TSTP Solution File: ALG269^2 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : ALG269^2 : 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 : n009.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 18:20:45 EDT 2024
% Result : Theorem 1.80s 0.57s
% Output : Refutation 1.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 67
% Syntax : Number of formulae : 261 ( 115 unt; 45 typ; 0 def)
% Number of atoms : 2241 ( 238 equ; 0 cnn)
% Maximal formula atoms : 3 ( 10 avg)
% Number of connectives : 10379 ( 113 ~; 98 |; 0 &;7964 @)
% ( 12 <=>;1000 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 545 ( 545 >; 0 *; 0 +; 0 <<)
% Number of symbols : 63 ( 59 usr; 49 con; 0-4 aty)
% (1192 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 1533 (1348 ^ 184 !; 0 ?;1533 :)
% ( 1 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
term: $tType ).
thf(type_def_7,type,
subst: $tType ).
thf(func_def_0,type,
term: $tType ).
thf(func_def_1,type,
subst: $tType ).
thf(func_def_2,type,
one: term ).
thf(func_def_3,type,
ap: term > term > term ).
thf(func_def_4,type,
lam: term > term ).
thf(func_def_5,type,
sub: term > subst > term ).
thf(func_def_6,type,
id: subst ).
thf(func_def_7,type,
sh: subst ).
thf(func_def_8,type,
push: term > subst > subst ).
thf(func_def_9,type,
comp: subst > subst > subst ).
thf(func_def_10,type,
var: term > $o ).
thf(func_def_18,type,
hoasap: subst > term > subst > term > term ).
thf(func_def_73,type,
hoaslam: subst > ( subst > term > term ) > term ).
thf(func_def_86,type,
hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).
thf(func_def_107,type,
hoasvar: subst > term > subst > $o ).
thf(func_def_121,type,
pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).
thf(func_def_142,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_143,type,
sK2: subst > term > subst > $o ).
thf(func_def_144,type,
sK3: term ).
thf(func_def_145,type,
sK4: term ).
thf(func_def_146,type,
sK5: term ).
thf(func_def_147,type,
sK6: subst ).
thf(func_def_148,type,
sK7: subst ).
thf(func_def_149,type,
sK8: subst ).
thf(func_def_150,type,
sK9: term ).
thf(func_def_151,type,
sK10: subst ).
thf(func_def_152,type,
sK11: term ).
thf(func_def_153,type,
sK12: subst ).
thf(func_def_154,type,
sK13: subst ).
thf(func_def_155,type,
sK14: subst ).
thf(func_def_156,type,
sK15: subst ).
thf(func_def_157,type,
sK16: term ).
thf(func_def_158,type,
sK17: subst ).
thf(func_def_159,type,
sK18: term ).
thf(func_def_160,type,
sK19: term ).
thf(func_def_161,type,
sK20: term ).
thf(func_def_162,type,
sK21: subst ).
thf(func_def_163,type,
sK22: subst ).
thf(func_def_164,type,
sK23: subst ).
thf(func_def_165,type,
sK24: subst ).
thf(func_def_166,type,
sK25: subst ).
thf(func_def_167,type,
sK26: subst ).
thf(func_def_168,type,
sK27: term ).
thf(f1556,plain,
$false,
inference(avatar_sat_refutation,[],[f651,f712,f770,f782,f879,f996,f1073,f1118,f1236,f1245,f1374,f1476,f1553]) ).
thf(f1553,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f1552]) ).
thf(f1552,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f1548]) ).
thf(f1548,plain,
( ( $true = $false )
| ~ spl0_1 ),
inference(superposition,[],[f620,f1529]) ).
thf(f1529,plain,
( ( $false
= ( !! @ term
@ ^ [Y0: term] :
( ( sK2 @ ( comp @ sK25 @ sK24 ) @ ( sub @ Y0 @ sK24 ) @ sK26 )
=> ( sK2 @ sK25 @ Y0 @ ( comp @ sK24 @ sK26 ) ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f1528]) ).
thf(f1528,plain,
( ( $false
= ( ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ ( comp @ sK25 @ sK24 ) @ ( sub @ Y1 @ sK24 ) @ Y0 )
=> ( sK2 @ sK25 @ Y1 @ ( comp @ sK24 @ Y0 ) ) ) )
@ sK26 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f1514]) ).
thf(f1514,plain,
( ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ ( comp @ sK25 @ sK24 ) @ ( sub @ Y1 @ sK24 ) @ Y0 )
=> ( sK2 @ sK25 @ Y1 @ ( comp @ sK24 @ Y0 ) ) ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f1513]) ).
thf(f1513,plain,
( ( $false
= ( ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sK2 @ ( comp @ Y0 @ sK24 ) @ ( sub @ Y2 @ sK24 ) @ Y1 )
=> ( sK2 @ Y0 @ Y2 @ ( comp @ sK24 @ Y1 ) ) ) ) )
@ sK25 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f1499]) ).
thf(f1499,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sK2 @ ( comp @ Y0 @ sK24 ) @ ( sub @ Y2 @ sK24 ) @ Y1 )
=> ( sK2 @ Y0 @ Y2 @ ( comp @ sK24 @ Y1 ) ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f1495]) ).
thf(f1495,plain,
( ( ( ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sK2 @ ( comp @ Y1 @ Y0 ) @ ( sub @ Y3 @ Y0 ) @ Y2 )
=> ( sK2 @ Y1 @ Y3 @ ( comp @ Y0 @ Y2 ) ) ) ) ) )
@ sK24 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f647]) ).
thf(f647,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sK2 @ ( comp @ Y1 @ Y0 ) @ ( sub @ Y3 @ Y0 ) @ Y2 )
=> ( sK2 @ Y1 @ Y3 @ ( comp @ Y0 @ Y2 ) ) ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f646]) ).
thf(f646,plain,
( spl0_1
<=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sK2 @ ( comp @ Y1 @ Y0 ) @ ( sub @ Y3 @ Y0 ) @ Y2 )
=> ( sK2 @ Y1 @ Y3 @ ( comp @ Y0 @ Y2 ) ) ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f620,plain,
! [X2: subst,X3: subst,X1: subst] :
( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( sK2 @ ( comp @ X3 @ X2 ) @ ( sub @ Y0 @ X2 ) @ X1 )
=> ( sK2 @ X3 @ Y0 @ ( comp @ X2 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[],[f619]) ).
thf(f619,plain,
! [X2: subst,X3: subst,X1: subst] :
( $true
= ( ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ ( comp @ Y0 @ X2 ) @ ( sub @ Y1 @ X2 ) @ X1 )
=> ( sK2 @ Y0 @ Y1 @ ( comp @ X2 @ X1 ) ) ) )
@ X3 ) ),
inference(pi_clausification,[],[f617]) ).
thf(f617,plain,
! [X2: subst,X1: subst] :
( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ ( comp @ Y0 @ X2 ) @ ( sub @ Y1 @ X2 ) @ X1 )
=> ( sK2 @ Y0 @ Y1 @ ( comp @ X2 @ X1 ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f616]) ).
thf(f616,plain,
! [X2: subst,X1: subst] :
( $true
= ( ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sK2 @ ( comp @ Y1 @ Y0 ) @ ( sub @ Y2 @ Y0 ) @ X1 )
=> ( sK2 @ Y1 @ Y2 @ ( comp @ Y0 @ X1 ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[],[f589]) ).
thf(f589,plain,
! [X1: subst] :
( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sK2 @ ( comp @ Y1 @ Y0 ) @ ( sub @ Y2 @ Y0 ) @ X1 )
=> ( sK2 @ Y1 @ Y2 @ ( comp @ Y0 @ X1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f588]) ).
thf(f588,plain,
! [X1: subst] :
( ( ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sK2 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) @ Y0 )
=> ( sK2 @ Y2 @ Y3 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[],[f585]) ).
thf(f585,plain,
( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sK2 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) @ Y0 )
=> ( sK2 @ Y2 @ Y3 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f562]) ).
thf(f562,plain,
( $false
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sK2 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) @ Y0 )
=> ( sK2 @ Y2 @ Y3 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ ( sub @ Y0 @ id ) )
=> ( sK2 @ id @ Y0 @ id ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y0 @ id )
=> ( ( sK2 @ id @ Y1 @ id )
=> ( sK2 @ id @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( sK2 @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( sK2 @ id @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] : ( sK2 @ id @ Y0 @ id ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f560]) ).
thf(f560,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK2 @ Y3 @ Y1 @ ( comp @ Y0 @ Y2 ) )
=> ( sK2 @ ( comp @ Y3 @ Y0 ) @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sK2 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y3 @ Y1 ) @ Y0 )
=> ( sK2 @ Y2 @ Y3 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ ( sub @ Y0 @ id ) )
=> ( sK2 @ id @ Y0 @ id ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y0 @ id )
=> ( ( sK2 @ id @ Y1 @ id )
=> ( sK2 @ id @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( sK2 @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( sK2 @ id @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] : ( sK2 @ id @ Y0 @ id ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f559]) ).
thf(f559,plain,
( $false
= ( ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y2 @ ( comp @ Y1 @ Y3 ) )
=> ( Y0 @ ( comp @ Y4 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y4 @ Y2 ) @ Y1 )
=> ( Y0 @ Y3 @ Y4 @ ( comp @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( Y1 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_clausification,[],[f556]) ).
thf(f556,plain,
( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y2 @ ( comp @ Y1 @ Y3 ) )
=> ( Y0 @ ( comp @ Y4 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y4 @ Y2 ) @ Y1 )
=> ( Y0 @ Y3 @ Y4 @ ( comp @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( Y1 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) )
= $false ),
inference(boolean_simplification,[],[f555]) ).
thf(f555,plain,
( ( $true
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y2 @ ( comp @ Y1 @ Y3 ) )
=> ( Y0 @ ( comp @ Y4 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y4 @ Y2 ) @ Y1 )
=> ( Y0 @ Y3 @ Y4 @ ( comp @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( Y1 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) )
= $false ),
inference(backward_demodulation,[],[f552,f554]) ).
thf(f554,plain,
( $true
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y1 @ Y4 @ ( comp @ Y3 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y4 @ Y3 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( Y1 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ Y1 ) @ id ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f552]) ).
thf(f552,plain,
( ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y1 @ Y4 @ ( comp @ Y3 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y4 @ Y3 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( Y1 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ Y1 ) @ id ) ) ) ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y2 @ ( comp @ Y1 @ Y3 ) )
=> ( Y0 @ ( comp @ Y4 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y4 @ Y2 ) @ Y1 )
=> ( Y0 @ Y3 @ Y4 @ ( comp @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( Y1 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) )
= $false ),
inference(boolean_simplification,[],[f551]) ).
thf(f551,plain,
( ( $true
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y1 @ Y4 @ ( comp @ Y3 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y4 @ Y3 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( Y1 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ Y1 ) @ id ) ) ) ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y2 @ ( comp @ Y1 @ Y3 ) )
=> ( Y0 @ ( comp @ Y4 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y4 @ Y2 ) @ Y1 )
=> ( Y0 @ Y3 @ Y4 @ ( comp @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( Y1 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ) )
= $false ),
inference(backward_demodulation,[],[f540,f550]) ).
thf(f550,plain,
( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y1 @ Y2 ) @ Y3 )
=> ( Y0 @ Y4 @ Y1 @ ( comp @ Y2 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f540]) ).
thf(f540,plain,
( ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y1 @ Y2 ) @ Y3 )
=> ( Y0 @ Y4 @ Y1 @ ( comp @ Y2 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y1 @ Y4 @ ( comp @ Y3 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y4 @ Y3 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( Y1 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ Y1 ) @ id ) ) ) ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y2 @ ( comp @ Y1 @ Y3 ) )
=> ( Y0 @ ( comp @ Y4 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y4 @ Y2 ) @ Y1 )
=> ( Y0 @ Y3 @ Y4 @ ( comp @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( Y1 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f531]) ).
thf(f531,plain,
( ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y2 @ ( comp @ Y1 @ Y3 ) )
=> ( Y0 @ ( comp @ Y4 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y3 )
=> ( Y0 @ Y2 @ Y4 @ ( comp @ Y1 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ 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 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y1 @ Y2 ) @ Y3 )
=> ( Y0 @ Y4 @ Y1 @ ( comp @ Y2 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y1 @ Y4 @ ( comp @ Y3 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y4 @ Y3 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( Y1 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ Y1 ) @ id ) ) ) ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y2 @ ( comp @ Y1 @ Y3 ) )
=> ( Y0 @ ( comp @ Y4 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y4 @ Y2 ) @ Y1 )
=> ( Y0 @ Y3 @ Y4 @ ( comp @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( Y1 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f528]) ).
