[f23]) ).
thf(f23,axiom,
( induction
= ( ! [X5: term > $o] :
( ! [X0: term] :
( ( var @ X0 )
=> ( X5 @ X0 ) )
=> ( ! [X0: term,X1: term] :
( ( X5 @ X0 )
=> ( ( X5 @ X1 )
=> ( X5 @ ( ap @ X0 @ X1 ) ) ) )
=> ( ! [X0: term] :
( ( X5 @ X0 )
=> ( X5 @ ( lam @ X0 ) ) )
=> ! [X0: term] : ( X5 @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',induction) ).
thf(f385,plain,
( lamnotvar
= ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f235]) ).
thf(f235,plain,
( lamnotvar
= ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) ) ),
inference(fool_elimination,[],[f234]) ).
thf(f234,plain,
( lamnotvar
= ( ! [X0: term] :
~ ( var @ ( lam @ X0 ) ) ) ),
inference(rectify,[],[f22]) ).
thf(f22,axiom,
( lamnotvar
= ( ! [X0: term] :
~ ( var @ ( lam @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lamnotvar) ).
thf(f347,plain,
( apnotvar
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f271]) ).
thf(f271,plain,
( apnotvar
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f270]) ).
thf(f270,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/sandbox2/benchmark/theBenchmark.p',apnotvar) ).
thf(f371,plain,
( lamnotap
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f296]) ).
thf(f296,plain,
( lamnotap
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y2 )
!= ( ap @ Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f295]) ).
thf(f295,plain,
! [X0: term,X1: term,X2: term] :
( ( ( lam @ X0 )
!= ( ap @ X2 @ X1 ) )
= lamnotap ),
inference(rectify,[],[f20]) ).
thf(f20,axiom,
! [X0: term,X6: term,X1: term] :
( ( ( lam @ X0 )
!= ( ap @ X1 @ X6 ) )
= lamnotap ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lamnotap) ).
thf(f372,plain,
( shinj
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( sub @ Y1 @ sh )
= ( sub @ Y0 @ sh ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f332]) ).
thf(f332,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/sandbox2/benchmark/theBenchmark.p',shinj) ).
thf(f346,plain,
( laminj
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f123]) ).
thf(f123,plain,
( laminj
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f18,axiom,
! [X0: term,X1: term] :
( ( ( ( lam @ X0 )
= ( lam @ X1 ) )
=> ( X0 = X1 ) )
= laminj ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',laminj) ).
thf(f419,plain,
( apinj2
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y0 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f315]) ).
thf(f315,plain,
( apinj2
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y3 @ Y2 )
= ( ap @ Y0 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f314]) ).
thf(f314,plain,
! [X0: term,X1: term,X2: term,X3: term] :
( ( ( ( ap @ X0 @ X1 )
= ( ap @ X3 @ X2 ) )
=> ( X1 = X2 ) )
= apinj2 ),
inference(rectify,[],[f17]) ).
thf(f17,axiom,
! [X1: term,X7: term,X6: term,X0: term] :
( ( ( ( ap @ X0 @ X6 )
= ( ap @ X1 @ X7 ) )
=> ( X6 = X7 ) )
= apinj2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apinj2) ).
thf(f404,plain,
( apinj1
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y1 )
= ( ap @ Y2 @ Y3 ) )
=> ( Y2 = Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f155]) ).
thf(f155,plain,
( apinj1
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y1 )
= ( ap @ Y2 @ Y3 ) )
=> ( Y2 = Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f154]) ).
thf(f154,plain,
( apinj1
= ( ! [X0: term,X1: term,X2: term,X3: term] :
( ( ( ap @ X3 @ X2 )
= ( ap @ X1 @ X0 ) )
=> ( X1 = X3 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f16,axiom,
( apinj1
= ( ! [X6: term,X0: term,X7: term,X1: term] :
( ( ( ap @ X0 @ X6 )
= ( ap @ X1 @ X7 ) )
=> ( X0 = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apinj1) ).
thf(f426,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,[],[f153]) ).
thf(f153,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,[],[f152]) ).
thf(f152,plain,
( ulamvarind
= ( ! [X0: term > $o] :
( ( X0 @ one )
=> ( ! [X1: term] :
( ( var @ X1 )
=> ( ( X0 @ X1 )
=> ( X0 @ ( sub @ X1 @ sh ) ) ) )
=> ! [X2: term] :
( ( var @ X2 )
=> ( X0 @ X2 ) ) ) ) ) ),
inference(rectify,[],[f15]) ).
thf(f15,axiom,
( ulamvarind
= ( ! [X5: term > $o] :
( ( X5 @ one )
=> ( ! [X0: term] :
( ( var @ X0 )
=> ( ( X5 @ X0 )
=> ( X5 @ ( sub @ X0 @ sh ) ) ) )
=> ! [X0: term] :
( ( var @ X0 )
=> ( X5 @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ulamvarind) ).
thf(f425,plain,
( ulamvarsh
= ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) ) ),
inference(cnf_transformation,[],[f197]) ).
thf(f197,plain,
( ulamvarsh
= ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) ) ),
inference(fool_elimination,[],[f196]) ).
thf(f196,plain,
! [X0: term] :
( ( ( var @ X0 )
=> ( var @ ( sub @ X0 @ sh ) ) )
= ulamvarsh ),
inference(rectify,[],[f14]) ).
thf(f14,axiom,
! [X0: term] :
( ( ( var @ X0 )
=> ( var @ ( sub @ X0 @ sh ) ) )
= ulamvarsh ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ulamvarsh) ).
thf(f435,plain,
( ulamvar1
= ( var @ one ) ),
inference(cnf_transformation,[],[f231]) ).
thf(f231,plain,
( ulamvar1
= ( var @ one ) ),
inference(fool_elimination,[],[f13]) ).
thf(f13,axiom,
( ulamvar1
= ( var @ one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ulamvar1) ).
thf(f395,plain,
( axscons
= ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) ) ),
inference(cnf_transformation,[],[f120]) ).
thf(f120,plain,
( axscons
= ( !! @ subst
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) ) ),
inference(fool_elimination,[],[f119]) ).
thf(f119,plain,
! [X0: subst] :
( ( ( push @ ( sub @ one @ X0 ) @ ( comp @ sh @ X0 ) )
= X0 )
= axscons ),
inference(rectify,[],[f12]) ).
thf(f12,axiom,
! [X2: subst] :
( ( ( push @ ( sub @ one @ X2 ) @ ( comp @ sh @ X2 ) )
= X2 )
= axscons ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axscons) ).
thf(f381,plain,
( axvarshift
= ( id
= ( push @ one @ sh ) ) ),
inference(cnf_transformation,[],[f284]) ).
thf(f284,plain,
( axvarshift
= ( id
= ( push @ one @ sh ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f11,axiom,
( axvarshift
= ( id
= ( push @ one @ sh ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axvarshift) ).
thf(f434,plain,
( axidr
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) ),
inference(cnf_transformation,[],[f207]) ).
thf(f207,plain,
( axidr
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) ) ),
inference(fool_elimination,[],[f206]) ).
thf(f206,plain,
! [X0: subst] :
( ( ( comp @ X0 @ id )
= X0 )
= axidr ),
inference(rectify,[],[f10]) ).
thf(f10,axiom,
! [X2: subst] :
( ( ( comp @ X2 @ id )
= X2 )
= axidr ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axidr) ).
thf(f400,plain,
( axmap
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y1 ) @ Y0 )
= ( push @ ( sub @ Y2 @ Y0 ) @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f327]) ).
thf(f327,plain,
( axmap
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y1 ) @ Y0 )
= ( push @ ( sub @ Y2 @ Y0 ) @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f326]) ).
thf(f326,plain,
! [X0: term,X1: subst,X2: subst] :
( ( ( comp @ ( push @ X0 @ X1 ) @ X2 )
= ( push @ ( sub @ X0 @ X2 ) @ ( comp @ X1 @ X2 ) ) )
= axmap ),
inference(rectify,[],[f9]) ).
thf(f9,axiom,
! [X0: term,X2: subst,X3: subst] :
( ( ( comp @ ( push @ X0 @ X2 ) @ X3 )
= ( push @ ( sub @ X0 @ X3 ) @ ( comp @ X2 @ X3 ) ) )
= axmap ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axmap) ).
thf(f392,plain,
( axassoc
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) )
= ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f185]) ).
thf(f185,plain,
( axassoc
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( comp @ Y1 @ ( comp @ Y2 @ Y0 ) )
= ( comp @ ( comp @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f184]) ).
thf(f184,plain,
! [X0: subst,X1: subst,X2: subst] :
( ( ( comp @ X1 @ ( comp @ X0 @ X2 ) )
= ( comp @ ( comp @ X1 @ X0 ) @ X2 ) )
= axassoc ),
inference(rectify,[],[f8]) ).
thf(f8,axiom,
! [X3: subst,X2: subst,X4: subst] :
( ( ( comp @ ( comp @ X2 @ X3 ) @ X4 )
= ( comp @ X2 @ ( comp @ X3 @ X4 ) ) )
= axassoc ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axassoc) ).
thf(f405,plain,
( axshiftcons
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) ) ),
inference(cnf_transformation,[],[f290]) ).
thf(f290,plain,
( axshiftcons
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) ) ),
inference(fool_elimination,[],[f289]) ).
thf(f289,plain,
( axshiftcons
= ( ! [X0: term,X1: subst] :
( ( comp @ sh @ ( push @ X0 @ X1 ) )
= X1 ) ) ),
inference(rectify,[],[f7]) ).
thf(f7,axiom,
( axshiftcons
= ( ! [X0: term,X2: subst] :
( ( comp @ sh @ ( push @ X0 @ X2 ) )
= X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axshiftcons) ).
thf(f374,plain,
( axidl
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) ),
inference(cnf_transformation,[],[f141]) ).
thf(f141,plain,
( axidl
= ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) ) ),
inference(fool_elimination,[],[f140]) ).
thf(f140,plain,
( axidl
= ( ! [X0: subst] :
( ( comp @ id @ X0 )
= X0 ) ) ),
inference(rectify,[],[f6]) ).
thf(f6,axiom,
( axidl
= ( ! [X2: subst] :
( ( comp @ id @ X2 )
= X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axidl) ).
thf(f354,plain,
( axclos
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f127]) ).
thf(f127,plain,
( axclos
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) )
= ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f126]) ).
thf(f126,plain,
! [X0: term,X1: subst,X2: subst] :
( ( ( sub @ X0 @ ( comp @ X1 @ X2 ) )
= ( sub @ ( sub @ X0 @ X1 ) @ X2 ) )
= axclos ),
inference(rectify,[],[f5]) ).
thf(f5,axiom,
! [X0: term,X2: subst,X3: subst] :
( ( ( sub @ ( sub @ X0 @ X2 ) @ X3 )
= ( sub @ X0 @ ( comp @ X2 @ X3 ) ) )
= axclos ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axclos) ).
thf(f416,plain,
( axabs
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) )
= ( sub @ ( lam @ Y0 ) @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f193]) ).
thf(f193,plain,
( axabs
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) )
= ( sub @ ( lam @ Y0 ) @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f192]) ).
thf(f192,plain,
! [X0: subst,X1: term] :
( ( ( lam @ ( sub @ X1 @ ( push @ one @ ( comp @ X0 @ sh ) ) ) )
= ( sub @ ( lam @ X1 ) @ X0 ) )
= axabs ),
inference(rectify,[],[f4]) ).
thf(f4,axiom,
! [X2: subst,X0: term] :
( ( ( sub @ ( lam @ X0 ) @ X2 )
= ( lam @ ( sub @ X0 @ ( push @ one @ ( comp @ X2 @ sh ) ) ) ) )
= axabs ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axabs) ).
thf(f391,plain,
( axvarid
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ),
inference(cnf_transformation,[],[f313]) ).
thf(f313,plain,
( axvarid
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f3,axiom,
( axvarid
= ( ! [X0: term] :
( ( sub @ X0 @ id )
= X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axvarid) ).
thf(f357,plain,
( axvarcons
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) ) ),
inference(cnf_transformation,[],[f125]) ).
thf(f125,plain,
( axvarcons
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) ) ),
inference(fool_elimination,[],[f124]) ).
thf(f124,plain,
( axvarcons
= ( ! [X0: subst,X1: term] :
( ( sub @ one @ ( push @ X1 @ X0 ) )
= X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
( axvarcons
= ( ! [X2: subst,X0: term] :
( ( sub @ one @ ( push @ X0 @ X2 ) )
= X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axvarcons) ).
thf(f439,plain,
( axapp
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( ap @ ( sub @ Y0 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( ap @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f163]) ).
thf(f163,plain,
( axapp
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( ap @ ( sub @ Y0 @ Y2 ) @ ( sub @ Y1 @ Y2 ) )
= ( sub @ ( ap @ Y0 @ Y1 ) @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f162]) ).
thf(f162,plain,
( axapp
= ( ! [X0: subst,X1: term,X2: term] :
( ( ap @ ( sub @ X2 @ X0 ) @ ( sub @ X1 @ X0 ) )
= ( sub @ ( ap @ X2 @ X1 ) @ X0 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
( axapp
= ( ! [X2: subst,X1: term,X0: term] :
( ( sub @ ( ap @ X0 @ X1 ) @ X2 )
= ( ap @ ( sub @ X0 @ X2 ) @ ( sub @ X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axapp) ).
thf(f401,plain,
( hoasinduction_lem2v2_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem2v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f216]) ).
thf(f216,plain,
( hoasinduction_lem2v2_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem2v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f215]) ).
thf(f215,plain,
( ( hoasinduction_lem2v2_gthm = axapp )
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem2v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f82]) ).
thf(f82,axiom,
( ( hoasinduction_lem2v2_gthm = axapp )
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem2v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem2v2_gthm) ).
thf(f396,plain,
( $true = ~ hoasinduction_lem2v2_gthm ),
inference(cnf_transformation,[],[f230]) ).
thf(f230,plain,
( $true = ~ hoasinduction_lem2v2_gthm ),
inference(fool_elimination,[],[f229]) ).
thf(f229,plain,
~ hoasinduction_lem2v2_gthm,
inference(rectify,[],[f115]) ).
thf(f115,negated_conjecture,
~ hoasinduction_lem2v2_gthm,
inference(negated_conjecture,[],[f114]) ).
thf(f114,conjecture,
hoasinduction_lem2v2_gthm,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(f1111,plain,
( ( $false
= ( sK18 @ sK20 ) )
| ( $false
= ( sK18 @ sK21 ) ) ),
inference(trivial_inequality_removal,[],[f1109]) ).
