%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV154^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:40:25 AM UTC 2026
% Result : Theorem 1.35s 1.28s
% Output : Refutation 1.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 23
% Syntax : Number of formulae : 381 ( 30 unt; 0 typ; 22 def)
% Number of atoms : 4100 ( 355 equ; 0 cnn)
% Maximal formula atoms : 4 ( 10 avg)
% Number of connectives : 11676 ( 550 ~;1115 |; 768 &;6769 @)
% ( 22 <=>;1136 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 577 ( 577 >; 0 *; 0 +; 0 <<)
% Number of symbols : 55 ( 51 usr; 48 con; 0-2 aty)
% (1316 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 1534 (1368 ^; 166 !; 0 ?;1534 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_21,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
sK2: a > a > $o ).
thf(func_def_23,type,
sK3: a > a > $o ).
thf(func_def_24,type,
sK4: a ).
thf(func_def_25,type,
sK5: a ).
thf(func_def_26,type,
sK6: a > $o ).
thf(func_def_27,type,
sK7: a ).
thf(func_def_28,type,
sK8: a ).
thf(func_def_29,type,
sK9: a ).
thf(func_def_30,type,
sK10: a > $o ).
thf(func_def_31,type,
sK11: a ).
thf(func_def_32,type,
sK12: a ).
thf(func_def_33,type,
sK13: a ).
thf(func_def_34,type,
sK14: a > $o ).
thf(func_def_35,type,
sK15: a ).
thf(func_def_36,type,
sK16: a ).
thf(func_def_37,type,
sK17: a ).
thf(func_def_38,type,
sK18: a ).
thf(func_def_39,type,
sK19: a ).
thf(func_def_40,type,
sK20: a ).
thf(func_def_41,type,
sK21: a ).
thf(func_def_42,type,
sK22: a ).
thf(func_def_43,type,
sK23: a ).
thf(func_def_44,type,
sK24: a ).
thf(func_def_45,type,
sK25: a ).
thf(func_def_46,type,
sK26: a ).
thf(func_def_47,type,
sK27: a ).
thf(func_def_48,type,
sK28: a ).
thf(func_def_49,type,
sK29: a ).
thf(f1844,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f34,f48,f233,f336,f443,f493,f523,f529,f536,f600,f610,f620,f794,f878,f916,f1067,f1080,f1093,f1341,f1400,f1455,f1815,f1843]) ).
thf(f1843,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f1842]) ).
thf(f1842,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(trivial_inequality_removal,[status(thm)],[f1841]) ).
thf(f1841,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(boolean_simplification,[status(thm)],[f1840]) ).
thf(f1840,plain,
( ( $true = ( ~ $true ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(boolean_simplification,[status(thm)],[f1839]) ).
thf(f1839,plain,
( ( $true
= ( ~ ( ( sK3 @ sK12 @ sK29 )
| $true ) ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[status(thm)],[f1837,f1825]) ).
thf(f1825,plain,
( ( $true
= ( sK2 @ sK12 @ sK29 ) )
| ~ spl0_9 ),
inference(binary_proxy_clausification,[status(thm)],[f1821]) ).
thf(f1821,plain,
( ( ( ( sK2 @ sK12 @ sK29 )
=> ( sK14 @ sK29 ) )
= $false )
| ~ spl0_9 ),
inference(beta_eta_normalization,[status(thm)],[f1819]) ).
thf(f1819,plain,
( ( ( ^ [Y0: a] :
( ( sK2 @ sK12 @ Y0 )
=> ( sK14 @ Y0 ) )
@ sK29 )
= $false )
| ~ spl0_9 ),
inference(sigma_clausification,[status(thm)],[f439]) ).
thf(f439,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK12 @ Y0 )
=> ( sK14 @ Y0 ) ) ) )
| ~ spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f438]) ).
thf(f438,definition,
( spl0_9
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK12 @ Y0 )
=> ( sK14 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition]) ).
thf(f1837,plain,
( ( $true
= ( ~ ( ( sK3 @ sK12 @ sK29 )
| ( sK2 @ sK12 @ sK29 ) ) ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(boolean_simplification,[status(thm)],[f1830]) ).
thf(f1830,plain,
( ( $true
= ( ( ( sK3 @ sK12 @ sK29 )
| ( sK2 @ sK12 @ sK29 ) )
=> $false ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[status(thm)],[f1660,f1824]) ).
thf(f1824,plain,
( ( $false
= ( sK14 @ sK29 ) )
| ~ spl0_9 ),
inference(binary_proxy_clausification,[status(thm)],[f1821]) ).
thf(f1660,plain,
( ! [X1: a] :
( $true
= ( ( ( sK3 @ sK12 @ X1 )
| ( sK2 @ sK12 @ X1 ) )
=> ( sK14 @ X1 ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(beta_eta_normalization,[status(thm)],[f1659]) ).
thf(f1659,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK3 @ sK12 @ Y0 )
| ( sK2 @ sK12 @ Y0 ) )
=> ( sK14 @ Y0 ) )
@ X1 ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(pi_clausification,[status(thm)],[f1506]) ).
thf(f1506,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK12 @ Y0 )
| ( sK2 @ sK12 @ Y0 ) )
=> ( sK14 @ Y0 ) ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(binary_proxy_clausification,[status(thm)],[f1482]) ).
thf(f1482,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK12 @ Y0 )
| ( sK2 @ sK12 @ Y0 ) )
=> ( sK14 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
& ( sK14 @ Y1 ) )
=> ( sK14 @ Y0 ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(binary_proxy_clausification,[status(thm)],[f1470]) ).
thf(f1470,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK12 @ Y0 )
| ( sK2 @ sK12 @ Y0 ) )
=> ( sK14 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
& ( sK14 @ Y1 ) )
=> ( sK14 @ Y0 ) ) ) ) )
=> ( sK14 @ sK13 ) )
= $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(beta_eta_normalization,[status(thm)],[f1469]) ).
thf(f1469,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK12 @ Y1 )
| ( sK2 @ sK12 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK13 ) )
@ sK14 )
= $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(sigma_clausification,[status(thm)],[f1458]) ).
thf(f1458,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK12 @ Y1 )
| ( sK2 @ sK12 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK13 ) ) )
= $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(boolean_simplification,[status(thm)],[f1457]) ).
thf(f1457,plain,
( ( $false
= ( $true
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK12 @ Y1 )
| ( sK2 @ sK12 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK13 ) ) ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(boolean_simplification,[status(thm)],[f1456]) ).
thf(f1456,plain,
( ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK13 ) ) )
| $true )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK12 @ Y1 )
| ( sK2 @ sK12 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK13 ) ) ) )
= $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[status(thm)],[f1106,f332]) ).
thf(f332,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK13 ) ) )
= $true )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f331]) ).
thf(f331,definition,
( spl0_7
<=> ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK13 ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f1106,plain,
( ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK13 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK13 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK12 @ Y1 )
| ( sK2 @ sK12 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK13 ) ) ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f1105]) ).
thf(f1105,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK12 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK12 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ sK12 @ Y2 )
| ( sK2 @ sK12 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK2 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
@ sK13 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f1102]) ).
thf(f1102,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK12 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK12 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ sK12 @ Y2 )
| ( sK2 @ sK12 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK2 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f1101]) ).
thf(f1101,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y0 @ Y3 )
| ( sK2 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK2 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
@ sK12 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y0 @ Y3 )
| ( sK2 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK2 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
= $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f46]) ).
thf(f46,definition,
( spl0_4
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y0 @ Y3 )
| ( sK2 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK2 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f1815,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[status(thm)],[f1814]) ).
thf(f1814,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(trivial_inequality_removal,[status(thm)],[f1813]) ).
thf(f1813,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(forward_demodulation,[status(thm)],[f1812,f1755]) ).
thf(f1755,plain,
( ( ( sK14 @ sK26 )
= $false )
| ~ spl0_10 ),
inference(binary_proxy_clausification,[status(thm)],[f1738]) ).
thf(f1738,plain,
( ( $false
= ( ( ( sK14 @ sK27 )
& ( sK2 @ sK27 @ sK26 ) )
=> ( sK14 @ sK26 ) ) )
| ~ spl0_10 ),
inference(beta_eta_normalization,[status(thm)],[f1737]) ).
thf(f1737,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK14 @ Y0 )
& ( sK2 @ Y0 @ sK26 ) )
=> ( sK14 @ sK26 ) )
@ sK27 ) )
| ~ spl0_10 ),
inference(sigma_clausification,[status(thm)],[f1725]) ).
thf(f1725,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK14 @ Y0 )
& ( sK2 @ Y0 @ sK26 ) )
=> ( sK14 @ sK26 ) ) ) )
| ~ spl0_10 ),
inference(beta_eta_normalization,[status(thm)],[f1723]) ).
thf(f1723,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK14 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK14 @ Y0 ) ) )
@ sK26 )
= $false )
| ~ spl0_10 ),
inference(sigma_clausification,[status(thm)],[f442]) ).
thf(f442,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK14 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK14 @ Y0 ) ) ) )
= $false )
| ~ spl0_10 ),
inference(avatar_component_clause,[status(thm)],[f441]) ).
thf(f441,definition,
( spl0_10
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK14 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK14 @ Y0 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition]) ).
thf(f1812,plain,
( ( $true
= ( sK14 @ sK26 ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(boolean_simplification,[status(thm)],[f1811]) ).
thf(f1811,plain,
( ( $true
= ( $true
=> ( sK14 @ sK26 ) ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(forward_demodulation,[status(thm)],[f1810,f1796]) ).
thf(f1796,plain,
( ( $true
= ( sK14 @ sK28 ) )
| ~ spl0_10 ),
inference(boolean_simplification,[status(thm)],[f1795]) ).
thf(f1795,plain,
( ( $true
= ( ( sK14 @ sK28 )
& $true ) )
| ~ spl0_10 ),
inference(backward_demodulation,[status(thm)],[f1790,f1793]) ).
thf(f1793,plain,
( ( $true
= ( sK2 @ sK28 @ sK26 ) )
| ~ spl0_10 ),
inference(binary_proxy_clausification,[status(thm)],[f1790]) ).
thf(f1790,plain,
( ( $true
= ( ( sK14 @ sK28 )
& ( sK2 @ sK28 @ sK26 ) ) )
| ~ spl0_10 ),
inference(not_proxy_clausification,[status(thm)],[f1773]) ).
thf(f1773,plain,
( ( ( ~ ( ( sK14 @ sK28 )
& ( sK2 @ sK28 @ sK26 ) ) )
= $false )
| ~ spl0_10 ),
inference(beta_eta_normalization,[status(thm)],[f1772]) ).
thf(f1772,plain,
( ( ( ^ [Y0: a] :
~ ( ( sK14 @ Y0 )
& ( sK2 @ Y0 @ sK26 ) )
@ sK28 )
= $false )
| ~ spl0_10 ),
inference(sigma_clausification,[status(thm)],[f1760]) ).
thf(f1760,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
~ ( ( sK14 @ Y0 )
& ( sK2 @ Y0 @ sK26 ) ) )
= $false )
| ~ spl0_10 ),
inference(boolean_simplification,[status(thm)],[f1758]) ).
thf(f1758,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK14 @ Y0 )
& ( sK2 @ Y0 @ sK26 ) )
=> $false ) )
= $false )
| ~ spl0_10 ),
inference(backward_demodulation,[status(thm)],[f1725,f1755]) ).
thf(f1810,plain,
( ( $true
= ( ( sK14 @ sK28 )
=> ( sK14 @ sK26 ) ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(boolean_simplification,[status(thm)],[f1809]) ).
thf(f1809,plain,
( ( ( ( $true
& ( sK14 @ sK28 ) )
=> ( sK14 @ sK26 ) )
= $true )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(boolean_simplification,[status(thm)],[f1805]) ).
thf(f1805,plain,
( ( $true
= ( ( ( $true
| ( sK3 @ sK28 @ sK26 ) )
& ( sK14 @ sK28 ) )
=> ( sK14 @ sK26 ) ) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(superposition,[status(thm)],[f1530,f1793]) ).
thf(f1530,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( ( ( sK2 @ X2 @ X1 )
| ( sK3 @ X2 @ X1 ) )
& ( sK14 @ X2 ) )
=> ( sK14 @ X1 ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(beta_eta_normalization,[status(thm)],[f1529]) ).
thf(f1529,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( ( sK2 @ Y0 @ X1 )
| ( sK3 @ Y0 @ X1 ) )
& ( sK14 @ Y0 ) )
=> ( sK14 @ X1 ) )
@ X2 ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(pi_clausification,[status(thm)],[f1519]) ).
thf(f1519,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( ( sK2 @ Y0 @ X1 )
| ( sK3 @ Y0 @ X1 ) )
& ( sK14 @ Y0 ) )
=> ( sK14 @ X1 ) ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(beta_eta_normalization,[status(thm)],[f1518]) ).
thf(f1518,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
& ( sK14 @ Y1 ) )
=> ( sK14 @ Y0 ) ) )
@ X1 ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(pi_clausification,[status(thm)],[f1508]) ).
thf(f1508,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
& ( sK14 @ Y1 ) )
=> ( sK14 @ Y0 ) ) ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(boolean_simplification,[status(thm)],[f1507]) ).
thf(f1507,plain,
( ( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
& ( sK14 @ Y1 ) )
=> ( sK14 @ Y0 ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(backward_demodulation,[status(thm)],[f1482,f1506]) ).
thf(f1455,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_29 ),
inference(avatar_contradiction_clause,[status(thm)],[f1454]) ).
thf(f1454,plain,
( $false
| ~ spl0_4
| ~ spl0_8
| ~ spl0_29 ),
inference(trivial_inequality_removal,[status(thm)],[f1453]) ).
thf(f1453,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_29 ),
inference(forward_demodulation,[status(thm)],[f1452,f1422]) ).
thf(f1422,plain,
( ( ( sK14 @ sK25 )
= $false )
| ~ spl0_29 ),
inference(binary_proxy_clausification,[status(thm)],[f1412]) ).
thf(f1412,plain,
( ( ( ( ( sK3 @ sK24 @ sK25 )
& ( sK14 @ sK24 ) )
=> ( sK14 @ sK25 ) )
= $false )
| ~ spl0_29 ),
inference(beta_eta_normalization,[status(thm)],[f1411]) ).
thf(f1411,plain,
( ( ( ^ [Y0: a] :
( ( ( sK3 @ sK24 @ Y0 )
& ( sK14 @ sK24 ) )
=> ( sK14 @ Y0 ) )
@ sK25 )
= $false )
| ~ spl0_29 ),
inference(sigma_clausification,[status(thm)],[f1407]) ).
thf(f1407,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK24 @ Y0 )
& ( sK14 @ sK24 ) )
=> ( sK14 @ Y0 ) ) )
= $false )
| ~ spl0_29 ),
inference(beta_eta_normalization,[status(thm)],[f1403]) ).
thf(f1403,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK14 @ Y0 ) )
=> ( sK14 @ Y1 ) ) )
@ sK24 )
= $false )
| ~ spl0_29 ),
inference(sigma_clausification,[status(thm)],[f1337]) ).
thf(f1337,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK14 @ Y0 ) )
=> ( sK14 @ Y1 ) ) ) )
= $false )
| ~ spl0_29 ),
inference(avatar_component_clause,[status(thm)],[f1336]) ).
thf(f1336,definition,
( spl0_29
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK14 @ Y0 ) )
=> ( sK14 @ Y1 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_29])],[avatar_definition]) ).
thf(f1452,plain,
( ( $true
= ( sK14 @ sK25 ) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_29 ),
inference(boolean_simplification,[status(thm)],[f1451]) ).
thf(f1451,plain,
( ( $true
= ( $true
=> ( sK14 @ sK25 ) ) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_29 ),
inference(forward_demodulation,[status(thm)],[f1448,f1435]) ).
thf(f1435,plain,
( ( $true
= ( sK14 @ sK24 ) )
| ~ spl0_29 ),
inference(binary_proxy_clausification,[status(thm)],[f1423]) ).
thf(f1423,plain,
( ( ( ( sK3 @ sK24 @ sK25 )
& ( sK14 @ sK24 ) )
= $true )
| ~ spl0_29 ),
inference(binary_proxy_clausification,[status(thm)],[f1412]) ).
thf(f1448,plain,
( ( $true
= ( ( sK14 @ sK24 )
=> ( sK14 @ sK25 ) ) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_29 ),
inference(boolean_simplification,[status(thm)],[f1447]) ).
thf(f1447,plain,
( ( $true
= ( ( $true
& ( sK14 @ sK24 ) )
=> ( sK14 @ sK25 ) ) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_29 ),
inference(boolean_simplification,[status(thm)],[f1445]) ).
thf(f1445,plain,
( ( $true
= ( ( ( ( sK2 @ sK24 @ sK25 )
| $true )
& ( sK14 @ sK24 ) )
=> ( sK14 @ sK25 ) ) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_29 ),
inference(superposition,[status(thm)],[f1239,f1438]) ).
thf(f1438,plain,
( ( $true
= ( sK3 @ sK24 @ sK25 ) )
| ~ spl0_29 ),
inference(boolean_simplification,[status(thm)],[f1437]) ).
thf(f1437,plain,
( ( ( ( sK3 @ sK24 @ sK25 )
& $true )
= $true )
| ~ spl0_29 ),
inference(backward_demodulation,[status(thm)],[f1423,f1435]) ).
thf(f1239,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( ( ( sK2 @ X2 @ X1 )
| ( sK3 @ X2 @ X1 ) )
& ( sK14 @ X2 ) )
=> ( sK14 @ X1 ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(beta_eta_normalization,[status(thm)],[f1238]) ).
thf(f1238,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( ( sK2 @ Y0 @ X1 )
| ( sK3 @ Y0 @ X1 ) )
& ( sK14 @ Y0 ) )
=> ( sK14 @ X1 ) )
@ X2 ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(pi_clausification,[status(thm)],[f1226]) ).
thf(f1226,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( ( sK2 @ Y0 @ X1 )
| ( sK3 @ Y0 @ X1 ) )
& ( sK14 @ Y0 ) )
=> ( sK14 @ X1 ) ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(beta_eta_normalization,[status(thm)],[f1225]) ).
thf(f1225,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
& ( sK14 @ Y1 ) )
=> ( sK14 @ Y0 ) ) )
@ X1 ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(pi_clausification,[status(thm)],[f1139]) ).
thf(f1139,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
& ( sK14 @ Y1 ) )
=> ( sK14 @ Y0 ) ) ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(binary_proxy_clausification,[status(thm)],[f1121]) ).
thf(f1121,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK12 @ Y0 )
| ( sK2 @ sK12 @ Y0 ) )
=> ( sK14 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
& ( sK14 @ Y1 ) )
=> ( sK14 @ Y0 ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(binary_proxy_clausification,[status(thm)],[f1117]) ).
thf(f1117,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK12 @ Y0 )
| ( sK2 @ sK12 @ Y0 ) )
=> ( sK14 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
& ( sK14 @ Y1 ) )
=> ( sK14 @ Y0 ) ) ) ) )
=> ( sK14 @ sK13 ) )
= $false )
| ~ spl0_4
| ~ spl0_8 ),
inference(beta_eta_normalization,[status(thm)],[f1116]) ).
thf(f1116,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK12 @ Y1 )
| ( sK2 @ sK12 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK13 ) )
@ sK14 )
= $false )
| ~ spl0_4
| ~ spl0_8 ),
inference(sigma_clausification,[status(thm)],[f1109]) ).
thf(f1109,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK12 @ Y1 )
| ( sK2 @ sK12 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK13 ) ) )
= $false )
| ~ spl0_4
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f1108]) ).
thf(f1108,plain,
( ( $false
= ( $true
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK12 @ Y1 )
| ( sK2 @ sK12 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK13 ) ) ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f1107]) ).
thf(f1107,plain,
( ( ( ( $true
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK13 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK12 @ Y1 )
| ( sK2 @ sK12 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK13 ) ) ) )
= $false )
| ~ spl0_4
| ~ spl0_8 ),
inference(forward_demodulation,[status(thm)],[f1106,f335]) ).
thf(f335,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK13 ) ) ) )
| ~ spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f334]) ).
thf(f334,definition,
( spl0_8
<=> ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK13 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition]) ).
thf(f1400,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_30 ),
inference(avatar_contradiction_clause,[status(thm)],[f1399]) ).
thf(f1399,plain,
( $false
| ~ spl0_4
| ~ spl0_8
| ~ spl0_30 ),
inference(trivial_inequality_removal,[status(thm)],[f1398]) ).
thf(f1398,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_30 ),
inference(boolean_simplification,[status(thm)],[f1397]) ).
thf(f1397,plain,
( ( $true = ( ~ $true ) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_30 ),
inference(boolean_simplification,[status(thm)],[f1396]) ).
thf(f1396,plain,
( ( ( ~ ( $true
| ( sK2 @ sK12 @ sK23 ) ) )
= $true )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_30 ),
inference(forward_demodulation,[status(thm)],[f1395,f1386]) ).
thf(f1386,plain,
( ( ( sK3 @ sK12 @ sK23 )
= $true )
| ~ spl0_30 ),
inference(binary_proxy_clausification,[status(thm)],[f1376]) ).
thf(f1376,plain,
( ( $false
= ( ( sK3 @ sK12 @ sK23 )
=> ( sK14 @ sK23 ) ) )
| ~ spl0_30 ),
inference(beta_eta_normalization,[status(thm)],[f1374]) ).
thf(f1374,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK3 @ sK12 @ Y0 )
=> ( sK14 @ Y0 ) )
@ sK23 ) )
| ~ spl0_30 ),
inference(sigma_clausification,[status(thm)],[f1340]) ).
thf(f1340,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK12 @ Y0 )
=> ( sK14 @ Y0 ) ) )
= $false )
| ~ spl0_30 ),
inference(avatar_component_clause,[status(thm)],[f1339]) ).
thf(f1339,definition,
( spl0_30
<=> ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK12 @ Y0 )
=> ( sK14 @ Y0 ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_30])],[avatar_definition]) ).
thf(f1395,plain,
( ( ( ~ ( ( sK3 @ sK12 @ sK23 )
| ( sK2 @ sK12 @ sK23 ) ) )
= $true )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_30 ),
inference(boolean_simplification,[status(thm)],[f1391]) ).
thf(f1391,plain,
( ( ( ( ( sK3 @ sK12 @ sK23 )
| ( sK2 @ sK12 @ sK23 ) )
=> $false )
= $true )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_30 ),
inference(superposition,[status(thm)],[f1147,f1388]) ).
thf(f1388,plain,
( ( $false
= ( sK14 @ sK23 ) )
| ~ spl0_30 ),
inference(boolean_simplification,[status(thm)],[f1387]) ).
thf(f1387,plain,
( ( ( $true
=> ( sK14 @ sK23 ) )
= $false )
| ~ spl0_30 ),
inference(backward_demodulation,[status(thm)],[f1376,f1386]) ).
thf(f1147,plain,
( ! [X1: a] :
( $true
= ( ( ( sK3 @ sK12 @ X1 )
| ( sK2 @ sK12 @ X1 ) )
=> ( sK14 @ X1 ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(beta_eta_normalization,[status(thm)],[f1146]) ).
thf(f1146,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK3 @ sK12 @ Y0 )
| ( sK2 @ sK12 @ Y0 ) )
=> ( sK14 @ Y0 ) )
@ X1 ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(pi_clausification,[status(thm)],[f1142]) ).
thf(f1142,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK12 @ Y0 )
| ( sK2 @ sK12 @ Y0 ) )
=> ( sK14 @ Y0 ) ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f1141]) ).
thf(f1141,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK12 @ Y0 )
| ( sK2 @ sK12 @ Y0 ) )
=> ( sK14 @ Y0 ) ) )
& $true ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(backward_demodulation,[status(thm)],[f1121,f1139]) ).
thf(f1341,plain,
( spl0_29
| spl0_30
| ~ spl0_4
| ~ spl0_8 ),
inference(avatar_split_clause,[status(thm)],[f1332,f334,f46,f1339,f1336]) ).
thf(f1332,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK14 @ Y0 ) )
=> ( sK14 @ Y1 ) ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK12 @ Y0 )
=> ( sK14 @ Y0 ) ) )
= $false )
| ~ spl0_4
| ~ spl0_8 ),
inference(binary_proxy_clausification,[status(thm)],[f1315]) ).
thf(f1315,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK12 @ Y0 )
=> ( sK14 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK14 @ Y0 ) )
=> ( sK14 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_4
| ~ spl0_8 ),
inference(not_proxy_clausification,[status(thm)],[f1133]) ).
thf(f1133,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK12 @ Y0 )
=> ( sK14 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK14 @ Y0 ) )
=> ( sK14 @ Y1 ) ) ) ) ) ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f1131]) ).
thf(f1131,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK12 @ Y0 )
=> ( sK14 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( sK14 @ Y0 ) )
=> ( sK14 @ Y1 ) ) ) ) )
=> $false ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f1125,f1123]) ).
thf(f1123,plain,
( ( $false
= ( sK14 @ sK13 ) )
| ~ spl0_4
| ~ spl0_8 ),
inference(boolean_simplification,[status(thm)],[f1122]) ).
thf(f1122,plain,
( ( ( $true
=> ( sK14 @ sK13 ) )
= $false )
| ~ spl0_4
| ~ spl0_8 ),
inference(backward_demodulation,[status(thm)],[f1117,f1121]) ).
thf(f1125,plain,
( ! [X1: a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ sK12 @ Y0 )
=> ( X1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ Y1 )
& ( X1 @ Y0 ) )
=> ( X1 @ Y1 ) ) ) ) )
=> ( X1 @ sK13 ) ) )
| ~ spl0_8 ),
inference(beta_eta_normalization,[status(thm)],[f1124]) ).
thf(f1124,plain,
( ! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK13 ) )
@ X1 )
= $true )
| ~ spl0_8 ),
inference(pi_clausification,[status(thm)],[f335]) ).
thf(f1093,plain,
( ~ spl0_3
| ~ spl0_21
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[status(thm)],[f1092]) ).
thf(f1092,plain,
( $false
| ~ spl0_3
| ~ spl0_21
| ~ spl0_23 ),
inference(trivial_inequality_removal,[status(thm)],[f1091]) ).
thf(f1091,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_21
| ~ spl0_23 ),
inference(forward_demodulation,[status(thm)],[f1090,f973]) ).
thf(f973,plain,
( ( ( sK10 @ sK20 )
= $false )
| ~ spl0_21 ),
inference(boolean_simplification,[status(thm)],[f972]) ).
thf(f972,plain,
( ( $false
= ( $true
=> ( sK10 @ sK20 ) ) )
| ~ spl0_21 ),
inference(backward_demodulation,[status(thm)],[f966,f971]) ).
thf(f971,plain,
( ( $true
= ( ( sK10 @ sK19 )
& ( ( sK2 @ sK19 @ sK20 )
| ( sK3 @ sK19 @ sK20 ) ) ) )
| ~ spl0_21 ),
inference(binary_proxy_clausification,[status(thm)],[f966]) ).