thf(f528,plain,
( ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y2 @ ( comp @ Y1 @ Y3 ) )
=> ( Y0 @ ( comp @ Y4 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y3 )
=> ( Y0 @ Y2 @ Y4 @ ( comp @ Y1 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ 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 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y1 @ Y2 ) @ Y3 )
=> ( Y0 @ Y4 @ Y1 @ ( comp @ Y2 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y1 @ Y4 @ ( comp @ Y3 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y4 @ Y3 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( Y1 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ Y1 ) @ id ) ) ) ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y2 @ ( comp @ Y1 @ Y3 ) )
=> ( Y0 @ ( comp @ Y4 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y4 @ Y2 ) @ Y1 )
=> ( Y0 @ Y3 @ Y4 @ ( comp @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( Y1 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f527]) ).
thf(f527,plain,
( $true
= ( ~ ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y2 @ ( comp @ Y1 @ Y3 ) )
=> ( Y0 @ ( comp @ Y4 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y3 )
=> ( Y0 @ Y2 @ Y4 @ ( comp @ Y1 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ 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 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y1 @ Y2 ) @ Y3 )
=> ( Y0 @ Y4 @ Y1 @ ( comp @ Y2 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y1 @ Y4 @ ( comp @ Y3 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y4 @ Y3 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( Y1 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ Y1 ) @ id ) ) ) ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y2 @ ( comp @ Y1 @ Y3 ) )
=> ( Y0 @ ( comp @ Y4 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y4 @ Y2 ) @ Y1 )
=> ( Y0 @ Y3 @ Y4 @ ( comp @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( Y1 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f526]) ).
thf(f526,plain,
( ( ~ ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y2 @ ( comp @ Y1 @ Y3 ) )
=> ( Y0 @ ( comp @ Y4 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y3 )
=> ( Y0 @ Y2 @ Y4 @ ( comp @ Y1 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( ^ [Y2: subst,Y3: term,Y4: subst] : ( var @ ( sub @ Y3 @ Y4 ) )
@ id
@ Y1
@ id )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ 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 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y1 @ Y2 ) @ Y3 )
=> ( Y0 @ Y4 @ Y1 @ ( comp @ Y2 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id
@ ( ^ [Y3: subst,Y4: term,Y5: subst,Y6: term] : ( ap @ ( sub @ Y4 @ Y5 ) @ Y6 )
@ id
@ Y2
@ id
@ Y1 )
@ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y1 @ Y4 @ ( comp @ Y3 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y4 @ Y3 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id
@ ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) )
@ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ Y1 ) @ id ) ) ) ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y2 @ ( comp @ Y1 @ Y3 ) )
=> ( Y0 @ ( comp @ Y4 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y4 @ Y2 ) @ Y1 )
=> ( Y0 @ Y3 @ Y4 @ ( comp @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( ^ [Y2: subst,Y3: term,Y4: subst] : ( var @ ( sub @ Y3 @ Y4 ) )
@ id
@ Y1
@ id )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id
@ ( ^ [Y3: subst,Y4: term,Y5: subst,Y6: term] : ( ap @ ( sub @ Y4 @ Y5 ) @ Y6 )
@ id
@ Y1
@ id
@ Y2 )
@ id ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id
@ ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) )
@ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f422,f471]) ).
thf(f471,plain,
( hoasinduction_lthm
= ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y2 @ ( comp @ Y1 @ Y3 ) )
=> ( Y0 @ ( comp @ Y4 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y3 )
=> ( Y0 @ Y2 @ Y4 @ ( comp @ Y1 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( ^ [Y2: subst,Y3: term,Y4: subst] : ( var @ ( sub @ Y3 @ Y4 ) )
@ id
@ Y1
@ id )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ 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 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y1 @ Y2 ) @ Y3 )
=> ( Y0 @ Y4 @ Y1 @ ( comp @ Y2 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id
@ ( ^ [Y3: subst,Y4: term,Y5: subst,Y6: term] : ( ap @ ( sub @ Y4 @ Y5 ) @ Y6 )
@ id
@ Y2
@ id
@ Y1 )
@ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y1 @ Y4 @ ( comp @ Y3 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y4 @ Y3 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id
@ ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) )
@ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ Y1 ) @ id ) ) ) ) ) ) )
=> ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y2 @ ( comp @ Y1 @ Y3 ) )
=> ( Y0 @ ( comp @ Y4 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y4 @ Y2 ) @ Y1 )
=> ( Y0 @ Y3 @ Y4 @ ( comp @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( ^ [Y2: subst,Y3: term,Y4: subst] : ( var @ ( sub @ Y3 @ Y4 ) )
@ id
@ Y1
@ id )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id
@ ( ^ [Y3: subst,Y4: term,Y5: subst,Y6: term] : ( ap @ ( sub @ Y4 @ Y5 ) @ Y6 )
@ id
@ Y1
@ id
@ Y2 )
@ id ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id
@ ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) )
@ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f404,f378,f467,f468,f469,f470]) ).
thf(f470,plain,
( hoasinduction
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y2 @ ( comp @ Y1 @ Y3 ) )
=> ( Y0 @ ( comp @ Y4 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y4 @ Y2 ) @ Y1 )
=> ( Y0 @ Y3 @ Y4 @ ( comp @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( ^ [Y2: subst,Y3: term,Y4: subst] : ( var @ ( sub @ Y3 @ Y4 ) )
@ id
@ Y1
@ id )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id
@ ( ^ [Y3: subst,Y4: term,Y5: subst,Y6: term] : ( ap @ ( sub @ Y4 @ Y5 ) @ Y6 )
@ id
@ Y1
@ id
@ Y2 )
@ id ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id
@ ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) )
@ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f363,f362,f439,f419]) ).
thf(f419,plain,
( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( lam @ ( Y1 @ sh @ one ) ) ) ),
inference(cnf_transformation,[],[f330]) ).
thf(f330,plain,
( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( lam @ ( Y1 @ sh @ one ) ) ) ),
inference(fool_elimination,[],[f329]) ).
thf(f329,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(f439,plain,
( hoasap
= ( ^ [Y0: subst,Y1: term,Y2: subst,Y3: term] : ( ap @ ( sub @ Y1 @ Y2 ) @ Y3 ) ) ),
inference(cnf_transformation,[],[f214]) ).
thf(f214,plain,
( hoasap
= ( ^ [Y0: subst,Y1: term,Y2: subst,Y3: term] : ( ap @ ( sub @ Y1 @ Y2 ) @ Y3 ) ) ),
inference(fool_elimination,[],[f213]) ).
thf(f213,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(f362,plain,
( hoasvar
= ( ^ [Y0: subst,Y1: term,Y2: subst] : ( var @ ( sub @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f306]) ).
thf(f306,plain,
( hoasvar
= ( ^ [Y0: subst,Y1: term,Y2: subst] : ( var @ ( sub @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f305]) ).
thf(f305,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(f363,plain,
( hoasinduction
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y2 @ ( comp @ Y1 @ Y3 ) )
=> ( Y0 @ ( comp @ Y4 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y4 @ Y2 ) @ Y1 )
=> ( Y0 @ Y3 @ Y4 @ ( comp @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( hoasvar @ id @ Y1 @ id )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( hoasap @ id @ Y1 @ id @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id
@ ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) )
@ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f247]) ).
thf(f247,plain,
( hoasinduction
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y2 @ ( comp @ Y1 @ Y3 ) )
=> ( Y0 @ ( comp @ Y4 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y4 @ Y2 ) @ Y1 )
=> ( Y0 @ Y3 @ Y4 @ ( comp @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( hoasvar @ id @ Y1 @ id )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y1 @ id )
=> ( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( hoasap @ id @ Y1 @ id @ Y2 ) @ id ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id
@ ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) )
@ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f246]) ).
thf(f246,plain,
! [X0: subst > term > subst > $o] :
( ( ! [X1: subst,X2: subst,X3: term,X4: subst] :
( ( X0 @ X1 @ X3 @ ( comp @ X4 @ X2 ) )
=> ( X0 @ ( comp @ X1 @ X4 ) @ ( sub @ X3 @ X4 ) @ X2 ) )
=> ( ! [X5: term,X6: subst,X7: subst,X8: subst] :
( ( X0 @ ( comp @ X6 @ X7 ) @ ( sub @ X5 @ X7 ) @ X8 )
=> ( X0 @ X6 @ X5 @ ( comp @ X7 @ X8 ) ) )
=> ( ! [X9: term] :
( ( hoasvar @ id @ X9 @ id )
=> ( X0 @ id @ X9 @ id ) )
=> ( ! [X10: term,X11: term] :
( ( X0 @ id @ X11 @ id )
=> ( ( X0 @ id @ X10 @ id )
=> ( X0 @ id @ ( hoasap @ id @ X11 @ id @ X10 ) @ id ) ) )
=> ( ! [X12: subst > term > term] :
( ! [X13: term,X14: subst,X15: subst] :
( ( sub @ ( X12 @ X15 @ X13 ) @ X14 )
= ( X12 @ ( comp @ X15 @ X14 ) @ ( sub @ X13 @ X14 ) ) )
=> ( ! [X16: term] :
( ( X0 @ id @ X16 @ id )
=> ( X0 @ id @ ( X12 @ id @ X16 ) @ id ) )
=> ( X0 @ id
@ ( hoaslam @ id
@ ^ [X17: subst,X18: term] : ( X12 @ X17 @ X18 ) )
@ id ) ) )
=> ! [X19: term] : ( X0 @ id @ X19 @ id ) ) ) ) ) )
= hoasinduction ),
inference(rectify,[],[f108]) ).
thf(f108,axiom,
! [X5: subst > term > subst > $o] :
( ( ! [X2: subst,X3: subst,X0: term,X4: subst] :
( ( X5 @ X2 @ X0 @ ( comp @ X4 @ X3 ) )
=> ( X5 @ ( comp @ X2 @ X4 ) @ ( sub @ X0 @ X4 ) @ X3 ) )
=> ( ! [X0: term,X2: subst,X4: subst,X3: subst] :
( ( X5 @ ( comp @ X2 @ X4 ) @ ( sub @ X0 @ X4 ) @ X3 )
=> ( X5 @ X2 @ X0 @ ( comp @ X4 @ X3 ) ) )
=> ( ! [X0: term] :
( ( hoasvar @ id @ X0 @ id )
=> ( X5 @ id @ X0 @ id ) )
=> ( ! [X1: term,X0: term] :
( ( X5 @ id @ X0 @ id )
=> ( ( X5 @ id @ X1 @ id )
=> ( X5 @ id @ ( hoasap @ id @ X0 @ id @ X1 ) @ id ) ) )
=> ( ! [X10: subst > term > term] :
( ! [X0: term,X3: subst,X2: subst] :
( ( sub @ ( X10 @ X2 @ X0 ) @ X3 )
= ( X10 @ ( comp @ X2 @ X3 ) @ ( sub @ X0 @ X3 ) ) )
=> ( ! [X0: term] :
( ( X5 @ id @ X0 @ id )
=> ( X5 @ id @ ( X10 @ id @ X0 ) @ id ) )
=> ( X5 @ id
@ ( hoaslam @ id
@ ^ [X2: subst,X0: term] : ( X10 @ X2 @ X0 ) )
@ id ) ) )
=> ! [X0: term] : ( X5 @ id @ X0 @ id ) ) ) ) ) )
= hoasinduction ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction) ).
thf(f469,plain,
( hoasinduction_lem3
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y1 @ Y4 @ ( comp @ Y3 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y4 @ Y3 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id
@ ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) )
@ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ Y1 ) @ id ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f342,f419]) ).
thf(f342,plain,
( hoasinduction_lem3
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y1 @ Y4 @ ( comp @ Y3 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y4 @ Y3 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id
@ ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) )
@ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ Y1 ) @ id ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f194]) ).
thf(f194,plain,
( hoasinduction_lem3
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y1 @ Y4 @ ( comp @ Y3 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y4 @ Y3 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id
@ ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) )
@ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ Y1 ) @ id ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f193]) ).
thf(f193,plain,
( hoasinduction_lem3
= ( ! [X0: subst > term > subst > $o] :
( ! [X1: term,X2: subst,X3: subst,X4: subst] :
( ( X0 @ X4 @ X1 @ ( comp @ X2 @ X3 ) )
=> ( X0 @ ( comp @ X4 @ X2 ) @ ( sub @ X1 @ X2 ) @ X3 ) )
=> ( ! [X5: subst,X6: subst,X7: term,X8: subst] :
( ( X0 @ ( comp @ X5 @ X6 ) @ ( sub @ X7 @ X6 ) @ X8 )
=> ( X0 @ X5 @ X7 @ ( comp @ X6 @ X8 ) ) )
=> ( ! [X9: subst > term > term] :
( ! [X10: term,X11: subst,X12: subst] :
( ( sub @ ( X9 @ X12 @ X10 ) @ X11 )
= ( X9 @ ( comp @ X12 @ X11 ) @ ( sub @ X10 @ X11 ) ) )
=> ( ! [X13: term] :
( ( X0 @ id @ X13 @ id )
=> ( X0 @ id @ ( X9 @ id @ X13 ) @ id ) )
=> ( X0 @ id
@ ( hoaslam @ id
@ ^ [X14: subst,X15: term] : ( X9 @ X14 @ X15 ) )
@ id ) ) )
=> ! [X16: term] :
( ! [X17: term] :
( ( X0 @ id @ X17 @ id )
=> ( X0 @ id @ ( sub @ X16 @ ( push @ X17 @ id ) ) @ id ) )
=> ( X0 @ id @ ( lam @ X16 ) @ id ) ) ) ) ) ) ),
inference(rectify,[],[f99]) ).
