TSTP Solution File: SEV141^5 by Vampire---4.9
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEV141^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 16:01:58 EDT 2024
% Result : Theorem 1.72s 0.59s
% Output : Refutation 1.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 16
% Syntax : Number of formulae : 256 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 2602 ( 246 equ; 0 cnn)
% Maximal formula atoms : 4 ( 10 avg)
% Number of connectives : 8248 ( 336 ~; 432 |; 429 &;5213 @)
% ( 15 <=>; 669 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 662 ( 662 >; 0 *; 0 +; 0 <<)
% Number of symbols : 59 ( 55 usr; 48 con; 0-2 aty)
% (1154 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 1409 (1255 ^ 154 !; 0 ?;1409 :)
% 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 > a > $o ).
thf(func_def_22,type,
sK3: a > a > $o ).
thf(func_def_23,type,
sK4: a ).
thf(func_def_24,type,
sK5: a ).
thf(func_def_25,type,
sK6: a > 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 ).
thf(func_def_30,type,
sK11: a ).
thf(func_def_31,type,
sK12: a ).
thf(func_def_32,type,
sK13: a ).
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 > a > $o ).
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 > a > $o ).
thf(func_def_44,type,
sK25: a ).
thf(func_def_45,type,
sK26: a ).
thf(func_def_46,type,
sK27: a ).
thf(func_def_47,type,
sK28: a ).
thf(func_def_48,type,
sK29: a ).
thf(func_def_49,type,
sK30: a > a > $o ).
thf(func_def_50,type,
sK31: a > a > $o ).
thf(func_def_51,type,
sK32: a ).
thf(func_def_52,type,
sK33: a ).
thf(func_def_53,type,
sK34: a > a > $o ).
thf(func_def_54,type,
sK35: a > a > $o ).
thf(func_def_55,type,
sK36: a ).
thf(func_def_56,type,
sK37: a ).
thf(func_def_57,type,
sK38: a ).
thf(func_def_58,type,
sK39: a ).
thf(func_def_59,type,
sK40: a ).
thf(f1844,plain,
$false,
inference(avatar_sat_refutation,[],[f27,f34,f105,f174,f213,f242,f393,f451,f516,f590,f609,f646,f1166,f1463,f1702,f1843]) ).
thf(f1843,plain,
( ~ spl0_1
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f1842]) ).
thf(f1842,plain,
( $false
| ~ spl0_1
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f1841]) ).
thf(f1841,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_9 ),
inference(boolean_simplification,[],[f1840]) ).
thf(f1840,plain,
( ( $true = ~ $true )
| ~ spl0_1
| ~ spl0_9 ),
inference(boolean_simplification,[],[f1839]) ).
thf(f1839,plain,
( ( $true
= ( ~ ( ( sK2 @ sK40 @ sK39 )
| $true ) ) )
| ~ spl0_1
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1834,f1826]) ).
thf(f1826,plain,
( ( ( sK3 @ sK40 @ sK39 )
= $true )
| ~ spl0_9 ),
inference(binary_proxy_clausification,[],[f1824]) ).
thf(f1824,plain,
( ( $false
= ( ( sK3 @ sK40 @ sK39 )
=> ( sK6 @ sK40 @ sK39 ) ) )
| ~ spl0_9 ),
inference(beta_eta_normalization,[],[f1823]) ).
thf(f1823,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK3 @ Y0 @ sK39 )
=> ( sK6 @ Y0 @ sK39 ) )
@ sK40 ) )
| ~ spl0_9 ),
inference(sigma_clausification,[],[f1817]) ).
thf(f1817,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ sK39 )
=> ( sK6 @ Y0 @ sK39 ) ) )
= $false )
| ~ spl0_9 ),
inference(beta_eta_normalization,[],[f1815]) ).
thf(f1815,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) )
@ sK39 ) )
| ~ spl0_9 ),
inference(sigma_clausification,[],[f212]) ).
thf(f212,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f211]) ).
thf(f211,plain,
( spl0_9
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
thf(f1834,plain,
( ( $true
= ( ~ ( ( sK2 @ sK40 @ sK39 )
| ( sK3 @ sK40 @ sK39 ) ) ) )
| ~ spl0_1
| ~ spl0_9 ),
inference(boolean_simplification,[],[f1832]) ).
thf(f1832,plain,
( ( $true
= ( ( ( sK2 @ sK40 @ sK39 )
| ( sK3 @ sK40 @ sK39 ) )
=> $false ) )
| ~ spl0_1
| ~ spl0_9 ),
inference(superposition,[],[f1533,f1828]) ).
thf(f1828,plain,
( ( ( sK6 @ sK40 @ sK39 )
= $false )
| ~ spl0_9 ),
inference(boolean_simplification,[],[f1827]) ).
thf(f1827,plain,
( ( $false
= ( $true
=> ( sK6 @ sK40 @ sK39 ) ) )
| ~ spl0_9 ),
inference(backward_demodulation,[],[f1824,f1826]) ).
thf(f1533,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( ( sK2 @ X1 @ X2 )
| ( sK3 @ X1 @ X2 ) )
=> ( sK6 @ X1 @ X2 ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f1532]) ).
thf(f1532,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK2 @ X1 @ Y0 )
| ( sK3 @ X1 @ Y0 ) )
=> ( sK6 @ X1 @ Y0 ) )
@ X2 ) )
| ~ spl0_1 ),
inference(pi_clausification,[],[f1527]) ).
thf(f1527,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ X1 @ Y0 )
| ( sK3 @ X1 @ Y0 ) )
=> ( sK6 @ X1 @ Y0 ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f1526]) ).
thf(f1526,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) )
@ X1 ) )
| ~ spl0_1 ),
inference(pi_clausification,[],[f1525]) ).
thf(f1525,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f1524]) ).
thf(f1524,plain,
( ( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_1 ),
inference(backward_demodulation,[],[f1471,f1523]) ).
thf(f1523,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f1471]) ).
thf(f1471,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f1469]) ).
thf(f1469,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
=> ( sK6 @ sK4 @ sK5 ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f1468]) ).
thf(f1468,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) )
@ sK6 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f23]) ).
thf(f23,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f22]) ).
thf(f22,plain,
( spl0_1
<=> ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f1702,plain,
( ~ spl0_1
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f1701]) ).
thf(f1701,plain,
( $false
| ~ spl0_1
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f1700]) ).
thf(f1700,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_6 ),
inference(forward_demodulation,[],[f1693,f1516]) ).
thf(f1516,plain,
( ( $false
= ( sK6 @ sK37 @ sK38 ) )
| ~ spl0_6 ),
inference(binary_proxy_clausification,[],[f1515]) ).
thf(f1515,plain,
( ( ( ( ( sK6 @ sK36 @ sK38 )
& ( sK6 @ sK37 @ sK36 ) )
=> ( sK6 @ sK37 @ sK38 ) )
= $false )
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f1514]) ).
thf(f1514,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK6 @ sK36 @ Y0 )
& ( sK6 @ sK37 @ sK36 ) )
=> ( sK6 @ sK37 @ Y0 ) )
@ sK38 ) )
| ~ spl0_6 ),
inference(sigma_clausification,[],[f1513]) ).
thf(f1513,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ sK36 @ Y0 )
& ( sK6 @ sK37 @ sK36 ) )
=> ( sK6 @ sK37 @ Y0 ) ) ) )
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f1512]) ).
thf(f1512,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ sK36 @ Y1 )
& ( sK6 @ Y0 @ sK36 ) )
=> ( sK6 @ Y0 @ Y1 ) ) )
@ sK37 )
= $false )
| ~ spl0_6 ),
inference(sigma_clausification,[],[f1499]) ).
thf(f1499,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ sK36 @ Y1 )
& ( sK6 @ Y0 @ sK36 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
= $false )
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f1497]) ).
thf(f1497,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y2 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y2 ) ) ) )
@ sK36 ) )
| ~ spl0_6 ),
inference(sigma_clausification,[],[f104]) ).
thf(f104,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y2 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y2 ) ) ) ) ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f103]) ).
thf(f103,plain,
( spl0_6
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y2 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y2 ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
thf(f1693,plain,
( ( $true
= ( sK6 @ sK37 @ sK38 ) )
| ~ spl0_1
| ~ spl0_6 ),
inference(boolean_simplification,[],[f1692]) ).
thf(f1692,plain,
( ( $true
= ( $true
=> ( sK6 @ sK37 @ sK38 ) ) )
| ~ spl0_1
| ~ spl0_6 ),
inference(superposition,[],[f1644,f1529]) ).