thf(f1109,plain,
( ( $true = $false )
| ( $false
= ( sK18 @ sK20 ) )
| ( $false
= ( sK18 @ sK21 ) ) ),
inference(superposition,[],[f858,f872]) ).
thf(f872,plain,
! [X2: term,X1: term] :
( ( $true
= ( sK18 @ ( ap @ X2 @ X1 ) ) )
| ( ( sK18 @ X1 )
= $false )
| ( ( sK18 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[],[f871]) ).
thf(f871,plain,
! [X2: term,X1: term] :
( ( ( sK18 @ X2 )
= $false )
| ( $true
= ( ( sK18 @ X1 )
=> ( sK18 @ ( ap @ X2 @ X1 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f870]) ).
thf(f870,plain,
! [X2: term,X1: term] :
( $true
= ( ( sK18 @ X2 )
=> ( ( sK18 @ X1 )
=> ( sK18 @ ( ap @ X2 @ X1 ) ) ) ) ),
inference(forward_demodulation,[],[f869,f553]) ).
thf(f553,plain,
! [X1: term] :
( ( sub @ X1 @ id )
= X1 ),
inference(equality_proxy_clausification,[],[f552]) ).
thf(f552,plain,
! [X1: term] :
( ( ( sub @ X1 @ id )
= X1 )
= $true ),
inference(beta_eta_normalization,[],[f551]) ).
thf(f551,plain,
! [X1: term] :
( $true
= ( ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 )
@ X1 ) ),
inference(pi_clausification,[],[f550]) ).
thf(f550,plain,
( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ),
inference(binary_proxy_clausification,[],[f542]) ).
thf(f869,plain,
! [X2: term,X1: term] :
( $true
= ( ( sK18 @ X2 )
=> ( ( sK18 @ X1 )
=> ( sK18 @ ( ap @ ( sub @ X2 @ id ) @ X1 ) ) ) ) ),
inference(forward_demodulation,[],[f868,f862]) ).
thf(f862,plain,
! [X1: term] :
( ( sK18 @ X1 )
= ( sK19 @ id @ X1 @ id ) ),
inference(binary_proxy_clausification,[],[f861]) ).
thf(f861,plain,
! [X1: term] :
( ( ( sK19 @ id @ X1 @ id )
= ( sK18 @ X1 ) )
= $true ),
inference(beta_eta_normalization,[],[f860]) ).
thf(f860,plain,
! [X1: term] :
( $true
= ( ^ [Y0: term] :
( ( sK19 @ id @ Y0 @ id )
= ( sK18 @ Y0 ) )
@ X1 ) ),
inference(pi_clausification,[],[f851]) ).
thf(f851,plain,
( ( !! @ term
@ ^ [Y0: term] :
( ( sK19 @ id @ Y0 @ id )
= ( sK18 @ Y0 ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f848]) ).
thf(f868,plain,
! [X2: term,X1: term] :
( $true
= ( ( sK18 @ X2 )
=> ( ( sK18 @ X1 )
=> ( sK19 @ id @ ( ap @ ( sub @ X2 @ id ) @ X1 ) @ id ) ) ) ),
inference(forward_demodulation,[],[f867,f862]) ).
thf(f867,plain,
! [X2: term,X1: term] :
( $true
= ( ( sK18 @ X2 )
=> ( ( sK19 @ id @ X1 @ id )
=> ( sK19 @ id @ ( ap @ ( sub @ X2 @ id ) @ X1 ) @ id ) ) ) ),
inference(forward_demodulation,[],[f866,f862]) ).
thf(f866,plain,
! [X2: term,X1: term] :
( $true
= ( ( sK19 @ id @ X2 @ id )
=> ( ( sK19 @ id @ X1 @ id )
=> ( sK19 @ id @ ( ap @ ( sub @ X2 @ id ) @ X1 ) @ id ) ) ) ),
inference(beta_eta_normalization,[],[f865]) ).
thf(f865,plain,
! [X2: term,X1: term] :
( $true
= ( ^ [Y0: term] :
( ( sK19 @ id @ Y0 @ id )
=> ( ( sK19 @ id @ X1 @ id )
=> ( sK19 @ id @ ( ap @ ( sub @ Y0 @ id ) @ X1 ) @ id ) ) )
@ X2 ) ),
inference(pi_clausification,[],[f864]) ).
thf(f864,plain,
! [X1: term] :
( ( !! @ term
@ ^ [Y0: term] :
( ( sK19 @ id @ Y0 @ id )
=> ( ( sK19 @ id @ X1 @ id )
=> ( sK19 @ id @ ( ap @ ( sub @ Y0 @ id ) @ X1 ) @ id ) ) ) )
= $true ),
inference(beta_eta_normalization,[],[f863]) ).
thf(f863,plain,
! [X1: term] :
( ( ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK19 @ id @ Y1 @ id )
=> ( ( sK19 @ id @ Y0 @ id )
=> ( sK19 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[],[f849]) ).
thf(f849,plain,
( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK19 @ id @ Y1 @ id )
=> ( ( sK19 @ id @ Y0 @ id )
=> ( sK19 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f837]) ).
thf(f858,plain,
( ( sK18 @ ( ap @ sK21 @ sK20 ) )
= $false ),
inference(binary_proxy_clausification,[],[f856]) ).
thf(f857,plain,
( $true
= ( sK18 @ sK21 ) ),
inference(binary_proxy_clausification,[],[f855]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG264^3 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.03/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.13/0.36 % Computer : n002.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Sat May 18 23:34:38 EDT 2024
% 0.13/0.36 % CPUTime :
% 0.13/0.36 This is a TH0_THM_EQU_NAR problem
% 0.13/0.36 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/sandbox2/benchmark/theBenchmark.p
% 0.20/0.39 % (23394)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.20/0.39 % (23392)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)
% 0.20/0.39 % (23390)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)
% 0.20/0.39 % (23389)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)
% 0.20/0.39 % (23391)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.39 % (23393)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)
% 0.20/0.39 % (23395)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)
% 0.20/0.39 % (23392)Instruction limit reached!
% 0.20/0.39 % (23392)------------------------------
% 0.20/0.39 % (23392)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.39 % (23392)Termination reason: Unknown
% 0.20/0.39 % (23392)Termination phase: shuffling
% 0.20/0.39
% 0.20/0.39 % (23392)Memory used [KB]: 1279
% 0.20/0.39 % (23392)Time elapsed: 0.003 s
% 0.20/0.39 % (23392)Instructions burned: 3 (million)
% 0.20/0.39 % (23392)------------------------------
% 0.20/0.39 % (23392)------------------------------
% 0.20/0.39 % (23389)Instruction limit reached!
% 0.20/0.39 % (23389)------------------------------
% 0.20/0.39 % (23389)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.39 % (23389)Termination reason: Unknown
% 0.20/0.39 % (23389)Termination phase: shuffling
% 0.20/0.39
% 0.20/0.39 % (23389)Memory used [KB]: 1279
% 0.20/0.39 % (23389)Time elapsed: 0.003 s
% 0.20/0.39 % (23389)Instructions burned: 4 (million)
% 0.20/0.39 % (23389)------------------------------
% 0.20/0.39 % (23389)------------------------------
% 0.20/0.39 % (23391)Instruction limit reached!
% 0.20/0.39 % (23391)------------------------------
% 0.20/0.39 % (23391)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.39 % (23391)Termination reason: Unknown
% 0.20/0.39 % (23391)Termination phase: shuffling
% 0.20/0.39
% 0.20/0.39 % (23391)Memory used [KB]: 1279
% 0.20/0.39 % (23391)Time elapsed: 0.003 s
% 0.20/0.39 % (23391)Instructions burned: 4 (million)
% 0.20/0.39 % (23391)------------------------------
% 0.20/0.39 % (23391)------------------------------
% 0.20/0.39 % (23388)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.20/0.39 % (23395)Instruction limit reached!
% 0.20/0.39 % (23395)------------------------------
% 0.20/0.39 % (23395)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.39 % (23395)Termination reason: Unknown
% 0.20/0.39 % (23395)Termination phase: shuffling
% 0.20/0.39
% 0.20/0.39 % (23395)Memory used [KB]: 1279
% 0.20/0.39 % (23395)Time elapsed: 0.004 s
% 0.20/0.39 % (23395)Instructions burned: 4 (million)
% 0.20/0.39 % (23395)------------------------------
% 0.20/0.39 % (23395)------------------------------
% 0.20/0.40 % (23394)Instruction limit reached!
% 0.20/0.40 % (23394)------------------------------
% 0.20/0.40 % (23394)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.40 % (23394)Termination reason: Unknown
% 0.20/0.40 % (23394)Termination phase: Property scanning
% 0.20/0.40
% 0.20/0.40 % (23394)Memory used [KB]: 1663
% 0.20/0.40 % (23394)Time elapsed: 0.010 s
% 0.20/0.40 % (23394)Instructions burned: 19 (million)
% 0.20/0.40 % (23394)------------------------------
% 0.20/0.40 % (23394)------------------------------
% 0.20/0.40 % (23390)Instruction limit reached!
% 0.20/0.40 % (23390)------------------------------
% 0.20/0.40 % (23390)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.40 % (23390)Termination reason: Unknown
% 0.20/0.40 % (23390)Termination phase: Property scanning
% 0.20/0.40
% 0.20/0.40 % (23390)Memory used [KB]: 1791
% 0.20/0.40 % (23390)Time elapsed: 0.013 s
% 0.20/0.40 % (23390)Instructions burned: 27 (million)
% 0.20/0.40 % (23390)------------------------------
% 0.20/0.40 % (23390)------------------------------
% 0.20/0.40 % (23397)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)
% 0.20/0.40 % (23398)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)
% 0.20/0.40 % (23399)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)
% 0.20/0.40 % (23398)Instruction limit reached!
% 0.20/0.40 % (23398)------------------------------
% 0.20/0.40 % (23398)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.40 % (23398)Termination reason: Unknown
% 0.20/0.40 % (23398)Termination phase: shuffling
% 0.20/0.40
% 0.20/0.40 % (23398)Memory used [KB]: 1279
% 0.20/0.40 % (23398)Time elapsed: 0.003 s
% 0.20/0.40 % (23398)Instructions burned: 3 (million)
% 0.20/0.40 % (23398)------------------------------
% 0.20/0.40 % (23398)------------------------------
% 0.20/0.41 % (23393)Refutation not found, incomplete strategy
% 0.20/0.41 % (23393)------------------------------
% 0.20/0.41 % (23393)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.41 % (23393)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.41
% 0.20/0.41
% 0.20/0.41 % (23393)Memory used [KB]: 6268
% 0.20/0.41 % (23393)Time elapsed: 0.019 s
% 0.20/0.41 % (23393)Instructions burned: 37 (million)
% 0.20/0.41 % (23393)------------------------------
% 0.20/0.41 % (23393)------------------------------
% 0.20/0.41 % (23396)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)
% 0.20/0.41 % (23397)Instruction limit reached!
% 0.20/0.41 % (23397)------------------------------
% 0.20/0.41 % (23397)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.41 % (23397)Termination reason: Unknown
% 0.20/0.41 % (23397)Termination phase: Property scanning
% 0.20/0.41
% 0.20/0.41 % (23397)Memory used [KB]: 1663
% 0.20/0.41 % (23397)Time elapsed: 0.009 s
% 0.20/0.41 % (23397)Instructions burned: 15 (million)
% 0.20/0.41 % (23397)------------------------------
% 0.20/0.41 % (23397)------------------------------
% 0.20/0.41 % (23401)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.20/0.42 % (23402)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)
% 0.20/0.42 % (23402)Instruction limit reached!
% 0.20/0.42 % (23402)------------------------------
% 0.20/0.42 % (23402)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.42 % (23402)Termination reason: Unknown
% 0.20/0.42 % (23402)Termination phase: shuffling
% 0.20/0.42
% 0.20/0.42 % (23402)Memory used [KB]: 1279
% 0.20/0.42 % (23402)Time elapsed: 0.003 s
% 0.20/0.42 % (23402)Instructions burned: 3 (million)
% 0.20/0.42 % (23402)------------------------------
% 0.20/0.42 % (23402)------------------------------
% 0.20/0.42 % (23403)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)
% 0.20/0.42 % (23401)Instruction limit reached!
% 0.20/0.42 % (23401)------------------------------
% 0.20/0.42 % (23401)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.42 % (23401)Termination reason: Unknown
% 0.20/0.42 % (23401)Termination phase: shuffling
% 0.20/0.42
% 0.20/0.42 % (23401)Memory used [KB]: 1535
% 0.20/0.42 % (23401)Time elapsed: 0.009 s
% 0.20/0.42 % (23401)Instructions burned: 17 (million)
% 0.20/0.42 % (23401)------------------------------
% 0.20/0.42 % (23401)------------------------------
% 0.20/0.42 % (23403)Instruction limit reached!
% 0.20/0.42 % (23403)------------------------------
% 0.20/0.42 % (23403)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.42 % (23403)Termination reason: Unknown
% 0.20/0.42 % (23403)Termination phase: shuffling
% 0.20/0.42
% 0.20/0.42 % (23403)Memory used [KB]: 1279
% 0.20/0.42 % (23403)Time elapsed: 0.003 s
% 0.20/0.42 % (23403)Instructions burned: 4 (million)
% 0.20/0.42 % (23403)------------------------------
% 0.20/0.42 % (23403)------------------------------
% 0.20/0.42 % (23404)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)
% 0.20/0.42 % (23396)Instruction limit reached!
% 0.20/0.42 % (23396)------------------------------
% 0.20/0.42 % (23396)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.42 % (23396)Termination reason: Unknown
% 0.20/0.42 % (23396)Termination phase: Property scanning
% 0.20/0.42
% 0.20/0.42 % (23396)Memory used [KB]: 1791
% 0.20/0.42 % (23396)Time elapsed: 0.017 s
% 0.20/0.42 % (23396)Instructions burned: 38 (million)
% 0.20/0.42 % (23396)------------------------------
% 0.20/0.42 % (23396)------------------------------
% 0.20/0.43 % (23400)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.43 % (23404)Instruction limit reached!