thf(f99,axiom,
( hoasinduction_lem3
= ( ! [X5: subst > term > subst > $o] :
( ! [X0: term,X4: subst,X3: subst,X2: subst] :
( ( X5 @ X2 @ X0 @ ( comp @ X4 @ X3 ) )
=> ( X5 @ ( comp @ X2 @ X4 ) @ ( sub @ X0 @ X4 ) @ X3 ) )
=> ( ! [X2: subst,X4: subst,X0: term,X3: subst] :
( ( X5 @ ( comp @ X2 @ X4 ) @ ( sub @ X0 @ X4 ) @ X3 )
=> ( X5 @ X2 @ X0 @ ( comp @ X4 @ X3 ) ) )
=> ( ! [X10: subst > term > term] :
( ! [X0: term,X3: subst,X2: subst] :
( ( sub @ ( X10 @ X2 @ X0 ) @ X3 )
= ( X10 @ ( comp @ X2 @ X3 ) @ ( sub @ X0 @ X3 ) ) )
=> ( ! [X0: term] :
( ( X5 @ id @ X0 @ id )
=> ( X5 @ id @ ( X10 @ id @ X0 ) @ id ) )
=> ( X5 @ id
@ ( hoaslam @ id
@ ^ [X2: subst,X0: term] : ( X10 @ X2 @ X0 ) )
@ id ) ) )
=> ! [X0: term] :
( ! [X1: term] :
( ( X5 @ id @ X1 @ id )
=> ( X5 @ id @ ( sub @ X0 @ ( push @ X1 @ id ) ) @ id ) )
=> ( X5 @ id @ ( lam @ X0 ) @ id ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3) ).
thf(f468,plain,
( hoasinduction_lem2
= ( !! @ ( 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 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y1 @ Y2 ) @ Y3 )
=> ( Y0 @ Y4 @ Y1 @ ( comp @ Y2 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id
@ ( ^ [Y3: subst,Y4: term,Y5: subst,Y6: term] : ( ap @ ( sub @ Y4 @ Y5 ) @ Y6 )
@ id
@ Y2
@ id
@ Y1 )
@ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f445,f439]) ).
thf(f445,plain,
( hoasinduction_lem2
= ( !! @ ( 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 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y1 @ Y2 ) @ Y3 )
=> ( Y0 @ Y4 @ Y1 @ ( comp @ Y2 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( hoasap @ id @ Y2 @ id @ Y1 ) @ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f292]) ).
thf(f292,plain,
( hoasinduction_lem2
= ( !! @ ( 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 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y1 @ Y2 ) @ Y3 )
=> ( Y0 @ Y4 @ Y1 @ ( comp @ Y2 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( hoasap @ id @ Y2 @ id @ Y1 ) @ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f291]) ).
thf(f291,plain,
( hoasinduction_lem2
= ( ! [X0: subst > term > subst > $o] :
( ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( X0 @ X4 @ X2 @ ( comp @ X1 @ X3 ) )
=> ( X0 @ ( comp @ X4 @ X1 ) @ ( sub @ X2 @ X1 ) @ X3 ) )
=> ( ! [X5: subst,X6: subst,X7: subst,X8: term] :
( ( X0 @ ( comp @ X5 @ X7 ) @ ( sub @ X8 @ X7 ) @ X6 )
=> ( X0 @ X5 @ X8 @ ( comp @ X7 @ X6 ) ) )
=> ( ! [X9: term,X10: term] :
( ( X0 @ id @ X9 @ id )
=> ( ( X0 @ id @ X10 @ id )
=> ( X0 @ id @ ( hoasap @ id @ X9 @ id @ X10 ) @ id ) ) )
=> ! [X11: term,X12: term] :
( ( X0 @ id @ X11 @ id )
=> ( ( X0 @ id @ X12 @ id )
=> ( X0 @ id @ ( ap @ X11 @ X12 ) @ id ) ) ) ) ) ) ) ),
inference(rectify,[],[f93]) ).
thf(f93,axiom,
( hoasinduction_lem2
= ( ! [X5: subst > term > subst > $o] :
( ! [X4: subst,X0: term,X3: subst,X2: subst] :
( ( X5 @ X2 @ X0 @ ( comp @ X4 @ X3 ) )
=> ( X5 @ ( comp @ X2 @ X4 ) @ ( sub @ X0 @ X4 ) @ X3 ) )
=> ( ! [X2: subst,X3: subst,X4: subst,X0: term] :
( ( 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 ) ) )
=> ! [X0: term,X1: term] :
( ( X5 @ id @ X0 @ id )
=> ( ( X5 @ id @ X1 @ id )
=> ( X5 @ id @ ( ap @ X0 @ X1 ) @ id ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem2) ).
thf(f467,plain,
( hoasinduction_lem1
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y2 @ ( comp @ Y1 @ Y3 ) )
=> ( Y0 @ ( comp @ Y4 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y3 )
=> ( Y0 @ Y2 @ Y4 @ ( comp @ Y1 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( ^ [Y2: subst,Y3: term,Y4: subst] : ( var @ ( sub @ Y3 @ Y4 ) )
@ id
@ Y1
@ id )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f429,f362]) ).
thf(f429,plain,
( hoasinduction_lem1
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y2 @ ( comp @ Y1 @ Y3 ) )
=> ( Y0 @ ( comp @ Y4 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y3 )
=> ( Y0 @ Y2 @ Y4 @ ( comp @ Y1 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( hoasvar @ id @ Y1 @ id )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f170]) ).
thf(f170,plain,
( hoasinduction_lem1
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y2 @ ( comp @ Y1 @ Y3 ) )
=> ( Y0 @ ( comp @ Y4 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y3 )
=> ( Y0 @ Y2 @ Y4 @ ( comp @ Y1 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( hoasvar @ id @ Y1 @ id )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f169]) ).
thf(f169,plain,
( hoasinduction_lem1
= ( ! [X0: subst > term > subst > $o] :
( ! [X1: subst,X2: subst,X3: term,X4: subst] :
( ( X0 @ X1 @ X3 @ ( comp @ X4 @ X2 ) )
=> ( X0 @ ( comp @ X1 @ X4 ) @ ( sub @ X3 @ X4 ) @ X2 ) )
=> ( ! [X5: term,X6: subst,X7: subst,X8: subst] :
( ( X0 @ ( comp @ X7 @ X8 ) @ ( sub @ X5 @ X8 ) @ X6 )
=> ( X0 @ X7 @ X5 @ ( comp @ X8 @ X6 ) ) )
=> ( ! [X9: term] :
( ( hoasvar @ id @ X9 @ id )
=> ( X0 @ id @ X9 @ id ) )
=> ! [X10: term] :
( ( var @ X10 )
=> ( X0 @ id @ X10 @ id ) ) ) ) ) ) ),
inference(rectify,[],[f90]) ).
thf(f90,axiom,
( hoasinduction_lem1
= ( ! [X5: subst > term > subst > $o] :
( ! [X2: subst,X3: subst,X0: term,X4: subst] :
( ( X5 @ X2 @ X0 @ ( comp @ X4 @ X3 ) )
=> ( X5 @ ( comp @ X2 @ X4 ) @ ( sub @ X0 @ X4 ) @ X3 ) )
=> ( ! [X0: term,X3: subst,X2: subst,X4: subst] :
( ( X5 @ ( comp @ X2 @ X4 ) @ ( sub @ X0 @ X4 ) @ X3 )
=> ( X5 @ X2 @ X0 @ ( comp @ X4 @ X3 ) ) )
=> ( ! [X0: term] :
( ( hoasvar @ id @ X0 @ id )
=> ( X5 @ id @ X0 @ id ) )
=> ! [X0: term] :
( ( var @ X0 )
=> ( X5 @ id @ X0 @ id ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem1) ).
thf(f378,plain,
( induction2
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f210]) ).
thf(f210,plain,
( induction2
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f209]) ).
thf(f209,plain,
( induction2
= ( ! [X0: term > $o] :
( ! [X1: term] :
( ( var @ X1 )
=> ( X0 @ X1 ) )
=> ( ! [X2: term,X3: term] :
( ( X0 @ X2 )
=> ( ( X0 @ X3 )
=> ( X0 @ ( ap @ X2 @ X3 ) ) ) )
=> ( ! [X4: term] :
( ! [X5: term] :
( ( X0 @ X5 )
=> ( X0 @ ( sub @ X4 @ ( push @ X5 @ id ) ) ) )
=> ( X0 @ ( lam @ X4 ) ) )
=> ! [X6: term] : ( X0 @ X6 ) ) ) ) ) ),
inference(rectify,[],[f46]) ).
thf(f46,axiom,
( induction2
= ( ! [X5: term > $o] :
( ! [X0: term] :
( ( var @ X0 )
=> ( X5 @ X0 ) )
=> ( ! [X0: term,X1: term] :
( ( X5 @ X0 )
=> ( ( X5 @ X1 )
=> ( X5 @ ( ap @ X0 @ X1 ) ) ) )
=> ( ! [X0: term] :
( ! [X1: term] :
( ( X5 @ X1 )
=> ( X5 @ ( sub @ X0 @ ( push @ X1 @ id ) ) ) )
=> ( X5 @ ( lam @ X0 ) ) )
=> ! [X0: term] : ( X5 @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',induction2) ).
thf(f404,plain,
( hoasinduction_lthm
= ( induction2
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> ( hoasinduction_lem3
=> hoasinduction ) ) ) ) ),
inference(cnf_transformation,[],[f288]) ).
thf(f288,plain,
( hoasinduction_lthm
= ( induction2
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> ( hoasinduction_lem3
=> hoasinduction ) ) ) ) ),
inference(fool_elimination,[],[f287]) ).
thf(f287,plain,
( induction2
=> ( ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> ( hoasinduction_lem3
=> hoasinduction ) ) )
= hoasinduction_lthm ) ),
inference(rectify,[],[f110]) ).
thf(f110,axiom,
( induction2
=> ( ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> ( hoasinduction_lem3
=> hoasinduction ) ) )
= hoasinduction_lthm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lthm) ).
thf(f422,plain,
( $true = ~ hoasinduction_lthm ),
inference(cnf_transformation,[],[f308]) ).
thf(f308,plain,
( $true = ~ hoasinduction_lthm ),
inference(fool_elimination,[],[f307]) ).
thf(f307,plain,
~ hoasinduction_lthm,
inference(rectify,[],[f115]) ).
thf(f115,negated_conjecture,
~ hoasinduction_lthm,
inference(negated_conjecture,[],[f114]) ).
thf(f114,conjecture,
hoasinduction_lthm,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(f1476,plain,
~ spl0_12,
inference(avatar_contradiction_clause,[],[f1475]) ).
thf(f1475,plain,
( $false
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f1471]) ).
thf(f1471,plain,
( ( $true = $false )
| ~ spl0_12 ),
inference(superposition,[],[f1453,f623]) ).
thf(f623,plain,
! [X2: subst,X3: subst,X1: subst,X4: term] :
( $true
= ( ( sK2 @ ( comp @ X3 @ X2 ) @ ( sub @ X4 @ X2 ) @ X1 )
=> ( sK2 @ X3 @ X4 @ ( comp @ X2 @ X1 ) ) ) ),
inference(beta_eta_normalization,[],[f621]) ).
thf(f621,plain,
! [X2: subst,X3: subst,X1: subst,X4: term] :
( $true
= ( ^ [Y0: term] :
( ( sK2 @ ( comp @ X3 @ X2 ) @ ( sub @ Y0 @ X2 ) @ X1 )
=> ( sK2 @ X3 @ Y0 @ ( comp @ X2 @ X1 ) ) )
@ X4 ) ),
inference(pi_clausification,[],[f620]) ).
thf(f1453,plain,
( ( ( ( sK2 @ ( comp @ sK23 @ sK21 ) @ ( sub @ sK20 @ sK21 ) @ sK22 )
=> ( sK2 @ sK23 @ sK20 @ ( comp @ sK21 @ sK22 ) ) )
= $false )
| ~ spl0_12 ),
inference(beta_eta_normalization,[],[f1452]) ).