thf(f966,plain,
( ( ( ( ( sK10 @ sK19 )
& ( ( sK2 @ sK19 @ sK20 )
| ( sK3 @ sK19 @ sK20 ) ) )
=> ( sK10 @ sK20 ) )
= $false )
| ~ spl0_21 ),
inference(beta_eta_normalization,[status(thm)],[f965]) ).
thf(f965,plain,
( ( ( ^ [Y0: a] :
( ( ( sK10 @ sK19 )
& ( ( sK2 @ sK19 @ Y0 )
| ( sK3 @ sK19 @ Y0 ) ) )
=> ( sK10 @ Y0 ) )
@ sK20 )
= $false )
| ~ spl0_21 ),
inference(sigma_clausification,[status(thm)],[f951]) ).
thf(f951,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK10 @ sK19 )
& ( ( sK2 @ sK19 @ Y0 )
| ( sK3 @ sK19 @ Y0 ) ) )
=> ( sK10 @ Y0 ) ) ) )
| ~ spl0_21 ),
inference(beta_eta_normalization,[status(thm)],[f945]) ).
thf(f945,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) )
@ sK19 )
= $false )
| ~ spl0_21 ),
inference(sigma_clausification,[status(thm)],[f790]) ).
thf(f790,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) ) )
| ~ spl0_21 ),
inference(avatar_component_clause,[status(thm)],[f789]) ).
thf(f789,definition,
( spl0_21
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_21])],[avatar_definition]) ).
thf(f1090,plain,
( ( ( sK10 @ sK20 )
= $true )
| ~ spl0_3
| ~ spl0_21
| ~ spl0_23 ),
inference(boolean_simplification,[status(thm)],[f1089]) ).
thf(f1089,plain,
( ( $true
= ( $true
=> ( sK10 @ sK20 ) ) )
| ~ spl0_3
| ~ spl0_21
| ~ spl0_23 ),
inference(forward_demodulation,[status(thm)],[f1086,f1051]) ).
thf(f1051,plain,
( ( $true
= ( sK10 @ sK19 ) )
| ~ spl0_21 ),
inference(binary_proxy_clausification,[status(thm)],[f971]) ).
thf(f1086,plain,
( ( $true
= ( ( sK10 @ sK19 )
=> ( sK10 @ sK20 ) ) )
| ~ spl0_3
| ~ spl0_23 ),
inference(boolean_simplification,[status(thm)],[f1085]) ).
thf(f1085,plain,
( ( $true
= ( ( ( sK10 @ sK19 )
& $true )
=> ( sK10 @ sK20 ) ) )
| ~ spl0_3
| ~ spl0_23 ),
inference(boolean_simplification,[status(thm)],[f1083]) ).
thf(f1083,plain,
( ( ( ( ( sK10 @ sK19 )
& ( $true
| ( sK2 @ sK19 @ sK20 ) ) )
=> ( sK10 @ sK20 ) )
= $true )
| ~ spl0_3
| ~ spl0_23 ),
inference(superposition,[status(thm)],[f820,f1063]) ).
thf(f1063,plain,
( ( $true
= ( sK3 @ sK19 @ sK20 ) )
| ~ spl0_23 ),
inference(avatar_component_clause,[status(thm)],[f1062]) ).
thf(f1062,definition,
( spl0_23
<=> ( $true
= ( sK3 @ sK19 @ sK20 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_23])],[avatar_definition]) ).
thf(f820,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( ( sK10 @ X1 )
& ( ( sK3 @ X1 @ X2 )
| ( sK2 @ X1 @ X2 ) ) )
=> ( sK10 @ X2 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f819]) ).
thf(f819,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK10 @ X1 )
& ( ( sK3 @ X1 @ Y0 )
| ( sK2 @ X1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) )
@ X2 ) )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f807]) ).
thf(f807,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK10 @ X1 )
& ( ( sK3 @ X1 @ Y0 )
| ( sK2 @ X1 @ Y0 ) ) )
=> ( sK10 @ Y0 ) ) )
= $true )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f804]) ).
thf(f804,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) )
@ X1 ) )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f718]) ).
thf(f718,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) )
= $true )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f691]) ).
thf(f691,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK9 @ Y0 )
| ( sK2 @ sK9 @ Y0 ) )
=> ( sK10 @ Y0 ) ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f679]) ).
thf(f679,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK9 @ Y0 )
| ( sK2 @ sK9 @ Y0 ) )
=> ( sK10 @ Y0 ) ) ) )
=> ( sK10 @ sK8 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f678]) ).
thf(f678,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK9 @ Y1 )
| ( sK2 @ sK9 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK8 ) )
@ sK10 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f662]) ).
thf(f662,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK9 @ Y1 )
| ( sK2 @ sK9 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK8 ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f652]) ).
thf(f652,plain,
( ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK9 @ Y1 )
| ( sK2 @ sK9 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK2 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK7 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK7 @ Y1 )
| ( sK2 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK8 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK9 @ Y1 )
| ( sK2 @ sK9 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK8 ) ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f651]) ).
thf(f651,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y2 )
| ( sK2 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK2 @ Y2 @ Y3 )
| ( sK3 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ sK7 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK3 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ sK7 @ Y2 )
| ( sK2 @ sK7 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK8 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK3 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y2 )
| ( sK2 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK8 ) ) ) )
@ sK9 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f642]) ).
thf(f642,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y2 )
| ( sK2 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK2 @ Y2 @ Y3 )
| ( sK3 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ sK7 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK3 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ sK7 @ Y2 )
| ( sK2 @ sK7 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK8 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK3 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y2 )
| ( sK2 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK8 ) ) ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f641]) ).
thf(f641,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y1 @ Y3 )
| ( sK2 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK2 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ sK7 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK3 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ sK7 @ Y3 )
| ( sK2 @ sK7 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK3 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y1 @ Y3 )
| ( sK2 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) )
@ sK8 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f630]) ).
thf(f630,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y1 @ Y3 )
| ( sK2 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK2 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ sK7 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK3 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ sK7 @ Y3 )
| ( sK2 @ sK7 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK3 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y1 @ Y3 )
| ( sK2 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f629]) ).
thf(f629,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y2 @ Y4 )
| ( sK2 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK2 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK3 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK2 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK3 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y2 @ Y4 )
| ( sK2 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) )
@ sK7 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y2 @ Y4 )
| ( sK2 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK2 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK3 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK2 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK3 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y2 @ Y4 )
| ( sK2 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) ) )
= $false )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f43]) ).
thf(f43,definition,
( spl0_3
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y2 @ Y4 )
| ( sK2 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK2 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK3 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK2 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK3 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y2 @ Y4 )
| ( sK2 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f1080,plain,
( ~ spl0_3
| ~ spl0_21
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[status(thm)],[f1079]) ).
thf(f1079,plain,
( $false
| ~ spl0_3
| ~ spl0_21
| ~ spl0_24 ),
inference(trivial_inequality_removal,[status(thm)],[f1078]) ).
thf(f1078,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_21
| ~ spl0_24 ),
inference(forward_demodulation,[status(thm)],[f1077,f973]) ).
thf(f1077,plain,
( ( ( sK10 @ sK20 )
= $true )
| ~ spl0_3
| ~ spl0_21
| ~ spl0_24 ),
inference(boolean_simplification,[status(thm)],[f1076]) ).
thf(f1076,plain,
( ( $true
= ( $true
=> ( sK10 @ sK20 ) ) )
| ~ spl0_3
| ~ spl0_21
| ~ spl0_24 ),
inference(forward_demodulation,[status(thm)],[f1073,f1051]) ).
thf(f1073,plain,
( ( $true
= ( ( sK10 @ sK19 )
=> ( sK10 @ sK20 ) ) )
| ~ spl0_3
| ~ spl0_24 ),
inference(boolean_simplification,[status(thm)],[f1072]) ).
thf(f1072,plain,
( ( $true
= ( ( ( sK10 @ sK19 )
& $true )
=> ( sK10 @ sK20 ) ) )
| ~ spl0_3
| ~ spl0_24 ),
inference(boolean_simplification,[status(thm)],[f1070]) ).
thf(f1070,plain,
( ( $true
= ( ( ( sK10 @ sK19 )
& ( ( sK3 @ sK19 @ sK20 )
| $true ) )
=> ( sK10 @ sK20 ) ) )
| ~ spl0_3
| ~ spl0_24 ),
inference(superposition,[status(thm)],[f820,f1066]) ).
thf(f1066,plain,
( ( ( sK2 @ sK19 @ sK20 )
= $true )
| ~ spl0_24 ),
inference(avatar_component_clause,[status(thm)],[f1065]) ).
thf(f1065,definition,
( spl0_24
<=> ( ( sK2 @ sK19 @ sK20 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_24])],[avatar_definition]) ).
thf(f1067,plain,
( spl0_23
| spl0_24
| ~ spl0_21 ),
inference(avatar_split_clause,[status(thm)],[f1060,f789,f1065,f1062]) ).
thf(f1060,plain,
( ( $true
= ( sK3 @ sK19 @ sK20 ) )
| ( ( sK2 @ sK19 @ sK20 )
= $true )
| ~ spl0_21 ),
inference(binary_proxy_clausification,[status(thm)],[f1053]) ).
thf(f1053,plain,
( ( $true
= ( ( sK2 @ sK19 @ sK20 )
| ( sK3 @ sK19 @ sK20 ) ) )
| ~ spl0_21 ),
inference(boolean_simplification,[status(thm)],[f1052]) ).
thf(f1052,plain,
( ( $true
= ( $true
& ( ( sK2 @ sK19 @ sK20 )
| ( sK3 @ sK19 @ sK20 ) ) ) )
| ~ spl0_21 ),
inference(backward_demodulation,[status(thm)],[f971,f1051]) ).
thf(f916,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[status(thm)],[f915]) ).
thf(f915,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_22 ),
inference(trivial_inequality_removal,[status(thm)],[f914]) ).
thf(f914,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_22 ),
inference(forward_demodulation,[status(thm)],[f913,f893]) ).
thf(f893,plain,
( ( ( sK10 @ sK11 )
= $false )
| ~ spl0_3
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f892]) ).
thf(f892,plain,
( ( ( $true
=> ( sK10 @ sK11 ) )
= $false )
| ~ spl0_3
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f891]) ).
thf(f891,plain,
( ( ( ( $true
| ( sK2 @ sK7 @ sK11 ) )
=> ( sK10 @ sK11 ) )
= $false )
| ~ spl0_3
| ~ spl0_6 ),
inference(backward_demodulation,[status(thm)],[f777,f232]) ).
thf(f232,plain,
( ( ( sK3 @ sK7 @ sK11 )
= $true )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f231]) ).
thf(f231,definition,
( spl0_6
<=> ( ( sK3 @ sK7 @ sK11 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f777,plain,
( ( ( ( ( sK3 @ sK7 @ sK11 )
| ( sK2 @ sK7 @ sK11 ) )
=> ( sK10 @ sK11 ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f773]) ).
thf(f773,plain,
( ( ( ^ [Y0: a] :
( ( ( sK3 @ sK7 @ Y0 )
| ( sK2 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) )
@ sK11 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f759]) ).
thf(f759,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK7 @ Y0 )
| ( sK2 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) ) ) )
| ~ spl0_3 ),
inference(not_proxy_clausification,[status(thm)],[f747]) ).
thf(f747,plain,
( ( ( ~ ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK7 @ Y0 )
| ( sK2 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) ) ) )
= $true )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f746]) ).
thf(f746,plain,
( ( $true
= ( ~ ( $true
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK7 @ Y0 )
| ( sK2 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) ) ) ) ) )
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f745,f718]) ).
thf(f745,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK7 @ Y0 )
| ( sK2 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f744]) ).
thf(f744,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK7 @ Y0 )
| ( sK2 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) ) ) )
=> $false ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f733,f693]) ).
thf(f693,plain,
( ( $false
= ( sK10 @ sK8 ) )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f692]) ).
thf(f692,plain,
( ( ( $true
=> ( sK10 @ sK8 ) )
= $false )
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f679,f691]) ).
thf(f733,plain,
( ! [X1: a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( X1 @ Y0 )
& ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) ) )
=> ( X1 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK7 @ Y0 )
| ( sK2 @ sK7 @ Y0 ) )
=> ( X1 @ Y0 ) ) ) )
=> ( X1 @ sK8 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f732]) ).
thf(f732,plain,
( ! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK7 @ Y1 )
| ( sK2 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK8 ) )
@ X1 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f694]) ).
thf(f694,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK7 @ Y1 )
| ( sK2 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK8 ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f663]) ).
thf(f663,plain,
( ( $true
= ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK9 @ Y1 )
| ( sK2 @ sK9 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK2 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK7 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK7 @ Y1 )
| ( sK2 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK8 ) ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f652]) ).
thf(f913,plain,
( ( $true
= ( sK10 @ sK11 ) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_22 ),
inference(boolean_simplification,[status(thm)],[f912]) ).
thf(f912,plain,
( ( $true
= ( $true
=> ( sK10 @ sK11 ) ) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_22 ),
inference(forward_demodulation,[status(thm)],[f907,f793]) ).
thf(f793,plain,
( ( $true
= ( sK10 @ sK7 ) )
| ~ spl0_22 ),
inference(avatar_component_clause,[status(thm)],[f792]) ).
thf(f792,definition,
( spl0_22
<=> ( $true
= ( sK10 @ sK7 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_22])],[avatar_definition]) ).
thf(f907,plain,
( ( $true
= ( ( sK10 @ sK7 )
=> ( sK10 @ sK11 ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f906]) ).
thf(f906,plain,
( ( ( ( ( sK10 @ sK7 )
& $true )
=> ( sK10 @ sK11 ) )
= $true )
| ~ spl0_3
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f904]) ).
thf(f904,plain,
( ( $true
= ( ( ( sK10 @ sK7 )
& ( $true
| ( sK2 @ sK7 @ sK11 ) ) )
=> ( sK10 @ sK11 ) ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f820,f232]) ).
thf(f878,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[status(thm)],[f877]) ).
thf(f877,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_22 ),
inference(trivial_inequality_removal,[status(thm)],[f876]) ).
thf(f876,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_22 ),
inference(forward_demodulation,[status(thm)],[f875,f780]) ).
thf(f780,plain,
( ( ( sK10 @ sK11 )
= $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[status(thm)],[f779]) ).
thf(f779,plain,
( ( ( $true
=> ( sK10 @ sK11 ) )
= $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[status(thm)],[f778]) ).
thf(f778,plain,
( ( $false
= ( ( ( sK3 @ sK7 @ sK11 )
| $true )
=> ( sK10 @ sK11 ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[status(thm)],[f777,f229]) ).
thf(f229,plain,
( ( $true
= ( sK2 @ sK7 @ sK11 ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f228]) ).
thf(f228,definition,
( spl0_5
<=> ( $true
= ( sK2 @ sK7 @ sK11 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f875,plain,
( ( $true
= ( sK10 @ sK11 ) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_22 ),
inference(boolean_simplification,[status(thm)],[f874]) ).
thf(f874,plain,
( ( $true
= ( $true
=> ( sK10 @ sK11 ) ) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_22 ),
inference(forward_demodulation,[status(thm)],[f850,f793]) ).
thf(f850,plain,
( ( $true
= ( ( sK10 @ sK7 )
=> ( sK10 @ sK11 ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[status(thm)],[f849]) ).
thf(f849,plain,
( ( ( ( ( sK10 @ sK7 )
& $true )
=> ( sK10 @ sK11 ) )
= $true )
| ~ spl0_3
| ~ spl0_5 ),
inference(boolean_simplification,[status(thm)],[f836]) ).
thf(f836,plain,
( ( $true
= ( ( ( sK10 @ sK7 )
& ( ( sK3 @ sK7 @ sK11 )
| $true ) )
=> ( sK10 @ sK11 ) ) )
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[status(thm)],[f820,f229]) ).
thf(f794,plain,
( spl0_21
| spl0_22
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f787,f43,f792,f789]) ).
thf(f787,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) ) )
| ( $true
= ( sK10 @ sK7 ) )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f784]) ).
thf(f784,plain,
( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) ) )
= $false )
| ( $true
= ( sK10 @ sK7 ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f721,f720]) ).
thf(f720,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK9 @ Y0 )
| ( sK2 @ sK9 @ Y0 ) )
=> ( sK10 @ Y0 ) ) )
= $true )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f719]) ).
thf(f719,plain,
( ( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK9 @ Y0 )
| ( sK2 @ sK9 @ Y0 ) )
=> ( sK10 @ Y0 ) ) ) ) )
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f691,f718]) ).
thf(f721,plain,
( ! [X1: a > $o] :
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK9 @ Y0 )
| ( sK2 @ sK9 @ Y0 ) )
=> ( X1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( X1 @ Y0 )
& ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) ) )
=> ( X1 @ Y1 ) ) ) ) ) )
| ( $true
= ( X1 @ sK7 ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f716]) ).
thf(f716,plain,
( ! [X1: a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK9 @ Y0 )
| ( sK2 @ sK9 @ Y0 ) )
=> ( X1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( X1 @ Y0 )
& ( ( sK2 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) ) )
=> ( X1 @ Y1 ) ) ) ) )
=> ( X1 @ sK7 ) )
= $true )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f715]) ).
thf(f715,plain,
( ! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK9 @ Y1 )
| ( sK2 @ sK9 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK2 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK7 ) )
@ X1 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f697]) ).
thf(f697,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK9 @ Y1 )
| ( sK2 @ sK9 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK2 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK7 ) ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f696]) ).
thf(f696,plain,
( ( $true
= ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK9 @ Y1 )
| ( sK2 @ sK9 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK2 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK7 ) ) )
& $true ) )
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f663,f694]) ).
thf(f620,plain,
( ~ spl0_14
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[status(thm)],[f619]) ).
thf(f619,plain,
( $false
| ~ spl0_14
| ~ spl0_18 ),
inference(trivial_inequality_removal,[status(thm)],[f618]) ).
thf(f618,plain,
( ( $true = $false )
| ~ spl0_14
| ~ spl0_18 ),
inference(forward_demodulation,[status(thm)],[f617,f547]) ).
thf(f547,plain,
( ( ( sK6 @ sK16 )
= $false )
| ~ spl0_14 ),
inference(binary_proxy_clausification,[status(thm)],[f546]) ).
thf(f546,plain,
( ( ( ( ( sK6 @ sK17 )
& ( ( sK2 @ sK17 @ sK16 )
| ( sK3 @ sK17 @ sK16 ) ) )
=> ( sK6 @ sK16 ) )
= $false )
| ~ spl0_14 ),
inference(beta_eta_normalization,[status(thm)],[f545]) ).
thf(f545,plain,
( ( ( ^ [Y0: a] :
( ( ( sK6 @ Y0 )
& ( ( sK2 @ Y0 @ sK16 )
| ( sK3 @ Y0 @ sK16 ) ) )
=> ( sK6 @ sK16 ) )
@ sK17 )
= $false )
| ~ spl0_14 ),
inference(sigma_clausification,[status(thm)],[f544]) ).
thf(f544,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ Y0 )
& ( ( sK2 @ Y0 @ sK16 )
| ( sK3 @ Y0 @ sK16 ) ) )
=> ( sK6 @ sK16 ) ) )
= $false )
| ~ spl0_14 ),
inference(beta_eta_normalization,[status(thm)],[f540]) ).
thf(f540,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) )
@ sK16 )
= $false )
| ~ spl0_14 ),
inference(sigma_clausification,[status(thm)],[f492]) ).
thf(f492,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) )
= $false )
| ~ spl0_14 ),
inference(avatar_component_clause,[status(thm)],[f491]) ).
thf(f491,definition,
( spl0_14
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_14])],[avatar_definition]) ).
thf(f617,plain,
( ( ( sK6 @ sK16 )
= $true )
| ~ spl0_14
| ~ spl0_18 ),
inference(boolean_simplification,[status(thm)],[f616]) ).
thf(f616,plain,
( ( ( $true
=> ( sK6 @ sK16 ) )
= $true )
| ~ spl0_14
| ~ spl0_18 ),
inference(forward_demodulation,[status(thm)],[f615,f584]) ).
thf(f584,plain,
( ( ( sK6 @ sK18 )
= $true )
| ~ spl0_14 ),
inference(boolean_simplification,[status(thm)],[f583]) ).
thf(f583,plain,
( ( $true
= ( ( sK6 @ sK18 )
& $true ) )
| ~ spl0_14 ),
inference(backward_demodulation,[status(thm)],[f569,f581]) ).
thf(f581,plain,
( ( ( ( sK2 @ sK18 @ sK16 )
| ( sK3 @ sK18 @ sK16 ) )
= $true )
| ~ spl0_14 ),
inference(binary_proxy_clausification,[status(thm)],[f569]) ).
thf(f569,plain,
( ( $true
= ( ( sK6 @ sK18 )
& ( ( sK2 @ sK18 @ sK16 )
| ( sK3 @ sK18 @ sK16 ) ) ) )
| ~ spl0_14 ),
inference(not_proxy_clausification,[status(thm)],[f565]) ).
thf(f565,plain,
( ( $false
= ( ~ ( ( sK6 @ sK18 )
& ( ( sK2 @ sK18 @ sK16 )
| ( sK3 @ sK18 @ sK16 ) ) ) ) )
| ~ spl0_14 ),
inference(beta_eta_normalization,[status(thm)],[f564]) ).
thf(f564,plain,
( ( ( ^ [Y0: a] :
~ ( ( sK6 @ Y0 )
& ( ( sK2 @ Y0 @ sK16 )
| ( sK3 @ Y0 @ sK16 ) ) )
@ sK18 )
= $false )
| ~ spl0_14 ),
inference(sigma_clausification,[status(thm)],[f552]) ).
thf(f552,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
~ ( ( sK6 @ Y0 )
& ( ( sK2 @ Y0 @ sK16 )
| ( sK3 @ Y0 @ sK16 ) ) ) )
= $false )
| ~ spl0_14 ),
inference(boolean_simplification,[status(thm)],[f550]) ).
thf(f550,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ Y0 )
& ( ( sK2 @ Y0 @ sK16 )
| ( sK3 @ Y0 @ sK16 ) ) )
=> $false ) )
= $false )
| ~ spl0_14 ),
inference(backward_demodulation,[status(thm)],[f544,f547]) ).
thf(f615,plain,
( ( ( ( sK6 @ sK18 )
=> ( sK6 @ sK16 ) )
= $true )
| ~ spl0_18 ),
inference(boolean_simplification,[status(thm)],[f614]) ).
thf(f614,plain,
( ( $true
= ( ( ( sK6 @ sK18 )
& $true )
=> ( sK6 @ sK16 ) ) )
| ~ spl0_18 ),
inference(boolean_simplification,[status(thm)],[f613]) ).
thf(f613,plain,
( ( ( ( ( sK6 @ sK18 )
& ( $true
| ( sK2 @ sK18 @ sK16 ) ) )
=> ( sK6 @ sK16 ) )
= $true )
| ~ spl0_18 ),
inference(superposition,[status(thm)],[f223,f599]) ).
thf(f599,plain,
( ( $true
= ( sK3 @ sK18 @ sK16 ) )
| ~ spl0_18 ),
inference(avatar_component_clause,[status(thm)],[f598]) ).
thf(f598,definition,
( spl0_18
<=> ( $true
= ( sK3 @ sK18 @ sK16 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_18])],[avatar_definition]) ).
thf(f223,plain,
! [X2: a,X1: a] :
( $true
= ( ( ( sK6 @ X2 )
& ( ( sK3 @ X2 @ X1 )
| ( sK2 @ X2 @ X1 ) ) )
=> ( sK6 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f222]) ).
thf(f222,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK6 @ Y0 )
& ( ( sK3 @ Y0 @ X1 )
| ( sK2 @ Y0 @ X1 ) ) )
=> ( sK6 @ X1 ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f212]) ).
thf(f212,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ Y0 )
& ( ( sK3 @ Y0 @ X1 )
| ( sK2 @ Y0 @ X1 ) ) )
=> ( sK6 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f211]) ).
thf(f211,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f55]) ).
thf(f55,plain,
( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f38,f54]) ).