% 0.20/0.43 % (23404)------------------------------
% 0.20/0.43 % (23404)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.43 % (23404)Termination reason: Unknown
% 0.20/0.43 % (23404)Termination phase: shuffling
% 0.20/0.43
% 0.20/0.43 % (23404)Memory used [KB]: 1407
% 0.20/0.43 % (23404)Time elapsed: 0.005 s
% 0.20/0.43 % (23404)Instructions burned: 8 (million)
% 0.20/0.43 % (23404)------------------------------
% 0.20/0.43 % (23404)------------------------------
% 0.20/0.43 % (23400)Instruction limit reached!
% 0.20/0.43 % (23400)------------------------------
% 0.20/0.43 % (23400)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.43 % (23400)Termination reason: Unknown
% 0.20/0.43 % (23400)Termination phase: shuffling
% 0.20/0.43
% 0.20/0.43 % (23400)Memory used [KB]: 1407
% 0.20/0.43 % (23400)Time elapsed: 0.004 s
% 0.20/0.43 % (23400)Instructions burned: 7 (million)
% 0.20/0.43 % (23400)------------------------------
% 0.20/0.43 % (23400)------------------------------
% 0.20/0.43 % (23405)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)
% 0.20/0.43 % (23405)Instruction limit reached!
% 0.20/0.43 % (23405)------------------------------
% 0.20/0.43 % (23405)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.43 % (23405)Termination reason: Unknown
% 0.20/0.43 % (23405)Termination phase: shuffling
% 0.20/0.43
% 0.20/0.43 % (23405)Memory used [KB]: 1279
% 0.20/0.43 % (23405)Time elapsed: 0.003 s
% 0.20/0.43 % (23405)Instructions burned: 3 (million)
% 0.20/0.43 % (23405)------------------------------
% 0.20/0.43 % (23405)------------------------------
% 0.20/0.43 % (23406)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.20/0.44 % (23406)Instruction limit reached!
% 0.20/0.44 % (23406)------------------------------
% 0.20/0.44 % (23406)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.44 % (23406)Termination reason: Unknown
% 0.20/0.44 % (23406)Termination phase: shuffling
% 0.20/0.44
% 0.20/0.44 % (23406)Memory used [KB]: 1279
% 0.20/0.44 % (23406)Time elapsed: 0.003 s
% 0.20/0.44 % (23406)Instructions burned: 4 (million)
% 0.20/0.44 % (23406)------------------------------
% 0.20/0.44 % (23406)------------------------------
% 0.20/0.44 % (23407)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)
% 0.20/0.44 % (23408)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.20/0.44 % (23409)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.20/0.44 % (23409)Instruction limit reached!
% 0.20/0.44 % (23409)------------------------------
% 0.20/0.44 % (23409)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.44 % (23409)Termination reason: Unknown
% 0.20/0.44 % (23409)Termination phase: shuffling
% 0.20/0.44
% 0.20/0.44 % (23409)Memory used [KB]: 1407
% 0.20/0.44 % (23409)Time elapsed: 0.005 s
% 0.20/0.44 % (23409)Instructions burned: 8 (million)
% 0.20/0.44 % (23410)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)
% 0.20/0.44 % (23409)------------------------------
% 0.20/0.44 % (23409)------------------------------
% 0.20/0.44 % (23407)Instruction limit reached!
% 0.20/0.44 % (23407)------------------------------
% 0.20/0.44 % (23407)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.44 % (23407)Termination reason: Unknown
% 0.20/0.44 % (23407)Termination phase: shuffling
% 0.20/0.44
% 0.20/0.44 % (23407)Memory used [KB]: 1663
% 0.20/0.44 % (23407)Time elapsed: 0.010 s
% 0.20/0.44 % (23407)Instructions burned: 20 (million)
% 0.20/0.44 % (23407)------------------------------
% 0.20/0.44 % (23407)------------------------------
% 0.20/0.45 % (23411)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)
% 0.20/0.45 % (23412)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.20/0.45 % (23412)Instruction limit reached!
% 0.20/0.45 % (23412)------------------------------
% 0.20/0.45 % (23412)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.45 % (23412)Termination reason: Unknown
% 0.20/0.45 % (23412)Termination phase: shuffling
% 0.20/0.45
% 0.20/0.45 % (23412)Memory used [KB]: 1279
% 0.20/0.45 % (23412)Time elapsed: 0.004 s
% 0.20/0.45 % (23412)Instructions burned: 5 (million)
% 0.20/0.45 % (23412)------------------------------
% 0.20/0.45 % (23412)------------------------------
% 0.20/0.45 % (23408)Refutation not found, incomplete strategy
% 0.20/0.45 % (23408)------------------------------
% 0.20/0.45 % (23408)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.45 % (23408)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.45
% 0.20/0.45
% 0.20/0.45 % (23408)Memory used [KB]: 6268
% 0.20/0.45 % (23408)Time elapsed: 0.015 s
% 0.20/0.45 % (23408)Instructions burned: 28 (million)
% 0.20/0.45 % (23408)------------------------------
% 0.20/0.45 % (23408)------------------------------
% 0.20/0.46 % (23388)Instruction limit reached!
% 0.20/0.46 % (23388)------------------------------
% 0.20/0.46 % (23388)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.46 % (23388)Termination reason: Unknown
% 0.20/0.46 % (23388)Termination phase: Saturation
% 0.20/0.46
% 0.20/0.46 % (23388)Memory used [KB]: 6652
% 0.20/0.46 % (23388)Time elapsed: 0.068 s
% 0.20/0.46 % (23388)Instructions burned: 183 (million)
% 0.20/0.46 % (23388)------------------------------
% 0.20/0.46 % (23388)------------------------------
% 0.20/0.46 % (23414)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2999ds/377Mi)
% 0.20/0.46 % (23411)Instruction limit reached!
% 0.20/0.46 % (23411)------------------------------
% 0.20/0.46 % (23411)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.46 % (23411)Termination reason: Unknown
% 0.20/0.46 % (23411)Termination phase: shuffling
% 0.20/0.46
% 0.20/0.46 % (23411)Memory used [KB]: 1663
% 0.20/0.46 % (23411)Time elapsed: 0.011 s
% 0.20/0.46 % (23411)Instructions burned: 21 (million)
% 0.20/0.46 % (23411)------------------------------
% 0.20/0.46 % (23411)------------------------------
% 0.20/0.46 % (23415)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on theBenchmark for (2999ds/779Mi)
% 0.20/0.47 % (23413)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)
% 0.20/0.47 % (23416)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on theBenchmark for (2999ds/19Mi)
% 0.20/0.47 % (23413)Instruction limit reached!
% 0.20/0.47 % (23413)------------------------------
% 0.20/0.47 % (23413)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.47 % (23413)Termination reason: Unknown
% 0.20/0.47 % (23413)Termination phase: shuffling
% 0.20/0.47
% 0.20/0.47 % (23413)Memory used [KB]: 1407
% 0.20/0.47 % (23413)Time elapsed: 0.004 s
% 0.20/0.47 % (23413)Instructions burned: 9 (million)
% 0.20/0.47 % (23413)------------------------------
% 0.20/0.47 % (23413)------------------------------
% 0.20/0.47 % (23417)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on theBenchmark for (2999ds/879Mi)
% 0.20/0.47 % (23418)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2999ds/17Mi)
% 0.20/0.47 % (23416)Instruction limit reached!
% 0.20/0.47 % (23416)------------------------------
% 0.20/0.47 % (23416)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.47 % (23416)Termination reason: Unknown
% 0.20/0.47 % (23416)Termination phase: shuffling
% 0.20/0.47
% 0.20/0.47 % (23416)Memory used [KB]: 1663
% 0.20/0.47 % (23416)Time elapsed: 0.010 s
% 0.20/0.47 % (23416)Instructions burned: 20 (million)
% 0.20/0.47 % (23416)------------------------------
% 0.20/0.47 % (23416)------------------------------
% 0.20/0.48 % (23419)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.48 % (23419)Instruction limit reached!
% 0.20/0.48 % (23419)------------------------------
% 0.20/0.48 % (23419)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.48 % (23419)Termination reason: Unknown
% 0.20/0.48 % (23419)Termination phase: shuffling
% 0.20/0.48
% 0.20/0.48 % (23419)Memory used [KB]: 1279
% 0.20/0.48 % (23419)Time elapsed: 0.003 s
% 0.20/0.48 % (23419)Instructions burned: 4 (million)
% 0.20/0.48 % (23419)------------------------------
% 0.20/0.48 % (23419)------------------------------
% 0.20/0.48 % (23418)Instruction limit reached!
% 0.20/0.48 % (23418)------------------------------
% 0.20/0.48 % (23418)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.48 % (23418)Termination reason: Unknown
% 0.20/0.48 % (23418)Termination phase: shuffling
% 0.20/0.48
% 0.20/0.48 % (23418)Memory used [KB]: 1663
% 0.20/0.48 % (23418)Time elapsed: 0.010 s
% 0.20/0.48 % (23418)Instructions burned: 19 (million)
% 0.20/0.48 % (23418)------------------------------
% 0.20/0.48 % (23418)------------------------------
% 0.20/0.49 % (23421)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 (2999ds/127Mi)
% 0.20/0.49 % (23420)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on theBenchmark for (2999ds/30Mi)
% 0.20/0.50 % (23422)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)
% 0.20/0.50 % (23417)Refutation not found, incomplete strategy
% 0.20/0.50 % (23417)------------------------------
% 0.20/0.50 % (23417)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.50 % (23417)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.50
% 0.20/0.50
% 0.20/0.50 % (23417)Memory used [KB]: 6268
% 0.20/0.50 % (23417)Time elapsed: 0.028 s
% 0.20/0.50 % (23417)Instructions burned: 61 (million)
% 0.20/0.50 % (23417)------------------------------
% 0.20/0.50 % (23417)------------------------------
% 0.20/0.50 % (23420)Instruction limit reached!
% 0.20/0.50 % (23420)------------------------------
% 0.20/0.50 % (23420)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.50 % (23420)Termination reason: Unknown
% 0.20/0.50 % (23420)Termination phase: Property scanning
% 0.20/0.50
% 0.20/0.50 % (23420)Memory used [KB]: 1791
% 0.20/0.50 % (23420)Time elapsed: 0.014 s
% 0.20/0.50 % (23420)Instructions burned: 31 (million)
% 0.20/0.50 % (23420)------------------------------
% 0.20/0.50 % (23420)------------------------------
% 0.20/0.51 % (23423)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)
% 0.20/0.52 % (23423)Instruction limit reached!
% 0.20/0.52 % (23423)------------------------------
% 0.20/0.52 % (23423)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.52 % (23423)Termination reason: Unknown
% 0.20/0.52 % (23423)Termination phase: shuffling
% 0.20/0.52
% 0.20/0.52 % (23423)Memory used [KB]: 1279
% 0.20/0.52 % (23423)Time elapsed: 0.003 s
% 0.20/0.52 % (23423)Instructions burned: 3 (million)
% 0.20/0.52 % (23423)------------------------------
% 0.20/0.52 % (23423)------------------------------
% 0.20/0.52 % (23424)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)
% 0.20/0.53 % (23424)Instruction limit reached!
% 0.20/0.53 % (23424)------------------------------
% 0.20/0.53 % (23424)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.53 % (23424)Termination reason: Unknown
% 0.20/0.53 % (23424)Termination phase: Property scanning
% 0.20/0.53
% 0.20/0.53 % (23424)Memory used [KB]: 1663
% 0.20/0.53 % (23424)Time elapsed: 0.011 s
% 0.20/0.53 % (23424)Instructions burned: 20 (million)
% 0.20/0.53 % (23424)------------------------------
% 0.20/0.53 % (23424)------------------------------
% 0.20/0.53 % (23425)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on theBenchmark for (2998ds/86Mi)
% 1.32/0.53 % (23421)Instruction limit reached!
% 1.32/0.53 % (23421)------------------------------
% 1.32/0.53 % (23421)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.32/0.53 % (23421)Termination reason: Unknown
% 1.32/0.53 % (23421)Termination phase: Saturation
% 1.32/0.53
% 1.32/0.53 % (23421)Memory used [KB]: 6524
% 1.32/0.53 % (23421)Time elapsed: 0.037 s
% 1.32/0.53 % (23421)Instructions burned: 130 (million)
% 1.32/0.53 % (23421)------------------------------
% 1.32/0.53 % (23421)------------------------------
% 1.32/0.54 % (23422)Instruction limit reached!
% 1.32/0.54 % (23422)------------------------------
% 1.32/0.54 % (23422)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.32/0.54 % (23422)Termination reason: Unknown
% 1.32/0.54 % (23422)Termination phase: Saturation
% 1.32/0.54
% 1.32/0.54 % (23422)Memory used [KB]: 6524
% 1.32/0.54 % (23422)Time elapsed: 0.042 s
% 1.32/0.54 % (23422)Instructions burned: 100 (million)
% 1.32/0.54 % (23422)------------------------------
% 1.32/0.54 % (23422)------------------------------
% 1.32/0.54 % (23426)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on theBenchmark for (2998ds/107Mi)
% 1.32/0.54 % (23427)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on theBenchmark for (2998ds/39Mi)
% 1.32/0.55 % (23428)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on theBenchmark for (2998ds/448Mi)
% 1.44/0.56 % (23427)Instruction limit reached!
% 1.44/0.56 % (23427)------------------------------
% 1.44/0.56 % (23427)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.44/0.56 % (23427)Termination reason: Unknown
% 1.44/0.56 % (23427)Termination phase: Property scanning
% 1.44/0.56
% 1.44/0.56 % (23427)Memory used [KB]: 1791
% 1.44/0.56 % (23427)Time elapsed: 0.013 s
% 1.44/0.56 % (23427)Instructions burned: 39 (million)
% 1.44/0.56 % (23427)------------------------------
% 1.44/0.56 % (23427)------------------------------
% 1.44/0.56 % (23429)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on theBenchmark for (2998ds/46Mi)
% 1.44/0.57 % (23425)Instruction limit reached!
% 1.44/0.57 % (23425)------------------------------
% 1.44/0.57 % (23425)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.44/0.57 % (23425)Termination reason: Unknown
% 1.44/0.57 % (23425)Termination phase: Property scanning
% 1.44/0.57
% 1.44/0.57 % (23425)Memory used [KB]: 2046
% 1.44/0.57 % (23425)Time elapsed: 0.036 s
% 1.44/0.57 % (23425)Instructions burned: 87 (million)
% 1.44/0.57 % (23425)------------------------------
% 1.44/0.57 % (23425)------------------------------
% 1.44/0.58 % (23429)Instruction limit reached!