thf(f1529,plain,
( ( $true
= ( sK6 @ sK36 @ sK38 ) )
| ~ spl0_6 ),
inference(binary_proxy_clausification,[],[f1517]) ).
thf(f1517,plain,
( ( $true
= ( ( sK6 @ sK36 @ sK38 )
& ( sK6 @ sK37 @ sK36 ) ) )
| ~ spl0_6 ),
inference(binary_proxy_clausification,[],[f1515]) ).
thf(f1644,plain,
( ! [X0: a] :
( $true
= ( ( sK6 @ sK36 @ X0 )
=> ( sK6 @ sK37 @ X0 ) ) )
| ~ spl0_1
| ~ spl0_6 ),
inference(boolean_simplification,[],[f1625]) ).
thf(f1625,plain,
( ! [X0: a] :
( $true
= ( ( ( sK6 @ sK36 @ X0 )
& $true )
=> ( sK6 @ sK37 @ X0 ) ) )
| ~ spl0_1
| ~ spl0_6 ),
inference(superposition,[],[f1606,f1531]) ).
thf(f1531,plain,
( ( $true
= ( sK6 @ sK37 @ sK36 ) )
| ~ spl0_6 ),
inference(boolean_simplification,[],[f1530]) ).
thf(f1530,plain,
( ( $true
= ( $true
& ( sK6 @ sK37 @ sK36 ) ) )
| ~ spl0_6 ),
inference(backward_demodulation,[],[f1517,f1529]) ).
thf(f1606,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ( ( sK6 @ X1 @ X2 )
& ( sK6 @ X3 @ X1 ) )
=> ( sK6 @ X3 @ X2 ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f1605]) ).
thf(f1605,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK6 @ X1 @ X2 )
& ( sK6 @ Y0 @ X1 ) )
=> ( sK6 @ Y0 @ X2 ) )
@ X3 ) )
| ~ spl0_1 ),
inference(pi_clausification,[],[f1602]) ).
thf(f1602,plain,
( ! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ X1 @ X2 )
& ( sK6 @ Y0 @ X1 ) )
=> ( sK6 @ Y0 @ X2 ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f1601]) ).
thf(f1601,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ X1 @ Y0 )
& ( sK6 @ Y1 @ X1 ) )
=> ( sK6 @ Y1 @ Y0 ) ) )
@ X2 ) )
| ~ spl0_1 ),
inference(pi_clausification,[],[f1594]) ).
thf(f1594,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ X1 @ Y0 )
& ( sK6 @ Y1 @ X1 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f1593]) ).
thf(f1593,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) )
@ X1 ) )
| ~ spl0_1 ),
inference(pi_clausification,[],[f1523]) ).
thf(f1463,plain,
( ~ spl0_2
| ~ spl0_19
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f1462]) ).
thf(f1462,plain,
( $false
| ~ spl0_2
| ~ spl0_19
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f1461]) ).
thf(f1461,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f1453,f1015]) ).
thf(f1015,plain,
( ( ( sK34 @ sK22 @ sK23 )
= $false )
| ~ spl0_2
| ~ spl0_19 ),
inference(boolean_simplification,[],[f1014]) ).
thf(f1014,plain,
( ( ( $true
=> ( sK34 @ sK22 @ sK23 ) )
= $false )
| ~ spl0_2
| ~ spl0_19 ),
inference(backward_demodulation,[],[f1004,f1013]) ).
thf(f1013,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK34 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK34 @ Y0 @ Y2 )
& ( sK34 @ Y1 @ Y0 ) )
=> ( sK34 @ Y1 @ Y2 ) ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_19 ),
inference(binary_proxy_clausification,[],[f1004]) ).
thf(f1004,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK34 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK34 @ Y0 @ Y2 )
& ( sK34 @ Y1 @ Y0 ) )
=> ( sK34 @ Y1 @ Y2 ) ) ) ) ) )
=> ( sK34 @ sK22 @ sK23 ) )
= $false )
| ~ spl0_2
| ~ spl0_19 ),
inference(beta_eta_normalization,[],[f1001]) ).
thf(f1001,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK22 @ sK23 ) )
@ sK34 )
= $false )
| ~ spl0_2
| ~ spl0_19 ),
inference(sigma_clausification,[],[f854]) ).
thf(f854,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK22 @ sK23 ) ) ) )
| ~ spl0_2
| ~ spl0_19 ),
inference(binary_proxy_clausification,[],[f845]) ).
thf(f845,plain,
( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK22 @ sK23 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK22 @ sK23 ) ) ) )
= $false )
| ~ spl0_2
| ~ spl0_19 ),
inference(not_proxy_clausification,[],[f655]) ).
thf(f655,plain,
( ( $true
= ( ~ ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK22 @ sK23 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK22 @ sK23 ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_19 ),
inference(boolean_simplification,[],[f653]) ).
thf(f653,plain,
( ( $true
= ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK22 @ sK23 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK22 @ sK23 ) ) ) )
=> $false ) )
| ~ spl0_2
| ~ spl0_19 ),
inference(superposition,[],[f650,f623]) ).
thf(f623,plain,
( ( ( sK18 @ sK22 @ sK23 )
= $false )
| ~ spl0_19 ),
inference(binary_proxy_clausification,[],[f622]) ).
thf(f622,plain,
( ( $false
= ( ( ( sK2 @ sK22 @ sK23 )
| ( sK3 @ sK22 @ sK23 ) )
=> ( sK18 @ sK22 @ sK23 ) ) )
| ~ spl0_19 ),
inference(beta_eta_normalization,[],[f621]) ).
thf(f621,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK2 @ sK22 @ Y0 )
| ( sK3 @ sK22 @ Y0 ) )
=> ( sK18 @ sK22 @ Y0 ) )
@ sK23 ) )
| ~ spl0_19 ),
inference(sigma_clausification,[],[f620]) ).
thf(f620,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK22 @ Y0 )
| ( sK3 @ sK22 @ Y0 ) )
=> ( sK18 @ sK22 @ Y0 ) ) )
= $false )
| ~ spl0_19 ),
inference(beta_eta_normalization,[],[f616]) ).
thf(f616,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( sK18 @ Y0 @ Y1 ) ) )
@ sK22 ) )
| ~ spl0_19 ),
inference(sigma_clausification,[],[f589]) ).
thf(f589,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( sK18 @ Y0 @ Y1 ) ) ) )
= $false )
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f588]) ).
thf(f588,plain,
( spl0_19
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( sK18 @ Y0 @ Y1 ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
thf(f650,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ X2 @ X1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ X2 @ X1 ) ) ) )
=> ( sK18 @ X2 @ X1 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f649]) ).
thf(f649,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ Y0 @ X1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 @ X1 ) ) ) )
=> ( sK18 @ Y0 @ X1 ) )
@ X2 ) )
| ~ spl0_2 ),
inference(pi_clausification,[],[f638]) ).
thf(f638,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ Y0 @ X1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 @ X1 ) ) ) )
=> ( sK18 @ Y0 @ X1 ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f637]) ).
thf(f637,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK18 @ Y1 @ Y0 ) ) )
@ X1 ) )
| ~ spl0_2 ),
inference(pi_clausification,[],[f543]) ).
thf(f543,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK18 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f536]) ).
thf(f536,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK18 @ Y0 @ Y2 )
& ( sK18 @ Y1 @ Y0 ) )
=> ( sK18 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK18 @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f534]) ).
thf(f534,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK18 @ Y0 @ Y2 )
& ( sK18 @ Y1 @ Y0 ) )
=> ( sK18 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK18 @ Y1 @ Y0 ) ) ) ) )
=> ( sK18 @ sK4 @ sK5 ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f533]) ).
thf(f533,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) )
@ sK18 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f26]) ).
thf(f26,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f25]) ).
thf(f25,plain,
( spl0_2
<=> ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f1453,plain,
( ( $true
= ( sK34 @ sK22 @ sK23 ) )
| ~ spl0_2
| ~ spl0_19
| ~ spl0_20 ),
inference(boolean_simplification,[],[f1448]) ).
thf(f1448,plain,
( ( ( $true
=> ( sK34 @ sK22 @ sK23 ) )
= $true )
| ~ spl0_2
| ~ spl0_19
| ~ spl0_20 ),
inference(superposition,[],[f1443,f642]) ).
thf(f642,plain,
( ( ( sK3 @ sK22 @ sK23 )
= $true )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f641]) ).
thf(f641,plain,
( spl0_20
<=> ( ( sK3 @ sK22 @ sK23 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
thf(f1443,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( sK3 @ X2 @ X1 )
=> ( sK34 @ X2 @ X1 ) ) )
| ~ spl0_2
| ~ spl0_19 ),
inference(beta_eta_normalization,[],[f1442]) ).
