%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV152^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n020.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 : Wed Feb 25 09:40:24 AM UTC 2026
% Result : Theorem 1.81s 1.58s
% Output : Refutation 1.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 20
% Syntax : Number of formulae : 325 ( 23 unt; 0 typ; 19 def)
% Number of atoms : 3498 ( 315 equ; 0 cnn)
% Maximal formula atoms : 5 ( 10 avg)
% Number of connectives : 10153 ( 469 ~; 971 |; 660 &;5881 @)
% ( 19 <=>;1008 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 522 ( 522 >; 0 *; 0 +; 0 <<)
% Number of symbols : 49 ( 45 usr; 42 con; 0-2 aty)
% (1145 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 1350 (1189 ^; 161 !; 0 ?;1350 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_20,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
sK2: a ).
thf(func_def_22,type,
sK3: a > a > $o ).
thf(func_def_23,type,
sK4: a > a > $o ).
thf(func_def_24,type,
sK5: a ).
thf(func_def_25,type,
sK6: a > $o ).
thf(func_def_26,type,
sK7: a ).
thf(func_def_27,type,
sK8: a ).
thf(func_def_28,type,
sK9: a ).
thf(func_def_29,type,
sK10: a > $o ).
thf(func_def_30,type,
sK11: a ).
thf(func_def_31,type,
sK12: a ).
thf(func_def_32,type,
sK13: a > $o ).
thf(func_def_33,type,
sK14: a ).
thf(func_def_34,type,
sK15: a ).
thf(func_def_35,type,
sK16: a ).
thf(func_def_36,type,
sK17: a ).
thf(func_def_37,type,
sK18: a ).
thf(func_def_38,type,
sK19: a ).
thf(func_def_39,type,
sK20: a ).
thf(func_def_40,type,
sK21: a ).
thf(func_def_41,type,
sK22: a ).
thf(func_def_42,type,
sK23: a ).
thf(func_def_43,type,
sK24: a ).
thf(func_def_44,type,
sK25: a ).
thf(func_def_45,type,
sK26: a ).
thf(f2309,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f39,f49,f245,f348,f402,f448,f454,f686,f762,f1067,f1193,f1217,f1245,f1304,f1308,f1367,f1684,f1990,f2028,f2308]) ).
thf(f2308,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[status(thm)],[f2307]) ).
thf(f2307,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(trivial_inequality_removal,[status(thm)],[f2306]) ).
thf(f2306,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(forward_demodulation,[status(thm)],[f2298,f2221]) ).
thf(f2221,plain,
( ( $false
= ( sK13 @ sK26 ) )
| ~ spl0_10 ),
inference(binary_proxy_clausification,[status(thm)],[f2104]) ).
thf(f2104,plain,
( ( ( ( sK3 @ sK12 @ sK26 )
=> ( sK13 @ sK26 ) )
= $false )
| ~ spl0_10 ),
inference(beta_eta_normalization,[status(thm)],[f2099]) ).
thf(f2099,plain,
( ( ( ^ [Y0: a] :
( ( sK3 @ sK12 @ Y0 )
=> ( sK13 @ Y0 ) )
@ sK26 )
= $false )
| ~ spl0_10 ),
inference(sigma_clausification,[status(thm)],[f347]) ).
thf(f347,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK12 @ Y0 )
=> ( sK13 @ Y0 ) ) )
= $false )
| ~ spl0_10 ),
inference(avatar_component_clause,[status(thm)],[f346]) ).
thf(f346,definition,
( spl0_10
<=> ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK12 @ Y0 )
=> ( sK13 @ Y0 ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition]) ).
thf(f2298,plain,
( ( $true
= ( sK13 @ sK26 ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(boolean_simplification,[status(thm)],[f2297]) ).
thf(f2297,plain,
( ( $true
= ( $true
=> ( sK13 @ sK26 ) ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(boolean_simplification,[status(thm)],[f2292]) ).
thf(f2292,plain,
( ( $true
= ( ( ( sK4 @ sK12 @ sK26 )
| $true )
=> ( sK13 @ sK26 ) ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(superposition,[status(thm)],[f2281,f2222]) ).
thf(f2222,plain,
( ( $true
= ( sK3 @ sK12 @ sK26 ) )
| ~ spl0_10 ),
inference(binary_proxy_clausification,[status(thm)],[f2104]) ).
thf(f2281,plain,
( ! [X1: a] :
( $true
= ( ( ( sK4 @ sK12 @ X1 )
| ( sK3 @ sK12 @ X1 ) )
=> ( sK13 @ X1 ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(beta_eta_normalization,[status(thm)],[f2280]) ).
thf(f2280,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK4 @ sK12 @ Y0 )
| ( sK3 @ sK12 @ Y0 ) )
=> ( sK13 @ Y0 ) )
@ X1 ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(pi_clausification,[status(thm)],[f2067]) ).
thf(f2067,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK12 @ Y0 )
| ( sK3 @ sK12 @ Y0 ) )
=> ( sK13 @ Y0 ) ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(binary_proxy_clausification,[status(thm)],[f2035]) ).
thf(f2035,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK12 @ Y0 )
| ( sK3 @ sK12 @ Y0 ) )
=> ( sK13 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
& ( sK13 @ Y1 ) )
=> ( sK13 @ Y0 ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(binary_proxy_clausification,[status(thm)],[f2033]) ).
thf(f2033,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK12 @ Y0 )
| ( sK3 @ sK12 @ Y0 ) )
=> ( sK13 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
& ( sK13 @ Y1 ) )
=> ( sK13 @ Y0 ) ) ) ) )
=> ( sK13 @ sK11 ) )
= $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(beta_eta_normalization,[status(thm)],[f2032]) ).
thf(f2032,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK12 @ Y1 )
| ( sK3 @ sK12 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK11 ) )
@ sK13 )
= $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(sigma_clausification,[status(thm)],[f2031]) ).
thf(f2031,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK12 @ Y1 )
| ( sK3 @ sK12 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK11 ) ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(boolean_simplification,[status(thm)],[f2030]) ).
thf(f2030,plain,
( ( ( $true
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK12 @ Y1 )
| ( sK3 @ sK12 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK11 ) ) ) )
= $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(boolean_simplification,[status(thm)],[f2029]) ).
thf(f2029,plain,
( ( $false
= ( ( $true
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK11 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK12 @ Y1 )
| ( sK3 @ sK12 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK11 ) ) ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(backward_demodulation,[status(thm)],[f1393,f241]) ).
thf(f241,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) ) ) )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f240]) ).
thf(f240,definition,
( spl0_7
<=> ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f1393,plain,
( ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK11 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK12 @ Y1 )
| ( sK3 @ sK12 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK11 ) ) ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f1392]) ).
thf(f1392,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( sK3 @ Y2 @ Y3 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK11 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ sK11 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y0 @ Y2 )
| ( sK3 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK4 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ sK11 ) ) ) )
@ sK12 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f1382]) ).
thf(f1382,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( sK3 @ Y2 @ Y3 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK11 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ sK11 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y0 @ Y2 )
| ( sK3 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK4 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ sK11 ) ) ) ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f1381]) ).
thf(f1381,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK3 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y1 @ Y3 )
| ( sK3 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK4 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) )
@ sK11 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK3 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y1 @ Y3 )
| ( sK3 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK4 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f47]) ).
thf(f47,definition,
( spl0_4
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK3 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y1 @ Y3 )
| ( sK3 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK4 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f2028,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[status(thm)],[f2027]) ).
thf(f2027,plain,
( $false
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(trivial_inequality_removal,[status(thm)],[f2026]) ).
thf(f2026,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(boolean_simplification,[status(thm)],[f2025]) ).
thf(f2025,plain,
( ( $true = ( ~ $true ) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(boolean_simplification,[status(thm)],[f2024]) ).
thf(f2024,plain,
( ( $true
= ( ~ ( $true
| ( sK3 @ sK12 @ sK25 ) ) ) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[status(thm)],[f2019,f2010]) ).
thf(f2010,plain,
( ( $true
= ( sK4 @ sK12 @ sK25 ) )
| ~ spl0_12 ),
inference(binary_proxy_clausification,[status(thm)],[f1996]) ).
thf(f1996,plain,
( ( $false
= ( ( sK4 @ sK12 @ sK25 )
=> ( sK13 @ sK25 ) ) )
| ~ spl0_12 ),
inference(beta_eta_normalization,[status(thm)],[f1994]) ).
thf(f1994,plain,
( ( ( ^ [Y0: a] :
( ( sK4 @ sK12 @ Y0 )
=> ( sK13 @ Y0 ) )
@ sK25 )
= $false )
| ~ spl0_12 ),
inference(sigma_clausification,[status(thm)],[f401]) ).
thf(f401,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ sK12 @ Y0 )
=> ( sK13 @ Y0 ) ) )
= $false )
| ~ spl0_12 ),
inference(avatar_component_clause,[status(thm)],[f400]) ).
thf(f400,definition,
( spl0_12
<=> ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ sK12 @ Y0 )
=> ( sK13 @ Y0 ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition]) ).
thf(f2019,plain,
( ( $true
= ( ~ ( ( sK4 @ sK12 @ sK25 )
| ( sK3 @ sK12 @ sK25 ) ) ) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(boolean_simplification,[status(thm)],[f2015]) ).
thf(f2015,plain,
( ( $true
= ( ( ( sK4 @ sK12 @ sK25 )
| ( sK3 @ sK12 @ sK25 ) )
=> $false ) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(superposition,[status(thm)],[f1905,f2009]) ).
thf(f2009,plain,
( ( ( sK13 @ sK25 )
= $false )
| ~ spl0_12 ),
inference(binary_proxy_clausification,[status(thm)],[f1996]) ).
thf(f1905,plain,
( ! [X1: a] :
( $true
= ( ( ( sK4 @ sK12 @ X1 )
| ( sK3 @ sK12 @ X1 ) )
=> ( sK13 @ X1 ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(beta_eta_normalization,[status(thm)],[f1904]) ).
thf(f1904,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK4 @ sK12 @ Y0 )
| ( sK3 @ sK12 @ Y0 ) )
=> ( sK13 @ Y0 ) )
@ X1 ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(pi_clausification,[status(thm)],[f1746]) ).
thf(f1746,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK12 @ Y0 )
| ( sK3 @ sK12 @ Y0 ) )
=> ( sK13 @ Y0 ) ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(binary_proxy_clausification,[status(thm)],[f1705]) ).
thf(f1705,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK12 @ Y0 )
| ( sK3 @ sK12 @ Y0 ) )
=> ( sK13 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
& ( sK13 @ Y1 ) )
=> ( sK13 @ Y0 ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(binary_proxy_clausification,[status(thm)],[f1698]) ).
thf(f1698,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK12 @ Y0 )
| ( sK3 @ sK12 @ Y0 ) )
=> ( sK13 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
& ( sK13 @ Y1 ) )
=> ( sK13 @ Y0 ) ) ) ) )
=> ( sK13 @ sK11 ) )
= $false )
| ~ spl0_4
| ~ spl0_8 ),
inference(beta_eta_normalization,[status(thm)],[f1697]) ).
thf(f1697,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK12 @ Y1 )
| ( sK3 @ sK12 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK11 ) )
@ sK13 )
= $false )
| ~ spl0_4
| ~ spl0_8 ),
inference(sigma_clausification,[status(thm)],[f1687]) ).
thf(f1687,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK12 @ Y1 )
| ( sK3 @ sK12 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK11 ) ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f1686]) ).
thf(f1686,plain,
( ( ( $true
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK12 @ Y1 )
| ( sK3 @ sK12 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK11 ) ) ) )
= $false )
| ~ spl0_4
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f1685]) ).
thf(f1685,plain,
( ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) ) )
| $true )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK12 @ Y1 )
| ( sK3 @ sK12 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK11 ) ) ) )
= $false )
| ~ spl0_4
| ~ spl0_8 ),
inference(backward_demodulation,[status(thm)],[f1393,f244]) ).
thf(f244,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK11 ) ) ) )
| ~ spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f243]) ).
thf(f243,definition,
( spl0_8
<=> ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK11 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition]) ).
thf(f1990,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[status(thm)],[f1989]) ).
thf(f1989,plain,
( $false
| ~ spl0_4
| ~ spl0_8
| ~ spl0_11 ),
inference(trivial_inequality_removal,[status(thm)],[f1988]) ).
thf(f1988,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_11 ),
inference(forward_demodulation,[status(thm)],[f1987,f1955]) ).
thf(f1955,plain,
( ( $false
= ( sK13 @ sK24 ) )
| ~ spl0_11 ),
inference(boolean_simplification,[status(thm)],[f1954]) ).
thf(f1954,plain,
( ( ( $true
=> ( sK13 @ sK24 ) )
= $false )
| ~ spl0_11 ),
inference(backward_demodulation,[status(thm)],[f1943,f1953]) ).
thf(f1953,plain,
( ( $true
= ( ( sK13 @ sK23 )
& ( sK4 @ sK23 @ sK24 ) ) )
| ~ spl0_11 ),
inference(binary_proxy_clausification,[status(thm)],[f1943]) ).
thf(f1943,plain,
( ( $false
= ( ( ( sK13 @ sK23 )
& ( sK4 @ sK23 @ sK24 ) )
=> ( sK13 @ sK24 ) ) )
| ~ spl0_11 ),
inference(beta_eta_normalization,[status(thm)],[f1942]) ).
thf(f1942,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK13 @ sK23 )
& ( sK4 @ sK23 @ Y0 ) )
=> ( sK13 @ Y0 ) )
@ sK24 ) )
| ~ spl0_11 ),
inference(sigma_clausification,[status(thm)],[f1931]) ).
thf(f1931,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK13 @ sK23 )
& ( sK4 @ sK23 @ Y0 ) )
=> ( sK13 @ Y0 ) ) )
= $false )
| ~ spl0_11 ),
inference(beta_eta_normalization,[status(thm)],[f1927]) ).
thf(f1927,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 )
& ( sK4 @ Y0 @ Y1 ) )
=> ( sK13 @ Y1 ) ) )
@ sK23 )
= $false )
| ~ spl0_11 ),
inference(sigma_clausification,[status(thm)],[f398]) ).
thf(f398,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 )
& ( sK4 @ Y0 @ Y1 ) )
=> ( sK13 @ Y1 ) ) ) )
= $false )
| ~ spl0_11 ),
inference(avatar_component_clause,[status(thm)],[f397]) ).
thf(f397,definition,
( spl0_11
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 )
& ( sK4 @ Y0 @ Y1 ) )
=> ( sK13 @ Y1 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition]) ).
thf(f1987,plain,
( ( $true
= ( sK13 @ sK24 ) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_11 ),
inference(boolean_simplification,[status(thm)],[f1986]) ).
thf(f1986,plain,
( ( ( $true
=> ( sK13 @ sK24 ) )
= $true )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_11 ),
inference(forward_demodulation,[status(thm)],[f1983,f1968]) ).
thf(f1968,plain,
( ( $true
= ( sK13 @ sK23 ) )
| ~ spl0_11 ),
inference(boolean_simplification,[status(thm)],[f1967]) ).
thf(f1967,plain,
( ( $true
= ( ( sK13 @ sK23 )
& $true ) )
| ~ spl0_11 ),
inference(backward_demodulation,[status(thm)],[f1953,f1965]) ).
thf(f1965,plain,
( ( $true
= ( sK4 @ sK23 @ sK24 ) )
| ~ spl0_11 ),
inference(binary_proxy_clausification,[status(thm)],[f1953]) ).
thf(f1983,plain,
( ( $true
= ( ( sK13 @ sK23 )
=> ( sK13 @ sK24 ) ) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_11 ),
inference(boolean_simplification,[status(thm)],[f1982]) ).
thf(f1982,plain,
( ( $true
= ( ( $true
& ( sK13 @ sK23 ) )
=> ( sK13 @ sK24 ) ) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_11 ),
inference(boolean_simplification,[status(thm)],[f1980]) ).
thf(f1980,plain,
( ( $true
= ( ( ( $true
| ( sK3 @ sK23 @ sK24 ) )
& ( sK13 @ sK23 ) )
=> ( sK13 @ sK24 ) ) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_11 ),
inference(superposition,[status(thm)],[f1772,f1965]) ).
thf(f1772,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( ( ( sK4 @ X2 @ X1 )
| ( sK3 @ X2 @ X1 ) )
& ( sK13 @ X2 ) )
=> ( sK13 @ X1 ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(beta_eta_normalization,[status(thm)],[f1771]) ).
thf(f1771,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( ( sK4 @ Y0 @ X1 )
| ( sK3 @ Y0 @ X1 ) )
& ( sK13 @ Y0 ) )
=> ( sK13 @ X1 ) )
@ X2 ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(pi_clausification,[status(thm)],[f1761]) ).
thf(f1761,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( ( sK4 @ Y0 @ X1 )
| ( sK3 @ Y0 @ X1 ) )
& ( sK13 @ Y0 ) )
=> ( sK13 @ X1 ) ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(beta_eta_normalization,[status(thm)],[f1760]) ).
thf(f1760,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
& ( sK13 @ Y1 ) )
=> ( sK13 @ Y0 ) ) )
@ X1 ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(pi_clausification,[status(thm)],[f1748]) ).
thf(f1748,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
& ( sK13 @ Y1 ) )
=> ( sK13 @ Y0 ) ) ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f1747]) ).
thf(f1747,plain,
( ( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
& ( sK13 @ Y1 ) )
=> ( sK13 @ Y0 ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(backward_demodulation,[status(thm)],[f1705,f1746]) ).
thf(f1684,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f1683]) ).
thf(f1683,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(trivial_inequality_removal,[status(thm)],[f1682]) ).
thf(f1682,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[status(thm)],[f1681,f1555]) ).
thf(f1555,plain,
( ( ( sK13 @ sK22 )
= $false )
| ~ spl0_9 ),
inference(boolean_simplification,[status(thm)],[f1554]) ).
thf(f1554,plain,
( ( $false
= ( $true
=> ( sK13 @ sK22 ) ) )
| ~ spl0_9 ),
inference(backward_demodulation,[status(thm)],[f1542,f1553]) ).
thf(f1553,plain,
( ( $true
= ( ( sK13 @ sK21 )
& ( sK3 @ sK21 @ sK22 ) ) )
| ~ spl0_9 ),
inference(binary_proxy_clausification,[status(thm)],[f1542]) ).
thf(f1542,plain,
( ( $false
= ( ( ( sK13 @ sK21 )
& ( sK3 @ sK21 @ sK22 ) )
=> ( sK13 @ sK22 ) ) )
| ~ spl0_9 ),
inference(beta_eta_normalization,[status(thm)],[f1541]) ).
thf(f1541,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK13 @ sK21 )
& ( sK3 @ sK21 @ Y0 ) )
=> ( sK13 @ Y0 ) )
@ sK22 ) )
| ~ spl0_9 ),
inference(sigma_clausification,[status(thm)],[f1500]) ).
thf(f1500,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK13 @ sK21 )
& ( sK3 @ sK21 @ Y0 ) )
=> ( sK13 @ Y0 ) ) ) )
| ~ spl0_9 ),
inference(beta_eta_normalization,[status(thm)],[f1498]) ).
thf(f1498,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 )
& ( sK3 @ Y0 @ Y1 ) )
=> ( sK13 @ Y1 ) ) )
@ sK21 ) )
| ~ spl0_9 ),
inference(sigma_clausification,[status(thm)],[f344]) ).
thf(f344,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 )
& ( sK3 @ Y0 @ Y1 ) )
=> ( sK13 @ Y1 ) ) ) )
= $false )
| ~ spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f343]) ).
thf(f343,definition,
( spl0_9
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 )
& ( sK3 @ Y0 @ Y1 ) )
=> ( sK13 @ Y1 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition]) ).
thf(f1681,plain,
( ( $true
= ( sK13 @ sK22 ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(boolean_simplification,[status(thm)],[f1680]) ).
thf(f1680,plain,
( ( $true
= ( $true
=> ( sK13 @ sK22 ) ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[status(thm)],[f1677,f1665]) ).
thf(f1665,plain,
( ( $true
= ( sK13 @ sK21 ) )
| ~ spl0_9 ),
inference(binary_proxy_clausification,[status(thm)],[f1553]) ).
thf(f1677,plain,
( ( $true
= ( ( sK13 @ sK21 )
=> ( sK13 @ sK22 ) ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(boolean_simplification,[status(thm)],[f1676]) ).
thf(f1676,plain,
( ( $true
= ( ( $true
& ( sK13 @ sK21 ) )
=> ( sK13 @ sK22 ) ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(boolean_simplification,[status(thm)],[f1674]) ).
thf(f1674,plain,
( ( $true
= ( ( ( ( sK4 @ sK21 @ sK22 )
| $true )
& ( sK13 @ sK21 ) )
=> ( sK13 @ sK22 ) ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[status(thm)],[f1566,f1667]) ).
thf(f1667,plain,
( ( $true
= ( sK3 @ sK21 @ sK22 ) )
| ~ spl0_9 ),
inference(boolean_simplification,[status(thm)],[f1666]) ).
thf(f1666,plain,
( ( $true
= ( $true
& ( sK3 @ sK21 @ sK22 ) ) )
| ~ spl0_9 ),
inference(backward_demodulation,[status(thm)],[f1553,f1665]) ).
thf(f1566,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( ( ( sK4 @ X2 @ X1 )
| ( sK3 @ X2 @ X1 ) )
& ( sK13 @ X2 ) )
=> ( sK13 @ X1 ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(beta_eta_normalization,[status(thm)],[f1565]) ).
thf(f1565,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( ( sK4 @ Y0 @ X1 )
| ( sK3 @ Y0 @ X1 ) )
& ( sK13 @ Y0 ) )
=> ( sK13 @ X1 ) )
@ X2 ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(pi_clausification,[status(thm)],[f1559]) ).
thf(f1559,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( ( sK4 @ Y0 @ X1 )
| ( sK3 @ Y0 @ X1 ) )
& ( sK13 @ Y0 ) )
=> ( sK13 @ X1 ) ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(beta_eta_normalization,[status(thm)],[f1558]) ).
thf(f1558,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
& ( sK13 @ Y1 ) )
=> ( sK13 @ Y0 ) ) )
@ X1 ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(pi_clausification,[status(thm)],[f1447]) ).
thf(f1447,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
& ( sK13 @ Y1 ) )
=> ( sK13 @ Y0 ) ) ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(binary_proxy_clausification,[status(thm)],[f1420]) ).
thf(f1420,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK12 @ Y0 )
| ( sK3 @ sK12 @ Y0 ) )
=> ( sK13 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
& ( sK13 @ Y1 ) )
=> ( sK13 @ Y0 ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(binary_proxy_clausification,[status(thm)],[f1408]) ).
thf(f1408,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK12 @ Y0 )
| ( sK3 @ sK12 @ Y0 ) )
=> ( sK13 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
& ( sK13 @ Y1 ) )
=> ( sK13 @ Y0 ) ) ) ) )
=> ( sK13 @ sK11 ) )
= $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(beta_eta_normalization,[status(thm)],[f1407]) ).
thf(f1407,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK12 @ Y1 )
| ( sK3 @ sK12 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK11 ) )
@ sK13 )
= $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(sigma_clausification,[status(thm)],[f1396]) ).
thf(f1396,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK12 @ Y1 )
| ( sK3 @ sK12 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK11 ) ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(boolean_simplification,[status(thm)],[f1395]) ).
thf(f1395,plain,
( ( ( $true
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK12 @ Y1 )
| ( sK3 @ sK12 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK11 ) ) ) )
= $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(boolean_simplification,[status(thm)],[f1394]) ).
thf(f1394,plain,
( ( $false
= ( ( $true
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK11 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK12 @ Y1 )
| ( sK3 @ sK12 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK11 ) ) ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[status(thm)],[f1393,f241]) ).
thf(f1367,plain,
( ~ spl0_1
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[status(thm)],[f1366]) ).
thf(f1366,plain,
( $false
| ~ spl0_1
| ~ spl0_14 ),
inference(trivial_inequality_removal,[status(thm)],[f1365]) ).
thf(f1365,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_14 ),
inference(backward_demodulation,[status(thm)],[f1323,f1364]) ).
thf(f1364,plain,
( ( ( sK6 @ sK14 )
= $false )
| ~ spl0_1
| ~ spl0_14 ),
inference(boolean_simplification,[status(thm)],[f1363]) ).
thf(f1363,plain,
( ( ( $true
=> ( sK6 @ sK14 ) )
= $false )
| ~ spl0_1
| ~ spl0_14 ),
inference(boolean_simplification,[status(thm)],[f1362]) ).
thf(f1362,plain,
( ( ( ( $true
| ( sK3 @ sK2 @ sK14 ) )
=> ( sK6 @ sK14 ) )
= $false )
| ~ spl0_1
| ~ spl0_14 ),
inference(forward_demodulation,[status(thm)],[f1359,f447]) ).
thf(f447,plain,
( ( $true
= ( sK4 @ sK2 @ sK14 ) )
| ~ spl0_14 ),
inference(avatar_component_clause,[status(thm)],[f446]) ).
thf(f446,definition,
( spl0_14
<=> ( $true
= ( sK4 @ sK2 @ sK14 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_14])],[avatar_definition]) ).
thf(f1359,plain,
( ( ( ( ( sK4 @ sK2 @ sK14 )
| ( sK3 @ sK2 @ sK14 ) )
=> ( sK6 @ sK14 ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f1357]) ).
thf(f1357,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK4 @ sK2 @ Y0 )
| ( sK3 @ sK2 @ Y0 ) )
=> ( sK6 @ Y0 ) )
@ sK14 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f1349]) ).
thf(f1349,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK2 @ Y0 )
| ( sK3 @ sK2 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
= $false )
| ~ spl0_1 ),
inference(not_proxy_clausification,[status(thm)],[f1338]) ).
thf(f1338,plain,
( ( $true
= ( ~ ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK2 @ Y0 )
| ( sK3 @ sK2 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f1337]) ).
thf(f1337,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK2 @ Y0 )
| ( sK3 @ sK2 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
=> $false ) )
| ~ spl0_1 ),
inference(forward_demodulation,[status(thm)],[f1335,f26]) ).
thf(f26,plain,
( ( sK6 @ sK5 )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK2 @ Y0 )
| ( sK4 @ sK2 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) )
=> ( sK6 @ sK5 ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f24]) ).