% 1.44/0.58 % (23429)------------------------------
% 1.44/0.58 % (23429)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.44/0.58 % (23429)Termination reason: Unknown
% 1.44/0.58 % (23429)Termination phase: SInE selection
% 1.44/0.58
% 1.44/0.58 % (23429)Memory used [KB]: 1791
% 1.44/0.58 % (23429)Time elapsed: 0.015 s
% 1.44/0.58 % (23429)Instructions burned: 47 (million)
% 1.44/0.58 % (23429)------------------------------
% 1.44/0.58 % (23429)------------------------------
% 1.44/0.58 % (23426)Instruction limit reached!
% 1.44/0.58 % (23426)------------------------------
% 1.44/0.58 % (23426)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.44/0.58 % (23430)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)
% 1.44/0.58 % (23426)Termination reason: Unknown
% 1.44/0.58 % (23426)Termination phase: Saturation
% 1.44/0.58
% 1.44/0.58 % (23426)Memory used [KB]: 6396
% 1.44/0.58 % (23426)Time elapsed: 0.045 s
% 1.44/0.58 % (23426)Instructions burned: 108 (million)
% 1.44/0.58 % (23426)------------------------------
% 1.44/0.58 % (23426)------------------------------
% 1.44/0.59 % (23431)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)
% 1.44/0.60 % (23432)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on theBenchmark for (2997ds/149Mi)
% 1.44/0.62 % (23430)Instruction limit reached!
% 1.44/0.62 % (23430)------------------------------
% 1.44/0.62 % (23430)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.44/0.62 % (23430)Termination reason: Unknown
% 1.44/0.62 % (23430)Termination phase: Saturation
% 1.44/0.62
% 1.44/0.62 % (23430)Memory used [KB]: 2046
% 1.44/0.62 % (23430)Time elapsed: 0.041 s
% 1.44/0.62 % (23430)Instructions burned: 100 (million)
% 1.44/0.62 % (23430)------------------------------
% 1.44/0.62 % (23430)------------------------------
% 1.93/0.63 % (23414)Instruction limit reached!
% 1.93/0.63 % (23414)------------------------------
% 1.93/0.63 % (23414)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.93/0.63 % (23414)Termination reason: Unknown
% 1.93/0.63 % (23414)Termination phase: Saturation
% 1.93/0.63
% 1.93/0.63 % (23414)Memory used [KB]: 7419
% 1.93/0.63 % (23414)Time elapsed: 0.175 s
% 1.93/0.63 % (23414)Instructions burned: 378 (million)
% 1.93/0.63 % (23414)------------------------------
% 1.93/0.63 % (23414)------------------------------
% 1.93/0.64 % (23433)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on theBenchmark for (2997ds/39Mi)
% 1.93/0.65 % (23434)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on theBenchmark for (2997ds/6Mi)
% 1.93/0.65 % (23434)Instruction limit reached!
% 1.93/0.65 % (23434)------------------------------
% 1.93/0.65 % (23434)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.93/0.65 % (23434)Termination reason: Unknown
% 1.93/0.65 % (23434)Termination phase: shuffling
% 1.93/0.65
% 1.93/0.65 % (23434)Memory used [KB]: 1279
% 1.93/0.65 % (23434)Time elapsed: 0.005 s
% 1.93/0.65 % (23434)Instructions burned: 6 (million)
% 1.93/0.65 % (23434)------------------------------
% 1.93/0.65 % (23434)------------------------------
% 1.93/0.65 % (23433)Instruction limit reached!
% 1.93/0.65 % (23433)------------------------------
% 1.93/0.65 % (23433)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.93/0.65 % (23433)Termination reason: Unknown
% 1.93/0.65 % (23433)Termination phase: Property scanning
% 1.93/0.65
% 1.93/0.65 % (23433)Memory used [KB]: 1791
% 1.93/0.65 % (23433)Time elapsed: 0.019 s
% 1.93/0.65 % (23433)Instructions burned: 41 (million)
% 1.93/0.65 % (23433)------------------------------
% 1.93/0.65 % (23433)------------------------------
% 1.93/0.66 % (23432)Instruction limit reached!
% 1.93/0.66 % (23432)------------------------------
% 1.93/0.66 % (23432)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.93/0.66 % (23432)Termination reason: Unknown
% 1.93/0.66 % (23432)Termination phase: Saturation
% 1.93/0.66
% 1.93/0.66 % (23432)Memory used [KB]: 6908
% 1.93/0.66 % (23432)Time elapsed: 0.067 s
% 1.93/0.66 % (23432)Instructions burned: 149 (million)
% 1.93/0.66 % (23432)------------------------------
% 1.93/0.66 % (23432)------------------------------
% 1.93/0.67 % (23436)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on theBenchmark for (2997ds/47Mi)
% 1.93/0.67 % (23435)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on theBenchmark for (2997ds/1087Mi)
% 2.20/0.68 % (23437)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on theBenchmark for (2997ds/44Mi)
% 2.20/0.69 % (23435)Refutation not found, incomplete strategy
% 2.20/0.69 % (23435)------------------------------
% 2.20/0.69 % (23435)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.20/0.69 % (23435)Termination reason: Refutation not found, incomplete strategy
% 2.20/0.69
% 2.20/0.69
% 2.20/0.69 % (23435)Memory used [KB]: 6268
% 2.20/0.69 % (23435)Time elapsed: 0.016 s
% 2.20/0.69 % (23435)Instructions burned: 29 (million)
% 2.20/0.69 % (23435)------------------------------
% 2.20/0.69 % (23435)------------------------------
% 2.20/0.69 % (23436)Instruction limit reached!
% 2.20/0.69 % (23436)------------------------------
% 2.20/0.69 % (23436)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.20/0.69 % (23436)Termination reason: Unknown
% 2.20/0.69 % (23436)Termination phase: Property scanning
% 2.20/0.69
% 2.20/0.69 % (23436)Memory used [KB]: 1791
% 2.20/0.69 % (23436)Time elapsed: 0.023 s
% 2.20/0.69 % (23436)Instructions burned: 48 (million)
% 2.20/0.69 % (23436)------------------------------
% 2.20/0.69 % (23436)------------------------------
% 2.20/0.70 % (23437)Instruction limit reached!
% 2.20/0.70 % (23437)------------------------------
% 2.20/0.70 % (23437)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.20/0.70 % (23437)Termination reason: Unknown
% 2.20/0.70 % (23437)Termination phase: Property scanning
% 2.20/0.70
% 2.20/0.70 % (23437)Memory used [KB]: 1791
% 2.20/0.70 % (23437)Time elapsed: 0.021 s
% 2.20/0.70 % (23437)Instructions burned: 44 (million)
% 2.20/0.70 % (23437)------------------------------
% 2.20/0.70 % (23437)------------------------------
% 2.20/0.70 % (23439)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on theBenchmark for (2996ds/432Mi)
% 2.20/0.70 % (23440)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on theBenchmark for (2996ds/62Mi)
% 2.20/0.72 % (23441)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on theBenchmark for (2996ds/31Mi)
% 2.20/0.73 % (23441)Instruction limit reached!
% 2.20/0.73 % (23441)------------------------------
% 2.20/0.73 % (23441)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.20/0.73 % (23441)Termination reason: Unknown
% 2.20/0.73 % (23441)Termination phase: Property scanning
% 2.20/0.73
% 2.20/0.73 % (23441)Memory used [KB]: 1791
% 2.20/0.73 % (23441)Time elapsed: 0.015 s
% 2.20/0.73 % (23441)Instructions burned: 31 (million)
% 2.20/0.73 % (23441)------------------------------
% 2.20/0.73 % (23441)------------------------------
% 2.20/0.73 % (23440)Instruction limit reached!
% 2.20/0.73 % (23440)------------------------------
% 2.20/0.73 % (23440)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.20/0.73 % (23440)Termination reason: Unknown
% 2.20/0.73 % (23440)Termination phase: Property scanning
% 2.20/0.73
% 2.20/0.73 % (23440)Memory used [KB]: 1791
% 2.20/0.73 % (23440)Time elapsed: 0.028 s
% 2.20/0.73 % (23440)Instructions burned: 62 (million)
% 2.20/0.73 % (23440)------------------------------
% 2.20/0.73 % (23440)------------------------------
% 2.56/0.74 % (23443)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on theBenchmark for (2996ds/453Mi)
% 2.56/0.74 % (23442)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on theBenchmark for (2996ds/96Mi)
% 2.56/0.75 % (23428)Instruction limit reached!
% 2.56/0.75 % (23428)------------------------------
% 2.56/0.75 % (23428)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.56/0.75 % (23428)Termination reason: Unknown
% 2.56/0.75 % (23428)Termination phase: Saturation
% 2.56/0.75
% 2.56/0.75 % (23428)Memory used [KB]: 7291
% 2.56/0.75 % (23428)Time elapsed: 0.204 s
% 2.56/0.75 % (23428)Instructions burned: 449 (million)
% 2.56/0.75 % (23428)------------------------------
% 2.56/0.75 % (23428)------------------------------
% 2.56/0.76 % (23431)Instruction limit reached!
% 2.56/0.76 % (23431)------------------------------
% 2.56/0.76 % (23431)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.56/0.76 % (23431)Termination reason: Unknown
% 2.56/0.76 % (23431)Termination phase: Saturation
% 2.56/0.76
% 2.56/0.76 % (23431)Memory used [KB]: 6780
% 2.56/0.76 % (23431)Time elapsed: 0.171 s
% 2.56/0.76 % (23431)Instructions burned: 507 (million)
% 2.56/0.76 % (23431)------------------------------
% 2.56/0.76 % (23431)------------------------------
% 3.00/0.77 % (23444)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on theBenchmark for (2996ds/71Mi)
% 3.00/0.77 % (23445)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on theBenchmark for (2996ds/83Mi)
% 3.00/0.78 % (23442)Instruction limit reached!
% 3.00/0.78 % (23442)------------------------------
% 3.00/0.78 % (23442)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.00/0.78 % (23442)Termination reason: Unknown
% 3.00/0.78 % (23442)Termination phase: Saturation
% 3.00/0.78
% 3.00/0.78 % (23442)Memory used [KB]: 6524
% 3.00/0.78 % (23442)Time elapsed: 0.039 s
% 3.00/0.78 % (23442)Instructions burned: 97 (million)
% 3.00/0.78 % (23442)------------------------------
% 3.00/0.78 % (23442)------------------------------
% 3.00/0.78 % (23444)Instruction limit reached!
% 3.00/0.78 % (23444)------------------------------
% 3.00/0.78 % (23444)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.00/0.78 % (23444)Termination reason: Unknown
% 3.00/0.78 % (23444)Termination phase: Function definition elimination
% 3.00/0.78
% 3.00/0.78 % (23444)Memory used [KB]: 1918
% 3.00/0.78 % (23444)Time elapsed: 0.020 s
% 3.00/0.78 % (23444)Instructions burned: 73 (million)
% 3.00/0.78 % (23444)------------------------------
% 3.00/0.78 % (23444)------------------------------
% 3.00/0.79 % (23447)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on theBenchmark for (2995ds/41Mi)
% 3.00/0.80 % (23446)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on theBenchmark for (2995ds/11Mi)
% 3.00/0.80 % (23446)Instruction limit reached!
% 3.00/0.80 % (23446)------------------------------
% 3.00/0.80 % (23446)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.00/0.80 % (23446)Termination reason: Unknown
% 3.00/0.80 % (23446)Termination phase: shuffling
% 3.00/0.80
% 3.00/0.80 % (23446)Memory used [KB]: 1407
% 3.00/0.80 % (23446)Time elapsed: 0.007 s
% 3.00/0.80 % (23446)Instructions burned: 12 (million)
% 3.00/0.80 % (23446)------------------------------
% 3.00/0.80 % (23446)------------------------------
% 3.00/0.80 % (23447)Instruction limit reached!
% 3.00/0.80 % (23447)------------------------------
% 3.00/0.80 % (23447)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.00/0.80 % (23447)Termination reason: Unknown
% 3.00/0.80 % (23447)Termination phase: Property scanning
% 3.00/0.80
% 3.00/0.80 % (23447)Memory used [KB]: 1791
% 3.00/0.80 % (23447)Time elapsed: 0.013 s
% 3.00/0.80 % (23447)Instructions burned: 43 (million)
% 3.00/0.80 % (23447)------------------------------
% 3.00/0.80 % (23447)------------------------------
% 3.00/0.81 % (23445)Instruction limit reached!
% 3.00/0.81 % (23445)------------------------------
% 3.00/0.81 % (23445)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.00/0.81 % (23445)Termination reason: Unknown
% 3.00/0.81 % (23445)Termination phase: Saturation
% 3.00/0.81
% 3.00/0.81 % (23445)Memory used [KB]: 6268
% 3.00/0.81 % (23445)Time elapsed: 0.037 s
% 3.00/0.81 % (23445)Instructions burned: 83 (million)
% 3.00/0.81 % (23445)------------------------------
% 3.00/0.81 % (23445)------------------------------
% 3.00/0.81 % (23448)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2995ds/6Mi)
% 3.00/0.81 % (23448)Instruction limit reached!
% 3.00/0.81 % (23448)------------------------------
% 3.00/0.81 % (23448)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.00/0.81 % (23448)Termination reason: Unknown
% 3.00/0.81 % (23448)Termination phase: shuffling
% 3.00/0.81
% 3.00/0.81 % (23448)Memory used [KB]: 1407
% 3.00/0.81 % (23448)Time elapsed: 0.004 s
% 3.00/0.81 % (23448)Instructions burned: 7 (million)
% 3.00/0.81 % (23448)------------------------------
% 3.00/0.81 % (23448)------------------------------
% 3.35/0.82 % (23415)Instruction limit reached!
% 3.35/0.82 % (23415)------------------------------
% 3.35/0.82 % (23415)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.35/0.82 % (23415)Termination reason: Unknown
% 3.35/0.82 % (23415)Termination phase: Saturation
% 3.35/0.82
% 3.35/0.82 % (23415)Memory used [KB]: 7803
% 3.35/0.82 % (23415)Time elapsed: 0.356 s
% 3.35/0.82 % (23415)Instructions burned: 780 (million)
% 3.35/0.82 % (23415)------------------------------
% 3.35/0.82 % (23415)------------------------------
% 3.35/0.82 % (23450)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on theBenchmark for (2995ds/343Mi)
% 3.35/0.82 % (23449)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on theBenchmark for (2995ds/150Mi)
% 3.35/0.83 % (23451)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on theBenchmark for (2995ds/109Mi)
% 3.35/0.84 % (23452)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on theBenchmark for (2995ds/253Mi)
% 3.35/0.85 % (23410)Instruction limit reached!