thf(f1452,plain,
( ( ( ^ [Y0: subst] :
( ( sK2 @ ( comp @ Y0 @ sK21 ) @ ( sub @ sK20 @ sK21 ) @ sK22 )
=> ( sK2 @ Y0 @ sK20 @ ( comp @ sK21 @ sK22 ) ) )
@ sK23 )
= $false )
| ~ spl0_12 ),
inference(sigma_clausification,[],[f1436]) ).
thf(f1436,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( sK2 @ ( comp @ Y0 @ sK21 ) @ ( sub @ sK20 @ sK21 ) @ sK22 )
=> ( sK2 @ Y0 @ sK20 @ ( comp @ sK21 @ sK22 ) ) ) )
= $false )
| ~ spl0_12 ),
inference(beta_eta_normalization,[],[f1435]) ).
thf(f1435,plain,
( ( $false
= ( ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sK2 @ ( comp @ Y1 @ sK21 ) @ ( sub @ sK20 @ sK21 ) @ Y0 )
=> ( sK2 @ Y1 @ sK20 @ ( comp @ sK21 @ Y0 ) ) ) )
@ sK22 ) )
| ~ spl0_12 ),
inference(sigma_clausification,[],[f1419]) ).
thf(f1419,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sK2 @ ( comp @ Y1 @ sK21 ) @ ( sub @ sK20 @ sK21 ) @ Y0 )
=> ( sK2 @ Y1 @ sK20 @ ( comp @ sK21 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_12 ),
inference(beta_eta_normalization,[],[f1418]) ).
thf(f1418,plain,
( ( ( ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sK2 @ ( comp @ Y2 @ Y0 ) @ ( sub @ sK20 @ Y0 ) @ Y1 )
=> ( sK2 @ Y2 @ sK20 @ ( comp @ Y0 @ Y1 ) ) ) ) )
@ sK21 )
= $false )
| ~ spl0_12 ),
inference(sigma_clausification,[],[f1400]) ).
thf(f1400,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sK2 @ ( comp @ Y2 @ Y0 ) @ ( sub @ sK20 @ Y0 ) @ Y1 )
=> ( sK2 @ Y2 @ sK20 @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
= $false )
| ~ spl0_12 ),
inference(beta_eta_normalization,[],[f1395]) ).
thf(f1395,plain,
( ( ( ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK2 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y0 @ Y1 ) @ Y2 )
=> ( sK2 @ Y3 @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
@ sK20 )
= $false )
| ~ spl0_12 ),
inference(sigma_clausification,[],[f1117]) ).
thf(f1117,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK2 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y0 @ Y1 ) @ Y2 )
=> ( sK2 @ Y3 @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) ) )
= $false )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f1116]) ).
thf(f1116,plain,
( spl0_12
<=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK2 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y0 @ Y1 ) @ Y2 )
=> ( sK2 @ Y3 @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
thf(f1374,plain,
~ spl0_11,
inference(avatar_contradiction_clause,[],[f1373]) ).
thf(f1373,plain,
( $false
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f1364]) ).
thf(f1364,plain,
( ( $true = $false )
| ~ spl0_11 ),
inference(superposition,[],[f1355,f642]) ).
thf(f642,plain,
! [X2: term,X1: term] :
( ( ( sK2 @ id @ X1 @ id )
=> ( ( sK2 @ id @ X2 @ id )
=> ( sK2 @ id @ ( ap @ ( sub @ X1 @ id ) @ X2 ) @ id ) ) )
= $true ),
inference(beta_eta_normalization,[],[f636]) ).
thf(f636,plain,
! [X2: term,X1: term] :
( $true
= ( ^ [Y0: term] :
( ( sK2 @ id @ X1 @ id )
=> ( ( sK2 @ id @ Y0 @ id )
=> ( sK2 @ id @ ( ap @ ( sub @ X1 @ id ) @ Y0 ) @ id ) ) )
@ X2 ) ),
inference(pi_clausification,[],[f635]) ).
thf(f635,plain,
! [X1: term] :
( ( !! @ term
@ ^ [Y0: term] :
( ( sK2 @ id @ X1 @ id )
=> ( ( sK2 @ id @ Y0 @ id )
=> ( sK2 @ id @ ( ap @ ( sub @ X1 @ id ) @ Y0 ) @ id ) ) ) )
= $true ),
inference(beta_eta_normalization,[],[f629]) ).
thf(f629,plain,
! [X1: term] :
( ( ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y0 @ id )
=> ( ( sK2 @ id @ Y1 @ id )
=> ( sK2 @ id @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[],[f608]) ).
thf(f608,plain,
( $true
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y0 @ id )
=> ( ( sK2 @ id @ Y1 @ id )
=> ( sK2 @ id @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f594]) ).
thf(f594,plain,
( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y0 @ id )
=> ( ( sK2 @ id @ Y1 @ id )
=> ( sK2 @ id @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( sK2 @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( sK2 @ id @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] : ( sK2 @ id @ Y0 @ id ) ) ) ) ),
inference(boolean_simplification,[],[f592]) ).
thf(f592,plain,
( $false
= ( $true
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y0 @ id )
=> ( ( sK2 @ id @ Y1 @ id )
=> ( sK2 @ id @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( sK2 @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( sK2 @ id @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] : ( sK2 @ id @ Y0 @ id ) ) ) ) ) ),
inference(backward_demodulation,[],[f587,f591]) ).
thf(f591,plain,
( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( var @ ( sub @ Y0 @ id ) )
=> ( sK2 @ id @ Y0 @ id ) ) ) ),
inference(binary_proxy_clausification,[],[f587]) ).
thf(f587,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ ( sub @ Y0 @ id ) )
=> ( sK2 @ id @ Y0 @ id ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y0 @ id )
=> ( ( sK2 @ id @ Y1 @ id )
=> ( sK2 @ id @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( sK2 @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( sK2 @ id @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] : ( sK2 @ id @ Y0 @ id ) ) ) ) )
= $false ),
inference(boolean_simplification,[],[f586]) ).
thf(f586,plain,
( $false
= ( $true
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ ( sub @ Y0 @ id ) )
=> ( sK2 @ id @ Y0 @ id ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y0 @ id )
=> ( ( sK2 @ id @ Y1 @ id )
=> ( sK2 @ id @ ( ap @ ( sub @ Y0 @ id ) @ Y1 ) @ id ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( sK2 @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( sK2 @ id @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] : ( sK2 @ id @ Y0 @ id ) ) ) ) ) ) ),
inference(backward_demodulation,[],[f562,f585]) ).
thf(f1355,plain,
( ( ( ( sK2 @ id @ sK19 @ id )
=> ( ( sK2 @ id @ sK18 @ id )
=> ( sK2 @ id @ ( ap @ ( sub @ sK19 @ id ) @ sK18 ) @ id ) ) )
= $false )
| ~ spl0_11 ),
inference(beta_eta_normalization,[],[f1351]) ).
thf(f1351,plain,
( ( $false
= ( ^ [Y0: term] :
( ( sK2 @ id @ Y0 @ id )
=> ( ( sK2 @ id @ sK18 @ id )
=> ( sK2 @ id @ ( ap @ ( sub @ Y0 @ id ) @ sK18 ) @ id ) ) )
@ sK19 ) )
| ~ spl0_11 ),
inference(sigma_clausification,[],[f1330]) ).
thf(f1330,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( ( sK2 @ id @ Y0 @ id )
=> ( ( sK2 @ id @ sK18 @ id )
=> ( sK2 @ id @ ( ap @ ( sub @ Y0 @ id ) @ sK18 ) @ id ) ) ) )
= $false )
| ~ spl0_11 ),
inference(beta_eta_normalization,[],[f1327]) ).
thf(f1327,plain,
( ( ( ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( ( sK2 @ id @ Y0 @ id )
=> ( sK2 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) )
@ sK18 )
= $false )
| ~ spl0_11 ),
inference(sigma_clausification,[],[f1316]) ).
thf(f1316,plain,
( ( $false
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( ( sK2 @ id @ Y0 @ id )
=> ( sK2 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) ) ) )
| ~ spl0_11 ),
inference(not_proxy_clausification,[],[f1114]) ).
thf(f1114,plain,
( ( $true
= ( ~ ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( ( sK2 @ id @ Y0 @ id )
=> ( sK2 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) ) ) ) )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f1113]) ).
thf(f1113,plain,
( spl0_11
<=> ( $true
= ( ~ ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( ( sK2 @ id @ Y0 @ id )
=> ( sK2 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
thf(f1245,plain,
( ~ spl0_4
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f1244]) ).
thf(f1244,plain,
( $false
| ~ spl0_4
| ~ spl0_8 ),
inference(trivial_inequality_removal,[],[f1243]) ).
thf(f1243,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_8 ),
inference(boolean_simplification,[],[f1242]) ).
thf(f1242,plain,
( ( $true = ~ $true )
| ~ spl0_4
| ~ spl0_8 ),
inference(forward_demodulation,[],[f711,f781]) ).
thf(f781,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( sK2 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( sK2 @ id @ ( lam @ Y0 ) @ id ) ) )
= $true )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f780]) ).
thf(f780,plain,
( spl0_8
<=> ( ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( sK2 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( sK2 @ id @ ( lam @ Y0 ) @ id ) ) )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
thf(f711,plain,
( ( $true
= ( ~ ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( sK2 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( sK2 @ id @ ( lam @ Y0 ) @ id ) ) ) ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f710]) ).
thf(f710,plain,
( spl0_4
<=> ( $true
= ( ~ ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( sK2 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( sK2 @ id @ ( lam @ Y0 ) @ id ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
thf(f1236,plain,
~ spl0_10,
inference(avatar_contradiction_clause,[],[f1235]) ).
thf(f1235,plain,
( $false
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f1231]) ).
thf(f1231,plain,
( ( $true = $false )
| ~ spl0_10 ),
inference(superposition,[],[f1209,f582]) ).
thf(f582,plain,
! [X2: term,X3: subst,X1: subst,X4: subst] :
( ( ( sK2 @ X4 @ X2 @ ( comp @ X1 @ X3 ) )
=> ( sK2 @ ( comp @ X4 @ X1 ) @ ( sub @ X2 @ X1 ) @ X3 ) )
= $true ),
inference(beta_eta_normalization,[],[f581]) ).
thf(f581,plain,
! [X2: term,X3: subst,X1: subst,X4: subst] :
( $true
= ( ^ [Y0: subst] :
( ( sK2 @ Y0 @ X2 @ ( comp @ X1 @ X3 ) )
=> ( sK2 @ ( comp @ Y0 @ X1 ) @ ( sub @ X2 @ X1 ) @ X3 ) )
@ X4 ) ),
inference(pi_clausification,[],[f580]) ).
thf(f580,plain,
! [X2: term,X3: subst,X1: subst] :
( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( ( sK2 @ Y0 @ X2 @ ( comp @ X1 @ X3 ) )
=> ( sK2 @ ( comp @ Y0 @ X1 ) @ ( sub @ X2 @ X1 ) @ X3 ) ) ) ),
inference(beta_eta_normalization,[],[f579]) ).
thf(f579,plain,
! [X2: term,X3: subst,X1: subst] :
( $true
= ( ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sK2 @ Y1 @ X2 @ ( comp @ X1 @ Y0 ) )
=> ( sK2 @ ( comp @ Y1 @ X1 ) @ ( sub @ X2 @ X1 ) @ Y0 ) ) )
@ X3 ) ),
inference(pi_clausification,[],[f574]) ).
thf(f574,plain,
! [X2: term,X1: subst] :
( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sK2 @ Y1 @ X2 @ ( comp @ X1 @ Y0 ) )
=> ( sK2 @ ( comp @ Y1 @ X1 ) @ ( sub @ X2 @ X1 ) @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[],[f572]) ).
thf(f572,plain,
! [X2: term,X1: subst] :
( $true
= ( ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sK2 @ Y2 @ Y0 @ ( comp @ X1 @ Y1 ) )
=> ( sK2 @ ( comp @ Y2 @ X1 ) @ ( sub @ Y0 @ X1 ) @ Y1 ) ) ) )
@ X2 ) ),
inference(pi_clausification,[],[f570]) ).
thf(f570,plain,
! [X1: subst] :
( $true
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sK2 @ Y2 @ Y0 @ ( comp @ X1 @ Y1 ) )
=> ( sK2 @ ( comp @ Y2 @ X1 ) @ ( sub @ Y0 @ X1 ) @ Y1 ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f568]) ).
thf(f568,plain,
! [X1: subst] :
( ( ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK2 @ Y3 @ Y1 @ ( comp @ Y0 @ Y2 ) )
=> ( sK2 @ ( comp @ Y3 @ Y0 ) @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[],[f563]) ).