thf(f24,plain,
( $false
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK2 @ Y1 )
| ( sK4 @ sK2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) )
@ sK6 ) ),
inference(sigma_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK2 @ Y1 )
| ( sK4 @ sK2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( $false
= ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK3 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y1 @ Y3 )
| ( sK3 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK4 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK3 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK4 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK3 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y1 @ Y4 )
| ( sK4 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y1 @ Y4 )
| ( sK4 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK4 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK2 @ Y1 )
| ( sK3 @ sK2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK5 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK2 @ Y1 )
| ( sK4 @ sK2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ^ [Y0: a] :
( ( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( sK3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y2 @ Y4 )
| ( sK3 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK4 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( sK3 @ Y6 @ Y5 )
| ( sK4 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y1 @ Y5 )
| ( sK4 @ Y1 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( sK3 @ Y6 @ Y5 )
| ( sK4 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y2 @ Y5 )
| ( sK4 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y2 @ Y5 )
| ( sK4 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( ( sK4 @ Y5 @ Y6 )
| ( sK3 @ Y5 @ Y6 ) ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ sK2 @ Y2 )
| ( sK3 @ sK2 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK3 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK3 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ sK2 @ Y2 )
| ( sK4 @ sK2 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
@ sK5 )
= $false ),
inference(sigma_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( !! @ a
@ ^ [Y0: a] :
( ( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( sK3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( sK4 @ Y4 @ Y5 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK4 @ Y2 @ Y4 )
| ( sK3 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK4 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( sK3 @ Y6 @ Y5 )
| ( sK4 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y1 @ Y5 )
| ( sK4 @ Y1 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( sK3 @ Y6 @ Y5 )
| ( sK4 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y2 @ Y5 )
| ( sK4 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y2 @ Y5 )
| ( sK4 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( ( sK4 @ Y5 @ Y6 )
| ( sK3 @ Y5 @ Y6 ) ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ sK2 @ Y2 )
| ( sK3 @ sK2 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK3 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK3 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ sK2 @ Y2 )
| ( sK4 @ sK2 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
( $false
= ( ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( sK3 @ Y5 @ Y6 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y3 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y3 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y3 @ Y5 )
| ( sK3 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( Y0 @ Y6 @ Y5 )
| ( sK3 @ Y6 @ Y5 ) )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y7 )
& ( ( sK3 @ Y7 @ Y6 )
| ( Y0 @ Y7 @ Y6 ) ) )
=> ( Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y2 @ Y6 )
| ( Y0 @ Y2 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y7 )
& ( ( sK3 @ Y7 @ Y6 )
| ( Y0 @ Y7 @ Y6 ) ) )
=> ( Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y3 @ Y6 )
| ( Y0 @ Y3 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y3 @ Y6 )
| ( Y0 @ Y3 @ Y6 ) )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y6 )
& ( ( Y0 @ Y6 @ Y7 )
| ( sK3 @ Y6 @ Y7 ) ) )
=> ( Y5 @ Y7 ) ) ) ) )
=> ( Y5 @ Y4 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ sK2 @ Y3 )
| ( sK3 @ sK2 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK3 @ Y4 @ Y3 )
| ( Y0 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK3 @ Y4 @ Y3 )
| ( Y0 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ sK2 @ Y3 )
| ( Y0 @ sK2 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
@ sK4 ) ),
inference(sigma_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( sK3 @ Y5 @ Y6 ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y3 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y3 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y3 @ Y5 )
| ( sK3 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( Y0 @ Y6 @ Y5 )
| ( sK3 @ Y6 @ Y5 ) )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y7 )
& ( ( sK3 @ Y7 @ Y6 )
| ( Y0 @ Y7 @ Y6 ) ) )
=> ( Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y2 @ Y6 )
| ( Y0 @ Y2 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y7 )
& ( ( sK3 @ Y7 @ Y6 )
| ( Y0 @ Y7 @ Y6 ) ) )
=> ( Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y3 @ Y6 )
| ( Y0 @ Y3 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y3 @ Y6 )
| ( Y0 @ Y3 @ Y6 ) )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y6 )
& ( ( Y0 @ Y6 @ Y7 )
| ( sK3 @ Y6 @ Y7 ) ) )
=> ( Y5 @ Y7 ) ) ) ) )
=> ( Y5 @ Y4 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ sK2 @ Y3 )
| ( sK3 @ sK2 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK3 @ Y4 @ Y3 )
| ( Y0 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK3 @ Y4 @ Y3 )
| ( Y0 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ sK2 @ Y3 )
| ( Y0 @ sK2 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
( $false
= ( ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y6 )
& ( Y0 @ Y6 @ Y7 ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y4 @ Y6 )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y3 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y4 @ Y6 )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y6 )
& ( Y1 @ Y6 @ Y7 ) )
=> ( Y5 @ Y7 ) ) ) ) )
=> ( Y5 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( ( Y1 @ Y4 @ Y6 )
| ( Y0 @ Y4 @ Y6 ) )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( ( Y1 @ Y7 @ Y6 )
| ( Y0 @ Y7 @ Y6 ) )
& ( Y5 @ Y7 ) )
=> ( Y5 @ Y6 ) ) ) ) )
=> ( Y5 @ Y3 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y8 )
& ( ( Y0 @ Y8 @ Y7 )
| ( Y1 @ Y8 @ Y7 ) ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y3 @ Y7 )
| ( Y1 @ Y3 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y8 )
& ( ( Y0 @ Y8 @ Y7 )
| ( Y1 @ Y8 @ Y7 ) ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y4 @ Y7 )
| ( Y1 @ Y4 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y4 @ Y7 )
| ( Y1 @ Y4 @ Y7 ) )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y7 )
& ( ( Y1 @ Y7 @ Y8 )
| ( Y0 @ Y7 @ Y8 ) ) )
=> ( Y6 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ sK2 @ Y4 )
| ( Y0 @ sK2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( Y0 @ Y5 @ Y4 )
| ( Y1 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( Y0 @ Y5 @ Y4 )
| ( Y1 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ sK2 @ Y4 )
| ( Y1 @ sK2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) )
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y6 )
& ( Y0 @ Y6 @ Y7 ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y4 @ Y6 )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y3 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y4 @ Y6 )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y6 )
& ( Y1 @ Y6 @ Y7 ) )
=> ( Y5 @ Y7 ) ) ) ) )
=> ( Y5 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( ( Y1 @ Y4 @ Y6 )
| ( Y0 @ Y4 @ Y6 ) )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( ( Y1 @ Y7 @ Y6 )
| ( Y0 @ Y7 @ Y6 ) )
& ( Y5 @ Y7 ) )
=> ( Y5 @ Y6 ) ) ) ) )
=> ( Y5 @ Y3 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y8 )
& ( ( Y0 @ Y8 @ Y7 )
| ( Y1 @ Y8 @ Y7 ) ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y3 @ Y7 )
| ( Y1 @ Y3 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y8 )
& ( ( Y0 @ Y8 @ Y7 )
| ( Y1 @ Y8 @ Y7 ) ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y4 @ Y7 )
| ( Y1 @ Y4 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y4 @ Y7 )
| ( Y1 @ Y4 @ Y7 ) )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y7 )
& ( ( Y1 @ Y7 @ Y8 )
| ( Y0 @ Y7 @ Y8 ) ) )
=> ( Y6 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ sK2 @ Y4 )
| ( Y0 @ sK2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( Y0 @ Y5 @ Y4 )
| ( Y1 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( Y0 @ Y5 @ Y4 )
| ( Y1 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ sK2 @ Y4 )
| ( Y1 @ sK2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
( $false
= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y7 )
& ( Y1 @ Y7 @ Y8 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y5 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y4 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y5 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y7 )
& ( Y2 @ Y7 @ Y8 ) )
=> ( Y6 @ Y8 ) ) ) ) )
=> ( Y6 @ Y4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( ( Y2 @ Y5 @ Y7 )
| ( Y1 @ Y5 @ Y7 ) )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( ( Y2 @ Y8 @ Y7 )
| ( Y1 @ Y8 @ Y7 ) )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y9 )
& ( ( Y1 @ Y9 @ Y8 )
| ( Y2 @ Y9 @ Y8 ) ) )
=> ( Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y4 @ Y8 )
| ( Y2 @ Y4 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y9 )
& ( ( Y1 @ Y9 @ Y8 )
| ( Y2 @ Y9 @ Y8 ) ) )
=> ( Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y5 @ Y8 )
| ( Y2 @ Y5 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y5 @ Y8 )
| ( Y2 @ Y5 @ Y8 ) )
=> ( Y7 @ Y8 ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y8 )
& ( ( Y2 @ Y8 @ Y9 )
| ( Y1 @ Y8 @ Y9 ) ) )
=> ( Y7 @ Y9 ) ) ) ) )
=> ( Y7 @ Y6 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y0 @ Y5 )
| ( Y1 @ Y0 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y1 @ Y6 @ Y5 )
| ( Y2 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y1 @ Y6 @ Y5 )
| ( Y2 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y0 @ Y5 )
| ( Y2 @ Y0 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y7 )
& ( Y1 @ Y7 @ Y8 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y5 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y4 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y5 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y7 )
& ( Y2 @ Y7 @ Y8 ) )
=> ( Y6 @ Y8 ) ) ) ) )
=> ( Y6 @ Y4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( ( Y2 @ Y5 @ Y7 )
| ( Y1 @ Y5 @ Y7 ) )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( ( Y2 @ Y8 @ Y7 )
| ( Y1 @ Y8 @ Y7 ) )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y9 )
& ( ( Y1 @ Y9 @ Y8 )
| ( Y2 @ Y9 @ Y8 ) ) )
=> ( Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y4 @ Y8 )
| ( Y2 @ Y4 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y9 )
& ( ( Y1 @ Y9 @ Y8 )
| ( Y2 @ Y9 @ Y8 ) ) )
=> ( Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y5 @ Y8 )
| ( Y2 @ Y5 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y5 @ Y8 )
| ( Y2 @ Y5 @ Y8 ) )
=> ( Y7 @ Y8 ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y8 )
& ( ( Y2 @ Y8 @ Y9 )
| ( Y1 @ Y8 @ Y9 ) ) )
=> ( Y7 @ Y9 ) ) ) ) )
=> ( Y7 @ Y6 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y0 @ Y5 )
| ( Y1 @ Y0 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y1 @ Y6 @ Y5 )
| ( Y2 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y1 @ Y6 @ Y5 )
| ( Y2 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y0 @ Y5 )
| ( Y2 @ Y0 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y7 )
& ( Y1 @ Y7 @ Y8 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y5 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y4 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y5 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y7 )
& ( Y2 @ Y7 @ Y8 ) )
=> ( Y6 @ Y8 ) ) ) ) )
=> ( Y6 @ Y4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( ( Y2 @ Y5 @ Y7 )
| ( Y1 @ Y5 @ Y7 ) )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( ( Y2 @ Y8 @ Y7 )
| ( Y1 @ Y8 @ Y7 ) )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y9 )
& ( ( Y1 @ Y9 @ Y8 )
| ( Y2 @ Y9 @ Y8 ) ) )
=> ( Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y4 @ Y8 )
| ( Y2 @ Y4 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y9 )
& ( ( Y1 @ Y9 @ Y8 )
| ( Y2 @ Y9 @ Y8 ) ) )
=> ( Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y5 @ Y8 )
| ( Y2 @ Y5 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y5 @ Y8 )
| ( Y2 @ Y5 @ Y8 ) )
=> ( Y7 @ Y8 ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y8 )
& ( ( Y2 @ Y8 @ Y9 )
| ( Y1 @ Y8 @ Y9 ) ) )
=> ( Y7 @ Y9 ) ) ) ) )
=> ( Y7 @ Y6 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y0 @ Y5 )
| ( Y1 @ Y0 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y1 @ Y6 @ Y5 )
| ( Y2 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y1 @ Y6 @ Y5 )
| ( Y2 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y0 @ Y5 )
| ( Y2 @ Y0 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y7 )
& ( Y1 @ Y7 @ Y8 ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y5 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y4 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y5 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y7 )
& ( Y2 @ Y7 @ Y8 ) )
=> ( Y6 @ Y8 ) ) ) ) )
=> ( Y6 @ Y4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( ( Y2 @ Y5 @ Y7 )
| ( Y1 @ Y5 @ Y7 ) )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( ( Y2 @ Y8 @ Y7 )
| ( Y1 @ Y8 @ Y7 ) )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y9 )
& ( ( Y1 @ Y9 @ Y8 )
| ( Y2 @ Y9 @ Y8 ) ) )
=> ( Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y4 @ Y8 )
| ( Y2 @ Y4 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y6 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y9 )
& ( ( Y1 @ Y9 @ Y8 )
| ( Y2 @ Y9 @ Y8 ) ) )
=> ( Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y5 @ Y8 )
| ( Y2 @ Y5 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y5 @ Y8 )
| ( Y2 @ Y5 @ Y8 ) )
=> ( Y7 @ Y8 ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y8 )
& ( ( Y2 @ Y8 @ Y9 )
| ( Y1 @ Y8 @ Y9 ) ) )
=> ( Y7 @ Y9 ) ) ) ) )
=> ( Y7 @ Y6 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y0 @ Y5 )
| ( Y1 @ Y0 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y1 @ Y6 @ Y5 )
| ( Y2 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y1 @ Y6 @ Y5 )
| ( Y2 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y0 @ Y5 )
| ( Y2 @ Y0 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a,X1: a > a > $o,X2: a > a > $o,X3: a] :
( ( ( ! [X4: a,X5: a,X6: a] :
( ( ! [X7: a > $o] :
( ( ! [X8: a] :
( ( ( X1 @ X5 @ X8 )
| ( X2 @ X5 @ X8 ) )
=> ( X7 @ X8 ) )
& ! [X9: a,X10: a] :
( ( ( ( X1 @ X9 @ X10 )
| ( X2 @ X9 @ X10 ) )
& ( X7 @ X9 ) )
=> ( X7 @ X10 ) ) )
=> ( X7 @ X6 ) )
& ! [X11: a > $o] :
( ( ! [X12: a] :
( ( ( X1 @ X6 @ X12 )
| ( X2 @ X6 @ X12 ) )
=> ( X11 @ X12 ) )
& ! [X13: a,X14: a] :
( ( ( ( X1 @ X13 @ X14 )
| ( X2 @ X13 @ X14 ) )
& ( X11 @ X13 ) )
=> ( X11 @ X14 ) ) )
=> ( X11 @ X4 ) ) )
=> ! [X15: a > $o] :
( ( ! [X16: a,X17: a] :
( ( ( ( X2 @ X17 @ X16 )
| ( X1 @ X17 @ X16 ) )
& ( X15 @ X17 ) )
=> ( X15 @ X16 ) )
& ! [X18: a] :
( ( ( X1 @ X5 @ X18 )
| ( X2 @ X5 @ X18 ) )
=> ( X15 @ X18 ) ) )
=> ( X15 @ X4 ) ) )
& ! [X19: a,X20: a] :
( ( ! [X21: a > $o] :
( ( ! [X22: a,X23: a] :
( ( ( X1 @ X23 @ X22 )
& ( X21 @ X23 ) )
=> ( X21 @ X22 ) )
& ! [X24: a] :
( ( X1 @ X19 @ X24 )
=> ( X21 @ X24 ) ) )
=> ( X21 @ X20 ) )
| ! [X25: a > $o] :
( ( ! [X26: a] :
( ( X2 @ X19 @ X26 )
=> ( X25 @ X26 ) )
& ! [X27: a,X28: a] :
( ( ( X2 @ X28 @ X27 )
& ( X25 @ X28 ) )
=> ( X25 @ X27 ) ) )
=> ( X25 @ X20 ) ) )
=> ! [X29: a > $o] :
( ( ! [X30: a,X31: a] :
( ( ( X29 @ X30 )
& ( ( X2 @ X30 @ X31 )
| ( X1 @ X30 @ X31 ) ) )
=> ( X29 @ X31 ) )
& ! [X32: a] :
( ( ( X2 @ X19 @ X32 )
| ( X1 @ X19 @ X32 ) )
=> ( X29 @ X32 ) ) )
=> ( X29 @ X20 ) ) ) )
=> ! [X33: a > $o] :
( ( ! [X34: a,X35: a] :
( ( ( ( X1 @ X34 @ X35 )
| ( X2 @ X34 @ X35 ) )
& ( X33 @ X34 ) )
=> ( X33 @ X35 ) )
& ! [X36: a] :
( ( ( X2 @ X3 @ X36 )
| ( X1 @ X3 @ X36 ) )
=> ( X33 @ X36 ) ) )
=> ( X33 @ X0 ) ) )
=> ! [X37: a > $o] :
( ( ! [X38: a] :
( ( ( X1 @ X3 @ X38 )
| ( X2 @ X3 @ X38 ) )
=> ( X37 @ X38 ) )
& ! [X39: a,X40: a] :
( ( ( ( X1 @ X39 @ X40 )
| ( X2 @ X39 @ X40 ) )
& ( X37 @ X39 ) )
=> ( X37 @ X40 ) ) )
=> ( X37 @ X0 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X3: a,X1: a > a > $o,X0: a > a > $o,X2: a] :
( ( ( ! [X10: a,X4: a,X5: a] :
( ( ! [X6: a > $o] :
( ( ! [X7: a] :
( ( ( X1 @ X4 @ X7 )
| ( X0 @ X4 @ X7 ) )
=> ( X6 @ X7 ) )
& ! [X8: a,X9: a] :
( ( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
& ( X6 @ X8 ) )
=> ( X6 @ X9 ) ) )
=> ( X6 @ X5 ) )
& ! [X6: a > $o] :
( ( ! [X7: a] :
( ( ( X1 @ X5 @ X7 )
| ( X0 @ X5 @ X7 ) )
=> ( X6 @ X7 ) )
& ! [X8: a,X9: a] :
( ( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
& ( X6 @ X8 ) )
=> ( X6 @ X9 ) ) )
=> ( X6 @ X10 ) ) )
=> ! [X6: a > $o] :
( ( ! [X9: a,X8: a] :
( ( ( ( X0 @ X8 @ X9 )
| ( X1 @ X8 @ X9 ) )
& ( X6 @ X8 ) )
=> ( X6 @ X9 ) )
& ! [X7: a] :
( ( ( X1 @ X4 @ X7 )
| ( X0 @ X4 @ X7 ) )
=> ( X6 @ X7 ) ) )
=> ( X6 @ X10 ) ) )
& ! [X4: a,X5: a] :
( ( ! [X6: a > $o] :
( ( ! [X9: a,X8: a] :
( ( ( X1 @ X8 @ X9 )
& ( X6 @ X8 ) )
=> ( X6 @ X9 ) )
& ! [X7: a] :
( ( X1 @ X4 @ X7 )
=> ( X6 @ X7 ) ) )
=> ( X6 @ X5 ) )
| ! [X6: a > $o] :
( ( ! [X7: a] :
( ( X0 @ X4 @ X7 )
=> ( X6 @ X7 ) )
& ! [X9: a,X8: a] :
( ( ( X0 @ X8 @ X9 )
& ( X6 @ X8 ) )
=> ( X6 @ X9 ) ) )
=> ( X6 @ X5 ) ) )
=> ! [X6: a > $o] :
( ( ! [X8: a,X9: a] :
( ( ( X6 @ X8 )
& ( ( X0 @ X8 @ X9 )
| ( X1 @ X8 @ X9 ) ) )
=> ( X6 @ X9 ) )
& ! [X7: a] :
( ( ( X0 @ X4 @ X7 )
| ( X1 @ X4 @ X7 ) )
=> ( X6 @ X7 ) ) )
=> ( X6 @ X5 ) ) ) )
=> ! [X6: a > $o] :
( ( ! [X8: a,X9: a] :
( ( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
& ( X6 @ X8 ) )
=> ( X6 @ X9 ) )
& ! [X7: a] :
( ( ( X0 @ X2 @ X7 )
| ( X1 @ X2 @ X7 ) )
=> ( X6 @ X7 ) ) )
=> ( X6 @ X3 ) ) )
=> ! [X6: a > $o] :
( ( ! [X7: a] :
( ( ( X1 @ X2 @ X7 )
| ( X0 @ X2 @ X7 ) )
=> ( X6 @ X7 ) )
& ! [X8: a,X9: a] :
( ( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
& ( X6 @ X8 ) )
=> ( X6 @ X9 ) ) )
=> ( X6 @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X3: a,X1: a > a > $o,X0: a > a > $o,X2: a] :
( ( ( ! [X10: a,X4: a,X5: a] :
( ( ! [X6: a > $o] :
( ( ! [X7: a] :
( ( ( X1 @ X4 @ X7 )
| ( X0 @ X4 @ X7 ) )
=> ( X6 @ X7 ) )
& ! [X8: a,X9: a] :
( ( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
& ( X6 @ X8 ) )
=> ( X6 @ X9 ) ) )
=> ( X6 @ X5 ) )
& ! [X6: a > $o] :
( ( ! [X7: a] :
( ( ( X1 @ X5 @ X7 )
| ( X0 @ X5 @ X7 ) )
=> ( X6 @ X7 ) )
& ! [X8: a,X9: a] :
( ( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
& ( X6 @ X8 ) )
=> ( X6 @ X9 ) ) )
=> ( X6 @ X10 ) ) )
=> ! [X6: a > $o] :
( ( ! [X9: a,X8: a] :
( ( ( ( X0 @ X8 @ X9 )
| ( X1 @ X8 @ X9 ) )
& ( X6 @ X8 ) )
=> ( X6 @ X9 ) )
& ! [X7: a] :
( ( ( X1 @ X4 @ X7 )
| ( X0 @ X4 @ X7 ) )
=> ( X6 @ X7 ) ) )
=> ( X6 @ X10 ) ) )
& ! [X4: a,X5: a] :
( ( ! [X6: a > $o] :
( ( ! [X9: a,X8: a] :
( ( ( X1 @ X8 @ X9 )
& ( X6 @ X8 ) )
=> ( X6 @ X9 ) )
& ! [X7: a] :
( ( X1 @ X4 @ X7 )
=> ( X6 @ X7 ) ) )
=> ( X6 @ X5 ) )
| ! [X6: a > $o] :
( ( ! [X7: a] :
( ( X0 @ X4 @ X7 )
=> ( X6 @ X7 ) )
& ! [X9: a,X8: a] :
( ( ( X0 @ X8 @ X9 )
& ( X6 @ X8 ) )
=> ( X6 @ X9 ) ) )
=> ( X6 @ X5 ) ) )
=> ! [X6: a > $o] :
( ( ! [X8: a,X9: a] :
( ( ( X6 @ X8 )
& ( ( X0 @ X8 @ X9 )
| ( X1 @ X8 @ X9 ) ) )
=> ( X6 @ X9 ) )
& ! [X7: a] :
( ( ( X0 @ X4 @ X7 )
| ( X1 @ X4 @ X7 ) )
=> ( X6 @ X7 ) ) )
=> ( X6 @ X5 ) ) ) )
=> ! [X6: a > $o] :
( ( ! [X8: a,X9: a] :
( ( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
& ( X6 @ X8 ) )
=> ( X6 @ X9 ) )
& ! [X7: a] :
( ( ( X0 @ X2 @ X7 )
| ( X1 @ X2 @ X7 ) )
=> ( X6 @ X7 ) ) )
=> ( X6 @ X3 ) ) )
=> ! [X6: a > $o] :
( ( ! [X7: a] :
( ( ( X1 @ X2 @ X7 )
| ( X0 @ X2 @ X7 ) )
=> ( X6 @ X7 ) )
& ! [X8: a,X9: a] :
( ( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
& ( X6 @ X8 ) )
=> ( X6 @ X9 ) ) )
=> ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.4pWI2wlH3y/DTF2THF_9846.p',cTHM251D_pme) ).
thf(f1335,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK2 @ Y0 )
| ( sK3 @ sK2 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
=> ( sK6 @ sK5 ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f1332]) ).
thf(f1332,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK2 @ Y0 )
| ( sK3 @ sK2 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
& $true )
=> ( sK6 @ sK5 ) ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f1316,f53]) ).
thf(f53,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK2 @ Y0 )
| ( sK4 @ sK2 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f1316,plain,
( ! [X1: a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK2 @ Y0 )
| ( sK3 @ sK2 @ Y0 ) )
=> ( X1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( X1 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( X1 @ Y0 ) ) ) ) )
=> ( X1 @ sK5 ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f1315]) ).
thf(f1315,plain,
( ! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK2 @ Y1 )
| ( sK3 @ sK2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK5 ) )
@ X1 ) )
| ~ spl0_1 ),
inference(pi_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK2 @ Y1 )
| ( sK3 @ sK2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK5 ) ) ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f34]) ).
thf(f34,definition,
( spl0_1
<=> ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK2 @ Y1 )
| ( sK3 @ sK2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK5 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f1323,plain,
( ( $true
= ( sK6 @ sK14 ) )
| ~ spl0_14 ),
inference(boolean_simplification,[status(thm)],[f1322]) ).
thf(f1322,plain,
( ( $true
= ( $true
=> ( sK6 @ sK14 ) ) )
| ~ spl0_14 ),
inference(boolean_simplification,[status(thm)],[f1318]) ).
thf(f1318,plain,
( ( $true
= ( ( ( sK3 @ sK2 @ sK14 )
| $true )
=> ( sK6 @ sK14 ) ) )
| ~ spl0_14 ),
inference(superposition,[status(thm)],[f59,f447]) ).
thf(f59,plain,
! [X1: a] :
( ( ( ( sK3 @ sK2 @ X1 )
| ( sK4 @ sK2 @ X1 ) )
=> ( sK6 @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f58]) ).
thf(f58,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK3 @ sK2 @ Y0 )
| ( sK4 @ sK2 @ Y0 ) )
=> ( sK6 @ Y0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK2 @ Y0 )
| ( sK4 @ sK2 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f54]) ).
thf(f54,plain,
( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK2 @ Y0 )
| ( sK4 @ sK2 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f27,f53]) ).
thf(f1308,plain,
( spl0_31
| ~ spl0_3
| ~ spl0_17
| ~ spl0_20 ),
inference(avatar_split_clause,[status(thm)],[f1307,f760,f681,f44,f1249]) ).
thf(f1249,definition,
( spl0_31
<=> ( $false
= ( sK10 @ sK7 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_31])],[avatar_definition]) ).
thf(f44,definition,
( spl0_3
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK3 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK4 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK3 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y1 @ Y4 )
| ( sK4 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y1 @ Y4 )
| ( sK4 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK4 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f681,definition,
( spl0_17
<=> ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK7 @ Y0 )
| ( sK4 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_17])],[avatar_definition]) ).
thf(f760,definition,
( spl0_20
<=> ( $true
= ( sK3 @ sK7 @ sK15 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_20])],[avatar_definition]) ).
thf(f1307,plain,
( ( $false
= ( sK10 @ sK7 ) )
| ~ spl0_3
| ~ spl0_17
| ~ spl0_20 ),
inference(trivial_inequality_removal,[status(thm)],[f1306]) ).
thf(f1306,plain,
( ( $false
= ( sK10 @ sK7 ) )
| ( $true = $false )
| ~ spl0_3
| ~ spl0_17
| ~ spl0_20 ),
inference(forward_demodulation,[status(thm)],[f1279,f737]) ).
thf(f737,plain,
( ( ( sK10 @ sK15 )
= $false )
| ~ spl0_17 ),
inference(boolean_simplification,[status(thm)],[f736]) ).
thf(f736,plain,
( ( $false
= ( $true
=> ( sK10 @ sK15 ) ) )
| ~ spl0_17 ),
inference(backward_demodulation,[status(thm)],[f711,f735]) ).
thf(f735,plain,
( ( $true
= ( ( sK3 @ sK7 @ sK15 )
| ( sK4 @ sK7 @ sK15 ) ) )
| ~ spl0_17 ),
inference(binary_proxy_clausification,[status(thm)],[f711]) ).
thf(f711,plain,
( ( ( ( ( sK3 @ sK7 @ sK15 )
| ( sK4 @ sK7 @ sK15 ) )
=> ( sK10 @ sK15 ) )
= $false )
| ~ spl0_17 ),
inference(beta_eta_normalization,[status(thm)],[f709]) ).
thf(f709,plain,
( ( ( ^ [Y0: a] :
( ( ( sK3 @ sK7 @ Y0 )
| ( sK4 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) )
@ sK15 )
= $false )
| ~ spl0_17 ),
inference(sigma_clausification,[status(thm)],[f682]) ).
thf(f682,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK7 @ Y0 )
| ( sK4 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) ) )
= $false )
| ~ spl0_17 ),
inference(avatar_component_clause,[status(thm)],[f681]) ).
thf(f1279,plain,
( ( $false
= ( sK10 @ sK7 ) )
| ( $true
= ( sK10 @ sK15 ) )
| ~ spl0_3
| ~ spl0_20 ),
inference(boolean_simplification,[status(thm)],[f1278]) ).
thf(f1278,plain,
( ( $true
= ( sK10 @ sK15 ) )
| ( ( ( sK10 @ sK7 )
& $true )
= $false )
| ~ spl0_3
| ~ spl0_20 ),
inference(boolean_simplification,[status(thm)],[f1271]) ).
thf(f1271,plain,
( ( $false
= ( ( sK10 @ sK7 )
& ( ( sK4 @ sK7 @ sK15 )
| $true ) ) )
| ( $true
= ( sK10 @ sK15 ) )
| ~ spl0_3
| ~ spl0_20 ),
inference(superposition,[status(thm)],[f561,f761]) ).
thf(f761,plain,
( ( $true
= ( sK3 @ sK7 @ sK15 ) )
| ~ spl0_20 ),
inference(avatar_component_clause,[status(thm)],[f760]) ).
thf(f561,plain,
( ! [X2: a,X1: a] :
( ( ( ( sK10 @ X1 )
& ( ( sK4 @ X1 @ X2 )
| ( sK3 @ X1 @ X2 ) ) )
= $false )
| ( ( sK10 @ X2 )
= $true ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f550]) ).
thf(f550,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( ( sK10 @ X1 )
& ( ( sK4 @ X1 @ X2 )
| ( sK3 @ X1 @ X2 ) ) )
=> ( sK10 @ X2 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f549]) ).
thf(f549,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK10 @ X1 )
& ( ( sK4 @ X1 @ Y0 )
| ( sK3 @ X1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) )
@ X2 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f539]) ).
thf(f539,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK10 @ X1 )
& ( ( sK4 @ X1 @ Y0 )
| ( sK3 @ X1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f538]) ).
thf(f538,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK4 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) )
@ X1 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f527]) ).
thf(f527,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK4 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f526]) ).
thf(f526,plain,
( ( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK4 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) ) ) )
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f519,f525]) ).
thf(f525,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK8 @ Y0 )
| ( sK4 @ sK8 @ Y0 ) )
=> ( sK10 @ Y0 ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f519]) ).
thf(f519,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK8 @ Y0 )
| ( sK4 @ sK8 @ Y0 ) )
=> ( sK10 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK4 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f507]) ).
thf(f507,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK8 @ Y0 )
| ( sK4 @ sK8 @ Y0 ) )
=> ( sK10 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK4 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) ) )
=> ( sK10 @ sK9 ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f506]) ).
thf(f506,plain,
( ( $false
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK8 @ Y1 )
| ( sK4 @ sK8 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK4 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK9 ) )
@ sK10 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f496]) ).
thf(f496,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK8 @ Y1 )
| ( sK4 @ sK8 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK4 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK9 ) ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f495]) ).
thf(f495,plain,
( ( $false
= ( $true
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK8 @ Y1 )
| ( sK4 @ sK8 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK4 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK9 ) ) ) ) )
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f484,f494]) ).
thf(f494,plain,
( ( $true
= ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK7 @ Y1 )
| ( sK4 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK8 @ Y1 )
| ( sK4 @ sK8 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK7 ) ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f484]) ).
thf(f484,plain,
( ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK7 @ Y1 )
| ( sK4 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK8 @ Y1 )
| ( sK4 @ sK8 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK7 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK8 @ Y1 )
| ( sK4 @ sK8 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK4 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK9 ) ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f483]) ).
thf(f483,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK3 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ sK7 @ Y2 )
| ( sK4 @ sK7 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK3 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ sK8 @ Y2 )
| ( sK4 @ sK8 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK7 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ sK8 @ Y2 )
| ( sK4 @ sK8 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK4 @ Y2 @ Y3 )
| ( sK3 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
@ sK9 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f471]) ).
thf(f471,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK3 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ sK7 @ Y2 )
| ( sK4 @ sK7 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK3 @ Y3 @ Y2 )
| ( sK4 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ sK8 @ Y2 )
| ( sK4 @ sK8 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK7 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ sK8 @ Y2 )
| ( sK4 @ sK8 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK4 @ Y2 @ Y3 )
| ( sK3 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f470]) ).
thf(f470,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK3 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ sK7 @ Y3 )
| ( sK4 @ sK7 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK3 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y0 @ Y3 )
| ( sK4 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ sK7 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y0 @ Y3 )
| ( sK4 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK4 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
@ sK8 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f461]) ).
thf(f461,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK3 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ sK7 @ Y3 )
| ( sK4 @ sK7 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK3 @ Y4 @ Y3 )
| ( sK4 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y0 @ Y3 )
| ( sK4 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ sK7 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y0 @ Y3 )
| ( sK4 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK4 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f460]) ).
thf(f460,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK3 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK4 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK3 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y1 @ Y4 )
| ( sK4 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y1 @ Y4 )
| ( sK4 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK4 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) )
@ sK7 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK3 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK4 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK3 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y1 @ Y4 )
| ( sK4 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y1 @ Y4 )
| ( sK4 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK4 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) )
= $false )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f44]) ).
thf(f1304,plain,
( spl0_18
| ~ spl0_3
| ~ spl0_31 ),
inference(avatar_split_clause,[status(thm)],[f1303,f1249,f44,f684]) ).
thf(f684,definition,
( spl0_18
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_18])],[avatar_definition]) ).
thf(f1303,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) ) ) )
= $false )
| ~ spl0_3
| ~ spl0_31 ),
inference(not_proxy_clausification,[status(thm)],[f1259]) ).
thf(f1259,plain,
( ( $true
= ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_31 ),
inference(boolean_simplification,[status(thm)],[f1257]) ).
thf(f1257,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) ) ) )
=> $false ) )
| ~ spl0_3
| ~ spl0_31 ),
inference(backward_demodulation,[status(thm)],[f769,f1250]) ).
thf(f1250,plain,
( ( $false
= ( sK10 @ sK7 ) )
| ~ spl0_31 ),
inference(avatar_component_clause,[status(thm)],[f1249]) ).
thf(f769,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) ) ) )
=> ( sK10 @ sK7 ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f767]) ).
thf(f767,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) ) ) )
& $true )
=> ( sK10 @ sK7 ) ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f748,f525]) ).
thf(f748,plain,
( ! [X1: a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( X1 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( X1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK8 @ Y0 )
| ( sK4 @ sK8 @ Y0 ) )
=> ( X1 @ Y0 ) ) ) )
=> ( X1 @ sK7 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f747]) ).
thf(f747,plain,
( ! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK8 @ Y1 )
| ( sK4 @ sK8 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK7 ) )
@ X1 ) )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f610]) ).
thf(f610,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK8 @ Y1 )
| ( sK4 @ sK8 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK7 ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f494]) ).
thf(f1245,plain,
( ~ spl0_3
| ~ spl0_18
| ~ spl0_29 ),
inference(avatar_contradiction_clause,[status(thm)],[f1244]) ).
thf(f1244,plain,
( $false
| ~ spl0_3
| ~ spl0_18
| ~ spl0_29 ),
inference(trivial_inequality_removal,[status(thm)],[f1243]) ).
thf(f1243,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_18
| ~ spl0_29 ),
inference(backward_demodulation,[status(thm)],[f1169,f1242]) ).
thf(f1242,plain,
( ( ( sK10 @ sK20 )
= $false )
| ~ spl0_3
| ~ spl0_18
| ~ spl0_29 ),
inference(trivial_inequality_removal,[status(thm)],[f1241]) ).
thf(f1241,plain,
( ( ( sK10 @ sK20 )
= $false )
| ( $true = $false )
| ~ spl0_3
| ~ spl0_18
| ~ spl0_29 ),
inference(forward_demodulation,[status(thm)],[f1238,f1119]) ).
thf(f1119,plain,
( ( $false
= ( sK10 @ sK18 ) )
| ~ spl0_18 ),
inference(boolean_simplification,[status(thm)],[f1118]) ).
thf(f1118,plain,
( ( $false
= ( $true
=> ( sK10 @ sK18 ) ) )
| ~ spl0_18 ),
inference(backward_demodulation,[status(thm)],[f1102,f1117]) ).
thf(f1117,plain,
( ( $true
= ( ( sK10 @ sK19 )
& ( ( sK3 @ sK19 @ sK18 )
| ( sK4 @ sK19 @ sK18 ) ) ) )
| ~ spl0_18 ),
inference(binary_proxy_clausification,[status(thm)],[f1102]) ).
thf(f1102,plain,
( ( ( ( ( sK10 @ sK19 )
& ( ( sK3 @ sK19 @ sK18 )
| ( sK4 @ sK19 @ sK18 ) ) )
=> ( sK10 @ sK18 ) )
= $false )
| ~ spl0_18 ),
inference(beta_eta_normalization,[status(thm)],[f1101]) ).
thf(f1101,plain,
( ( ( ^ [Y0: a] :
( ( ( sK10 @ Y0 )
& ( ( sK3 @ Y0 @ sK18 )
| ( sK4 @ Y0 @ sK18 ) ) )
=> ( sK10 @ sK18 ) )
@ sK19 )
= $false )
| ~ spl0_18 ),
inference(sigma_clausification,[status(thm)],[f1084]) ).
thf(f1084,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK10 @ Y0 )
& ( ( sK3 @ Y0 @ sK18 )
| ( sK4 @ Y0 @ sK18 ) ) )
=> ( sK10 @ sK18 ) ) ) )
| ~ spl0_18 ),
inference(beta_eta_normalization,[status(thm)],[f1079]) ).
thf(f1079,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) ) )
@ sK18 )
= $false )
| ~ spl0_18 ),
inference(sigma_clausification,[status(thm)],[f685]) ).
thf(f685,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) ) ) )
= $false )
| ~ spl0_18 ),
inference(avatar_component_clause,[status(thm)],[f684]) ).
thf(f1238,plain,
( ( ( sK10 @ sK20 )
= $false )
| ( $true
= ( sK10 @ sK18 ) )
| ~ spl0_3
| ~ spl0_29 ),
inference(boolean_simplification,[status(thm)],[f1237]) ).