thf(f54,plain,
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK5 @ Y0 )
| ( sK2 @ sK5 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK5 @ Y0 )
| ( sK2 @ sK5 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK5 @ Y0 )
| ( sK2 @ sK5 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK3 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) ) )
=> ( sK6 @ sK4 ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK5 @ Y1 )
| ( sK2 @ sK5 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 ) )
@ sK6 )
= $false ),
inference(sigma_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK5 @ Y1 )
| ( sK2 @ sK5 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK5 @ Y1 )
| ( sK2 @ sK5 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK3 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y0 @ Y3 )
| ( sK2 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK2 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y2 @ Y4 )
| ( sK2 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK2 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK3 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK2 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK3 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y2 @ Y4 )
| ( sK2 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK5 @ Y1 )
| ( sK3 @ sK5 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
( $false
= ( ^ [Y0: a] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y2 )
| ( sK2 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK3 @ Y3 @ Y2 )
| ( sK2 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ sK4 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y1 @ Y4 )
| ( sK2 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK2 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y3 @ Y5 )
| ( sK2 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( ( sK2 @ Y5 @ Y6 )
| ( sK3 @ Y5 @ Y6 ) ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( ( sK3 @ Y5 @ Y6 )
| ( sK2 @ Y5 @ Y6 ) ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y1 @ Y5 )
| ( sK2 @ Y1 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( ( sK3 @ Y5 @ Y6 )
| ( sK2 @ Y5 @ Y6 ) ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y3 @ Y5 )
| ( sK2 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y0 @ Y2 )
| ( sK3 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK2 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ sK4 ) ) ) ) )
@ sK5 ) ),
inference(sigma_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( !! @ a
@ ^ [Y0: a] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y2 )
| ( sK2 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK3 @ Y3 @ Y2 )
| ( sK2 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ sK4 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y1 @ Y4 )
| ( sK2 @ Y1 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( ( sK2 @ Y5 @ Y4 )
| ( sK3 @ Y5 @ Y4 ) )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y3 @ Y5 )
| ( sK2 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( ( sK2 @ Y5 @ Y6 )
| ( sK3 @ Y5 @ Y6 ) ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( ( sK3 @ Y5 @ Y6 )
| ( sK2 @ Y5 @ Y6 ) ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y1 @ Y5 )
| ( sK2 @ Y1 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( ( sK3 @ Y5 @ Y6 )
| ( sK2 @ Y5 @ Y6 ) ) )
=> ( Y4 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y3 @ Y5 )
| ( sK2 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y0 @ Y2 )
| ( sK3 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( ( sK2 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ sK4 ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y1 @ Y3 )
| ( sK2 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK3 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y5 @ Y6 )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( sK2 @ Y6 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y2 @ Y5 )
| ( sK2 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( sK2 @ Y6 @ Y5 )
| ( sK3 @ Y6 @ Y5 ) )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y4 @ Y6 )
| ( sK2 @ Y4 @ Y6 ) )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y6 )
& ( ( sK2 @ Y6 @ Y7 )
| ( sK3 @ Y6 @ Y7 ) ) )
=> ( Y5 @ Y7 ) ) ) ) )
=> ( Y5 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y6 )
& ( ( sK3 @ Y6 @ Y7 )
| ( sK2 @ Y6 @ Y7 ) ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y2 @ Y6 )
| ( sK2 @ Y2 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y6 )
& ( ( sK3 @ Y6 @ Y7 )
| ( sK2 @ Y6 @ Y7 ) ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y4 @ Y6 )
| ( sK2 @ Y4 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y3 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y1 @ Y3 )
| ( sK3 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK2 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) )
@ sK4 ) ),
inference(sigma_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y1 @ Y3 )
| ( sK2 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK3 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y5 @ Y6 )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( sK2 @ Y6 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( sK3 @ Y2 @ Y5 )
| ( sK2 @ Y2 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( ( sK2 @ Y6 @ Y5 )
| ( sK3 @ Y6 @ Y5 ) )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y4 @ Y6 )
| ( sK2 @ Y4 @ Y6 ) )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y6 )
& ( ( sK2 @ Y6 @ Y7 )
| ( sK3 @ Y6 @ Y7 ) ) )
=> ( Y5 @ Y7 ) ) ) ) )
=> ( Y5 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y6 )
& ( ( sK3 @ Y6 @ Y7 )
| ( sK2 @ Y6 @ Y7 ) ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y2 @ Y6 )
| ( sK2 @ Y2 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y6 )
& ( ( sK3 @ Y6 @ Y7 )
| ( sK2 @ Y6 @ Y7 ) ) )
=> ( Y5 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( ( sK3 @ Y4 @ Y6 )
| ( sK2 @ Y4 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y3 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y1 @ Y3 )
| ( sK3 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( ( sK2 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
( $false
= ( ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y2 @ Y4 )
| ( sK2 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( Y0 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y3 @ Y6 )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y6 @ Y7 )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) ) )
=> ( Y5 @ Y4 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y7 )
& ( sK2 @ Y7 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y3 @ Y6 )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y3 @ Y6 )
| ( sK2 @ Y3 @ Y6 ) )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( ( sK2 @ Y7 @ Y6 )
| ( Y0 @ Y7 @ Y6 ) )
& ( Y5 @ Y7 ) )
=> ( Y5 @ Y6 ) ) ) ) )
=> ( Y5 @ Y4 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y5 @ Y7 )
| ( sK2 @ Y5 @ Y7 ) )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y7 )
& ( ( sK2 @ Y7 @ Y8 )
| ( Y0 @ Y7 @ Y8 ) ) )
=> ( Y6 @ Y8 ) ) ) ) )
=> ( Y6 @ Y3 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y7 )
& ( ( Y0 @ Y7 @ Y8 )
| ( sK2 @ Y7 @ Y8 ) ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y3 @ Y7 )
| ( sK2 @ Y3 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y7 )
& ( ( Y0 @ Y7 @ Y8 )
| ( sK2 @ Y7 @ Y8 ) ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y5 @ Y7 )
| ( sK2 @ Y5 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y4 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y2 @ Y4 )
| ( Y0 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK2 @ Y5 @ Y4 )
| ( Y0 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) ) )
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y2 @ Y4 )
| ( sK2 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( Y0 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y3 @ Y6 )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y6 @ Y7 )
& ( Y5 @ Y6 ) )
=> ( Y5 @ Y7 ) ) ) ) )
=> ( Y5 @ Y4 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y5 @ Y7 )
& ( sK2 @ Y7 @ Y6 ) )
=> ( Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y3 @ Y6 )
=> ( Y5 @ Y6 ) ) ) )
=> ( Y5 @ Y4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y5: a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y3 @ Y6 )
| ( sK2 @ Y3 @ Y6 ) )
=> ( Y5 @ Y6 ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( ( sK2 @ Y7 @ Y6 )
| ( Y0 @ Y7 @ Y6 ) )
& ( Y5 @ Y7 ) )
=> ( Y5 @ Y6 ) ) ) ) )
=> ( Y5 @ Y4 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y5 @ Y7 )
| ( sK2 @ Y5 @ Y7 ) )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y7 )
& ( ( sK2 @ Y7 @ Y8 )
| ( Y0 @ Y7 @ Y8 ) ) )
=> ( Y6 @ Y8 ) ) ) ) )
=> ( Y6 @ Y3 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y7 )
& ( ( Y0 @ Y7 @ Y8 )
| ( sK2 @ Y7 @ Y8 ) ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y3 @ Y7 )
| ( sK2 @ Y3 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y7 )
& ( ( Y0 @ Y7 @ Y8 )
| ( sK2 @ Y7 @ Y8 ) ) )
=> ( Y6 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y5 @ Y7 )
| ( sK2 @ Y5 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y4 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y2 @ Y4 )
| ( Y0 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( ( sK2 @ Y5 @ Y4 )
| ( Y0 @ Y5 @ Y4 ) ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
( $false
= ( ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y3 @ Y5 )
| ( Y0 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y1 @ Y6 @ Y5 )
| ( Y0 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y7 @ Y8 )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y8 )
& ( Y0 @ Y8 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y0 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( ( Y1 @ Y4 @ Y7 )
| ( Y0 @ Y4 @ Y7 ) )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( ( Y0 @ Y8 @ Y7 )
| ( Y1 @ Y8 @ Y7 ) )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y6 @ Y8 )
| ( Y0 @ Y6 @ Y8 ) )
=> ( Y7 @ Y8 ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y8 )
& ( ( Y0 @ Y8 @ Y9 )
| ( Y1 @ Y8 @ Y9 ) ) )
=> ( Y7 @ Y9 ) ) ) ) )
=> ( Y7 @ Y4 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y8 )
& ( ( Y1 @ Y8 @ Y9 )
| ( Y0 @ Y8 @ Y9 ) ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y4 @ Y8 )
| ( Y0 @ Y4 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y5 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y8 )
& ( ( Y1 @ Y8 @ Y9 )
| ( Y0 @ Y8 @ Y9 ) ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y6 @ Y8 )
| ( Y0 @ Y6 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y5 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y3 @ Y5 )
| ( Y1 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y0 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 ) ) ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y3 @ Y5 )
| ( Y0 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y1 @ Y6 @ Y5 )
| ( Y0 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y7 @ Y8 )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y8 )
& ( Y0 @ Y8 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y0 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( ( Y1 @ Y4 @ Y7 )
| ( Y0 @ Y4 @ Y7 ) )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( ( Y0 @ Y8 @ Y7 )
| ( Y1 @ Y8 @ Y7 ) )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y6 @ Y8 )
| ( Y0 @ Y6 @ Y8 ) )
=> ( Y7 @ Y8 ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y8 )
& ( ( Y0 @ Y8 @ Y9 )
| ( Y1 @ Y8 @ Y9 ) ) )
=> ( Y7 @ Y9 ) ) ) ) )
=> ( Y7 @ Y4 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y8 )
& ( ( Y1 @ Y8 @ Y9 )
| ( Y0 @ Y8 @ Y9 ) ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y4 @ Y8 )
| ( Y0 @ Y4 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y5 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y8 )
& ( ( Y1 @ Y8 @ Y9 )
| ( Y0 @ Y8 @ Y9 ) ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y6 @ Y8 )
| ( Y0 @ Y6 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y5 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y3 @ Y5 )
| ( Y1 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y0 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 ) ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y3 @ Y5 )
| ( Y0 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y1 @ Y6 @ Y5 )
| ( Y0 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y7 @ Y8 )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y8 )
& ( Y0 @ Y8 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y0 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( ( Y1 @ Y4 @ Y7 )
| ( Y0 @ Y4 @ Y7 ) )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( ( Y0 @ Y8 @ Y7 )
| ( Y1 @ Y8 @ Y7 ) )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y6 @ Y8 )
| ( Y0 @ Y6 @ Y8 ) )
=> ( Y7 @ Y8 ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y8 )
& ( ( Y0 @ Y8 @ Y9 )
| ( Y1 @ Y8 @ Y9 ) ) )
=> ( Y7 @ Y9 ) ) ) ) )
=> ( Y7 @ Y4 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y8 )
& ( ( Y1 @ Y8 @ Y9 )
| ( Y0 @ Y8 @ Y9 ) ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y4 @ Y8 )
| ( Y0 @ Y4 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y5 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y8 )
& ( ( Y1 @ Y8 @ Y9 )
| ( Y0 @ Y8 @ Y9 ) ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y6 @ Y8 )
| ( Y0 @ Y6 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y5 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y3 @ Y5 )
| ( Y1 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y0 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y3 @ Y5 )
| ( Y0 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y1 @ Y6 @ Y5 )
| ( Y0 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 ) ) )
| ~ ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y7 @ Y8 )
& ( Y6 @ Y7 ) )
=> ( Y6 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y6 @ Y8 )
& ( Y0 @ Y8 @ Y7 ) )
=> ( Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( ( Y0 @ Y4 @ Y7 )
=> ( Y6 @ Y7 ) ) ) )
=> ( Y6 @ Y5 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y6: a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( ( ( Y1 @ Y4 @ Y7 )
| ( Y0 @ Y4 @ Y7 ) )
=> ( Y6 @ Y7 ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( ( Y0 @ Y8 @ Y7 )
| ( Y1 @ Y8 @ Y7 ) )
& ( Y6 @ Y8 ) )
=> ( Y6 @ Y7 ) ) ) ) )
=> ( Y6 @ Y5 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y6 @ Y8 )
| ( Y0 @ Y6 @ Y8 ) )
=> ( Y7 @ Y8 ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y8 )
& ( ( Y0 @ Y8 @ Y9 )
| ( Y1 @ Y8 @ Y9 ) ) )
=> ( Y7 @ Y9 ) ) ) ) )
=> ( Y7 @ Y4 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y8 )
& ( ( Y1 @ Y8 @ Y9 )
| ( Y0 @ Y8 @ Y9 ) ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y4 @ Y8 )
| ( Y0 @ Y4 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y5 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y7: a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y7 @ Y8 )
& ( ( Y1 @ Y8 @ Y9 )
| ( Y0 @ Y8 @ Y9 ) ) )
=> ( Y7 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y6 @ Y8 )
| ( Y0 @ Y6 @ Y8 ) )
=> ( Y7 @ Y8 ) ) ) )
=> ( Y7 @ Y5 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y3 @ Y5 )
| ( Y1 @ Y3 @ Y5 ) )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( ( Y0 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a,X1: a,X2: a > a > $o,X3: a > a > $o] :
( ~ ( ( ! [X4: a,X5: a,X6: a] :
( ( ! [X7: a > $o] :
( ( ! [X8: a] :
( ( ( X3 @ X6 @ X8 )
| ( X2 @ X6 @ X8 ) )
=> ( X7 @ X8 ) )
& ! [X9: a,X10: a] :
( ( ( ( X3 @ X10 @ X9 )
| ( X2 @ X10 @ X9 ) )
& ( X7 @ X10 ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X5 ) )
& ! [X11: a > $o] :
( ( ! [X12: a,X13: a] :
( ( ( ( X2 @ X13 @ X12 )
| ( X3 @ X13 @ X12 ) )
& ( X11 @ X13 ) )
=> ( X11 @ X12 ) )
& ! [X14: a] :
( ( ( X3 @ X4 @ X14 )
| ( X2 @ X4 @ X14 ) )
=> ( X11 @ X14 ) ) )
=> ( X11 @ X6 ) ) )
=> ! [X15: a > $o] :
( ( ! [X16: a] :
( ( ( X3 @ X4 @ X16 )
| ( X2 @ X4 @ X16 ) )
=> ( X15 @ X16 ) )
& ! [X17: a,X18: a] :
( ( ( ( X3 @ X18 @ X17 )
| ( X2 @ X18 @ X17 ) )
& ( X15 @ X18 ) )
=> ( X15 @ X17 ) ) )
=> ( X15 @ X5 ) ) )
& ! [X19: a,X20: a] :
( ( ! [X21: a > $o] :
( ( ! [X22: a] :
( ( X3 @ X20 @ X22 )
=> ( X21 @ X22 ) )
& ! [X23: a,X24: a] :
( ( ( X3 @ X23 @ X24 )
& ( X21 @ X23 ) )
=> ( X21 @ X24 ) ) )
=> ( X21 @ X19 ) )
| ! [X25: a > $o] :
( ( ! [X26: a,X27: a] :
( ( ( X25 @ X27 )
& ( X2 @ X27 @ X26 ) )
=> ( X25 @ X26 ) )
& ! [X28: a] :
( ( X2 @ X20 @ X28 )
=> ( X25 @ X28 ) ) )
=> ( X25 @ X19 ) ) )
=> ! [X29: a > $o] :
( ( ! [X30: a,X31: a] :
( ( ( X29 @ X30 )
& ( ( X2 @ X30 @ X31 )
| ( X3 @ X30 @ X31 ) ) )
=> ( X29 @ X31 ) )
& ! [X32: a] :
( ( ( X3 @ X20 @ X32 )
| ( X2 @ X20 @ X32 ) )
=> ( X29 @ X32 ) ) )
=> ( X29 @ X19 ) ) ) )
=> ! [X33: a > $o] :
( ( ! [X34: a,X35: a] :
( ( ( ( X2 @ X34 @ X35 )
| ( X3 @ X34 @ X35 ) )
& ( X33 @ X34 ) )
=> ( X33 @ X35 ) )
& ! [X36: a] :
( ( ( X2 @ X0 @ X36 )
| ( X3 @ X0 @ X36 ) )
=> ( X33 @ X36 ) ) )
=> ( X33 @ X1 ) ) )
| ! [X37: a > $o] :
( ( ! [X38: a,X39: a] :
( ( ( ( X3 @ X38 @ X39 )
| ( X2 @ X38 @ X39 ) )
& ( X37 @ X38 ) )
=> ( X37 @ X39 ) )
& ! [X40: a] :
( ( ( X3 @ X0 @ X40 )
| ( X2 @ X0 @ X40 ) )
=> ( X37 @ X40 ) ) )
=> ( X37 @ X1 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X2: a,X3: a,X0: a > a > $o,X1: a > a > $o] :
( ~ ( ( ! [X8: a,X10: a,X9: a] :
( ( ! [X4: a > $o] :
( ( ! [X5: a] :
( ( ( X1 @ X9 @ X5 )
| ( X0 @ X9 @ X5 ) )
=> ( X4 @ X5 ) )
& ! [X7: a,X6: a] :
( ( ( ( X1 @ X6 @ X7 )
| ( X0 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X10 ) )
& ! [X4: a > $o] :
( ( ! [X7: a,X6: a] :
( ( ( ( X0 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) )
& ! [X5: a] :
( ( ( X1 @ X8 @ X5 )
| ( X0 @ X8 @ X5 ) )
=> ( X4 @ X5 ) ) )
=> ( X4 @ X9 ) ) )
=> ! [X4: a > $o] :
( ( ! [X5: a] :
( ( ( X1 @ X8 @ X5 )
| ( X0 @ X8 @ X5 ) )
=> ( X4 @ X5 ) )
& ! [X7: a,X6: a] :
( ( ( ( X1 @ X6 @ X7 )
| ( X0 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X10 ) ) )
& ! [X9: a,X8: a] :
( ( ! [X4: a > $o] :
( ( ! [X5: a] :
( ( X1 @ X8 @ X5 )
=> ( X4 @ X5 ) )
& ! [X6: a,X7: a] :
( ( ( X1 @ X6 @ X7 )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X9 ) )
| ! [X4: a > $o] :
( ( ! [X7: a,X6: a] :
( ( ( X4 @ X6 )
& ( X0 @ X6 @ X7 ) )
=> ( X4 @ X7 ) )
& ! [X5: a] :
( ( X0 @ X8 @ X5 )
=> ( X4 @ X5 ) ) )
=> ( X4 @ X9 ) ) )
=> ! [X4: a > $o] :
( ( ! [X6: a,X7: a] :
( ( ( X4 @ X6 )
& ( ( X0 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) ) )
=> ( X4 @ X7 ) )
& ! [X5: a] :
( ( ( X1 @ X8 @ X5 )
| ( X0 @ X8 @ X5 ) )
=> ( X4 @ X5 ) ) )
=> ( X4 @ X9 ) ) ) )
=> ! [X4: a > $o] :
( ( ! [X6: a,X7: a] :
( ( ( ( X0 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) )
& ! [X5: a] :
( ( ( X0 @ X2 @ X5 )
| ( X1 @ X2 @ X5 ) )
=> ( X4 @ X5 ) ) )
=> ( X4 @ X3 ) ) )
| ! [X4: a > $o] :
( ( ! [X6: a,X7: a] :
( ( ( ( X1 @ X6 @ X7 )
| ( X0 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) )
& ! [X5: a] :
( ( ( X1 @ X2 @ X5 )
| ( X0 @ X2 @ X5 ) )
=> ( X4 @ X5 ) ) )
=> ( X4 @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X2: a,X3: a,X0: a > a > $o,X1: a > a > $o] :
( ~ ( ( ! [X8: a,X10: a,X9: a] :
( ( ! [X4: a > $o] :
( ( ! [X5: a] :
( ( ( X1 @ X9 @ X5 )
| ( X0 @ X9 @ X5 ) )
=> ( X4 @ X5 ) )
& ! [X7: a,X6: a] :
( ( ( ( X1 @ X6 @ X7 )
| ( X0 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X10 ) )
& ! [X4: a > $o] :
( ( ! [X7: a,X6: a] :
( ( ( ( X0 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) )
& ! [X5: a] :
( ( ( X1 @ X8 @ X5 )
| ( X0 @ X8 @ X5 ) )
=> ( X4 @ X5 ) ) )
=> ( X4 @ X9 ) ) )
=> ! [X4: a > $o] :
( ( ! [X5: a] :
( ( ( X1 @ X8 @ X5 )
| ( X0 @ X8 @ X5 ) )
=> ( X4 @ X5 ) )
& ! [X7: a,X6: a] :
( ( ( ( X1 @ X6 @ X7 )
| ( X0 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X10 ) ) )
& ! [X9: a,X8: a] :
( ( ! [X4: a > $o] :
( ( ! [X5: a] :
( ( X1 @ X8 @ X5 )
=> ( X4 @ X5 ) )
& ! [X6: a,X7: a] :
( ( ( X1 @ X6 @ X7 )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X9 ) )
| ! [X4: a > $o] :
( ( ! [X7: a,X6: a] :
( ( ( X4 @ X6 )
& ( X0 @ X6 @ X7 ) )
=> ( X4 @ X7 ) )
& ! [X5: a] :
( ( X0 @ X8 @ X5 )
=> ( X4 @ X5 ) ) )
=> ( X4 @ X9 ) ) )
=> ! [X4: a > $o] :
( ( ! [X6: a,X7: a] :
( ( ( X4 @ X6 )
& ( ( X0 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) ) )
=> ( X4 @ X7 ) )
& ! [X5: a] :
( ( ( X1 @ X8 @ X5 )
| ( X0 @ X8 @ X5 ) )
=> ( X4 @ X5 ) ) )
=> ( X4 @ X9 ) ) ) )
=> ! [X4: a > $o] :
( ( ! [X6: a,X7: a] :
( ( ( ( X0 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) )
& ! [X5: a] :
( ( ( X0 @ X2 @ X5 )
| ( X1 @ X2 @ X5 ) )
=> ( X4 @ X5 ) ) )
=> ( X4 @ X3 ) ) )
| ! [X4: a > $o] :
( ( ! [X6: a,X7: a] :
( ( ( ( X1 @ X6 @ X7 )
| ( X0 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) )
& ! [X5: a] :
( ( ( X1 @ X2 @ X5 )
| ( X0 @ X2 @ X5 ) )
=> ( X4 @ X5 ) ) )
=> ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.MNEUYGSWeg/DTF2THF_13164.p',cTHM251G_pme) ).
thf(f610,plain,
( ~ spl0_14
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[status(thm)],[f609]) ).
thf(f609,plain,
( $false
| ~ spl0_14
| ~ spl0_17 ),
inference(trivial_inequality_removal,[status(thm)],[f608]) ).
thf(f608,plain,
( ( $true = $false )
| ~ spl0_14
| ~ spl0_17 ),
inference(forward_demodulation,[status(thm)],[f607,f547]) ).
thf(f607,plain,
( ( ( sK6 @ sK16 )
= $true )
| ~ spl0_14
| ~ spl0_17 ),
inference(boolean_simplification,[status(thm)],[f606]) ).
thf(f606,plain,
( ( ( $true
=> ( sK6 @ sK16 ) )
= $true )
| ~ spl0_14
| ~ spl0_17 ),
inference(forward_demodulation,[status(thm)],[f605,f584]) ).
thf(f605,plain,
( ( ( ( sK6 @ sK18 )
=> ( sK6 @ sK16 ) )
= $true )
| ~ spl0_17 ),
inference(boolean_simplification,[status(thm)],[f604]) ).
thf(f604,plain,
( ( $true
= ( ( ( sK6 @ sK18 )
& $true )
=> ( sK6 @ sK16 ) ) )
| ~ spl0_17 ),
inference(boolean_simplification,[status(thm)],[f603]) ).
thf(f603,plain,
( ( $true
= ( ( ( sK6 @ sK18 )
& ( ( sK3 @ sK18 @ sK16 )
| $true ) )
=> ( sK6 @ sK16 ) ) )
| ~ spl0_17 ),
inference(superposition,[status(thm)],[f223,f596]) ).
thf(f596,plain,
( ( ( sK2 @ sK18 @ sK16 )
= $true )
| ~ spl0_17 ),
inference(avatar_component_clause,[status(thm)],[f595]) ).
thf(f595,definition,
( spl0_17
<=> ( ( sK2 @ sK18 @ sK16 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_17])],[avatar_definition]) ).
thf(f600,plain,
( spl0_17
| spl0_18
| ~ spl0_14 ),
inference(avatar_split_clause,[status(thm)],[f593,f491,f598,f595]) ).
thf(f593,plain,
( ( $true
= ( sK3 @ sK18 @ sK16 ) )
| ( ( sK2 @ sK18 @ sK16 )
= $true )
| ~ spl0_14 ),
inference(binary_proxy_clausification,[status(thm)],[f581]) ).
thf(f536,plain,
( ~ spl0_13
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[status(thm)],[f535]) ).
thf(f535,plain,
( $false
| ~ spl0_13
| ~ spl0_15 ),
inference(trivial_inequality_removal,[status(thm)],[f534]) ).
thf(f534,plain,
( ( $true = $false )
| ~ spl0_13
| ~ spl0_15 ),
inference(boolean_simplification,[status(thm)],[f533]) ).
thf(f533,plain,
( ( $true = ( ~ $true ) )
| ~ spl0_13
| ~ spl0_15 ),
inference(boolean_simplification,[status(thm)],[f531]) ).
thf(f531,plain,
( ( $true
= ( ~ ( ( sK3 @ sK5 @ sK15 )
| $true ) ) )
| ~ spl0_13
| ~ spl0_15 ),
inference(backward_demodulation,[status(thm)],[f512,f519]) ).
thf(f519,plain,
( ( ( sK2 @ sK5 @ sK15 )
= $true )
| ~ spl0_15 ),
inference(avatar_component_clause,[status(thm)],[f518]) ).
thf(f518,definition,
( spl0_15
<=> ( ( sK2 @ sK5 @ sK15 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_15])],[avatar_definition]) ).
thf(f512,plain,
( ( ( ~ ( ( sK3 @ sK5 @ sK15 )
| ( sK2 @ sK5 @ sK15 ) ) )
= $true )
| ~ spl0_13 ),
inference(boolean_simplification,[status(thm)],[f510]) ).
thf(f510,plain,
( ( $true
= ( ( ( sK3 @ sK5 @ sK15 )
| ( sK2 @ sK5 @ sK15 ) )
=> $false ) )
| ~ spl0_13 ),
inference(superposition,[status(thm)],[f60,f501]) ).
thf(f501,plain,
( ( ( sK6 @ sK15 )
= $false )
| ~ spl0_13 ),
inference(binary_proxy_clausification,[status(thm)],[f500]) ).
thf(f500,plain,
( ( ( ( ( sK2 @ sK5 @ sK15 )
| ( sK3 @ sK5 @ sK15 ) )
=> ( sK6 @ sK15 ) )
= $false )
| ~ spl0_13 ),
inference(beta_eta_normalization,[status(thm)],[f496]) ).
thf(f496,plain,
( ( ( ^ [Y0: a] :
( ( ( sK2 @ sK5 @ Y0 )
| ( sK3 @ sK5 @ Y0 ) )
=> ( sK6 @ Y0 ) )
@ sK15 )
= $false )
| ~ spl0_13 ),
inference(sigma_clausification,[status(thm)],[f489]) ).
thf(f489,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK5 @ Y0 )
| ( sK3 @ sK5 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
= $false )
| ~ spl0_13 ),
inference(avatar_component_clause,[status(thm)],[f488]) ).
thf(f488,definition,
( spl0_13
<=> ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK5 @ Y0 )
| ( sK3 @ sK5 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition]) ).
thf(f60,plain,
! [X1: a] :
( ( ( ( sK3 @ sK5 @ X1 )
| ( sK2 @ sK5 @ X1 ) )
=> ( sK6 @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f59]) ).
thf(f59,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK3 @ sK5 @ Y0 )
| ( sK2 @ sK5 @ Y0 ) )
=> ( sK6 @ Y0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f54]) ).
thf(f529,plain,
( ~ spl0_13
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[status(thm)],[f528]) ).
thf(f528,plain,
( $false
| ~ spl0_13
| ~ spl0_16 ),
inference(trivial_inequality_removal,[status(thm)],[f527]) ).
thf(f527,plain,
( ( $true = $false )
| ~ spl0_13
| ~ spl0_16 ),
inference(boolean_simplification,[status(thm)],[f526]) ).
thf(f526,plain,
( ( $true = ( ~ $true ) )
| ~ spl0_13
| ~ spl0_16 ),
inference(boolean_simplification,[status(thm)],[f524]) ).
thf(f524,plain,
( ( $true
= ( ~ ( $true
| ( sK2 @ sK5 @ sK15 ) ) ) )
| ~ spl0_13
| ~ spl0_16 ),
inference(backward_demodulation,[status(thm)],[f512,f522]) ).
thf(f522,plain,
( ( $true
= ( sK3 @ sK5 @ sK15 ) )
| ~ spl0_16 ),
inference(avatar_component_clause,[status(thm)],[f521]) ).
thf(f521,definition,
( spl0_16
<=> ( $true
= ( sK3 @ sK5 @ sK15 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_16])],[avatar_definition]) ).
thf(f523,plain,
( spl0_15
| spl0_16
| ~ spl0_13 ),
inference(avatar_split_clause,[status(thm)],[f516,f488,f521,f518]) ).