thf(f1442,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK3 @ Y0 @ X1 )
=> ( sK34 @ Y0 @ X1 ) )
@ X2 ) )
| ~ spl0_2
| ~ spl0_19 ),
inference(pi_clausification,[],[f1438]) ).
thf(f1438,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ X1 )
=> ( sK34 @ Y0 @ X1 ) ) ) )
| ~ spl0_2
| ~ spl0_19 ),
inference(beta_eta_normalization,[],[f1437]) ).
thf(f1437,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK34 @ Y1 @ Y0 ) ) )
@ X1 ) )
| ~ spl0_2
| ~ spl0_19 ),
inference(pi_clausification,[],[f1275]) ).
thf(f1275,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK34 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_2
| ~ spl0_19 ),
inference(binary_proxy_clausification,[],[f1013]) ).
thf(f1166,plain,
( ~ spl0_2
| ~ spl0_19
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f1165]) ).
thf(f1165,plain,
( $false
| ~ spl0_2
| ~ spl0_19
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f1164]) ).
thf(f1164,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_19
| ~ spl0_21 ),
inference(forward_demodulation,[],[f1149,f870]) ).
thf(f870,plain,
( ( ( sK31 @ sK22 @ sK23 )
= $false )
| ~ spl0_2
| ~ spl0_19 ),
inference(boolean_simplification,[],[f869]) ).
thf(f869,plain,
( ( ( $true
=> ( sK31 @ sK22 @ sK23 ) )
= $false )
| ~ spl0_2
| ~ spl0_19 ),
inference(backward_demodulation,[],[f861,f868]) ).
thf(f868,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y2 @ Y1 )
& ( sK31 @ Y0 @ Y2 ) )
=> ( sK31 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK31 @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_19 ),
inference(binary_proxy_clausification,[],[f861]) ).
thf(f861,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK31 @ Y2 @ Y1 )
& ( sK31 @ Y0 @ Y2 ) )
=> ( sK31 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK31 @ Y1 @ Y0 ) ) ) ) )
=> ( sK31 @ sK22 @ sK23 ) )
= $false )
| ~ spl0_2
| ~ spl0_19 ),
inference(beta_eta_normalization,[],[f859]) ).
thf(f859,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK22 @ sK23 ) )
@ sK31 )
= $false )
| ~ spl0_2
| ~ spl0_19 ),
inference(sigma_clausification,[],[f858]) ).
thf(f858,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK22 @ sK23 ) ) )
= $false )
| ~ spl0_2
| ~ spl0_19 ),
inference(boolean_simplification,[],[f857]) ).
thf(f857,plain,
( ( ( $false
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK22 @ sK23 ) ) ) )
= $false )
| ~ spl0_2
| ~ spl0_19 ),
inference(backward_demodulation,[],[f845,f854]) ).
thf(f1149,plain,
( ( $true
= ( sK31 @ sK22 @ sK23 ) )
| ~ spl0_2
| ~ spl0_19
| ~ spl0_21 ),
inference(boolean_simplification,[],[f1146]) ).
thf(f1146,plain,
( ( ( $true
=> ( sK31 @ sK22 @ sK23 ) )
= $true )
| ~ spl0_2
| ~ spl0_19
| ~ spl0_21 ),
inference(superposition,[],[f1136,f645]) ).
thf(f645,plain,
( ( ( sK2 @ sK22 @ sK23 )
= $true )
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f644]) ).
thf(f644,plain,
( spl0_21
<=> ( ( sK2 @ sK22 @ sK23 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
thf(f1136,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( sK2 @ X2 @ X1 )
=> ( sK31 @ X2 @ X1 ) ) )
| ~ spl0_2
| ~ spl0_19 ),
inference(beta_eta_normalization,[],[f1135]) ).
thf(f1135,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( sK2 @ Y0 @ X1 )
=> ( sK31 @ Y0 @ X1 ) )
@ X2 )
= $true )
| ~ spl0_2
| ~ spl0_19 ),
inference(pi_clausification,[],[f1129]) ).
thf(f1129,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ X1 )
=> ( sK31 @ Y0 @ X1 ) ) ) )
| ~ spl0_2
| ~ spl0_19 ),
inference(beta_eta_normalization,[],[f1126]) ).
thf(f1126,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK31 @ Y1 @ Y0 ) ) )
@ X1 ) )
| ~ spl0_2
| ~ spl0_19 ),
inference(pi_clausification,[],[f915]) ).
thf(f915,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK31 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_2
| ~ spl0_19 ),
inference(binary_proxy_clausification,[],[f868]) ).
thf(f646,plain,
( spl0_20
| spl0_21
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f639,f588,f644,f641]) ).
thf(f639,plain,
( ( ( sK3 @ sK22 @ sK23 )
= $true )
| ( ( sK2 @ sK22 @ sK23 )
= $true )
| ~ spl0_19 ),
inference(binary_proxy_clausification,[],[f624]) ).
thf(f624,plain,
( ( $true
= ( ( sK2 @ sK22 @ sK23 )
| ( sK3 @ sK22 @ sK23 ) ) )
| ~ spl0_19 ),
inference(binary_proxy_clausification,[],[f622]) ).
thf(f609,plain,
( ~ spl0_2
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f608]) ).
thf(f608,plain,
( $false
| ~ spl0_2
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f605]) ).
thf(f605,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_18 ),
inference(superposition,[],[f552,f601]) ).
thf(f601,plain,
( ( ( ( ( sK18 @ sK19 @ sK20 )
& ( sK18 @ sK21 @ sK19 ) )
=> ( sK18 @ sK21 @ sK20 ) )
= $false )
| ~ spl0_18 ),
inference(beta_eta_normalization,[],[f600]) ).
thf(f600,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK18 @ sK19 @ sK20 )
& ( sK18 @ Y0 @ sK19 ) )
=> ( sK18 @ Y0 @ sK20 ) )
@ sK21 ) )
| ~ spl0_18 ),
inference(sigma_clausification,[],[f599]) ).
thf(f599,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK18 @ sK19 @ sK20 )
& ( sK18 @ Y0 @ sK19 ) )
=> ( sK18 @ Y0 @ sK20 ) ) ) )
| ~ spl0_18 ),
inference(beta_eta_normalization,[],[f598]) ).
thf(f598,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK18 @ sK19 @ Y0 )
& ( sK18 @ Y1 @ sK19 ) )
=> ( sK18 @ Y1 @ Y0 ) ) )
@ sK20 )
= $false )
| ~ spl0_18 ),
inference(sigma_clausification,[],[f597]) ).
thf(f597,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK18 @ sK19 @ Y0 )
& ( sK18 @ Y1 @ sK19 ) )
=> ( sK18 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_18 ),
inference(beta_eta_normalization,[],[f593]) ).
thf(f593,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK18 @ Y0 @ Y1 )
& ( sK18 @ Y2 @ Y0 ) )
=> ( sK18 @ Y2 @ Y1 ) ) ) )
@ sK19 ) )
| ~ spl0_18 ),
inference(sigma_clausification,[],[f586]) ).
thf(f586,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK18 @ Y0 @ Y1 )
& ( sK18 @ Y2 @ Y0 ) )
=> ( sK18 @ Y2 @ Y1 ) ) ) ) ) )
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f585]) ).
thf(f585,plain,
( spl0_18
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK18 @ Y0 @ Y1 )
& ( sK18 @ Y2 @ Y0 ) )
=> ( sK18 @ Y2 @ Y1 ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
thf(f552,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ( ( sK18 @ X1 @ X3 )
& ( sK18 @ X2 @ X1 ) )
=> ( sK18 @ X2 @ X3 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f551]) ).
thf(f551,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK18 @ X1 @ Y0 )
& ( sK18 @ X2 @ X1 ) )
=> ( sK18 @ X2 @ Y0 ) )
@ X3 ) )
| ~ spl0_2 ),
inference(pi_clausification,[],[f550]) ).
thf(f550,plain,
( ! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK18 @ X1 @ Y0 )
& ( sK18 @ X2 @ X1 ) )
=> ( sK18 @ X2 @ Y0 ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f549]) ).
thf(f549,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK18 @ X1 @ Y1 )
& ( sK18 @ Y0 @ X1 ) )
=> ( sK18 @ Y0 @ Y1 ) ) )
@ X2 ) )
| ~ spl0_2 ),
inference(pi_clausification,[],[f548]) ).
thf(f548,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK18 @ X1 @ Y1 )
& ( sK18 @ Y0 @ X1 ) )
=> ( sK18 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f547]) ).