thf(f1237,plain,
( ( ( ( sK10 @ sK20 )
& $true )
= $false )
| ( $true
= ( sK10 @ sK18 ) )
| ~ spl0_3
| ~ spl0_29 ),
inference(boolean_simplification,[status(thm)],[f1232]) ).
thf(f1232,plain,
( ( $true
= ( sK10 @ sK18 ) )
| ( ( ( sK10 @ sK20 )
& ( ( sK4 @ sK20 @ sK18 )
| $true ) )
= $false )
| ~ spl0_3
| ~ spl0_29 ),
inference(superposition,[status(thm)],[f561,f1189]) ).
thf(f1189,plain,
( ( $true
= ( sK3 @ sK20 @ sK18 ) )
| ~ spl0_29 ),
inference(avatar_component_clause,[status(thm)],[f1188]) ).
thf(f1188,definition,
( spl0_29
<=> ( $true
= ( sK3 @ sK20 @ sK18 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_29])],[avatar_definition]) ).
thf(f1169,plain,
( ( $true
= ( sK10 @ sK20 ) )
| ~ spl0_18 ),
inference(binary_proxy_clausification,[status(thm)],[f1153]) ).
thf(f1153,plain,
( ( $true
= ( ( sK10 @ sK20 )
& ( ( sK3 @ sK20 @ sK18 )
| ( sK4 @ sK20 @ sK18 ) ) ) )
| ~ spl0_18 ),
inference(not_proxy_clausification,[status(thm)],[f1136]) ).
thf(f1136,plain,
( ( $false
= ( ~ ( ( sK10 @ sK20 )
& ( ( sK3 @ sK20 @ sK18 )
| ( sK4 @ sK20 @ sK18 ) ) ) ) )
| ~ spl0_18 ),
inference(beta_eta_normalization,[status(thm)],[f1135]) ).
thf(f1135,plain,
( ( $false
= ( ^ [Y0: a] :
~ ( ( sK10 @ Y0 )
& ( ( sK3 @ Y0 @ sK18 )
| ( sK4 @ Y0 @ sK18 ) ) )
@ sK20 ) )
| ~ spl0_18 ),
inference(sigma_clausification,[status(thm)],[f1121]) ).
thf(f1121,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
~ ( ( sK10 @ Y0 )
& ( ( sK3 @ Y0 @ sK18 )
| ( sK4 @ Y0 @ sK18 ) ) ) ) )
| ~ spl0_18 ),
inference(boolean_simplification,[status(thm)],[f1120]) ).
thf(f1120,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK10 @ Y0 )
& ( ( sK3 @ Y0 @ sK18 )
| ( sK4 @ Y0 @ sK18 ) ) )
=> $false ) )
= $false )
| ~ spl0_18 ),
inference(backward_demodulation,[status(thm)],[f1084,f1119]) ).
thf(f1217,plain,
( ~ spl0_3
| ~ spl0_18
| ~ spl0_30 ),
inference(avatar_contradiction_clause,[status(thm)],[f1216]) ).
thf(f1216,plain,
( $false
| ~ spl0_3
| ~ spl0_18
| ~ spl0_30 ),
inference(trivial_inequality_removal,[status(thm)],[f1215]) ).
thf(f1215,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_18
| ~ spl0_30 ),
inference(backward_demodulation,[status(thm)],[f1169,f1214]) ).
thf(f1214,plain,
( ( ( sK10 @ sK20 )
= $false )
| ~ spl0_3
| ~ spl0_18
| ~ spl0_30 ),
inference(trivial_inequality_removal,[status(thm)],[f1213]) ).
thf(f1213,plain,
( ( ( sK10 @ sK20 )
= $false )
| ( $true = $false )
| ~ spl0_3
| ~ spl0_18
| ~ spl0_30 ),
inference(forward_demodulation,[status(thm)],[f1205,f1119]) ).
thf(f1205,plain,
( ( $true
= ( sK10 @ sK18 ) )
| ( ( sK10 @ sK20 )
= $false )
| ~ spl0_3
| ~ spl0_30 ),
inference(boolean_simplification,[status(thm)],[f1204]) ).
thf(f1204,plain,
( ( $true
= ( sK10 @ sK18 ) )
| ( ( ( sK10 @ sK20 )
& $true )
= $false )
| ~ spl0_3
| ~ spl0_30 ),
inference(boolean_simplification,[status(thm)],[f1199]) ).
thf(f1199,plain,
( ( ( ( sK10 @ sK20 )
& ( $true
| ( sK3 @ sK20 @ sK18 ) ) )
= $false )
| ( $true
= ( sK10 @ sK18 ) )
| ~ spl0_3
| ~ spl0_30 ),
inference(superposition,[status(thm)],[f561,f1192]) ).
thf(f1192,plain,
( ( $true
= ( sK4 @ sK20 @ sK18 ) )
| ~ spl0_30 ),
inference(avatar_component_clause,[status(thm)],[f1191]) ).
thf(f1191,definition,
( spl0_30
<=> ( $true
= ( sK4 @ sK20 @ sK18 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_30])],[avatar_definition]) ).
thf(f1193,plain,
( spl0_29
| spl0_30
| ~ spl0_18 ),
inference(avatar_split_clause,[status(thm)],[f1184,f684,f1191,f1188]) ).
thf(f1184,plain,
( ( $true
= ( sK3 @ sK20 @ sK18 ) )
| ( $true
= ( sK4 @ sK20 @ sK18 ) )
| ~ spl0_18 ),
inference(binary_proxy_clausification,[status(thm)],[f1171]) ).
thf(f1171,plain,
( ( $true
= ( ( sK3 @ sK20 @ sK18 )
| ( sK4 @ sK20 @ sK18 ) ) )
| ~ spl0_18 ),
inference(boolean_simplification,[status(thm)],[f1170]) ).
thf(f1170,plain,
( ( $true
= ( $true
& ( ( sK3 @ sK20 @ sK18 )
| ( sK4 @ sK20 @ sK18 ) ) ) )
| ~ spl0_18 ),
inference(backward_demodulation,[status(thm)],[f1153,f1169]) ).
thf(f1067,plain,
( spl0_18
| ~ spl0_3
| ~ spl0_17
| ~ spl0_19 ),
inference(avatar_split_clause,[status(thm)],[f1066,f757,f681,f44,f684]) ).
thf(f757,definition,
( spl0_19
<=> ( $true
= ( sK4 @ sK7 @ sK15 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_19])],[avatar_definition]) ).
thf(f1066,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) ) ) )
= $false )
| ~ spl0_3
| ~ spl0_17
| ~ spl0_19 ),
inference(not_proxy_clausification,[status(thm)],[f800]) ).
thf(f800,plain,
( ( $true
= ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) ) ) ) ) )
| ~ spl0_3
| ~ spl0_17
| ~ spl0_19 ),
inference(boolean_simplification,[status(thm)],[f799]) ).
thf(f799,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) ) ) )
=> $false ) )
| ~ spl0_3
| ~ spl0_17
| ~ spl0_19 ),
inference(backward_demodulation,[status(thm)],[f769,f797]) ).
thf(f797,plain,
( ( $false
= ( sK10 @ sK7 ) )
| ~ spl0_3
| ~ spl0_17
| ~ spl0_19 ),
inference(not_proxy_clausification,[status(thm)],[f794]) ).
thf(f794,plain,
( ( $true
= ( ~ ( sK10 @ sK7 ) ) )
| ~ spl0_3
| ~ spl0_17
| ~ spl0_19 ),
inference(boolean_simplification,[status(thm)],[f793]) ).
thf(f793,plain,
( ( $true
= ( ( sK10 @ sK7 )
=> $false ) )
| ~ spl0_3
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_demodulation,[status(thm)],[f792,f737]) ).
thf(f792,plain,
( ( $true
= ( ( sK10 @ sK7 )
=> ( sK10 @ sK15 ) ) )
| ~ spl0_3
| ~ spl0_19 ),
inference(boolean_simplification,[status(thm)],[f791]) ).
thf(f791,plain,
( ( $true
= ( ( ( sK10 @ sK7 )
& $true )
=> ( sK10 @ sK15 ) ) )
| ~ spl0_3
| ~ spl0_19 ),
inference(boolean_simplification,[status(thm)],[f785]) ).
thf(f785,plain,
( ( $true
= ( ( ( sK10 @ sK7 )
& ( $true
| ( sK3 @ sK7 @ sK15 ) ) )
=> ( sK10 @ sK15 ) ) )
| ~ spl0_3
| ~ spl0_19 ),
inference(superposition,[status(thm)],[f550,f758]) ).
thf(f758,plain,
( ( $true
= ( sK4 @ sK7 @ sK15 ) )
| ~ spl0_19 ),
inference(avatar_component_clause,[status(thm)],[f757]) ).
thf(f762,plain,
( spl0_19
| spl0_20
| ~ spl0_17 ),
inference(avatar_split_clause,[status(thm)],[f749,f681,f760,f757]) ).
thf(f749,plain,
( ( $true
= ( sK4 @ sK7 @ sK15 ) )
| ( $true
= ( sK3 @ sK7 @ sK15 ) )
| ~ spl0_17 ),
inference(binary_proxy_clausification,[status(thm)],[f735]) ).
thf(f686,plain,
( spl0_17
| spl0_18
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f677,f44,f684,f681]) ).
thf(f677,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK7 @ Y0 )
| ( sK4 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) ) ) )
= $false )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f665]) ).
thf(f665,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK7 @ Y0 )
| ( sK4 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) ) ) )
= $false )
| ~ spl0_3 ),
inference(not_proxy_clausification,[status(thm)],[f644]) ).
thf(f644,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK7 @ Y0 )
| ( sK4 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f642]) ).
thf(f642,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK7 @ Y0 )
| ( sK4 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) ) ) )
=> $false ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f623,f518]) ).
thf(f518,plain,
( ( $false
= ( sK10 @ sK9 ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f507]) ).
thf(f623,plain,
( ! [X1: a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( X1 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( X1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK7 @ Y0 )
| ( sK4 @ sK7 @ Y0 ) )
=> ( X1 @ Y0 ) ) ) )
=> ( X1 @ sK9 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f622]) ).
thf(f622,plain,
( ! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK7 @ Y1 )
| ( sK4 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) )
@ X1 ) )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f613]) ).
thf(f613,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK7 @ Y1 )
| ( sK4 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f612]) ).
thf(f612,plain,
( ( $true
= ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK7 @ Y1 )
| ( sK4 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) )
& $true ) )
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f494,f610]) ).
thf(f454,plain,
( ~ spl0_1
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[status(thm)],[f453]) ).
thf(f453,plain,
( $false
| ~ spl0_1
| ~ spl0_13 ),
inference(trivial_inequality_removal,[status(thm)],[f452]) ).
thf(f452,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_13 ),
inference(boolean_simplification,[status(thm)],[f451]) ).
thf(f451,plain,
( ( $true = ( ~ $true ) )
| ~ spl0_1
| ~ spl0_13 ),
inference(boolean_simplification,[status(thm)],[f449]) ).
thf(f449,plain,
( ( $true
= ( ~ ( $true
| ( sK4 @ sK2 @ sK14 ) ) ) )
| ~ spl0_1
| ~ spl0_13 ),
inference(backward_demodulation,[status(thm)],[f437,f444]) ).
thf(f444,plain,
( ( $true
= ( sK3 @ sK2 @ sK14 ) )
| ~ spl0_13 ),
inference(avatar_component_clause,[status(thm)],[f443]) ).
thf(f443,definition,
( spl0_13
<=> ( $true
= ( sK3 @ sK2 @ sK14 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition]) ).
thf(f437,plain,
( ( $true
= ( ~ ( ( sK3 @ sK2 @ sK14 )
| ( sK4 @ sK2 @ sK14 ) ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f435]) ).
thf(f435,plain,
( ( $true
= ( ( ( sK3 @ sK2 @ sK14 )
| ( sK4 @ sK2 @ sK14 ) )
=> $false ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f59,f431]) ).
thf(f431,plain,
( ( ( sK6 @ sK14 )
= $false )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f430]) ).
thf(f430,plain,
( ( ( $true
=> ( sK6 @ sK14 ) )
= $false )
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f425,f429]) ).
thf(f429,plain,
( ( $true
= ( ( sK4 @ sK2 @ sK14 )
| ( sK3 @ sK2 @ sK14 ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f425]) ).
thf(f425,plain,
( ( ( ( ( sK4 @ sK2 @ sK14 )
| ( sK3 @ sK2 @ sK14 ) )
=> ( sK6 @ sK14 ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f423]) ).
thf(f423,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK4 @ sK2 @ Y0 )
| ( sK3 @ sK2 @ Y0 ) )
=> ( sK6 @ Y0 ) )
@ sK14 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f420]) ).
thf(f420,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK2 @ Y0 )
| ( sK3 @ sK2 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
= $false )
| ~ spl0_1 ),
inference(not_proxy_clausification,[status(thm)],[f417]) ).
thf(f417,plain,
( ( $true
= ( ~ ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK2 @ Y0 )
| ( sK3 @ sK2 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f416]) ).
thf(f416,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK2 @ Y0 )
| ( sK3 @ sK2 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
=> $false ) )
| ~ spl0_1 ),
inference(forward_demodulation,[status(thm)],[f414,f26]) ).
thf(f414,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK2 @ Y0 )
| ( sK3 @ sK2 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
=> ( sK6 @ sK5 ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f411]) ).
thf(f411,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK2 @ Y0 )
| ( sK3 @ sK2 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
& $true )
=> ( sK6 @ sK5 ) ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f406,f53]) ).
thf(f406,plain,
( ! [X1: a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK2 @ Y0 )
| ( sK3 @ sK2 @ Y0 ) )
=> ( X1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( X1 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK4 @ Y1 @ Y0 ) ) )
=> ( X1 @ Y0 ) ) ) ) )
=> ( X1 @ sK5 ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f405]) ).
thf(f405,plain,
( ! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK2 @ Y1 )
| ( sK3 @ sK2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK5 ) )
@ X1 ) )
| ~ spl0_1 ),
inference(pi_clausification,[status(thm)],[f35]) ).
thf(f448,plain,
( spl0_13
| spl0_14
| ~ spl0_1 ),
inference(avatar_split_clause,[status(thm)],[f441,f34,f446,f443]) ).
thf(f441,plain,
( ( $true
= ( sK4 @ sK2 @ sK14 ) )
| ( $true
= ( sK3 @ sK2 @ sK14 ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f429]) ).
thf(f402,plain,
( spl0_11
| spl0_12
| ~ spl0_4
| ~ spl0_8 ),
inference(avatar_split_clause,[status(thm)],[f393,f243,f47,f400,f397]) ).
thf(f393,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ sK12 @ Y0 )
=> ( sK13 @ Y0 ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 )
& ( sK4 @ Y0 @ Y1 ) )
=> ( sK13 @ Y1 ) ) ) )
= $false )
| ~ spl0_4
| ~ spl0_8 ),
inference(binary_proxy_clausification,[status(thm)],[f387]) ).
thf(f387,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ sK12 @ Y0 )
=> ( sK13 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 )
& ( sK4 @ Y0 @ Y1 ) )
=> ( sK13 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_4
| ~ spl0_8 ),
inference(not_proxy_clausification,[status(thm)],[f384]) ).
thf(f384,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ sK12 @ Y0 )
=> ( sK13 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 )
& ( sK4 @ Y0 @ Y1 ) )
=> ( sK13 @ Y1 ) ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f380]) ).
thf(f380,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ sK12 @ Y0 )
=> ( sK13 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 )
& ( sK4 @ Y0 @ Y1 ) )
=> ( sK13 @ Y1 ) ) ) ) )
=> $false ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f378,f233]) ).
thf(f233,plain,
( ( ( sK13 @ sK11 )
= $false )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f232]) ).
thf(f232,plain,
( ( $false
= ( $true
=> ( sK13 @ sK11 ) ) )
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f229,f231]) ).
thf(f231,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK12 @ Y0 )
| ( sK3 @ sK12 @ Y0 ) )
=> ( sK13 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
& ( sK13 @ Y1 ) )
=> ( sK13 @ Y0 ) ) ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f229]) ).
thf(f229,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ sK12 @ Y0 )
| ( sK3 @ sK12 @ Y0 ) )
=> ( sK13 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK4 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
& ( sK13 @ Y1 ) )
=> ( sK13 @ Y0 ) ) ) ) )
=> ( sK13 @ sK11 ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f228]) ).
thf(f228,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK12 @ Y1 )
| ( sK3 @ sK12 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK11 ) )
@ sK13 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f222]) ).
thf(f222,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK12 @ Y1 )
| ( sK3 @ sK12 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK11 ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f221]) ).
thf(f221,plain,
( ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK11 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK12 @ Y1 )
| ( sK3 @ sK12 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK4 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK11 ) ) ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f220]) ).
thf(f220,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( sK3 @ Y2 @ Y3 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK11 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ sK11 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y0 @ Y2 )
| ( sK3 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK4 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ sK11 ) ) ) )
@ sK12 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f219]) ).
thf(f219,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( sK3 @ Y2 @ Y3 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK11 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( sK4 @ Y2 @ Y3 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ sK11 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y0 @ Y2 )
| ( sK3 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK4 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ sK11 ) ) ) ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f218]) ).
thf(f218,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK3 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y1 @ Y3 )
| ( sK3 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK4 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) )
@ sK11 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f48]) ).
thf(f378,plain,
( ! [X1: a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ sK12 @ Y0 )
=> ( X1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( X1 @ Y0 )
& ( sK4 @ Y0 @ Y1 ) )
=> ( X1 @ Y1 ) ) ) ) )
=> ( X1 @ sK11 ) ) )
| ~ spl0_8 ),
inference(beta_eta_normalization,[status(thm)],[f377]) ).
thf(f377,plain,
( ! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK11 ) )
@ X1 ) )
| ~ spl0_8 ),
inference(pi_clausification,[status(thm)],[f244]) ).
thf(f348,plain,
( spl0_9
| spl0_10
| ~ spl0_4
| ~ spl0_7 ),
inference(avatar_split_clause,[status(thm)],[f339,f240,f47,f346,f343]) ).
thf(f339,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 )
& ( sK3 @ Y0 @ Y1 ) )
=> ( sK13 @ Y1 ) ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK12 @ Y0 )
=> ( sK13 @ Y0 ) ) )
= $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(binary_proxy_clausification,[status(thm)],[f320]) ).
thf(f320,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 )
& ( sK3 @ Y0 @ Y1 ) )
=> ( sK13 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK12 @ Y0 )
=> ( sK13 @ Y0 ) ) ) )
= $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(not_proxy_clausification,[status(thm)],[f257]) ).
thf(f257,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 )
& ( sK3 @ Y0 @ Y1 ) )
=> ( sK13 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK12 @ Y0 )
=> ( sK13 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_4
| ~ spl0_7 ),
inference(boolean_simplification,[status(thm)],[f256]) ).
thf(f256,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK13 @ Y0 )
& ( sK3 @ Y0 @ Y1 ) )
=> ( sK13 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK12 @ Y0 )
=> ( sK13 @ Y0 ) ) ) )
=> $false ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[status(thm)],[f251,f233]) ).
thf(f251,plain,
( ! [X1: a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( X1 @ Y0 )
& ( sK3 @ Y0 @ Y1 ) )
=> ( X1 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK12 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
=> ( X1 @ sK11 ) ) )
| ~ spl0_7 ),
inference(beta_eta_normalization,[status(thm)],[f250]) ).
thf(f250,plain,
( ! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) )
@ X1 ) )
| ~ spl0_7 ),
inference(pi_clausification,[status(thm)],[f241]) ).
thf(f245,plain,
( spl0_7
| spl0_8
| ~ spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f238,f47,f243,f240]) ).
thf(f238,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK11 ) ) ) )
| ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f223]) ).
thf(f223,plain,
( ( $true
= ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK11 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK4 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK11 ) ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f221]) ).
thf(f49,plain,
( spl0_3
| spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f42,f37,f47,f44]) ).
thf(f37,definition,
( spl0_2
<=> ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK3 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y1 @ Y3 )
| ( sK3 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK4 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK3 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK4 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK3 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y1 @ Y4 )
| ( sK4 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y1 @ Y4 )
| ( sK4 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK4 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f42,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK3 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y1 @ Y3 )
| ( sK3 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK4 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK3 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK4 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK3 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y1 @ Y4 )
| ( sK4 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y1 @ Y4 )
| ( sK4 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK4 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK3 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y1 @ Y3 )
| ( sK3 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK4 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK3 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK4 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK3 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y1 @ Y4 )
| ( sK4 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y1 @ Y4 )
| ( sK4 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK4 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f37]) ).
thf(f39,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f32,f37,f34]) ).
thf(f32,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK2 @ Y1 )
| ( sK3 @ sK2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK5 ) ) ) )
| ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK3 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y1 @ Y3 )
| ( sK3 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK4 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK3 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK4 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK3 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y1 @ Y4 )
| ( sK4 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y1 @ Y4 )
| ( sK4 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK4 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK3 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK4 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y1 @ Y3 )
| ( sK3 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK4 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK3 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK4 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK3 @ Y5 @ Y4 )
| ( sK4 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y1 @ Y4 )
| ( sK4 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y1 @ Y4 )
| ( sK4 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK4 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ sK2 @ Y1 )
| ( sK3 @ sK2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK4 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV152^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n020.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:41:12 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.21/0.47 ---- Original DTF file ---
% 0.21/0.47 thf(spec,logic,$$dhol).
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 % File : SEV152^5 : TPTP v9.2.1. Released v4.0.0.
% 0.21/0.47 % Domain : Set Theory (Relations)
% 0.21/0.47 % Problem : TPS problem from TRANSITIVE-CLOSURE
% 0.21/0.47 % Version : Especial.
% 0.21/0.47 % English :
% 0.21/0.47
% 0.21/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.21/0.47 % Source : [Bro09]
% 0.21/0.47 % Names : tps_1219 [Bro09]
% 0.21/0.47
% 0.21/0.47 % Status : Theorem
% 0.21/0.47 % Rating : 0.33 v9.1.0, 0.38 v9.0.0, 0.42 v8.2.0, 0.27 v8.1.0, 0.42 v7.5.0, 0.58 v7.4.0, 0.44 v7.3.0, 0.50 v7.1.0, 0.57 v7.0.0, 0.62 v6.4.0, 0.71 v6.3.0, 0.83 v6.1.0, 0.67 v6.0.0, 0.50 v5.5.0, 0.40 v5.4.0, 0.75 v5.3.0, 0.50 v5.2.0, 0.75 v4.1.0, 1.00 v4.0.0
% 0.21/0.47 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.21/0.47 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.21/0.47 % Maximal formula atoms : 0 ( 0 avg)
% 0.21/0.47 % Number of connectives : 147 ( 0 ~; 13 |; 18 &; 88 @)
% 0.21/0.47 % ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% 0.21/0.47 % Maximal formula depth : 23 ( 23 avg)
% 0.21/0.47 % Number of types : 2 ( 1 usr)
% 0.21/0.47 % Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% 0.21/0.47 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.21/0.47 % Number of variables : 41 ( 0 ^; 41 !; 0 ?; 41 :)
% 0.21/0.47 % SPC : TH0_THM_NEQ_NAR
% 0.21/0.47
% 0.21/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.21/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.21/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.21/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 thf(a_type,type,
% 0.21/0.47 a: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(cTHM251D_pme,conjecture,
% 0.21/0.47 ! [R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
% 0.21/0.47 ( ( ( ! [Xx0: a,Xy0: a] :
% 0.21/0.47 ( ( ! [Xq: a > $o] :
% 0.21/0.47 ( ( ! [Xw: a] :
% 0.21/0.47 ( ( R @ Xx0 @ Xw )
% 0.21/0.47 => ( Xq @ Xw ) )
% 0.21/0.47 & ! [Xu: a,Xv: a] :
% 0.21/0.47 ( ( ( Xq @ Xu )
% 0.21/0.47 & ( R @ Xu @ Xv ) )
% 0.21/0.47 => ( Xq @ Xv ) ) )
% 0.21/0.47 => ( Xq @ Xy0 ) )
% 0.21/0.47 | ! [Xq: a > $o] :
% 0.21/0.47 ( ( ! [Xw: a] :
% 0.21/0.47 ( ( S @ Xx0 @ Xw )
% 0.21/0.47 => ( Xq @ Xw ) )
% 0.21/0.47 & ! [Xu: a,Xv: a] :
% 0.21/0.47 ( ( ( Xq @ Xu )
% 0.21/0.47 & ( S @ Xu @ Xv ) )
% 0.21/0.47 => ( Xq @ Xv ) ) )
% 0.21/0.47 => ( Xq @ Xy0 ) ) )
% 0.21/0.47 => ! [Xq: a > $o] :
% 0.21/0.47 ( ( ! [Xw: a] :
% 0.21/0.47 ( ( ( R @ Xx0 @ Xw )
% 0.21/0.47 | ( S @ Xx0 @ Xw ) )
% 0.21/0.47 => ( Xq @ Xw ) )
% 0.21/0.47 & ! [Xu: a,Xv: a] :
% 0.21/0.47 ( ( ( Xq @ Xu )
% 0.21/0.47 & ( ( R @ Xu @ Xv )
% 0.21/0.47 | ( S @ Xu @ Xv ) ) )
% 0.21/0.47 => ( Xq @ Xv ) ) )
% 0.21/0.47 => ( Xq @ Xy0 ) ) )
% 0.21/0.47 & ! [Xx0: a,Xy0: a,Xz: a] :
% 0.21/0.47 ( ( ! [Xq: a > $o] :
% 0.21/0.47 ( ( ! [Xw: a] :
% 0.21/0.47 ( ( ( R @ Xx0 @ Xw )
% 0.21/0.47 | ( S @ Xx0 @ Xw ) )
% 0.21/0.47 => ( Xq @ Xw ) )
% 0.21/0.47 & ! [Xu: a,Xv: a] :
% 0.21/0.47 ( ( ( Xq @ Xu )
% 0.21/0.47 & ( ( R @ Xu @ Xv )
% 0.21/0.47 | ( S @ Xu @ Xv ) ) )
% 0.21/0.47 => ( Xq @ Xv ) ) )
% 0.21/0.47 => ( Xq @ Xy0 ) )
% 0.21/0.47 & ! [Xq: a > $o] :
% 0.21/0.47 ( ( ! [Xw: a] :
% 0.21/0.47 ( ( ( R @ Xy0 @ Xw )
% 0.21/0.47 | ( S @ Xy0 @ Xw ) )
% 0.21/0.47 => ( Xq @ Xw ) )
% 0.21/0.47 & ! [Xu: a,Xv: a] :
% 0.21/0.47 ( ( ( Xq @ Xu )
% 0.21/0.47 & ( ( R @ Xu @ Xv )
% 0.21/0.47 | ( S @ Xu @ Xv ) ) )
% 0.21/0.47 => ( Xq @ Xv ) ) )
% 0.21/0.47 => ( Xq @ Xz ) ) )
% 0.21/0.47 => ! [Xq: a > $o] :
% 0.21/0.47 ( ( ! [Xw: a] :
% 0.21/0.47 ( ( ( R @ Xx0 @ Xw )
% 0.21/0.47 | ( S @ Xx0 @ Xw ) )
% 0.21/0.47 => ( Xq @ Xw ) )
% 0.21/0.47 & ! [Xu: a,Xv: a] :
% 0.21/0.47 ( ( ( Xq @ Xu )
% 0.21/0.47 & ( ( R @ Xu @ Xv )
% 0.21/0.47 | ( S @ Xu @ Xv ) ) )
% 0.21/0.47 => ( Xq @ Xv ) ) )
% 0.21/0.47 => ( Xq @ Xz ) ) ) )
% 0.21/0.47 => ! [Xq: a > $o] :
% 0.21/0.47 ( ( ! [Xw: a] :
% 0.21/0.47 ( ( ( R @ Xx @ Xw )
% 0.21/0.47 | ( S @ Xx @ Xw ) )
% 0.21/0.47 => ( Xq @ Xw ) )
% 0.21/0.47 & ! [Xu: a,Xv: a] :
% 0.21/0.47 ( ( ( Xq @ Xu )
% 0.21/0.47 & ( ( R @ Xu @ Xv )
% 0.21/0.47 | ( S @ Xu @ Xv ) ) )
% 0.21/0.47 => ( Xq @ Xv ) ) )
% 0.21/0.47 => ( Xq @ Xy ) ) )
% 0.21/0.47 => ! [Xq: a > $o] :
% 0.21/0.47 ( ( ! [Xw: a] :
% 0.21/0.47 ( ( ( R @ Xx @ Xw )
% 0.21/0.47 | ( S @ Xx @ Xw ) )
% 0.21/0.47 => ( Xq @ Xw ) )
% 0.21/0.47 & ! [Xu: a,Xv: a] :
% 0.21/0.47 ( ( ( Xq @ Xu )
% 0.21/0.47 & ( ( R @ Xu @ Xv )
% 0.21/0.47 | ( S @ Xu @ Xv ) ) )
% 0.21/0.47 => ( Xq @ Xv ) ) )
% 0.21/0.47 => ( Xq @ Xy ) ) ) ).
% 0.21/0.47
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 ------------------------
% 1.64/1.37 ---- Embedded in THF ---
% 1.64/1.37 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.64/1.37 %%% Generated on Tue Feb 24 12:41:13 EST 2026
% 1.64/1.37 %%% using '$$dhol' embedding, version 1.3.0.
% 1.64/1.37 %%% Logic specification used:
% 1.64/1.37 %%% thf(spec, logic, $$dhol).
% 1.64/1.37
% 1.64/1.37 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.4pWI2wlH3y/DTF2DTF9846.p
% See solution above
% 1.64/1.37 ------------------------
% 1.64/1.38 ---- Cleaned THF ---
% 1.64/1.38 thf(a_type,type,
% 1.64/1.38 a: $tType ).