thf(f516,plain,
( ( $true
= ( sK3 @ sK5 @ sK15 ) )
| ( ( sK2 @ sK5 @ sK15 )
= $true )
| ~ spl0_13 ),
inference(binary_proxy_clausification,[status(thm)],[f502]) ).
thf(f502,plain,
( ( ( ( sK2 @ sK5 @ sK15 )
| ( sK3 @ sK5 @ sK15 ) )
= $true )
| ~ spl0_13 ),
inference(binary_proxy_clausification,[status(thm)],[f500]) ).
thf(f493,plain,
( spl0_13
| spl0_14
| ~ spl0_1 ),
inference(avatar_split_clause,[status(thm)],[f484,f29,f491,f488]) ).
thf(f29,definition,
( spl0_1
<=> ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK5 @ Y1 )
| ( sK3 @ sK5 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f484,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK5 @ Y0 )
| ( sK3 @ sK5 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) )
= $false )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f481]) ).
thf(f481,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK5 @ Y0 )
| ( sK3 @ sK5 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) ) ) )
| ~ spl0_1 ),
inference(not_proxy_clausification,[status(thm)],[f478]) ).
thf(f478,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK5 @ Y0 )
| ( sK3 @ sK5 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) ) ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f475]) ).
thf(f475,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK5 @ Y0 )
| ( sK3 @ sK5 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) ) )
=> ( sK6 @ Y0 ) ) ) ) )
=> $false )
= $true )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f473,f40]) ).
thf(f40,plain,
( ( sK6 @ sK4 )
= $false ),
inference(boolean_simplification,[status(thm)],[f39]) ).
thf(f39,plain,
( $false
= ( $true
=> ( sK6 @ sK4 ) ) ),
inference(backward_demodulation,[status(thm)],[f26,f38]) ).
thf(f473,plain,
( ! [X1: a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK5 @ Y0 )
| ( sK3 @ sK5 @ Y0 ) )
=> ( X1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( X1 @ Y1 )
& ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) ) )
=> ( X1 @ Y0 ) ) ) ) )
=> ( X1 @ sK4 ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f472]) ).
thf(f472,plain,
( ! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK5 @ Y1 )
| ( sK3 @ sK5 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 ) )
@ X1 )
= $true )
| ~ spl0_1 ),
inference(pi_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK5 @ Y1 )
| ( sK3 @ sK5 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 ) ) ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f29]) ).
thf(f443,plain,
( spl0_9
| spl0_10
| ~ spl0_4
| ~ spl0_7 ),
inference(avatar_split_clause,[status(thm)],[f434,f331,f46,f441,f438]) ).
thf(f434,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK12 @ Y0 )
=> ( sK14 @ Y0 ) ) ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK14 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK14 @ Y0 ) ) ) )
= $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(binary_proxy_clausification,[status(thm)],[f428]) ).
thf(f428,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK14 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK14 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK12 @ Y0 )
=> ( sK14 @ Y0 ) ) ) ) )
| ~ spl0_4
| ~ spl0_7 ),
inference(not_proxy_clausification,[status(thm)],[f380]) ).
thf(f380,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK14 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK14 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK12 @ Y0 )
=> ( sK14 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_4
| ~ spl0_7 ),
inference(boolean_simplification,[status(thm)],[f377]) ).
thf(f377,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK14 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK14 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK12 @ Y0 )
=> ( sK14 @ Y0 ) ) ) )
=> $false )
= $true )
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[status(thm)],[f358,f296]) ).
thf(f296,plain,
( ( $false
= ( sK14 @ sK13 ) )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f295]) ).
thf(f295,plain,
( ( ( $true
=> ( sK14 @ sK13 ) )
= $false )
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f292,f294]) ).
thf(f294,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK12 @ Y0 )
| ( sK2 @ sK12 @ Y0 ) )
=> ( sK14 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
& ( sK14 @ Y1 ) )
=> ( sK14 @ Y0 ) ) ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f292]) ).
thf(f292,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK12 @ Y0 )
| ( sK2 @ sK12 @ Y0 ) )
=> ( sK14 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( ( sK2 @ Y1 @ Y0 )
| ( sK3 @ Y1 @ Y0 ) )
& ( sK14 @ Y1 ) )
=> ( sK14 @ Y0 ) ) ) ) )
=> ( sK14 @ sK13 ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f291]) ).
thf(f291,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK12 @ Y1 )
| ( sK2 @ sK12 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK13 ) )
@ sK14 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f277]) ).
thf(f277,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK12 @ Y1 )
| ( sK2 @ sK12 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK13 ) ) )
= $false )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f276]) ).
thf(f276,plain,
( ( $false
= ( $true
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK12 @ Y1 )
| ( sK2 @ sK12 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK13 ) ) ) ) )
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f257,f275]) ).
thf(f275,plain,
( ( $true
= ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK13 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK13 ) ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f257]) ).
thf(f257,plain,
( ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK13 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK13 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK12 @ Y1 )
| ( sK2 @ sK12 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK13 ) ) ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f256]) ).
thf(f256,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK12 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK12 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ sK12 @ Y2 )
| ( sK2 @ sK12 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK2 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
@ sK13 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f239]) ).
thf(f239,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ sK12 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK12 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ sK12 @ Y2 )
| ( sK2 @ sK12 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( ( sK2 @ Y3 @ Y2 )
| ( sK3 @ Y3 @ Y2 ) )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f238]) ).
thf(f238,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y0 @ Y3 )
| ( sK2 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK2 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
@ sK12 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f47]) ).
thf(f358,plain,
( ! [X1: a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( X1 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( X1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK12 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
=> ( X1 @ sK13 ) ) )
| ~ spl0_7 ),
inference(beta_eta_normalization,[status(thm)],[f357]) ).
thf(f357,plain,
( ! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK13 ) )
@ X1 ) )
| ~ spl0_7 ),
inference(pi_clausification,[status(thm)],[f332]) ).
thf(f336,plain,
( spl0_7
| spl0_8
| ~ spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f329,f46,f334,f331]) ).
thf(f329,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK13 ) ) )
= $true )
| ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ sK12 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK13 ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f275]) ).
thf(f233,plain,
( spl0_5
| spl0_6
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f224,f43,f231,f228]) ).
thf(f224,plain,
( ( ( sK3 @ sK7 @ sK11 )
= $true )
| ( $true
= ( sK2 @ sK7 @ sK11 ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f206]) ).
thf(f206,plain,
( ( $true
= ( ( sK3 @ sK7 @ sK11 )
| ( sK2 @ sK7 @ sK11 ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f204]) ).
thf(f204,plain,
( ( ( ( ( sK3 @ sK7 @ sK11 )
| ( sK2 @ sK7 @ sK11 ) )
=> ( sK10 @ sK11 ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f200]) ).
thf(f200,plain,
( ( ( ^ [Y0: a] :
( ( ( sK3 @ sK7 @ Y0 )
| ( sK2 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) )
@ sK11 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f197]) ).
thf(f197,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK7 @ Y0 )
| ( sK2 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) ) ) )
| ~ spl0_3 ),
inference(not_proxy_clausification,[status(thm)],[f148]) ).
thf(f148,plain,
( ( ( ~ ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK7 @ Y0 )
| ( sK2 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) ) ) )
= $true )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f147]) ).
thf(f147,plain,
( ( $true
= ( ~ ( $true
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK7 @ Y0 )
| ( sK2 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) ) ) ) ) )
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f146,f90]) ).
thf(f90,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) )
= $true )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f89]) ).
thf(f89,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) )
& $true )
= $true )
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f82,f87]) ).
thf(f87,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK9 @ Y0 )
| ( sK2 @ sK9 @ Y0 ) )
=> ( sK10 @ Y0 ) ) )
= $true )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f82]) ).
thf(f82,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK9 @ Y0 )
| ( sK2 @ sK9 @ Y0 ) )
=> ( sK10 @ Y0 ) ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f74]) ).
thf(f74,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK9 @ Y0 )
| ( sK2 @ sK9 @ Y0 ) )
=> ( sK10 @ Y0 ) ) ) )
=> ( sK10 @ sK8 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f73]) ).
thf(f73,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK9 @ Y1 )
| ( sK2 @ sK9 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK8 ) )
@ sK10 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f69]) ).
thf(f69,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK9 @ Y1 )
| ( sK2 @ sK9 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK8 ) ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f68]) ).
thf(f68,plain,
( ( ( $true
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK9 @ Y1 )
| ( sK2 @ sK9 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK8 ) ) ) )
= $false )
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f62,f67]) ).
thf(f67,plain,
( ( $true
= ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK9 @ Y1 )
| ( sK2 @ sK9 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK2 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK7 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK7 @ Y1 )
| ( sK2 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK8 ) ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f62]) ).
thf(f62,plain,
( ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK9 @ Y1 )
| ( sK2 @ sK9 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK2 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK7 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK7 @ Y1 )
| ( sK2 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK8 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK9 @ Y1 )
| ( sK2 @ sK9 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK8 ) ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f61]) ).
thf(f61,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y2 )
| ( sK2 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK2 @ Y2 @ Y3 )
| ( sK3 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ sK7 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK3 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ sK7 @ Y2 )
| ( sK2 @ sK7 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK8 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK3 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y2 )
| ( sK2 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK8 ) ) ) )
@ sK9 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y2 )
| ( sK2 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK2 @ Y2 @ Y3 )
| ( sK3 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ sK7 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK3 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ sK7 @ Y2 )
| ( sK2 @ sK7 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK8 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( ( sK3 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y0 @ Y2 )
| ( sK2 @ Y0 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK8 ) ) ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f57]) ).
thf(f57,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y1 @ Y3 )
| ( sK2 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK2 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ sK7 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK3 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ sK7 @ Y3 )
| ( sK2 @ sK7 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK3 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y1 @ Y3 )
| ( sK2 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) )
@ sK8 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y1 @ Y3 )
| ( sK2 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK2 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ sK7 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK3 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ sK7 @ Y3 )
| ( sK2 @ sK7 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( ( sK3 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y1 @ Y3 )
| ( sK2 @ Y1 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f51]) ).
thf(f51,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y2 @ Y4 )
| ( sK2 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK2 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK3 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK2 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK3 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y2 @ Y4 )
| ( sK2 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) )
@ sK7 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f44]) ).
thf(f146,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK7 @ Y0 )
| ( sK2 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f143]) ).
thf(f143,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK10 @ Y0 )
& ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) ) )
=> ( sK10 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK7 @ Y0 )
| ( sK2 @ sK7 @ Y0 ) )
=> ( sK10 @ Y0 ) ) ) )
=> $false ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f132,f81]) ).
thf(f81,plain,
( ( $false
= ( sK10 @ sK8 ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f74]) ).
thf(f132,plain,
( ! [X1: a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( X1 @ Y0 )
& ( ( sK3 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) ) )
=> ( X1 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ sK7 @ Y0 )
| ( sK2 @ sK7 @ Y0 ) )
=> ( X1 @ Y0 ) ) ) )
=> ( X1 @ sK8 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f131]) ).
thf(f131,plain,
( ! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK7 @ Y1 )
| ( sK2 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK8 ) )
@ X1 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f127]) ).
thf(f127,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK7 @ Y1 )
| ( sK2 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK8 ) ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f126]) ).
thf(f126,plain,
( ( $true
= ( $true
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK3 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK7 @ Y1 )
| ( sK2 @ sK7 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK8 ) ) ) ) )
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f67,f125]) ).
thf(f125,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ sK9 @ Y1 )
| ( sK2 @ sK9 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( ( sK2 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK7 ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f67]) ).
thf(f48,plain,
( spl0_3
| spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f41,f32,f46,f43]) ).
thf(f32,definition,
( spl0_2
<=> ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y0 @ Y3 )
| ( sK2 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK2 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y2 @ Y4 )
| ( sK2 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK2 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK3 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK2 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK3 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y2 @ Y4 )
| ( sK2 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f41,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y0 @ Y3 )
| ( sK2 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK2 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y2 @ Y4 )
| ( sK2 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK2 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK3 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK2 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK3 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y2 @ Y4 )
| ( sK2 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y0 @ Y3 )
| ( sK2 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK2 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y2 @ Y4 )
| ( sK2 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK2 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK3 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK2 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK3 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y2 @ Y4 )
| ( sK2 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f32]) ).
thf(f34,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f27,f32,f29]) ).
thf(f27,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK5 @ Y1 )
| ( sK3 @ sK5 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 ) ) ) )
| ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y0 @ Y3 )
| ( sK2 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK2 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y2 @ Y4 )
| ( sK2 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK2 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK3 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK2 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK3 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y2 @ Y4 )
| ( sK2 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y0 @ Y3 )
| ( sK2 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK2 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y2 @ Y4 )
| ( sK2 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK2 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK3 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK2 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK3 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y2 @ Y4 )
| ( sK2 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK5 @ Y1 )
| ( sK3 @ sK5 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ~ ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y0 @ Y3 )
| ( sK2 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK2 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y2 @ Y4 )
| ( sK2 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK2 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK3 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK2 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK3 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y2 @ Y4 )
| ( sK2 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK5 @ Y1 )
| ( sK3 @ sK5 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 ) ) ) ) )
= $false ),
inference(boolean_simplification,[status(thm)],[f20]) ).
thf(f20,plain,
( ( $false
| ~ ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
| ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y0 @ Y3 )
| ( sK2 @ Y0 @ Y3 ) )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( ( sK2 @ Y4 @ Y3 )
| ( sK3 @ Y4 @ Y3 ) )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y2 @ Y4 )
| ( sK2 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK2 @ Y4 @ Y5 )
| ( sK3 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK3 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y0 @ Y4 )
| ( sK2 @ Y0 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( ( sK3 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y2 @ Y4 )
| ( sK2 @ Y2 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ sK5 @ Y1 )
| ( sK3 @ sK5 @ Y1 ) )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( ( sK2 @ Y2 @ Y1 )
| ( sK3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 ) ) ) ) )
= $false ),
inference(backward_demodulation,[status(thm)],[f17,f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV154^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.32 % Computer : n010.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Feb 24 12:40:48 EST 2026
% 0.12/0.32 % CPUTime :
% 0.12/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.42 ---- Original DTF file ---
% 0.17/0.42 thf(spec,logic,$$dhol).
% 0.17/0.42 %------------------------------------------------------------------------------
% 0.17/0.42 % File : SEV154^5 : TPTP v9.2.1. Released v4.0.0.
% 0.17/0.42 % Domain : Set Theory (Relations)
% 0.17/0.42 % Problem : TPS problem from TRANSITIVE-CLOSURE
% 0.17/0.42 % Version : Especial.
% 0.17/0.42 % English :
% 0.17/0.42
% 0.17/0.42 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.17/0.42 % Source : [Bro09]
% 0.17/0.42 % Names : tps_1221 [Bro09]
% 0.17/0.42
% 0.17/0.42 % Status : Theorem
% 0.17/0.42 % Rating : 0.33 v9.1.0, 0.38 v9.0.0, 0.42 v8.2.0, 0.27 v8.1.0, 0.42 v7.5.0, 0.58 v7.4.0, 0.44 v7.3.0, 0.50 v7.1.0, 0.57 v7.0.0, 0.62 v6.4.0, 0.71 v6.3.0, 0.83 v6.1.0, 0.67 v6.0.0, 0.50 v5.5.0, 0.40 v5.4.0, 0.50 v5.2.0, 1.00 v5.0.0, 0.75 v4.1.0, 1.00 v4.0.0
% 0.17/0.42 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.17/0.42 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.17/0.42 % Maximal formula atoms : 0 ( 0 avg)
% 0.17/0.42 % Number of connectives : 148 ( 1 ~; 14 |; 18 &; 88 @)
% 0.17/0.42 % ( 0 <=>; 27 =>; 0 <=; 0 <~>)
% 0.17/0.42 % Maximal formula depth : 24 ( 24 avg)
% 0.17/0.42 % Number of types : 2 ( 1 usr)
% 0.17/0.42 % Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% 0.17/0.42 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.17/0.42 % Number of variables : 41 ( 0 ^; 41 !; 0 ?; 41 :)
% 0.17/0.42 % SPC : TH0_THM_NEQ_NAR
% 0.17/0.42
% 0.17/0.42 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.17/0.42 % project in the Department of Mathematical Sciences at Carnegie
% 0.17/0.42 % Mellon University. Distributed under the Creative Commons copyleft
% 0.17/0.42 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.17/0.42 %------------------------------------------------------------------------------
% 0.17/0.42 thf(a_type,type,
% 0.17/0.42 a: $tType ).
% 0.17/0.42
% 0.17/0.42 thf(cTHM251G_pme,conjecture,
% 0.17/0.42 ! [R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
% 0.17/0.42 ( ! [Xq: a > $o] :
% 0.17/0.42 ( ( ! [Xw: a] :
% 0.17/0.42 ( ( ( R @ Xx @ Xw )
% 0.17/0.42 | ( S @ Xx @ Xw ) )
% 0.17/0.42 => ( Xq @ Xw ) )
% 0.17/0.42 & ! [Xu: a,Xv: a] :
% 0.17/0.42 ( ( ( Xq @ Xu )
% 0.17/0.42 & ( ( R @ Xu @ Xv )
% 0.17/0.42 | ( S @ Xu @ Xv ) ) )
% 0.17/0.42 => ( Xq @ Xv ) ) )
% 0.17/0.42 => ( Xq @ Xy ) )
% 0.17/0.42 | ~ ( ( ! [Xx0: a,Xy0: a] :
% 0.17/0.42 ( ( ! [Xq: a > $o] :
% 0.17/0.42 ( ( ! [Xw: a] :
% 0.17/0.42 ( ( R @ Xx0 @ Xw )
% 0.17/0.42 => ( Xq @ Xw ) )
% 0.17/0.42 & ! [Xu: a,Xv: a] :
% 0.17/0.42 ( ( ( Xq @ Xu )
% 0.17/0.42 & ( R @ Xu @ Xv ) )
% 0.17/0.42 => ( Xq @ Xv ) ) )
% 0.17/0.42 => ( Xq @ Xy0 ) )
% 0.17/0.42 | ! [Xq: a > $o] :
% 0.17/0.42 ( ( ! [Xw: a] :
% 0.17/0.42 ( ( S @ Xx0 @ Xw )
% 0.17/0.42 => ( Xq @ Xw ) )
% 0.17/0.42 & ! [Xu: a,Xv: a] :
% 0.17/0.42 ( ( ( Xq @ Xu )
% 0.17/0.42 & ( S @ Xu @ Xv ) )
% 0.17/0.42 => ( Xq @ Xv ) ) )
% 0.17/0.42 => ( Xq @ Xy0 ) ) )
% 0.17/0.42 => ! [Xq: a > $o] :
% 0.17/0.42 ( ( ! [Xw: a] :
% 0.17/0.42 ( ( ( R @ Xx0 @ Xw )
% 0.17/0.42 | ( S @ Xx0 @ Xw ) )
% 0.17/0.42 => ( Xq @ Xw ) )
% 0.17/0.42 & ! [Xu: a,Xv: a] :
% 0.17/0.42 ( ( ( Xq @ Xu )
% 0.17/0.42 & ( ( R @ Xu @ Xv )
% 0.17/0.42 | ( S @ Xu @ Xv ) ) )
% 0.17/0.42 => ( Xq @ Xv ) ) )
% 0.17/0.42 => ( Xq @ Xy0 ) ) )
% 0.17/0.42 & ! [Xx0: a,Xy0: a,Xz: a] :
% 0.17/0.42 ( ( ! [Xq: a > $o] :
% 0.17/0.42 ( ( ! [Xw: a] :
% 0.17/0.42 ( ( ( R @ Xx0 @ Xw )
% 0.17/0.42 | ( S @ Xx0 @ Xw ) )
% 0.17/0.42 => ( Xq @ Xw ) )
% 0.17/0.42 & ! [Xu: a,Xv: a] :
% 0.17/0.42 ( ( ( Xq @ Xu )
% 0.17/0.42 & ( ( R @ Xu @ Xv )
% 0.17/0.42 | ( S @ Xu @ Xv ) ) )
% 0.17/0.42 => ( Xq @ Xv ) ) )
% 0.17/0.42 => ( Xq @ Xy0 ) )
% 0.17/0.42 & ! [Xq: a > $o] :
% 0.17/0.42 ( ( ! [Xw: a] :
% 0.17/0.42 ( ( ( R @ Xy0 @ Xw )
% 0.17/0.42 | ( S @ Xy0 @ Xw ) )
% 0.17/0.42 => ( Xq @ Xw ) )
% 0.17/0.42 & ! [Xu: a,Xv: a] :
% 0.17/0.42 ( ( ( Xq @ Xu )
% 0.17/0.42 & ( ( R @ Xu @ Xv )
% 0.17/0.42 | ( S @ Xu @ Xv ) ) )
% 0.17/0.42 => ( Xq @ Xv ) ) )
% 0.17/0.42 => ( Xq @ Xz ) ) )
% 0.17/0.42 => ! [Xq: a > $o] :
% 0.17/0.42 ( ( ! [Xw: a] :
% 0.17/0.42 ( ( ( R @ Xx0 @ Xw )
% 0.17/0.42 | ( S @ Xx0 @ Xw ) )
% 0.17/0.42 => ( Xq @ Xw ) )
% 0.17/0.42 & ! [Xu: a,Xv: a] :
% 0.17/0.42 ( ( ( Xq @ Xu )
% 0.17/0.42 & ( ( R @ Xu @ Xv )
% 0.17/0.42 | ( S @ Xu @ Xv ) ) )
% 0.17/0.42 => ( Xq @ Xv ) ) )
% 0.17/0.42 => ( Xq @ Xz ) ) ) )
% 0.17/0.42 => ! [Xq: a > $o] :
% 0.17/0.42 ( ( ! [Xw: a] :
% 0.17/0.42 ( ( ( R @ Xx @ Xw )
% 0.17/0.42 | ( S @ Xx @ Xw ) )
% 0.17/0.42 => ( Xq @ Xw ) )
% 0.17/0.42 & ! [Xu: a,Xv: a] :
% 0.17/0.42 ( ( ( Xq @ Xu )
% 0.17/0.42 & ( ( R @ Xu @ Xv )
% 0.17/0.42 | ( S @ Xu @ Xv ) ) )
% 0.17/0.42 => ( Xq @ Xv ) ) )
% 0.17/0.42 => ( Xq @ Xy ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 %------------------------------------------------------------------------------
% 0.17/0.42 ------------------------
% 1.32/1.12 ---- Embedded in THF ---
% 1.32/1.12 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.32/1.12 %%% Generated on Tue Feb 24 12:40:48 EST 2026
% 1.32/1.12 %%% using '$$dhol' embedding, version 1.3.0.
% 1.32/1.12 %%% Logic specification used:
% 1.32/1.12 %%% thf(spec, logic, $$dhol).
% 1.32/1.12
% 1.32/1.12 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.MNEUYGSWeg/DTF2DTF13164.p
% See solution above
% 1.32/1.12 ------------------------
% 1.32/1.13 ---- Cleaned THF ---
% 1.32/1.13 thf(a_type,type,
% 1.32/1.13 a: $tType ).
% 1.32/1.13
% 1.32/1.13 thf(cTHM251G_pme,conjecture,
% 1.32/1.13 ! [R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
% 1.32/1.13 ( ! [Xq: a > $o] :
% 1.32/1.13 ( ( ! [Xw: a] :
% 1.32/1.13 ( ( ( R @ Xx @ Xw )
% 1.32/1.13 | ( S @ Xx @ Xw ) )
% 1.32/1.13 => ( Xq @ Xw ) )
% 1.32/1.13 & ! [Xu: a,Xv: a] :
% 1.32/1.13 ( ( ( Xq @ Xu )
% 1.32/1.13 & ( ( R @ Xu @ Xv )
% 1.32/1.13 | ( S @ Xu @ Xv ) ) )
% 1.32/1.13 => ( Xq @ Xv ) ) )
% 1.32/1.13 => ( Xq @ Xy ) )
% 1.32/1.13 | ~ ( ( ! [Xx0: a,Xy0: a] :
% 1.32/1.13 ( ( ! [Xq: a > $o] :
% 1.32/1.13 ( ( ! [Xw: a] :
% 1.32/1.13 ( ( R @ Xx0 @ Xw )
% 1.32/1.13 => ( Xq @ Xw ) )
% 1.32/1.13 & ! [Xu: a,Xv: a] :
% 1.32/1.13 ( ( ( Xq @ Xu )
% 1.32/1.13 & ( R @ Xu @ Xv ) )
% 1.32/1.13 => ( Xq @ Xv ) ) )
% 1.32/1.13 => ( Xq @ Xy0 ) )
% 1.32/1.13 | ! [Xq: a > $o] :
% 1.32/1.13 ( ( ! [Xw: a] :
% 1.32/1.13 ( ( S @ Xx0 @ Xw )
% 1.32/1.13 => ( Xq @ Xw ) )
% 1.32/1.13 & ! [Xu: a,Xv: a] :
% 1.32/1.13 ( ( ( Xq @ Xu )
% 1.32/1.13 & ( S @ Xu @ Xv ) )
% 1.32/1.13 => ( Xq @ Xv ) ) )
% 1.32/1.13 => ( Xq @ Xy0 ) ) )
% 1.32/1.13 => ! [Xq: a > $o] :
% 1.32/1.13 ( ( ! [Xw: a] :
% 1.32/1.13 ( ( ( R @ Xx0 @ Xw )
% 1.32/1.13 | ( S @ Xx0 @ Xw ) )
% 1.32/1.13 => ( Xq @ Xw ) )
% 1.32/1.13 & ! [Xu: a,Xv: a] :
% 1.32/1.13 ( ( ( Xq @ Xu )
% 1.32/1.13 & ( ( R @ Xu @ Xv )
% 1.32/1.13 | ( S @ Xu @ Xv ) ) )
% 1.32/1.13 => ( Xq @ Xv ) ) )
% 1.32/1.13 => ( Xq @ Xy0 ) ) )
% 1.32/1.13 & ! [Xx0: a,Xy0: a,Xz: a] :
% 1.32/1.13 ( ( ! [Xq: a > $o] :
% 1.32/1.13 ( ( ! [Xw: a] :
% 1.32/1.13 ( ( ( R @ Xx0 @ Xw )
% 1.32/1.13 | ( S @ Xx0 @ Xw ) )
% 1.32/1.13 => ( Xq @ Xw ) )
% 1.32/1.13 & ! [Xu: a,Xv: a] :
% 1.32/1.13 ( ( ( Xq @ Xu )
% 1.32/1.13 & ( ( R @ Xu @ Xv )
% 1.32/1.13 | ( S @ Xu @ Xv ) ) )
% 1.32/1.13 => ( Xq @ Xv ) ) )
% 1.32/1.13 => ( Xq @ Xy0 ) )
% 1.32/1.13 & ! [Xq: a > $o] :
% 1.32/1.13 ( ( ! [Xw: a] :
% 1.32/1.13 ( ( ( R @ Xy0 @ Xw )
% 1.32/1.13 | ( S @ Xy0 @ Xw ) )
% 1.32/1.13 => ( Xq @ Xw ) )
% 1.32/1.13 & ! [Xu: a,Xv: a] :
% 1.32/1.13 ( ( ( Xq @ Xu )
% 1.32/1.13 & ( ( R @ Xu @ Xv )
% 1.32/1.13 | ( S @ Xu @ Xv ) ) )
% 1.32/1.13 => ( Xq @ Xv ) ) )
% 1.32/1.13 => ( Xq @ Xz ) ) )
% 1.32/1.13 => ! [Xq: a > $o] :
% 1.32/1.13 ( ( ! [Xw: a] :
% 1.32/1.13 ( ( ( R @ Xx0 @ Xw )
% 1.32/1.13 | ( S @ Xx0 @ Xw ) )
% 1.32/1.13 => ( Xq @ Xw ) )
% 1.32/1.13 & ! [Xu: a,Xv: a] :
% 1.32/1.13 ( ( ( Xq @ Xu )
% 1.32/1.13 & ( ( R @ Xu @ Xv )
% 1.32/1.13 | ( S @ Xu @ Xv ) ) )
% 1.32/1.13 => ( Xq @ Xv ) ) )
% 1.32/1.13 => ( Xq @ Xz ) ) ) )
% 1.32/1.13 => ! [Xq: a > $o] :
% 1.32/1.13 ( ( ! [Xw: a] :
% 1.32/1.13 ( ( ( R @ Xx @ Xw )
% 1.32/1.13 | ( S @ Xx @ Xw ) )
% 1.32/1.13 => ( Xq @ Xw ) )
% 1.32/1.13 & ! [Xu: a,Xv: a] :
% 1.32/1.13 ( ( ( Xq @ Xu )
% 1.32/1.13 & ( ( R @ Xu @ Xv )
% 1.32/1.13 | ( S @ Xu @ Xv ) ) )
% 1.32/1.13 => ( Xq @ Xv ) ) )
% 1.32/1.13 => ( Xq @ Xy ) ) ) ) ).