thf(f563,plain,
( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK2 @ Y3 @ Y1 @ ( comp @ Y0 @ Y2 ) )
=> ( sK2 @ ( comp @ Y3 @ Y0 ) @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f560]) ).
thf(f1209,plain,
( ( $false
= ( ( sK2 @ sK14 @ sK16 @ ( comp @ sK17 @ sK15 ) )
=> ( sK2 @ ( comp @ sK14 @ sK17 ) @ ( sub @ sK16 @ sK17 ) @ sK15 ) ) )
| ~ spl0_10 ),
inference(beta_eta_normalization,[],[f1208]) ).
thf(f1208,plain,
( ( $false
= ( ^ [Y0: subst] :
( ( sK2 @ sK14 @ sK16 @ ( comp @ Y0 @ sK15 ) )
=> ( sK2 @ ( comp @ sK14 @ Y0 ) @ ( sub @ sK16 @ Y0 ) @ sK15 ) )
@ sK17 ) )
| ~ spl0_10 ),
inference(sigma_clausification,[],[f1186]) ).
thf(f1186,plain,
( ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( ( sK2 @ sK14 @ sK16 @ ( comp @ Y0 @ sK15 ) )
=> ( sK2 @ ( comp @ sK14 @ Y0 ) @ ( sub @ sK16 @ Y0 ) @ sK15 ) ) ) )
| ~ spl0_10 ),
inference(beta_eta_normalization,[],[f1184]) ).
thf(f1184,plain,
( ( $false
= ( ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sK2 @ sK14 @ Y0 @ ( comp @ Y1 @ sK15 ) )
=> ( sK2 @ ( comp @ sK14 @ Y1 ) @ ( sub @ Y0 @ Y1 ) @ sK15 ) ) )
@ sK16 ) )
| ~ spl0_10 ),
inference(sigma_clausification,[],[f1164]) ).
thf(f1164,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sK2 @ sK14 @ Y0 @ ( comp @ Y1 @ sK15 ) )
=> ( sK2 @ ( comp @ sK14 @ Y1 ) @ ( sub @ Y0 @ Y1 ) @ sK15 ) ) ) )
= $false )
| ~ spl0_10 ),
inference(beta_eta_normalization,[],[f1163]) ).
thf(f1163,plain,
( ( ( ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sK2 @ sK14 @ Y1 @ ( comp @ Y2 @ Y0 ) )
=> ( sK2 @ ( comp @ sK14 @ Y2 ) @ ( sub @ Y1 @ Y2 ) @ Y0 ) ) ) )
@ sK15 )
= $false )
| ~ spl0_10 ),
inference(sigma_clausification,[],[f1142]) ).
thf(f1142,plain,
( ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sK2 @ sK14 @ Y1 @ ( comp @ Y2 @ Y0 ) )
=> ( sK2 @ ( comp @ sK14 @ Y2 ) @ ( sub @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) )
| ~ spl0_10 ),
inference(beta_eta_normalization,[],[f1140]) ).
thf(f1140,plain,
( ( $false
= ( ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK2 @ Y0 @ Y2 @ ( comp @ Y3 @ Y1 ) )
=> ( sK2 @ ( comp @ Y0 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 ) ) ) ) )
@ sK14 ) )
| ~ spl0_10 ),
inference(sigma_clausification,[],[f1072]) ).
thf(f1072,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK2 @ Y0 @ Y2 @ ( comp @ Y3 @ Y1 ) )
=> ( sK2 @ ( comp @ Y0 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 ) ) ) ) ) )
= $false )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f1071]) ).
thf(f1071,plain,
( spl0_10
<=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK2 @ Y0 @ Y2 @ ( comp @ Y3 @ Y1 ) )
=> ( sK2 @ ( comp @ Y0 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 ) ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
thf(f1118,plain,
( spl0_11
| spl0_12
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f1111,f1068,f1116,f1113]) ).
thf(f1068,plain,
( spl0_9
<=> ( $true
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK2 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y0 @ Y1 ) @ Y2 )
=> ( sK2 @ Y3 @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) ) )
=> ~ ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( ( sK2 @ id @ Y0 @ id )
=> ( sK2 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
thf(f1111,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK2 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y0 @ Y1 ) @ Y2 )
=> ( sK2 @ Y3 @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) ) )
= $false )
| ( $true
= ( ~ ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( ( sK2 @ id @ Y0 @ id )
=> ( sK2 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) ) ) ) )
| ~ spl0_9 ),
inference(binary_proxy_clausification,[],[f1069]) ).
thf(f1069,plain,
( ( $true
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK2 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y0 @ Y1 ) @ Y2 )
=> ( sK2 @ Y3 @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) ) )
=> ~ ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( ( sK2 @ id @ Y0 @ id )
=> ( sK2 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) ) ) ) )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f1068]) ).
thf(f1073,plain,
( spl0_9
| spl0_10
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f1066,f707,f1071,f1068]) ).
thf(f707,plain,
( spl0_3
<=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( ( sK2 @ id @ Y0 @ id )
=> ( sK2 @ id @ ( ap @ Y1 @ Y0 ) @ id ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
thf(f1066,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK2 @ Y0 @ Y2 @ ( comp @ Y3 @ Y1 ) )
=> ( sK2 @ ( comp @ Y0 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 ) ) ) ) ) )
= $false )
| ( $true
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK2 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y0 @ Y1 ) @ Y2 )
=> ( sK2 @ Y3 @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) ) )
=> ~ ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( ( sK2 @ id @ Y0 @ id )
=> ( sK2 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f721]) ).
thf(f721,plain,
( ( $true
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK2 @ Y0 @ Y2 @ ( comp @ Y3 @ Y1 ) )
=> ( sK2 @ ( comp @ Y0 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK2 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y0 @ Y1 ) @ Y2 )
=> ( sK2 @ Y3 @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) ) )
=> ~ ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( ( sK2 @ id @ Y0 @ id )
=> ( sK2 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) ) ) ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[],[f717]) ).
thf(f717,plain,
( ( $true
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK2 @ Y0 @ Y2 @ ( comp @ Y3 @ Y1 ) )
=> ( sK2 @ ( comp @ Y0 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK2 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y0 @ Y1 ) @ Y2 )
=> ( sK2 @ Y3 @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( ( sK2 @ id @ Y0 @ id )
=> ( sK2 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) ) )
=> $false ) ) ) )
| ~ spl0_3 ),
inference(superposition,[],[f558,f708]) ).
thf(f708,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( ( sK2 @ id @ Y0 @ id )
=> ( sK2 @ id @ ( ap @ Y1 @ Y0 ) @ id ) ) ) ) )
= $false )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f707]) ).
thf(f558,plain,
! [X1: subst > term > subst > $o] :
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( X1 @ Y0 @ Y2 @ ( comp @ Y3 @ Y1 ) )
=> ( X1 @ ( comp @ Y0 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( X1 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y0 @ Y1 ) @ Y2 )
=> ( X1 @ Y3 @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( X1 @ id @ Y1 @ id )
=> ( ( X1 @ id @ Y0 @ id )
=> ( X1 @ id @ ( ap @ ( sub @ Y1 @ id ) @ Y0 ) @ id ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( X1 @ id @ Y1 @ id )
=> ( ( X1 @ id @ Y0 @ id )
=> ( X1 @ id @ ( ap @ Y1 @ Y0 ) @ id ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[],[f557]) ).
thf(f557,plain,
! [X1: subst > term > subst > $o] :
( $true
= ( ^ [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 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y1 @ Y2 ) @ Y3 )
=> ( Y0 @ Y4 @ Y1 @ ( comp @ Y2 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ 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] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( ( Y0 @ id @ Y1 @ id )
=> ( Y0 @ id @ ( ap @ Y2 @ Y1 ) @ id ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[],[f550]) ).
thf(f996,plain,
~ spl0_7,
inference(avatar_contradiction_clause,[],[f995]) ).
thf(f995,plain,
( $false
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f992]) ).
thf(f992,plain,
( ( $true = $false )
| ~ spl0_7 ),
inference(superposition,[],[f623,f971]) ).
thf(f971,plain,
( ( ( ( sK2 @ ( comp @ sK13 @ sK12 ) @ ( sub @ sK11 @ sK12 ) @ sK10 )
=> ( sK2 @ sK13 @ sK11 @ ( comp @ sK12 @ sK10 ) ) )
= $false )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f970]) ).
thf(f970,plain,
( ( ( ^ [Y0: subst] :
( ( sK2 @ ( comp @ Y0 @ sK12 ) @ ( sub @ sK11 @ sK12 ) @ sK10 )
=> ( sK2 @ Y0 @ sK11 @ ( comp @ sK12 @ sK10 ) ) )
@ sK13 )
= $false )
| ~ spl0_7 ),
inference(sigma_clausification,[],[f952]) ).
thf(f952,plain,
( ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( ( sK2 @ ( comp @ Y0 @ sK12 ) @ ( sub @ sK11 @ sK12 ) @ sK10 )
=> ( sK2 @ Y0 @ sK11 @ ( comp @ sK12 @ sK10 ) ) ) ) )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f951]) ).
thf(f951,plain,
( ( ( ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sK2 @ ( comp @ Y1 @ Y0 ) @ ( sub @ sK11 @ Y0 ) @ sK10 )
=> ( sK2 @ Y1 @ sK11 @ ( comp @ Y0 @ sK10 ) ) ) )
@ sK12 )
= $false )
| ~ spl0_7 ),
inference(sigma_clausification,[],[f925]) ).
thf(f925,plain,
( ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sK2 @ ( comp @ Y1 @ Y0 ) @ ( sub @ sK11 @ Y0 ) @ sK10 )
=> ( sK2 @ Y1 @ sK11 @ ( comp @ Y0 @ sK10 ) ) ) ) ) )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f921]) ).
thf(f921,plain,
( ( ( ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sK2 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y0 @ Y1 ) @ sK10 )
=> ( sK2 @ Y2 @ Y0 @ ( comp @ Y1 @ sK10 ) ) ) ) )
@ sK11 )
= $false )
| ~ spl0_7 ),
inference(sigma_clausification,[],[f905]) ).
thf(f905,plain,
( ( $false
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sK2 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y0 @ Y1 ) @ sK10 )
=> ( sK2 @ Y2 @ Y0 @ ( comp @ Y1 @ sK10 ) ) ) ) ) ) )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f901]) ).
thf(f901,plain,
( ( $false
= ( ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK2 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) @ Y0 )
=> ( sK2 @ Y3 @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) )
@ sK10 ) )
| ~ spl0_7 ),
inference(sigma_clausification,[],[f778]) ).
thf(f778,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK2 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) @ Y0 )
=> ( sK2 @ Y3 @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) )
= $false )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f777]) ).
thf(f777,plain,
( spl0_7
<=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK2 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) @ Y0 )
=> ( sK2 @ Y3 @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
thf(f879,plain,
~ spl0_6,
inference(avatar_contradiction_clause,[],[f878]) ).
thf(f878,plain,
( $false
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f874]) ).
thf(f874,plain,
( ( $true = $false )
| ~ spl0_6 ),
inference(superposition,[],[f828,f582]) ).
thf(f828,plain,
( ( $false
= ( ( sK2 @ sK6 @ sK9 @ ( comp @ sK8 @ sK7 ) )
=> ( sK2 @ ( comp @ sK6 @ sK8 ) @ ( sub @ sK9 @ sK8 ) @ sK7 ) ) )
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f826]) ).
thf(f826,plain,
( ( ( ^ [Y0: term] :
( ( sK2 @ sK6 @ Y0 @ ( comp @ sK8 @ sK7 ) )
=> ( sK2 @ ( comp @ sK6 @ sK8 ) @ ( sub @ Y0 @ sK8 ) @ sK7 ) )
@ sK9 )
= $false )
| ~ spl0_6 ),
inference(sigma_clausification,[],[f810]) ).
thf(f810,plain,
( ( $false
= ( !! @ term
@ ^ [Y0: term] :
( ( sK2 @ sK6 @ Y0 @ ( comp @ sK8 @ sK7 ) )
=> ( sK2 @ ( comp @ sK6 @ sK8 ) @ ( sub @ Y0 @ sK8 ) @ sK7 ) ) ) )
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f809]) ).
thf(f809,plain,
( ( ( ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ sK6 @ Y1 @ ( comp @ Y0 @ sK7 ) )
=> ( sK2 @ ( comp @ sK6 @ Y0 ) @ ( sub @ Y1 @ Y0 ) @ sK7 ) ) )
@ sK8 )
= $false )
| ~ spl0_6 ),
inference(sigma_clausification,[],[f797]) ).