thf(f547,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK18 @ Y0 @ Y2 )
& ( sK18 @ Y1 @ Y0 ) )
=> ( sK18 @ Y1 @ Y2 ) ) ) )
@ X1 ) )
| ~ spl0_2 ),
inference(pi_clausification,[],[f546]) ).
thf(f546,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK18 @ Y0 @ Y2 )
& ( sK18 @ Y1 @ Y0 ) )
=> ( sK18 @ Y1 @ Y2 ) ) ) ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f545]) ).
thf(f545,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK18 @ Y0 @ Y2 )
& ( sK18 @ Y1 @ Y0 ) )
=> ( sK18 @ Y1 @ Y2 ) ) ) ) )
& $true ) )
| ~ spl0_2 ),
inference(backward_demodulation,[],[f536,f543]) ).
thf(f590,plain,
( spl0_18
| spl0_19
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f581,f25,f588,f585]) ).
thf(f581,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( sK18 @ Y0 @ Y1 ) ) ) )
= $false )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK18 @ Y0 @ Y1 )
& ( sK18 @ Y2 @ Y0 ) )
=> ( sK18 @ Y2 @ Y1 ) ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f578]) ).
thf(f578,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK18 @ Y0 @ Y1 )
& ( sK18 @ Y2 @ Y0 ) )
=> ( sK18 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( sK18 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(not_proxy_clausification,[],[f542]) ).
thf(f542,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK18 @ Y0 @ Y1 )
& ( sK18 @ Y2 @ Y0 ) )
=> ( sK18 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( sK18 @ Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f541]) ).
thf(f541,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK18 @ Y0 @ Y1 )
& ( sK18 @ Y2 @ Y0 ) )
=> ( sK18 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( sK18 @ Y0 @ Y1 ) ) ) ) )
=> $false ) )
| ~ spl0_2 ),
inference(superposition,[],[f519,f535]) ).
thf(f535,plain,
( ( $false
= ( sK18 @ sK4 @ sK5 ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f534]) ).
thf(f519,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y0 @ Y1 )
& ( X1 @ Y2 @ Y0 ) )
=> ( X1 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( X1 @ Y0 @ Y1 ) ) ) ) )
=> ( X1 @ sK4 @ sK5 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f518]) ).
thf(f518,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) )
@ X1 ) )
| ~ spl0_2 ),
inference(pi_clausification,[],[f517]) ).
thf(f517,plain,
( ( $false
!= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) ) )
| ~ spl0_2 ),
inference(backward_demodulation,[],[f18,f26]) ).
thf(f18,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) )
!= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) ) ),
inference(beta_eta_normalization,[],[f17]) ).
thf(f17,plain,
( ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK3 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK4 @ Y0 ) ) )
@ sK5 )
!= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK3 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y5 @ Y7 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK4 @ Y0 ) ) )
@ sK5 ) ),
inference(negative_extensionality,[],[f16]) ).
thf(f16,plain,
( ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK3 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK4 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK3 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y5 @ Y7 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK4 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[],[f15]) ).
thf(f15,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK4 )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK3 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y8 )
& ( Y5 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y8 ) ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y7 )
& ( Y5 @ Y6 @ Y8 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK2 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK4 ) ),
inference(negative_extensionality,[],[f14]) ).
thf(f14,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK3 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y8 )
& ( Y5 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y8 ) ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y7 )
& ( Y5 @ Y6 @ Y8 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK2 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(equality_proxy_clausification,[],[f13]) ).
thf(f13,plain,
( ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK3 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y8 )
& ( Y5 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y8 ) ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y7 )
& ( Y5 @ Y6 @ Y8 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK2 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f12]) ).
thf(f12,plain,
( ( ^ [Y0: a > a > $o] :
( ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y9 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y9 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y7 @ Y9 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( sK2 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( Y0 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[],[f11]) ).
thf(f11,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y9 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y9 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y7 @ Y9 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( sK2 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( Y0 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f10]) ).
thf(f10,plain,
( $false
= ( ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y1 @ Y9 @ Y8 )
=> ( Y7 @ Y9 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y10 )
& ( Y7 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y10 ) ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y9 )
& ( Y7 @ Y8 @ Y10 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y0 @ Y9 @ Y8 )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_clausification,[],[f7]) ).
thf(f7,plain,
( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y1 @ Y9 @ Y8 )
=> ( Y7 @ Y9 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y10 )
& ( Y7 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y10 ) ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y9 )
& ( Y7 @ Y8 @ Y10 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y0 @ Y9 @ Y8 )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y1 @ Y9 @ Y8 )
=> ( Y7 @ Y9 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y10 )
& ( Y7 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y10 ) ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y9 )
& ( Y7 @ Y8 @ Y10 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y0 @ Y9 @ Y8 )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y1 @ Y9 @ Y8 )
=> ( Y7 @ Y9 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y10 )
& ( Y7 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y10 ) ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y9 )
& ( Y7 @ Y8 @ Y10 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y0 @ Y9 @ Y8 )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y6 @ Y5 ) ) ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
~ ! [X0: a > a > $o,X1: a > a > $o] :
( ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ! [X5: a,X6: a] :
( ( ! [X7: a > a > $o] :
( ( ! [X8: a,X9: a] :
( ( X1 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) )
& ! [X10: a,X11: a,X12: a] :
( ( ( X7 @ X12 @ X10 )
& ( X7 @ X10 @ X11 ) )
=> ( X7 @ X12 @ X11 ) ) )
=> ( X7 @ X5 @ X6 ) )
| ! [X13: a > a > $o] :
( ( ! [X14: a,X15: a,X16: a] :
( ( ( X13 @ X15 @ X16 )
& ( X13 @ X16 @ X14 ) )
=> ( X13 @ X15 @ X14 ) )
& ! [X17: a,X18: a] :
( ( X0 @ X17 @ X18 )
=> ( X13 @ X17 @ X18 ) ) )
=> ( X13 @ X5 @ X6 ) ) )
=> ( X4 @ X5 @ X6 ) )
& ! [X19: a,X20: a,X21: a] :
( ( ( X4 @ X20 @ X21 )
& ( X4 @ X21 @ X19 ) )
=> ( X4 @ X20 @ X19 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
= ( ^ [X22: a,X23: a] :
! [X24: a > a > $o] :
( ( ! [X25: a,X26: a] :
( ( ( X0 @ X26 @ X25 )
| ( X1 @ X26 @ X25 ) )
=> ( X24 @ X26 @ X25 ) )
& ! [X27: a,X28: a,X29: a] :
( ( ( X24 @ X27 @ X29 )
& ( X24 @ X29 @ X28 ) )
=> ( X24 @ X27 @ X28 ) ) )
=> ( X24 @ X22 @ X23 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > a > $o,X1: a > a > $o] :
( ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ! [X5: a,X6: a] :
( ( ! [X8: a > a > $o] :
( ( ! [X9: a,X10: a] :
( ( X1 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) )
& ! [X10: a,X7: a,X9: a] :
( ( ( X8 @ X9 @ X10 )
& ( X8 @ X10 @ X7 ) )
=> ( X8 @ X9 @ X7 ) ) )
=> ( X8 @ X5 @ X6 ) )
| ! [X8: a > a > $o] :
( ( ! [X7: a,X9: a,X10: a] :
( ( ( X8 @ X9 @ X10 )
& ( X8 @ X10 @ X7 ) )
=> ( X8 @ X9 @ X7 ) )
& ! [X9: a,X10: a] :
( ( X0 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) ) )
=> ( X8 @ X5 @ X6 ) ) )
=> ( X4 @ X5 @ X6 ) )
& ! [X7: a,X5: a,X6: a] :
( ( ( X4 @ X5 @ X6 )
& ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
= ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ! [X6: a,X5: a] :
( ( ( X0 @ X5 @ X6 )
| ( X1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
& ! [X5: a,X7: a,X6: a] :
( ( ( X4 @ X5 @ X6 )
& ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
! [X0: a > a > $o,X1: a > a > $o] :
( ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ! [X5: a,X6: a] :
( ( ! [X8: a > a > $o] :
( ( ! [X9: a,X10: a] :
( ( X1 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) )
& ! [X10: a,X7: a,X9: a] :
( ( ( X8 @ X9 @ X10 )
& ( X8 @ X10 @ X7 ) )
=> ( X8 @ X9 @ X7 ) ) )
=> ( X8 @ X5 @ X6 ) )
| ! [X8: a > a > $o] :
( ( ! [X7: a,X9: a,X10: a] :
( ( ( X8 @ X9 @ X10 )
& ( X8 @ X10 @ X7 ) )
=> ( X8 @ X9 @ X7 ) )
& ! [X9: a,X10: a] :
( ( X0 @ X9 @ X10 )
=> ( X8 @ X9 @ X10 ) ) )
=> ( X8 @ X5 @ X6 ) ) )
=> ( X4 @ X5 @ X6 ) )
& ! [X7: a,X5: a,X6: a] :
( ( ( X4 @ X5 @ X6 )
& ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
= ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ! [X6: a,X5: a] :
( ( ( X0 @ X5 @ X6 )
| ( X1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
& ! [X5: a,X7: a,X6: a] :
( ( ( X4 @ X5 @ X6 )
& ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM250_pme) ).