% 1.64/1.38
% 1.64/1.38 thf(cTHM251D_pme,conjecture,
% 1.64/1.38 ! [R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
% 1.64/1.38 ( ( ( ! [Xx0: a,Xy0: a] :
% 1.64/1.38 ( ( ! [Xq: a > $o] :
% 1.64/1.38 ( ( ! [Xw: a] :
% 1.64/1.38 ( ( R @ Xx0 @ Xw )
% 1.64/1.38 => ( Xq @ Xw ) )
% 1.64/1.38 & ! [Xu: a,Xv: a] :
% 1.64/1.38 ( ( ( Xq @ Xu )
% 1.64/1.38 & ( R @ Xu @ Xv ) )
% 1.64/1.38 => ( Xq @ Xv ) ) )
% 1.64/1.38 => ( Xq @ Xy0 ) )
% 1.64/1.38 | ! [Xq: a > $o] :
% 1.64/1.38 ( ( ! [Xw: a] :
% 1.64/1.38 ( ( S @ Xx0 @ Xw )
% 1.64/1.38 => ( Xq @ Xw ) )
% 1.64/1.38 & ! [Xu: a,Xv: a] :
% 1.64/1.38 ( ( ( Xq @ Xu )
% 1.64/1.38 & ( S @ Xu @ Xv ) )
% 1.64/1.38 => ( Xq @ Xv ) ) )
% 1.64/1.38 => ( Xq @ Xy0 ) ) )
% 1.64/1.38 => ! [Xq: a > $o] :
% 1.64/1.38 ( ( ! [Xw: a] :
% 1.64/1.38 ( ( ( R @ Xx0 @ Xw )
% 1.64/1.38 | ( S @ Xx0 @ Xw ) )
% 1.64/1.38 => ( Xq @ Xw ) )
% 1.64/1.38 & ! [Xu: a,Xv: a] :
% 1.64/1.38 ( ( ( Xq @ Xu )
% 1.64/1.38 & ( ( R @ Xu @ Xv )
% 1.64/1.38 | ( S @ Xu @ Xv ) ) )
% 1.64/1.38 => ( Xq @ Xv ) ) )
% 1.64/1.38 => ( Xq @ Xy0 ) ) )
% 1.64/1.38 & ! [Xx0: a,Xy0: a,Xz: a] :
% 1.64/1.38 ( ( ! [Xq: a > $o] :
% 1.64/1.38 ( ( ! [Xw: a] :
% 1.64/1.38 ( ( ( R @ Xx0 @ Xw )
% 1.64/1.38 | ( S @ Xx0 @ Xw ) )
% 1.64/1.38 => ( Xq @ Xw ) )
% 1.64/1.38 & ! [Xu: a,Xv: a] :
% 1.64/1.38 ( ( ( Xq @ Xu )
% 1.64/1.38 & ( ( R @ Xu @ Xv )
% 1.64/1.38 | ( S @ Xu @ Xv ) ) )
% 1.64/1.38 => ( Xq @ Xv ) ) )
% 1.64/1.38 => ( Xq @ Xy0 ) )
% 1.64/1.38 & ! [Xq: a > $o] :
% 1.64/1.38 ( ( ! [Xw: a] :
% 1.64/1.38 ( ( ( R @ Xy0 @ Xw )
% 1.64/1.38 | ( S @ Xy0 @ Xw ) )
% 1.64/1.38 => ( Xq @ Xw ) )
% 1.64/1.38 & ! [Xu: a,Xv: a] :
% 1.64/1.38 ( ( ( Xq @ Xu )
% 1.64/1.38 & ( ( R @ Xu @ Xv )
% 1.64/1.38 | ( S @ Xu @ Xv ) ) )
% 1.64/1.38 => ( Xq @ Xv ) ) )
% 1.64/1.38 => ( Xq @ Xz ) ) )
% 1.64/1.38 => ! [Xq: a > $o] :
% 1.64/1.38 ( ( ! [Xw: a] :
% 1.64/1.38 ( ( ( R @ Xx0 @ Xw )
% 1.64/1.38 | ( S @ Xx0 @ Xw ) )
% 1.64/1.38 => ( Xq @ Xw ) )
% 1.64/1.38 & ! [Xu: a,Xv: a] :
% 1.64/1.38 ( ( ( Xq @ Xu )
% 1.64/1.38 & ( ( R @ Xu @ Xv )
% 1.64/1.38 | ( S @ Xu @ Xv ) ) )
% 1.64/1.38 => ( Xq @ Xv ) ) )
% 1.64/1.38 => ( Xq @ Xz ) ) ) )
% 1.64/1.38 => ! [Xq: a > $o] :
% 1.64/1.38 ( ( ! [Xw: a] :
% 1.64/1.38 ( ( ( R @ Xx @ Xw )
% 1.64/1.38 | ( S @ Xx @ Xw ) )
% 1.64/1.38 => ( Xq @ Xw ) )
% 1.64/1.38 & ! [Xu: a,Xv: a] :
% 1.64/1.38 ( ( ( Xq @ Xu )
% 1.64/1.38 & ( ( R @ Xu @ Xv )
% 1.64/1.38 | ( S @ Xu @ Xv ) ) )
% 1.64/1.38 => ( Xq @ Xv ) ) )
% 1.64/1.38 => ( Xq @ Xy ) ) )
% 1.64/1.38 => ! [Xq: a > $o] :
% 1.64/1.38 ( ( ! [Xw: a] :
% 1.64/1.38 ( ( ( R @ Xx @ Xw )
% 1.64/1.38 | ( S @ Xx @ Xw ) )
% 1.64/1.38 => ( Xq @ Xw ) )
% 1.64/1.38 & ! [Xu: a,Xv: a] :
% 1.64/1.38 ( ( ( Xq @ Xu )
% 1.64/1.38 & ( ( R @ Xu @ Xv )
% 1.64/1.38 | ( S @ Xu @ Xv ) ) )
% 1.64/1.38 => ( Xq @ Xv ) ) )
% 1.64/1.38 => ( Xq @ Xy ) ) ) ).
% 1.64/1.38 ------------------------
% 1.64/1.39 % (10014)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_9846 for (2999ds/183Mi)
% 1.64/1.39 % (10020)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_9846 for (2999ds/18Mi)
% 1.64/1.39 % (10019)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_9846 for (2999ds/275Mi)
% 1.64/1.39 % (10018)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_9846 for (2999ds/2Mi)
% 1.64/1.39 % (10018)Instruction limit reached!
% 1.64/1.39 % (10018)------------------------------
% 1.64/1.39 % (10018)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.39 % (10018)Termination reason: Unknown
% 1.64/1.39 % (10018)Termination phase: shuffling
% 1.64/1.39
% 1.64/1.39 % (10018)Memory used [KB]: 1023
% 1.64/1.39 % (10018)Time elapsed: 0.003 s
% 1.64/1.39 % (10018)Instructions burned: 3 (million)
% 1.64/1.39 % (10018)------------------------------
% 1.64/1.39 % (10018)------------------------------
% 1.64/1.40 % (10015)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 DTF2THF_9846 for (2999ds/4Mi)
% 1.81/1.40 % (10020)Instruction limit reached!
% 1.81/1.40 % (10020)------------------------------
% 1.81/1.40 % (10020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.40 % (10020)Termination reason: Unknown
% 1.81/1.40 % (10020)Termination phase: Saturation
% 1.81/1.40
% 1.81/1.40 % (10020)Memory used [KB]: 5628
% 1.81/1.40 % (10020)Time elapsed: 0.007 s
% 1.81/1.40 % (10020)Instructions burned: 19 (million)
% 1.81/1.40 % (10020)------------------------------
% 1.81/1.40 % (10020)------------------------------
% 1.81/1.40 % (10016)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 DTF2THF_9846 for (2999ds/27Mi)
% 1.81/1.40 % (10017)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_9846 for (2999ds/2Mi)
% 1.81/1.40 % (10015)Instruction limit reached!
% 1.81/1.40 % (10015)------------------------------
% 1.81/1.40 % (10015)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.40 % (10015)Termination reason: Unknown
% 1.81/1.40 % (10015)Termination phase: Preprocessing 3
% 1.81/1.40
% 1.81/1.40 % (10015)Memory used [KB]: 1023
% 1.81/1.40 % (10015)Time elapsed: 0.005 s
% 1.81/1.40 % (10015)Instructions burned: 5 (million)
% 1.81/1.40 % (10015)------------------------------
% 1.81/1.40 % (10015)------------------------------
% 1.81/1.40 % (10017)Instruction limit reached!
% 1.81/1.40 % (10017)------------------------------
% 1.81/1.40 % (10017)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.40 % (10017)Termination reason: Unknown
% 1.81/1.40 % (10017)Termination phase: shuffling
% 1.81/1.40
% 1.81/1.40 % (10017)Memory used [KB]: 1023
% 1.81/1.40 % (10017)Time elapsed: 0.003 s
% 1.81/1.40 % (10017)Instructions burned: 2 (million)
% 1.81/1.40 % (10017)------------------------------
% 1.81/1.40 % (10017)------------------------------
% 1.81/1.41 % (10022)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 DTF2THF_9846 for (2999ds/37Mi)
% 1.81/1.41 % (10021)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_9846 for (2999ds/3Mi)
% 1.81/1.41 % (10021)Instruction limit reached!
% 1.81/1.41 % (10021)------------------------------
% 1.81/1.41 % (10021)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.41 % (10021)Termination reason: Unknown
% 1.81/1.41 % (10021)Termination phase: Preprocessing 3
% 1.81/1.41
% 1.81/1.41 % (10021)Memory used [KB]: 1023
% 1.81/1.41 % (10021)Time elapsed: 0.004 s
% 1.81/1.41 % (10021)Instructions burned: 4 (million)
% 1.81/1.41 % (10021)------------------------------
% 1.81/1.41 % (10021)------------------------------
% 1.81/1.41 % (10016)Instruction limit reached!
% 1.81/1.41 % (10016)------------------------------
% 1.81/1.41 % (10016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.41 % (10016)Termination reason: Unknown
% 1.81/1.41 % (10016)Termination phase: Saturation
% 1.81/1.41
% 1.81/1.41 % (10016)Memory used [KB]: 5756
% 1.81/1.41 % (10016)Time elapsed: 0.020 s
% 1.81/1.41 % (10016)Instructions burned: 27 (million)
% 1.81/1.41 % (10016)------------------------------
% 1.81/1.41 % (10016)------------------------------
% 1.81/1.42 % (10023)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 DTF2THF_9846 for (2999ds/15Mi)
% 1.81/1.42 % (10024)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_9846 for (2999ds/3Mi)
% 1.81/1.42 % (10022)Instruction limit reached!
% 1.81/1.42 % (10022)------------------------------
% 1.81/1.42 % (10022)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.42 % (10022)Termination reason: Unknown
% 1.81/1.42 % (10022)Termination phase: Saturation
% 1.81/1.42
% 1.81/1.42 % (10022)Memory used [KB]: 5628
% 1.81/1.42 % (10022)Time elapsed: 0.012 s
% 1.81/1.42 % (10022)Instructions burned: 37 (million)
% 1.81/1.42 % (10022)------------------------------
% 1.81/1.42 % (10022)------------------------------
% 1.81/1.42 % (10024)Instruction limit reached!
% 1.81/1.42 % (10024)------------------------------
% 1.81/1.42 % (10024)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.42 % (10024)Termination reason: Unknown
% 1.81/1.42 % (10024)Termination phase: Naming
% 1.81/1.42
% 1.81/1.42 % (10024)Memory used [KB]: 1023
% 1.81/1.42 % (10024)Time elapsed: 0.004 s
% 1.81/1.42 % (10024)Instructions burned: 4 (million)
% 1.81/1.42 % (10024)------------------------------
% 1.81/1.42 % (10024)------------------------------
% 1.81/1.42 % (10023)Instruction limit reached!
% 1.81/1.42 % (10023)------------------------------
% 1.81/1.42 % (10023)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.42 % (10023)Termination reason: Unknown
% 1.81/1.42 % (10023)Termination phase: Saturation
% 1.81/1.42
% 1.81/1.42 % (10023)Memory used [KB]: 5756
% 1.81/1.42 % (10023)Time elapsed: 0.011 s
% 1.81/1.42 % (10023)Instructions burned: 16 (million)
% 1.81/1.42 % (10023)------------------------------
% 1.81/1.42 % (10023)------------------------------
% 1.81/1.43 % (10026)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_9846 for (2999ds/7Mi)
% 1.81/1.43 % (10025)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 DTF2THF_9846 for (2999ds/1041Mi)
% 1.81/1.43 % (10026)Instruction limit reached!
% 1.81/1.43 % (10026)------------------------------
% 1.81/1.43 % (10026)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.43 % (10026)Termination reason: Unknown
% 1.81/1.43 % (10026)Termination phase: Property scanning
% 1.81/1.43
% 1.81/1.43 % (10026)Memory used [KB]: 1151
% 1.81/1.43 % (10026)Time elapsed: 0.006 s
% 1.81/1.43 % (10026)Instructions burned: 8 (million)
% 1.81/1.43 % (10026)------------------------------
% 1.81/1.43 % (10026)------------------------------
% 1.81/1.44 % (10028)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 DTF2THF_9846 for (2999ds/3Mi)
% 1.81/1.44 % (10028)Instruction limit reached!
% 1.81/1.44 % (10028)------------------------------
% 1.81/1.44 % (10028)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.44 % (10028)Termination reason: Unknown
% 1.81/1.44 % (10028)Termination phase: Naming
% 1.81/1.44
% 1.81/1.44 % (10028)Memory used [KB]: 1023
% 1.81/1.44 % (10028)Time elapsed: 0.004 s
% 1.81/1.44 % (10028)Instructions burned: 4 (million)
% 1.81/1.44 % (10028)------------------------------
% 1.81/1.44 % (10028)------------------------------
% 1.81/1.44 % (10029)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 DTF2THF_9846 for (2999ds/3Mi)
% 1.81/1.44 % (10014)Instruction limit reached!
% 1.81/1.44 % (10014)------------------------------
% 1.81/1.44 % (10014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.44 % (10014)Termination reason: Unknown
% 1.81/1.44 % (10014)Termination phase: Saturation
% 1.81/1.44
% 1.81/1.44 % (10014)Memory used [KB]: 6524
% 1.81/1.44 % (10014)Time elapsed: 0.056 s
% 1.81/1.44 % (10014)Instructions burned: 184 (million)
% 1.81/1.44 % (10014)------------------------------
% 1.81/1.44 % (10014)------------------------------
% 1.81/1.44 % (10029)Instruction limit reached!
% 1.81/1.44 % (10029)------------------------------
% 1.81/1.44 % (10029)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.44 % (10029)Termination reason: Unknown
% 1.81/1.44 % (10029)Termination phase: Naming
% 1.81/1.44
% 1.81/1.44 % (10029)Memory used [KB]: 1023
% 1.81/1.44 % (10029)Time elapsed: 0.004 s
% 1.81/1.44 % (10029)Instructions burned: 4 (million)
% 1.81/1.44 % (10029)------------------------------
% 1.81/1.44 % (10029)------------------------------
% 1.81/1.45 % (10027)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_9846 for (2999ds/16Mi)
% 1.81/1.45 % (10030)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_9846 for (2999ds/7Mi)
% 1.81/1.45 % (10030)Instruction limit reached!
% 1.81/1.45 % (10030)------------------------------
% 1.81/1.45 % (10030)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.45 % (10030)Termination reason: Unknown
% 1.81/1.45 % (10030)Termination phase: Property scanning
% 1.81/1.45
% 1.81/1.45 % (10030)Memory used [KB]: 1151
% 1.81/1.45 % (10030)Time elapsed: 0.006 s
% 1.81/1.45 % (10030)Instructions burned: 7 (million)
% 1.81/1.45 % (10030)------------------------------
% 1.81/1.45 % (10030)------------------------------
% 1.81/1.45 % (10032)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_9846 for (2999ds/4Mi)
% 1.81/1.46 % (10031)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_9846 for (2999ds/3Mi)
% 1.81/1.46 % (10032)Instruction limit reached!
% 1.81/1.46 % (10032)------------------------------
% 1.81/1.46 % (10032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.46 % (10032)Termination reason: Unknown
% 1.81/1.46 % (10032)Termination phase: Preprocessing 3
% 1.81/1.46
% 1.81/1.46 % (10032)Memory used [KB]: 1151
% 1.81/1.46 % (10032)Time elapsed: 0.003 s
% 1.81/1.46 % (10032)Instructions burned: 6 (million)
% 1.81/1.46 % (10032)------------------------------
% 1.81/1.46 % (10032)------------------------------
% 1.81/1.46 % (10027)Instruction limit reached!
% 1.81/1.46 % (10027)------------------------------
% 1.81/1.46 % (10027)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.46 % (10027)Termination reason: Unknown
% 1.81/1.46 % (10027)Termination phase: Property scanning
% 1.81/1.46
% 1.81/1.46 % (10027)Memory used [KB]: 1151
% 1.81/1.46 % (10027)Time elapsed: 0.012 s
% 1.81/1.46 % (10027)Instructions burned: 19 (million)
% 1.81/1.46 % (10027)------------------------------
% 1.81/1.46 % (10027)------------------------------
% 1.81/1.46 % (10031)Instruction limit reached!
% 1.81/1.46 % (10031)------------------------------
% 1.81/1.46 % (10031)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.46 % (10031)Termination reason: Unknown
% 1.81/1.46 % (10031)Termination phase: Property scanning
% 1.81/1.46
% 1.81/1.46 % (10031)Memory used [KB]: 1023
% 1.81/1.46 % (10031)Time elapsed: 0.004 s
% 1.81/1.46 % (10031)Instructions burned: 4 (million)
% 1.81/1.46 % (10031)------------------------------
% 1.81/1.46 % (10031)------------------------------
% 1.81/1.46 % (10033)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_9846 for (2999ds/18Mi)
% 1.81/1.46 % (10035)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_9846 for (2999ds/6Mi)
% 1.81/1.47 % (10036)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 DTF2THF_9846 for (2999ds/902Mi)
% 1.81/1.47 % (10035)Instruction limit reached!
% 1.81/1.47 % (10035)------------------------------
% 1.81/1.47 % (10035)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.47 % (10035)Termination reason: Unknown
% 1.81/1.47 % (10035)Termination phase: Property scanning
% 1.81/1.47
% 1.81/1.47 % (10035)Memory used [KB]: 1151
% 1.81/1.47 % (10035)Time elapsed: 0.003 s
% 1.81/1.47 % (10035)Instructions burned: 8 (million)
% 1.81/1.47 % (10035)------------------------------
% 1.81/1.47 % (10035)------------------------------
% 1.81/1.47 % (10037)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 DTF2THF_9846 for (2999ds/21Mi)
% 1.81/1.47 % (10034)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_9846 for (2999ds/710Mi)
% 1.81/1.47 % (10033)Instruction limit reached!
% 1.81/1.47 % (10033)------------------------------
% 1.81/1.47 % (10033)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.47 % (10033)Termination reason: Unknown
% 1.81/1.47 % (10033)Termination phase: Saturation
% 1.81/1.47
% 1.81/1.47 % (10033)Memory used [KB]: 5756
% 1.81/1.47 % (10033)Time elapsed: 0.012 s
% 1.81/1.47 % (10033)Instructions burned: 18 (million)
% 1.81/1.47 % (10033)------------------------------
% 1.81/1.47 % (10033)------------------------------
% 1.81/1.48 % (10038)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_9846 for (2999ds/5Mi)
% 1.81/1.48 % (10038)Instruction limit reached!
% 1.81/1.48 % (10038)------------------------------
% 1.81/1.48 % (10038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.48 % (10038)Termination reason: Unknown
% 1.81/1.48 % (10038)Termination phase: Property scanning
% 1.81/1.48
% 1.81/1.48 % (10038)Memory used [KB]: 1023
% 1.81/1.48 % (10038)Time elapsed: 0.002 s
% 1.81/1.48 % (10038)Instructions burned: 5 (million)
% 1.81/1.48 % (10038)------------------------------
% 1.81/1.48 % (10038)------------------------------
% 1.81/1.48 % (10037)Instruction limit reached!
% 1.81/1.48 % (10037)------------------------------
% 1.81/1.48 % (10037)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.48 % (10037)Termination reason: Unknown
% 1.81/1.48 % (10037)Termination phase: Saturation
% 1.81/1.48
% 1.81/1.48 % (10037)Memory used [KB]: 5884
% 1.81/1.48 % (10037)Time elapsed: 0.009 s
% 1.81/1.48 % (10037)Instructions burned: 22 (million)
% 1.81/1.48 % (10037)------------------------------
% 1.81/1.48 % (10037)------------------------------
% 1.81/1.48 % (10019)Instruction limit reached!
% 1.81/1.48 % (10019)------------------------------
% 1.81/1.48 % (10019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.48 % (10019)Termination reason: Unknown
% 1.81/1.48 % (10019)Termination phase: Saturation
% 1.81/1.48
% 1.81/1.48 % (10019)Memory used [KB]: 6396
% 1.81/1.48 % (10019)Time elapsed: 0.092 s
% 1.81/1.48 % (10019)Instructions burned: 276 (million)
% 1.81/1.48 % (10019)------------------------------
% 1.81/1.48 % (10019)------------------------------
% 1.81/1.49 % (10040)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_9846 for (2999ds/377Mi)
% 1.81/1.49 % (10039)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 DTF2THF_9846 for (2999ds/6Mi)
% 1.81/1.49 % (10041)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 DTF2THF_9846 for (2999ds/779Mi)
% 1.81/1.49 % (10039)Instruction limit reached!
% 1.81/1.49 % (10039)------------------------------
% 1.81/1.49 % (10039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.49 % (10039)Termination reason: Unknown
% 1.81/1.49 % (10039)Termination phase: Saturation
% 1.81/1.49
% 1.81/1.49 % (10039)Memory used [KB]: 5500
% 1.81/1.49 % (10039)Time elapsed: 0.005 s
% 1.81/1.49 % (10039)Instructions burned: 8 (million)
% 1.81/1.49 % (10039)------------------------------
% 1.81/1.49 % (10039)------------------------------
% 1.81/1.49 % (10042)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 DTF2THF_9846 for (2999ds/19Mi)
% 1.81/1.50 % (10042)Instruction limit reached!
% 1.81/1.50 % (10042)------------------------------
% 1.81/1.50 % (10042)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.50 % (10042)Termination reason: Unknown
% 1.81/1.50 % (10042)Termination phase: Saturation
% 1.81/1.50
% 1.81/1.50 % (10042)Memory used [KB]: 5500
% 1.81/1.50 % (10042)Time elapsed: 0.007 s
% 1.81/1.50 % (10042)Instructions burned: 19 (million)
% 1.81/1.50 % (10042)------------------------------
% 1.81/1.50 % (10042)------------------------------
% 1.81/1.50 % (10046)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_9846 for (2999ds/879Mi)
% 1.81/1.51 % (10049)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_9846 for (2998ds/17Mi)
% 1.81/1.51 % (10049)Instruction limit reached!
% 1.81/1.51 % (10049)------------------------------
% 1.81/1.51 % (10049)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.51 % (10049)Termination reason: Unknown
% 1.81/1.51 % (10049)Termination phase: Saturation
% 1.81/1.51
% 1.81/1.51 % (10049)Memory used [KB]: 5756
% 1.81/1.51 % (10049)Time elapsed: 0.008 s
% 1.81/1.51 % (10049)Instructions burned: 18 (million)
% 1.81/1.51 % (10049)------------------------------
% 1.81/1.51 % (10049)------------------------------
% 1.81/1.52 % (10057)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_9846 for (2998ds/3Mi)
% 1.81/1.52 % (10057)Instruction limit reached!
% 1.81/1.52 % (10057)------------------------------
% 1.81/1.52 % (10057)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.52 % (10057)Termination reason: Unknown
% 1.81/1.52 % (10057)Termination phase: Preprocessing 3
% 1.81/1.52
% 1.81/1.52 % (10057)Memory used [KB]: 1023
% 1.81/1.52 % (10057)Time elapsed: 0.003 s
% 1.81/1.52 % (10057)Instructions burned: 4 (million)
% 1.81/1.52 % (10057)------------------------------
% 1.81/1.52 % (10057)------------------------------
% 1.81/1.53 % (10063)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_9846 for (2998ds/30Mi)
% 1.81/1.55 % (10063)Instruction limit reached!
% 1.81/1.55 % (10063)------------------------------
% 1.81/1.55 % (10063)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.55 % (10063)Termination reason: Unknown
% 1.81/1.55 % (10063)Termination phase: Saturation
% 1.81/1.55
% 1.81/1.55 % (10063)Memory used [KB]: 5756
% 1.81/1.55 % (10063)Time elapsed: 0.033 s
% 1.81/1.55 % (10063)Instructions burned: 31 (million)
% 1.81/1.55 % (10063)------------------------------
% 1.81/1.55 % (10063)------------------------------
% 1.81/1.56 % (10071)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_9846 for (2998ds/127Mi)
% 1.81/1.56 % (10025)First to succeed.
% 1.81/1.58 % (10025)Refutation found. Thanks to Tanya!
% 1.81/1.58 % SZS status Theorem for DTF2THF_9846
% 1.81/1.58 % SZS output start Proof for DTF2THF_9846
% 1.81/1.58 thf(type_def_5, type, a: $tType).
% 1.81/1.58 thf(func_def_0, type, a: $tType).
% 1.81/1.58 thf(func_def_20, type, ph1: !>[X0: $tType]:(X0)).
% 1.81/1.58 thf(func_def_21, type, sK2: a).
% 1.81/1.58 thf(func_def_22, type, sK3: a > a > $o).
% 1.81/1.58 thf(func_def_23, type, sK4: a > a > $o).
% 1.81/1.58 thf(func_def_24, type, sK5: a).
% 1.81/1.58 thf(func_def_25, type, sK6: a > $o).
% 1.81/1.58 thf(func_def_26, type, sK7: a).
% 1.81/1.58 thf(func_def_27, type, sK8: a).
% 1.81/1.58 thf(func_def_28, type, sK9: a).
% 1.81/1.58 thf(func_def_29, type, sK10: a > $o).
% 1.81/1.58 thf(func_def_30, type, sK11: a).
% 1.81/1.58 thf(func_def_31, type, sK12: a).
% 1.81/1.58 thf(func_def_32, type, sK13: a > $o).
% 1.81/1.58 thf(func_def_33, type, sK14: a).
% 1.81/1.58 thf(func_def_34, type, sK15: a).
% 1.81/1.58 thf(func_def_35, type, sK16: a).
% 1.81/1.58 thf(func_def_36, type, sK17: a).
% 1.81/1.58 thf(func_def_37, type, sK18: a).
% 1.81/1.58 thf(func_def_38, type, sK19: a).
% 1.81/1.58 thf(func_def_39, type, sK20: a).
% 1.81/1.58 thf(func_def_40, type, sK21: a).
% 1.81/1.58 thf(func_def_41, type, sK22: a).
% 1.81/1.58 thf(func_def_42, type, sK23: a).
% 1.81/1.58 thf(func_def_43, type, sK24: a).
% 1.81/1.58 thf(func_def_44, type, sK25: a).
% 1.81/1.58 thf(func_def_45, type, sK26: a).
% 1.81/1.58 thf(f2309,plain,(
% 1.81/1.58 $false),
% 1.81/1.58 inference(avatar_sat_refutation,[status(thm)],[f39,f49,f245,f348,f402,f448,f454,f686,f762,f1067,f1193,f1217,f1245,f1304,f1308,f1367,f1684,f1990,f2028,f2308])).
% 1.81/1.58 thf(f2308,plain,(
% 1.81/1.58 ~spl0_4 | ~spl0_7 | ~spl0_10),
% 1.81/1.58 inference(avatar_contradiction_clause,[status(thm)],[f2307])).
% 1.81/1.58 thf(f2307,plain,(
% 1.81/1.58 $false | (~spl0_4 | ~spl0_7 | ~spl0_10)),
% 1.81/1.58 inference(trivial_inequality_removal,[status(thm)],[f2306])).
% 1.81/1.58 thf(f2306,plain,(
% 1.81/1.58 ($true = $false) | (~spl0_4 | ~spl0_7 | ~spl0_10)),
% 1.81/1.58 inference(forward_demodulation,[status(thm)],[f2298,f2221])).
% 1.81/1.58 thf(f2221,plain,(
% 1.81/1.58 ($false = (sK13 @ sK26)) | ~spl0_10),
% 1.81/1.58 inference(binary_proxy_clausification,[status(thm)],[f2104])).
% 1.81/1.58 thf(f2104,plain,(
% 1.81/1.58 (((sK3 @ sK12 @ sK26) => (sK13 @ sK26)) = $false) | ~spl0_10),
% 1.81/1.58 inference(beta_eta_normalization,[status(thm)],[f2099])).
% 1.81/1.58 thf(f2099,plain,(
% 1.81/1.58 (((^[Y0 : a]: ((sK3 @ sK12 @ Y0) => (sK13 @ Y0))) @ sK26) = $false) | ~spl0_10),
% 1.81/1.58 inference(sigma_clausification,[status(thm)],[f347])).
% 1.81/1.58 thf(f347,plain,(
% 1.81/1.58 ((!! @ a @ (^[Y0 : a]: ((sK3 @ sK12 @ Y0) => (sK13 @ Y0)))) = $false) | ~spl0_10),
% 1.81/1.58 inference(avatar_component_clause,[status(thm)],[f346])).
% 1.81/1.58 thf(f346,definition,(
% 1.81/1.58 spl0_10 <=> ((!! @ a @ (^[Y0 : a]: ((sK3 @ sK12 @ Y0) => (sK13 @ Y0)))) = $false)),
% 1.81/1.58 introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition])).
% 1.81/1.58 thf(f2298,plain,(
% 1.81/1.58 ($true = (sK13 @ sK26)) | (~spl0_4 | ~spl0_7 | ~spl0_10)),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f2297])).
% 1.81/1.58 thf(f2297,plain,(
% 1.81/1.58 ($true = ($true => (sK13 @ sK26))) | (~spl0_4 | ~spl0_7 | ~spl0_10)),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f2292])).
% 1.81/1.58 thf(f2292,plain,(
% 1.81/1.58 ($true = (((sK4 @ sK12 @ sK26) | $true) => (sK13 @ sK26))) | (~spl0_4 | ~spl0_7 | ~spl0_10)),
% 1.81/1.58 inference(superposition,[status(thm)],[f2281,f2222])).
% 1.81/1.58 thf(f2222,plain,(
% 1.81/1.58 ($true = (sK3 @ sK12 @ sK26)) | ~spl0_10),
% 1.81/1.58 inference(binary_proxy_clausification,[status(thm)],[f2104])).
% 1.81/1.58 thf(f2281,plain,(
% 1.81/1.58 ( ! [X1 : a] : (($true = (((sK4 @ sK12 @ X1) | (sK3 @ sK12 @ X1)) => (sK13 @ X1)))) ) | (~spl0_4 | ~spl0_7)),
% 1.81/1.58 inference(beta_eta_normalization,[status(thm)],[f2280])).
% 1.81/1.58 thf(f2280,plain,(
% 1.81/1.58 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (((sK4 @ sK12 @ Y0) | (sK3 @ sK12 @ Y0)) => (sK13 @ Y0))) @ X1))) ) | (~spl0_4 | ~spl0_7)),
% 1.81/1.58 inference(pi_clausification,[status(thm)],[f2067])).
% 1.81/1.58 thf(f2067,plain,(
% 1.81/1.58 ($true = (!! @ a @ (^[Y0 : a]: (((sK4 @ sK12 @ Y0) | (sK3 @ sK12 @ Y0)) => (sK13 @ Y0))))) | (~spl0_4 | ~spl0_7)),
% 1.81/1.58 inference(binary_proxy_clausification,[status(thm)],[f2035])).
% 1.81/1.58 thf(f2035,plain,(
% 1.81/1.58 ($true = ((!! @ a @ (^[Y0 : a]: (((sK4 @ sK12 @ Y0) | (sK3 @ sK12 @ Y0)) => (sK13 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK4 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) & (sK13 @ Y1)) => (sK13 @ Y0)))))))) | (~spl0_4 | ~spl0_7)),
% 1.81/1.58 inference(binary_proxy_clausification,[status(thm)],[f2033])).
% 1.81/1.58 thf(f2033,plain,(
% 1.81/1.58 ((((!! @ a @ (^[Y0 : a]: (((sK4 @ sK12 @ Y0) | (sK3 @ sK12 @ Y0)) => (sK13 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK4 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) & (sK13 @ Y1)) => (sK13 @ Y0))))))) => (sK13 @ sK11)) = $false) | (~spl0_4 | ~spl0_7)),
% 1.81/1.58 inference(beta_eta_normalization,[status(thm)],[f2032])).
% 1.81/1.58 thf(f2032,plain,(
% 1.81/1.58 (((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK12 @ Y1) | (sK3 @ sK12 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK4 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1))))))) => (Y0 @ sK11))) @ sK13) = $false) | (~spl0_4 | ~spl0_7)),
% 1.81/1.58 inference(sigma_clausification,[status(thm)],[f2031])).
% 1.81/1.58 thf(f2031,plain,(
% 1.81/1.58 ($false = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK12 @ Y1) | (sK3 @ sK12 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK4 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1))))))) => (Y0 @ sK11))))) | (~spl0_4 | ~spl0_7)),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f2030])).
% 1.81/1.58 thf(f2030,plain,(
% 1.81/1.58 (($true => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK12 @ Y1) | (sK3 @ sK12 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK4 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1))))))) => (Y0 @ sK11))))) = $false) | (~spl0_4 | ~spl0_7)),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f2029])).
% 1.81/1.58 thf(f2029,plain,(
% 1.81/1.58 ($false = (($true | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK4 @ sK12 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK4 @ Y1 @ Y2)) => (Y0 @ Y2))))))) => (Y0 @ sK11))))) => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK12 @ Y1) | (sK3 @ sK12 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK4 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1))))))) => (Y0 @ sK11)))))) | (~spl0_4 | ~spl0_7)),
% 1.81/1.58 inference(backward_demodulation,[status(thm)],[f1393,f241])).
% 1.81/1.58 thf(f241,plain,(
% 1.81/1.58 ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK3 @ Y1 @ Y2)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ sK12 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK11))))) | ~spl0_7),
% 1.81/1.58 inference(avatar_component_clause,[status(thm)],[f240])).
% 1.81/1.58 thf(f240,definition,(
% 1.81/1.58 spl0_7 <=> ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK3 @ Y1 @ Y2)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ sK12 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK11)))))),
% 1.81/1.58 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 1.81/1.58 thf(f1393,plain,(
% 1.81/1.58 ((((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK3 @ Y1 @ Y2)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ sK12 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK11)))) | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK4 @ sK12 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK4 @ Y1 @ Y2)) => (Y0 @ Y2))))))) => (Y0 @ sK11))))) => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK12 @ Y1) | (sK3 @ sK12 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK4 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1))))))) => (Y0 @ sK11))))) = $false) | ~spl0_4),
% 1.81/1.58 inference(beta_eta_normalization,[status(thm)],[f1392])).