% 1.32/1.13 ------------------------
% 1.32/1.14 % (13332)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_13164 for (3000ds/2Mi)
% 1.32/1.14 % (13328)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_13164 for (3000ds/183Mi)
% 1.32/1.14 % (13330)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_13164 for (3000ds/27Mi)
% 1.32/1.14 % (13331)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_13164 for (3000ds/2Mi)
% 1.32/1.14 % (13334)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_13164 for (3000ds/18Mi)
% 1.32/1.14 % (13329)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_13164 for (3000ds/4Mi)
% 1.32/1.14 % (13331)Instruction limit reached!
% 1.32/1.14 % (13331)------------------------------
% 1.32/1.14 % (13331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.32/1.14 % (13331)Termination reason: Unknown
% 1.32/1.14 % (13331)Termination phase: shuffling
% 1.32/1.14
% 1.32/1.14 % (13331)Memory used [KB]: 1023
% 1.32/1.14 % (13331)Time elapsed: 0.002 s
% 1.32/1.14 % (13331)Instructions burned: 2 (million)
% 1.32/1.14 % (13331)------------------------------
% 1.32/1.14 % (13331)------------------------------
% 1.32/1.14 % (13332)Instruction limit reached!
% 1.32/1.14 % (13332)------------------------------
% 1.32/1.14 % (13332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.32/1.14 % (13332)Termination reason: Unknown
% 1.32/1.14 % (13332)Termination phase: shuffling
% 1.32/1.14
% 1.32/1.14 % (13332)Memory used [KB]: 1023
% 1.32/1.14 % (13332)Time elapsed: 0.002 s
% 1.32/1.14 % (13332)Instructions burned: 2 (million)
% 1.32/1.14 % (13332)------------------------------
% 1.32/1.14 % (13332)------------------------------
% 1.32/1.14 % (13329)Instruction limit reached!
% 1.32/1.14 % (13329)------------------------------
% 1.32/1.14 % (13329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.32/1.14 % (13329)Termination reason: Unknown
% 1.32/1.14 % (13329)Termination phase: Preprocessing 3
% 1.32/1.14
% 1.32/1.14 % (13329)Memory used [KB]: 1023
% 1.32/1.14 % (13329)Time elapsed: 0.003 s
% 1.32/1.14 % (13329)Instructions burned: 4 (million)
% 1.32/1.14 % (13329)------------------------------
% 1.32/1.14 % (13329)------------------------------
% 1.32/1.14 % (13333)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_13164 for (3000ds/275Mi)
% 1.32/1.15 % (13334)Instruction limit reached!
% 1.32/1.15 % (13334)------------------------------
% 1.32/1.15 % (13334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.32/1.15 % (13334)Termination reason: Unknown
% 1.32/1.15 % (13334)Termination phase: Saturation
% 1.32/1.15
% 1.32/1.15 % (13334)Memory used [KB]: 5628
% 1.32/1.15 % (13334)Time elapsed: 0.007 s
% 1.32/1.15 % (13334)Instructions burned: 19 (million)
% 1.32/1.15 % (13334)------------------------------
% 1.32/1.15 % (13334)------------------------------
% 1.32/1.15 % (13330)Instruction limit reached!
% 1.32/1.15 % (13330)------------------------------
% 1.32/1.15 % (13330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.32/1.15 % (13330)Termination reason: Unknown
% 1.32/1.15 % (13330)Termination phase: Saturation
% 1.32/1.15
% 1.32/1.15 % (13330)Memory used [KB]: 5756
% 1.32/1.15 % (13330)Time elapsed: 0.010 s
% 1.32/1.15 % (13330)Instructions burned: 27 (million)
% 1.32/1.15 % (13330)------------------------------
% 1.32/1.15 % (13330)------------------------------
% 1.32/1.15 % (13342)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_13164 for (2999ds/3Mi)
% 1.32/1.15 % (13343)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_13164 for (2999ds/37Mi)
% 1.32/1.15 % (13344)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_13164 for (2999ds/15Mi)
% 1.32/1.15 % (13342)Instruction limit reached!
% 1.32/1.15 % (13342)------------------------------
% 1.32/1.15 % (13342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.32/1.15 % (13342)Termination reason: Unknown
% 1.32/1.15 % (13342)Termination phase: Naming
% 1.32/1.15
% 1.32/1.15 % (13342)Memory used [KB]: 1023
% 1.32/1.15 % (13342)Time elapsed: 0.002 s
% 1.32/1.15 % (13342)Instructions burned: 3 (million)
% 1.32/1.15 % (13342)------------------------------
% 1.32/1.15 % (13342)------------------------------
% 1.32/1.16 % (13345)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_13164 for (2999ds/3Mi)
% 1.32/1.16 % (13344)Instruction limit reached!
% 1.32/1.16 % (13344)------------------------------
% 1.32/1.16 % (13344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.32/1.16 % (13344)Termination reason: Unknown
% 1.32/1.16 % (13344)Termination phase: Saturation
% 1.32/1.16
% 1.32/1.16 % (13344)Memory used [KB]: 5756
% 1.32/1.16 % (13344)Time elapsed: 0.006 s
% 1.32/1.16 % (13344)Instructions burned: 16 (million)
% 1.32/1.16 % (13344)------------------------------
% 1.32/1.16 % (13344)------------------------------
% 1.32/1.16 % (13345)Instruction limit reached!
% 1.32/1.16 % (13345)------------------------------
% 1.32/1.16 % (13345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.32/1.16 % (13345)Termination reason: Unknown
% 1.32/1.16 % (13345)Termination phase: shuffling
% 1.32/1.16
% 1.32/1.16 % (13345)Memory used [KB]: 1023
% 1.32/1.16 % (13345)Time elapsed: 0.002 s
% 1.32/1.16 % (13345)Instructions burned: 3 (million)
% 1.32/1.16 % (13345)------------------------------
% 1.32/1.16 % (13345)------------------------------
% 1.32/1.16 % (13346)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_13164 for (2999ds/1041Mi)
% 1.32/1.16 % (13343)Instruction limit reached!
% 1.32/1.16 % (13343)------------------------------
% 1.32/1.16 % (13343)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.32/1.16 % (13343)Termination reason: Unknown
% 1.32/1.16 % (13343)Termination phase: Saturation
% 1.32/1.16
% 1.32/1.16 % (13343)Memory used [KB]: 5628
% 1.32/1.16 % (13343)Time elapsed: 0.011 s
% 1.32/1.16 % (13343)Instructions burned: 37 (million)
% 1.32/1.16 % (13343)------------------------------
% 1.32/1.16 % (13343)------------------------------
% 1.32/1.16 % (13347)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_13164 for (2999ds/7Mi)
% 1.32/1.16 % (13347)Instruction limit reached!
% 1.32/1.16 % (13347)------------------------------
% 1.32/1.16 % (13347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.32/1.16 % (13347)Termination reason: Unknown
% 1.32/1.16 % (13347)Termination phase: Saturation
% 1.32/1.16
% 1.32/1.16 % (13347)Memory used [KB]: 1151
% 1.32/1.16 % (13347)Time elapsed: 0.004 s
% 1.32/1.16 % (13347)Instructions burned: 10 (million)
% 1.32/1.16 % (13347)------------------------------
% 1.32/1.16 % (13347)------------------------------
% 1.32/1.17 % (13348)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_13164 for (2999ds/16Mi)
% 1.32/1.17 % (13349)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_13164 for (2999ds/3Mi)
% 1.32/1.17 % (13349)Instruction limit reached!
% 1.32/1.17 % (13349)------------------------------
% 1.32/1.17 % (13349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.32/1.17 % (13349)Termination reason: Unknown
% 1.32/1.17 % (13349)Termination phase: Naming
% 1.32/1.17
% 1.32/1.17 % (13349)Memory used [KB]: 1023
% 1.32/1.17 % (13349)Time elapsed: 0.002 s
% 1.32/1.17 % (13349)Instructions burned: 3 (million)
% 1.32/1.17 % (13349)------------------------------
% 1.32/1.17 % (13349)------------------------------
% 1.32/1.17 % (13351)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_13164 for (2999ds/3Mi)
% 1.32/1.17 % (13348)Instruction limit reached!
% 1.32/1.17 % (13348)------------------------------
% 1.32/1.17 % (13348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.32/1.17 % (13348)Termination reason: Unknown
% 1.32/1.17 % (13348)Termination phase: Saturation
% 1.32/1.17
% 1.32/1.17 % (13348)Memory used [KB]: 5628
% 1.32/1.17 % (13348)Time elapsed: 0.006 s
% 1.32/1.17 % (13348)Instructions burned: 19 (million)
% 1.32/1.17 % (13348)------------------------------
% 1.32/1.17 % (13348)------------------------------
% 1.32/1.17 % (13351)Instruction limit reached!
% 1.32/1.17 % (13351)------------------------------
% 1.32/1.17 % (13351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.32/1.17 % (13351)Termination reason: Unknown
% 1.32/1.17 % (13351)Termination phase: Naming
% 1.32/1.17
% 1.32/1.17 % (13351)Memory used [KB]: 1023
% 1.32/1.17 % (13351)Time elapsed: 0.002 s
% 1.32/1.17 % (13351)Instructions burned: 4 (million)
% 1.32/1.17 % (13351)------------------------------
% 1.32/1.17 % (13351)------------------------------
% 1.32/1.17 % (13356)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_13164 for (2999ds/7Mi)
% 1.32/1.17 % (13356)Instruction limit reached!
% 1.32/1.17 % (13356)------------------------------
% 1.32/1.17 % (13356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.32/1.17 % (13356)Termination reason: Unknown
% 1.32/1.17 % (13356)Termination phase: Property scanning
% 1.32/1.17
% 1.32/1.17 % (13356)Memory used [KB]: 1151
% 1.32/1.17 % (13356)Time elapsed: 0.003 s
% 1.32/1.17 % (13356)Instructions burned: 8 (million)
% 1.32/1.17 % (13356)------------------------------
% 1.32/1.17 % (13356)------------------------------
% 1.32/1.18 % (13360)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_13164 for (2999ds/3Mi)
% 1.32/1.18 % (13360)Instruction limit reached!
% 1.32/1.18 % (13360)------------------------------
% 1.32/1.18 % (13360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.32/1.18 % (13360)Termination reason: Unknown
% 1.32/1.18 % (13360)Termination phase: Property scanning
% 1.32/1.18
% 1.32/1.18 % (13360)Memory used [KB]: 1023
% 1.32/1.18 % (13360)Time elapsed: 0.002 s
% 1.32/1.18 % (13360)Instructions burned: 5 (million)
% 1.32/1.18 % (13360)------------------------------
% 1.32/1.18 % (13360)------------------------------
% 1.32/1.18 % (13364)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_13164 for (2999ds/4Mi)
% 1.32/1.18 % (13365)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_13164 for (2999ds/18Mi)
% 1.32/1.18 % (13364)Instruction limit reached!
% 1.32/1.18 % (13364)------------------------------
% 1.32/1.18 % (13364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.32/1.18 % (13364)Termination reason: Unknown
% 1.32/1.18 % (13364)Termination phase: Preprocessing 3
% 1.32/1.18
% 1.32/1.18 % (13364)Memory used [KB]: 1023
% 1.32/1.18 % (13364)Time elapsed: 0.002 s
% 1.32/1.18 % (13364)Instructions burned: 4 (million)
% 1.32/1.18 % (13364)------------------------------
% 1.32/1.18 % (13364)------------------------------
% 1.32/1.18 % (13367)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_13164 for (2999ds/710Mi)
% 1.32/1.19 % (13365)Instruction limit reached!
% 1.32/1.19 % (13365)------------------------------
% 1.32/1.19 % (13365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.32/1.19 % (13365)Termination reason: Unknown
% 1.32/1.19 % (13365)Termination phase: Saturation
% 1.32/1.19
% 1.32/1.19 % (13365)Memory used [KB]: 5756
% 1.32/1.19 % (13365)Time elapsed: 0.007 s
% 1.32/1.19 % (13365)Instructions burned: 20 (million)
% 1.32/1.19 % (13365)------------------------------
% 1.32/1.19 % (13365)------------------------------
% 1.32/1.19 % (13369)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_13164 for (2999ds/6Mi)
% 1.32/1.19 % (13369)Instruction limit reached!
% 1.32/1.19 % (13369)------------------------------
% 1.32/1.19 % (13369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.32/1.19 % (13369)Termination reason: Unknown
% 1.32/1.19 % (13369)Termination phase: Property scanning
% 1.32/1.19
% 1.32/1.19 % (13369)Memory used [KB]: 1151
% 1.32/1.19 % (13369)Time elapsed: 0.003 s
% 1.32/1.19 % (13369)Instructions burned: 8 (million)
% 1.32/1.19 % (13369)------------------------------
% 1.32/1.19 % (13369)------------------------------
% 1.32/1.19 % (13372)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_13164 for (2999ds/902Mi)
% 1.32/1.20 % (13377)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_13164 for (2999ds/21Mi)
% 1.32/1.20 % (13328)Instruction limit reached!
% 1.32/1.20 % (13328)------------------------------
% 1.32/1.20 % (13328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.32/1.20 % (13328)Termination reason: Unknown
% 1.32/1.20 % (13328)Termination phase: Saturation
% 1.32/1.20
% 1.32/1.20 % (13328)Memory used [KB]: 6524
% 1.32/1.20 % (13328)Time elapsed: 0.057 s
% 1.32/1.20 % (13328)Instructions burned: 185 (million)
% 1.32/1.20 % (13328)------------------------------
% 1.32/1.20 % (13328)------------------------------
% 1.35/1.20 % (13379)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_13164 for (2999ds/5Mi)
% 1.35/1.20 % (13379)Instruction limit reached!
% 1.35/1.20 % (13379)------------------------------
% 1.35/1.20 % (13379)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.35/1.20 % (13379)Termination reason: Unknown
% 1.35/1.20 % (13379)Termination phase: Saturation
% 1.35/1.20
% 1.35/1.20 % (13379)Memory used [KB]: 5500
% 1.35/1.20 % (13379)Time elapsed: 0.003 s
% 1.35/1.20 % (13379)Instructions burned: 7 (million)
% 1.35/1.20 % (13379)------------------------------
% 1.35/1.20 % (13379)------------------------------
% 1.35/1.20 % (13377)Instruction limit reached!
% 1.35/1.20 % (13377)------------------------------
% 1.35/1.20 % (13377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.35/1.20 % (13377)Termination reason: Unknown
% 1.35/1.20 % (13377)Termination phase: Saturation
% 1.35/1.20
% 1.35/1.20 % (13377)Memory used [KB]: 5756
% 1.35/1.20 % (13377)Time elapsed: 0.008 s
% 1.35/1.20 % (13377)Instructions burned: 23 (million)
% 1.35/1.20 % (13377)------------------------------
% 1.35/1.20 % (13377)------------------------------
% 1.35/1.21 % (13380)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_13164 for (2999ds/6Mi)
% 1.35/1.21 % (13380)Instruction limit reached!
% 1.35/1.21 % (13380)------------------------------
% 1.35/1.21 % (13380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.35/1.21 % (13380)Termination reason: Unknown
% 1.35/1.21 % (13380)Termination phase: Saturation
% 1.35/1.21
% 1.35/1.21 % (13380)Memory used [KB]: 1023
% 1.35/1.21 % (13380)Time elapsed: 0.003 s
% 1.35/1.21 % (13380)Instructions burned: 7 (million)
% 1.35/1.21 % (13380)------------------------------
% 1.35/1.21 % (13380)------------------------------
% 1.35/1.21 % (13381)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_13164 for (2999ds/377Mi)
% 1.35/1.21 % (13382)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_13164 for (2999ds/779Mi)
% 1.35/1.22 % (13388)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_13164 for (2999ds/19Mi)
% 1.35/1.22 % (13388)Instruction limit reached!
% 1.35/1.22 % (13388)------------------------------
% 1.35/1.22 % (13388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.35/1.22 % (13388)Termination reason: Unknown
% 1.35/1.22 % (13388)Termination phase: Saturation
% 1.35/1.22
% 1.35/1.22 % (13388)Memory used [KB]: 5500
% 1.35/1.22 % (13388)Time elapsed: 0.007 s
% 1.35/1.22 % (13388)Instructions burned: 22 (million)
% 1.35/1.22 % (13388)------------------------------
% 1.35/1.22 % (13388)------------------------------
% 1.35/1.23 % (13400)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_13164 for (2999ds/879Mi)
% 1.35/1.25 % (13333)Instruction limit reached!
% 1.35/1.25 % (13333)------------------------------
% 1.35/1.25 % (13333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.35/1.25 % (13333)Termination reason: Unknown
% 1.35/1.25 % (13333)Termination phase: Saturation
% 1.35/1.25
% 1.35/1.25 % (13333)Memory used [KB]: 6268
% 1.35/1.25 % (13333)Time elapsed: 0.105 s
% 1.35/1.25 % (13333)Instructions burned: 276 (million)
% 1.35/1.25 % (13333)------------------------------
% 1.35/1.25 % (13333)------------------------------
% 1.35/1.26 % (13409)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_13164 for (2998ds/17Mi)
% 1.35/1.26 % (13409)Instruction limit reached!
% 1.35/1.26 % (13409)------------------------------
% 1.35/1.26 % (13409)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.35/1.26 % (13409)Termination reason: Unknown
% 1.35/1.26 % (13409)Termination phase: Saturation
% 1.35/1.26
% 1.35/1.26 % (13409)Memory used [KB]: 5756
% 1.35/1.26 % (13409)Time elapsed: 0.007 s
% 1.35/1.26 % (13409)Instructions burned: 18 (million)
% 1.35/1.26 % (13409)------------------------------
% 1.35/1.26 % (13409)------------------------------
% 1.35/1.27 % (13346)First to succeed.
% 1.35/1.27 % (13421)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_13164 for (2998ds/3Mi)
% 1.35/1.27 % (13421)Instruction limit reached!
% 1.35/1.27 % (13421)------------------------------
% 1.35/1.27 % (13421)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.35/1.27 % (13421)Termination reason: Unknown
% 1.35/1.27 % (13421)Termination phase: Preprocessing 3
% 1.35/1.27
% 1.35/1.27 % (13421)Memory used [KB]: 1023
% 1.35/1.27 % (13421)Time elapsed: 0.002 s
% 1.35/1.27 % (13421)Instructions burned: 4 (million)
% 1.35/1.27 % (13421)------------------------------
% 1.35/1.27 % (13421)------------------------------
% 1.35/1.28 % (13346)Refutation found. Thanks to Tanya!
% 1.35/1.28 % SZS status Theorem for DTF2THF_13164
% 1.35/1.28 % SZS output start Proof for DTF2THF_13164
% 1.35/1.28 thf(type_def_5, type, a: $tType).
% 1.35/1.28 thf(func_def_0, type, a: $tType).
% 1.35/1.28 thf(func_def_21, type, ph1: !>[X0: $tType]:(X0)).
% 1.35/1.28 thf(func_def_22, type, sK2: a > a > $o).
% 1.35/1.28 thf(func_def_23, type, sK3: a > a > $o).
% 1.35/1.28 thf(func_def_24, type, sK4: a).
% 1.35/1.28 thf(func_def_25, type, sK5: a).
% 1.35/1.28 thf(func_def_26, type, sK6: a > $o).
% 1.35/1.28 thf(func_def_27, type, sK7: a).
% 1.35/1.28 thf(func_def_28, type, sK8: a).
% 1.35/1.28 thf(func_def_29, type, sK9: a).
% 1.35/1.28 thf(func_def_30, type, sK10: a > $o).
% 1.35/1.28 thf(func_def_31, type, sK11: a).
% 1.35/1.28 thf(func_def_32, type, sK12: a).
% 1.35/1.28 thf(func_def_33, type, sK13: a).
% 1.35/1.28 thf(func_def_34, type, sK14: a > $o).
% 1.35/1.28 thf(func_def_35, type, sK15: a).
% 1.35/1.28 thf(func_def_36, type, sK16: a).
% 1.35/1.28 thf(func_def_37, type, sK17: a).
% 1.35/1.28 thf(func_def_38, type, sK18: a).
% 1.35/1.28 thf(func_def_39, type, sK19: a).
% 1.35/1.28 thf(func_def_40, type, sK20: a).
% 1.35/1.28 thf(func_def_41, type, sK21: a).
% 1.35/1.28 thf(func_def_42, type, sK22: a).
% 1.35/1.28 thf(func_def_43, type, sK23: a).
% 1.35/1.28 thf(func_def_44, type, sK24: a).
% 1.35/1.28 thf(func_def_45, type, sK25: a).
% 1.35/1.28 thf(func_def_46, type, sK26: a).
% 1.35/1.28 thf(func_def_47, type, sK27: a).
% 1.35/1.28 thf(func_def_48, type, sK28: a).
% 1.35/1.28 thf(func_def_49, type, sK29: a).
% 1.35/1.28 thf(f1844,plain,(
% 1.35/1.28 $false),
% 1.35/1.28 inference(avatar_sat_refutation,[status(thm)],[f34,f48,f233,f336,f443,f493,f523,f529,f536,f600,f610,f620,f794,f878,f916,f1067,f1080,f1093,f1341,f1400,f1455,f1815,f1843])).
% 1.35/1.28 thf(f1843,plain,(
% 1.35/1.28 ~spl0_4 | ~spl0_7 | ~spl0_9),
% 1.35/1.28 inference(avatar_contradiction_clause,[status(thm)],[f1842])).
% 1.35/1.28 thf(f1842,plain,(
% 1.35/1.28 $false | (~spl0_4 | ~spl0_7 | ~spl0_9)),
% 1.35/1.28 inference(trivial_inequality_removal,[status(thm)],[f1841])).
% 1.35/1.28 thf(f1841,plain,(
% 1.35/1.28 ($true = $false) | (~spl0_4 | ~spl0_7 | ~spl0_9)),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f1840])).
% 1.35/1.28 thf(f1840,plain,(
% 1.35/1.28 ($true = (~ $true)) | (~spl0_4 | ~spl0_7 | ~spl0_9)),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f1839])).
% 1.35/1.28 thf(f1839,plain,(
% 1.35/1.28 ($true = (~ ((sK3 @ sK12 @ sK29) | $true))) | (~spl0_4 | ~spl0_7 | ~spl0_9)),
% 1.35/1.28 inference(forward_demodulation,[status(thm)],[f1837,f1825])).
% 1.35/1.28 thf(f1825,plain,(
% 1.35/1.28 ($true = (sK2 @ sK12 @ sK29)) | ~spl0_9),
% 1.35/1.28 inference(binary_proxy_clausification,[status(thm)],[f1821])).
% 1.35/1.28 thf(f1821,plain,(
% 1.35/1.28 (((sK2 @ sK12 @ sK29) => (sK14 @ sK29)) = $false) | ~spl0_9),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f1819])).
% 1.35/1.28 thf(f1819,plain,(
% 1.35/1.28 (((^[Y0 : a]: ((sK2 @ sK12 @ Y0) => (sK14 @ Y0))) @ sK29) = $false) | ~spl0_9),
% 1.35/1.28 inference(sigma_clausification,[status(thm)],[f439])).
% 1.35/1.28 thf(f439,plain,(
% 1.35/1.28 ($false = (!! @ a @ (^[Y0 : a]: ((sK2 @ sK12 @ Y0) => (sK14 @ Y0))))) | ~spl0_9),
% 1.35/1.28 inference(avatar_component_clause,[status(thm)],[f438])).
% 1.35/1.28 thf(f438,definition,(
% 1.35/1.28 spl0_9 <=> ($false = (!! @ a @ (^[Y0 : a]: ((sK2 @ sK12 @ Y0) => (sK14 @ Y0)))))),
% 1.35/1.28 introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition])).
% 1.35/1.28 thf(f1837,plain,(
% 1.35/1.28 ($true = (~ ((sK3 @ sK12 @ sK29) | (sK2 @ sK12 @ sK29)))) | (~spl0_4 | ~spl0_7 | ~spl0_9)),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f1830])).
% 1.35/1.28 thf(f1830,plain,(
% 1.35/1.28 ($true = (((sK3 @ sK12 @ sK29) | (sK2 @ sK12 @ sK29)) => $false)) | (~spl0_4 | ~spl0_7 | ~spl0_9)),
% 1.35/1.28 inference(superposition,[status(thm)],[f1660,f1824])).
% 1.35/1.28 thf(f1824,plain,(
% 1.35/1.28 ($false = (sK14 @ sK29)) | ~spl0_9),
% 1.35/1.28 inference(binary_proxy_clausification,[status(thm)],[f1821])).
% 1.35/1.28 thf(f1660,plain,(
% 1.35/1.28 ( ! [X1 : a] : (($true = (((sK3 @ sK12 @ X1) | (sK2 @ sK12 @ X1)) => (sK14 @ X1)))) ) | (~spl0_4 | ~spl0_7)),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f1659])).