thf(f516,plain,
( ~ spl0_1
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f515]) ).
thf(f515,plain,
( $false
| ~ spl0_1
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f514]) ).
thf(f514,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_12 ),
inference(boolean_simplification,[],[f513]) ).
thf(f513,plain,
( ( $true = ~ $true )
| ~ spl0_1
| ~ spl0_12 ),
inference(boolean_simplification,[],[f512]) ).
thf(f512,plain,
( ( $true
= ( ~ ( $true
| ( sK3 @ sK16 @ sK15 ) ) ) )
| ~ spl0_1
| ~ spl0_12 ),
inference(forward_demodulation,[],[f510,f497]) ).
thf(f497,plain,
( ( $true
= ( sK2 @ sK16 @ sK15 ) )
| ~ spl0_12 ),
inference(binary_proxy_clausification,[],[f481]) ).
thf(f481,plain,
( ( ( ( sK2 @ sK16 @ sK15 )
=> ( sK6 @ sK16 @ sK15 ) )
= $false )
| ~ spl0_12 ),
inference(beta_eta_normalization,[],[f480]) ).
thf(f480,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK2 @ Y0 @ sK15 )
=> ( sK6 @ Y0 @ sK15 ) )
@ sK16 ) )
| ~ spl0_12 ),
inference(sigma_clausification,[],[f474]) ).
thf(f474,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ sK15 )
=> ( sK6 @ Y0 @ sK15 ) ) )
= $false )
| ~ spl0_12 ),
inference(beta_eta_normalization,[],[f470]) ).
thf(f470,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) )
@ sK15 ) )
| ~ spl0_12 ),
inference(sigma_clausification,[],[f389]) ).
thf(f389,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f388]) ).
thf(f388,plain,
( spl0_12
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
thf(f510,plain,
( ( $true
= ( ~ ( ( sK2 @ sK16 @ sK15 )
| ( sK3 @ sK16 @ sK15 ) ) ) )
| ~ spl0_1
| ~ spl0_12 ),
inference(boolean_simplification,[],[f505]) ).
thf(f505,plain,
( ( $true
= ( ( ( sK2 @ sK16 @ sK15 )
| ( sK3 @ sK16 @ sK15 ) )
=> $false ) )
| ~ spl0_1
| ~ spl0_12 ),
inference(superposition,[],[f61,f496]) ).
thf(f496,plain,
( ( $false
= ( sK6 @ sK16 @ sK15 ) )
| ~ spl0_12 ),
inference(binary_proxy_clausification,[],[f481]) ).
thf(f61,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( ( sK2 @ X1 @ X2 )
| ( sK3 @ X1 @ X2 ) )
=> ( sK6 @ X1 @ X2 ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f60]) ).
thf(f60,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK2 @ X1 @ Y0 )
| ( sK3 @ X1 @ Y0 ) )
=> ( sK6 @ X1 @ Y0 ) )
@ X2 ) )
| ~ spl0_1 ),
inference(pi_clausification,[],[f57]) ).
thf(f57,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ X1 @ Y0 )
| ( sK3 @ X1 @ Y0 ) )
=> ( sK6 @ X1 @ Y0 ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f56]) ).
thf(f56,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) )
@ X1 ) )
| ~ spl0_1 ),
inference(pi_clausification,[],[f49]) ).
thf(f49,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f44]) ).
thf(f44,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f42]) ).
thf(f42,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
=> ( sK6 @ sK4 @ sK5 ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f41]) ).
thf(f41,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) )
@ sK6 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f23]) ).
thf(f451,plain,
( ~ spl0_1
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f450]) ).
thf(f450,plain,
( $false
| ~ spl0_1
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f446]) ).
thf(f446,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_13 ),
inference(superposition,[],[f426,f68]) ).
thf(f68,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ( ( sK6 @ X1 @ X2 )
& ( sK6 @ X3 @ X1 ) )
=> ( sK6 @ X3 @ X2 ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f67]) ).
thf(f67,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK6 @ X1 @ X2 )
& ( sK6 @ Y0 @ X1 ) )
=> ( sK6 @ Y0 @ X2 ) )
@ X3 ) )
| ~ spl0_1 ),
inference(pi_clausification,[],[f63]) ).
thf(f63,plain,
( ! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ X1 @ X2 )
& ( sK6 @ Y0 @ X1 ) )
=> ( sK6 @ Y0 @ X2 ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f62]) ).
thf(f62,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ X1 @ Y0 )
& ( sK6 @ Y1 @ X1 ) )
=> ( sK6 @ Y1 @ Y0 ) ) )
@ X2 ) )
| ~ spl0_1 ),
inference(pi_clausification,[],[f59]) ).
thf(f59,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ X1 @ Y0 )
& ( sK6 @ Y1 @ X1 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f58]) ).
thf(f58,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) )
@ X1 ) )
| ~ spl0_1 ),
inference(pi_clausification,[],[f52]) ).
thf(f52,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f51]) ).
thf(f51,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) ) )
& $true ) )
| ~ spl0_1 ),
inference(backward_demodulation,[],[f44,f49]) ).
thf(f426,plain,
( ( ( ( ( sK6 @ sK14 @ sK13 )
& ( sK6 @ sK12 @ sK14 ) )
=> ( sK6 @ sK12 @ sK13 ) )
= $false )
| ~ spl0_13 ),
inference(beta_eta_normalization,[],[f425]) ).
thf(f425,plain,
( ( ( ^ [Y0: a] :
( ( ( sK6 @ Y0 @ sK13 )
& ( sK6 @ sK12 @ Y0 ) )
=> ( sK6 @ sK12 @ sK13 ) )
@ sK14 )
= $false )
| ~ spl0_13 ),
inference(sigma_clausification,[],[f420]) ).
thf(f420,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ Y0 @ sK13 )
& ( sK6 @ sK12 @ Y0 ) )
=> ( sK6 @ sK12 @ sK13 ) ) ) )
| ~ spl0_13 ),
inference(beta_eta_normalization,[],[f419]) ).
thf(f419,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 @ Y0 )
& ( sK6 @ sK12 @ Y1 ) )
=> ( sK6 @ sK12 @ Y0 ) ) )
@ sK13 )
= $false )
| ~ spl0_13 ),
inference(sigma_clausification,[],[f406]) ).
thf(f406,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 @ Y0 )
& ( sK6 @ sK12 @ Y1 ) )
=> ( sK6 @ sK12 @ Y0 ) ) ) ) )
| ~ spl0_13 ),
inference(beta_eta_normalization,[],[f404]) ).
thf(f404,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y1 )
& ( sK6 @ Y0 @ Y2 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
@ sK12 ) )
| ~ spl0_13 ),
inference(sigma_clausification,[],[f392]) ).
thf(f392,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y1 )
& ( sK6 @ Y0 @ Y2 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f391]) ).
thf(f391,plain,
( spl0_13
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y1 )
& ( sK6 @ Y0 @ Y2 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
thf(f393,plain,
( spl0_12
| spl0_13
| ~ spl0_5
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f384,f172,f100,f391,f388]) ).
thf(f100,plain,
( spl0_5
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
thf(f172,plain,
( spl0_8
<=> ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
thf(f384,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y1 )
& ( sK6 @ Y0 @ Y2 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_5
| ~ spl0_8 ),
inference(binary_proxy_clausification,[],[f375]) ).
thf(f375,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y1 )
& ( sK6 @ Y0 @ Y2 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_5
| ~ spl0_8 ),
inference(not_proxy_clausification,[],[f323]) ).
thf(f323,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y1 )
& ( sK6 @ Y0 @ Y2 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl0_5
| ~ spl0_8 ),
inference(boolean_simplification,[],[f319]) ).
thf(f319,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y1 )
& ( sK6 @ Y0 @ Y2 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
=> $false ) )
| ~ spl0_5
| ~ spl0_8 ),
inference(superposition,[],[f314,f280]) ).