% 1.81/1.58 thf(f1392,plain,(
% 1.81/1.58 (((^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & (sK3 @ Y2 @ Y3)) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: ((sK3 @ Y0 @ Y2) => (Y1 @ Y2))))) => (Y1 @ sK11)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK4 @ Y0 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & (sK4 @ Y2 @ Y3)) => (Y1 @ Y3))))))) => (Y1 @ sK11))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK4 @ Y0 @ Y2) | (sK3 @ Y0 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((((sK4 @ Y3 @ Y2) | (sK3 @ Y3 @ Y2)) & (Y1 @ Y3)) => (Y1 @ Y2))))))) => (Y1 @ sK11)))))) @ sK12) = $false) | ~spl0_4),
% 1.81/1.58 inference(sigma_clausification,[status(thm)],[f1382])).
% 1.81/1.58 thf(f1382,plain,(
% 1.81/1.58 ((!! @ a @ (^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & (sK3 @ Y2 @ Y3)) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: ((sK3 @ Y0 @ Y2) => (Y1 @ Y2))))) => (Y1 @ sK11)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK4 @ Y0 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & (sK4 @ Y2 @ Y3)) => (Y1 @ Y3))))))) => (Y1 @ sK11))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK4 @ Y0 @ Y2) | (sK3 @ Y0 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((((sK4 @ Y3 @ Y2) | (sK3 @ Y3 @ Y2)) & (Y1 @ Y3)) => (Y1 @ Y2))))))) => (Y1 @ sK11))))))) = $false) | ~spl0_4),
% 1.81/1.58 inference(beta_eta_normalization,[status(thm)],[f1381])).
% 1.81/1.58 thf(f1381,plain,(
% 1.81/1.58 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK3 @ Y3 @ Y4)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK3 @ Y1 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y0)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK4 @ Y1 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK4 @ Y3 @ Y4)) => (Y2 @ Y4))))))) => (Y2 @ Y0))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK4 @ Y1 @ Y3) | (sK3 @ Y1 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((((sK4 @ Y4 @ Y3) | (sK3 @ Y4 @ Y3)) & (Y2 @ Y4)) => (Y2 @ Y3))))))) => (Y2 @ Y0)))))))) @ sK11) = $false) | ~spl0_4),
% 1.81/1.58 inference(sigma_clausification,[status(thm)],[f48])).
% 1.81/1.58 thf(f48,plain,(
% 1.81/1.58 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK3 @ Y3 @ Y4)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK3 @ Y1 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y0)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK4 @ Y1 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK4 @ Y3 @ Y4)) => (Y2 @ Y4))))))) => (Y2 @ Y0))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK4 @ Y1 @ Y3) | (sK3 @ Y1 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((((sK4 @ Y4 @ Y3) | (sK3 @ Y4 @ Y3)) & (Y2 @ Y4)) => (Y2 @ Y3))))))) => (Y2 @ Y0)))))))))) | ~spl0_4),
% 1.81/1.58 inference(avatar_component_clause,[status(thm)],[f47])).
% 1.81/1.58 thf(f47,definition,(
% 1.81/1.58 spl0_4 <=> ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK3 @ Y3 @ Y4)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK3 @ Y1 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y0)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK4 @ Y1 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK4 @ Y3 @ Y4)) => (Y2 @ Y4))))))) => (Y2 @ Y0))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK4 @ Y1 @ Y3) | (sK3 @ Y1 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((((sK4 @ Y4 @ Y3) | (sK3 @ Y4 @ Y3)) & (Y2 @ Y4)) => (Y2 @ Y3))))))) => (Y2 @ Y0))))))))))),
% 1.81/1.58 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.81/1.58 thf(f2028,plain,(
% 1.81/1.58 ~spl0_4 | ~spl0_8 | ~spl0_12),
% 1.81/1.58 inference(avatar_contradiction_clause,[status(thm)],[f2027])).
% 1.81/1.58 thf(f2027,plain,(
% 1.81/1.58 $false | (~spl0_4 | ~spl0_8 | ~spl0_12)),
% 1.81/1.58 inference(trivial_inequality_removal,[status(thm)],[f2026])).
% 1.81/1.58 thf(f2026,plain,(
% 1.81/1.58 ($true = $false) | (~spl0_4 | ~spl0_8 | ~spl0_12)),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f2025])).
% 1.81/1.58 thf(f2025,plain,(
% 1.81/1.58 ($true = (~ $true)) | (~spl0_4 | ~spl0_8 | ~spl0_12)),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f2024])).
% 1.81/1.58 thf(f2024,plain,(
% 1.81/1.58 ($true = (~ ($true | (sK3 @ sK12 @ sK25)))) | (~spl0_4 | ~spl0_8 | ~spl0_12)),
% 1.81/1.58 inference(forward_demodulation,[status(thm)],[f2019,f2010])).
% 1.81/1.58 thf(f2010,plain,(
% 1.81/1.58 ($true = (sK4 @ sK12 @ sK25)) | ~spl0_12),
% 1.81/1.58 inference(binary_proxy_clausification,[status(thm)],[f1996])).
% 1.81/1.58 thf(f1996,plain,(
% 1.81/1.58 ($false = ((sK4 @ sK12 @ sK25) => (sK13 @ sK25))) | ~spl0_12),
% 1.81/1.58 inference(beta_eta_normalization,[status(thm)],[f1994])).
% 1.81/1.58 thf(f1994,plain,(
% 1.81/1.58 (((^[Y0 : a]: ((sK4 @ sK12 @ Y0) => (sK13 @ Y0))) @ sK25) = $false) | ~spl0_12),
% 1.81/1.58 inference(sigma_clausification,[status(thm)],[f401])).
% 1.81/1.58 thf(f401,plain,(
% 1.81/1.58 ((!! @ a @ (^[Y0 : a]: ((sK4 @ sK12 @ Y0) => (sK13 @ Y0)))) = $false) | ~spl0_12),
% 1.81/1.58 inference(avatar_component_clause,[status(thm)],[f400])).
% 1.81/1.58 thf(f400,definition,(
% 1.81/1.58 spl0_12 <=> ((!! @ a @ (^[Y0 : a]: ((sK4 @ sK12 @ Y0) => (sK13 @ Y0)))) = $false)),
% 1.81/1.58 introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition])).
% 1.81/1.58 thf(f2019,plain,(
% 1.81/1.58 ($true = (~ ((sK4 @ sK12 @ sK25) | (sK3 @ sK12 @ sK25)))) | (~spl0_4 | ~spl0_8 | ~spl0_12)),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f2015])).
% 1.81/1.58 thf(f2015,plain,(
% 1.81/1.58 ($true = (((sK4 @ sK12 @ sK25) | (sK3 @ sK12 @ sK25)) => $false)) | (~spl0_4 | ~spl0_8 | ~spl0_12)),
% 1.81/1.58 inference(superposition,[status(thm)],[f1905,f2009])).
% 1.81/1.58 thf(f2009,plain,(
% 1.81/1.58 ((sK13 @ sK25) = $false) | ~spl0_12),
% 1.81/1.58 inference(binary_proxy_clausification,[status(thm)],[f1996])).
% 1.81/1.58 thf(f1905,plain,(
% 1.81/1.58 ( ! [X1 : a] : (($true = (((sK4 @ sK12 @ X1) | (sK3 @ sK12 @ X1)) => (sK13 @ X1)))) ) | (~spl0_4 | ~spl0_8)),
% 1.81/1.58 inference(beta_eta_normalization,[status(thm)],[f1904])).
% 1.81/1.58 thf(f1904,plain,(
% 1.81/1.58 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (((sK4 @ sK12 @ Y0) | (sK3 @ sK12 @ Y0)) => (sK13 @ Y0))) @ X1))) ) | (~spl0_4 | ~spl0_8)),
% 1.81/1.58 inference(pi_clausification,[status(thm)],[f1746])).
% 1.81/1.58 thf(f1746,plain,(
% 1.81/1.58 ($true = (!! @ a @ (^[Y0 : a]: (((sK4 @ sK12 @ Y0) | (sK3 @ sK12 @ Y0)) => (sK13 @ Y0))))) | (~spl0_4 | ~spl0_8)),
% 1.81/1.58 inference(binary_proxy_clausification,[status(thm)],[f1705])).
% 1.81/1.58 thf(f1705,plain,(
% 1.81/1.58 ($true = ((!! @ a @ (^[Y0 : a]: (((sK4 @ sK12 @ Y0) | (sK3 @ sK12 @ Y0)) => (sK13 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK4 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) & (sK13 @ Y1)) => (sK13 @ Y0)))))))) | (~spl0_4 | ~spl0_8)),
% 1.81/1.58 inference(binary_proxy_clausification,[status(thm)],[f1698])).
% 1.81/1.58 thf(f1698,plain,(
% 1.81/1.58 ((((!! @ a @ (^[Y0 : a]: (((sK4 @ sK12 @ Y0) | (sK3 @ sK12 @ Y0)) => (sK13 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK4 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) & (sK13 @ Y1)) => (sK13 @ Y0))))))) => (sK13 @ sK11)) = $false) | (~spl0_4 | ~spl0_8)),
% 1.81/1.58 inference(beta_eta_normalization,[status(thm)],[f1697])).
% 1.81/1.58 thf(f1697,plain,(
% 1.81/1.58 (((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK12 @ Y1) | (sK3 @ sK12 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK4 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1))))))) => (Y0 @ sK11))) @ sK13) = $false) | (~spl0_4 | ~spl0_8)),
% 1.81/1.58 inference(sigma_clausification,[status(thm)],[f1687])).
% 1.81/1.58 thf(f1687,plain,(
% 1.81/1.58 ($false = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK12 @ Y1) | (sK3 @ sK12 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK4 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1))))))) => (Y0 @ sK11))))) | (~spl0_4 | ~spl0_8)),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f1686])).
% 1.81/1.58 thf(f1686,plain,(
% 1.81/1.58 (($true => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK12 @ Y1) | (sK3 @ sK12 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK4 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1))))))) => (Y0 @ sK11))))) = $false) | (~spl0_4 | ~spl0_8)),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f1685])).
% 1.81/1.58 thf(f1685,plain,(
% 1.81/1.58 ((((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK3 @ Y1 @ Y2)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ sK12 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK11)))) | $true) => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK12 @ Y1) | (sK3 @ sK12 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK4 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1))))))) => (Y0 @ sK11))))) = $false) | (~spl0_4 | ~spl0_8)),
% 1.81/1.58 inference(backward_demodulation,[status(thm)],[f1393,f244])).
% 1.81/1.58 thf(f244,plain,(
% 1.81/1.58 ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK4 @ sK12 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK4 @ Y1 @ Y2)) => (Y0 @ Y2))))))) => (Y0 @ sK11))))) | ~spl0_8),
% 1.81/1.58 inference(avatar_component_clause,[status(thm)],[f243])).
% 1.81/1.58 thf(f243,definition,(
% 1.81/1.58 spl0_8 <=> ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK4 @ sK12 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK4 @ Y1 @ Y2)) => (Y0 @ Y2))))))) => (Y0 @ sK11)))))),
% 1.81/1.58 introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition])).
% 1.81/1.58 thf(f1990,plain,(
% 1.81/1.58 ~spl0_4 | ~spl0_8 | ~spl0_11),
% 1.81/1.58 inference(avatar_contradiction_clause,[status(thm)],[f1989])).
% 1.81/1.58 thf(f1989,plain,(
% 1.81/1.58 $false | (~spl0_4 | ~spl0_8 | ~spl0_11)),
% 1.81/1.58 inference(trivial_inequality_removal,[status(thm)],[f1988])).
% 1.81/1.58 thf(f1988,plain,(
% 1.81/1.58 ($true = $false) | (~spl0_4 | ~spl0_8 | ~spl0_11)),
% 1.81/1.58 inference(forward_demodulation,[status(thm)],[f1987,f1955])).
% 1.81/1.58 thf(f1955,plain,(
% 1.81/1.58 ($false = (sK13 @ sK24)) | ~spl0_11),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f1954])).
% 1.81/1.58 thf(f1954,plain,(
% 1.81/1.58 (($true => (sK13 @ sK24)) = $false) | ~spl0_11),
% 1.81/1.58 inference(backward_demodulation,[status(thm)],[f1943,f1953])).
% 1.81/1.58 thf(f1953,plain,(
% 1.81/1.58 ($true = ((sK13 @ sK23) & (sK4 @ sK23 @ sK24))) | ~spl0_11),
% 1.81/1.58 inference(binary_proxy_clausification,[status(thm)],[f1943])).
% 1.81/1.58 thf(f1943,plain,(
% 1.81/1.58 ($false = (((sK13 @ sK23) & (sK4 @ sK23 @ sK24)) => (sK13 @ sK24))) | ~spl0_11),
% 1.81/1.58 inference(beta_eta_normalization,[status(thm)],[f1942])).
% 1.81/1.58 thf(f1942,plain,(
% 1.81/1.58 ($false = ((^[Y0 : a]: (((sK13 @ sK23) & (sK4 @ sK23 @ Y0)) => (sK13 @ Y0))) @ sK24)) | ~spl0_11),
% 1.81/1.58 inference(sigma_clausification,[status(thm)],[f1931])).
% 1.81/1.58 thf(f1931,plain,(
% 1.81/1.58 ((!! @ a @ (^[Y0 : a]: (((sK13 @ sK23) & (sK4 @ sK23 @ Y0)) => (sK13 @ Y0)))) = $false) | ~spl0_11),
% 1.81/1.58 inference(beta_eta_normalization,[status(thm)],[f1927])).
% 1.81/1.58 thf(f1927,plain,(
% 1.81/1.58 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ Y0) & (sK4 @ Y0 @ Y1)) => (sK13 @ Y1))))) @ sK23) = $false) | ~spl0_11),
% 1.81/1.58 inference(sigma_clausification,[status(thm)],[f398])).
% 1.81/1.58 thf(f398,plain,(
% 1.81/1.58 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ Y0) & (sK4 @ Y0 @ Y1)) => (sK13 @ Y1)))))) = $false) | ~spl0_11),
% 1.81/1.58 inference(avatar_component_clause,[status(thm)],[f397])).
% 1.81/1.58 thf(f397,definition,(
% 1.81/1.58 spl0_11 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ Y0) & (sK4 @ Y0 @ Y1)) => (sK13 @ Y1)))))) = $false)),
% 1.81/1.58 introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition])).
% 1.81/1.58 thf(f1987,plain,(
% 1.81/1.58 ($true = (sK13 @ sK24)) | (~spl0_4 | ~spl0_8 | ~spl0_11)),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f1986])).
% 1.81/1.58 thf(f1986,plain,(
% 1.81/1.58 (($true => (sK13 @ sK24)) = $true) | (~spl0_4 | ~spl0_8 | ~spl0_11)),
% 1.81/1.58 inference(forward_demodulation,[status(thm)],[f1983,f1968])).
% 1.81/1.58 thf(f1968,plain,(
% 1.81/1.58 ($true = (sK13 @ sK23)) | ~spl0_11),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f1967])).
% 1.81/1.58 thf(f1967,plain,(
% 1.81/1.58 ($true = ((sK13 @ sK23) & $true)) | ~spl0_11),
% 1.81/1.58 inference(backward_demodulation,[status(thm)],[f1953,f1965])).
% 1.81/1.58 thf(f1965,plain,(
% 1.81/1.58 ($true = (sK4 @ sK23 @ sK24)) | ~spl0_11),
% 1.81/1.58 inference(binary_proxy_clausification,[status(thm)],[f1953])).
% 1.81/1.58 thf(f1983,plain,(
% 1.81/1.58 ($true = ((sK13 @ sK23) => (sK13 @ sK24))) | (~spl0_4 | ~spl0_8 | ~spl0_11)),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f1982])).
% 1.81/1.58 thf(f1982,plain,(
% 1.81/1.58 ($true = (($true & (sK13 @ sK23)) => (sK13 @ sK24))) | (~spl0_4 | ~spl0_8 | ~spl0_11)),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f1980])).
% 1.81/1.58 thf(f1980,plain,(
% 1.81/1.58 ($true = ((($true | (sK3 @ sK23 @ sK24)) & (sK13 @ sK23)) => (sK13 @ sK24))) | (~spl0_4 | ~spl0_8 | ~spl0_11)),
% 1.81/1.58 inference(superposition,[status(thm)],[f1772,f1965])).
% 1.81/1.58 thf(f1772,plain,(
% 1.81/1.58 ( ! [X2 : a,X1 : a] : (($true = ((((sK4 @ X2 @ X1) | (sK3 @ X2 @ X1)) & (sK13 @ X2)) => (sK13 @ X1)))) ) | (~spl0_4 | ~spl0_8)),
% 1.81/1.58 inference(beta_eta_normalization,[status(thm)],[f1771])).
% 1.81/1.58 thf(f1771,plain,(
% 1.81/1.58 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: ((((sK4 @ Y0 @ X1) | (sK3 @ Y0 @ X1)) & (sK13 @ Y0)) => (sK13 @ X1))) @ X2))) ) | (~spl0_4 | ~spl0_8)),
% 1.81/1.58 inference(pi_clausification,[status(thm)],[f1761])).
% 1.81/1.58 thf(f1761,plain,(
% 1.81/1.58 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: ((((sK4 @ Y0 @ X1) | (sK3 @ Y0 @ X1)) & (sK13 @ Y0)) => (sK13 @ X1)))))) ) | (~spl0_4 | ~spl0_8)),
% 1.81/1.58 inference(beta_eta_normalization,[status(thm)],[f1760])).
% 1.81/1.58 thf(f1760,plain,(
% 1.81/1.58 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK4 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) & (sK13 @ Y1)) => (sK13 @ Y0))))) @ X1))) ) | (~spl0_4 | ~spl0_8)),
% 1.81/1.58 inference(pi_clausification,[status(thm)],[f1748])).
% 1.81/1.58 thf(f1748,plain,(
% 1.81/1.58 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK4 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) & (sK13 @ Y1)) => (sK13 @ Y0))))))) | (~spl0_4 | ~spl0_8)),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f1747])).
% 1.81/1.58 thf(f1747,plain,(
% 1.81/1.58 ($true = ($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK4 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) & (sK13 @ Y1)) => (sK13 @ Y0)))))))) | (~spl0_4 | ~spl0_8)),
% 1.81/1.58 inference(backward_demodulation,[status(thm)],[f1705,f1746])).
% 1.81/1.58 thf(f1684,plain,(
% 1.81/1.58 ~spl0_4 | ~spl0_7 | ~spl0_9),
% 1.81/1.58 inference(avatar_contradiction_clause,[status(thm)],[f1683])).
% 1.81/1.58 thf(f1683,plain,(
% 1.81/1.58 $false | (~spl0_4 | ~spl0_7 | ~spl0_9)),
% 1.81/1.58 inference(trivial_inequality_removal,[status(thm)],[f1682])).
% 1.81/1.58 thf(f1682,plain,(
% 1.81/1.58 ($true = $false) | (~spl0_4 | ~spl0_7 | ~spl0_9)),
% 1.81/1.58 inference(forward_demodulation,[status(thm)],[f1681,f1555])).
% 1.81/1.58 thf(f1555,plain,(
% 1.81/1.58 ((sK13 @ sK22) = $false) | ~spl0_9),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f1554])).
% 1.81/1.58 thf(f1554,plain,(
% 1.81/1.58 ($false = ($true => (sK13 @ sK22))) | ~spl0_9),
% 1.81/1.58 inference(backward_demodulation,[status(thm)],[f1542,f1553])).
% 1.81/1.58 thf(f1553,plain,(
% 1.81/1.58 ($true = ((sK13 @ sK21) & (sK3 @ sK21 @ sK22))) | ~spl0_9),
% 1.81/1.58 inference(binary_proxy_clausification,[status(thm)],[f1542])).
% 1.81/1.58 thf(f1542,plain,(
% 1.81/1.58 ($false = (((sK13 @ sK21) & (sK3 @ sK21 @ sK22)) => (sK13 @ sK22))) | ~spl0_9),
% 1.81/1.58 inference(beta_eta_normalization,[status(thm)],[f1541])).
% 1.81/1.58 thf(f1541,plain,(
% 1.81/1.58 ($false = ((^[Y0 : a]: (((sK13 @ sK21) & (sK3 @ sK21 @ Y0)) => (sK13 @ Y0))) @ sK22)) | ~spl0_9),
% 1.81/1.58 inference(sigma_clausification,[status(thm)],[f1500])).
% 1.81/1.58 thf(f1500,plain,(
% 1.81/1.58 ($false = (!! @ a @ (^[Y0 : a]: (((sK13 @ sK21) & (sK3 @ sK21 @ Y0)) => (sK13 @ Y0))))) | ~spl0_9),
% 1.81/1.58 inference(beta_eta_normalization,[status(thm)],[f1498])).
% 1.81/1.58 thf(f1498,plain,(
% 1.81/1.58 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ Y0) & (sK3 @ Y0 @ Y1)) => (sK13 @ Y1))))) @ sK21)) | ~spl0_9),
% 1.81/1.58 inference(sigma_clausification,[status(thm)],[f344])).
% 1.81/1.58 thf(f344,plain,(
% 1.81/1.58 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ Y0) & (sK3 @ Y0 @ Y1)) => (sK13 @ Y1)))))) = $false) | ~spl0_9),
% 1.81/1.58 inference(avatar_component_clause,[status(thm)],[f343])).
% 1.81/1.58 thf(f343,definition,(
% 1.81/1.58 spl0_9 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ Y0) & (sK3 @ Y0 @ Y1)) => (sK13 @ Y1)))))) = $false)),
% 1.81/1.58 introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition])).
% 1.81/1.58 thf(f1681,plain,(
% 1.81/1.58 ($true = (sK13 @ sK22)) | (~spl0_4 | ~spl0_7 | ~spl0_9)),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f1680])).
% 1.81/1.58 thf(f1680,plain,(
% 1.81/1.58 ($true = ($true => (sK13 @ sK22))) | (~spl0_4 | ~spl0_7 | ~spl0_9)),
% 1.81/1.58 inference(forward_demodulation,[status(thm)],[f1677,f1665])).
% 1.81/1.58 thf(f1665,plain,(
% 1.81/1.58 ($true = (sK13 @ sK21)) | ~spl0_9),
% 1.81/1.58 inference(binary_proxy_clausification,[status(thm)],[f1553])).
% 1.81/1.58 thf(f1677,plain,(
% 1.81/1.58 ($true = ((sK13 @ sK21) => (sK13 @ sK22))) | (~spl0_4 | ~spl0_7 | ~spl0_9)),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f1676])).
% 1.81/1.58 thf(f1676,plain,(
% 1.81/1.58 ($true = (($true & (sK13 @ sK21)) => (sK13 @ sK22))) | (~spl0_4 | ~spl0_7 | ~spl0_9)),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f1674])).
% 1.81/1.58 thf(f1674,plain,(
% 1.81/1.58 ($true = ((((sK4 @ sK21 @ sK22) | $true) & (sK13 @ sK21)) => (sK13 @ sK22))) | (~spl0_4 | ~spl0_7 | ~spl0_9)),
% 1.81/1.58 inference(superposition,[status(thm)],[f1566,f1667])).
% 1.81/1.58 thf(f1667,plain,(
% 1.81/1.58 ($true = (sK3 @ sK21 @ sK22)) | ~spl0_9),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f1666])).
% 1.81/1.58 thf(f1666,plain,(
% 1.81/1.58 ($true = ($true & (sK3 @ sK21 @ sK22))) | ~spl0_9),
% 1.81/1.58 inference(backward_demodulation,[status(thm)],[f1553,f1665])).
% 1.81/1.58 thf(f1566,plain,(
% 1.81/1.58 ( ! [X2 : a,X1 : a] : (($true = ((((sK4 @ X2 @ X1) | (sK3 @ X2 @ X1)) & (sK13 @ X2)) => (sK13 @ X1)))) ) | (~spl0_4 | ~spl0_7)),
% 1.81/1.58 inference(beta_eta_normalization,[status(thm)],[f1565])).
% 1.81/1.58 thf(f1565,plain,(
% 1.81/1.58 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: ((((sK4 @ Y0 @ X1) | (sK3 @ Y0 @ X1)) & (sK13 @ Y0)) => (sK13 @ X1))) @ X2))) ) | (~spl0_4 | ~spl0_7)),
% 1.81/1.58 inference(pi_clausification,[status(thm)],[f1559])).
% 1.81/1.58 thf(f1559,plain,(
% 1.81/1.58 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: ((((sK4 @ Y0 @ X1) | (sK3 @ Y0 @ X1)) & (sK13 @ Y0)) => (sK13 @ X1)))))) ) | (~spl0_4 | ~spl0_7)),
% 1.81/1.58 inference(beta_eta_normalization,[status(thm)],[f1558])).
% 1.81/1.58 thf(f1558,plain,(
% 1.81/1.58 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK4 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) & (sK13 @ Y1)) => (sK13 @ Y0))))) @ X1))) ) | (~spl0_4 | ~spl0_7)),
% 1.81/1.58 inference(pi_clausification,[status(thm)],[f1447])).
% 1.81/1.58 thf(f1447,plain,(
% 1.81/1.58 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK4 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) & (sK13 @ Y1)) => (sK13 @ Y0))))))) | (~spl0_4 | ~spl0_7)),
% 1.81/1.58 inference(binary_proxy_clausification,[status(thm)],[f1420])).
% 1.81/1.58 thf(f1420,plain,(
% 1.81/1.58 ($true = ((!! @ a @ (^[Y0 : a]: (((sK4 @ sK12 @ Y0) | (sK3 @ sK12 @ Y0)) => (sK13 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK4 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) & (sK13 @ Y1)) => (sK13 @ Y0)))))))) | (~spl0_4 | ~spl0_7)),
% 1.81/1.58 inference(binary_proxy_clausification,[status(thm)],[f1408])).
% 1.81/1.58 thf(f1408,plain,(
% 1.81/1.58 ((((!! @ a @ (^[Y0 : a]: (((sK4 @ sK12 @ Y0) | (sK3 @ sK12 @ Y0)) => (sK13 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK4 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) & (sK13 @ Y1)) => (sK13 @ Y0))))))) => (sK13 @ sK11)) = $false) | (~spl0_4 | ~spl0_7)),
% 1.81/1.58 inference(beta_eta_normalization,[status(thm)],[f1407])).
% 1.81/1.58 thf(f1407,plain,(
% 1.81/1.58 (((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK12 @ Y1) | (sK3 @ sK12 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK4 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1))))))) => (Y0 @ sK11))) @ sK13) = $false) | (~spl0_4 | ~spl0_7)),
% 1.81/1.58 inference(sigma_clausification,[status(thm)],[f1396])).
% 1.81/1.58 thf(f1396,plain,(
% 1.81/1.58 ($false = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK12 @ Y1) | (sK3 @ sK12 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK4 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1))))))) => (Y0 @ sK11))))) | (~spl0_4 | ~spl0_7)),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f1395])).
% 1.81/1.58 thf(f1395,plain,(
% 1.81/1.58 (($true => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK12 @ Y1) | (sK3 @ sK12 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK4 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1))))))) => (Y0 @ sK11))))) = $false) | (~spl0_4 | ~spl0_7)),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f1394])).
% 1.81/1.58 thf(f1394,plain,(
% 1.81/1.58 ($false = (($true | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK4 @ sK12 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK4 @ Y1 @ Y2)) => (Y0 @ Y2))))))) => (Y0 @ sK11))))) => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK12 @ Y1) | (sK3 @ sK12 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK4 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1))))))) => (Y0 @ sK11)))))) | (~spl0_4 | ~spl0_7)),
% 1.81/1.58 inference(forward_demodulation,[status(thm)],[f1393,f241])).
% 1.81/1.58 thf(f1367,plain,(
% 1.81/1.58 ~spl0_1 | ~spl0_14),
% 1.81/1.58 inference(avatar_contradiction_clause,[status(thm)],[f1366])).
% 1.81/1.58 thf(f1366,plain,(
% 1.81/1.58 $false | (~spl0_1 | ~spl0_14)),
% 1.81/1.58 inference(trivial_inequality_removal,[status(thm)],[f1365])).
% 1.81/1.58 thf(f1365,plain,(
% 1.81/1.58 ($true = $false) | (~spl0_1 | ~spl0_14)),
% 1.81/1.58 inference(backward_demodulation,[status(thm)],[f1323,f1364])).
% 1.81/1.58 thf(f1364,plain,(
% 1.81/1.58 ((sK6 @ sK14) = $false) | (~spl0_1 | ~spl0_14)),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f1363])).
% 1.81/1.58 thf(f1363,plain,(
% 1.81/1.58 (($true => (sK6 @ sK14)) = $false) | (~spl0_1 | ~spl0_14)),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f1362])).
% 1.81/1.58 thf(f1362,plain,(
% 1.81/1.58 ((($true | (sK3 @ sK2 @ sK14)) => (sK6 @ sK14)) = $false) | (~spl0_1 | ~spl0_14)),
% 1.81/1.58 inference(forward_demodulation,[status(thm)],[f1359,f447])).
% 1.81/1.58 thf(f447,plain,(
% 1.81/1.58 ($true = (sK4 @ sK2 @ sK14)) | ~spl0_14),
% 1.81/1.58 inference(avatar_component_clause,[status(thm)],[f446])).
% 1.81/1.58 thf(f446,definition,(
% 1.81/1.58 spl0_14 <=> ($true = (sK4 @ sK2 @ sK14))),
% 1.81/1.58 introduced(definition,[new_symbols(naming,[spl0_14])],[avatar_definition])).
% 1.81/1.58 thf(f1359,plain,(
% 1.81/1.58 ((((sK4 @ sK2 @ sK14) | (sK3 @ sK2 @ sK14)) => (sK6 @ sK14)) = $false) | ~spl0_1),
% 1.81/1.58 inference(beta_eta_normalization,[status(thm)],[f1357])).
% 1.81/1.58 thf(f1357,plain,(
% 1.81/1.58 ($false = ((^[Y0 : a]: (((sK4 @ sK2 @ Y0) | (sK3 @ sK2 @ Y0)) => (sK6 @ Y0))) @ sK14)) | ~spl0_1),
% 1.81/1.58 inference(sigma_clausification,[status(thm)],[f1349])).
% 1.81/1.58 thf(f1349,plain,(
% 1.81/1.58 ((!! @ a @ (^[Y0 : a]: (((sK4 @ sK2 @ Y0) | (sK3 @ sK2 @ Y0)) => (sK6 @ Y0)))) = $false) | ~spl0_1),
% 1.81/1.58 inference(not_proxy_clausification,[status(thm)],[f1338])).
% 1.81/1.58 thf(f1338,plain,(
% 1.81/1.58 ($true = (~ (!! @ a @ (^[Y0 : a]: (((sK4 @ sK2 @ Y0) | (sK3 @ sK2 @ Y0)) => (sK6 @ Y0)))))) | ~spl0_1),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f1337])).
% 1.81/1.58 thf(f1337,plain,(
% 1.81/1.58 ($true = ((!! @ a @ (^[Y0 : a]: (((sK4 @ sK2 @ Y0) | (sK3 @ sK2 @ Y0)) => (sK6 @ Y0)))) => $false)) | ~spl0_1),
% 1.81/1.58 inference(forward_demodulation,[status(thm)],[f1335,f26])).
% 1.81/1.58 thf(f26,plain,(
% 1.81/1.58 ((sK6 @ sK5) = $false)),
% 1.81/1.58 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.81/1.58 thf(f25,plain,(
% 1.81/1.58 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & ((sK3 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0))) => (sK6 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (((sK3 @ sK2 @ Y0) | (sK4 @ sK2 @ Y0)) => (sK6 @ Y0))))) => (sK6 @ sK5)) = $false)),
% 1.81/1.58 inference(beta_eta_normalization,[status(thm)],[f24])).
% 1.81/1.58 thf(f24,plain,(
% 1.81/1.58 ($false = ((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK3 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1))) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (((sK3 @ sK2 @ Y1) | (sK4 @ sK2 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK5))) @ sK6))),
% 1.81/1.58 inference(sigma_clausification,[status(thm)],[f18])).