% 3.35/0.85 % (23410)------------------------------
% 3.35/0.85 % (23410)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.35/0.85 % (23410)Termination reason: Unknown
% 3.35/0.85 % (23410)Termination phase: Saturation
% 3.35/0.85
% 3.35/0.85 % (23410)Memory used [KB]: 13944
% 3.35/0.85 % (23410)Time elapsed: 0.407 s
% 3.35/0.85 % (23410)Instructions burned: 902 (million)
% 3.35/0.85 % (23410)------------------------------
% 3.35/0.85 % (23410)------------------------------
% 3.45/0.86 % (23449)Instruction limit reached!
% 3.45/0.86 % (23449)------------------------------
% 3.45/0.86 % (23449)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.45/0.86 % (23449)Termination reason: Unknown
% 3.45/0.86 % (23449)Termination phase: Property scanning
% 3.45/0.86
% 3.45/0.86 % (23449)Memory used [KB]: 2942
% 3.45/0.86 % (23449)Time elapsed: 0.041 s
% 3.45/0.86 % (23449)Instructions burned: 152 (million)
% 3.45/0.86 % (23449)------------------------------
% 3.45/0.86 % (23449)------------------------------
% 3.45/0.86 % (23453)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on theBenchmark for (2995ds/140Mi)
% 3.45/0.87 % (23399)Instruction limit reached!
% 3.45/0.87 % (23399)------------------------------
% 3.45/0.87 % (23399)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.45/0.87 % (23399)Termination reason: Unknown
% 3.45/0.87 % (23399)Termination phase: Saturation
% 3.45/0.87
% 3.45/0.87 % (23399)Memory used [KB]: 9594
% 3.45/0.87 % (23399)Time elapsed: 0.468 s
% 3.45/0.87 % (23399)Instructions burned: 1041 (million)
% 3.45/0.87 % (23399)------------------------------
% 3.45/0.87 % (23399)------------------------------
% 3.45/0.87 % (23454)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on theBenchmark for (2995ds/614Mi)
% 3.45/0.87 % (23451)Instruction limit reached!
% 3.45/0.87 % (23451)------------------------------
% 3.45/0.87 % (23451)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.45/0.87 % (23451)Termination reason: Unknown
% 3.45/0.87 % (23451)Termination phase: Saturation
% 3.45/0.87
% 3.45/0.87 % (23451)Memory used [KB]: 6524
% 3.45/0.87 % (23451)Time elapsed: 0.045 s
% 3.45/0.87 % (23451)Instructions burned: 110 (million)
% 3.45/0.87 % (23451)------------------------------
% 3.45/0.87 % (23451)------------------------------
% 3.45/0.87 % (23439)Instruction limit reached!
% 3.45/0.87 % (23439)------------------------------
% 3.45/0.87 % (23439)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.45/0.87 % (23439)Termination reason: Unknown
% 3.45/0.87 % (23439)Termination phase: Saturation
% 3.45/0.87
% 3.45/0.87 % (23439)Memory used [KB]: 2686
% 3.45/0.87 % (23439)Time elapsed: 0.172 s
% 3.45/0.87 % (23439)Instructions burned: 433 (million)
% 3.45/0.87 % (23439)------------------------------
% 3.45/0.87 % (23439)------------------------------
% 3.45/0.88 % (23456)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on theBenchmark for (2995ds/339Mi)
% 3.45/0.89 % (23455)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on theBenchmark for (2995ds/202Mi)
% 3.45/0.89 % (23457)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=283:si=on:rtra=on_0 on theBenchmark for (2995ds/283Mi)
% 3.45/0.89 % (23453)Refutation not found, incomplete strategy
% 3.45/0.89 % (23453)------------------------------
% 3.45/0.89 % (23453)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.45/0.89 % (23453)Termination reason: Refutation not found, incomplete strategy
% 3.45/0.89
% 3.45/0.89
% 3.45/0.89 % (23453)Memory used [KB]: 6268
% 3.45/0.89 % (23453)Time elapsed: 0.024 s
% 3.45/0.89 % (23453)Instructions burned: 52 (million)
% 3.45/0.89 % (23453)------------------------------
% 3.45/0.89 % (23453)------------------------------
% 3.45/0.90 % (23455)Refutation not found, incomplete strategy
% 3.45/0.90 % (23455)------------------------------
% 3.45/0.90 % (23455)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.45/0.90 % (23455)Termination reason: Refutation not found, incomplete strategy
% 3.45/0.90
% 3.45/0.90
% 3.45/0.90 % (23455)Memory used [KB]: 6140
% 3.45/0.90 % (23455)Time elapsed: 0.016 s
% 3.45/0.90 % (23455)Instructions burned: 30 (million)
% 3.45/0.90 % (23455)------------------------------
% 3.45/0.90 % (23455)------------------------------
% 3.45/0.91 % (23458)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on theBenchmark for (2994ds/134Mi)
% 3.45/0.91 % (23459)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on theBenchmark for (2994ds/298Mi)
% 3.83/0.94 % (23458)Instruction limit reached!
% 3.83/0.94 % (23458)------------------------------
% 3.83/0.94 % (23458)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.83/0.94 % (23458)Termination reason: Unknown
% 3.83/0.94 % (23458)Termination phase: Saturation
% 3.83/0.94
% 3.83/0.94 % (23458)Memory used [KB]: 6524
% 3.83/0.94 % (23458)Time elapsed: 0.034 s
% 3.83/0.94 % (23458)Instructions burned: 137 (million)
% 3.83/0.94 % (23458)------------------------------
% 3.83/0.94 % (23458)------------------------------
% 3.83/0.94 % (23443)Instruction limit reached!
% 3.83/0.94 % (23443)------------------------------
% 3.83/0.94 % (23443)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.83/0.94 % (23443)Termination reason: Unknown
% 3.83/0.94 % (23443)Termination phase: Saturation
% 3.83/0.94
% 3.83/0.94 % (23443)Memory used [KB]: 7419
% 3.83/0.94 % (23443)Time elapsed: 0.201 s
% 3.83/0.94 % (23443)Instructions burned: 453 (million)
% 3.83/0.94 % (23443)------------------------------
% 3.83/0.94 % (23443)------------------------------
% 3.83/0.95 % (23460)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on theBenchmark for (2994ds/192Mi)
% 3.83/0.96 % (23452)Instruction limit reached!
% 3.83/0.96 % (23452)------------------------------
% 3.83/0.96 % (23452)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.83/0.96 % (23452)Termination reason: Unknown
% 3.83/0.96 % (23452)Termination phase: Saturation
% 3.83/0.96
% 3.83/0.96 % (23452)Memory used [KB]: 7675
% 3.83/0.96 % (23452)Time elapsed: 0.150 s
% 3.83/0.96 % (23452)Instructions burned: 253 (million)
% 3.83/0.96 % (23452)------------------------------
% 3.83/0.96 % (23452)------------------------------
% 3.83/0.96 % (23461)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on theBenchmark for (2994ds/258Mi)
% 4.22/0.98 % (23450)Instruction limit reached!
% 4.22/0.98 % (23450)------------------------------
% 4.22/0.98 % (23450)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.22/0.98 % (23450)Termination reason: Unknown
% 4.22/0.98 % (23450)Termination phase: Saturation
% 4.22/0.98
% 4.22/0.98 % (23450)Memory used [KB]: 7547
% 4.22/0.98 % (23450)Time elapsed: 0.158 s
% 4.22/0.98 % (23450)Instructions burned: 343 (million)
% 4.22/0.98 % (23450)------------------------------
% 4.22/0.98 % (23450)------------------------------
% 4.22/0.98 % (23462)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on theBenchmark for (2993ds/90Mi)
% 4.22/1.00 % (23457)Instruction limit reached!
% 4.22/1.00 % (23457)------------------------------
% 4.22/1.00 % (23457)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.22/1.00 % (23457)Termination reason: Unknown
% 4.22/1.00 % (23457)Termination phase: Saturation
% 4.22/1.00
% 4.22/1.00 % (23457)Memory used [KB]: 7036
% 4.22/1.00 % (23457)Time elapsed: 0.134 s
% 4.22/1.00 % (23457)Instructions burned: 284 (million)
% 4.22/1.00 % (23457)------------------------------
% 4.22/1.00 % (23457)------------------------------
% 4.22/1.00 % (23456)Instruction limit reached!
% 4.22/1.00 % (23456)------------------------------
% 4.22/1.00 % (23456)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.22/1.00 % (23456)Termination reason: Unknown
% 4.22/1.00 % (23456)Termination phase: Saturation
% 4.22/1.00
% 4.22/1.00 % (23456)Memory used [KB]: 6908
% 4.22/1.00 % (23456)Time elapsed: 0.116 s
% 4.22/1.00 % (23456)Instructions burned: 341 (million)
% 4.22/1.00 % (23456)------------------------------
% 4.22/1.00 % (23456)------------------------------
% 4.22/1.01 % (23463)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on theBenchmark for (2993ds/231Mi)
% 4.22/1.01 % (23464)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on theBenchmark for (2993ds/458Mi)
% 4.22/1.01 % (23465)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on theBenchmark for (2993ds/31Mi)
% 4.22/1.01 % (23462)Instruction limit reached!
% 4.22/1.01 % (23462)------------------------------
% 4.22/1.01 % (23462)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.22/1.01 % (23462)Termination reason: Unknown
% 4.22/1.01 % (23462)Termination phase: Property scanning
% 4.22/1.01
% 4.22/1.01 % (23462)Memory used [KB]: 2174
% 4.22/1.01 % (23462)Time elapsed: 0.039 s
% 4.22/1.01 % (23462)Instructions burned: 92 (million)
% 4.22/1.01 % (23462)------------------------------
% 4.22/1.01 % (23462)------------------------------
% 4.22/1.02 % (23465)Instruction limit reached!
% 4.22/1.02 % (23465)------------------------------
% 4.22/1.02 % (23465)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.22/1.03 % (23465)Termination reason: Unknown
% 4.22/1.03 % (23465)Termination phase: Property scanning
% 4.22/1.03
% 4.22/1.03 % (23465)Memory used [KB]: 1791
% 4.22/1.03 % (23465)Time elapsed: 0.015 s
% 4.22/1.03 % (23465)Instructions burned: 32 (million)
% 4.22/1.03 % (23465)------------------------------
% 4.22/1.03 % (23465)------------------------------
% 4.22/1.03 % (23466)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on theBenchmark for (2993ds/297Mi)
% 4.22/1.04 % (23460)Instruction limit reached!
% 4.22/1.04 % (23460)------------------------------
% 4.22/1.04 % (23460)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.22/1.04 % (23460)Termination reason: Unknown
% 4.22/1.04 % (23460)Termination phase: Saturation
% 4.22/1.04
% 4.22/1.04 % (23460)Memory used [KB]: 6780
% 4.22/1.04 % (23460)Time elapsed: 0.078 s
% 4.22/1.04 % (23460)Instructions burned: 193 (million)
% 4.22/1.04 % (23460)------------------------------
% 4.22/1.04 % (23460)------------------------------
% 4.80/1.05 % (23467)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on theBenchmark for (2993ds/987Mi)
% 4.80/1.05 % (23459)Instruction limit reached!
% 4.80/1.05 % (23459)------------------------------
% 4.80/1.05 % (23459)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.80/1.05 % (23459)Termination reason: Unknown
% 4.80/1.05 % (23459)Termination phase: Saturation
% 4.80/1.05
% 4.80/1.05 % (23459)Memory used [KB]: 7291
% 4.80/1.05 % (23459)Time elapsed: 0.136 s
% 4.80/1.05 % (23459)Instructions burned: 298 (million)
% 4.80/1.05 % (23459)------------------------------
% 4.80/1.05 % (23459)------------------------------
% 4.80/1.05 % (23468)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on theBenchmark for (2993ds/182Mi)
% 4.80/1.06 % (23461)Instruction limit reached!
% 4.80/1.06 % (23461)------------------------------
% 4.80/1.06 % (23461)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.80/1.06 % (23461)Termination reason: Unknown
% 4.80/1.06 % (23461)Termination phase: Saturation
% 4.80/1.06
% 4.80/1.06 % (23461)Memory used [KB]: 6908
% 4.80/1.06 % (23461)Time elapsed: 0.101 s
% 4.80/1.06 % (23461)Instructions burned: 259 (million)
% 4.80/1.06 % (23461)------------------------------
% 4.80/1.06 % (23461)------------------------------
% 4.80/1.06 % (23469)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on theBenchmark for (2993ds/182Mi)
% 5.47/1.08 % (23470)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on theBenchmark for (2992ds/154Mi)
% 5.47/1.12 % (23470)Instruction limit reached!
% 5.47/1.12 % (23470)------------------------------
% 5.47/1.12 % (23470)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 5.47/1.12 % (23470)Termination reason: Unknown
% 5.47/1.12 % (23470)Termination phase: Saturation
% 5.47/1.12
% 5.47/1.12 % (23470)Memory used [KB]: 6524
% 5.47/1.12 % (23470)Time elapsed: 0.038 s
% 5.47/1.12 % (23470)Instructions burned: 155 (million)
% 5.47/1.12 % (23470)------------------------------
% 5.47/1.12 % (23470)------------------------------
% 5.47/1.12 % (23454)Instruction limit reached!
% 5.47/1.12 % (23454)------------------------------
% 5.47/1.12 % (23454)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 5.47/1.12 % (23454)Termination reason: Unknown
% 5.47/1.12 % (23454)Termination phase: Saturation
% 5.47/1.12
% 5.47/1.12 % (23454)Memory used [KB]: 7675
% 5.47/1.12 % (23454)Time elapsed: 0.252 s
% 5.47/1.12 % (23468)Instruction limit reached!
% 5.47/1.12 % (23468)------------------------------
% 5.47/1.12 % (23468)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 5.47/1.12 % (23468)Termination reason: Unknown
% 5.47/1.12 % (23468)Termination phase: Saturation
% 5.47/1.12
% 5.47/1.12 % (23468)Memory used [KB]: 6652
% 5.47/1.12 % (23468)Time elapsed: 0.075 s
% 5.47/1.12 % (23468)Instructions burned: 184 (million)
% 5.47/1.12 % (23468)------------------------------
% 5.47/1.12 % (23468)------------------------------
% 5.47/1.12 % (23454)Instructions burned: 614 (million)
% 5.47/1.12 % (23454)------------------------------
% 5.47/1.12 % (23454)------------------------------
% 5.47/1.13 % (23471)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on theBenchmark for (2992ds/79Mi)
% 5.47/1.13 % (23463)Instruction limit reached!