thf(f280,plain,
( ( $false
= ( sK6 @ sK8 @ sK7 ) )
| ~ spl0_5
| ~ spl0_8 ),
inference(boolean_simplification,[],[f279]) ).
thf(f279,plain,
( ( $false
= ( $true
=> ( sK6 @ sK8 @ sK7 ) ) )
| ~ spl0_5
| ~ spl0_8 ),
inference(boolean_simplification,[],[f278]) ).
thf(f278,plain,
( ( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) )
| $true )
=> ( sK6 @ sK8 @ sK7 ) )
= $false )
| ~ spl0_5
| ~ spl0_8 ),
inference(forward_demodulation,[],[f277,f173]) ).
thf(f173,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f172]) ).
thf(f277,plain,
( ( $false
= ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) )
=> ( sK6 @ sK8 @ sK7 ) ) )
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f276]) ).
thf(f276,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) ) )
=> ( sK6 @ Y0 @ sK7 ) )
@ sK8 )
= $false )
| ~ spl0_5 ),
inference(sigma_clausification,[],[f269]) ).
thf(f269,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) ) )
=> ( sK6 @ Y0 @ sK7 ) ) ) )
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f265]) ).
thf(f265,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y1 @ Y0 ) ) )
@ sK7 ) )
| ~ spl0_5 ),
inference(sigma_clausification,[],[f101]) ).
thf(f101,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f100]) ).
thf(f314,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y2 @ Y1 )
& ( X1 @ Y0 @ Y2 ) )
=> ( X1 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( X1 @ Y1 @ Y0 ) ) ) ) )
=> ( X1 @ sK8 @ sK7 ) ) )
| ~ spl0_8 ),
inference(beta_eta_normalization,[],[f313]) ).
thf(f313,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) )
@ X1 ) )
| ~ spl0_8 ),
inference(pi_clausification,[],[f173]) ).
thf(f242,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f241]) ).
thf(f241,plain,
( $false
| ~ spl0_1
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f240]) ).
thf(f240,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_4 ),
inference(forward_demodulation,[],[f33,f23]) ).
thf(f33,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f32]) ).
thf(f32,plain,
( spl0_4
<=> ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
thf(f213,plain,
( spl0_9
| spl0_6
| ~ spl0_5
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f207,f169,f100,f103,f211]) ).
thf(f169,plain,
( spl0_7
<=> ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
thf(f207,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
= $false )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y2 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y2 ) ) ) ) ) )
| ~ spl0_5
| ~ spl0_7 ),
inference(binary_proxy_clausification,[],[f197]) ).
thf(f197,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y2 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y2 ) ) ) ) ) ) )
| ~ spl0_5
| ~ spl0_7 ),
inference(not_proxy_clausification,[],[f190]) ).
thf(f190,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y2 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y2 ) ) ) ) ) ) ) )
| ~ spl0_5
| ~ spl0_7 ),
inference(boolean_simplification,[],[f189]) ).
thf(f189,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y2 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y2 ) ) ) ) ) )
=> $false ) )
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[],[f181,f140]) ).
thf(f140,plain,
( ( $false
= ( sK6 @ sK8 @ sK7 ) )
| ~ spl0_5 ),
inference(boolean_simplification,[],[f139]) ).
thf(f139,plain,
( ( $false
= ( $true
=> ( sK6 @ sK8 @ sK7 ) ) )
| ~ spl0_5 ),
inference(backward_demodulation,[],[f129,f138]) ).
thf(f138,plain,
( ( $true
= ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) ) )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f129]) ).
thf(f129,plain,
( ( $false
= ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) )
=> ( sK6 @ sK8 @ sK7 ) ) )
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f128]) ).
thf(f128,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) ) )
=> ( sK6 @ Y0 @ sK7 ) )
@ sK8 )
= $false )
| ~ spl0_5 ),
inference(sigma_clausification,[],[f116]) ).
thf(f116,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 @ sK7 ) ) ) )
=> ( sK6 @ Y0 @ sK7 ) ) ) )
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f114]) ).
thf(f114,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y1 @ Y0 ) ) )
@ sK7 ) )
| ~ spl0_5 ),
inference(sigma_clausification,[],[f101]) ).
thf(f181,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( X1 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y0 @ Y2 )
& ( X1 @ Y1 @ Y0 ) )
=> ( X1 @ Y1 @ Y2 ) ) ) ) ) )
=> ( X1 @ sK8 @ sK7 ) ) )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f180]) ).
thf(f180,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) )
@ X1 ) )
| ~ spl0_7 ),
inference(pi_clausification,[],[f170]) ).
thf(f170,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f169]) ).
thf(f174,plain,
( spl0_7
| spl0_8
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f167,f100,f172,f169]) ).
thf(f167,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) )
| ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK8 @ sK7 ) ) ) )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f138]) ).
thf(f105,plain,
( spl0_5
| spl0_6
| ~ spl0_1
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f96,f29,f22,f103,f100]) ).
thf(f29,plain,
( spl0_3
<=> ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
thf(f96,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y2 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y2 ) ) ) ) ) )
| ~ spl0_1
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f87]) ).
thf(f87,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y2 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_1
| ~ spl0_3 ),
inference(not_proxy_clausification,[],[f55]) ).
thf(f55,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y2 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl0_1
| ~ spl0_3 ),
inference(boolean_simplification,[],[f54]) ).
thf(f54,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y2 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
=> $false )
= $true )
| ~ spl0_1
| ~ spl0_3 ),
inference(superposition,[],[f48,f46]) ).
thf(f46,plain,
( ( $false
= ( sK6 @ sK4 @ sK5 ) )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f45]) ).
thf(f45,plain,
( ( $false
= ( $true
=> ( sK6 @ sK4 @ sK5 ) ) )
| ~ spl0_1 ),
inference(backward_demodulation,[],[f42,f44]) ).
thf(f48,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y0 @ Y2 )
& ( X1 @ Y1 @ Y0 ) )
=> ( X1 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( X1 @ Y1 @ Y0 ) ) ) ) )
=> ( X1 @ sK4 @ sK5 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f47]) ).
thf(f47,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) )
@ X1 ) )
| ~ spl0_3 ),
inference(pi_clausification,[],[f30]) ).
thf(f30,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f29]) ).
thf(f34,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f19,f32,f29]) ).
thf(f19,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) ) )
| ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f18]) ).
thf(f27,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f20,f25,f22]) ).
thf(f20,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) ) )
| ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEV141^5 : TPTP v8.2.0. Released v4.0.0.
% 0.12/0.12 % Command : run_vampire %s %d THM
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 21 18:31:09 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.19/0.35 This is a TH0_THM_EQU_NAR problem
% 0.19/0.35 Running higher-order theorem proving
% 0.19/0.35 Running /export/starexec/sandbox/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox/benchmark/theBenchmark.p -m 16384 -t 300
% 0.19/0.38 % (3869)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.19/0.38 % (3871)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.19/0.38 % (3870)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.19/0.38 % (3872)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.38 % (3873)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.38 % (3874)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.19/0.38 % (3875)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.19/0.38 % (3872)Instruction limit reached!
% 0.19/0.38 % (3872)------------------------------
% 0.19/0.38 % (3872)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.38 % (3872)Termination reason: Unknown
% 0.19/0.38 % (3872)Termination phase: Unused predicate definition removal
% 0.19/0.38
% 0.19/0.38 % (3872)Memory used [KB]: 1023
% 0.19/0.38 % (3872)Time elapsed: 0.004 s
% 0.19/0.38 % (3872)Instructions burned: 3 (million)
% 0.19/0.38 % (3872)------------------------------
% 0.19/0.38 % (3872)------------------------------
% 0.19/0.38 % (3873)Instruction limit reached!
% 0.19/0.38 % (3873)------------------------------
% 0.19/0.38 % (3873)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.38 % (3873)Termination reason: Unknown
% 0.19/0.38 % (3873)Termination phase: Unused predicate definition removal
% 0.19/0.38
% 0.19/0.38 % (3873)Memory used [KB]: 1023
% 0.19/0.38 % (3873)Time elapsed: 0.004 s
% 0.19/0.38 % (3873)Instructions burned: 3 (million)
% 0.19/0.38 % (3873)------------------------------
% 0.19/0.38 % (3873)------------------------------
% 0.19/0.38 % (3870)Instruction limit reached!