% 1.81/1.58 thf(f18,plain,(
% 1.81/1.58 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK3 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1))) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (((sK3 @ sK2 @ Y1) | (sK4 @ sK2 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK5)))) = $false)),
% 1.81/1.58 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.81/1.58 thf(f17,plain,(
% 1.81/1.58 ($false = ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK3 @ Y3 @ Y4)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK3 @ Y1 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y0)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK4 @ Y1 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK4 @ Y3 @ Y4)) => (Y2 @ Y4))))))) => (Y2 @ Y0))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK4 @ Y1 @ Y3) | (sK3 @ Y1 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((((sK4 @ Y4 @ Y3) | (sK3 @ Y4 @ Y3)) & (Y2 @ Y4)) => (Y2 @ Y3))))))) => (Y2 @ Y0))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & ((sK3 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4))) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y0 @ Y4) | (sK4 @ Y0 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y2)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & ((sK3 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4))) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y1 @ Y4) | (sK4 @ Y1 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y0))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK3 @ Y1 @ Y4) | (sK4 @ Y1 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK4 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y2)))))))))))) => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK2 @ Y1) | (sK3 @ sK2 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK3 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1))) => (Y0 @ Y1))))))) => (Y0 @ sK5))))) => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK3 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1))) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (((sK3 @ sK2 @ Y1) | (sK4 @ sK2 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK5))))))),
% 1.81/1.58 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.81/1.58 thf(f16,plain,(
% 1.81/1.58 (((^[Y0 : a]: ((((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & (sK3 @ Y4 @ Y5)) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: ((sK3 @ Y2 @ Y4) => (Y3 @ Y4))))) => (Y3 @ Y1)))) | (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((sK4 @ Y2 @ Y4) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & (sK4 @ Y4 @ Y5)) => (Y3 @ Y5))))))) => (Y3 @ Y1))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK4 @ Y2 @ Y4) | (sK3 @ Y2 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((((sK4 @ Y5 @ Y4) | (sK3 @ Y5 @ Y4)) & (Y3 @ Y5)) => (Y3 @ Y4))))))) => (Y3 @ Y1))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & ((sK3 @ Y6 @ Y5) | (sK4 @ Y6 @ Y5))) => (Y4 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (((sK3 @ Y1 @ Y5) | (sK4 @ Y1 @ Y5)) => (Y4 @ Y5))))) => (Y4 @ Y3)))) & (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & ((sK3 @ Y6 @ Y5) | (sK4 @ Y6 @ Y5))) => (Y4 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (((sK3 @ Y2 @ Y5) | (sK4 @ Y2 @ Y5)) => (Y4 @ Y5))))) => (Y4 @ Y1))))) => (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (((sK3 @ Y2 @ Y5) | (sK4 @ Y2 @ Y5)) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & ((sK4 @ Y5 @ Y6) | (sK3 @ Y5 @ Y6))) => (Y4 @ Y6))))))) => (Y4 @ Y3)))))))))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK4 @ sK2 @ Y2) | (sK3 @ sK2 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & ((sK3 @ Y3 @ Y2) | (sK4 @ Y3 @ Y2))) => (Y1 @ Y2))))))) => (Y1 @ Y0))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & ((sK3 @ Y3 @ Y2) | (sK4 @ Y3 @ Y2))) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (((sK3 @ sK2 @ Y2) | (sK4 @ sK2 @ Y2)) => (Y1 @ Y2))))) => (Y1 @ Y0)))))) @ sK5) = $false)),
% 1.81/1.58 inference(sigma_clausification,[status(thm)],[f15])).
% 1.81/1.58 thf(f15,plain,(
% 1.81/1.58 ((!! @ a @ (^[Y0 : a]: ((((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & (sK3 @ Y4 @ Y5)) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: ((sK3 @ Y2 @ Y4) => (Y3 @ Y4))))) => (Y3 @ Y1)))) | (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((sK4 @ Y2 @ Y4) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & (sK4 @ Y4 @ Y5)) => (Y3 @ Y5))))))) => (Y3 @ Y1))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK4 @ Y2 @ Y4) | (sK3 @ Y2 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((((sK4 @ Y5 @ Y4) | (sK3 @ Y5 @ Y4)) & (Y3 @ Y5)) => (Y3 @ Y4))))))) => (Y3 @ Y1))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & ((sK3 @ Y6 @ Y5) | (sK4 @ Y6 @ Y5))) => (Y4 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (((sK3 @ Y1 @ Y5) | (sK4 @ Y1 @ Y5)) => (Y4 @ Y5))))) => (Y4 @ Y3)))) & (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & ((sK3 @ Y6 @ Y5) | (sK4 @ Y6 @ Y5))) => (Y4 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (((sK3 @ Y2 @ Y5) | (sK4 @ Y2 @ Y5)) => (Y4 @ Y5))))) => (Y4 @ Y1))))) => (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (((sK3 @ Y2 @ Y5) | (sK4 @ Y2 @ Y5)) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & ((sK4 @ Y5 @ Y6) | (sK3 @ Y5 @ Y6))) => (Y4 @ Y6))))))) => (Y4 @ Y3)))))))))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK4 @ sK2 @ Y2) | (sK3 @ sK2 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & ((sK3 @ Y3 @ Y2) | (sK4 @ Y3 @ Y2))) => (Y1 @ Y2))))))) => (Y1 @ Y0))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & ((sK3 @ Y3 @ Y2) | (sK4 @ Y3 @ Y2))) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (((sK3 @ sK2 @ Y2) | (sK4 @ sK2 @ Y2)) => (Y1 @ Y2))))) => (Y1 @ Y0))))))) = $false)),
% 1.81/1.58 inference(beta_eta_normalization,[status(thm)],[f14])).
% 1.81/1.58 thf(f14,plain,(
% 1.81/1.58 ($false = ((^[Y0 : a > a > $o]: (!! @ a @ (^[Y1 : a]: ((((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & (sK3 @ Y5 @ Y6)) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: ((sK3 @ Y3 @ Y5) => (Y4 @ Y5))))) => (Y4 @ Y2)))) | (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y0 @ Y3 @ Y5) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & (Y0 @ Y5 @ Y6)) => (Y4 @ Y6))))))) => (Y4 @ Y2))))) => (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (((Y0 @ Y3 @ Y5) | (sK3 @ Y3 @ Y5)) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((((Y0 @ Y6 @ Y5) | (sK3 @ Y6 @ Y5)) & (Y4 @ Y6)) => (Y4 @ Y5))))))) => (Y4 @ Y2))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y5 @ Y7) & ((sK3 @ Y7 @ Y6) | (Y0 @ Y7 @ Y6))) => (Y5 @ Y6)))))) & (!! @ a @ (^[Y6 : a]: (((sK3 @ Y2 @ Y6) | (Y0 @ Y2 @ Y6)) => (Y5 @ Y6))))) => (Y5 @ Y4)))) & (!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y5 @ Y7) & ((sK3 @ Y7 @ Y6) | (Y0 @ Y7 @ Y6))) => (Y5 @ Y6)))))) & (!! @ a @ (^[Y6 : a]: (((sK3 @ Y3 @ Y6) | (Y0 @ Y3 @ Y6)) => (Y5 @ Y6))))) => (Y5 @ Y2))))) => (!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (((sK3 @ Y3 @ Y6) | (Y0 @ Y3 @ Y6)) => (Y5 @ Y6)))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y5 @ Y6) & ((Y0 @ Y6 @ Y7) | (sK3 @ Y6 @ Y7))) => (Y5 @ Y7))))))) => (Y5 @ Y4)))))))))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((Y0 @ sK2 @ Y3) | (sK3 @ sK2 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & ((sK3 @ Y4 @ Y3) | (Y0 @ Y4 @ Y3))) => (Y2 @ Y3))))))) => (Y2 @ Y1))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & ((sK3 @ Y4 @ Y3) | (Y0 @ Y4 @ Y3))) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (((sK3 @ sK2 @ Y3) | (Y0 @ sK2 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ Y1)))))))) @ sK4))),
% 1.81/1.58 inference(sigma_clausification,[status(thm)],[f13])).
% 1.81/1.58 thf(f13,plain,(
% 1.81/1.58 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ a @ (^[Y1 : a]: ((((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & (sK3 @ Y5 @ Y6)) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: ((sK3 @ Y3 @ Y5) => (Y4 @ Y5))))) => (Y4 @ Y2)))) | (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y0 @ Y3 @ Y5) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & (Y0 @ Y5 @ Y6)) => (Y4 @ Y6))))))) => (Y4 @ Y2))))) => (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (((Y0 @ Y3 @ Y5) | (sK3 @ Y3 @ Y5)) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((((Y0 @ Y6 @ Y5) | (sK3 @ Y6 @ Y5)) & (Y4 @ Y6)) => (Y4 @ Y5))))))) => (Y4 @ Y2))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y5 @ Y7) & ((sK3 @ Y7 @ Y6) | (Y0 @ Y7 @ Y6))) => (Y5 @ Y6)))))) & (!! @ a @ (^[Y6 : a]: (((sK3 @ Y2 @ Y6) | (Y0 @ Y2 @ Y6)) => (Y5 @ Y6))))) => (Y5 @ Y4)))) & (!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y5 @ Y7) & ((sK3 @ Y7 @ Y6) | (Y0 @ Y7 @ Y6))) => (Y5 @ Y6)))))) & (!! @ a @ (^[Y6 : a]: (((sK3 @ Y3 @ Y6) | (Y0 @ Y3 @ Y6)) => (Y5 @ Y6))))) => (Y5 @ Y2))))) => (!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (((sK3 @ Y3 @ Y6) | (Y0 @ Y3 @ Y6)) => (Y5 @ Y6)))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y5 @ Y6) & ((Y0 @ Y6 @ Y7) | (sK3 @ Y6 @ Y7))) => (Y5 @ Y7))))))) => (Y5 @ Y4)))))))))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((Y0 @ sK2 @ Y3) | (sK3 @ sK2 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & ((sK3 @ Y4 @ Y3) | (Y0 @ Y4 @ Y3))) => (Y2 @ Y3))))))) => (Y2 @ Y1))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & ((sK3 @ Y4 @ Y3) | (Y0 @ Y4 @ Y3))) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (((sK3 @ sK2 @ Y3) | (Y0 @ sK2 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ Y1))))))))) = $false)),
% 1.81/1.58 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.81/1.58 thf(f12,plain,(
% 1.81/1.58 ($false = ((^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ a @ (^[Y2 : a]: ((((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y5 @ Y6) & (Y0 @ Y6 @ Y7)) => (Y5 @ Y7)))))) & (!! @ a @ (^[Y6 : a]: ((Y0 @ Y4 @ Y6) => (Y5 @ Y6))))) => (Y5 @ Y3)))) | (!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: ((Y1 @ Y4 @ Y6) => (Y5 @ Y6)))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y5 @ Y6) & (Y1 @ Y6 @ Y7)) => (Y5 @ Y7))))))) => (Y5 @ Y3))))) => (!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (((Y1 @ Y4 @ Y6) | (Y0 @ Y4 @ Y6)) => (Y5 @ Y6)))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((((Y1 @ Y7 @ Y6) | (Y0 @ Y7 @ Y6)) & (Y5 @ Y7)) => (Y5 @ Y6))))))) => (Y5 @ Y3))))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y8) & ((Y0 @ Y8 @ Y7) | (Y1 @ Y8 @ Y7))) => (Y6 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: (((Y0 @ Y3 @ Y7) | (Y1 @ Y3 @ Y7)) => (Y6 @ Y7))))) => (Y6 @ Y5)))) & (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y8) & ((Y0 @ Y8 @ Y7) | (Y1 @ Y8 @ Y7))) => (Y6 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: (((Y0 @ Y4 @ Y7) | (Y1 @ Y4 @ Y7)) => (Y6 @ Y7))))) => (Y6 @ Y3))))) => (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (((Y0 @ Y4 @ Y7) | (Y1 @ Y4 @ Y7)) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y7) & ((Y1 @ Y7 @ Y8) | (Y0 @ Y7 @ Y8))) => (Y6 @ Y8))))))) => (Y6 @ Y5)))))))))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((Y1 @ sK2 @ Y4) | (Y0 @ sK2 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & ((Y0 @ Y5 @ Y4) | (Y1 @ Y5 @ Y4))) => (Y3 @ Y4))))))) => (Y3 @ Y2))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & ((Y0 @ Y5 @ Y4) | (Y1 @ Y5 @ Y4))) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (((Y0 @ sK2 @ Y4) | (Y1 @ sK2 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y2)))))))))) @ sK3))),
% 1.81/1.58 inference(sigma_clausification,[status(thm)],[f11])).
% 1.81/1.58 thf(f11,plain,(
% 1.81/1.58 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ a @ (^[Y2 : a]: ((((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y5 @ Y6) & (Y0 @ Y6 @ Y7)) => (Y5 @ Y7)))))) & (!! @ a @ (^[Y6 : a]: ((Y0 @ Y4 @ Y6) => (Y5 @ Y6))))) => (Y5 @ Y3)))) | (!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: ((Y1 @ Y4 @ Y6) => (Y5 @ Y6)))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y5 @ Y6) & (Y1 @ Y6 @ Y7)) => (Y5 @ Y7))))))) => (Y5 @ Y3))))) => (!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (((Y1 @ Y4 @ Y6) | (Y0 @ Y4 @ Y6)) => (Y5 @ Y6)))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((((Y1 @ Y7 @ Y6) | (Y0 @ Y7 @ Y6)) & (Y5 @ Y7)) => (Y5 @ Y6))))))) => (Y5 @ Y3))))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y8) & ((Y0 @ Y8 @ Y7) | (Y1 @ Y8 @ Y7))) => (Y6 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: (((Y0 @ Y3 @ Y7) | (Y1 @ Y3 @ Y7)) => (Y6 @ Y7))))) => (Y6 @ Y5)))) & (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y8) & ((Y0 @ Y8 @ Y7) | (Y1 @ Y8 @ Y7))) => (Y6 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: (((Y0 @ Y4 @ Y7) | (Y1 @ Y4 @ Y7)) => (Y6 @ Y7))))) => (Y6 @ Y3))))) => (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (((Y0 @ Y4 @ Y7) | (Y1 @ Y4 @ Y7)) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y7) & ((Y1 @ Y7 @ Y8) | (Y0 @ Y7 @ Y8))) => (Y6 @ Y8))))))) => (Y6 @ Y5)))))))))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((Y1 @ sK2 @ Y4) | (Y0 @ sK2 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & ((Y0 @ Y5 @ Y4) | (Y1 @ Y5 @ Y4))) => (Y3 @ Y4))))))) => (Y3 @ Y2))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & ((Y0 @ Y5 @ Y4) | (Y1 @ Y5 @ Y4))) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (((Y0 @ sK2 @ Y4) | (Y1 @ sK2 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y2))))))))))) = $false)),
% 1.81/1.58 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.81/1.58 thf(f10,plain,(
% 1.81/1.58 ($false = ((^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (!! @ a @ (^[Y3 : a]: ((((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y7) & (Y1 @ Y7 @ Y8)) => (Y6 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: ((Y1 @ Y5 @ Y7) => (Y6 @ Y7))))) => (Y6 @ Y4)))) | (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: ((Y2 @ Y5 @ Y7) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y7) & (Y2 @ Y7 @ Y8)) => (Y6 @ Y8))))))) => (Y6 @ Y4))))) => (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (((Y2 @ Y5 @ Y7) | (Y1 @ Y5 @ Y7)) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((((Y2 @ Y8 @ Y7) | (Y1 @ Y8 @ Y7)) & (Y6 @ Y8)) => (Y6 @ Y7))))))) => (Y6 @ Y4))))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y9) & ((Y1 @ Y9 @ Y8) | (Y2 @ Y9 @ Y8))) => (Y7 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: (((Y1 @ Y4 @ Y8) | (Y2 @ Y4 @ Y8)) => (Y7 @ Y8))))) => (Y7 @ Y6)))) & (!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y9) & ((Y1 @ Y9 @ Y8) | (Y2 @ Y9 @ Y8))) => (Y7 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: (((Y1 @ Y5 @ Y8) | (Y2 @ Y5 @ Y8)) => (Y7 @ Y8))))) => (Y7 @ Y4))))) => (!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (((Y1 @ Y5 @ Y8) | (Y2 @ Y5 @ Y8)) => (Y7 @ Y8)))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y8) & ((Y2 @ Y8 @ Y9) | (Y1 @ Y8 @ Y9))) => (Y7 @ Y9))))))) => (Y7 @ Y6)))))))))))) => (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (((Y2 @ Y0 @ Y5) | (Y1 @ Y0 @ Y5)) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & ((Y1 @ Y6 @ Y5) | (Y2 @ Y6 @ Y5))) => (Y4 @ Y5))))))) => (Y4 @ Y3))))) => (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & ((Y1 @ Y6 @ Y5) | (Y2 @ Y6 @ Y5))) => (Y4 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (((Y1 @ Y0 @ Y5) | (Y2 @ Y0 @ Y5)) => (Y4 @ Y5))))) => (Y4 @ Y3)))))))))))) @ sK2))),
% 1.81/1.58 inference(sigma_clausification,[status(thm)],[f7])).
% 1.81/1.58 thf(f7,plain,(
% 1.81/1.58 ($false = (!! @ a @ (^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (!! @ a @ (^[Y3 : a]: ((((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y7) & (Y1 @ Y7 @ Y8)) => (Y6 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: ((Y1 @ Y5 @ Y7) => (Y6 @ Y7))))) => (Y6 @ Y4)))) | (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: ((Y2 @ Y5 @ Y7) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y7) & (Y2 @ Y7 @ Y8)) => (Y6 @ Y8))))))) => (Y6 @ Y4))))) => (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (((Y2 @ Y5 @ Y7) | (Y1 @ Y5 @ Y7)) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((((Y2 @ Y8 @ Y7) | (Y1 @ Y8 @ Y7)) & (Y6 @ Y8)) => (Y6 @ Y7))))))) => (Y6 @ Y4))))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y9) & ((Y1 @ Y9 @ Y8) | (Y2 @ Y9 @ Y8))) => (Y7 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: (((Y1 @ Y4 @ Y8) | (Y2 @ Y4 @ Y8)) => (Y7 @ Y8))))) => (Y7 @ Y6)))) & (!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y9) & ((Y1 @ Y9 @ Y8) | (Y2 @ Y9 @ Y8))) => (Y7 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: (((Y1 @ Y5 @ Y8) | (Y2 @ Y5 @ Y8)) => (Y7 @ Y8))))) => (Y7 @ Y4))))) => (!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (((Y1 @ Y5 @ Y8) | (Y2 @ Y5 @ Y8)) => (Y7 @ Y8)))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y8) & ((Y2 @ Y8 @ Y9) | (Y1 @ Y8 @ Y9))) => (Y7 @ Y9))))))) => (Y7 @ Y6)))))))))))) => (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (((Y2 @ Y0 @ Y5) | (Y1 @ Y0 @ Y5)) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & ((Y1 @ Y6 @ Y5) | (Y2 @ Y6 @ Y5))) => (Y4 @ Y5))))))) => (Y4 @ Y3))))) => (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & ((Y1 @ Y6 @ Y5) | (Y2 @ Y6 @ Y5))) => (Y4 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (((Y1 @ Y0 @ Y5) | (Y2 @ Y0 @ Y5)) => (Y4 @ Y5))))) => (Y4 @ Y3))))))))))))))),
% 1.81/1.58 inference(not_proxy_clausification,[status(thm)],[f6])).
% 1.81/1.58 thf(f6,plain,(
% 1.81/1.58 ($true = (~ (!! @ a @ (^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (!! @ a @ (^[Y3 : a]: ((((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y7) & (Y1 @ Y7 @ Y8)) => (Y6 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: ((Y1 @ Y5 @ Y7) => (Y6 @ Y7))))) => (Y6 @ Y4)))) | (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: ((Y2 @ Y5 @ Y7) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y7) & (Y2 @ Y7 @ Y8)) => (Y6 @ Y8))))))) => (Y6 @ Y4))))) => (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (((Y2 @ Y5 @ Y7) | (Y1 @ Y5 @ Y7)) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((((Y2 @ Y8 @ Y7) | (Y1 @ Y8 @ Y7)) & (Y6 @ Y8)) => (Y6 @ Y7))))))) => (Y6 @ Y4))))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y9) & ((Y1 @ Y9 @ Y8) | (Y2 @ Y9 @ Y8))) => (Y7 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: (((Y1 @ Y4 @ Y8) | (Y2 @ Y4 @ Y8)) => (Y7 @ Y8))))) => (Y7 @ Y6)))) & (!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y9) & ((Y1 @ Y9 @ Y8) | (Y2 @ Y9 @ Y8))) => (Y7 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: (((Y1 @ Y5 @ Y8) | (Y2 @ Y5 @ Y8)) => (Y7 @ Y8))))) => (Y7 @ Y4))))) => (!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (((Y1 @ Y5 @ Y8) | (Y2 @ Y5 @ Y8)) => (Y7 @ Y8)))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y8) & ((Y2 @ Y8 @ Y9) | (Y1 @ Y8 @ Y9))) => (Y7 @ Y9))))))) => (Y7 @ Y6)))))))))))) => (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (((Y2 @ Y0 @ Y5) | (Y1 @ Y0 @ Y5)) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & ((Y1 @ Y6 @ Y5) | (Y2 @ Y6 @ Y5))) => (Y4 @ Y5))))))) => (Y4 @ Y3))))) => (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & ((Y1 @ Y6 @ Y5) | (Y2 @ Y6 @ Y5))) => (Y4 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (((Y1 @ Y0 @ Y5) | (Y2 @ Y0 @ Y5)) => (Y4 @ Y5))))) => (Y4 @ Y3)))))))))))))))),
% 1.81/1.58 inference(cnf_transformation,[status(thm)],[f5])).
% 1.81/1.58 thf(f5,plain,(
% 1.81/1.58 ($true = (~ (!! @ a @ (^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (!! @ a @ (^[Y3 : a]: ((((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y7) & (Y1 @ Y7 @ Y8)) => (Y6 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: ((Y1 @ Y5 @ Y7) => (Y6 @ Y7))))) => (Y6 @ Y4)))) | (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: ((Y2 @ Y5 @ Y7) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y7) & (Y2 @ Y7 @ Y8)) => (Y6 @ Y8))))))) => (Y6 @ Y4))))) => (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (((Y2 @ Y5 @ Y7) | (Y1 @ Y5 @ Y7)) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((((Y2 @ Y8 @ Y7) | (Y1 @ Y8 @ Y7)) & (Y6 @ Y8)) => (Y6 @ Y7))))))) => (Y6 @ Y4))))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y9) & ((Y1 @ Y9 @ Y8) | (Y2 @ Y9 @ Y8))) => (Y7 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: (((Y1 @ Y4 @ Y8) | (Y2 @ Y4 @ Y8)) => (Y7 @ Y8))))) => (Y7 @ Y6)))) & (!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y9) & ((Y1 @ Y9 @ Y8) | (Y2 @ Y9 @ Y8))) => (Y7 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: (((Y1 @ Y5 @ Y8) | (Y2 @ Y5 @ Y8)) => (Y7 @ Y8))))) => (Y7 @ Y4))))) => (!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (((Y1 @ Y5 @ Y8) | (Y2 @ Y5 @ Y8)) => (Y7 @ Y8)))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y8) & ((Y2 @ Y8 @ Y9) | (Y1 @ Y8 @ Y9))) => (Y7 @ Y9))))))) => (Y7 @ Y6)))))))))))) => (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (((Y2 @ Y0 @ Y5) | (Y1 @ Y0 @ Y5)) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & ((Y1 @ Y6 @ Y5) | (Y2 @ Y6 @ Y5))) => (Y4 @ Y5))))))) => (Y4 @ Y3))))) => (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & ((Y1 @ Y6 @ Y5) | (Y2 @ Y6 @ Y5))) => (Y4 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (((Y1 @ Y0 @ Y5) | (Y2 @ Y0 @ Y5)) => (Y4 @ Y5))))) => (Y4 @ Y3)))))))))))))))),
% 1.81/1.58 inference(fool_elimination,[status(thm)],[f4])).
% 1.81/1.58 thf(f4,plain,(
% 1.81/1.58 ~! [X0 : a,X1 : a > a > $o,X2 : a > a > $o,X3 : a] : (((! [X4 : a,X5 : a,X6 : a] : ((! [X7 : a > $o] : ((! [X8 : a] : (((X1 @ X5 @ X8) | (X2 @ X5 @ X8)) => (X7 @ X8)) & ! [X9 : a,X10 : a] : ((((X1 @ X9 @ X10) | (X2 @ X9 @ X10)) & (X7 @ X9)) => (X7 @ X10))) => (X7 @ X6)) & ! [X11 : a > $o] : ((! [X12 : a] : (((X1 @ X6 @ X12) | (X2 @ X6 @ X12)) => (X11 @ X12)) & ! [X13 : a,X14 : a] : ((((X1 @ X13 @ X14) | (X2 @ X13 @ X14)) & (X11 @ X13)) => (X11 @ X14))) => (X11 @ X4))) => ! [X15 : a > $o] : ((! [X16 : a,X17 : a] : ((((X2 @ X17 @ X16) | (X1 @ X17 @ X16)) & (X15 @ X17)) => (X15 @ X16)) & ! [X18 : a] : (((X1 @ X5 @ X18) | (X2 @ X5 @ X18)) => (X15 @ X18))) => (X15 @ X4))) & ! [X19 : a,X20 : a] : ((! [X21 : a > $o] : ((! [X22 : a,X23 : a] : (((X1 @ X23 @ X22) & (X21 @ X23)) => (X21 @ X22)) & ! [X24 : a] : ((X1 @ X19 @ X24) => (X21 @ X24))) => (X21 @ X20)) | ! [X25 : a > $o] : ((! [X26 : a] : ((X2 @ X19 @ X26) => (X25 @ X26)) & ! [X27 : a,X28 : a] : (((X2 @ X28 @ X27) & (X25 @ X28)) => (X25 @ X27))) => (X25 @ X20))) => ! [X29 : a > $o] : ((! [X30 : a,X31 : a] : (((X29 @ X30) & ((X2 @ X30 @ X31) | (X1 @ X30 @ X31))) => (X29 @ X31)) & ! [X32 : a] : (((X2 @ X19 @ X32) | (X1 @ X19 @ X32)) => (X29 @ X32))) => (X29 @ X20)))) => ! [X33 : a > $o] : ((! [X34 : a,X35 : a] : ((((X1 @ X34 @ X35) | (X2 @ X34 @ X35)) & (X33 @ X34)) => (X33 @ X35)) & ! [X36 : a] : (((X2 @ X3 @ X36) | (X1 @ X3 @ X36)) => (X33 @ X36))) => (X33 @ X0))) => ! [X37 : a > $o] : ((! [X38 : a] : (((X1 @ X3 @ X38) | (X2 @ X3 @ X38)) => (X37 @ X38)) & ! [X39 : a,X40 : a] : ((((X1 @ X39 @ X40) | (X2 @ X39 @ X40)) & (X37 @ X39)) => (X37 @ X40))) => (X37 @ X0)))),
% 1.81/1.58 inference(rectify,[status(thm)],[f2])).
% 1.81/1.58 thf(f2,negated_conjecture,(
% 1.81/1.58 ~! [X3 : a,X1 : a > a > $o,X0 : a > a > $o,X2 : a] : (((! [X10 : a,X4 : a,X5 : a] : ((! [X6 : a > $o] : ((! [X7 : a] : (((X1 @ X4 @ X7) | (X0 @ X4 @ X7)) => (X6 @ X7)) & ! [X8 : a,X9 : a] : ((((X1 @ X8 @ X9) | (X0 @ X8 @ X9)) & (X6 @ X8)) => (X6 @ X9))) => (X6 @ X5)) & ! [X6 : a > $o] : ((! [X7 : a] : (((X1 @ X5 @ X7) | (X0 @ X5 @ X7)) => (X6 @ X7)) & ! [X8 : a,X9 : a] : ((((X1 @ X8 @ X9) | (X0 @ X8 @ X9)) & (X6 @ X8)) => (X6 @ X9))) => (X6 @ X10))) => ! [X6 : a > $o] : ((! [X9 : a,X8 : a] : ((((X0 @ X8 @ X9) | (X1 @ X8 @ X9)) & (X6 @ X8)) => (X6 @ X9)) & ! [X7 : a] : (((X1 @ X4 @ X7) | (X0 @ X4 @ X7)) => (X6 @ X7))) => (X6 @ X10))) & ! [X4 : a,X5 : a] : ((! [X6 : a > $o] : ((! [X9 : a,X8 : a] : (((X1 @ X8 @ X9) & (X6 @ X8)) => (X6 @ X9)) & ! [X7 : a] : ((X1 @ X4 @ X7) => (X6 @ X7))) => (X6 @ X5)) | ! [X6 : a > $o] : ((! [X7 : a] : ((X0 @ X4 @ X7) => (X6 @ X7)) & ! [X9 : a,X8 : a] : (((X0 @ X8 @ X9) & (X6 @ X8)) => (X6 @ X9))) => (X6 @ X5))) => ! [X6 : a > $o] : ((! [X8 : a,X9 : a] : (((X6 @ X8) & ((X0 @ X8 @ X9) | (X1 @ X8 @ X9))) => (X6 @ X9)) & ! [X7 : a] : (((X0 @ X4 @ X7) | (X1 @ X4 @ X7)) => (X6 @ X7))) => (X6 @ X5)))) => ! [X6 : a > $o] : ((! [X8 : a,X9 : a] : ((((X1 @ X8 @ X9) | (X0 @ X8 @ X9)) & (X6 @ X8)) => (X6 @ X9)) & ! [X7 : a] : (((X0 @ X2 @ X7) | (X1 @ X2 @ X7)) => (X6 @ X7))) => (X6 @ X3))) => ! [X6 : a > $o] : ((! [X7 : a] : (((X1 @ X2 @ X7) | (X0 @ X2 @ X7)) => (X6 @ X7)) & ! [X8 : a,X9 : a] : ((((X1 @ X8 @ X9) | (X0 @ X8 @ X9)) & (X6 @ X8)) => (X6 @ X9))) => (X6 @ X3)))),
% 1.81/1.58 inference(negated_conjecture,[status(cth)],[f1])).
% 1.81/1.58 thf(f1,conjecture,(
% 1.81/1.58 ! [X3 : a,X1 : a > a > $o,X0 : a > a > $o,X2 : a] : (((! [X10 : a,X4 : a,X5 : a] : ((! [X6 : a > $o] : ((! [X7 : a] : (((X1 @ X4 @ X7) | (X0 @ X4 @ X7)) => (X6 @ X7)) & ! [X8 : a,X9 : a] : ((((X1 @ X8 @ X9) | (X0 @ X8 @ X9)) & (X6 @ X8)) => (X6 @ X9))) => (X6 @ X5)) & ! [X6 : a > $o] : ((! [X7 : a] : (((X1 @ X5 @ X7) | (X0 @ X5 @ X7)) => (X6 @ X7)) & ! [X8 : a,X9 : a] : ((((X1 @ X8 @ X9) | (X0 @ X8 @ X9)) & (X6 @ X8)) => (X6 @ X9))) => (X6 @ X10))) => ! [X6 : a > $o] : ((! [X9 : a,X8 : a] : ((((X0 @ X8 @ X9) | (X1 @ X8 @ X9)) & (X6 @ X8)) => (X6 @ X9)) & ! [X7 : a] : (((X1 @ X4 @ X7) | (X0 @ X4 @ X7)) => (X6 @ X7))) => (X6 @ X10))) & ! [X4 : a,X5 : a] : ((! [X6 : a > $o] : ((! [X9 : a,X8 : a] : (((X1 @ X8 @ X9) & (X6 @ X8)) => (X6 @ X9)) & ! [X7 : a] : ((X1 @ X4 @ X7) => (X6 @ X7))) => (X6 @ X5)) | ! [X6 : a > $o] : ((! [X7 : a] : ((X0 @ X4 @ X7) => (X6 @ X7)) & ! [X9 : a,X8 : a] : (((X0 @ X8 @ X9) & (X6 @ X8)) => (X6 @ X9))) => (X6 @ X5))) => ! [X6 : a > $o] : ((! [X8 : a,X9 : a] : (((X6 @ X8) & ((X0 @ X8 @ X9) | (X1 @ X8 @ X9))) => (X6 @ X9)) & ! [X7 : a] : (((X0 @ X4 @ X7) | (X1 @ X4 @ X7)) => (X6 @ X7))) => (X6 @ X5)))) => ! [X6 : a > $o] : ((! [X8 : a,X9 : a] : ((((X1 @ X8 @ X9) | (X0 @ X8 @ X9)) & (X6 @ X8)) => (X6 @ X9)) & ! [X7 : a] : (((X0 @ X2 @ X7) | (X1 @ X2 @ X7)) => (X6 @ X7))) => (X6 @ X3))) => ! [X6 : a > $o] : ((! [X7 : a] : (((X1 @ X2 @ X7) | (X0 @ X2 @ X7)) => (X6 @ X7)) & ! [X8 : a,X9 : a] : ((((X1 @ X8 @ X9) | (X0 @ X8 @ X9)) & (X6 @ X8)) => (X6 @ X9))) => (X6 @ X3)))),
% 1.81/1.58 file('/export/starexec/sandbox2/tmp/tmp.4pWI2wlH3y/DTF2THF_9846.p',cTHM251D_pme)).