thf(f797,plain,
( ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ sK6 @ Y1 @ ( comp @ Y0 @ sK7 ) )
=> ( sK2 @ ( comp @ sK6 @ Y0 ) @ ( sub @ Y1 @ Y0 ) @ sK7 ) ) ) ) )
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f796]) ).
thf(f796,plain,
( ( ( ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sK2 @ sK6 @ Y2 @ ( comp @ Y1 @ Y0 ) )
=> ( sK2 @ ( comp @ sK6 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) )
@ sK7 )
= $false )
| ~ spl0_6 ),
inference(sigma_clausification,[],[f791]) ).
thf(f791,plain,
( ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sK2 @ sK6 @ Y2 @ ( comp @ Y1 @ Y0 ) )
=> ( sK2 @ ( comp @ sK6 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y0 ) ) ) ) ) )
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f788]) ).
thf(f788,plain,
( ( ( ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sK2 @ Y0 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( sK2 @ ( comp @ Y0 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) )
@ sK6 )
= $false )
| ~ spl0_6 ),
inference(sigma_clausification,[],[f769]) ).
thf(f769,plain,
( ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sK2 @ Y0 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( sK2 @ ( comp @ Y0 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f768]) ).
thf(f768,plain,
( spl0_6
<=> ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sK2 @ Y0 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( sK2 @ ( comp @ Y0 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
thf(f782,plain,
( spl0_7
| spl0_8
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f775,f765,f780,f777]) ).
thf(f765,plain,
( spl0_5
<=> ( $true
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK2 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) @ Y0 )
=> ( sK2 @ Y3 @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( sK2 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( sK2 @ id @ ( lam @ Y0 ) @ id ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
thf(f775,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK2 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) @ Y0 )
=> ( sK2 @ Y3 @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) )
= $false )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( sK2 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( sK2 @ id @ ( lam @ Y0 ) @ id ) ) )
= $true )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f766]) ).
thf(f766,plain,
( ( $true
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK2 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) @ Y0 )
=> ( sK2 @ Y3 @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( sK2 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( sK2 @ id @ ( lam @ Y0 ) @ id ) ) ) ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f765]) ).
thf(f770,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f763,f768,f765]) ).
thf(f763,plain,
( ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sK2 @ Y0 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( sK2 @ ( comp @ Y0 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK2 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) @ Y0 )
=> ( sK2 @ Y3 @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( sK2 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( sK2 @ id @ ( lam @ Y0 ) @ id ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f693]) ).
thf(f693,plain,
( $true
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sK2 @ Y0 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( sK2 @ ( comp @ Y0 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK2 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) @ Y0 )
=> ( sK2 @ Y3 @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( sK2 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( sK2 @ id @ ( lam @ Y0 ) @ id ) ) ) ) ) ),
inference(boolean_simplification,[],[f692]) ).
thf(f692,plain,
( $true
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sK2 @ Y0 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( sK2 @ ( comp @ Y0 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK2 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) @ Y0 )
=> ( sK2 @ Y3 @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) )
=> ( $true
=> ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( sK2 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( sK2 @ id @ ( lam @ Y0 ) @ id ) ) ) ) ) ) ),
inference(superposition,[],[f615,f667]) ).
thf(f667,plain,
( $true
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( sK2 @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( sK2 @ id @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) ) ),
inference(binary_proxy_clausification,[],[f607]) ).
thf(f607,plain,
( $false
= ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( sK2 @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( sK2 @ id @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] : ( sK2 @ id @ Y0 @ id ) ) ) ),
inference(binary_proxy_clausification,[],[f594]) ).
thf(f615,plain,
! [X1: subst > term > subst > $o] :
( $true
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( X1 @ Y0 @ Y3 @ ( comp @ Y2 @ Y1 ) )
=> ( X1 @ ( comp @ Y0 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( X1 @ ( comp @ Y3 @ Y2 ) @ ( sub @ Y1 @ Y2 ) @ Y0 )
=> ( X1 @ Y3 @ Y1 @ ( comp @ Y2 @ Y0 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 )
= ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( X1 @ id @ Y1 @ id )
=> ( X1 @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( X1 @ id @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( X1 @ id @ Y1 @ id )
=> ( X1 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( X1 @ id @ ( lam @ Y0 ) @ id ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f614]) ).
thf(f614,plain,
! [X1: subst > term > subst > $o] :
( ( ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ Y1 @ Y4 @ ( comp @ Y3 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y4 @ Y3 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ ( comp @ Y4 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 )
= ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( Y1 @ sh @ one ) ) @ id ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ Y1 ) @ id ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[],[f554]) ).
thf(f712,plain,
( spl0_3
| spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f705,f649,f710,f707]) ).
thf(f649,plain,
( spl0_2
<=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK2 @ id @ Y0 @ id ) ) )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f705,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( ( sK2 @ id @ Y0 @ id )
=> ( sK2 @ id @ ( ap @ Y1 @ Y0 ) @ id ) ) ) ) )
= $false )
| ( $true
= ( ~ ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( sK2 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( sK2 @ id @ ( lam @ Y0 ) @ id ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f678]) ).
thf(f678,plain,
( ( $true
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( ( sK2 @ id @ Y0 @ id )
=> ( sK2 @ id @ ( ap @ Y1 @ Y0 ) @ id ) ) ) ) )
=> ~ ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( sK2 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( sK2 @ id @ ( lam @ Y0 ) @ id ) ) ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f677]) ).
thf(f677,plain,
( ( $true
= ( $true
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( ( sK2 @ id @ Y0 @ id )
=> ( sK2 @ id @ ( ap @ Y1 @ Y0 ) @ id ) ) ) ) )
=> ~ ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( sK2 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( sK2 @ id @ ( lam @ Y0 ) @ id ) ) ) ) ) )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f675,f650]) ).
thf(f650,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK2 @ id @ Y0 @ id ) ) )
= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f649]) ).
thf(f675,plain,
( $true
= ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK2 @ id @ Y0 @ id ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( ( sK2 @ id @ Y0 @ id )
=> ( sK2 @ id @ ( ap @ Y1 @ Y0 ) @ id ) ) ) ) )
=> ~ ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( sK2 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( sK2 @ id @ ( lam @ Y0 ) @ id ) ) ) ) ) ),
inference(boolean_simplification,[],[f674]) ).
thf(f674,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK2 @ id @ Y0 @ id ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( ( sK2 @ id @ Y0 @ id )
=> ( sK2 @ id @ ( ap @ Y1 @ Y0 ) @ id ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK2 @ id @ Y1 @ id )
=> ( sK2 @ id @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) @ id ) ) )
=> ( sK2 @ id @ ( lam @ Y0 ) @ id ) ) )
=> $false ) ) )
= $true ),
inference(beta_eta_normalization,[],[f673]) ).
thf(f673,plain,
( $true
= ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( ^ [Y1: term] : ( sK2 @ id @ Y1 @ id )
@ Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ^ [Y2: term] : ( sK2 @ id @ Y2 @ id )
@ Y1 )
=> ( ( ^ [Y2: term] : ( sK2 @ id @ Y2 @ id )
@ Y0 )
=> ( ^ [Y2: term] : ( sK2 @ id @ Y2 @ id )
@ ( ap @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( ^ [Y2: term] : ( sK2 @ id @ Y2 @ id )
@ Y1 )
=> ( ^ [Y2: term] : ( sK2 @ id @ Y2 @ id )
@ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( ^ [Y1: term] : ( sK2 @ id @ Y1 @ id )
@ ( lam @ Y0 ) ) ) )
=> $false ) ) ) ),
inference(superposition,[],[f538,f666]) ).
thf(f666,plain,
( ( !! @ term
@ ^ [Y0: term] : ( sK2 @ id @ Y0 @ id ) )
= $false ),
inference(binary_proxy_clausification,[],[f607]) ).
thf(f538,plain,
! [X1: term > $o] :
( $true
= ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( X1 @ Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( X1 @ Y1 )
=> ( ( X1 @ Y0 )
=> ( X1 @ ( ap @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( X1 @ Y1 )
=> ( X1 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( X1 @ ( lam @ Y0 ) ) ) )
=> ( !! @ term @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[],[f537]) ).
thf(f537,plain,
! [X1: term > $o] :
( ( ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[],[f532]) ).
thf(f532,plain,
( $true
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( ap @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !! @ term @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f528]) ).
thf(f651,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f644,f649,f646]) ).
thf(f644,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sK2 @ ( comp @ Y1 @ Y0 ) @ ( sub @ Y3 @ Y0 ) @ Y2 )
=> ( sK2 @ Y1 @ Y3 @ ( comp @ Y0 @ Y2 ) ) ) ) ) ) )
= $false )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK2 @ id @ Y0 @ id ) ) )
= $true ) ),
inference(binary_proxy_clausification,[],[f595]) ).
thf(f595,plain,
( $true
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sK2 @ ( comp @ Y1 @ Y0 ) @ ( sub @ Y3 @ Y0 ) @ Y2 )
=> ( sK2 @ Y1 @ Y3 @ ( comp @ Y0 @ Y2 ) ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK2 @ id @ Y0 @ id ) ) ) ) ),
inference(boolean_simplification,[],[f593]) ).
thf(f593,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sK2 @ ( comp @ Y1 @ Y0 ) @ ( sub @ Y3 @ Y0 ) @ Y2 )
=> ( sK2 @ Y1 @ Y3 @ ( comp @ Y0 @ Y2 ) ) ) ) ) ) )
=> ( $true
=> ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK2 @ id @ Y0 @ id ) ) ) ) )
= $true ),
inference(backward_demodulation,[],[f571,f591]) ).
thf(f571,plain,
( $true
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sK2 @ ( comp @ Y1 @ Y0 ) @ ( sub @ Y3 @ Y0 ) @ Y2 )
=> ( sK2 @ Y1 @ Y3 @ ( comp @ Y0 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ ( sub @ Y0 @ id ) )
=> ( sK2 @ id @ Y0 @ id ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK2 @ id @ Y0 @ id ) ) ) ) ) ),
inference(boolean_simplification,[],[f569]) ).
thf(f569,plain,
( $true
= ( $true
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sK2 @ ( comp @ Y1 @ Y0 ) @ ( sub @ Y3 @ Y0 ) @ Y2 )
=> ( sK2 @ Y1 @ Y3 @ ( comp @ Y0 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ ( sub @ Y0 @ id ) )
=> ( sK2 @ id @ Y0 @ id ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK2 @ id @ Y0 @ id ) ) ) ) ) ) ),
inference(superposition,[],[f547,f563]) ).
thf(f547,plain,
! [X1: subst > term > subst > $o] :
( $true
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( X1 @ Y3 @ Y1 @ ( comp @ Y0 @ Y2 ) )
=> ( X1 @ ( comp @ Y3 @ Y0 ) @ ( sub @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( X1 @ ( comp @ Y1 @ Y0 ) @ ( sub @ Y3 @ Y0 ) @ Y2 )
=> ( X1 @ Y1 @ Y3 @ ( comp @ Y0 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ ( sub @ Y0 @ id ) )
=> ( X1 @ id @ Y0 @ id ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( X1 @ id @ Y0 @ id ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f546]) ).
thf(f546,plain,
! [X1: subst > term > subst > $o] :
( $true
= ( ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y2 @ ( comp @ Y1 @ Y3 ) )
=> ( Y0 @ ( comp @ Y4 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y3 )
=> ( Y0 @ Y2 @ Y4 @ ( comp @ Y1 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[],[f541]) ).
thf(f541,plain,
( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y4 @ Y2 @ ( comp @ Y1 @ Y3 ) )
=> ( Y0 @ ( comp @ Y4 @ Y1 ) @ ( sub @ Y2 @ Y1 ) @ Y3 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ ( comp @ Y2 @ Y1 ) @ ( sub @ Y4 @ Y1 ) @ Y3 )
=> ( Y0 @ Y2 @ Y4 @ ( comp @ Y1 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f531]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.08 % Problem : ALG269^2 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.01/0.10 % 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
% 0.10/0.32 % Computer : n009.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Sat May 18 22:41:38 EDT 2024
% 0.10/0.32 % CPUTime :
% 0.10/0.32 This is a TH0_THM_EQU_NAR problem
% 0.10/0.32 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
% 0.17/0.34 % (11430)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)
% 0.17/0.35 % (11422)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)
% 0.17/0.35 % (11421)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.17/0.35 % (11431)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.17/0.35 % (11427)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)
% 0.17/0.35 % (11422)Instruction limit reached!
% 0.17/0.35 % (11422)------------------------------
% 0.17/0.35 % (11422)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.35 % (11422)Termination reason: Unknown
% 0.17/0.35 % (11422)Termination phase: shuffling
% 0.17/0.35
% 0.17/0.35 % (11422)Memory used [KB]: 1279
% 0.17/0.35 % (11422)Time elapsed: 0.005 s
% 0.17/0.35 % (11422)Instructions burned: 5 (million)
% 0.17/0.35 % (11422)------------------------------
% 0.17/0.35 % (11422)------------------------------
% 0.17/0.35 % (11427)Instruction limit reached!