% 1.35/1.28 thf(f1659,plain,(
% 1.35/1.28 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (((sK3 @ sK12 @ Y0) | (sK2 @ sK12 @ Y0)) => (sK14 @ Y0))) @ X1))) ) | (~spl0_4 | ~spl0_7)),
% 1.35/1.28 inference(pi_clausification,[status(thm)],[f1506])).
% 1.35/1.28 thf(f1506,plain,(
% 1.35/1.28 ($true = (!! @ a @ (^[Y0 : a]: (((sK3 @ sK12 @ Y0) | (sK2 @ sK12 @ Y0)) => (sK14 @ Y0))))) | (~spl0_4 | ~spl0_7)),
% 1.35/1.28 inference(binary_proxy_clausification,[status(thm)],[f1482])).
% 1.35/1.28 thf(f1482,plain,(
% 1.35/1.28 ($true = ((!! @ a @ (^[Y0 : a]: (((sK3 @ sK12 @ Y0) | (sK2 @ sK12 @ Y0)) => (sK14 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) & (sK14 @ Y1)) => (sK14 @ Y0)))))))) | (~spl0_4 | ~spl0_7)),
% 1.35/1.28 inference(binary_proxy_clausification,[status(thm)],[f1470])).
% 1.35/1.28 thf(f1470,plain,(
% 1.35/1.28 ((((!! @ a @ (^[Y0 : a]: (((sK3 @ sK12 @ Y0) | (sK2 @ sK12 @ Y0)) => (sK14 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) & (sK14 @ Y1)) => (sK14 @ Y0))))))) => (sK14 @ sK13)) = $false) | (~spl0_4 | ~spl0_7)),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f1469])).
% 1.35/1.28 thf(f1469,plain,(
% 1.35/1.28 (((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK3 @ sK12 @ Y1) | (sK2 @ sK12 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK2 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1))))))) => (Y0 @ sK13))) @ sK14) = $false) | (~spl0_4 | ~spl0_7)),
% 1.35/1.28 inference(sigma_clausification,[status(thm)],[f1458])).
% 1.35/1.28 thf(f1458,plain,(
% 1.35/1.28 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK3 @ sK12 @ Y1) | (sK2 @ sK12 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK2 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1))))))) => (Y0 @ sK13)))) = $false) | (~spl0_4 | ~spl0_7)),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f1457])).
% 1.35/1.28 thf(f1457,plain,(
% 1.35/1.28 ($false = ($true => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK3 @ sK12 @ Y1) | (sK2 @ sK12 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK2 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1))))))) => (Y0 @ sK13)))))) | (~spl0_4 | ~spl0_7)),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f1456])).
% 1.35/1.28 thf(f1456,plain,(
% 1.35/1.28 ((((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK3 @ sK12 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2))))))) => (Y0 @ sK13)))) | $true) => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK3 @ sK12 @ Y1) | (sK2 @ sK12 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK2 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1))))))) => (Y0 @ sK13))))) = $false) | (~spl0_4 | ~spl0_7)),
% 1.35/1.28 inference(forward_demodulation,[status(thm)],[f1106,f332])).
% 1.35/1.28 thf(f332,plain,(
% 1.35/1.28 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK12 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK13)))) = $true) | ~spl0_7),
% 1.35/1.28 inference(avatar_component_clause,[status(thm)],[f331])).
% 1.35/1.28 thf(f331,definition,(
% 1.35/1.28 spl0_7 <=> ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK12 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK13)))) = $true)),
% 1.35/1.28 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 1.35/1.28 thf(f1106,plain,(
% 1.35/1.28 ((((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK3 @ sK12 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2))))))) => (Y0 @ sK13)))) | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK12 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK13))))) => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK3 @ sK12 @ Y1) | (sK2 @ sK12 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK2 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1))))))) => (Y0 @ sK13))))) = $false) | ~spl0_4),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f1105])).
% 1.35/1.28 thf(f1105,plain,(
% 1.35/1.28 (((^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK3 @ sK12 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y2 @ Y3) & (Y1 @ Y2)) => (Y1 @ Y3))))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & (sK2 @ Y3 @ Y2)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ sK12 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK3 @ sK12 @ Y2) | (sK2 @ sK12 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((((sK2 @ Y3 @ Y2) | (sK3 @ Y3 @ Y2)) & (Y1 @ Y3)) => (Y1 @ Y2))))))) => (Y1 @ Y0)))))) @ sK13) = $false) | ~spl0_4),
% 1.35/1.28 inference(sigma_clausification,[status(thm)],[f1102])).
% 1.35/1.28 thf(f1102,plain,(
% 1.35/1.28 ((!! @ a @ (^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK3 @ sK12 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y2 @ Y3) & (Y1 @ Y2)) => (Y1 @ Y3))))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & (sK2 @ Y3 @ Y2)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ sK12 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK3 @ sK12 @ Y2) | (sK2 @ sK12 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((((sK2 @ Y3 @ Y2) | (sK3 @ Y3 @ Y2)) & (Y1 @ Y3)) => (Y1 @ Y2))))))) => (Y1 @ Y0))))))) = $false) | ~spl0_4),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f1101])).
% 1.35/1.28 thf(f1101,plain,(
% 1.35/1.28 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK3 @ Y0 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y3 @ Y4) & (Y2 @ Y3)) => (Y2 @ Y4))))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & (sK2 @ Y4 @ Y3)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK3 @ Y0 @ Y3) | (sK2 @ Y0 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((((sK2 @ Y4 @ Y3) | (sK3 @ Y4 @ Y3)) & (Y2 @ Y4)) => (Y2 @ Y3))))))) => (Y2 @ Y1)))))))) @ sK12)) | ~spl0_4),
% 1.35/1.28 inference(sigma_clausification,[status(thm)],[f47])).
% 1.35/1.28 thf(f47,plain,(
% 1.35/1.28 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK3 @ Y0 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y3 @ Y4) & (Y2 @ Y3)) => (Y2 @ Y4))))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & (sK2 @ Y4 @ Y3)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK3 @ Y0 @ Y3) | (sK2 @ Y0 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((((sK2 @ Y4 @ Y3) | (sK3 @ Y4 @ Y3)) & (Y2 @ Y4)) => (Y2 @ Y3))))))) => (Y2 @ Y1))))))))) = $false) | ~spl0_4),
% 1.35/1.28 inference(avatar_component_clause,[status(thm)],[f46])).
% 1.35/1.28 thf(f46,definition,(
% 1.35/1.28 spl0_4 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK3 @ Y0 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y3 @ Y4) & (Y2 @ Y3)) => (Y2 @ Y4))))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & (sK2 @ Y4 @ Y3)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK3 @ Y0 @ Y3) | (sK2 @ Y0 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((((sK2 @ Y4 @ Y3) | (sK3 @ Y4 @ Y3)) & (Y2 @ Y4)) => (Y2 @ Y3))))))) => (Y2 @ Y1))))))))) = $false)),
% 1.35/1.28 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.35/1.28 thf(f1815,plain,(
% 1.35/1.28 ~spl0_4 | ~spl0_7 | ~spl0_10),
% 1.35/1.28 inference(avatar_contradiction_clause,[status(thm)],[f1814])).
% 1.35/1.28 thf(f1814,plain,(
% 1.35/1.28 $false | (~spl0_4 | ~spl0_7 | ~spl0_10)),
% 1.35/1.28 inference(trivial_inequality_removal,[status(thm)],[f1813])).
% 1.35/1.28 thf(f1813,plain,(
% 1.35/1.28 ($true = $false) | (~spl0_4 | ~spl0_7 | ~spl0_10)),
% 1.35/1.28 inference(forward_demodulation,[status(thm)],[f1812,f1755])).
% 1.35/1.28 thf(f1755,plain,(
% 1.35/1.28 ((sK14 @ sK26) = $false) | ~spl0_10),
% 1.35/1.28 inference(binary_proxy_clausification,[status(thm)],[f1738])).
% 1.35/1.28 thf(f1738,plain,(
% 1.35/1.28 ($false = (((sK14 @ sK27) & (sK2 @ sK27 @ sK26)) => (sK14 @ sK26))) | ~spl0_10),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f1737])).
% 1.35/1.28 thf(f1737,plain,(
% 1.35/1.28 ($false = ((^[Y0 : a]: (((sK14 @ Y0) & (sK2 @ Y0 @ sK26)) => (sK14 @ sK26))) @ sK27)) | ~spl0_10),
% 1.35/1.28 inference(sigma_clausification,[status(thm)],[f1725])).
% 1.35/1.28 thf(f1725,plain,(
% 1.35/1.28 ($false = (!! @ a @ (^[Y0 : a]: (((sK14 @ Y0) & (sK2 @ Y0 @ sK26)) => (sK14 @ sK26))))) | ~spl0_10),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f1723])).
% 1.35/1.28 thf(f1723,plain,(
% 1.35/1.28 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK14 @ Y1) & (sK2 @ Y1 @ Y0)) => (sK14 @ Y0))))) @ sK26) = $false) | ~spl0_10),
% 1.35/1.28 inference(sigma_clausification,[status(thm)],[f442])).
% 1.35/1.28 thf(f442,plain,(
% 1.35/1.28 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK14 @ Y1) & (sK2 @ Y1 @ Y0)) => (sK14 @ Y0)))))) = $false) | ~spl0_10),
% 1.35/1.28 inference(avatar_component_clause,[status(thm)],[f441])).
% 1.35/1.28 thf(f441,definition,(
% 1.35/1.28 spl0_10 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK14 @ Y1) & (sK2 @ Y1 @ Y0)) => (sK14 @ Y0)))))) = $false)),
% 1.35/1.28 introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition])).
% 1.35/1.28 thf(f1812,plain,(
% 1.35/1.28 ($true = (sK14 @ sK26)) | (~spl0_4 | ~spl0_7 | ~spl0_10)),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f1811])).
% 1.35/1.28 thf(f1811,plain,(
% 1.35/1.28 ($true = ($true => (sK14 @ sK26))) | (~spl0_4 | ~spl0_7 | ~spl0_10)),
% 1.35/1.28 inference(forward_demodulation,[status(thm)],[f1810,f1796])).
% 1.35/1.28 thf(f1796,plain,(
% 1.35/1.28 ($true = (sK14 @ sK28)) | ~spl0_10),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f1795])).
% 1.35/1.28 thf(f1795,plain,(
% 1.35/1.28 ($true = ((sK14 @ sK28) & $true)) | ~spl0_10),
% 1.35/1.28 inference(backward_demodulation,[status(thm)],[f1790,f1793])).
% 1.35/1.28 thf(f1793,plain,(
% 1.35/1.28 ($true = (sK2 @ sK28 @ sK26)) | ~spl0_10),
% 1.35/1.28 inference(binary_proxy_clausification,[status(thm)],[f1790])).
% 1.35/1.28 thf(f1790,plain,(
% 1.35/1.28 ($true = ((sK14 @ sK28) & (sK2 @ sK28 @ sK26))) | ~spl0_10),
% 1.35/1.28 inference(not_proxy_clausification,[status(thm)],[f1773])).
% 1.35/1.28 thf(f1773,plain,(
% 1.35/1.28 ((~ ((sK14 @ sK28) & (sK2 @ sK28 @ sK26))) = $false) | ~spl0_10),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f1772])).
% 1.35/1.28 thf(f1772,plain,(
% 1.35/1.28 (((^[Y0 : a]: (~ ((sK14 @ Y0) & (sK2 @ Y0 @ sK26)))) @ sK28) = $false) | ~spl0_10),
% 1.35/1.28 inference(sigma_clausification,[status(thm)],[f1760])).
% 1.35/1.28 thf(f1760,plain,(
% 1.35/1.28 ((!! @ a @ (^[Y0 : a]: (~ ((sK14 @ Y0) & (sK2 @ Y0 @ sK26))))) = $false) | ~spl0_10),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f1758])).
% 1.35/1.28 thf(f1758,plain,(
% 1.35/1.28 ((!! @ a @ (^[Y0 : a]: (((sK14 @ Y0) & (sK2 @ Y0 @ sK26)) => $false))) = $false) | ~spl0_10),
% 1.35/1.28 inference(backward_demodulation,[status(thm)],[f1725,f1755])).
% 1.35/1.28 thf(f1810,plain,(
% 1.35/1.28 ($true = ((sK14 @ sK28) => (sK14 @ sK26))) | (~spl0_4 | ~spl0_7 | ~spl0_10)),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f1809])).
% 1.35/1.28 thf(f1809,plain,(
% 1.35/1.28 ((($true & (sK14 @ sK28)) => (sK14 @ sK26)) = $true) | (~spl0_4 | ~spl0_7 | ~spl0_10)),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f1805])).
% 1.35/1.28 thf(f1805,plain,(
% 1.35/1.28 ($true = ((($true | (sK3 @ sK28 @ sK26)) & (sK14 @ sK28)) => (sK14 @ sK26))) | (~spl0_4 | ~spl0_7 | ~spl0_10)),
% 1.35/1.28 inference(superposition,[status(thm)],[f1530,f1793])).
% 1.35/1.28 thf(f1530,plain,(
% 1.35/1.28 ( ! [X2 : a,X1 : a] : (($true = ((((sK2 @ X2 @ X1) | (sK3 @ X2 @ X1)) & (sK14 @ X2)) => (sK14 @ X1)))) ) | (~spl0_4 | ~spl0_7)),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f1529])).
% 1.35/1.28 thf(f1529,plain,(
% 1.35/1.28 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: ((((sK2 @ Y0 @ X1) | (sK3 @ Y0 @ X1)) & (sK14 @ Y0)) => (sK14 @ X1))) @ X2))) ) | (~spl0_4 | ~spl0_7)),
% 1.35/1.28 inference(pi_clausification,[status(thm)],[f1519])).
% 1.35/1.28 thf(f1519,plain,(
% 1.35/1.28 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: ((((sK2 @ Y0 @ X1) | (sK3 @ Y0 @ X1)) & (sK14 @ Y0)) => (sK14 @ X1)))))) ) | (~spl0_4 | ~spl0_7)),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f1518])).
% 1.35/1.28 thf(f1518,plain,(
% 1.35/1.28 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) & (sK14 @ Y1)) => (sK14 @ Y0))))) @ X1))) ) | (~spl0_4 | ~spl0_7)),
% 1.35/1.28 inference(pi_clausification,[status(thm)],[f1508])).
% 1.35/1.28 thf(f1508,plain,(
% 1.35/1.28 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) & (sK14 @ Y1)) => (sK14 @ Y0))))))) | (~spl0_4 | ~spl0_7)),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f1507])).
% 1.35/1.28 thf(f1507,plain,(
% 1.35/1.28 ($true = ($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) & (sK14 @ Y1)) => (sK14 @ Y0)))))))) | (~spl0_4 | ~spl0_7)),
% 1.35/1.28 inference(backward_demodulation,[status(thm)],[f1482,f1506])).
% 1.35/1.28 thf(f1455,plain,(
% 1.35/1.28 ~spl0_4 | ~spl0_8 | ~spl0_29),
% 1.35/1.28 inference(avatar_contradiction_clause,[status(thm)],[f1454])).
% 1.35/1.28 thf(f1454,plain,(
% 1.35/1.28 $false | (~spl0_4 | ~spl0_8 | ~spl0_29)),
% 1.35/1.28 inference(trivial_inequality_removal,[status(thm)],[f1453])).
% 1.35/1.28 thf(f1453,plain,(
% 1.35/1.28 ($true = $false) | (~spl0_4 | ~spl0_8 | ~spl0_29)),
% 1.35/1.28 inference(forward_demodulation,[status(thm)],[f1452,f1422])).
% 1.35/1.28 thf(f1422,plain,(
% 1.35/1.28 ((sK14 @ sK25) = $false) | ~spl0_29),
% 1.35/1.28 inference(binary_proxy_clausification,[status(thm)],[f1412])).
% 1.35/1.28 thf(f1412,plain,(
% 1.35/1.28 ((((sK3 @ sK24 @ sK25) & (sK14 @ sK24)) => (sK14 @ sK25)) = $false) | ~spl0_29),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f1411])).
% 1.35/1.28 thf(f1411,plain,(
% 1.35/1.28 (((^[Y0 : a]: (((sK3 @ sK24 @ Y0) & (sK14 @ sK24)) => (sK14 @ Y0))) @ sK25) = $false) | ~spl0_29),
% 1.35/1.28 inference(sigma_clausification,[status(thm)],[f1407])).
% 1.35/1.28 thf(f1407,plain,(
% 1.35/1.28 ((!! @ a @ (^[Y0 : a]: (((sK3 @ sK24 @ Y0) & (sK14 @ sK24)) => (sK14 @ Y0)))) = $false) | ~spl0_29),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f1403])).
% 1.35/1.28 thf(f1403,plain,(
% 1.35/1.28 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) & (sK14 @ Y0)) => (sK14 @ Y1))))) @ sK24) = $false) | ~spl0_29),
% 1.35/1.28 inference(sigma_clausification,[status(thm)],[f1337])).
% 1.35/1.28 thf(f1337,plain,(
% 1.35/1.28 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) & (sK14 @ Y0)) => (sK14 @ Y1)))))) = $false) | ~spl0_29),
% 1.35/1.28 inference(avatar_component_clause,[status(thm)],[f1336])).
% 1.35/1.28 thf(f1336,definition,(
% 1.35/1.28 spl0_29 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) & (sK14 @ Y0)) => (sK14 @ Y1)))))) = $false)),
% 1.35/1.28 introduced(definition,[new_symbols(naming,[spl0_29])],[avatar_definition])).
% 1.35/1.28 thf(f1452,plain,(
% 1.35/1.28 ($true = (sK14 @ sK25)) | (~spl0_4 | ~spl0_8 | ~spl0_29)),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f1451])).
% 1.35/1.28 thf(f1451,plain,(
% 1.35/1.28 ($true = ($true => (sK14 @ sK25))) | (~spl0_4 | ~spl0_8 | ~spl0_29)),
% 1.35/1.28 inference(forward_demodulation,[status(thm)],[f1448,f1435])).
% 1.35/1.28 thf(f1435,plain,(
% 1.35/1.28 ($true = (sK14 @ sK24)) | ~spl0_29),
% 1.35/1.28 inference(binary_proxy_clausification,[status(thm)],[f1423])).
% 1.35/1.28 thf(f1423,plain,(
% 1.35/1.28 (((sK3 @ sK24 @ sK25) & (sK14 @ sK24)) = $true) | ~spl0_29),
% 1.35/1.28 inference(binary_proxy_clausification,[status(thm)],[f1412])).
% 1.35/1.28 thf(f1448,plain,(
% 1.35/1.28 ($true = ((sK14 @ sK24) => (sK14 @ sK25))) | (~spl0_4 | ~spl0_8 | ~spl0_29)),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f1447])).
% 1.35/1.28 thf(f1447,plain,(
% 1.35/1.28 ($true = (($true & (sK14 @ sK24)) => (sK14 @ sK25))) | (~spl0_4 | ~spl0_8 | ~spl0_29)),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f1445])).
% 1.35/1.28 thf(f1445,plain,(
% 1.35/1.28 ($true = ((((sK2 @ sK24 @ sK25) | $true) & (sK14 @ sK24)) => (sK14 @ sK25))) | (~spl0_4 | ~spl0_8 | ~spl0_29)),
% 1.35/1.28 inference(superposition,[status(thm)],[f1239,f1438])).
% 1.35/1.28 thf(f1438,plain,(
% 1.35/1.28 ($true = (sK3 @ sK24 @ sK25)) | ~spl0_29),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f1437])).
% 1.35/1.28 thf(f1437,plain,(
% 1.35/1.28 (((sK3 @ sK24 @ sK25) & $true) = $true) | ~spl0_29),
% 1.35/1.28 inference(backward_demodulation,[status(thm)],[f1423,f1435])).
% 1.35/1.28 thf(f1239,plain,(
% 1.35/1.28 ( ! [X2 : a,X1 : a] : (($true = ((((sK2 @ X2 @ X1) | (sK3 @ X2 @ X1)) & (sK14 @ X2)) => (sK14 @ X1)))) ) | (~spl0_4 | ~spl0_8)),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f1238])).
% 1.35/1.28 thf(f1238,plain,(
% 1.35/1.28 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: ((((sK2 @ Y0 @ X1) | (sK3 @ Y0 @ X1)) & (sK14 @ Y0)) => (sK14 @ X1))) @ X2))) ) | (~spl0_4 | ~spl0_8)),
% 1.35/1.28 inference(pi_clausification,[status(thm)],[f1226])).
% 1.35/1.28 thf(f1226,plain,(
% 1.35/1.28 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: ((((sK2 @ Y0 @ X1) | (sK3 @ Y0 @ X1)) & (sK14 @ Y0)) => (sK14 @ X1)))))) ) | (~spl0_4 | ~spl0_8)),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f1225])).
% 1.35/1.28 thf(f1225,plain,(
% 1.35/1.28 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) & (sK14 @ Y1)) => (sK14 @ Y0))))) @ X1))) ) | (~spl0_4 | ~spl0_8)),
% 1.35/1.28 inference(pi_clausification,[status(thm)],[f1139])).
% 1.35/1.28 thf(f1139,plain,(
% 1.35/1.28 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) & (sK14 @ Y1)) => (sK14 @ Y0))))))) | (~spl0_4 | ~spl0_8)),
% 1.35/1.28 inference(binary_proxy_clausification,[status(thm)],[f1121])).
% 1.35/1.28 thf(f1121,plain,(
% 1.35/1.28 ($true = ((!! @ a @ (^[Y0 : a]: (((sK3 @ sK12 @ Y0) | (sK2 @ sK12 @ Y0)) => (sK14 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) & (sK14 @ Y1)) => (sK14 @ Y0)))))))) | (~spl0_4 | ~spl0_8)),
% 1.35/1.28 inference(binary_proxy_clausification,[status(thm)],[f1117])).
% 1.35/1.28 thf(f1117,plain,(
% 1.35/1.28 ((((!! @ a @ (^[Y0 : a]: (((sK3 @ sK12 @ Y0) | (sK2 @ sK12 @ Y0)) => (sK14 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) & (sK14 @ Y1)) => (sK14 @ Y0))))))) => (sK14 @ sK13)) = $false) | (~spl0_4 | ~spl0_8)),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f1116])).
% 1.35/1.28 thf(f1116,plain,(
% 1.35/1.28 (((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK3 @ sK12 @ Y1) | (sK2 @ sK12 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK2 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1))))))) => (Y0 @ sK13))) @ sK14) = $false) | (~spl0_4 | ~spl0_8)),
% 1.35/1.28 inference(sigma_clausification,[status(thm)],[f1109])).
% 1.35/1.28 thf(f1109,plain,(
% 1.35/1.28 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK3 @ sK12 @ Y1) | (sK2 @ sK12 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK2 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1))))))) => (Y0 @ sK13)))) = $false) | (~spl0_4 | ~spl0_8)),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f1108])).
% 1.35/1.28 thf(f1108,plain,(
% 1.35/1.28 ($false = ($true => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK3 @ sK12 @ Y1) | (sK2 @ sK12 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK2 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1))))))) => (Y0 @ sK13)))))) | (~spl0_4 | ~spl0_8)),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f1107])).
% 1.35/1.28 thf(f1107,plain,(
% 1.35/1.28 ((($true | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK12 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK13))))) => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK3 @ sK12 @ Y1) | (sK2 @ sK12 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK2 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1))))))) => (Y0 @ sK13))))) = $false) | (~spl0_4 | ~spl0_8)),
% 1.35/1.28 inference(forward_demodulation,[status(thm)],[f1106,f335])).
% 1.35/1.28 thf(f335,plain,(
% 1.35/1.28 ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK3 @ sK12 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2))))))) => (Y0 @ sK13))))) | ~spl0_8),
% 1.35/1.28 inference(avatar_component_clause,[status(thm)],[f334])).
% 1.35/1.28 thf(f334,definition,(
% 1.35/1.28 spl0_8 <=> ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK3 @ sK12 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2))))))) => (Y0 @ sK13)))))),
% 1.35/1.28 introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition])).
% 1.35/1.28 thf(f1400,plain,(
% 1.35/1.28 ~spl0_4 | ~spl0_8 | ~spl0_30),
% 1.35/1.28 inference(avatar_contradiction_clause,[status(thm)],[f1399])).
% 1.35/1.28 thf(f1399,plain,(
% 1.35/1.28 $false | (~spl0_4 | ~spl0_8 | ~spl0_30)),
% 1.35/1.28 inference(trivial_inequality_removal,[status(thm)],[f1398])).
% 1.35/1.28 thf(f1398,plain,(
% 1.35/1.28 ($true = $false) | (~spl0_4 | ~spl0_8 | ~spl0_30)),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f1397])).
% 1.35/1.28 thf(f1397,plain,(
% 1.35/1.28 ($true = (~ $true)) | (~spl0_4 | ~spl0_8 | ~spl0_30)),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f1396])).
% 1.35/1.28 thf(f1396,plain,(
% 1.35/1.28 ((~ ($true | (sK2 @ sK12 @ sK23))) = $true) | (~spl0_4 | ~spl0_8 | ~spl0_30)),
% 1.35/1.28 inference(forward_demodulation,[status(thm)],[f1395,f1386])).
% 1.35/1.28 thf(f1386,plain,(
% 1.35/1.28 ((sK3 @ sK12 @ sK23) = $true) | ~spl0_30),
% 1.35/1.28 inference(binary_proxy_clausification,[status(thm)],[f1376])).
% 1.35/1.28 thf(f1376,plain,(
% 1.35/1.28 ($false = ((sK3 @ sK12 @ sK23) => (sK14 @ sK23))) | ~spl0_30),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f1374])).
% 1.35/1.28 thf(f1374,plain,(
% 1.35/1.28 ($false = ((^[Y0 : a]: ((sK3 @ sK12 @ Y0) => (sK14 @ Y0))) @ sK23)) | ~spl0_30),
% 1.35/1.28 inference(sigma_clausification,[status(thm)],[f1340])).
% 1.35/1.28 thf(f1340,plain,(
% 1.35/1.28 ((!! @ a @ (^[Y0 : a]: ((sK3 @ sK12 @ Y0) => (sK14 @ Y0)))) = $false) | ~spl0_30),
% 1.35/1.28 inference(avatar_component_clause,[status(thm)],[f1339])).
% 1.35/1.28 thf(f1339,definition,(
% 1.35/1.28 spl0_30 <=> ((!! @ a @ (^[Y0 : a]: ((sK3 @ sK12 @ Y0) => (sK14 @ Y0)))) = $false)),
% 1.35/1.28 introduced(definition,[new_symbols(naming,[spl0_30])],[avatar_definition])).
% 1.35/1.28 thf(f1395,plain,(
% 1.35/1.28 ((~ ((sK3 @ sK12 @ sK23) | (sK2 @ sK12 @ sK23))) = $true) | (~spl0_4 | ~spl0_8 | ~spl0_30)),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f1391])).