% 5.47/1.13 % (23463)------------------------------
% 5.47/1.13 % (23463)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 5.47/1.13 % (23463)Termination reason: Unknown
% 5.47/1.13 % (23463)Termination phase: Saturation
% 5.47/1.13
% 5.47/1.13 % (23463)Memory used [KB]: 8059
% 5.47/1.13 % (23463)Time elapsed: 0.139 s
% 5.47/1.13 % (23463)Instructions burned: 232 (million)
% 5.47/1.13 % (23463)------------------------------
% 5.47/1.13 % (23463)------------------------------
% 5.91/1.14 % (23473)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on theBenchmark for (2992ds/114Mi)
% 5.91/1.14 % (23472)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on theBenchmark for (2992ds/216Mi)
% 5.91/1.14 % (23474)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on theBenchmark for (2992ds/922Mi)
% 5.91/1.15 % (23471)Instruction limit reached!
% 5.91/1.15 % (23471)------------------------------
% 5.91/1.15 % (23471)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 5.91/1.15 % (23471)Termination reason: Unknown
% 5.91/1.15 % (23471)Termination phase: Function definition elimination
% 5.91/1.15
% 5.91/1.15 % (23471)Memory used [KB]: 2046
% 5.91/1.15 % (23471)Time elapsed: 0.021 s
% 5.91/1.15 % (23471)Instructions burned: 82 (million)
% 5.91/1.15 % (23471)------------------------------
% 5.91/1.15 % (23471)------------------------------
% 5.91/1.15 % (23469)Instruction limit reached!
% 5.91/1.15 % (23469)------------------------------
% 5.91/1.15 % (23469)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 5.91/1.15 % (23469)Termination reason: Unknown
% 5.91/1.15 % (23469)Termination phase: Saturation
% 5.91/1.15
% 5.91/1.15 % (23469)Memory used [KB]: 9338
% 5.91/1.15 % (23469)Time elapsed: 0.090 s
% 5.91/1.15 % (23469)Instructions burned: 182 (million)
% 5.91/1.15 % (23469)------------------------------
% 5.91/1.15 % (23469)------------------------------
% 5.91/1.15 % (23466)Instruction limit reached!
% 5.91/1.15 % (23466)------------------------------
% 5.91/1.15 % (23466)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 5.91/1.15 % (23466)Termination reason: Unknown
% 5.91/1.15 % (23466)Termination phase: Saturation
% 5.91/1.15
% 5.91/1.15 % (23466)Memory used [KB]: 6652
% 5.91/1.15 % (23466)Time elapsed: 0.127 s
% 5.91/1.15 % (23466)Instructions burned: 299 (million)
% 5.91/1.15 % (23466)------------------------------
% 5.91/1.15 % (23466)------------------------------
% 5.91/1.16 % (23475)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on theBenchmark for (2992ds/182Mi)
% 6.08/1.17 % (23477)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on theBenchmark for (2992ds/50Mi)
% 6.08/1.17 % (23476)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on theBenchmark for (2992ds/164Mi)
% 6.08/1.18 % (23473)Instruction limit reached!
% 6.08/1.18 % (23473)------------------------------
% 6.08/1.18 % (23473)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.08/1.18 % (23473)Termination reason: Unknown
% 6.08/1.18 % (23473)Termination phase: Saturation
% 6.08/1.18
% 6.08/1.18 % (23473)Memory used [KB]: 6908
% 6.08/1.18 % (23473)Time elapsed: 0.047 s
% 6.08/1.18 % (23473)Instructions burned: 116 (million)
% 6.08/1.18 % (23473)------------------------------
% 6.08/1.18 % (23473)------------------------------
% 6.08/1.19 % (23477)Instruction limit reached!
% 6.08/1.19 % (23477)------------------------------
% 6.08/1.19 % (23477)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.08/1.19 % (23477)Termination reason: Unknown
% 6.08/1.19 % (23477)Termination phase: Property scanning
% 6.08/1.19
% 6.08/1.19 % (23477)Memory used [KB]: 1791
% 6.08/1.19 % (23477)Time elapsed: 0.024 s
% 6.08/1.19 % (23477)Instructions burned: 52 (million)
% 6.08/1.19 % (23477)------------------------------
% 6.08/1.19 % (23477)------------------------------
% 6.08/1.20 % (23479)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on theBenchmark for (2991ds/1021Mi)
% 6.08/1.20 % (23478)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on theBenchmark for (2991ds/368Mi)
% 6.08/1.21 % (23475)Instruction limit reached!
% 6.08/1.21 % (23475)------------------------------
% 6.08/1.21 % (23475)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.08/1.21 % (23475)Termination reason: Unknown
% 6.08/1.21 % (23475)Termination phase: Saturation
% 6.08/1.21
% 6.08/1.21 % (23475)Memory used [KB]: 6652
% 6.08/1.21 % (23475)Time elapsed: 0.049 s
% 6.08/1.21 % (23475)Instructions burned: 182 (million)
% 6.08/1.21 % (23475)------------------------------
% 6.08/1.21 % (23475)------------------------------
% 6.08/1.22 % (23472)Instruction limit reached!
% 6.08/1.22 % (23472)------------------------------
% 6.08/1.22 % (23472)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.08/1.22 % (23472)Termination reason: Unknown
% 6.08/1.22 % (23472)Termination phase: Saturation
% 6.08/1.22
% 6.08/1.22 % (23472)Memory used [KB]: 6652
% 6.08/1.22 % (23472)Time elapsed: 0.085 s
% 6.08/1.22 % (23472)Instructions burned: 218 (million)
% 6.08/1.22 % (23472)------------------------------
% 6.08/1.22 % (23472)------------------------------
% 6.08/1.22 % (23464)Instruction limit reached!
% 6.08/1.22 % (23464)------------------------------
% 6.08/1.22 % (23464)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.08/1.22 % (23464)Termination reason: Unknown
% 6.08/1.22 % (23464)Termination phase: Saturation
% 6.08/1.22
% 6.08/1.22 % (23464)Memory used [KB]: 7931
% 6.08/1.22 % (23464)Time elapsed: 0.212 s
% 6.08/1.22 % (23464)Instructions burned: 459 (million)
% 6.08/1.22 % (23464)------------------------------
% 6.08/1.22 % (23464)------------------------------
% 6.08/1.23 % (23480)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on theBenchmark for (2991ds/267Mi)
% 6.45/1.23 % (23481)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on theBenchmark for (2991ds/204Mi)
% 6.45/1.24 % (23482)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on theBenchmark for (2991ds/26Mi)
% 6.45/1.24 % (23476)Instruction limit reached!
% 6.45/1.24 % (23476)------------------------------
% 6.45/1.24 % (23476)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.45/1.24 % (23476)Termination reason: Unknown
% 6.45/1.24 % (23476)Termination phase: Saturation
% 6.45/1.24
% 6.45/1.24 % (23476)Memory used [KB]: 2046
% 6.45/1.24 % (23476)Time elapsed: 0.070 s
% 6.45/1.24 % (23476)Instructions burned: 164 (million)
% 6.45/1.24 % (23476)------------------------------
% 6.45/1.24 % (23476)------------------------------
% 6.45/1.25 % (23482)Instruction limit reached!
% 6.45/1.25 % (23482)------------------------------
% 6.45/1.25 % (23482)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.45/1.25 % (23482)Termination reason: Unknown
% 6.45/1.25 % (23482)Termination phase: Property scanning
% 6.45/1.25
% 6.45/1.25 % (23482)Memory used [KB]: 1791
% 6.45/1.25 % (23482)Time elapsed: 0.014 s
% 6.45/1.25 % (23482)Instructions burned: 28 (million)
% 6.45/1.25 % (23482)------------------------------
% 6.45/1.25 % (23482)------------------------------
% 6.45/1.25 % (23483)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on theBenchmark for (2991ds/53Mi)
% 6.58/1.26 % (23484)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on theBenchmark for (2991ds/4436Mi)
% 6.58/1.27 % (23483)Instruction limit reached!
% 6.58/1.27 % (23483)------------------------------
% 6.58/1.27 % (23483)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.58/1.27 % (23483)Termination reason: Unknown
% 6.58/1.27 % (23483)Termination phase: Property scanning
% 6.58/1.27
% 6.58/1.27 % (23483)Memory used [KB]: 1791
% 6.58/1.27 % (23483)Time elapsed: 0.025 s
% 6.58/1.27 % (23483)Instructions burned: 54 (million)
% 6.58/1.27 % (23483)------------------------------
% 6.58/1.27 % (23483)------------------------------
% 6.58/1.28 % (23484)Refutation not found, incomplete strategy
% 6.58/1.28 % (23484)------------------------------
% 6.58/1.28 % (23484)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.58/1.28 % (23484)Termination reason: Refutation not found, incomplete strategy
% 6.58/1.28
% 6.58/1.28
% 6.58/1.28 % (23484)Memory used [KB]: 6268
% 6.58/1.28 % (23484)Time elapsed: 0.017 s
% 6.58/1.28 % (23484)Instructions burned: 29 (million)
% 6.58/1.28 % (23484)------------------------------
% 6.58/1.28 % (23484)------------------------------
% 6.58/1.29 % (23485)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on theBenchmark for (2990ds/1539Mi)
% 6.58/1.29 % (23486)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on theBenchmark for (2990ds/408Mi)
% 6.58/1.31 % (23478)Instruction limit reached!
% 6.58/1.31 % (23478)------------------------------
% 6.58/1.31 % (23478)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.58/1.31 % (23478)Termination reason: Unknown
% 6.58/1.31 % (23478)Termination phase: Saturation
% 6.58/1.31
% 6.58/1.31 % (23478)Memory used [KB]: 7036
% 6.58/1.31 % (23478)Time elapsed: 0.131 s
% 6.58/1.31 % (23478)Instructions burned: 369 (million)
% 6.58/1.31 % (23478)------------------------------
% 6.58/1.31 % (23478)------------------------------
% 6.58/1.31 % (23487)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on theBenchmark for (2990ds/5205Mi)
% 6.58/1.32 % (23481)Instruction limit reached!
% 6.58/1.32 % (23481)------------------------------
% 6.58/1.32 % (23481)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.58/1.32 % (23481)Termination reason: Unknown
% 6.58/1.32 % (23481)Termination phase: Saturation
% 6.58/1.32
% 6.58/1.32 % (23481)Memory used [KB]: 6780
% 6.58/1.32 % (23481)Time elapsed: 0.087 s
% 6.58/1.32 % (23481)Instructions burned: 205 (million)
% 6.58/1.32 % (23481)------------------------------
% 6.58/1.32 % (23481)------------------------------
% 6.58/1.33 % (23480)Instruction limit reached!
% 6.58/1.33 % (23480)------------------------------
% 6.58/1.33 % (23480)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.58/1.33 % (23480)Termination reason: Unknown
% 6.58/1.33 % (23480)Termination phase: Saturation
% 6.58/1.33
% 6.58/1.33 % (23480)Memory used [KB]: 6908
% 6.58/1.33 % (23480)Time elapsed: 0.103 s
% 6.58/1.33 % (23480)Instructions burned: 268 (million)
% 6.58/1.33 % (23480)------------------------------
% 6.58/1.33 % (23480)------------------------------
% 7.06/1.34 % (23488)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on theBenchmark for (2990ds/1913Mi)
% 7.06/1.34 % (23489)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on theBenchmark for (2990ds/4350Mi)
% 7.09/1.36 % (23489)Refutation not found, incomplete strategy
% 7.09/1.36 % (23489)------------------------------
% 7.09/1.36 % (23489)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.09/1.36 % (23489)Termination reason: Refutation not found, incomplete strategy
% 7.09/1.36
% 7.09/1.36
% 7.09/1.36 % (23489)Memory used [KB]: 6268
% 7.09/1.36 % (23489)Time elapsed: 0.025 s
% 7.09/1.36 % (23489)Instructions burned: 55 (million)
% 7.09/1.36 % (23489)------------------------------
% 7.09/1.36 % (23489)------------------------------
% 7.09/1.38 % (23490)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on theBenchmark for (2990ds/68Mi)
% 7.09/1.41 % (23490)Instruction limit reached!
% 7.09/1.41 % (23490)------------------------------
% 7.09/1.41 % (23490)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.09/1.41 % (23490)Termination reason: Unknown
% 7.09/1.41 % (23490)Termination phase: Function definition elimination
% 7.09/1.41
% 7.09/1.41 % (23490)Memory used [KB]: 1791
% 7.09/1.41 % (23490)Time elapsed: 0.031 s
% 7.09/1.41 % (23490)Instructions burned: 70 (million)
% 7.09/1.41 % (23490)------------------------------
% 7.09/1.41 % (23490)------------------------------
% 7.09/1.43 % (23491)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on theBenchmark for (2989ds/358Mi)
% 7.24/1.44 % (23467)Instruction limit reached!
% 7.24/1.44 % (23467)------------------------------
% 7.24/1.44 % (23467)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.24/1.44 % (23467)Termination reason: Unknown
% 7.24/1.44 % (23467)Termination phase: Saturation
% 7.24/1.44
% 7.24/1.44 % (23467)Memory used [KB]: 7419
% 7.24/1.44 % (23467)Time elapsed: 0.411 s
% 7.24/1.44 % (23467)Instructions burned: 989 (million)
% 7.24/1.44 % (23467)------------------------------
% 7.24/1.44 % (23467)------------------------------
% 7.24/1.45 % (23492)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on theBenchmark for (2989ds/31Mi)
% 7.25/1.47 % (23492)Instruction limit reached!
% 7.25/1.47 % (23492)------------------------------
% 7.25/1.47 % (23492)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.25/1.47 % (23492)Termination reason: Unknown
% 7.25/1.47 % (23492)Termination phase: Property scanning
% 7.25/1.47
% 7.25/1.47 % (23492)Memory used [KB]: 1791
% 7.25/1.47 % (23492)Time elapsed: 0.015 s
% 7.25/1.47 % (23492)Instructions burned: 31 (million)
% 7.25/1.47 % (23492)------------------------------
% 7.25/1.47 % (23492)------------------------------
% 7.25/1.48 % (23493)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on theBenchmark for (2989ds/279Mi)
% 7.25/1.49 % (23486)Instruction limit reached!