% 0.17/0.35 % (11427)------------------------------
% 0.17/0.35 % (11427)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.35 % (11427)Termination reason: Unknown
% 0.17/0.35 % (11427)Termination phase: shuffling
% 0.17/0.35
% 0.17/0.35 % (11427)Memory used [KB]: 1279
% 0.17/0.35 % (11427)Time elapsed: 0.004 s
% 0.17/0.35 % (11427)Instructions burned: 3 (million)
% 0.17/0.35 % (11427)------------------------------
% 0.17/0.35 % (11427)------------------------------
% 0.17/0.35 % (11426)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.17/0.36 % (11426)Instruction limit reached!
% 0.17/0.36 % (11426)------------------------------
% 0.17/0.36 % (11426)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.36 % (11426)Termination reason: Unknown
% 0.17/0.36 % (11426)Termination phase: shuffling
% 0.17/0.36
% 0.17/0.36 % (11426)Memory used [KB]: 1279
% 0.17/0.36 % (11426)Time elapsed: 0.004 s
% 0.17/0.36 % (11426)Instructions burned: 2 (million)
% 0.17/0.36 % (11426)------------------------------
% 0.17/0.36 % (11426)------------------------------
% 0.17/0.36 % (11431)Instruction limit reached!
% 0.17/0.36 % (11431)------------------------------
% 0.17/0.36 % (11431)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.36 % (11431)Termination reason: Unknown
% 0.17/0.36 % (11431)Termination phase: Property scanning
% 0.17/0.36
% 0.17/0.36 % (11431)Memory used [KB]: 1663
% 0.17/0.36 % (11431)Time elapsed: 0.015 s
% 0.17/0.36 % (11431)Instructions burned: 19 (million)
% 0.17/0.36 % (11431)------------------------------
% 0.17/0.36 % (11431)------------------------------
% 0.17/0.36 % (11424)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)
% 0.17/0.36 % (11430)Refutation not found, incomplete strategy
% 0.17/0.36 % (11430)------------------------------
% 0.17/0.36 % (11430)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.36 % (11430)Termination reason: Refutation not found, incomplete strategy
% 0.17/0.36
% 0.17/0.36
% 0.17/0.36 % (11430)Memory used [KB]: 6396
% 0.17/0.36 % (11430)Time elapsed: 0.020 s
% 0.17/0.36 % (11430)Instructions burned: 44 (million)
% 0.17/0.36 % (11430)------------------------------
% 0.17/0.36 % (11430)------------------------------
% 0.17/0.36 % (11432)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)
% 0.17/0.37 % (11432)Instruction limit reached!
% 0.17/0.37 % (11432)------------------------------
% 0.17/0.37 % (11432)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.37 % (11432)Termination reason: Unknown
% 0.17/0.37 % (11432)Termination phase: shuffling
% 0.17/0.37
% 0.17/0.37 % (11432)Memory used [KB]: 1279
% 0.17/0.37 % (11432)Time elapsed: 0.005 s
% 0.17/0.37 % (11432)Instructions burned: 5 (million)
% 0.17/0.37 % (11432)------------------------------
% 0.17/0.37 % (11432)------------------------------
% 0.17/0.37 % (11445)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)
% 0.17/0.37 % (11446)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)
% 0.17/0.37 % (11448)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)
% 0.17/0.37 % (11448)Instruction limit reached!
% 0.17/0.37 % (11448)------------------------------
% 0.17/0.37 % (11448)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.37 % (11448)Termination reason: Unknown
% 0.17/0.37 % (11448)Termination phase: shuffling
% 0.17/0.37
% 0.17/0.37 % (11448)Memory used [KB]: 1279
% 0.17/0.37 % (11448)Time elapsed: 0.003 s
% 0.17/0.37 % (11448)Instructions burned: 3 (million)
% 0.17/0.37 % (11448)------------------------------
% 0.17/0.37 % (11448)------------------------------
% 0.17/0.38 % (11424)Instruction limit reached!
% 0.17/0.38 % (11424)------------------------------
% 0.17/0.38 % (11424)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.38 % (11424)Termination reason: Unknown
% 0.17/0.38 % (11424)Termination phase: shuffling
% 0.17/0.38
% 0.17/0.38 % (11424)Memory used [KB]: 1791
% 0.17/0.38 % (11424)Time elapsed: 0.015 s
% 0.17/0.38 % (11424)Instructions burned: 27 (million)
% 0.17/0.38 % (11424)------------------------------
% 0.17/0.38 % (11424)------------------------------
% 0.17/0.38 % (11446)Instruction limit reached!
% 0.17/0.38 % (11446)------------------------------
% 0.17/0.38 % (11446)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.38 % (11446)Termination reason: Unknown
% 0.17/0.38 % (11446)Termination phase: Property scanning
% 0.17/0.38
% 0.17/0.38 % (11446)Memory used [KB]: 1663
% 0.17/0.38 % (11446)Time elapsed: 0.012 s
% 0.17/0.38 % (11446)Instructions burned: 15 (million)
% 0.17/0.38 % (11446)------------------------------
% 0.17/0.38 % (11446)------------------------------
% 0.17/0.38 % (11449)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)
% 0.17/0.38 % (11450)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.17/0.38 % (11450)Instruction limit reached!
% 0.17/0.38 % (11450)------------------------------
% 0.17/0.38 % (11450)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.38 % (11450)Termination reason: Unknown
% 0.17/0.38 % (11450)Termination phase: shuffling
% 0.17/0.38
% 0.17/0.38 % (11450)Memory used [KB]: 1407
% 0.17/0.38 % (11450)Time elapsed: 0.005 s
% 0.17/0.38 % (11450)Instructions burned: 8 (million)
% 0.17/0.38 % (11450)------------------------------
% 0.17/0.38 % (11450)------------------------------
% 0.17/0.39 % (11445)Instruction limit reached!
% 0.17/0.39 % (11445)------------------------------
% 0.17/0.39 % (11445)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.39 % (11445)Termination reason: Unknown
% 0.17/0.39 % (11445)Termination phase: Property scanning
% 0.17/0.39
% 0.17/0.39 % (11445)Memory used [KB]: 1791
% 0.17/0.39 % (11445)Time elapsed: 0.020 s
% 0.17/0.39 % (11445)Instructions burned: 38 (million)
% 0.17/0.39 % (11445)------------------------------
% 0.17/0.39 % (11445)------------------------------
% 0.17/0.39 % (11452)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)
% 0.17/0.39 % (11453)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)
% 0.17/0.39 % (11452)Instruction limit reached!
% 0.17/0.39 % (11452)------------------------------
% 0.17/0.39 % (11452)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.39 % (11452)Termination reason: Unknown
% 0.17/0.39 % (11452)Termination phase: shuffling
% 0.17/0.39
% 0.17/0.39 % (11452)Memory used [KB]: 1279
% 0.17/0.39 % (11452)Time elapsed: 0.004 s
% 0.17/0.39 % (11452)Instructions burned: 4 (million)
% 0.17/0.39 % (11452)------------------------------
% 0.17/0.39 % (11452)------------------------------
% 0.17/0.39 % (11453)Instruction limit reached!
% 0.17/0.39 % (11453)------------------------------
% 0.17/0.39 % (11453)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.39 % (11453)Termination reason: Unknown
% 0.17/0.39 % (11453)Termination phase: shuffling
% 0.17/0.39
% 0.17/0.39 % (11453)Memory used [KB]: 1279
% 0.17/0.39 % (11453)Time elapsed: 0.004 s
% 0.17/0.39 % (11453)Instructions burned: 4 (million)
% 0.17/0.39 % (11453)------------------------------
% 0.17/0.39 % (11453)------------------------------
% 0.17/0.39 % (11451)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.17/0.40 % (11455)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)
% 0.17/0.40 % (11455)Instruction limit reached!
% 0.17/0.40 % (11455)------------------------------
% 0.17/0.40 % (11455)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.40 % (11455)Termination reason: Unknown
% 0.17/0.40 % (11455)Termination phase: shuffling
% 0.17/0.40
% 0.17/0.40 % (11455)Memory used [KB]: 1279
% 0.17/0.40 % (11455)Time elapsed: 0.003 s
% 0.17/0.40 % (11455)Instructions burned: 3 (million)
% 0.17/0.40 % (11455)------------------------------
% 0.17/0.40 % (11455)------------------------------
% 0.17/0.40 % (11456)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.17/0.40 % (11451)Instruction limit reached!
% 0.17/0.40 % (11451)------------------------------
% 0.17/0.40 % (11451)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.40 % (11451)Termination reason: Unknown
% 0.17/0.40 % (11451)Termination phase: shuffling
% 0.17/0.40
% 0.17/0.40 % (11451)Memory used [KB]: 1535
% 0.17/0.40 % (11451)Time elapsed: 0.012 s
% 0.17/0.40 % (11451)Instructions burned: 17 (million)
% 0.17/0.40 % (11451)------------------------------
% 0.17/0.40 % (11451)------------------------------
% 0.17/0.41 % (11456)Instruction limit reached!
% 0.17/0.41 % (11456)------------------------------
% 0.17/0.41 % (11456)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.41 % (11456)Termination reason: Unknown
% 0.17/0.41 % (11456)Termination phase: shuffling
% 0.17/0.41
% 0.17/0.41 % (11456)Memory used [KB]: 1279
% 0.17/0.41 % (11456)Time elapsed: 0.005 s
% 0.17/0.41 % (11456)Instructions burned: 4 (million)
% 0.17/0.41 % (11456)------------------------------
% 0.17/0.41 % (11456)------------------------------
% 0.17/0.41 % (11457)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)
% 0.17/0.41 % (11454)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)
% 0.17/0.41 % (11459)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.17/0.41 % (11454)Instruction limit reached!
% 0.17/0.41 % (11454)------------------------------
% 0.17/0.41 % (11454)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.41 % (11454)Termination reason: Unknown
% 0.17/0.41 % (11454)Termination phase: shuffling
% 0.17/0.41
% 0.17/0.41 % (11454)Memory used [KB]: 1407
% 0.17/0.41 % (11454)Time elapsed: 0.006 s
% 0.17/0.41 % (11454)Instructions burned: 7 (million)
% 0.17/0.41 % (11454)------------------------------
% 0.17/0.41 % (11454)------------------------------
% 0.17/0.41 % (11459)Instruction limit reached!
% 0.17/0.41 % (11459)------------------------------
% 0.17/0.41 % (11459)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.41 % (11457)Instruction limit reached!
% 0.17/0.41 % (11457)------------------------------
% 0.17/0.41 % (11457)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.41 % (11457)Termination reason: Unknown
% 0.17/0.41 % (11457)Termination phase: shuffling
% 0.17/0.41
% 0.17/0.41 % (11457)Memory used [KB]: 1663
% 0.17/0.41 % (11457)Time elapsed: 0.010 s
% 0.17/0.41 % (11457)Instructions burned: 19 (million)
% 0.17/0.41 % (11457)------------------------------
% 0.17/0.41 % (11457)------------------------------
% 0.17/0.41 % (11459)Termination reason: Unknown
% 0.17/0.41 % (11459)Termination phase: shuffling
% 0.17/0.41
% 0.17/0.41 % (11459)Memory used [KB]: 1407
% 0.17/0.41 % (11459)Time elapsed: 0.005 s
% 0.17/0.41 % (11459)Instructions burned: 7 (million)
% 0.17/0.41 % (11459)------------------------------
% 0.17/0.41 % (11459)------------------------------
% 0.17/0.41 % (11458)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.17/0.42 % (11460)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)
% 0.17/0.43 % (11461)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)
% 0.17/0.43 % (11462)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.17/0.43 % (11464)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2999ds/377Mi)
% 0.17/0.43 % (11462)Instruction limit reached!
% 0.17/0.43 % (11462)------------------------------
% 0.17/0.43 % (11462)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.43 % (11462)Termination reason: Unknown
% 0.17/0.43 % (11462)Termination phase: shuffling
% 0.17/0.43
% 0.17/0.43 % (11462)Memory used [KB]: 1279
% 0.17/0.43 % (11462)Time elapsed: 0.005 s
% 0.17/0.43 % (11462)Instructions burned: 6 (million)
% 0.17/0.43 % (11462)------------------------------
% 0.17/0.43 % (11462)------------------------------
% 0.17/0.43 % (11463)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)
% 0.17/0.43 % (11458)Refutation not found, incomplete strategy
% 0.17/0.43 % (11458)------------------------------
% 0.17/0.43 % (11458)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.43 % (11458)Termination reason: Refutation not found, incomplete strategy
% 0.17/0.43
% 0.17/0.43
% 0.17/0.43 % (11458)Memory used [KB]: 6140
% 0.17/0.43 % (11458)Time elapsed: 0.041 s
% 0.17/0.43 % (11458)Instructions burned: 25 (million)
% 0.17/0.43 % (11458)------------------------------
% 0.17/0.43 % (11458)------------------------------
% 0.17/0.43 % (11463)Instruction limit reached!