% 1.81/1.58 thf(f1335,plain,(
% 1.81/1.58 ($true = ((!! @ a @ (^[Y0 : a]: (((sK4 @ sK2 @ Y0) | (sK3 @ sK2 @ Y0)) => (sK6 @ Y0)))) => (sK6 @ sK5))) | ~spl0_1),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f1332])).
% 1.81/1.58 thf(f1332,plain,(
% 1.81/1.58 ($true = (((!! @ a @ (^[Y0 : a]: (((sK4 @ sK2 @ Y0) | (sK3 @ sK2 @ Y0)) => (sK6 @ Y0)))) & $true) => (sK6 @ sK5))) | ~spl0_1),
% 1.81/1.58 inference(superposition,[status(thm)],[f1316,f53])).
% 1.81/1.58 thf(f53,plain,(
% 1.81/1.58 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & ((sK3 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0))) => (sK6 @ Y0)))))))),
% 1.81/1.58 inference(binary_proxy_clausification,[status(thm)],[f27])).
% 1.81/1.58 thf(f27,plain,(
% 1.81/1.58 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & ((sK3 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0))) => (sK6 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (((sK3 @ sK2 @ Y0) | (sK4 @ sK2 @ Y0)) => (sK6 @ Y0))))))),
% 1.81/1.58 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.81/1.58 thf(f1316,plain,(
% 1.81/1.58 ( ! [X1 : a > $o] : (($true = (((!! @ a @ (^[Y0 : a]: (((sK4 @ sK2 @ Y0) | (sK3 @ sK2 @ Y0)) => (X1 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((X1 @ Y1) & ((sK3 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0))) => (X1 @ Y0))))))) => (X1 @ sK5)))) ) | ~spl0_1),
% 1.81/1.58 inference(beta_eta_normalization,[status(thm)],[f1315])).
% 1.81/1.58 thf(f1315,plain,(
% 1.81/1.58 ( ! [X1 : a > $o] : (($true = ((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK2 @ Y1) | (sK3 @ sK2 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK3 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1))) => (Y0 @ Y1))))))) => (Y0 @ sK5))) @ X1))) ) | ~spl0_1),
% 1.81/1.58 inference(pi_clausification,[status(thm)],[f35])).
% 1.81/1.58 thf(f35,plain,(
% 1.81/1.58 ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK2 @ Y1) | (sK3 @ sK2 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK3 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1))) => (Y0 @ Y1))))))) => (Y0 @ sK5))))) | ~spl0_1),
% 1.81/1.58 inference(avatar_component_clause,[status(thm)],[f34])).
% 1.81/1.58 thf(f34,definition,(
% 1.81/1.58 spl0_1 <=> ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK2 @ Y1) | (sK3 @ sK2 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK3 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1))) => (Y0 @ Y1))))))) => (Y0 @ sK5)))))),
% 1.81/1.58 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.81/1.58 thf(f1323,plain,(
% 1.81/1.58 ($true = (sK6 @ sK14)) | ~spl0_14),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f1322])).
% 1.81/1.58 thf(f1322,plain,(
% 1.81/1.58 ($true = ($true => (sK6 @ sK14))) | ~spl0_14),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f1318])).
% 1.81/1.58 thf(f1318,plain,(
% 1.81/1.58 ($true = (((sK3 @ sK2 @ sK14) | $true) => (sK6 @ sK14))) | ~spl0_14),
% 1.81/1.58 inference(superposition,[status(thm)],[f59,f447])).
% 1.81/1.58 thf(f59,plain,(
% 1.81/1.58 ( ! [X1 : a] : (((((sK3 @ sK2 @ X1) | (sK4 @ sK2 @ X1)) => (sK6 @ X1)) = $true)) )),
% 1.81/1.58 inference(beta_eta_normalization,[status(thm)],[f58])).
% 1.81/1.58 thf(f58,plain,(
% 1.81/1.58 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (((sK3 @ sK2 @ Y0) | (sK4 @ sK2 @ Y0)) => (sK6 @ Y0))) @ X1))) )),
% 1.81/1.58 inference(pi_clausification,[status(thm)],[f55])).
% 1.81/1.58 thf(f55,plain,(
% 1.81/1.58 ((!! @ a @ (^[Y0 : a]: (((sK3 @ sK2 @ Y0) | (sK4 @ sK2 @ Y0)) => (sK6 @ Y0)))) = $true)),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f54])).
% 1.81/1.58 thf(f54,plain,(
% 1.81/1.58 ($true = ($true & (!! @ a @ (^[Y0 : a]: (((sK3 @ sK2 @ Y0) | (sK4 @ sK2 @ Y0)) => (sK6 @ Y0))))))),
% 1.81/1.58 inference(backward_demodulation,[status(thm)],[f27,f53])).
% 1.81/1.58 thf(f1308,plain,(
% 1.81/1.58 spl0_31 | ~spl0_3 | ~spl0_17 | ~spl0_20),
% 1.81/1.58 inference(avatar_split_clause,[status(thm)],[f1307,f760,f681,f44,f1249])).
% 1.81/1.58 thf(f1249,definition,(
% 1.81/1.58 spl0_31 <=> ($false = (sK10 @ sK7))),
% 1.81/1.58 introduced(definition,[new_symbols(naming,[spl0_31])],[avatar_definition])).
% 1.81/1.58 thf(f44,definition,(
% 1.81/1.58 spl0_3 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & ((sK3 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4))) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y0 @ Y4) | (sK4 @ Y0 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y2)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & ((sK3 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4))) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y1 @ Y4) | (sK4 @ Y1 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y0))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK3 @ Y1 @ Y4) | (sK4 @ Y1 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK4 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y2))))))))))) = $false)),
% 1.81/1.58 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.81/1.58 thf(f681,definition,(
% 1.81/1.58 spl0_17 <=> ((!! @ a @ (^[Y0 : a]: (((sK3 @ sK7 @ Y0) | (sK4 @ sK7 @ Y0)) => (sK10 @ Y0)))) = $false)),
% 1.81/1.58 introduced(definition,[new_symbols(naming,[spl0_17])],[avatar_definition])).
% 1.81/1.58 thf(f760,definition,(
% 1.81/1.58 spl0_20 <=> ($true = (sK3 @ sK7 @ sK15))),
% 1.81/1.58 introduced(definition,[new_symbols(naming,[spl0_20])],[avatar_definition])).
% 1.81/1.58 thf(f1307,plain,(
% 1.81/1.58 ($false = (sK10 @ sK7)) | (~spl0_3 | ~spl0_17 | ~spl0_20)),
% 1.81/1.58 inference(trivial_inequality_removal,[status(thm)],[f1306])).
% 1.81/1.58 thf(f1306,plain,(
% 1.81/1.58 ($false = (sK10 @ sK7)) | ($true = $false) | (~spl0_3 | ~spl0_17 | ~spl0_20)),
% 1.81/1.58 inference(forward_demodulation,[status(thm)],[f1279,f737])).
% 1.81/1.58 thf(f737,plain,(
% 1.81/1.58 ((sK10 @ sK15) = $false) | ~spl0_17),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f736])).
% 1.81/1.58 thf(f736,plain,(
% 1.81/1.58 ($false = ($true => (sK10 @ sK15))) | ~spl0_17),
% 1.81/1.58 inference(backward_demodulation,[status(thm)],[f711,f735])).
% 1.81/1.58 thf(f735,plain,(
% 1.81/1.58 ($true = ((sK3 @ sK7 @ sK15) | (sK4 @ sK7 @ sK15))) | ~spl0_17),
% 1.81/1.58 inference(binary_proxy_clausification,[status(thm)],[f711])).
% 1.81/1.58 thf(f711,plain,(
% 1.81/1.58 ((((sK3 @ sK7 @ sK15) | (sK4 @ sK7 @ sK15)) => (sK10 @ sK15)) = $false) | ~spl0_17),
% 1.81/1.58 inference(beta_eta_normalization,[status(thm)],[f709])).
% 1.81/1.58 thf(f709,plain,(
% 1.81/1.58 (((^[Y0 : a]: (((sK3 @ sK7 @ Y0) | (sK4 @ sK7 @ Y0)) => (sK10 @ Y0))) @ sK15) = $false) | ~spl0_17),
% 1.81/1.58 inference(sigma_clausification,[status(thm)],[f682])).
% 1.81/1.58 thf(f682,plain,(
% 1.81/1.58 ((!! @ a @ (^[Y0 : a]: (((sK3 @ sK7 @ Y0) | (sK4 @ sK7 @ Y0)) => (sK10 @ Y0)))) = $false) | ~spl0_17),
% 1.81/1.58 inference(avatar_component_clause,[status(thm)],[f681])).
% 1.81/1.58 thf(f1279,plain,(
% 1.81/1.58 ($false = (sK10 @ sK7)) | ($true = (sK10 @ sK15)) | (~spl0_3 | ~spl0_20)),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f1278])).
% 1.81/1.58 thf(f1278,plain,(
% 1.81/1.58 ($true = (sK10 @ sK15)) | (((sK10 @ sK7) & $true) = $false) | (~spl0_3 | ~spl0_20)),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f1271])).
% 1.81/1.58 thf(f1271,plain,(
% 1.81/1.58 ($false = ((sK10 @ sK7) & ((sK4 @ sK7 @ sK15) | $true))) | ($true = (sK10 @ sK15)) | (~spl0_3 | ~spl0_20)),
% 1.81/1.58 inference(superposition,[status(thm)],[f561,f761])).
% 1.81/1.58 thf(f761,plain,(
% 1.81/1.58 ($true = (sK3 @ sK7 @ sK15)) | ~spl0_20),
% 1.81/1.58 inference(avatar_component_clause,[status(thm)],[f760])).
% 1.81/1.58 thf(f561,plain,(
% 1.81/1.58 ( ! [X2 : a,X1 : a] : ((((sK10 @ X1) & ((sK4 @ X1 @ X2) | (sK3 @ X1 @ X2))) = $false) | ((sK10 @ X2) = $true)) ) | ~spl0_3),
% 1.81/1.58 inference(binary_proxy_clausification,[status(thm)],[f550])).
% 1.81/1.58 thf(f550,plain,(
% 1.81/1.58 ( ! [X2 : a,X1 : a] : (($true = (((sK10 @ X1) & ((sK4 @ X1 @ X2) | (sK3 @ X1 @ X2))) => (sK10 @ X2)))) ) | ~spl0_3),
% 1.81/1.58 inference(beta_eta_normalization,[status(thm)],[f549])).
% 1.81/1.58 thf(f549,plain,(
% 1.81/1.58 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: (((sK10 @ X1) & ((sK4 @ X1 @ Y0) | (sK3 @ X1 @ Y0))) => (sK10 @ Y0))) @ X2) = $true)) ) | ~spl0_3),
% 1.81/1.58 inference(pi_clausification,[status(thm)],[f539])).
% 1.81/1.58 thf(f539,plain,(
% 1.81/1.58 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (((sK10 @ X1) & ((sK4 @ X1 @ Y0) | (sK3 @ X1 @ Y0))) => (sK10 @ Y0)))))) ) | ~spl0_3),
% 1.81/1.58 inference(beta_eta_normalization,[status(thm)],[f538])).
% 1.81/1.58 thf(f538,plain,(
% 1.81/1.58 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((sK4 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1))) => (sK10 @ Y1))))) @ X1) = $true)) ) | ~spl0_3),
% 1.81/1.58 inference(pi_clausification,[status(thm)],[f527])).
% 1.81/1.58 thf(f527,plain,(
% 1.81/1.58 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((sK4 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1))) => (sK10 @ Y1))))))) | ~spl0_3),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f526])).
% 1.81/1.58 thf(f526,plain,(
% 1.81/1.58 ($true = ($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((sK4 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1))) => (sK10 @ Y1)))))))) | ~spl0_3),
% 1.81/1.58 inference(backward_demodulation,[status(thm)],[f519,f525])).
% 1.81/1.58 thf(f525,plain,(
% 1.81/1.58 ($true = (!! @ a @ (^[Y0 : a]: (((sK3 @ sK8 @ Y0) | (sK4 @ sK8 @ Y0)) => (sK10 @ Y0))))) | ~spl0_3),
% 1.81/1.58 inference(binary_proxy_clausification,[status(thm)],[f519])).
% 1.81/1.58 thf(f519,plain,(
% 1.81/1.58 ($true = ((!! @ a @ (^[Y0 : a]: (((sK3 @ sK8 @ Y0) | (sK4 @ sK8 @ Y0)) => (sK10 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((sK4 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1))) => (sK10 @ Y1)))))))) | ~spl0_3),
% 1.81/1.58 inference(binary_proxy_clausification,[status(thm)],[f507])).
% 1.81/1.58 thf(f507,plain,(
% 1.81/1.58 ((((!! @ a @ (^[Y0 : a]: (((sK3 @ sK8 @ Y0) | (sK4 @ sK8 @ Y0)) => (sK10 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((sK4 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1))) => (sK10 @ Y1))))))) => (sK10 @ sK9)) = $false) | ~spl0_3),
% 1.81/1.58 inference(beta_eta_normalization,[status(thm)],[f506])).
% 1.81/1.58 thf(f506,plain,(
% 1.81/1.58 ($false = ((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK3 @ sK8 @ Y1) | (sK4 @ sK8 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK4 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK9))) @ sK10)) | ~spl0_3),
% 1.81/1.58 inference(sigma_clausification,[status(thm)],[f496])).
% 1.81/1.58 thf(f496,plain,(
% 1.81/1.58 ($false = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK3 @ sK8 @ Y1) | (sK4 @ sK8 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK4 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK9))))) | ~spl0_3),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f495])).
% 1.81/1.58 thf(f495,plain,(
% 1.81/1.58 ($false = ($true => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK3 @ sK8 @ Y1) | (sK4 @ sK8 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK4 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK9)))))) | ~spl0_3),
% 1.81/1.58 inference(backward_demodulation,[status(thm)],[f484,f494])).
% 1.81/1.58 thf(f494,plain,(
% 1.81/1.58 ($true = ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK3 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1))) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (((sK3 @ sK7 @ Y1) | (sK4 @ sK7 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK9)))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK3 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1))) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (((sK3 @ sK8 @ Y1) | (sK4 @ sK8 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK7)))))) | ~spl0_3),
% 1.81/1.58 inference(binary_proxy_clausification,[status(thm)],[f484])).
% 1.81/1.58 thf(f484,plain,(
% 1.81/1.58 ((((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK3 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1))) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (((sK3 @ sK7 @ Y1) | (sK4 @ sK7 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK9)))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK3 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1))) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (((sK3 @ sK8 @ Y1) | (sK4 @ sK8 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK7))))) => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK3 @ sK8 @ Y1) | (sK4 @ sK8 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK4 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK9))))) = $false) | ~spl0_3),
% 1.81/1.58 inference(beta_eta_normalization,[status(thm)],[f483])).
% 1.81/1.58 thf(f483,plain,(
% 1.81/1.58 (((^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & ((sK3 @ Y3 @ Y2) | (sK4 @ Y3 @ Y2))) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (((sK3 @ sK7 @ Y2) | (sK4 @ sK7 @ Y2)) => (Y1 @ Y2))))) => (Y1 @ Y0)))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & ((sK3 @ Y3 @ Y2) | (sK4 @ Y3 @ Y2))) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (((sK3 @ sK8 @ Y2) | (sK4 @ sK8 @ Y2)) => (Y1 @ Y2))))) => (Y1 @ sK7))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK3 @ sK8 @ Y2) | (sK4 @ sK8 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((sK4 @ Y2 @ Y3) | (sK3 @ Y2 @ Y3))) => (Y1 @ Y3))))))) => (Y1 @ Y0)))))) @ sK9) = $false) | ~spl0_3),
% 1.81/1.58 inference(sigma_clausification,[status(thm)],[f471])).
% 1.81/1.58 thf(f471,plain,(
% 1.81/1.58 ($false = (!! @ a @ (^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & ((sK3 @ Y3 @ Y2) | (sK4 @ Y3 @ Y2))) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (((sK3 @ sK7 @ Y2) | (sK4 @ sK7 @ Y2)) => (Y1 @ Y2))))) => (Y1 @ Y0)))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & ((sK3 @ Y3 @ Y2) | (sK4 @ Y3 @ Y2))) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (((sK3 @ sK8 @ Y2) | (sK4 @ sK8 @ Y2)) => (Y1 @ Y2))))) => (Y1 @ sK7))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK3 @ sK8 @ Y2) | (sK4 @ sK8 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((sK4 @ Y2 @ Y3) | (sK3 @ Y2 @ Y3))) => (Y1 @ Y3))))))) => (Y1 @ Y0)))))))) | ~spl0_3),
% 1.81/1.58 inference(beta_eta_normalization,[status(thm)],[f470])).
% 1.81/1.58 thf(f470,plain,(
% 1.81/1.58 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & ((sK3 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3))) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (((sK3 @ sK7 @ Y3) | (sK4 @ sK7 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ Y1)))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & ((sK3 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3))) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (((sK3 @ Y0 @ Y3) | (sK4 @ Y0 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ sK7))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK3 @ Y0 @ Y3) | (sK4 @ Y0 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK4 @ Y3 @ Y4) | (sK3 @ Y3 @ Y4))) => (Y2 @ Y4))))))) => (Y2 @ Y1)))))))) @ sK8)) | ~spl0_3),
% 1.81/1.58 inference(sigma_clausification,[status(thm)],[f461])).
% 1.81/1.58 thf(f461,plain,(
% 1.81/1.58 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & ((sK3 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3))) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (((sK3 @ sK7 @ Y3) | (sK4 @ sK7 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ Y1)))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & ((sK3 @ Y4 @ Y3) | (sK4 @ Y4 @ Y3))) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (((sK3 @ Y0 @ Y3) | (sK4 @ Y0 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ sK7))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK3 @ Y0 @ Y3) | (sK4 @ Y0 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK4 @ Y3 @ Y4) | (sK3 @ Y3 @ Y4))) => (Y2 @ Y4))))))) => (Y2 @ Y1)))))))))) | ~spl0_3),
% 1.81/1.58 inference(beta_eta_normalization,[status(thm)],[f460])).
% 1.81/1.58 thf(f460,plain,(
% 1.81/1.58 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & ((sK3 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4))) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y0 @ Y4) | (sK4 @ Y0 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y2)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & ((sK3 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4))) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y1 @ Y4) | (sK4 @ Y1 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y0))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK3 @ Y1 @ Y4) | (sK4 @ Y1 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK4 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y2)))))))))) @ sK7)) | ~spl0_3),
% 1.81/1.58 inference(sigma_clausification,[status(thm)],[f45])).
% 1.81/1.58 thf(f45,plain,(
% 1.81/1.58 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & ((sK3 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4))) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y0 @ Y4) | (sK4 @ Y0 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y2)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & ((sK3 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4))) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y1 @ Y4) | (sK4 @ Y1 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y0))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK3 @ Y1 @ Y4) | (sK4 @ Y1 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK4 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y2))))))))))) = $false) | ~spl0_3),
% 1.81/1.58 inference(avatar_component_clause,[status(thm)],[f44])).
% 1.81/1.58 thf(f1304,plain,(
% 1.81/1.58 spl0_18 | ~spl0_3 | ~spl0_31),
% 1.81/1.58 inference(avatar_split_clause,[status(thm)],[f1303,f1249,f44,f684])).
% 1.81/1.58 thf(f684,definition,(
% 1.81/1.58 spl0_18 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y1) & ((sK3 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0))) => (sK10 @ Y0)))))) = $false)),
% 1.81/1.58 introduced(definition,[new_symbols(naming,[spl0_18])],[avatar_definition])).
% 1.81/1.58 thf(f1303,plain,(
% 1.81/1.58 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y1) & ((sK3 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0))) => (sK10 @ Y0)))))) = $false) | (~spl0_3 | ~spl0_31)),
% 1.81/1.58 inference(not_proxy_clausification,[status(thm)],[f1259])).
% 1.81/1.58 thf(f1259,plain,(
% 1.81/1.58 ($true = (~ (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y1) & ((sK3 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0))) => (sK10 @ Y0)))))))) | (~spl0_3 | ~spl0_31)),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f1257])).
% 1.81/1.58 thf(f1257,plain,(
% 1.81/1.58 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y1) & ((sK3 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0))) => (sK10 @ Y0)))))) => $false)) | (~spl0_3 | ~spl0_31)),
% 1.81/1.58 inference(backward_demodulation,[status(thm)],[f769,f1250])).
% 1.81/1.58 thf(f1250,plain,(
% 1.81/1.58 ($false = (sK10 @ sK7)) | ~spl0_31),
% 1.81/1.58 inference(avatar_component_clause,[status(thm)],[f1249])).
% 1.81/1.58 thf(f769,plain,(
% 1.81/1.58 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y1) & ((sK3 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0))) => (sK10 @ Y0)))))) => (sK10 @ sK7))) | ~spl0_3),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f767])).
% 1.81/1.58 thf(f767,plain,(
% 1.81/1.58 ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y1) & ((sK3 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0))) => (sK10 @ Y0)))))) & $true) => (sK10 @ sK7))) | ~spl0_3),
% 1.81/1.58 inference(superposition,[status(thm)],[f748,f525])).
% 1.81/1.58 thf(f748,plain,(
% 1.81/1.58 ( ! [X1 : a > $o] : (($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((X1 @ Y1) & ((sK3 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0))) => (X1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (((sK3 @ sK8 @ Y0) | (sK4 @ sK8 @ Y0)) => (X1 @ Y0))))) => (X1 @ sK7)))) ) | ~spl0_3),
% 1.81/1.58 inference(beta_eta_normalization,[status(thm)],[f747])).
% 1.81/1.58 thf(f747,plain,(
% 1.81/1.58 ( ! [X1 : a > $o] : (($true = ((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK3 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1))) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (((sK3 @ sK8 @ Y1) | (sK4 @ sK8 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK7))) @ X1))) ) | ~spl0_3),
% 1.81/1.58 inference(pi_clausification,[status(thm)],[f610])).
% 1.81/1.58 thf(f610,plain,(
% 1.81/1.58 ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK3 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1))) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (((sK3 @ sK8 @ Y1) | (sK4 @ sK8 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK7))))) | ~spl0_3),
% 1.81/1.58 inference(binary_proxy_clausification,[status(thm)],[f494])).
% 1.81/1.58 thf(f1245,plain,(
% 1.81/1.58 ~spl0_3 | ~spl0_18 | ~spl0_29),
% 1.81/1.58 inference(avatar_contradiction_clause,[status(thm)],[f1244])).
% 1.81/1.58 thf(f1244,plain,(
% 1.81/1.58 $false | (~spl0_3 | ~spl0_18 | ~spl0_29)),
% 1.81/1.58 inference(trivial_inequality_removal,[status(thm)],[f1243])).
% 1.81/1.58 thf(f1243,plain,(
% 1.81/1.58 ($true = $false) | (~spl0_3 | ~spl0_18 | ~spl0_29)),
% 1.81/1.58 inference(backward_demodulation,[status(thm)],[f1169,f1242])).
% 1.81/1.58 thf(f1242,plain,(
% 1.81/1.58 ((sK10 @ sK20) = $false) | (~spl0_3 | ~spl0_18 | ~spl0_29)),
% 1.81/1.58 inference(trivial_inequality_removal,[status(thm)],[f1241])).
% 1.81/1.58 thf(f1241,plain,(
% 1.81/1.58 ((sK10 @ sK20) = $false) | ($true = $false) | (~spl0_3 | ~spl0_18 | ~spl0_29)),
% 1.81/1.58 inference(forward_demodulation,[status(thm)],[f1238,f1119])).
% 1.81/1.58 thf(f1119,plain,(
% 1.81/1.58 ($false = (sK10 @ sK18)) | ~spl0_18),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f1118])).
% 1.81/1.58 thf(f1118,plain,(
% 1.81/1.58 ($false = ($true => (sK10 @ sK18))) | ~spl0_18),
% 1.81/1.58 inference(backward_demodulation,[status(thm)],[f1102,f1117])).
% 1.81/1.58 thf(f1117,plain,(
% 1.81/1.58 ($true = ((sK10 @ sK19) & ((sK3 @ sK19 @ sK18) | (sK4 @ sK19 @ sK18)))) | ~spl0_18),
% 1.81/1.58 inference(binary_proxy_clausification,[status(thm)],[f1102])).
% 1.81/1.58 thf(f1102,plain,(
% 1.81/1.58 ((((sK10 @ sK19) & ((sK3 @ sK19 @ sK18) | (sK4 @ sK19 @ sK18))) => (sK10 @ sK18)) = $false) | ~spl0_18),
% 1.81/1.58 inference(beta_eta_normalization,[status(thm)],[f1101])).
% 1.81/1.58 thf(f1101,plain,(
% 1.81/1.58 (((^[Y0 : a]: (((sK10 @ Y0) & ((sK3 @ Y0 @ sK18) | (sK4 @ Y0 @ sK18))) => (sK10 @ sK18))) @ sK19) = $false) | ~spl0_18),
% 1.81/1.58 inference(sigma_clausification,[status(thm)],[f1084])).
% 1.81/1.58 thf(f1084,plain,(
% 1.81/1.58 ($false = (!! @ a @ (^[Y0 : a]: (((sK10 @ Y0) & ((sK3 @ Y0 @ sK18) | (sK4 @ Y0 @ sK18))) => (sK10 @ sK18))))) | ~spl0_18),
% 1.81/1.58 inference(beta_eta_normalization,[status(thm)],[f1079])).
% 1.81/1.58 thf(f1079,plain,(
% 1.81/1.58 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y1) & ((sK3 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0))) => (sK10 @ Y0))))) @ sK18) = $false) | ~spl0_18),
% 1.81/1.58 inference(sigma_clausification,[status(thm)],[f685])).
% 1.81/1.58 thf(f685,plain,(
% 1.81/1.58 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y1) & ((sK3 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0))) => (sK10 @ Y0)))))) = $false) | ~spl0_18),
% 1.81/1.58 inference(avatar_component_clause,[status(thm)],[f684])).
% 1.81/1.58 thf(f1238,plain,(
% 1.81/1.58 ((sK10 @ sK20) = $false) | ($true = (sK10 @ sK18)) | (~spl0_3 | ~spl0_29)),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f1237])).
% 1.81/1.58 thf(f1237,plain,(
% 1.81/1.58 (((sK10 @ sK20) & $true) = $false) | ($true = (sK10 @ sK18)) | (~spl0_3 | ~spl0_29)),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f1232])).
% 1.81/1.58 thf(f1232,plain,(
% 1.81/1.58 ($true = (sK10 @ sK18)) | (((sK10 @ sK20) & ((sK4 @ sK20 @ sK18) | $true)) = $false) | (~spl0_3 | ~spl0_29)),
% 1.81/1.58 inference(superposition,[status(thm)],[f561,f1189])).
% 1.81/1.58 thf(f1189,plain,(
% 1.81/1.58 ($true = (sK3 @ sK20 @ sK18)) | ~spl0_29),
% 1.81/1.58 inference(avatar_component_clause,[status(thm)],[f1188])).
% 1.81/1.58 thf(f1188,definition,(
% 1.81/1.58 spl0_29 <=> ($true = (sK3 @ sK20 @ sK18))),
% 1.81/1.58 introduced(definition,[new_symbols(naming,[spl0_29])],[avatar_definition])).
% 1.81/1.58 thf(f1169,plain,(
% 1.81/1.58 ($true = (sK10 @ sK20)) | ~spl0_18),
% 1.81/1.58 inference(binary_proxy_clausification,[status(thm)],[f1153])).
% 1.81/1.58 thf(f1153,plain,(
% 1.81/1.58 ($true = ((sK10 @ sK20) & ((sK3 @ sK20 @ sK18) | (sK4 @ sK20 @ sK18)))) | ~spl0_18),
% 1.81/1.58 inference(not_proxy_clausification,[status(thm)],[f1136])).
% 1.81/1.58 thf(f1136,plain,(
% 1.81/1.58 ($false = (~ ((sK10 @ sK20) & ((sK3 @ sK20 @ sK18) | (sK4 @ sK20 @ sK18))))) | ~spl0_18),
% 1.81/1.58 inference(beta_eta_normalization,[status(thm)],[f1135])).
% 1.81/1.58 thf(f1135,plain,(
% 1.81/1.58 ($false = ((^[Y0 : a]: (~ ((sK10 @ Y0) & ((sK3 @ Y0 @ sK18) | (sK4 @ Y0 @ sK18))))) @ sK20)) | ~spl0_18),
% 1.81/1.58 inference(sigma_clausification,[status(thm)],[f1121])).
% 1.81/1.58 thf(f1121,plain,(
% 1.81/1.58 ($false = (!! @ a @ (^[Y0 : a]: (~ ((sK10 @ Y0) & ((sK3 @ Y0 @ sK18) | (sK4 @ Y0 @ sK18))))))) | ~spl0_18),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f1120])).
% 1.81/1.58 thf(f1120,plain,(
% 1.81/1.58 ((!! @ a @ (^[Y0 : a]: (((sK10 @ Y0) & ((sK3 @ Y0 @ sK18) | (sK4 @ Y0 @ sK18))) => $false))) = $false) | ~spl0_18),
% 1.81/1.58 inference(backward_demodulation,[status(thm)],[f1084,f1119])).
% 1.81/1.58 thf(f1217,plain,(
% 1.81/1.58 ~spl0_3 | ~spl0_18 | ~spl0_30),
% 1.81/1.58 inference(avatar_contradiction_clause,[status(thm)],[f1216])).
% 1.81/1.58 thf(f1216,plain,(
% 1.81/1.58 $false | (~spl0_3 | ~spl0_18 | ~spl0_30)),
% 1.81/1.58 inference(trivial_inequality_removal,[status(thm)],[f1215])).
% 1.81/1.58 thf(f1215,plain,(
% 1.81/1.58 ($true = $false) | (~spl0_3 | ~spl0_18 | ~spl0_30)),
% 1.81/1.58 inference(backward_demodulation,[status(thm)],[f1169,f1214])).
% 1.81/1.58 thf(f1214,plain,(
% 1.81/1.58 ((sK10 @ sK20) = $false) | (~spl0_3 | ~spl0_18 | ~spl0_30)),
% 1.81/1.58 inference(trivial_inequality_removal,[status(thm)],[f1213])).
% 1.81/1.58 thf(f1213,plain,(
% 1.81/1.58 ((sK10 @ sK20) = $false) | ($true = $false) | (~spl0_3 | ~spl0_18 | ~spl0_30)),
% 1.81/1.58 inference(forward_demodulation,[status(thm)],[f1205,f1119])).
% 1.81/1.58 thf(f1205,plain,(
% 1.81/1.58 ($true = (sK10 @ sK18)) | ((sK10 @ sK20) = $false) | (~spl0_3 | ~spl0_30)),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f1204])).
% 1.81/1.58 thf(f1204,plain,(
% 1.81/1.58 ($true = (sK10 @ sK18)) | (((sK10 @ sK20) & $true) = $false) | (~spl0_3 | ~spl0_30)),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f1199])).
% 1.81/1.58 thf(f1199,plain,(
% 1.81/1.58 (((sK10 @ sK20) & ($true | (sK3 @ sK20 @ sK18))) = $false) | ($true = (sK10 @ sK18)) | (~spl0_3 | ~spl0_30)),
% 1.81/1.58 inference(superposition,[status(thm)],[f561,f1192])).