% 0.19/0.38 % (3870)------------------------------
% 0.19/0.38 % (3870)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.38 % (3870)Termination reason: Unknown
% 0.19/0.38 % (3870)Termination phase: Saturation
% 0.19/0.38
% 0.19/0.38 % (3870)Memory used [KB]: 1023
% 0.19/0.38 % (3870)Time elapsed: 0.005 s
% 0.19/0.38 % (3870)Instructions burned: 4 (million)
% 0.19/0.38 % (3870)------------------------------
% 0.19/0.38 % (3870)------------------------------
% 0.19/0.39 % (3875)Instruction limit reached!
% 0.19/0.39 % (3875)------------------------------
% 0.19/0.39 % (3875)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.39 % (3875)Termination reason: Unknown
% 0.19/0.39 % (3875)Termination phase: Saturation
% 0.19/0.39
% 0.19/0.39 % (3875)Memory used [KB]: 5628
% 0.19/0.39 % (3875)Time elapsed: 0.013 s
% 0.19/0.39 % (3875)Instructions burned: 19 (million)
% 0.19/0.39 % (3875)------------------------------
% 0.19/0.39 % (3875)------------------------------
% 0.19/0.39 % (3871)Instruction limit reached!
% 0.19/0.39 % (3871)------------------------------
% 0.19/0.39 % (3871)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.39 % (3871)Termination reason: Unknown
% 0.19/0.39 % (3871)Termination phase: Saturation
% 0.19/0.39
% 0.19/0.39 % (3871)Memory used [KB]: 5628
% 0.19/0.39 % (3871)Time elapsed: 0.017 s
% 0.19/0.39 % (3871)Instructions burned: 27 (million)
% 0.19/0.39 % (3871)------------------------------
% 0.19/0.39 % (3871)------------------------------
% 0.19/0.39 % (3876)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.39 % (3877)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.19/0.39 % (3878)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.19/0.39 % (3876)Instruction limit reached!
% 0.19/0.39 % (3876)------------------------------
% 0.19/0.39 % (3876)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.39 % (3876)Termination reason: Unknown
% 0.19/0.39 % (3876)Termination phase: Preprocessing 3
% 0.19/0.39
% 0.19/0.39 % (3876)Memory used [KB]: 1023
% 0.19/0.39 % (3876)Time elapsed: 0.004 s
% 0.19/0.39 % (3876)Instructions burned: 3 (million)
% 0.19/0.39 % (3876)------------------------------
% 0.19/0.39 % (3876)------------------------------
% 0.19/0.40 % (3879)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.40 % (3878)Instruction limit reached!
% 0.19/0.40 % (3878)------------------------------
% 0.19/0.40 % (3878)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.40 % (3878)Termination reason: Unknown
% 0.19/0.40 % (3878)Termination phase: Saturation
% 0.19/0.40
% 0.19/0.40 % (3878)Memory used [KB]: 5628
% 0.19/0.40 % (3878)Time elapsed: 0.011 s
% 0.19/0.40 % (3878)Instructions burned: 16 (million)
% 0.19/0.40 % (3878)------------------------------
% 0.19/0.40 % (3878)------------------------------
% 0.19/0.40 % (3879)Instruction limit reached!
% 0.19/0.40 % (3879)------------------------------
% 0.19/0.40 % (3879)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.40 % (3879)Termination reason: Unknown
% 0.19/0.40 % (3879)Termination phase: Preprocessing 3
% 0.19/0.40
% 0.19/0.40 % (3879)Memory used [KB]: 1023
% 0.19/0.40 % (3879)Time elapsed: 0.004 s
% 0.19/0.40 % (3879)Instructions burned: 3 (million)
% 0.19/0.40 % (3879)------------------------------
% 0.19/0.40 % (3879)------------------------------
% 0.19/0.41 % (3880)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.19/0.41 % (3881)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.41 % (3877)Instruction limit reached!
% 0.19/0.41 % (3877)------------------------------
% 0.19/0.41 % (3877)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.41 % (3877)Termination reason: Unknown
% 0.19/0.41 % (3877)Termination phase: Saturation
% 0.19/0.41
% 0.19/0.41 % (3877)Memory used [KB]: 5628
% 0.19/0.41 % (3877)Time elapsed: 0.023 s
% 0.19/0.41 % (3877)Instructions burned: 38 (million)
% 0.19/0.41 % (3877)------------------------------
% 0.19/0.41 % (3877)------------------------------
% 0.19/0.41 % (3881)Instruction limit reached!
% 0.19/0.41 % (3881)------------------------------
% 0.19/0.41 % (3881)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.41 % (3881)Termination reason: Unknown
% 0.19/0.41 % (3881)Termination phase: Saturation
% 0.19/0.41
% 0.19/0.41 % (3881)Memory used [KB]: 1023
% 0.19/0.41 % (3881)Time elapsed: 0.007 s
% 0.19/0.41 % (3881)Instructions burned: 8 (million)
% 0.19/0.41 % (3881)------------------------------
% 0.19/0.41 % (3881)------------------------------
% 0.22/0.42 % (3882)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.22/0.42 % (3883)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.22/0.42 % (3883)Instruction limit reached!
% 0.22/0.42 % (3883)------------------------------
% 0.22/0.42 % (3883)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.42 % (3883)Termination reason: Unknown
% 0.22/0.42 % (3883)Termination phase: Preprocessing 3
% 0.22/0.42
% 0.22/0.42 % (3883)Memory used [KB]: 1023
% 0.22/0.42 % (3883)Time elapsed: 0.004 s
% 0.22/0.42 % (3883)Instructions burned: 3 (million)
% 0.22/0.42 % (3883)------------------------------
% 0.22/0.42 % (3883)------------------------------
% 0.22/0.43 % (3882)Instruction limit reached!
% 0.22/0.43 % (3882)------------------------------
% 0.22/0.43 % (3882)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.43 % (3882)Termination reason: Unknown
% 0.22/0.43 % (3882)Termination phase: Saturation
% 0.22/0.43
% 0.22/0.43 % (3882)Memory used [KB]: 5756
% 0.22/0.43 % (3882)Time elapsed: 0.013 s
% 0.22/0.43 % (3882)Instructions burned: 16 (million)
% 0.22/0.43 % (3882)------------------------------
% 0.22/0.43 % (3882)------------------------------
% 0.22/0.43 % (3884)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.22/0.43 % (3885)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.22/0.43 % (3884)Instruction limit reached!
% 0.22/0.43 % (3884)------------------------------
% 0.22/0.43 % (3884)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.43 % (3884)Termination reason: Unknown
% 0.22/0.43 % (3884)Termination phase: Preprocessing 3
% 0.22/0.43
% 0.22/0.43 % (3884)Memory used [KB]: 1023
% 0.22/0.43 % (3884)Time elapsed: 0.004 s
% 0.22/0.43 % (3884)Instructions burned: 3 (million)
% 0.22/0.43 % (3884)------------------------------
% 0.22/0.43 % (3884)------------------------------
% 0.22/0.44 % (3885)Instruction limit reached!
% 0.22/0.44 % (3885)------------------------------
% 0.22/0.44 % (3885)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.44 % (3885)Termination reason: Unknown
% 0.22/0.44 % (3885)Termination phase: Saturation
% 0.22/0.44
% 0.22/0.44 % (3885)Memory used [KB]: 5500
% 0.22/0.44 % (3885)Time elapsed: 0.007 s
% 0.22/0.44 % (3885)Instructions burned: 8 (million)
% 0.22/0.44 % (3885)------------------------------
% 0.22/0.44 % (3885)------------------------------
% 0.22/0.44 % (3886)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.22/0.44 % (3886)Instruction limit reached!
% 0.22/0.44 % (3886)------------------------------
% 0.22/0.44 % (3886)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.44 % (3886)Termination reason: Unknown
% 0.22/0.44 % (3886)Termination phase: Clausification
% 0.22/0.44
% 0.22/0.44 % (3886)Memory used [KB]: 1023
% 0.22/0.44 % (3886)Time elapsed: 0.004 s
% 0.22/0.44 % (3886)Instructions burned: 4 (million)
% 0.22/0.44 % (3886)------------------------------
% 0.22/0.44 % (3886)------------------------------
% 0.22/0.44 % (3887)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.22/0.45 % (3888)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.22/0.45 % (3887)Instruction limit reached!
% 0.22/0.45 % (3887)------------------------------
% 0.22/0.45 % (3887)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.45 % (3887)Termination reason: Unknown
% 0.22/0.45 % (3887)Termination phase: Saturation
% 0.22/0.45
% 0.22/0.45 % (3887)Memory used [KB]: 5500
% 0.22/0.45 % (3887)Time elapsed: 0.005 s
% 0.22/0.45 % (3887)Instructions burned: 5 (million)
% 0.22/0.45 % (3887)------------------------------
% 0.22/0.45 % (3887)------------------------------
% 0.22/0.45 % (3889)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.22/0.45 % (3890)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.22/0.46 % (3888)Instruction limit reached!