% 1.35/1.28 thf(f1391,plain,(
% 1.35/1.28 ((((sK3 @ sK12 @ sK23) | (sK2 @ sK12 @ sK23)) => $false) = $true) | (~spl0_4 | ~spl0_8 | ~spl0_30)),
% 1.35/1.28 inference(superposition,[status(thm)],[f1147,f1388])).
% 1.35/1.28 thf(f1388,plain,(
% 1.35/1.28 ($false = (sK14 @ sK23)) | ~spl0_30),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f1387])).
% 1.35/1.28 thf(f1387,plain,(
% 1.35/1.28 (($true => (sK14 @ sK23)) = $false) | ~spl0_30),
% 1.35/1.28 inference(backward_demodulation,[status(thm)],[f1376,f1386])).
% 1.35/1.28 thf(f1147,plain,(
% 1.35/1.28 ( ! [X1 : a] : (($true = (((sK3 @ sK12 @ X1) | (sK2 @ sK12 @ X1)) => (sK14 @ X1)))) ) | (~spl0_4 | ~spl0_8)),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f1146])).
% 1.35/1.28 thf(f1146,plain,(
% 1.35/1.28 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (((sK3 @ sK12 @ Y0) | (sK2 @ sK12 @ Y0)) => (sK14 @ Y0))) @ X1))) ) | (~spl0_4 | ~spl0_8)),
% 1.35/1.28 inference(pi_clausification,[status(thm)],[f1142])).
% 1.35/1.28 thf(f1142,plain,(
% 1.35/1.28 ($true = (!! @ a @ (^[Y0 : a]: (((sK3 @ sK12 @ Y0) | (sK2 @ sK12 @ Y0)) => (sK14 @ Y0))))) | (~spl0_4 | ~spl0_8)),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f1141])).
% 1.35/1.28 thf(f1141,plain,(
% 1.35/1.28 ($true = ((!! @ a @ (^[Y0 : a]: (((sK3 @ sK12 @ Y0) | (sK2 @ sK12 @ Y0)) => (sK14 @ Y0)))) & $true)) | (~spl0_4 | ~spl0_8)),
% 1.35/1.28 inference(backward_demodulation,[status(thm)],[f1121,f1139])).
% 1.35/1.28 thf(f1341,plain,(
% 1.35/1.28 spl0_29 | spl0_30 | ~spl0_4 | ~spl0_8),
% 1.35/1.28 inference(avatar_split_clause,[status(thm)],[f1332,f334,f46,f1339,f1336])).
% 1.35/1.28 thf(f1332,plain,(
% 1.35/1.28 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) & (sK14 @ Y0)) => (sK14 @ Y1)))))) = $false) | ((!! @ a @ (^[Y0 : a]: ((sK3 @ sK12 @ Y0) => (sK14 @ Y0)))) = $false) | (~spl0_4 | ~spl0_8)),
% 1.35/1.28 inference(binary_proxy_clausification,[status(thm)],[f1315])).
% 1.35/1.28 thf(f1315,plain,(
% 1.35/1.28 (((!! @ a @ (^[Y0 : a]: ((sK3 @ sK12 @ Y0) => (sK14 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) & (sK14 @ Y0)) => (sK14 @ Y1))))))) = $false) | (~spl0_4 | ~spl0_8)),
% 1.35/1.28 inference(not_proxy_clausification,[status(thm)],[f1133])).
% 1.35/1.28 thf(f1133,plain,(
% 1.35/1.28 ($true = (~ ((!! @ a @ (^[Y0 : a]: ((sK3 @ sK12 @ Y0) => (sK14 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) & (sK14 @ Y0)) => (sK14 @ Y1))))))))) | (~spl0_4 | ~spl0_8)),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f1131])).
% 1.35/1.28 thf(f1131,plain,(
% 1.35/1.28 ($true = (((!! @ a @ (^[Y0 : a]: ((sK3 @ sK12 @ Y0) => (sK14 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) & (sK14 @ Y0)) => (sK14 @ Y1))))))) => $false)) | (~spl0_4 | ~spl0_8)),
% 1.35/1.28 inference(superposition,[status(thm)],[f1125,f1123])).
% 1.35/1.28 thf(f1123,plain,(
% 1.35/1.28 ($false = (sK14 @ sK13)) | (~spl0_4 | ~spl0_8)),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f1122])).
% 1.35/1.28 thf(f1122,plain,(
% 1.35/1.28 (($true => (sK14 @ sK13)) = $false) | (~spl0_4 | ~spl0_8)),
% 1.35/1.28 inference(backward_demodulation,[status(thm)],[f1117,f1121])).
% 1.35/1.28 thf(f1125,plain,(
% 1.35/1.28 ( ! [X1 : a > $o] : (($true = (((!! @ a @ (^[Y0 : a]: ((sK3 @ sK12 @ Y0) => (X1 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) & (X1 @ Y0)) => (X1 @ Y1))))))) => (X1 @ sK13)))) ) | ~spl0_8),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f1124])).
% 1.35/1.28 thf(f1124,plain,(
% 1.35/1.28 ( ! [X1 : a > $o] : ((((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK3 @ sK12 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2))))))) => (Y0 @ sK13))) @ X1) = $true)) ) | ~spl0_8),
% 1.35/1.28 inference(pi_clausification,[status(thm)],[f335])).
% 1.35/1.28 thf(f1093,plain,(
% 1.35/1.28 ~spl0_3 | ~spl0_21 | ~spl0_23),
% 1.35/1.28 inference(avatar_contradiction_clause,[status(thm)],[f1092])).
% 1.35/1.28 thf(f1092,plain,(
% 1.35/1.28 $false | (~spl0_3 | ~spl0_21 | ~spl0_23)),
% 1.35/1.28 inference(trivial_inequality_removal,[status(thm)],[f1091])).
% 1.35/1.28 thf(f1091,plain,(
% 1.35/1.28 ($true = $false) | (~spl0_3 | ~spl0_21 | ~spl0_23)),
% 1.35/1.28 inference(forward_demodulation,[status(thm)],[f1090,f973])).
% 1.35/1.28 thf(f973,plain,(
% 1.35/1.28 ((sK10 @ sK20) = $false) | ~spl0_21),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f972])).
% 1.35/1.28 thf(f972,plain,(
% 1.35/1.28 ($false = ($true => (sK10 @ sK20))) | ~spl0_21),
% 1.35/1.28 inference(backward_demodulation,[status(thm)],[f966,f971])).
% 1.35/1.28 thf(f971,plain,(
% 1.35/1.28 ($true = ((sK10 @ sK19) & ((sK2 @ sK19 @ sK20) | (sK3 @ sK19 @ sK20)))) | ~spl0_21),
% 1.35/1.28 inference(binary_proxy_clausification,[status(thm)],[f966])).
% 1.35/1.28 thf(f966,plain,(
% 1.35/1.28 ((((sK10 @ sK19) & ((sK2 @ sK19 @ sK20) | (sK3 @ sK19 @ sK20))) => (sK10 @ sK20)) = $false) | ~spl0_21),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f965])).
% 1.35/1.28 thf(f965,plain,(
% 1.35/1.28 (((^[Y0 : a]: (((sK10 @ sK19) & ((sK2 @ sK19 @ Y0) | (sK3 @ sK19 @ Y0))) => (sK10 @ Y0))) @ sK20) = $false) | ~spl0_21),
% 1.35/1.28 inference(sigma_clausification,[status(thm)],[f951])).
% 1.35/1.28 thf(f951,plain,(
% 1.35/1.28 ($false = (!! @ a @ (^[Y0 : a]: (((sK10 @ sK19) & ((sK2 @ sK19 @ Y0) | (sK3 @ sK19 @ Y0))) => (sK10 @ Y0))))) | ~spl0_21),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f945])).
% 1.35/1.28 thf(f945,plain,(
% 1.35/1.28 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((sK2 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1))) => (sK10 @ Y1))))) @ sK19) = $false) | ~spl0_21),
% 1.35/1.28 inference(sigma_clausification,[status(thm)],[f790])).
% 1.35/1.28 thf(f790,plain,(
% 1.35/1.28 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((sK2 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1))) => (sK10 @ Y1))))))) | ~spl0_21),
% 1.35/1.28 inference(avatar_component_clause,[status(thm)],[f789])).
% 1.35/1.28 thf(f789,definition,(
% 1.35/1.28 spl0_21 <=> ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((sK2 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1))) => (sK10 @ Y1)))))))),
% 1.35/1.28 introduced(definition,[new_symbols(naming,[spl0_21])],[avatar_definition])).
% 1.35/1.28 thf(f1090,plain,(
% 1.35/1.28 ((sK10 @ sK20) = $true) | (~spl0_3 | ~spl0_21 | ~spl0_23)),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f1089])).
% 1.35/1.28 thf(f1089,plain,(
% 1.35/1.28 ($true = ($true => (sK10 @ sK20))) | (~spl0_3 | ~spl0_21 | ~spl0_23)),
% 1.35/1.28 inference(forward_demodulation,[status(thm)],[f1086,f1051])).
% 1.35/1.28 thf(f1051,plain,(
% 1.35/1.28 ($true = (sK10 @ sK19)) | ~spl0_21),
% 1.35/1.28 inference(binary_proxy_clausification,[status(thm)],[f971])).
% 1.35/1.28 thf(f1086,plain,(
% 1.35/1.28 ($true = ((sK10 @ sK19) => (sK10 @ sK20))) | (~spl0_3 | ~spl0_23)),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f1085])).
% 1.35/1.28 thf(f1085,plain,(
% 1.35/1.28 ($true = (((sK10 @ sK19) & $true) => (sK10 @ sK20))) | (~spl0_3 | ~spl0_23)),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f1083])).
% 1.35/1.28 thf(f1083,plain,(
% 1.35/1.28 ((((sK10 @ sK19) & ($true | (sK2 @ sK19 @ sK20))) => (sK10 @ sK20)) = $true) | (~spl0_3 | ~spl0_23)),
% 1.35/1.28 inference(superposition,[status(thm)],[f820,f1063])).
% 1.35/1.28 thf(f1063,plain,(
% 1.35/1.28 ($true = (sK3 @ sK19 @ sK20)) | ~spl0_23),
% 1.35/1.28 inference(avatar_component_clause,[status(thm)],[f1062])).
% 1.35/1.28 thf(f1062,definition,(
% 1.35/1.28 spl0_23 <=> ($true = (sK3 @ sK19 @ sK20))),
% 1.35/1.28 introduced(definition,[new_symbols(naming,[spl0_23])],[avatar_definition])).
% 1.35/1.28 thf(f820,plain,(
% 1.35/1.28 ( ! [X2 : a,X1 : a] : (($true = (((sK10 @ X1) & ((sK3 @ X1 @ X2) | (sK2 @ X1 @ X2))) => (sK10 @ X2)))) ) | ~spl0_3),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f819])).
% 1.35/1.28 thf(f819,plain,(
% 1.35/1.28 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: (((sK10 @ X1) & ((sK3 @ X1 @ Y0) | (sK2 @ X1 @ Y0))) => (sK10 @ Y0))) @ X2))) ) | ~spl0_3),
% 1.35/1.28 inference(pi_clausification,[status(thm)],[f807])).
% 1.35/1.28 thf(f807,plain,(
% 1.35/1.28 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: (((sK10 @ X1) & ((sK3 @ X1 @ Y0) | (sK2 @ X1 @ Y0))) => (sK10 @ Y0)))) = $true)) ) | ~spl0_3),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f804])).
% 1.35/1.28 thf(f804,plain,(
% 1.35/1.28 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((sK3 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1))) => (sK10 @ Y1))))) @ X1))) ) | ~spl0_3),
% 1.35/1.28 inference(pi_clausification,[status(thm)],[f718])).
% 1.35/1.28 thf(f718,plain,(
% 1.35/1.28 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((sK3 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1))) => (sK10 @ Y1)))))) = $true) | ~spl0_3),
% 1.35/1.28 inference(binary_proxy_clausification,[status(thm)],[f691])).
% 1.35/1.28 thf(f691,plain,(
% 1.35/1.28 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((sK3 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1))) => (sK10 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (((sK3 @ sK9 @ Y0) | (sK2 @ sK9 @ Y0)) => (sK10 @ Y0)))))) | ~spl0_3),
% 1.35/1.28 inference(binary_proxy_clausification,[status(thm)],[f679])).
% 1.35/1.28 thf(f679,plain,(
% 1.35/1.28 ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((sK3 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1))) => (sK10 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (((sK3 @ sK9 @ Y0) | (sK2 @ sK9 @ Y0)) => (sK10 @ Y0))))) => (sK10 @ sK8))) | ~spl0_3),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f678])).
% 1.35/1.28 thf(f678,plain,(
% 1.35/1.28 (((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK3 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2))) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK3 @ sK9 @ Y1) | (sK2 @ sK9 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK8))) @ sK10) = $false) | ~spl0_3),
% 1.35/1.28 inference(sigma_clausification,[status(thm)],[f662])).
% 1.35/1.28 thf(f662,plain,(
% 1.35/1.28 ($false = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK3 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2))) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK3 @ sK9 @ Y1) | (sK2 @ sK9 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK8))))) | ~spl0_3),
% 1.35/1.28 inference(binary_proxy_clausification,[status(thm)],[f652])).
% 1.35/1.28 thf(f652,plain,(
% 1.35/1.28 ((((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK3 @ sK9 @ Y1) | (sK2 @ sK9 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK2 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK7)))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK3 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2))) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK3 @ sK7 @ Y1) | (sK2 @ sK7 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK8))))) => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK3 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2))) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK3 @ sK9 @ Y1) | (sK2 @ sK9 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK8))))) = $false) | ~spl0_3),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f651])).
% 1.35/1.28 thf(f651,plain,(
% 1.35/1.28 (((^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK3 @ Y0 @ Y2) | (sK2 @ Y0 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((sK2 @ Y2 @ Y3) | (sK3 @ Y2 @ Y3))) => (Y1 @ Y3))))))) => (Y1 @ sK7)))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((sK3 @ Y2 @ Y3) | (sK2 @ Y2 @ Y3))) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (((sK3 @ sK7 @ Y2) | (sK2 @ sK7 @ Y2)) => (Y1 @ Y2))))) => (Y1 @ sK8))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((sK3 @ Y2 @ Y3) | (sK2 @ Y2 @ Y3))) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (((sK3 @ Y0 @ Y2) | (sK2 @ Y0 @ Y2)) => (Y1 @ Y2))))) => (Y1 @ sK8)))))) @ sK9) = $false) | ~spl0_3),
% 1.35/1.28 inference(sigma_clausification,[status(thm)],[f642])).
% 1.35/1.28 thf(f642,plain,(
% 1.35/1.28 ((!! @ a @ (^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK3 @ Y0 @ Y2) | (sK2 @ Y0 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((sK2 @ Y2 @ Y3) | (sK3 @ Y2 @ Y3))) => (Y1 @ Y3))))))) => (Y1 @ sK7)))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((sK3 @ Y2 @ Y3) | (sK2 @ Y2 @ Y3))) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (((sK3 @ sK7 @ Y2) | (sK2 @ sK7 @ Y2)) => (Y1 @ Y2))))) => (Y1 @ sK8))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((sK3 @ Y2 @ Y3) | (sK2 @ Y2 @ Y3))) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (((sK3 @ Y0 @ Y2) | (sK2 @ Y0 @ Y2)) => (Y1 @ Y2))))) => (Y1 @ sK8))))))) = $false) | ~spl0_3),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f641])).
% 1.35/1.28 thf(f641,plain,(
% 1.35/1.28 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK3 @ Y1 @ Y3) | (sK2 @ Y1 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK2 @ Y3 @ Y4) | (sK3 @ Y3 @ Y4))) => (Y2 @ Y4))))))) => (Y2 @ sK7)))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK3 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4))) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (((sK3 @ sK7 @ Y3) | (sK2 @ sK7 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ Y0))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK3 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4))) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (((sK3 @ Y1 @ Y3) | (sK2 @ Y1 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ Y0)))))))) @ sK8) = $false) | ~spl0_3),
% 1.35/1.28 inference(sigma_clausification,[status(thm)],[f630])).
% 1.35/1.28 thf(f630,plain,(
% 1.35/1.28 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK3 @ Y1 @ Y3) | (sK2 @ Y1 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK2 @ Y3 @ Y4) | (sK3 @ Y3 @ Y4))) => (Y2 @ Y4))))))) => (Y2 @ sK7)))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK3 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4))) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (((sK3 @ sK7 @ Y3) | (sK2 @ sK7 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ Y0))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK3 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4))) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (((sK3 @ Y1 @ Y3) | (sK2 @ Y1 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ Y0))))))))) = $false) | ~spl0_3),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f629])).
% 1.35/1.28 thf(f629,plain,(
% 1.35/1.28 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK3 @ Y2 @ Y4) | (sK2 @ Y2 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK2 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y0)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK3 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5))) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y0 @ Y4) | (sK2 @ Y0 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y1))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK3 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5))) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y2 @ Y4) | (sK2 @ Y2 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y1)))))))))) @ sK7) = $false) | ~spl0_3),
% 1.35/1.28 inference(sigma_clausification,[status(thm)],[f44])).
% 1.35/1.28 thf(f44,plain,(
% 1.35/1.28 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK3 @ Y2 @ Y4) | (sK2 @ Y2 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK2 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y0)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK3 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5))) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y0 @ Y4) | (sK2 @ Y0 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y1))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK3 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5))) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y2 @ Y4) | (sK2 @ Y2 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y1))))))))))) = $false) | ~spl0_3),
% 1.35/1.28 inference(avatar_component_clause,[status(thm)],[f43])).
% 1.35/1.28 thf(f43,definition,(
% 1.35/1.28 spl0_3 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK3 @ Y2 @ Y4) | (sK2 @ Y2 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK2 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y0)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK3 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5))) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y0 @ Y4) | (sK2 @ Y0 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y1))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK3 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5))) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y2 @ Y4) | (sK2 @ Y2 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y1))))))))))) = $false)),
% 1.35/1.28 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.35/1.28 thf(f1080,plain,(
% 1.35/1.28 ~spl0_3 | ~spl0_21 | ~spl0_24),
% 1.35/1.28 inference(avatar_contradiction_clause,[status(thm)],[f1079])).
% 1.35/1.28 thf(f1079,plain,(
% 1.35/1.28 $false | (~spl0_3 | ~spl0_21 | ~spl0_24)),
% 1.35/1.28 inference(trivial_inequality_removal,[status(thm)],[f1078])).
% 1.35/1.28 thf(f1078,plain,(
% 1.35/1.28 ($true = $false) | (~spl0_3 | ~spl0_21 | ~spl0_24)),
% 1.35/1.28 inference(forward_demodulation,[status(thm)],[f1077,f973])).
% 1.35/1.28 thf(f1077,plain,(
% 1.35/1.28 ((sK10 @ sK20) = $true) | (~spl0_3 | ~spl0_21 | ~spl0_24)),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f1076])).
% 1.35/1.28 thf(f1076,plain,(
% 1.35/1.28 ($true = ($true => (sK10 @ sK20))) | (~spl0_3 | ~spl0_21 | ~spl0_24)),
% 1.35/1.28 inference(forward_demodulation,[status(thm)],[f1073,f1051])).
% 1.35/1.28 thf(f1073,plain,(
% 1.35/1.28 ($true = ((sK10 @ sK19) => (sK10 @ sK20))) | (~spl0_3 | ~spl0_24)),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f1072])).
% 1.35/1.28 thf(f1072,plain,(
% 1.35/1.28 ($true = (((sK10 @ sK19) & $true) => (sK10 @ sK20))) | (~spl0_3 | ~spl0_24)),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f1070])).
% 1.35/1.28 thf(f1070,plain,(
% 1.35/1.28 ($true = (((sK10 @ sK19) & ((sK3 @ sK19 @ sK20) | $true)) => (sK10 @ sK20))) | (~spl0_3 | ~spl0_24)),
% 1.35/1.28 inference(superposition,[status(thm)],[f820,f1066])).
% 1.35/1.28 thf(f1066,plain,(
% 1.35/1.28 ((sK2 @ sK19 @ sK20) = $true) | ~spl0_24),
% 1.35/1.28 inference(avatar_component_clause,[status(thm)],[f1065])).
% 1.35/1.28 thf(f1065,definition,(
% 1.35/1.28 spl0_24 <=> ((sK2 @ sK19 @ sK20) = $true)),
% 1.35/1.28 introduced(definition,[new_symbols(naming,[spl0_24])],[avatar_definition])).
% 1.35/1.28 thf(f1067,plain,(
% 1.35/1.28 spl0_23 | spl0_24 | ~spl0_21),
% 1.35/1.28 inference(avatar_split_clause,[status(thm)],[f1060,f789,f1065,f1062])).
% 1.35/1.28 thf(f1060,plain,(
% 1.35/1.28 ($true = (sK3 @ sK19 @ sK20)) | ((sK2 @ sK19 @ sK20) = $true) | ~spl0_21),
% 1.35/1.28 inference(binary_proxy_clausification,[status(thm)],[f1053])).
% 1.35/1.28 thf(f1053,plain,(
% 1.35/1.28 ($true = ((sK2 @ sK19 @ sK20) | (sK3 @ sK19 @ sK20))) | ~spl0_21),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f1052])).
% 1.35/1.28 thf(f1052,plain,(
% 1.35/1.28 ($true = ($true & ((sK2 @ sK19 @ sK20) | (sK3 @ sK19 @ sK20)))) | ~spl0_21),
% 1.35/1.28 inference(backward_demodulation,[status(thm)],[f971,f1051])).
% 1.35/1.28 thf(f916,plain,(
% 1.35/1.28 ~spl0_3 | ~spl0_6 | ~spl0_22),
% 1.35/1.28 inference(avatar_contradiction_clause,[status(thm)],[f915])).
% 1.35/1.28 thf(f915,plain,(
% 1.35/1.28 $false | (~spl0_3 | ~spl0_6 | ~spl0_22)),
% 1.35/1.28 inference(trivial_inequality_removal,[status(thm)],[f914])).
% 1.35/1.28 thf(f914,plain,(
% 1.35/1.28 ($true = $false) | (~spl0_3 | ~spl0_6 | ~spl0_22)),
% 1.35/1.28 inference(forward_demodulation,[status(thm)],[f913,f893])).
% 1.35/1.28 thf(f893,plain,(
% 1.35/1.28 ((sK10 @ sK11) = $false) | (~spl0_3 | ~spl0_6)),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f892])).
% 1.35/1.28 thf(f892,plain,(
% 1.35/1.28 (($true => (sK10 @ sK11)) = $false) | (~spl0_3 | ~spl0_6)),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f891])).
% 1.35/1.28 thf(f891,plain,(
% 1.35/1.28 ((($true | (sK2 @ sK7 @ sK11)) => (sK10 @ sK11)) = $false) | (~spl0_3 | ~spl0_6)),
% 1.35/1.28 inference(backward_demodulation,[status(thm)],[f777,f232])).
% 1.35/1.28 thf(f232,plain,(
% 1.35/1.28 ((sK3 @ sK7 @ sK11) = $true) | ~spl0_6),
% 1.35/1.28 inference(avatar_component_clause,[status(thm)],[f231])).
% 1.35/1.28 thf(f231,definition,(
% 1.35/1.28 spl0_6 <=> ((sK3 @ sK7 @ sK11) = $true)),
% 1.35/1.28 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.35/1.28 thf(f777,plain,(
% 1.35/1.28 ((((sK3 @ sK7 @ sK11) | (sK2 @ sK7 @ sK11)) => (sK10 @ sK11)) = $false) | ~spl0_3),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f773])).
% 1.35/1.28 thf(f773,plain,(
% 1.35/1.28 (((^[Y0 : a]: (((sK3 @ sK7 @ Y0) | (sK2 @ sK7 @ Y0)) => (sK10 @ Y0))) @ sK11) = $false) | ~spl0_3),
% 1.35/1.28 inference(sigma_clausification,[status(thm)],[f759])).
% 1.35/1.28 thf(f759,plain,(
% 1.35/1.28 ($false = (!! @ a @ (^[Y0 : a]: (((sK3 @ sK7 @ Y0) | (sK2 @ sK7 @ Y0)) => (sK10 @ Y0))))) | ~spl0_3),
% 1.35/1.28 inference(not_proxy_clausification,[status(thm)],[f747])).
% 1.35/1.28 thf(f747,plain,(
% 1.35/1.28 ((~ (!! @ a @ (^[Y0 : a]: (((sK3 @ sK7 @ Y0) | (sK2 @ sK7 @ Y0)) => (sK10 @ Y0))))) = $true) | ~spl0_3),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f746])).
% 1.35/1.28 thf(f746,plain,(
% 1.35/1.28 ($true = (~ ($true & (!! @ a @ (^[Y0 : a]: (((sK3 @ sK7 @ Y0) | (sK2 @ sK7 @ Y0)) => (sK10 @ Y0))))))) | ~spl0_3),
% 1.35/1.28 inference(forward_demodulation,[status(thm)],[f745,f718])).
% 1.35/1.28 thf(f745,plain,(
% 1.35/1.28 ((~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((sK3 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1))) => (sK10 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (((sK3 @ sK7 @ Y0) | (sK2 @ sK7 @ Y0)) => (sK10 @ Y0)))))) = $true) | ~spl0_3),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f744])).
% 1.35/1.28 thf(f744,plain,(
% 1.35/1.28 ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((sK3 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1))) => (sK10 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (((sK3 @ sK7 @ Y0) | (sK2 @ sK7 @ Y0)) => (sK10 @ Y0))))) => $false)) | ~spl0_3),
% 1.35/1.28 inference(superposition,[status(thm)],[f733,f693])).
% 1.35/1.28 thf(f693,plain,(
% 1.35/1.28 ($false = (sK10 @ sK8)) | ~spl0_3),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f692])).
% 1.35/1.28 thf(f692,plain,(
% 1.35/1.28 (($true => (sK10 @ sK8)) = $false) | ~spl0_3),
% 1.35/1.28 inference(backward_demodulation,[status(thm)],[f679,f691])).
% 1.35/1.28 thf(f733,plain,(
% 1.35/1.28 ( ! [X1 : a > $o] : (($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((X1 @ Y0) & ((sK3 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1))) => (X1 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (((sK3 @ sK7 @ Y0) | (sK2 @ sK7 @ Y0)) => (X1 @ Y0))))) => (X1 @ sK8)))) ) | ~spl0_3),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f732])).
% 1.35/1.28 thf(f732,plain,(
% 1.35/1.28 ( ! [X1 : a > $o] : ((((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK3 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2))) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK3 @ sK7 @ Y1) | (sK2 @ sK7 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK8))) @ X1) = $true)) ) | ~spl0_3),
% 1.35/1.28 inference(pi_clausification,[status(thm)],[f694])).