% 7.25/1.49 % (23486)------------------------------
% 7.25/1.49 % (23486)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.25/1.49 % (23486)Termination reason: Unknown
% 7.25/1.49 % (23486)Termination phase: Saturation
% 7.25/1.49
% 7.25/1.49 % (23486)Memory used [KB]: 9338
% 7.25/1.49 % (23486)Time elapsed: 0.201 s
% 7.25/1.49 % (23486)Instructions burned: 409 (million)
% 7.25/1.49 % (23486)------------------------------
% 7.25/1.49 % (23486)------------------------------
% 7.25/1.51 % (23494)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on theBenchmark for (2988ds/258Mi)
% 7.50/1.58 % (23491)Instruction limit reached!
% 7.50/1.58 % (23491)------------------------------
% 7.50/1.58 % (23491)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.50/1.58 % (23491)Termination reason: Unknown
% 7.50/1.58 % (23491)Termination phase: Saturation
% 7.50/1.58
% 7.50/1.58 % (23491)Memory used [KB]: 7164
% 7.50/1.58 % (23491)Time elapsed: 0.176 s
% 7.50/1.58 % (23491)Instructions burned: 360 (million)
% 7.50/1.58 % (23491)------------------------------
% 7.50/1.58 % (23491)------------------------------
% 7.50/1.59 % (23493)Instruction limit reached!
% 7.50/1.59 % (23493)------------------------------
% 7.50/1.59 % (23493)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.50/1.59 % (23493)Termination reason: Unknown
% 7.50/1.59 % (23493)Termination phase: Saturation
% 7.50/1.59
% 7.50/1.59 % (23493)Memory used [KB]: 6780
% 7.50/1.59 % (23493)Time elapsed: 0.114 s
% 7.50/1.59 % (23493)Instructions burned: 279 (million)
% 7.50/1.59 % (23493)------------------------------
% 7.50/1.59 % (23493)------------------------------
% 7.50/1.59 % (23495)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on theBenchmark for (2987ds/26Mi)
% 7.50/1.60 % (23495)Instruction limit reached!
% 7.50/1.60 % (23495)------------------------------
% 7.50/1.60 % (23495)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.50/1.60 % (23495)Termination reason: Unknown
% 7.50/1.60 % (23495)Termination phase: shuffling
% 7.50/1.60
% 7.50/1.60 % (23495)Memory used [KB]: 1791
% 7.50/1.60 % (23495)Time elapsed: 0.008 s
% 7.50/1.60 % (23495)Instructions burned: 26 (million)
% 7.50/1.60 % (23495)------------------------------
% 7.50/1.60 % (23495)------------------------------
% 7.50/1.61 % (23474)Instruction limit reached!
% 7.50/1.61 % (23474)------------------------------
% 7.50/1.61 % (23474)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.50/1.61 % (23474)Termination reason: Unknown
% 7.50/1.61 % (23496)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on theBenchmark for (2987ds/995Mi)
% 7.50/1.61 % (23474)Termination phase: Saturation
% 7.50/1.61
% 7.50/1.61 % (23474)Memory used [KB]: 11769
% 7.50/1.61 % (23474)Time elapsed: 0.466 s
% 7.50/1.61 % (23474)Instructions burned: 922 (million)
% 7.50/1.61 % (23474)------------------------------
% 7.50/1.61 % (23474)------------------------------
% 7.50/1.62 % (23494)Instruction limit reached!
% 7.50/1.62 % (23494)------------------------------
% 7.50/1.62 % (23494)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.50/1.62 % (23494)Termination reason: Unknown
% 7.50/1.62 % (23494)Termination phase: Saturation
% 7.50/1.62
% 7.50/1.62 % (23494)Memory used [KB]: 7419
% 7.50/1.62 % (23494)Time elapsed: 0.112 s
% 7.50/1.62 % (23494)Instructions burned: 258 (million)
% 7.50/1.62 % (23494)------------------------------
% 7.50/1.62 % (23494)------------------------------
% 7.50/1.62 % (23497)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on theBenchmark for (2987ds/373Mi)
% 7.50/1.62 % (23498)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on theBenchmark for (2987ds/253Mi)
% 9.83/1.65 % (23499)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on theBenchmark for (2987ds/832Mi)
% 10.10/1.69 % (23479)Instruction limit reached!
% 10.10/1.69 % (23479)------------------------------
% 10.10/1.69 % (23479)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 10.10/1.69 % (23479)Termination reason: Unknown
% 10.10/1.69 % (23479)Termination phase: Saturation
% 10.10/1.69
% 10.10/1.69 % (23479)Memory used [KB]: 11257
% 10.10/1.69 % (23479)Time elapsed: 0.485 s
% 10.10/1.69 % (23479)Instructions burned: 1022 (million)
% 10.10/1.69 % (23479)------------------------------
% 10.10/1.69 % (23479)------------------------------
% 10.10/1.71 % (23499)Refutation not found, incomplete strategy
% 10.10/1.71 % (23499)------------------------------
% 10.10/1.71 % (23499)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 10.10/1.71 % (23499)Termination reason: Refutation not found, incomplete strategy
% 10.10/1.71
% 10.10/1.71
% 10.10/1.71 % (23499)Memory used [KB]: 8315
% 10.10/1.71 % (23499)Time elapsed: 0.077 s
% 10.10/1.71 % (23499)Instructions burned: 178 (million)
% 10.10/1.71 % (23499)------------------------------
% 10.10/1.71 % (23499)------------------------------
% 10.10/1.71 % (23500)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on theBenchmark for (2986ds/668Mi)
% 10.10/1.72 % (23501)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=40:si=on:rtra=on_0 on theBenchmark for (2986ds/40Mi)
% 10.10/1.72 % (23498)Instruction limit reached!
% 10.10/1.72 % (23498)------------------------------
% 10.10/1.72 % (23498)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 10.10/1.72 % (23498)Termination reason: Unknown
% 10.10/1.72 % (23498)Termination phase: Saturation
% 10.10/1.72
% 10.10/1.72 % (23498)Memory used [KB]: 6780
% 10.10/1.72 % (23498)Time elapsed: 0.104 s
% 10.10/1.72 % (23498)Instructions burned: 253 (million)
% 10.10/1.72 % (23498)------------------------------
% 10.10/1.72 % (23498)------------------------------
% 10.10/1.73 % (23501)Instruction limit reached!
% 10.10/1.73 % (23501)------------------------------
% 10.10/1.73 % (23501)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 10.10/1.73 % (23501)Termination reason: Unknown
% 10.10/1.73 % (23501)Termination phase: Property scanning
% 10.10/1.73
% 10.10/1.73 % (23501)Memory used [KB]: 1791
% 10.10/1.73 % (23501)Time elapsed: 0.013 s
% 10.10/1.73 % (23501)Instructions burned: 43 (million)
% 10.10/1.73 % (23501)------------------------------
% 10.10/1.73 % (23501)------------------------------
% 10.10/1.74 % (23502)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on theBenchmark for (2986ds/294Mi)
% 10.56/1.75 % (23503)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on theBenchmark for (2986ds/187Mi)
% 10.64/1.77 % (23497)Instruction limit reached!
% 10.64/1.77 % (23497)------------------------------
% 10.64/1.77 % (23497)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 10.64/1.77 % (23497)Termination reason: Unknown
% 10.64/1.77 % (23497)Termination phase: Saturation
% 10.64/1.77
% 10.64/1.77 % (23497)Memory used [KB]: 7547
% 10.64/1.77 % (23497)Time elapsed: 0.154 s
% 10.64/1.77 % (23497)Instructions burned: 375 (million)
% 10.64/1.77 % (23497)------------------------------
% 10.64/1.77 % (23497)------------------------------
% 10.64/1.80 % (23504)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on theBenchmark for (2985ds/371Mi)
% 10.86/1.83 % (23503)Instruction limit reached!
% 10.86/1.83 % (23503)------------------------------
% 10.86/1.83 % (23503)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 10.86/1.83 % (23503)Termination reason: Unknown
% 10.86/1.83 % (23503)Termination phase: Saturation
% 10.86/1.83
% 10.86/1.83 % (23503)Memory used [KB]: 6780
% 10.86/1.83 % (23503)Time elapsed: 0.101 s
% 10.86/1.83 % (23503)Instructions burned: 189 (million)
% 10.86/1.83 % (23503)------------------------------
% 10.86/1.83 % (23503)------------------------------
% 11.03/1.85 % (23505)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on theBenchmark for (2985ds/1827Mi)
% 11.03/1.88 % (23502)Instruction limit reached!
% 11.03/1.88 % (23502)------------------------------
% 11.03/1.88 % (23502)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 11.03/1.88 % (23502)Termination reason: Unknown
% 11.03/1.88 % (23502)Termination phase: Saturation
% 11.03/1.88
% 11.03/1.88 % (23502)Memory used [KB]: 7291
% 11.03/1.88 % (23502)Time elapsed: 0.150 s
% 11.03/1.88 % (23502)Instructions burned: 295 (million)
% 11.03/1.88 % (23502)------------------------------
% 11.03/1.88 % (23502)------------------------------
% 11.03/1.89 % (23506)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on theBenchmark for (2984ds/70Mi)
% 11.03/1.91 % (23506)Instruction limit reached!
% 11.03/1.91 % (23506)------------------------------
% 11.03/1.91 % (23506)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 11.03/1.91 % (23506)Termination reason: Unknown
% 11.03/1.91 % (23506)Termination phase: Function definition elimination
% 11.03/1.91
% 11.03/1.91 % (23506)Memory used [KB]: 1791
% 11.03/1.91 % (23506)Time elapsed: 0.021 s
% 11.03/1.91 % (23506)Instructions burned: 70 (million)
% 11.03/1.91 % (23506)------------------------------
% 11.03/1.91 % (23506)------------------------------
% 11.03/1.92 % (23507)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on theBenchmark for (2984ds/316Mi)
% 11.54/1.94 % (23504)Instruction limit reached!
% 11.54/1.94 % (23504)------------------------------
% 11.54/1.94 % (23504)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 11.54/1.94 % (23504)Termination reason: Unknown
% 11.54/1.94 % (23504)Termination phase: Saturation
% 11.54/1.94
% 11.54/1.94 % (23504)Memory used [KB]: 7675
% 11.54/1.94 % (23504)Time elapsed: 0.163 s
% 11.54/1.94 % (23504)Instructions burned: 372 (million)
% 11.54/1.94 % (23504)------------------------------
% 11.54/1.94 % (23504)------------------------------
% 11.54/1.96 % (23508)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on theBenchmark for (2984ds/932Mi)
% 11.88/1.99 % (23500)Instruction limit reached!
% 11.88/1.99 % (23500)------------------------------
% 11.88/1.99 % (23500)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 11.88/1.99 % (23500)Termination reason: Unknown
% 11.88/1.99 % (23500)Termination phase: Saturation
% 11.88/1.99
% 11.88/1.99 % (23500)Memory used [KB]: 12153
% 11.88/1.99 % (23500)Time elapsed: 0.286 s
% 11.88/1.99 % (23500)Instructions burned: 669 (million)
% 11.88/1.99 % (23500)------------------------------
% 11.88/1.99 % (23500)------------------------------
% 11.88/2.00 % (23507)Instruction limit reached!
% 11.88/2.00 % (23507)------------------------------
% 11.88/2.00 % (23507)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 11.88/2.00 % (23507)Termination reason: Unknown
% 11.88/2.00 % (23507)Termination phase: Saturation
% 11.88/2.00
% 11.88/2.00 % (23507)Memory used [KB]: 6908
% 11.88/2.00 % (23507)Time elapsed: 0.082 s
% 11.88/2.00 % (23507)Instructions burned: 317 (million)
% 11.88/2.00 % (23507)------------------------------
% 11.88/2.00 % (23507)------------------------------
% 11.88/2.01 % (23509)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on theBenchmark for (2983ds/4714Mi)
% 11.88/2.02 % (23485)Instruction limit reached!
% 11.88/2.02 % (23485)------------------------------
% 11.88/2.02 % (23485)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 11.88/2.02 % (23485)Termination reason: Unknown
% 11.88/2.02 % (23485)Termination phase: Saturation
% 11.88/2.02
% 11.88/2.02 % (23485)Memory used [KB]: 9338
% 11.88/2.02 % (23485)Time elapsed: 0.728 s
% 11.88/2.02 % (23485)Instructions burned: 1539 (million)
% 11.88/2.02 % (23485)------------------------------
% 11.88/2.02 % (23485)------------------------------
% 11.88/2.02 % (23496)Instruction limit reached!
% 11.88/2.02 % (23496)------------------------------
% 11.88/2.02 % (23496)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 11.88/2.02 % (23496)Termination reason: Unknown
% 11.88/2.02 % (23496)Termination phase: Saturation
% 11.88/2.02
% 11.88/2.02 % (23496)Memory used [KB]: 8187
% 11.88/2.02 % (23496)Time elapsed: 0.437 s
% 11.88/2.02 % (23496)Instructions burned: 995 (million)
% 11.88/2.02 % (23496)------------------------------
% 11.88/2.02 % (23496)------------------------------
% 11.88/2.02 % (23510)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on theBenchmark for (2983ds/8250Mi)
% 11.88/2.04 % (23512)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on theBenchmark for (2983ds/794Mi)
% 11.88/2.05 % (23511)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on theBenchmark for (2983ds/770Mi)
% 12.53/2.08 % (23512)Refutation not found, incomplete strategy
% 12.53/2.08 % (23512)------------------------------
% 12.53/2.08 % (23512)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 12.53/2.08 % (23512)Termination reason: Refutation not found, incomplete strategy
% 12.53/2.08
% 12.53/2.08
% 12.53/2.08 % (23512)Memory used [KB]: 2430
% 12.53/2.08 % (23512)Time elapsed: 0.049 s
% 12.53/2.08 % (23512)Instructions burned: 121 (million)
% 12.53/2.08 % (23512)------------------------------
% 12.53/2.08 % (23512)------------------------------
% 12.53/2.10 % (23513)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on theBenchmark for (2982ds/464Mi)
% 14.32/2.25 % (23511)Refutation not found, incomplete strategy
% 14.32/2.25 % (23511)------------------------------
% 14.32/2.25 % (23511)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 14.32/2.25 % (23511)Termination reason: Refutation not found, incomplete strategy
% 14.32/2.25
% 14.32/2.25
% 14.32/2.25 % (23511)Memory used [KB]: 7803
% 14.32/2.25 % (23511)Time elapsed: 0.215 s
% 14.32/2.25 % (23511)Instructions burned: 402 (million)
% 14.32/2.25 % (23511)------------------------------
% 14.32/2.25 % (23511)------------------------------
% 14.32/2.26 % (23514)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on theBenchmark for (2981ds/1376Mi)
% 14.32/2.26 % (23488)Instruction limit reached!