% 1.81/1.58 thf(f1192,plain,(
% 1.81/1.58 ($true = (sK4 @ sK20 @ sK18)) | ~spl0_30),
% 1.81/1.58 inference(avatar_component_clause,[status(thm)],[f1191])).
% 1.81/1.58 thf(f1191,definition,(
% 1.81/1.58 spl0_30 <=> ($true = (sK4 @ sK20 @ sK18))),
% 1.81/1.58 introduced(definition,[new_symbols(naming,[spl0_30])],[avatar_definition])).
% 1.81/1.58 thf(f1193,plain,(
% 1.81/1.58 spl0_29 | spl0_30 | ~spl0_18),
% 1.81/1.58 inference(avatar_split_clause,[status(thm)],[f1184,f684,f1191,f1188])).
% 1.81/1.58 thf(f1184,plain,(
% 1.81/1.58 ($true = (sK3 @ sK20 @ sK18)) | ($true = (sK4 @ sK20 @ sK18)) | ~spl0_18),
% 1.81/1.58 inference(binary_proxy_clausification,[status(thm)],[f1171])).
% 1.81/1.58 thf(f1171,plain,(
% 1.81/1.58 ($true = ((sK3 @ sK20 @ sK18) | (sK4 @ sK20 @ sK18))) | ~spl0_18),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f1170])).
% 1.81/1.58 thf(f1170,plain,(
% 1.81/1.58 ($true = ($true & ((sK3 @ sK20 @ sK18) | (sK4 @ sK20 @ sK18)))) | ~spl0_18),
% 1.81/1.58 inference(backward_demodulation,[status(thm)],[f1153,f1169])).
% 1.81/1.58 thf(f1067,plain,(
% 1.81/1.58 spl0_18 | ~spl0_3 | ~spl0_17 | ~spl0_19),
% 1.81/1.58 inference(avatar_split_clause,[status(thm)],[f1066,f757,f681,f44,f684])).
% 1.81/1.58 thf(f757,definition,(
% 1.81/1.58 spl0_19 <=> ($true = (sK4 @ sK7 @ sK15))),
% 1.81/1.58 introduced(definition,[new_symbols(naming,[spl0_19])],[avatar_definition])).
% 1.81/1.58 thf(f1066,plain,(
% 1.81/1.58 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y1) & ((sK3 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0))) => (sK10 @ Y0)))))) = $false) | (~spl0_3 | ~spl0_17 | ~spl0_19)),
% 1.81/1.58 inference(not_proxy_clausification,[status(thm)],[f800])).
% 1.81/1.58 thf(f800,plain,(
% 1.81/1.58 ($true = (~ (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y1) & ((sK3 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0))) => (sK10 @ Y0)))))))) | (~spl0_3 | ~spl0_17 | ~spl0_19)),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f799])).
% 1.81/1.58 thf(f799,plain,(
% 1.81/1.58 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y1) & ((sK3 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0))) => (sK10 @ Y0)))))) => $false)) | (~spl0_3 | ~spl0_17 | ~spl0_19)),
% 1.81/1.58 inference(backward_demodulation,[status(thm)],[f769,f797])).
% 1.81/1.58 thf(f797,plain,(
% 1.81/1.58 ($false = (sK10 @ sK7)) | (~spl0_3 | ~spl0_17 | ~spl0_19)),
% 1.81/1.58 inference(not_proxy_clausification,[status(thm)],[f794])).
% 1.81/1.58 thf(f794,plain,(
% 1.81/1.58 ($true = (~ (sK10 @ sK7))) | (~spl0_3 | ~spl0_17 | ~spl0_19)),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f793])).
% 1.81/1.58 thf(f793,plain,(
% 1.81/1.58 ($true = ((sK10 @ sK7) => $false)) | (~spl0_3 | ~spl0_17 | ~spl0_19)),
% 1.81/1.58 inference(forward_demodulation,[status(thm)],[f792,f737])).
% 1.81/1.58 thf(f792,plain,(
% 1.81/1.58 ($true = ((sK10 @ sK7) => (sK10 @ sK15))) | (~spl0_3 | ~spl0_19)),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f791])).
% 1.81/1.58 thf(f791,plain,(
% 1.81/1.58 ($true = (((sK10 @ sK7) & $true) => (sK10 @ sK15))) | (~spl0_3 | ~spl0_19)),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f785])).
% 1.81/1.58 thf(f785,plain,(
% 1.81/1.58 ($true = (((sK10 @ sK7) & ($true | (sK3 @ sK7 @ sK15))) => (sK10 @ sK15))) | (~spl0_3 | ~spl0_19)),
% 1.81/1.58 inference(superposition,[status(thm)],[f550,f758])).
% 1.81/1.58 thf(f758,plain,(
% 1.81/1.58 ($true = (sK4 @ sK7 @ sK15)) | ~spl0_19),
% 1.81/1.58 inference(avatar_component_clause,[status(thm)],[f757])).
% 1.81/1.58 thf(f762,plain,(
% 1.81/1.58 spl0_19 | spl0_20 | ~spl0_17),
% 1.81/1.58 inference(avatar_split_clause,[status(thm)],[f749,f681,f760,f757])).
% 1.81/1.58 thf(f749,plain,(
% 1.81/1.58 ($true = (sK4 @ sK7 @ sK15)) | ($true = (sK3 @ sK7 @ sK15)) | ~spl0_17),
% 1.81/1.58 inference(binary_proxy_clausification,[status(thm)],[f735])).
% 1.81/1.58 thf(f686,plain,(
% 1.81/1.58 spl0_17 | spl0_18 | ~spl0_3),
% 1.81/1.58 inference(avatar_split_clause,[status(thm)],[f677,f44,f684,f681])).
% 1.81/1.58 thf(f677,plain,(
% 1.81/1.58 ((!! @ a @ (^[Y0 : a]: (((sK3 @ sK7 @ Y0) | (sK4 @ sK7 @ Y0)) => (sK10 @ Y0)))) = $false) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y1) & ((sK3 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0))) => (sK10 @ Y0)))))) = $false) | ~spl0_3),
% 1.81/1.58 inference(binary_proxy_clausification,[status(thm)],[f665])).
% 1.81/1.58 thf(f665,plain,(
% 1.81/1.58 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y1) & ((sK3 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0))) => (sK10 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (((sK3 @ sK7 @ Y0) | (sK4 @ sK7 @ Y0)) => (sK10 @ Y0))))) = $false) | ~spl0_3),
% 1.81/1.58 inference(not_proxy_clausification,[status(thm)],[f644])).
% 1.81/1.58 thf(f644,plain,(
% 1.81/1.58 ((~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y1) & ((sK3 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0))) => (sK10 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (((sK3 @ sK7 @ Y0) | (sK4 @ sK7 @ Y0)) => (sK10 @ Y0)))))) = $true) | ~spl0_3),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f642])).
% 1.81/1.58 thf(f642,plain,(
% 1.81/1.58 ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y1) & ((sK3 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0))) => (sK10 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (((sK3 @ sK7 @ Y0) | (sK4 @ sK7 @ Y0)) => (sK10 @ Y0))))) => $false)) | ~spl0_3),
% 1.81/1.58 inference(superposition,[status(thm)],[f623,f518])).
% 1.81/1.58 thf(f518,plain,(
% 1.81/1.58 ($false = (sK10 @ sK9)) | ~spl0_3),
% 1.81/1.58 inference(binary_proxy_clausification,[status(thm)],[f507])).
% 1.81/1.58 thf(f623,plain,(
% 1.81/1.58 ( ! [X1 : a > $o] : (($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((X1 @ Y1) & ((sK3 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0))) => (X1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (((sK3 @ sK7 @ Y0) | (sK4 @ sK7 @ Y0)) => (X1 @ Y0))))) => (X1 @ sK9)))) ) | ~spl0_3),
% 1.81/1.58 inference(beta_eta_normalization,[status(thm)],[f622])).
% 1.81/1.58 thf(f622,plain,(
% 1.81/1.58 ( ! [X1 : a > $o] : (($true = ((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK3 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1))) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (((sK3 @ sK7 @ Y1) | (sK4 @ sK7 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK9))) @ X1))) ) | ~spl0_3),
% 1.81/1.58 inference(pi_clausification,[status(thm)],[f613])).
% 1.81/1.58 thf(f613,plain,(
% 1.81/1.58 ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK3 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1))) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (((sK3 @ sK7 @ Y1) | (sK4 @ sK7 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK9))))) | ~spl0_3),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f612])).
% 1.81/1.58 thf(f612,plain,(
% 1.81/1.58 ($true = ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK3 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1))) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (((sK3 @ sK7 @ Y1) | (sK4 @ sK7 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK9)))) & $true)) | ~spl0_3),
% 1.81/1.58 inference(backward_demodulation,[status(thm)],[f494,f610])).
% 1.81/1.58 thf(f454,plain,(
% 1.81/1.58 ~spl0_1 | ~spl0_13),
% 1.81/1.58 inference(avatar_contradiction_clause,[status(thm)],[f453])).
% 1.81/1.58 thf(f453,plain,(
% 1.81/1.58 $false | (~spl0_1 | ~spl0_13)),
% 1.81/1.58 inference(trivial_inequality_removal,[status(thm)],[f452])).
% 1.81/1.58 thf(f452,plain,(
% 1.81/1.58 ($true = $false) | (~spl0_1 | ~spl0_13)),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f451])).
% 1.81/1.58 thf(f451,plain,(
% 1.81/1.58 ($true = (~ $true)) | (~spl0_1 | ~spl0_13)),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f449])).
% 1.81/1.58 thf(f449,plain,(
% 1.81/1.58 ($true = (~ ($true | (sK4 @ sK2 @ sK14)))) | (~spl0_1 | ~spl0_13)),
% 1.81/1.58 inference(backward_demodulation,[status(thm)],[f437,f444])).
% 1.81/1.58 thf(f444,plain,(
% 1.81/1.58 ($true = (sK3 @ sK2 @ sK14)) | ~spl0_13),
% 1.81/1.58 inference(avatar_component_clause,[status(thm)],[f443])).
% 1.81/1.58 thf(f443,definition,(
% 1.81/1.58 spl0_13 <=> ($true = (sK3 @ sK2 @ sK14))),
% 1.81/1.58 introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition])).
% 1.81/1.58 thf(f437,plain,(
% 1.81/1.58 ($true = (~ ((sK3 @ sK2 @ sK14) | (sK4 @ sK2 @ sK14)))) | ~spl0_1),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f435])).
% 1.81/1.58 thf(f435,plain,(
% 1.81/1.58 ($true = (((sK3 @ sK2 @ sK14) | (sK4 @ sK2 @ sK14)) => $false)) | ~spl0_1),
% 1.81/1.58 inference(superposition,[status(thm)],[f59,f431])).
% 1.81/1.58 thf(f431,plain,(
% 1.81/1.58 ((sK6 @ sK14) = $false) | ~spl0_1),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f430])).
% 1.81/1.58 thf(f430,plain,(
% 1.81/1.58 (($true => (sK6 @ sK14)) = $false) | ~spl0_1),
% 1.81/1.58 inference(backward_demodulation,[status(thm)],[f425,f429])).
% 1.81/1.58 thf(f429,plain,(
% 1.81/1.58 ($true = ((sK4 @ sK2 @ sK14) | (sK3 @ sK2 @ sK14))) | ~spl0_1),
% 1.81/1.58 inference(binary_proxy_clausification,[status(thm)],[f425])).
% 1.81/1.58 thf(f425,plain,(
% 1.81/1.58 ((((sK4 @ sK2 @ sK14) | (sK3 @ sK2 @ sK14)) => (sK6 @ sK14)) = $false) | ~spl0_1),
% 1.81/1.58 inference(beta_eta_normalization,[status(thm)],[f423])).
% 1.81/1.58 thf(f423,plain,(
% 1.81/1.58 ($false = ((^[Y0 : a]: (((sK4 @ sK2 @ Y0) | (sK3 @ sK2 @ Y0)) => (sK6 @ Y0))) @ sK14)) | ~spl0_1),
% 1.81/1.58 inference(sigma_clausification,[status(thm)],[f420])).
% 1.81/1.58 thf(f420,plain,(
% 1.81/1.58 ((!! @ a @ (^[Y0 : a]: (((sK4 @ sK2 @ Y0) | (sK3 @ sK2 @ Y0)) => (sK6 @ Y0)))) = $false) | ~spl0_1),
% 1.81/1.58 inference(not_proxy_clausification,[status(thm)],[f417])).
% 1.81/1.58 thf(f417,plain,(
% 1.81/1.58 ($true = (~ (!! @ a @ (^[Y0 : a]: (((sK4 @ sK2 @ Y0) | (sK3 @ sK2 @ Y0)) => (sK6 @ Y0)))))) | ~spl0_1),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f416])).
% 1.81/1.58 thf(f416,plain,(
% 1.81/1.58 ($true = ((!! @ a @ (^[Y0 : a]: (((sK4 @ sK2 @ Y0) | (sK3 @ sK2 @ Y0)) => (sK6 @ Y0)))) => $false)) | ~spl0_1),
% 1.81/1.58 inference(forward_demodulation,[status(thm)],[f414,f26])).
% 1.81/1.58 thf(f414,plain,(
% 1.81/1.58 ($true = ((!! @ a @ (^[Y0 : a]: (((sK4 @ sK2 @ Y0) | (sK3 @ sK2 @ Y0)) => (sK6 @ Y0)))) => (sK6 @ sK5))) | ~spl0_1),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f411])).
% 1.81/1.58 thf(f411,plain,(
% 1.81/1.58 ($true = (((!! @ a @ (^[Y0 : a]: (((sK4 @ sK2 @ Y0) | (sK3 @ sK2 @ Y0)) => (sK6 @ Y0)))) & $true) => (sK6 @ sK5))) | ~spl0_1),
% 1.81/1.58 inference(superposition,[status(thm)],[f406,f53])).
% 1.81/1.58 thf(f406,plain,(
% 1.81/1.58 ( ! [X1 : a > $o] : (($true = (((!! @ a @ (^[Y0 : a]: (((sK4 @ sK2 @ Y0) | (sK3 @ sK2 @ Y0)) => (X1 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((X1 @ Y1) & ((sK3 @ Y1 @ Y0) | (sK4 @ Y1 @ Y0))) => (X1 @ Y0))))))) => (X1 @ sK5)))) ) | ~spl0_1),
% 1.81/1.58 inference(beta_eta_normalization,[status(thm)],[f405])).
% 1.81/1.58 thf(f405,plain,(
% 1.81/1.58 ( ! [X1 : a > $o] : (($true = ((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK2 @ Y1) | (sK3 @ sK2 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK3 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1))) => (Y0 @ Y1))))))) => (Y0 @ sK5))) @ X1))) ) | ~spl0_1),
% 1.81/1.58 inference(pi_clausification,[status(thm)],[f35])).
% 1.81/1.58 thf(f448,plain,(
% 1.81/1.58 spl0_13 | spl0_14 | ~spl0_1),
% 1.81/1.58 inference(avatar_split_clause,[status(thm)],[f441,f34,f446,f443])).
% 1.81/1.58 thf(f441,plain,(
% 1.81/1.58 ($true = (sK4 @ sK2 @ sK14)) | ($true = (sK3 @ sK2 @ sK14)) | ~spl0_1),
% 1.81/1.58 inference(binary_proxy_clausification,[status(thm)],[f429])).
% 1.81/1.58 thf(f402,plain,(
% 1.81/1.58 spl0_11 | spl0_12 | ~spl0_4 | ~spl0_8),
% 1.81/1.58 inference(avatar_split_clause,[status(thm)],[f393,f243,f47,f400,f397])).
% 1.81/1.58 thf(f393,plain,(
% 1.81/1.58 ((!! @ a @ (^[Y0 : a]: ((sK4 @ sK12 @ Y0) => (sK13 @ Y0)))) = $false) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ Y0) & (sK4 @ Y0 @ Y1)) => (sK13 @ Y1)))))) = $false) | (~spl0_4 | ~spl0_8)),
% 1.81/1.58 inference(binary_proxy_clausification,[status(thm)],[f387])).
% 1.81/1.58 thf(f387,plain,(
% 1.81/1.58 (((!! @ a @ (^[Y0 : a]: ((sK4 @ sK12 @ Y0) => (sK13 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ Y0) & (sK4 @ Y0 @ Y1)) => (sK13 @ Y1))))))) = $false) | (~spl0_4 | ~spl0_8)),
% 1.81/1.58 inference(not_proxy_clausification,[status(thm)],[f384])).
% 1.81/1.58 thf(f384,plain,(
% 1.81/1.58 ($true = (~ ((!! @ a @ (^[Y0 : a]: ((sK4 @ sK12 @ Y0) => (sK13 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ Y0) & (sK4 @ Y0 @ Y1)) => (sK13 @ Y1))))))))) | (~spl0_4 | ~spl0_8)),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f380])).
% 1.81/1.58 thf(f380,plain,(
% 1.81/1.58 ($true = (((!! @ a @ (^[Y0 : a]: ((sK4 @ sK12 @ Y0) => (sK13 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ Y0) & (sK4 @ Y0 @ Y1)) => (sK13 @ Y1))))))) => $false)) | (~spl0_4 | ~spl0_8)),
% 1.81/1.58 inference(superposition,[status(thm)],[f378,f233])).
% 1.81/1.58 thf(f233,plain,(
% 1.81/1.58 ((sK13 @ sK11) = $false) | ~spl0_4),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f232])).
% 1.81/1.58 thf(f232,plain,(
% 1.81/1.58 ($false = ($true => (sK13 @ sK11))) | ~spl0_4),
% 1.81/1.58 inference(backward_demodulation,[status(thm)],[f229,f231])).
% 1.81/1.58 thf(f231,plain,(
% 1.81/1.58 ($true = ((!! @ a @ (^[Y0 : a]: (((sK4 @ sK12 @ Y0) | (sK3 @ sK12 @ Y0)) => (sK13 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK4 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) & (sK13 @ Y1)) => (sK13 @ Y0)))))))) | ~spl0_4),
% 1.81/1.58 inference(binary_proxy_clausification,[status(thm)],[f229])).
% 1.81/1.58 thf(f229,plain,(
% 1.81/1.58 ((((!! @ a @ (^[Y0 : a]: (((sK4 @ sK12 @ Y0) | (sK3 @ sK12 @ Y0)) => (sK13 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK4 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) & (sK13 @ Y1)) => (sK13 @ Y0))))))) => (sK13 @ sK11)) = $false) | ~spl0_4),
% 1.81/1.58 inference(beta_eta_normalization,[status(thm)],[f228])).
% 1.81/1.58 thf(f228,plain,(
% 1.81/1.58 (((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK12 @ Y1) | (sK3 @ sK12 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK4 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1))))))) => (Y0 @ sK11))) @ sK13) = $false) | ~spl0_4),
% 1.81/1.58 inference(sigma_clausification,[status(thm)],[f222])).
% 1.81/1.58 thf(f222,plain,(
% 1.81/1.58 ($false = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK12 @ Y1) | (sK3 @ sK12 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK4 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1))))))) => (Y0 @ sK11))))) | ~spl0_4),
% 1.81/1.58 inference(binary_proxy_clausification,[status(thm)],[f221])).
% 1.81/1.58 thf(f221,plain,(
% 1.81/1.58 ((((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK3 @ Y1 @ Y2)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ sK12 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK11)))) | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK4 @ sK12 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK4 @ Y1 @ Y2)) => (Y0 @ Y2))))))) => (Y0 @ sK11))))) => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK12 @ Y1) | (sK3 @ sK12 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK4 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1))))))) => (Y0 @ sK11))))) = $false) | ~spl0_4),
% 1.81/1.58 inference(beta_eta_normalization,[status(thm)],[f220])).
% 1.81/1.58 thf(f220,plain,(
% 1.81/1.58 (((^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & (sK3 @ Y2 @ Y3)) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: ((sK3 @ Y0 @ Y2) => (Y1 @ Y2))))) => (Y1 @ sK11)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK4 @ Y0 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & (sK4 @ Y2 @ Y3)) => (Y1 @ Y3))))))) => (Y1 @ sK11))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK4 @ Y0 @ Y2) | (sK3 @ Y0 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((((sK4 @ Y3 @ Y2) | (sK3 @ Y3 @ Y2)) & (Y1 @ Y3)) => (Y1 @ Y2))))))) => (Y1 @ sK11)))))) @ sK12) = $false) | ~spl0_4),
% 1.81/1.58 inference(sigma_clausification,[status(thm)],[f219])).
% 1.81/1.58 thf(f219,plain,(
% 1.81/1.58 ((!! @ a @ (^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & (sK3 @ Y2 @ Y3)) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: ((sK3 @ Y0 @ Y2) => (Y1 @ Y2))))) => (Y1 @ sK11)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK4 @ Y0 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & (sK4 @ Y2 @ Y3)) => (Y1 @ Y3))))))) => (Y1 @ sK11))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK4 @ Y0 @ Y2) | (sK3 @ Y0 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((((sK4 @ Y3 @ Y2) | (sK3 @ Y3 @ Y2)) & (Y1 @ Y3)) => (Y1 @ Y2))))))) => (Y1 @ sK11))))))) = $false) | ~spl0_4),
% 1.81/1.58 inference(beta_eta_normalization,[status(thm)],[f218])).
% 1.81/1.58 thf(f218,plain,(
% 1.81/1.58 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK3 @ Y3 @ Y4)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK3 @ Y1 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y0)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK4 @ Y1 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK4 @ Y3 @ Y4)) => (Y2 @ Y4))))))) => (Y2 @ Y0))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK4 @ Y1 @ Y3) | (sK3 @ Y1 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((((sK4 @ Y4 @ Y3) | (sK3 @ Y4 @ Y3)) & (Y2 @ Y4)) => (Y2 @ Y3))))))) => (Y2 @ Y0)))))))) @ sK11) = $false) | ~spl0_4),
% 1.81/1.58 inference(sigma_clausification,[status(thm)],[f48])).
% 1.81/1.58 thf(f378,plain,(
% 1.81/1.58 ( ! [X1 : a > $o] : (($true = (((!! @ a @ (^[Y0 : a]: ((sK4 @ sK12 @ Y0) => (X1 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((X1 @ Y0) & (sK4 @ Y0 @ Y1)) => (X1 @ Y1))))))) => (X1 @ sK11)))) ) | ~spl0_8),
% 1.81/1.58 inference(beta_eta_normalization,[status(thm)],[f377])).
% 1.81/1.58 thf(f377,plain,(
% 1.81/1.58 ( ! [X1 : a > $o] : (($true = ((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK4 @ sK12 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK4 @ Y1 @ Y2)) => (Y0 @ Y2))))))) => (Y0 @ sK11))) @ X1))) ) | ~spl0_8),
% 1.81/1.58 inference(pi_clausification,[status(thm)],[f244])).
% 1.81/1.58 thf(f348,plain,(
% 1.81/1.58 spl0_9 | spl0_10 | ~spl0_4 | ~spl0_7),
% 1.81/1.58 inference(avatar_split_clause,[status(thm)],[f339,f240,f47,f346,f343])).
% 1.81/1.58 thf(f339,plain,(
% 1.81/1.58 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ Y0) & (sK3 @ Y0 @ Y1)) => (sK13 @ Y1)))))) = $false) | ((!! @ a @ (^[Y0 : a]: ((sK3 @ sK12 @ Y0) => (sK13 @ Y0)))) = $false) | (~spl0_4 | ~spl0_7)),
% 1.81/1.58 inference(binary_proxy_clausification,[status(thm)],[f320])).
% 1.81/1.58 thf(f320,plain,(
% 1.81/1.58 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ Y0) & (sK3 @ Y0 @ Y1)) => (sK13 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: ((sK3 @ sK12 @ Y0) => (sK13 @ Y0))))) = $false) | (~spl0_4 | ~spl0_7)),
% 1.81/1.58 inference(not_proxy_clausification,[status(thm)],[f257])).
% 1.81/1.58 thf(f257,plain,(
% 1.81/1.58 ((~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ Y0) & (sK3 @ Y0 @ Y1)) => (sK13 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: ((sK3 @ sK12 @ Y0) => (sK13 @ Y0)))))) = $true) | (~spl0_4 | ~spl0_7)),
% 1.81/1.58 inference(boolean_simplification,[status(thm)],[f256])).
% 1.81/1.58 thf(f256,plain,(
% 1.81/1.58 ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ Y0) & (sK3 @ Y0 @ Y1)) => (sK13 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: ((sK3 @ sK12 @ Y0) => (sK13 @ Y0))))) => $false)) | (~spl0_4 | ~spl0_7)),
% 1.81/1.58 inference(superposition,[status(thm)],[f251,f233])).
% 1.81/1.58 thf(f251,plain,(
% 1.81/1.58 ( ! [X1 : a > $o] : (($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((X1 @ Y0) & (sK3 @ Y0 @ Y1)) => (X1 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: ((sK3 @ sK12 @ Y0) => (X1 @ Y0))))) => (X1 @ sK11)))) ) | ~spl0_7),
% 1.81/1.58 inference(beta_eta_normalization,[status(thm)],[f250])).
% 1.81/1.58 thf(f250,plain,(
% 1.81/1.58 ( ! [X1 : a > $o] : (($true = ((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK3 @ Y1 @ Y2)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ sK12 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK11))) @ X1))) ) | ~spl0_7),
% 1.81/1.58 inference(pi_clausification,[status(thm)],[f241])).
% 1.81/1.58 thf(f245,plain,(
% 1.81/1.58 spl0_7 | spl0_8 | ~spl0_4),
% 1.81/1.58 inference(avatar_split_clause,[status(thm)],[f238,f47,f243,f240])).
% 1.81/1.58 thf(f238,plain,(
% 1.81/1.58 ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK4 @ sK12 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK4 @ Y1 @ Y2)) => (Y0 @ Y2))))))) => (Y0 @ sK11))))) | ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK3 @ Y1 @ Y2)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ sK12 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK11))))) | ~spl0_4),
% 1.81/1.58 inference(binary_proxy_clausification,[status(thm)],[f223])).
% 1.81/1.58 thf(f223,plain,(
% 1.81/1.58 ($true = ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK3 @ Y1 @ Y2)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK3 @ sK12 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK11)))) | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK4 @ sK12 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK4 @ Y1 @ Y2)) => (Y0 @ Y2))))))) => (Y0 @ sK11)))))) | ~spl0_4),
% 1.81/1.58 inference(binary_proxy_clausification,[status(thm)],[f221])).
% 1.81/1.58 thf(f49,plain,(
% 1.81/1.58 spl0_3 | spl0_4 | ~spl0_2),
% 1.81/1.58 inference(avatar_split_clause,[status(thm)],[f42,f37,f47,f44])).
% 1.81/1.58 thf(f37,definition,(
% 1.81/1.58 spl0_2 <=> ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK3 @ Y3 @ Y4)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK3 @ Y1 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y0)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK4 @ Y1 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK4 @ Y3 @ Y4)) => (Y2 @ Y4))))))) => (Y2 @ Y0))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK4 @ Y1 @ Y3) | (sK3 @ Y1 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((((sK4 @ Y4 @ Y3) | (sK3 @ Y4 @ Y3)) & (Y2 @ Y4)) => (Y2 @ Y3))))))) => (Y2 @ Y0))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & ((sK3 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4))) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y0 @ Y4) | (sK4 @ Y0 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y2)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & ((sK3 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4))) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y1 @ Y4) | (sK4 @ Y1 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y0))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK3 @ Y1 @ Y4) | (sK4 @ Y1 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK4 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y2)))))))))))))),
% 1.81/1.58 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.81/1.58 thf(f42,plain,(
% 1.81/1.58 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK3 @ Y3 @ Y4)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK3 @ Y1 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y0)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK4 @ Y1 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK4 @ Y3 @ Y4)) => (Y2 @ Y4))))))) => (Y2 @ Y0))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK4 @ Y1 @ Y3) | (sK3 @ Y1 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((((sK4 @ Y4 @ Y3) | (sK3 @ Y4 @ Y3)) & (Y2 @ Y4)) => (Y2 @ Y3))))))) => (Y2 @ Y0)))))))))) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & ((sK3 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4))) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y0 @ Y4) | (sK4 @ Y0 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y2)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & ((sK3 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4))) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y1 @ Y4) | (sK4 @ Y1 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y0))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK3 @ Y1 @ Y4) | (sK4 @ Y1 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK4 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y2))))))))))) = $false) | ~spl0_2),
% 1.81/1.58 inference(binary_proxy_clausification,[status(thm)],[f38])).
% 1.81/1.58 thf(f38,plain,(
% 1.81/1.58 ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK3 @ Y3 @ Y4)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK3 @ Y1 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y0)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK4 @ Y1 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK4 @ Y3 @ Y4)) => (Y2 @ Y4))))))) => (Y2 @ Y0))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK4 @ Y1 @ Y3) | (sK3 @ Y1 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((((sK4 @ Y4 @ Y3) | (sK3 @ Y4 @ Y3)) & (Y2 @ Y4)) => (Y2 @ Y3))))))) => (Y2 @ Y0))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & ((sK3 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4))) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y0 @ Y4) | (sK4 @ Y0 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y2)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & ((sK3 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4))) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y1 @ Y4) | (sK4 @ Y1 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y0))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK3 @ Y1 @ Y4) | (sK4 @ Y1 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK4 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y2))))))))))))) | ~spl0_2),
% 1.81/1.58 inference(avatar_component_clause,[status(thm)],[f37])).
% 1.81/1.58 thf(f39,plain,(
% 1.81/1.58 spl0_1 | spl0_2),
% 1.81/1.58 inference(avatar_split_clause,[status(thm)],[f32,f37,f34])).
% 1.81/1.58 thf(f32,plain,(
% 1.81/1.58 ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK2 @ Y1) | (sK3 @ sK2 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK3 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1))) => (Y0 @ Y1))))))) => (Y0 @ sK5))))) | ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK3 @ Y3 @ Y4)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK3 @ Y1 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y0)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK4 @ Y1 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK4 @ Y3 @ Y4)) => (Y2 @ Y4))))))) => (Y2 @ Y0))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK4 @ Y1 @ Y3) | (sK3 @ Y1 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((((sK4 @ Y4 @ Y3) | (sK3 @ Y4 @ Y3)) & (Y2 @ Y4)) => (Y2 @ Y3))))))) => (Y2 @ Y0))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & ((sK3 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4))) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y0 @ Y4) | (sK4 @ Y0 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y2)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & ((sK3 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4))) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y1 @ Y4) | (sK4 @ Y1 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y0))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK3 @ Y1 @ Y4) | (sK4 @ Y1 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK4 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y2)))))))))))))),
% 1.81/1.58 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.81/1.58 thf(f19,plain,(
% 1.81/1.58 ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK3 @ Y3 @ Y4)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK3 @ Y1 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y0)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK4 @ Y1 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK4 @ Y3 @ Y4)) => (Y2 @ Y4))))))) => (Y2 @ Y0))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK4 @ Y1 @ Y3) | (sK3 @ Y1 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((((sK4 @ Y4 @ Y3) | (sK3 @ Y4 @ Y3)) & (Y2 @ Y4)) => (Y2 @ Y3))))))) => (Y2 @ Y0))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & ((sK3 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4))) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y0 @ Y4) | (sK4 @ Y0 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y2)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & ((sK3 @ Y5 @ Y4) | (sK4 @ Y5 @ Y4))) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y1 @ Y4) | (sK4 @ Y1 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y0))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK3 @ Y1 @ Y4) | (sK4 @ Y1 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK4 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y2)))))))))))) => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK4 @ sK2 @ Y1) | (sK3 @ sK2 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK3 @ Y2 @ Y1) | (sK4 @ Y2 @ Y1))) => (Y0 @ Y1))))))) => (Y0 @ sK5))))))),
% 1.81/1.58 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.81/1.58 % SZS output end Proof for DTF2THF_9846
% 1.81/1.58 % (10025)------------------------------
% 1.81/1.58 % (10025)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.58 % (10025)Termination reason: Refutation
% 1.81/1.58
% 1.81/1.58 % (10025)Memory used [KB]: 7036
% 1.81/1.58 % (10025)Time elapsed: 0.145 s
% 1.81/1.58 % (10025)Instructions burned: 401 (million)
% 1.81/1.58 % (10025)------------------------------
% 1.81/1.58 % (10025)------------------------------
% 1.81/1.58 % (10013)Success in time 0.181 s
%------------------------------------------------------------------------------