% 0.17/0.43 % (11463)------------------------------
% 0.17/0.43 % (11463)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.43 % (11463)Termination reason: Unknown
% 0.17/0.43 % (11463)Termination phase: shuffling
% 0.17/0.43
% 0.17/0.43 % (11463)Memory used [KB]: 1407
% 0.17/0.43 % (11463)Time elapsed: 0.005 s
% 0.17/0.43 % (11463)Instructions burned: 7 (million)
% 0.17/0.43 % (11463)------------------------------
% 0.17/0.43 % (11463)------------------------------
% 0.17/0.44 % (11461)Instruction limit reached!
% 0.17/0.44 % (11461)------------------------------
% 0.17/0.44 % (11461)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.44 % (11461)Termination reason: Unknown
% 0.17/0.44 % (11461)Termination phase: shuffling
% 0.17/0.44
% 0.17/0.44 % (11461)Memory used [KB]: 1663
% 0.17/0.44 % (11461)Time elapsed: 0.013 s
% 0.17/0.44 % (11461)Instructions burned: 21 (million)
% 0.17/0.44 % (11461)------------------------------
% 0.17/0.44 % (11461)------------------------------
% 0.17/0.45 % (11421)Instruction limit reached!
% 0.17/0.45 % (11421)------------------------------
% 0.17/0.45 % (11421)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.45 % (11421)Termination reason: Unknown
% 0.17/0.45 % (11421)Termination phase: Saturation
% 0.17/0.45
% 0.17/0.45 % (11421)Memory used [KB]: 7036
% 0.17/0.45 % (11421)Time elapsed: 0.098 s
% 0.17/0.45 % (11421)Instructions burned: 183 (million)
% 0.17/0.45 % (11421)------------------------------
% 0.17/0.45 % (11421)------------------------------
% 0.17/0.45 % (11466)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on theBenchmark for (2998ds/19Mi)
% 0.17/0.45 % (11465)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on theBenchmark for (2998ds/779Mi)
% 0.17/0.45 % (11467)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on theBenchmark for (2998ds/879Mi)
% 0.17/0.45 % (11468)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2998ds/17Mi)
% 0.17/0.45 % (11466)Instruction limit reached!
% 0.17/0.45 % (11466)------------------------------
% 0.17/0.45 % (11466)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.45 % (11466)Termination reason: Unknown
% 0.17/0.45 % (11466)Termination phase: shuffling
% 0.17/0.45
% 0.17/0.45 % (11466)Memory used [KB]: 1663
% 0.17/0.45 % (11466)Time elapsed: 0.010 s
% 0.17/0.45 % (11466)Instructions burned: 19 (million)
% 0.17/0.45 % (11466)------------------------------
% 0.17/0.45 % (11466)------------------------------
% 0.17/0.46 % (11469)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi)
% 0.17/0.46 % (11469)Instruction limit reached!
% 0.17/0.46 % (11469)------------------------------
% 0.17/0.46 % (11469)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.46 % (11469)Termination reason: Unknown
% 0.17/0.46 % (11469)Termination phase: shuffling
% 0.17/0.46
% 0.17/0.46 % (11469)Memory used [KB]: 1279
% 0.17/0.46 % (11469)Time elapsed: 0.003 s
% 0.17/0.46 % (11469)Instructions burned: 4 (million)
% 0.17/0.46 % (11469)------------------------------
% 0.17/0.46 % (11469)------------------------------
% 0.17/0.46 % (11468)Instruction limit reached!
% 0.17/0.46 % (11468)------------------------------
% 0.17/0.46 % (11468)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.46 % (11468)Termination reason: Unknown
% 0.17/0.46 % (11468)Termination phase: shuffling
% 0.17/0.46
% 0.17/0.46 % (11468)Memory used [KB]: 1663
% 0.17/0.46 % (11468)Time elapsed: 0.012 s
% 0.17/0.46 % (11468)Instructions burned: 18 (million)
% 0.17/0.46 % (11468)------------------------------
% 0.17/0.46 % (11468)------------------------------
% 0.17/0.46 % (11470)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on theBenchmark for (2998ds/30Mi)
% 0.17/0.47 % (11471)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on theBenchmark for (2998ds/127Mi)
% 0.17/0.47 % (11467)Refutation not found, incomplete strategy
% 0.17/0.47 % (11467)------------------------------
% 0.17/0.47 % (11467)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.47 % (11467)Termination reason: Refutation not found, incomplete strategy
% 0.17/0.47
% 0.17/0.47
% 0.17/0.47 % (11467)Memory used [KB]: 6268
% 0.17/0.47 % (11467)Time elapsed: 0.025 s
% 0.17/0.47 % (11467)Instructions burned: 56 (million)
% 0.17/0.47 % (11467)------------------------------
% 0.17/0.47 % (11467)------------------------------
% 0.17/0.47 % (11470)Instruction limit reached!
% 0.17/0.47 % (11470)------------------------------
% 0.17/0.47 % (11470)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.47 % (11470)Termination reason: Unknown
% 0.17/0.47 % (11470)Termination phase: Property scanning
% 0.17/0.47
% 0.17/0.47 % (11470)Memory used [KB]: 1791
% 0.17/0.47 % (11470)Time elapsed: 0.010 s
% 0.17/0.47 % (11470)Instructions burned: 32 (million)
% 0.17/0.47 % (11470)------------------------------
% 0.17/0.47 % (11470)------------------------------
% 0.17/0.48 % (11472)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)
% 0.17/0.48 % (11473)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)
% 0.17/0.48 % (11473)Instruction limit reached!
% 0.17/0.48 % (11473)------------------------------
% 0.17/0.48 % (11473)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.48 % (11473)Termination reason: Unknown
% 0.17/0.48 % (11473)Termination phase: shuffling
% 0.17/0.48
% 0.17/0.48 % (11473)Memory used [KB]: 1279
% 0.17/0.48 % (11473)Time elapsed: 0.003 s
% 0.17/0.48 % (11473)Instructions burned: 3 (million)
% 0.17/0.48 % (11473)------------------------------
% 0.17/0.48 % (11473)------------------------------
% 0.17/0.49 % (11474)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)
% 0.17/0.49 % (11475)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on theBenchmark for (2998ds/86Mi)
% 0.17/0.50 % (11474)Instruction limit reached!
% 0.17/0.50 % (11474)------------------------------
% 0.17/0.50 % (11474)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.50 % (11474)Termination reason: Unknown
% 0.17/0.50 % (11474)Termination phase: Property scanning
% 0.17/0.50
% 0.17/0.50 % (11474)Memory used [KB]: 1663
% 0.17/0.50 % (11474)Time elapsed: 0.011 s
% 0.17/0.50 % (11474)Instructions burned: 20 (million)
% 0.17/0.50 % (11474)------------------------------
% 0.17/0.50 % (11474)------------------------------
% 0.17/0.50 % (11471)Instruction limit reached!
% 0.17/0.50 % (11471)------------------------------
% 0.17/0.50 % (11471)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.50 % (11471)Termination reason: Unknown
% 0.17/0.50 % (11471)Termination phase: Saturation
% 0.17/0.50
% 0.17/0.50 % (11471)Memory used [KB]: 6652
% 0.17/0.50 % (11471)Time elapsed: 0.035 s
% 0.17/0.50 % (11471)Instructions burned: 129 (million)
% 0.17/0.50 % (11471)------------------------------
% 0.17/0.50 % (11471)------------------------------
% 0.17/0.51 % (11472)Instruction limit reached!
% 0.17/0.51 % (11472)------------------------------
% 0.17/0.51 % (11472)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.51 % (11472)Termination reason: Unknown
% 0.17/0.51 % (11472)Termination phase: Saturation
% 0.17/0.51
% 0.17/0.51 % (11472)Memory used [KB]: 6524
% 0.17/0.51 % (11472)Time elapsed: 0.028 s
% 0.17/0.51 % (11472)Instructions burned: 101 (million)
% 0.17/0.51 % (11472)------------------------------
% 0.17/0.51 % (11472)------------------------------
% 0.17/0.51 % (11476)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on theBenchmark for (2998ds/107Mi)
% 0.17/0.51 % (11475)Instruction limit reached!
% 0.17/0.51 % (11475)------------------------------
% 0.17/0.51 % (11475)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.51 % (11475)Termination reason: Unknown
% 0.17/0.51 % (11475)Termination phase: Saturation
% 0.17/0.51
% 0.17/0.51 % (11475)Memory used [KB]: 6524
% 0.17/0.51 % (11477)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)
% 0.17/0.51 % (11475)Time elapsed: 0.022 s
% 0.17/0.51 % (11475)Instructions burned: 88 (million)
% 0.17/0.51 % (11475)------------------------------
% 0.17/0.51 % (11475)------------------------------
% 0.17/0.51 % (11478)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)
% 0.17/0.52 % (11479)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)
% 0.17/0.52 % (11477)Instruction limit reached!
% 0.17/0.52 % (11477)------------------------------
% 0.17/0.52 % (11477)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.52 % (11477)Termination reason: Unknown
% 0.17/0.52 % (11477)Termination phase: Property scanning
% 0.17/0.52
% 0.17/0.52 % (11477)Memory used [KB]: 1791
% 0.17/0.52 % (11477)Time elapsed: 0.012 s
% 0.17/0.52 % (11477)Instructions burned: 41 (million)
% 0.17/0.52 % (11477)------------------------------
% 0.17/0.52 % (11477)------------------------------
% 0.17/0.53 % (11480)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 (2998ds/98Mi)
% 0.17/0.53 % (11449)First to succeed.
% 0.17/0.53 % (11479)Instruction limit reached!
% 0.17/0.53 % (11479)------------------------------
% 0.17/0.53 % (11479)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.53 % (11479)Termination reason: Unknown
% 0.17/0.53 % (11479)Termination phase: SInE selection
% 0.17/0.53
% 0.17/0.53 % (11479)Memory used [KB]: 1791
% 0.17/0.53 % (11479)Time elapsed: 0.015 s
% 0.17/0.53 % (11479)Instructions burned: 46 (million)
% 0.17/0.53 % (11479)------------------------------
% 0.17/0.53 % (11479)------------------------------
% 0.17/0.54 % (11476)Instruction limit reached!
% 0.17/0.54 % (11476)------------------------------
% 0.17/0.54 % (11476)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.54 % (11476)Termination reason: Unknown
% 0.17/0.54 % (11476)Termination phase: Saturation
% 0.17/0.54
% 0.17/0.54 % (11476)Memory used [KB]: 6524
% 0.17/0.54 % (11476)Time elapsed: 0.029 s
% 0.17/0.54 % (11476)Instructions burned: 108 (million)
% 0.17/0.54 % (11476)------------------------------
% 0.17/0.54 % (11476)------------------------------
% 0.17/0.54 % (11481)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)
% 0.17/0.55 % (11482)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)
% 0.17/0.56 % (11480)Instruction limit reached!
% 0.17/0.56 % (11480)------------------------------
% 0.17/0.56 % (11480)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.56 % (11480)Termination reason: Unknown
% 0.17/0.56 % (11480)Termination phase: Saturation
% 0.17/0.56
% 0.17/0.56 % (11480)Memory used [KB]: 2046
% 0.17/0.56 % (11480)Time elapsed: 0.028 s
% 0.17/0.56 % (11480)Instructions burned: 99 (million)
% 0.17/0.56 % (11480)------------------------------
% 0.17/0.56 % (11480)------------------------------
% 1.80/0.57 % (11449)Refutation found. Thanks to Tanya!
% 1.80/0.57 % SZS status Theorem for theBenchmark
% 1.80/0.57 % SZS output start Proof for theBenchmark
% See solution above
% 1.80/0.57 % (11449)------------------------------
% 1.80/0.57 % (11449)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.80/0.57 % (11449)Termination reason: Refutation
% 1.80/0.57
% 1.80/0.57 % (11449)Memory used [KB]: 8187
% 1.80/0.57 % (11449)Time elapsed: 0.175 s
% 1.80/0.57 % (11449)Instructions burned: 427 (million)
% 1.80/0.57 % (11449)------------------------------
% 1.80/0.57 % (11449)------------------------------
% 1.80/0.57 % (11419)Success in time 0.236 s
% 1.80/0.57 % Vampire---4.8 exiting
%------------------------------------------------------------------------------