% 14.32/2.26 % (23488)------------------------------
% 14.32/2.26 % (23488)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 14.32/2.26 % (23488)Termination reason: Unknown
% 14.32/2.26 % (23488)Termination phase: Saturation
% 14.32/2.26
% 14.32/2.26 % (23488)Memory used [KB]: 4733
% 14.32/2.27 % (23488)Time elapsed: 0.941 s
% 14.32/2.27 % (23488)Instructions burned: 1913 (million)
% 14.32/2.27 % (23488)------------------------------
% 14.32/2.27 % (23488)------------------------------
% 14.32/2.28 % (23515)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on theBenchmark for (2981ds/906Mi)
% 14.68/2.30 % (23513)Instruction limit reached!
% 14.68/2.30 % (23513)------------------------------
% 14.68/2.30 % (23513)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 14.68/2.30 % (23513)Termination reason: Unknown
% 14.68/2.30 % (23513)Termination phase: Saturation
% 14.68/2.30
% 14.68/2.30 % (23513)Memory used [KB]: 7419
% 14.68/2.30 % (23513)Time elapsed: 0.207 s
% 14.68/2.30 % (23513)Instructions burned: 465 (million)
% 14.68/2.30 % (23513)------------------------------
% 14.68/2.30 % (23513)------------------------------
% 14.68/2.32 % (23516)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on theBenchmark for (2980ds/434Mi)
% 14.94/2.38 % (23508)Instruction limit reached!
% 14.94/2.38 % (23508)------------------------------
% 14.94/2.38 % (23508)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 14.94/2.38 % (23508)Termination reason: Unknown
% 14.94/2.38 % (23508)Termination phase: Saturation
% 14.94/2.38
% 14.94/2.38 % (23508)Memory used [KB]: 8315
% 14.94/2.38 % (23508)Time elapsed: 0.428 s
% 14.94/2.38 % (23508)Instructions burned: 933 (million)
% 14.94/2.38 % (23508)------------------------------
% 14.94/2.38 % (23508)------------------------------
% 14.94/2.40 % (23517)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on theBenchmark for (2979ds/865Mi)
% 15.60/2.53 % (23516)Instruction limit reached!
% 15.60/2.53 % (23516)------------------------------
% 15.60/2.53 % (23516)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 15.60/2.53 % (23516)Termination reason: Unknown
% 15.60/2.53 % (23516)Termination phase: Saturation
% 15.60/2.53
% 15.60/2.53 % (23516)Memory used [KB]: 7675
% 15.60/2.53 % (23516)Time elapsed: 0.226 s
% 15.60/2.53 % (23516)Instructions burned: 434 (million)
% 15.60/2.53 % (23516)------------------------------
% 15.60/2.53 % (23516)------------------------------
% 16.01/2.56 % (23518)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on theBenchmark for (2978ds/593Mi)
% 16.63/2.70 % (23515)Instruction limit reached!
% 16.63/2.70 % (23515)------------------------------
% 16.63/2.70 % (23515)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 16.63/2.70 % (23515)Termination reason: Unknown
% 16.63/2.70 % (23515)Termination phase: Saturation
% 16.63/2.70
% 16.63/2.70 % (23515)Memory used [KB]: 8571
% 16.63/2.70 % (23515)Time elapsed: 0.424 s
% 16.63/2.70 % (23515)Instructions burned: 907 (million)
% 16.63/2.70 % (23515)------------------------------
% 16.63/2.70 % (23515)------------------------------
% 16.63/2.72 % (23519)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on theBenchmark for (2976ds/443Mi)
% 16.63/2.73 % (23505)Instruction limit reached!
% 16.63/2.73 % (23505)------------------------------
% 16.63/2.73 % (23505)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 16.63/2.73 % (23505)Termination reason: Unknown
% 16.63/2.73 % (23505)Termination phase: Saturation
% 16.63/2.73
% 16.63/2.73 % (23505)Memory used [KB]: 13688
% 16.63/2.73 % (23505)Time elapsed: 0.882 s
% 16.63/2.73 % (23505)Instructions burned: 1827 (million)
% 16.63/2.73 % (23505)------------------------------
% 16.63/2.73 % (23505)------------------------------
% 17.26/2.76 % (23520)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on theBenchmark for (2976ds/594Mi)
% 17.26/2.77 % (23514)Instruction limit reached!
% 17.26/2.77 % (23514)------------------------------
% 17.26/2.77 % (23514)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 17.26/2.77 % (23514)Termination reason: Unknown
% 17.26/2.77 % (23514)Termination phase: Saturation
% 17.26/2.77
% 17.26/2.77 % (23514)Memory used [KB]: 9594
% 17.26/2.77 % (23514)Time elapsed: 0.527 s
% 17.26/2.77 % (23514)Instructions burned: 1376 (million)
% 17.26/2.77 % (23514)------------------------------
% 17.26/2.77 % (23514)------------------------------
% 17.26/2.77 % (23517)Instruction limit reached!
% 17.26/2.77 % (23517)------------------------------
% 17.26/2.77 % (23517)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 17.26/2.77 % (23517)Termination reason: Unknown
% 17.26/2.77 % (23517)Termination phase: Saturation
% 17.26/2.77
% 17.26/2.77 % (23517)Memory used [KB]: 8827
% 17.26/2.77 % (23517)Time elapsed: 0.375 s
% 17.26/2.77 % (23517)Instructions burned: 865 (million)
% 17.26/2.77 % (23517)------------------------------
% 17.26/2.77 % (23517)------------------------------
% 17.26/2.78 % (23521)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on theBenchmark for (2976ds/327Mi)
% 17.26/2.79 % (23522)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on theBenchmark for (2976ds/5411Mi)
% 17.26/2.81 % (23522)Refutation not found, incomplete strategy
% 17.26/2.81 % (23522)------------------------------
% 17.26/2.81 % (23522)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 17.26/2.81 % (23522)Termination reason: Refutation not found, incomplete strategy
% 17.26/2.81
% 17.26/2.81
% 17.26/2.81 % (23522)Memory used [KB]: 6268
% 17.26/2.81 % (23522)Time elapsed: 0.021 s
% 17.26/2.81 % (23522)Instructions burned: 35 (million)
% 17.26/2.81 % (23522)------------------------------
% 17.26/2.81 % (23522)------------------------------
% 17.26/2.82 % (23523)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on theBenchmark for (2975ds/1762Mi)
% 17.26/2.83 % (23518)Instruction limit reached!
% 17.26/2.83 % (23518)------------------------------
% 17.26/2.83 % (23518)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 17.26/2.83 % (23518)Termination reason: Unknown
% 17.26/2.83 % (23518)Termination phase: Saturation
% 17.26/2.83
% 17.26/2.83 % (23518)Memory used [KB]: 7547
% 17.26/2.83 % (23518)Time elapsed: 0.302 s
% 17.26/2.83 % (23518)Instructions burned: 594 (million)
% 17.26/2.83 % (23518)------------------------------
% 17.26/2.83 % (23518)------------------------------
% 18.67/2.86 % (23524)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on theBenchmark for (2975ds/96Mi)
% 18.67/2.89 % (23521)Instruction limit reached!
% 18.67/2.89 % (23521)------------------------------
% 18.67/2.89 % (23521)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 18.67/2.89 % (23521)Termination reason: Unknown
% 18.67/2.89 % (23521)Termination phase: Saturation
% 18.67/2.89
% 18.67/2.89 % (23521)Memory used [KB]: 10106
% 18.67/2.89 % (23521)Time elapsed: 0.112 s
% 18.67/2.89 % (23521)Instructions burned: 327 (million)
% 18.67/2.89 % (23521)------------------------------
% 18.67/2.89 % (23521)------------------------------
% 18.67/2.89 % (23524)Instruction limit reached!
% 18.67/2.89 % (23524)------------------------------
% 18.67/2.89 % (23524)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 18.67/2.89 % (23524)Termination reason: Unknown
% 18.67/2.89 % (23524)Termination phase: Saturation
% 18.67/2.89
% 18.67/2.89 % (23524)Memory used [KB]: 6524
% 18.67/2.89 % (23524)Time elapsed: 0.062 s
% 18.67/2.89 % (23524)Instructions burned: 97 (million)
% 18.67/2.89 % (23524)------------------------------
% 18.67/2.89 % (23524)------------------------------
% 19.46/2.91 % (23526)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on theBenchmark for (2974ds/90Mi)
% 19.46/2.91 % (23525)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on theBenchmark for (2974ds/503Mi)
% 19.46/2.92 % (23519)Instruction limit reached!
% 19.46/2.92 % (23519)------------------------------
% 19.46/2.92 % (23519)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 19.46/2.92 % (23519)Termination reason: Unknown
% 19.46/2.92 % (23519)Termination phase: Saturation
% 19.46/2.92
% 19.46/2.92 % (23519)Memory used [KB]: 7291
% 19.46/2.92 % (23519)Time elapsed: 0.204 s
% 19.46/2.92 % (23519)Instructions burned: 444 (million)
% 19.46/2.92 % (23519)------------------------------
% 19.46/2.92 % (23519)------------------------------
% 19.46/2.94 % (23527)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on theBenchmark for (2974ds/593Mi)
% 19.46/2.94 % (23526)Instruction limit reached!
% 19.46/2.94 % (23526)------------------------------
% 19.46/2.94 % (23526)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 19.46/2.94 % (23526)Termination reason: Unknown
% 19.46/2.94 % (23526)Termination phase: Property scanning
% 19.46/2.94
% 19.46/2.94 % (23526)Memory used [KB]: 2174
% 19.46/2.94 % (23526)Time elapsed: 0.037 s
% 19.46/2.94 % (23526)Instructions burned: 91 (million)
% 19.46/2.94 % (23526)------------------------------
% 19.46/2.94 % (23526)------------------------------
% 19.83/2.96 % (23528)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on theBenchmark for (2974ds/1512Mi)
% 19.83/3.03 % (23520)Instruction limit reached!
% 19.83/3.03 % (23520)------------------------------
% 19.83/3.03 % (23520)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 19.83/3.03 % (23520)Termination reason: Unknown
% 19.83/3.03 % (23520)Termination phase: Saturation
% 19.83/3.03
% 19.83/3.03 % (23520)Memory used [KB]: 7419
% 19.83/3.03 % (23520)Time elapsed: 0.303 s
% 19.83/3.03 % (23520)Instructions burned: 595 (million)
% 19.83/3.03 % (23520)------------------------------
% 19.83/3.03 % (23520)------------------------------
% 19.83/3.04 % (23525)Refutation not found, non-redundant clauses discarded% (23525)------------------------------
% 19.83/3.04 % (23525)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 19.83/3.04 % (23525)Termination reason: Refutation not found, non-redundant clauses discarded
% 19.83/3.04
% 19.83/3.04 % (23525)Memory used [KB]: 7419
% 19.83/3.04 % (23525)Time elapsed: 0.156 s
% 19.83/3.04 % (23525)Instructions burned: 448 (million)
% 19.83/3.04 % (23525)------------------------------
% 19.83/3.04 % (23525)------------------------------
% 19.83/3.05 % (23530)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on theBenchmark for (2973ds/501Mi)
% 19.83/3.05 % (23529)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on theBenchmark for (2973ds/569Mi)
% 20.40/3.06 % (23528)Refutation not found, incomplete strategy
% 20.40/3.06 % (23528)------------------------------
% 20.40/3.06 % (23528)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 20.40/3.06 % (23528)Termination reason: Refutation not found, incomplete strategy
% 20.40/3.06
% 20.40/3.06
% 20.40/3.06 % (23528)Memory used [KB]: 8315
% 20.40/3.06 % (23528)Time elapsed: 0.123 s
% 20.40/3.06 % (23528)Instructions burned: 209 (million)
% 20.40/3.06 % (23528)------------------------------
% 20.40/3.06 % (23528)------------------------------
% 20.40/3.08 % (23531)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on theBenchmark for (2973ds/562Mi)
% 20.84/3.21 % (23529)First to succeed.
% 20.84/3.21 % (23527)Instruction limit reached!
% 20.84/3.21 % (23527)------------------------------
% 20.84/3.21 % (23527)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 20.84/3.21 % (23527)Termination reason: Unknown
% 20.84/3.21 % (23527)Termination phase: Saturation
% 20.84/3.21
% 20.84/3.21 % (23527)Memory used [KB]: 7931
% 20.84/3.21 % (23527)Time elapsed: 0.299 s
% 20.84/3.21 % (23527)Instructions burned: 595 (million)
% 20.84/3.21 % (23527)------------------------------
% 20.84/3.21 % (23527)------------------------------
% 20.84/3.22 % (23532)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on theBenchmark for (2971ds/406Mi)
% 21.52/3.26 % (23532)Refutation not found, incomplete strategy
% 21.52/3.26 % (23532)------------------------------
% 21.52/3.26 % (23532)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 21.52/3.26 % (23532)Termination reason: Refutation not found, incomplete strategy
% 21.52/3.26
% 21.52/3.26
% 21.52/3.26 % (23532)Memory used [KB]: 6780
% 21.52/3.26 % (23532)Time elapsed: 0.065 s
% 21.52/3.26 % (23532)Instructions burned: 128 (million)
% 21.52/3.26 % (23532)------------------------------
% 21.52/3.26 % (23532)------------------------------
% 21.52/3.26 % (23529)Refutation found. Thanks to Tanya!
% 21.52/3.26 % SZS status Theorem for theBenchmark
% 21.52/3.26 % SZS output start Proof for theBenchmark
% See solution above
% 21.52/3.27 % (23529)------------------------------
% 21.52/3.27 % (23529)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 21.52/3.27 % (23529)Termination reason: Refutation
% 21.52/3.27
% 21.52/3.27 % (23529)Memory used [KB]: 10234
% 21.52/3.27 % (23529)Time elapsed: 0.234 s
% 21.52/3.27 % (23529)Instructions burned: 386 (million)
% 21.52/3.27 % (23529)------------------------------
% 21.52/3.27 % (23529)------------------------------
% 21.52/3.27 % (23387)Success in time 2.882 s
% 21.52/3.27 % Vampire---4.8 exiting
%------------------------------------------------------------------------------