% 0.22/0.46 % (3888)------------------------------
% 0.22/0.46 % (3888)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.46 % (3888)Termination reason: Unknown
% 0.22/0.46 % (3888)Termination phase: Saturation
% 0.22/0.46
% 0.22/0.46 % (3888)Memory used [KB]: 5500
% 0.22/0.46 % (3888)Time elapsed: 0.012 s
% 0.22/0.46 % (3888)Instructions burned: 18 (million)
% 0.22/0.46 % (3888)------------------------------
% 0.22/0.46 % (3888)------------------------------
% 0.22/0.46 % (3890)Instruction limit reached!
% 0.22/0.46 % (3890)------------------------------
% 0.22/0.46 % (3890)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.46 % (3890)Termination reason: Unknown
% 0.22/0.46 % (3890)Termination phase: Saturation
% 0.22/0.46
% 0.22/0.46 % (3890)Memory used [KB]: 5500
% 0.22/0.46 % (3890)Time elapsed: 0.006 s
% 0.22/0.46 % (3890)Instructions burned: 6 (million)
% 0.22/0.46 % (3890)------------------------------
% 0.22/0.46 % (3890)------------------------------
% 0.22/0.46 % (3891)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on theBenchmark for (2999ds/902Mi)
% 0.22/0.47 % (3892)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on theBenchmark for (2999ds/21Mi)
% 0.22/0.47 % (3893)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.22/0.48 % (3869)Instruction limit reached!
% 0.22/0.48 % (3869)------------------------------
% 0.22/0.48 % (3869)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.48 % (3869)Termination reason: Unknown
% 0.22/0.48 % (3869)Termination phase: Saturation
% 0.22/0.48
% 0.22/0.48 % (3869)Memory used [KB]: 6524
% 0.22/0.48 % (3869)Time elapsed: 0.103 s
% 0.22/0.48 % (3869)Instructions burned: 184 (million)
% 0.22/0.48 % (3869)------------------------------
% 0.22/0.48 % (3869)------------------------------
% 0.22/0.48 % (3893)Instruction limit reached!
% 0.22/0.48 % (3893)------------------------------
% 0.22/0.48 % (3893)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.48 % (3893)Termination reason: Unknown
% 0.22/0.48 % (3893)Termination phase: Saturation
% 0.22/0.48
% 0.22/0.48 % (3893)Memory used [KB]: 5500
% 0.22/0.48 % (3893)Time elapsed: 0.005 s
% 0.22/0.48 % (3893)Instructions burned: 6 (million)
% 0.22/0.48 % (3893)------------------------------
% 0.22/0.48 % (3893)------------------------------
% 0.22/0.48 % (3892)Instruction limit reached!
% 0.22/0.48 % (3892)------------------------------
% 0.22/0.48 % (3892)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.48 % (3892)Termination reason: Unknown
% 0.22/0.48 % (3892)Termination phase: Saturation
% 0.22/0.48
% 0.22/0.48 % (3892)Memory used [KB]: 5628
% 0.22/0.48 % (3892)Time elapsed: 0.014 s
% 0.22/0.48 % (3892)Instructions burned: 22 (million)
% 0.22/0.48 % (3892)------------------------------
% 0.22/0.48 % (3892)------------------------------
% 0.22/0.49 % (3895)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2998ds/377Mi)
% 0.22/0.49 % (3894)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on theBenchmark for (2998ds/6Mi)
% 0.22/0.49 % (3894)Instruction limit reached!
% 0.22/0.49 % (3894)------------------------------
% 0.22/0.49 % (3894)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.49 % (3894)Termination reason: Unknown
% 0.22/0.49 % (3894)Termination phase: Saturation
% 0.22/0.49
% 0.22/0.49 % (3894)Memory used [KB]: 5500
% 0.22/0.49 % (3894)Time elapsed: 0.003 s
% 0.22/0.49 % (3894)Instructions burned: 6 (million)
% 0.22/0.49 % (3894)------------------------------
% 0.22/0.49 % (3894)------------------------------
% 0.22/0.49 % (3896)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on theBenchmark for (2998ds/779Mi)
% 0.22/0.50 % (3897)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on theBenchmark for (2998ds/19Mi)
% 0.22/0.51 % (3897)Instruction limit reached!
% 0.22/0.51 % (3897)------------------------------
% 0.22/0.51 % (3897)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.51 % (3897)Termination reason: Unknown
% 0.22/0.51 % (3897)Termination phase: Saturation
% 0.22/0.51
% 0.22/0.51 % (3897)Memory used [KB]: 5500
% 0.22/0.51 % (3897)Time elapsed: 0.008 s
% 0.22/0.51 % (3897)Instructions burned: 20 (million)
% 0.22/0.51 % (3897)------------------------------
% 0.22/0.51 % (3897)------------------------------
% 0.22/0.51 % (3874)Instruction limit reached!
% 0.22/0.51 % (3874)------------------------------
% 0.22/0.51 % (3874)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.51 % (3874)Termination reason: Unknown
% 0.22/0.51 % (3874)Termination phase: Saturation
% 0.22/0.51
% 0.22/0.51 % (3874)Memory used [KB]: 7164
% 0.22/0.51 % (3874)Time elapsed: 0.137 s
% 0.22/0.51 % (3874)Instructions burned: 277 (million)
% 0.22/0.51 % (3874)------------------------------
% 0.22/0.51 % (3874)------------------------------
% 0.22/0.52 % (3898)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on theBenchmark for (2998ds/879Mi)
% 0.22/0.52 % (3899)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2998ds/17Mi)
% 0.22/0.53 % (3899)Instruction limit reached!
% 0.22/0.53 % (3899)------------------------------
% 0.22/0.53 % (3899)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.53 % (3899)Termination reason: Unknown
% 0.22/0.53 % (3899)Termination phase: Saturation
% 0.22/0.53
% 0.22/0.53 % (3899)Memory used [KB]: 5756
% 0.22/0.53 % (3899)Time elapsed: 0.008 s
% 0.22/0.53 % (3899)Instructions burned: 20 (million)
% 0.22/0.53 % (3899)------------------------------
% 0.22/0.53 % (3899)------------------------------
% 0.22/0.53 % (3900)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi)
% 0.22/0.54 % (3900)Instruction limit reached!
% 0.22/0.54 % (3900)------------------------------
% 0.22/0.54 % (3900)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.54 % (3900)Termination reason: Unknown
% 0.22/0.54 % (3900)Termination phase: Property scanning
% 0.22/0.54
% 0.22/0.54 % (3900)Memory used [KB]: 1023
% 0.22/0.54 % (3900)Time elapsed: 0.003 s
% 0.22/0.54 % (3900)Instructions burned: 4 (million)
% 0.22/0.54 % (3900)------------------------------
% 0.22/0.54 % (3900)------------------------------
% 0.22/0.54 % (3901)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on theBenchmark for (2998ds/30Mi)
% 0.22/0.55 % (3901)Refutation not found, incomplete strategy
% 0.22/0.55 % (3901)------------------------------
% 0.22/0.55 % (3901)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.55 % (3901)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.55
% 0.22/0.55
% 0.22/0.55 % (3901)Memory used [KB]: 5500
% 0.22/0.55 % (3901)Time elapsed: 0.006 s
% 0.22/0.55 % (3901)Instructions burned: 13 (million)
% 0.22/0.55 % (3901)------------------------------
% 0.22/0.55 % (3901)------------------------------
% 0.22/0.56 % (3902)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on theBenchmark for (2998ds/127Mi)
% 1.56/0.58 % (3880)First to succeed.
% 1.72/0.59 % (3880)Refutation found. Thanks to Tanya!
% 1.72/0.59 % SZS status Theorem for theBenchmark
% 1.72/0.59 % SZS output start Proof for theBenchmark
% See solution above
% 1.72/0.60 % (3880)------------------------------
% 1.72/0.60 % (3880)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 1.72/0.60 % (3880)Termination reason: Refutation
% 1.72/0.60
% 1.72/0.60 % (3880)Memory used [KB]: 7036
% 1.72/0.60 % (3880)Time elapsed: 0.189 s
% 1.72/0.60 % (3880)Instructions burned: 391 (million)
% 1.72/0.60 % (3880)------------------------------
% 1.72/0.60 % (3880)------------------------------
% 1.72/0.60 % (3868)Success in time 0.211 s
%------------------------------------------------------------------------------