% 1.35/1.28 thf(f694,plain,(
% 1.35/1.28 ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK3 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2))) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK3 @ sK7 @ Y1) | (sK2 @ sK7 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK8))))) | ~spl0_3),
% 1.35/1.28 inference(binary_proxy_clausification,[status(thm)],[f663])).
% 1.35/1.28 thf(f663,plain,(
% 1.35/1.28 ($true = ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK3 @ sK9 @ Y1) | (sK2 @ sK9 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK2 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK7)))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK3 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2))) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK3 @ sK7 @ Y1) | (sK2 @ sK7 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK8)))))) | ~spl0_3),
% 1.35/1.28 inference(binary_proxy_clausification,[status(thm)],[f652])).
% 1.35/1.28 thf(f913,plain,(
% 1.35/1.28 ($true = (sK10 @ sK11)) | (~spl0_3 | ~spl0_6 | ~spl0_22)),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f912])).
% 1.35/1.28 thf(f912,plain,(
% 1.35/1.28 ($true = ($true => (sK10 @ sK11))) | (~spl0_3 | ~spl0_6 | ~spl0_22)),
% 1.35/1.28 inference(forward_demodulation,[status(thm)],[f907,f793])).
% 1.35/1.28 thf(f793,plain,(
% 1.35/1.28 ($true = (sK10 @ sK7)) | ~spl0_22),
% 1.35/1.28 inference(avatar_component_clause,[status(thm)],[f792])).
% 1.35/1.28 thf(f792,definition,(
% 1.35/1.28 spl0_22 <=> ($true = (sK10 @ sK7))),
% 1.35/1.28 introduced(definition,[new_symbols(naming,[spl0_22])],[avatar_definition])).
% 1.35/1.28 thf(f907,plain,(
% 1.35/1.28 ($true = ((sK10 @ sK7) => (sK10 @ sK11))) | (~spl0_3 | ~spl0_6)),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f906])).
% 1.35/1.28 thf(f906,plain,(
% 1.35/1.28 ((((sK10 @ sK7) & $true) => (sK10 @ sK11)) = $true) | (~spl0_3 | ~spl0_6)),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f904])).
% 1.35/1.28 thf(f904,plain,(
% 1.35/1.28 ($true = (((sK10 @ sK7) & ($true | (sK2 @ sK7 @ sK11))) => (sK10 @ sK11))) | (~spl0_3 | ~spl0_6)),
% 1.35/1.28 inference(superposition,[status(thm)],[f820,f232])).
% 1.35/1.28 thf(f878,plain,(
% 1.35/1.28 ~spl0_3 | ~spl0_5 | ~spl0_22),
% 1.35/1.28 inference(avatar_contradiction_clause,[status(thm)],[f877])).
% 1.35/1.28 thf(f877,plain,(
% 1.35/1.28 $false | (~spl0_3 | ~spl0_5 | ~spl0_22)),
% 1.35/1.28 inference(trivial_inequality_removal,[status(thm)],[f876])).
% 1.35/1.28 thf(f876,plain,(
% 1.35/1.28 ($true = $false) | (~spl0_3 | ~spl0_5 | ~spl0_22)),
% 1.35/1.28 inference(forward_demodulation,[status(thm)],[f875,f780])).
% 1.35/1.28 thf(f780,plain,(
% 1.35/1.28 ((sK10 @ sK11) = $false) | (~spl0_3 | ~spl0_5)),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f779])).
% 1.35/1.28 thf(f779,plain,(
% 1.35/1.28 (($true => (sK10 @ sK11)) = $false) | (~spl0_3 | ~spl0_5)),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f778])).
% 1.35/1.28 thf(f778,plain,(
% 1.35/1.28 ($false = (((sK3 @ sK7 @ sK11) | $true) => (sK10 @ sK11))) | (~spl0_3 | ~spl0_5)),
% 1.35/1.28 inference(forward_demodulation,[status(thm)],[f777,f229])).
% 1.35/1.28 thf(f229,plain,(
% 1.35/1.28 ($true = (sK2 @ sK7 @ sK11)) | ~spl0_5),
% 1.35/1.28 inference(avatar_component_clause,[status(thm)],[f228])).
% 1.35/1.28 thf(f228,definition,(
% 1.35/1.28 spl0_5 <=> ($true = (sK2 @ sK7 @ sK11))),
% 1.35/1.28 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.35/1.28 thf(f875,plain,(
% 1.35/1.28 ($true = (sK10 @ sK11)) | (~spl0_3 | ~spl0_5 | ~spl0_22)),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f874])).
% 1.35/1.28 thf(f874,plain,(
% 1.35/1.28 ($true = ($true => (sK10 @ sK11))) | (~spl0_3 | ~spl0_5 | ~spl0_22)),
% 1.35/1.28 inference(forward_demodulation,[status(thm)],[f850,f793])).
% 1.35/1.28 thf(f850,plain,(
% 1.35/1.28 ($true = ((sK10 @ sK7) => (sK10 @ sK11))) | (~spl0_3 | ~spl0_5)),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f849])).
% 1.35/1.28 thf(f849,plain,(
% 1.35/1.28 ((((sK10 @ sK7) & $true) => (sK10 @ sK11)) = $true) | (~spl0_3 | ~spl0_5)),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f836])).
% 1.35/1.28 thf(f836,plain,(
% 1.35/1.28 ($true = (((sK10 @ sK7) & ((sK3 @ sK7 @ sK11) | $true)) => (sK10 @ sK11))) | (~spl0_3 | ~spl0_5)),
% 1.35/1.28 inference(superposition,[status(thm)],[f820,f229])).
% 1.35/1.28 thf(f794,plain,(
% 1.35/1.28 spl0_21 | spl0_22 | ~spl0_3),
% 1.35/1.28 inference(avatar_split_clause,[status(thm)],[f787,f43,f792,f789])).
% 1.35/1.28 thf(f787,plain,(
% 1.35/1.28 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((sK2 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1))) => (sK10 @ Y1))))))) | ($true = (sK10 @ sK7)) | ~spl0_3),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f784])).
% 1.35/1.28 thf(f784,plain,(
% 1.35/1.28 (($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((sK2 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1))) => (sK10 @ Y1))))))) = $false) | ($true = (sK10 @ sK7)) | ~spl0_3),
% 1.35/1.28 inference(superposition,[status(thm)],[f721,f720])).
% 1.35/1.28 thf(f720,plain,(
% 1.35/1.28 ((!! @ a @ (^[Y0 : a]: (((sK3 @ sK9 @ Y0) | (sK2 @ sK9 @ Y0)) => (sK10 @ Y0)))) = $true) | ~spl0_3),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f719])).
% 1.35/1.28 thf(f719,plain,(
% 1.35/1.28 ($true = ($true & (!! @ a @ (^[Y0 : a]: (((sK3 @ sK9 @ Y0) | (sK2 @ sK9 @ Y0)) => (sK10 @ Y0)))))) | ~spl0_3),
% 1.35/1.28 inference(backward_demodulation,[status(thm)],[f691,f718])).
% 1.35/1.28 thf(f721,plain,(
% 1.35/1.28 ( ! [X1 : a > $o] : (($false = ((!! @ a @ (^[Y0 : a]: (((sK3 @ sK9 @ Y0) | (sK2 @ sK9 @ Y0)) => (X1 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((X1 @ Y0) & ((sK2 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1))) => (X1 @ Y1)))))))) | ($true = (X1 @ sK7))) ) | ~spl0_3),
% 1.35/1.28 inference(binary_proxy_clausification,[status(thm)],[f716])).
% 1.35/1.28 thf(f716,plain,(
% 1.35/1.28 ( ! [X1 : a > $o] : (((((!! @ a @ (^[Y0 : a]: (((sK3 @ sK9 @ Y0) | (sK2 @ sK9 @ Y0)) => (X1 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((X1 @ Y0) & ((sK2 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1))) => (X1 @ Y1))))))) => (X1 @ sK7)) = $true)) ) | ~spl0_3),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f715])).
% 1.35/1.28 thf(f715,plain,(
% 1.35/1.28 ( ! [X1 : a > $o] : ((((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK3 @ sK9 @ Y1) | (sK2 @ sK9 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK2 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK7))) @ X1) = $true)) ) | ~spl0_3),
% 1.35/1.28 inference(pi_clausification,[status(thm)],[f697])).
% 1.35/1.28 thf(f697,plain,(
% 1.35/1.28 ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK3 @ sK9 @ Y1) | (sK2 @ sK9 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK2 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK7))))) | ~spl0_3),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f696])).
% 1.35/1.28 thf(f696,plain,(
% 1.35/1.28 ($true = ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK3 @ sK9 @ Y1) | (sK2 @ sK9 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK2 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK7)))) & $true)) | ~spl0_3),
% 1.35/1.28 inference(backward_demodulation,[status(thm)],[f663,f694])).
% 1.35/1.28 thf(f620,plain,(
% 1.35/1.28 ~spl0_14 | ~spl0_18),
% 1.35/1.28 inference(avatar_contradiction_clause,[status(thm)],[f619])).
% 1.35/1.28 thf(f619,plain,(
% 1.35/1.28 $false | (~spl0_14 | ~spl0_18)),
% 1.35/1.28 inference(trivial_inequality_removal,[status(thm)],[f618])).
% 1.35/1.28 thf(f618,plain,(
% 1.35/1.28 ($true = $false) | (~spl0_14 | ~spl0_18)),
% 1.35/1.28 inference(forward_demodulation,[status(thm)],[f617,f547])).
% 1.35/1.28 thf(f547,plain,(
% 1.35/1.28 ((sK6 @ sK16) = $false) | ~spl0_14),
% 1.35/1.28 inference(binary_proxy_clausification,[status(thm)],[f546])).
% 1.35/1.28 thf(f546,plain,(
% 1.35/1.28 ((((sK6 @ sK17) & ((sK2 @ sK17 @ sK16) | (sK3 @ sK17 @ sK16))) => (sK6 @ sK16)) = $false) | ~spl0_14),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f545])).
% 1.35/1.28 thf(f545,plain,(
% 1.35/1.28 (((^[Y0 : a]: (((sK6 @ Y0) & ((sK2 @ Y0 @ sK16) | (sK3 @ Y0 @ sK16))) => (sK6 @ sK16))) @ sK17) = $false) | ~spl0_14),
% 1.35/1.28 inference(sigma_clausification,[status(thm)],[f544])).
% 1.35/1.28 thf(f544,plain,(
% 1.35/1.28 ((!! @ a @ (^[Y0 : a]: (((sK6 @ Y0) & ((sK2 @ Y0 @ sK16) | (sK3 @ Y0 @ sK16))) => (sK6 @ sK16)))) = $false) | ~spl0_14),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f540])).
% 1.35/1.28 thf(f540,plain,(
% 1.35/1.28 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & ((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0))) => (sK6 @ Y0))))) @ sK16) = $false) | ~spl0_14),
% 1.35/1.28 inference(sigma_clausification,[status(thm)],[f492])).
% 1.35/1.28 thf(f492,plain,(
% 1.35/1.28 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & ((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0))) => (sK6 @ Y0)))))) = $false) | ~spl0_14),
% 1.35/1.28 inference(avatar_component_clause,[status(thm)],[f491])).
% 1.35/1.28 thf(f491,definition,(
% 1.35/1.28 spl0_14 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & ((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0))) => (sK6 @ Y0)))))) = $false)),
% 1.35/1.28 introduced(definition,[new_symbols(naming,[spl0_14])],[avatar_definition])).
% 1.35/1.28 thf(f617,plain,(
% 1.35/1.28 ((sK6 @ sK16) = $true) | (~spl0_14 | ~spl0_18)),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f616])).
% 1.35/1.28 thf(f616,plain,(
% 1.35/1.28 (($true => (sK6 @ sK16)) = $true) | (~spl0_14 | ~spl0_18)),
% 1.35/1.28 inference(forward_demodulation,[status(thm)],[f615,f584])).
% 1.35/1.28 thf(f584,plain,(
% 1.35/1.28 ((sK6 @ sK18) = $true) | ~spl0_14),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f583])).
% 1.35/1.28 thf(f583,plain,(
% 1.35/1.28 ($true = ((sK6 @ sK18) & $true)) | ~spl0_14),
% 1.35/1.28 inference(backward_demodulation,[status(thm)],[f569,f581])).
% 1.35/1.28 thf(f581,plain,(
% 1.35/1.28 (((sK2 @ sK18 @ sK16) | (sK3 @ sK18 @ sK16)) = $true) | ~spl0_14),
% 1.35/1.28 inference(binary_proxy_clausification,[status(thm)],[f569])).
% 1.35/1.28 thf(f569,plain,(
% 1.35/1.28 ($true = ((sK6 @ sK18) & ((sK2 @ sK18 @ sK16) | (sK3 @ sK18 @ sK16)))) | ~spl0_14),
% 1.35/1.28 inference(not_proxy_clausification,[status(thm)],[f565])).
% 1.35/1.28 thf(f565,plain,(
% 1.35/1.28 ($false = (~ ((sK6 @ sK18) & ((sK2 @ sK18 @ sK16) | (sK3 @ sK18 @ sK16))))) | ~spl0_14),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f564])).
% 1.35/1.28 thf(f564,plain,(
% 1.35/1.28 (((^[Y0 : a]: (~ ((sK6 @ Y0) & ((sK2 @ Y0 @ sK16) | (sK3 @ Y0 @ sK16))))) @ sK18) = $false) | ~spl0_14),
% 1.35/1.28 inference(sigma_clausification,[status(thm)],[f552])).
% 1.35/1.28 thf(f552,plain,(
% 1.35/1.28 ((!! @ a @ (^[Y0 : a]: (~ ((sK6 @ Y0) & ((sK2 @ Y0 @ sK16) | (sK3 @ Y0 @ sK16)))))) = $false) | ~spl0_14),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f550])).
% 1.35/1.28 thf(f550,plain,(
% 1.35/1.28 ((!! @ a @ (^[Y0 : a]: (((sK6 @ Y0) & ((sK2 @ Y0 @ sK16) | (sK3 @ Y0 @ sK16))) => $false))) = $false) | ~spl0_14),
% 1.35/1.28 inference(backward_demodulation,[status(thm)],[f544,f547])).
% 1.35/1.28 thf(f615,plain,(
% 1.35/1.28 (((sK6 @ sK18) => (sK6 @ sK16)) = $true) | ~spl0_18),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f614])).
% 1.35/1.28 thf(f614,plain,(
% 1.35/1.28 ($true = (((sK6 @ sK18) & $true) => (sK6 @ sK16))) | ~spl0_18),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f613])).
% 1.35/1.28 thf(f613,plain,(
% 1.35/1.28 ((((sK6 @ sK18) & ($true | (sK2 @ sK18 @ sK16))) => (sK6 @ sK16)) = $true) | ~spl0_18),
% 1.35/1.28 inference(superposition,[status(thm)],[f223,f599])).
% 1.35/1.28 thf(f599,plain,(
% 1.35/1.28 ($true = (sK3 @ sK18 @ sK16)) | ~spl0_18),
% 1.35/1.28 inference(avatar_component_clause,[status(thm)],[f598])).
% 1.35/1.28 thf(f598,definition,(
% 1.35/1.28 spl0_18 <=> ($true = (sK3 @ sK18 @ sK16))),
% 1.35/1.28 introduced(definition,[new_symbols(naming,[spl0_18])],[avatar_definition])).
% 1.35/1.28 thf(f223,plain,(
% 1.35/1.28 ( ! [X2 : a,X1 : a] : (($true = (((sK6 @ X2) & ((sK3 @ X2 @ X1) | (sK2 @ X2 @ X1))) => (sK6 @ X1)))) )),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f222])).
% 1.35/1.28 thf(f222,plain,(
% 1.35/1.28 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: (((sK6 @ Y0) & ((sK3 @ Y0 @ X1) | (sK2 @ Y0 @ X1))) => (sK6 @ X1))) @ X2))) )),
% 1.35/1.28 inference(pi_clausification,[status(thm)],[f212])).
% 1.35/1.28 thf(f212,plain,(
% 1.35/1.28 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (((sK6 @ Y0) & ((sK3 @ Y0 @ X1) | (sK2 @ Y0 @ X1))) => (sK6 @ X1)))))) )),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f211])).
% 1.35/1.28 thf(f211,plain,(
% 1.35/1.28 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & ((sK3 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0))) => (sK6 @ Y0))))) @ X1))) )),
% 1.35/1.28 inference(pi_clausification,[status(thm)],[f56])).
% 1.35/1.28 thf(f56,plain,(
% 1.35/1.28 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & ((sK3 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0))) => (sK6 @ Y0)))))))),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f55])).
% 1.35/1.28 thf(f55,plain,(
% 1.35/1.28 ($true = ($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & ((sK3 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0))) => (sK6 @ Y0))))))))),
% 1.35/1.28 inference(backward_demodulation,[status(thm)],[f38,f54])).
% 1.35/1.28 thf(f54,plain,(
% 1.35/1.28 ((!! @ a @ (^[Y0 : a]: (((sK3 @ sK5 @ Y0) | (sK2 @ sK5 @ Y0)) => (sK6 @ Y0)))) = $true)),
% 1.35/1.28 inference(binary_proxy_clausification,[status(thm)],[f38])).
% 1.35/1.28 thf(f38,plain,(
% 1.35/1.28 ($true = ((!! @ a @ (^[Y0 : a]: (((sK3 @ sK5 @ Y0) | (sK2 @ sK5 @ Y0)) => (sK6 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & ((sK3 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0))) => (sK6 @ Y0))))))))),
% 1.35/1.28 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 1.35/1.28 thf(f26,plain,(
% 1.35/1.28 ((((!! @ a @ (^[Y0 : a]: (((sK3 @ sK5 @ Y0) | (sK2 @ sK5 @ Y0)) => (sK6 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & ((sK3 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0))) => (sK6 @ Y0))))))) => (sK6 @ sK4)) = $false)),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f25])).
% 1.35/1.28 thf(f25,plain,(
% 1.35/1.28 (((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK3 @ sK5 @ Y1) | (sK2 @ sK5 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK3 @ Y2 @ Y1) | (sK2 @ Y2 @ Y1))) => (Y0 @ Y1))))))) => (Y0 @ sK4))) @ sK6) = $false)),
% 1.35/1.28 inference(sigma_clausification,[status(thm)],[f19])).
% 1.35/1.28 thf(f19,plain,(
% 1.35/1.28 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK3 @ sK5 @ Y1) | (sK2 @ sK5 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK3 @ Y2 @ Y1) | (sK2 @ Y2 @ Y1))) => (Y0 @ Y1))))))) => (Y0 @ sK4)))) = $false)),
% 1.35/1.28 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.35/1.28 thf(f17,plain,(
% 1.35/1.28 (((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK3 @ sK5 @ Y1) | (sK2 @ sK5 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK3 @ Y2 @ Y1) | (sK2 @ Y2 @ Y1))) => (Y0 @ Y1))))))) => (Y0 @ sK4)))) | (~ (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK3 @ Y0 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y3 @ Y4) & (Y2 @ Y3)) => (Y2 @ Y4))))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & (sK2 @ Y4 @ Y3)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK3 @ Y0 @ Y3) | (sK2 @ Y0 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((((sK2 @ Y4 @ Y3) | (sK3 @ Y4 @ Y3)) & (Y2 @ Y4)) => (Y2 @ Y3))))))) => (Y2 @ Y1))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK3 @ Y2 @ Y4) | (sK2 @ Y2 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK2 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y0)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK3 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5))) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y0 @ Y4) | (sK2 @ Y0 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y1))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK3 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5))) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y2 @ Y4) | (sK2 @ Y2 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y1)))))))))))) => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK2 @ sK5 @ Y1) | (sK3 @ sK5 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK2 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1))) => (Y0 @ Y1))))))) => (Y0 @ sK4))))))) = $false)),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.35/1.28 thf(f16,plain,(
% 1.35/1.28 ($false = ((^[Y0 : a]: ((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK3 @ Y0 @ Y2) | (sK2 @ Y0 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & ((sK3 @ Y3 @ Y2) | (sK2 @ Y3 @ Y2))) => (Y1 @ Y2))))))) => (Y1 @ sK4)))) | (~ (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((sK3 @ Y1 @ Y4) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y4 @ Y5) & (Y3 @ Y4)) => (Y3 @ Y5))))))) => (Y3 @ Y2)))) | (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & (sK2 @ Y5 @ Y4)) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: ((sK2 @ Y1 @ Y4) => (Y3 @ Y4))))) => (Y3 @ Y2))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK3 @ Y1 @ Y4) | (sK2 @ Y1 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((((sK2 @ Y5 @ Y4) | (sK3 @ Y5 @ Y4)) & (Y3 @ Y5)) => (Y3 @ Y4))))))) => (Y3 @ Y2))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (((sK3 @ Y3 @ Y5) | (sK2 @ Y3 @ Y5)) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & ((sK2 @ Y5 @ Y6) | (sK3 @ Y5 @ Y6))) => (Y4 @ Y6))))))) => (Y4 @ Y1)))) & (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & ((sK3 @ Y5 @ Y6) | (sK2 @ Y5 @ Y6))) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (((sK3 @ Y1 @ Y5) | (sK2 @ Y1 @ Y5)) => (Y4 @ Y5))))) => (Y4 @ Y2))))) => (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & ((sK3 @ Y5 @ Y6) | (sK2 @ Y5 @ Y6))) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (((sK3 @ Y3 @ Y5) | (sK2 @ Y3 @ Y5)) => (Y4 @ Y5))))) => (Y4 @ Y2)))))))))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK2 @ Y0 @ Y2) | (sK3 @ Y0 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & ((sK2 @ Y3 @ Y2) | (sK3 @ Y3 @ Y2))) => (Y1 @ Y2))))))) => (Y1 @ sK4)))))))) @ sK5))),
% 1.35/1.28 inference(sigma_clausification,[status(thm)],[f15])).
% 1.35/1.28 thf(f15,plain,(
% 1.35/1.28 ((!! @ a @ (^[Y0 : a]: ((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK3 @ Y0 @ Y2) | (sK2 @ Y0 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & ((sK3 @ Y3 @ Y2) | (sK2 @ Y3 @ Y2))) => (Y1 @ Y2))))))) => (Y1 @ sK4)))) | (~ (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((sK3 @ Y1 @ Y4) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y4 @ Y5) & (Y3 @ Y4)) => (Y3 @ Y5))))))) => (Y3 @ Y2)))) | (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & (sK2 @ Y5 @ Y4)) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: ((sK2 @ Y1 @ Y4) => (Y3 @ Y4))))) => (Y3 @ Y2))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK3 @ Y1 @ Y4) | (sK2 @ Y1 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((((sK2 @ Y5 @ Y4) | (sK3 @ Y5 @ Y4)) & (Y3 @ Y5)) => (Y3 @ Y4))))))) => (Y3 @ Y2))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (((sK3 @ Y3 @ Y5) | (sK2 @ Y3 @ Y5)) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & ((sK2 @ Y5 @ Y6) | (sK3 @ Y5 @ Y6))) => (Y4 @ Y6))))))) => (Y4 @ Y1)))) & (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & ((sK3 @ Y5 @ Y6) | (sK2 @ Y5 @ Y6))) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (((sK3 @ Y1 @ Y5) | (sK2 @ Y1 @ Y5)) => (Y4 @ Y5))))) => (Y4 @ Y2))))) => (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & ((sK3 @ Y5 @ Y6) | (sK2 @ Y5 @ Y6))) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (((sK3 @ Y3 @ Y5) | (sK2 @ Y3 @ Y5)) => (Y4 @ Y5))))) => (Y4 @ Y2)))))))))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK2 @ Y0 @ Y2) | (sK3 @ Y0 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & ((sK2 @ Y3 @ Y2) | (sK3 @ Y3 @ Y2))) => (Y1 @ Y2))))))) => (Y1 @ sK4))))))))) = $false)),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f14])).
% 1.35/1.28 thf(f14,plain,(
% 1.35/1.28 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK3 @ Y1 @ Y3) | (sK2 @ Y1 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & ((sK3 @ Y4 @ Y3) | (sK2 @ Y4 @ Y3))) => (Y2 @ Y3))))))) => (Y2 @ Y0)))) | (~ (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((sK3 @ Y2 @ Y5) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((sK3 @ Y5 @ Y6) & (Y4 @ Y5)) => (Y4 @ Y6))))))) => (Y4 @ Y3)))) | (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & (sK2 @ Y6 @ Y5)) => (Y4 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: ((sK2 @ Y2 @ Y5) => (Y4 @ Y5))))) => (Y4 @ Y3))))) => (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (((sK3 @ Y2 @ Y5) | (sK2 @ Y2 @ Y5)) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((((sK2 @ Y6 @ Y5) | (sK3 @ Y6 @ Y5)) & (Y4 @ Y6)) => (Y4 @ Y5))))))) => (Y4 @ Y3))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (((sK3 @ Y4 @ Y6) | (sK2 @ Y4 @ Y6)) => (Y5 @ Y6)))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y5 @ Y6) & ((sK2 @ Y6 @ Y7) | (sK3 @ Y6 @ Y7))) => (Y5 @ Y7))))))) => (Y5 @ Y2)))) & (!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y5 @ Y6) & ((sK3 @ Y6 @ Y7) | (sK2 @ Y6 @ Y7))) => (Y5 @ Y7)))))) & (!! @ a @ (^[Y6 : a]: (((sK3 @ Y2 @ Y6) | (sK2 @ Y2 @ Y6)) => (Y5 @ Y6))))) => (Y5 @ Y3))))) => (!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y5 @ Y6) & ((sK3 @ Y6 @ Y7) | (sK2 @ Y6 @ Y7))) => (Y5 @ Y7)))))) & (!! @ a @ (^[Y6 : a]: (((sK3 @ Y4 @ Y6) | (sK2 @ Y4 @ Y6)) => (Y5 @ Y6))))) => (Y5 @ Y3)))))))))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK2 @ Y1 @ Y3) | (sK3 @ Y1 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & ((sK2 @ Y4 @ Y3) | (sK3 @ Y4 @ Y3))) => (Y2 @ Y3))))))) => (Y2 @ Y0)))))))))) @ sK4))),
% 1.35/1.28 inference(sigma_clausification,[status(thm)],[f13])).
% 1.35/1.28 thf(f13,plain,(
% 1.35/1.28 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK3 @ Y1 @ Y3) | (sK2 @ Y1 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & ((sK3 @ Y4 @ Y3) | (sK2 @ Y4 @ Y3))) => (Y2 @ Y3))))))) => (Y2 @ Y0)))) | (~ (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((sK3 @ Y2 @ Y5) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((sK3 @ Y5 @ Y6) & (Y4 @ Y5)) => (Y4 @ Y6))))))) => (Y4 @ Y3)))) | (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & (sK2 @ Y6 @ Y5)) => (Y4 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: ((sK2 @ Y2 @ Y5) => (Y4 @ Y5))))) => (Y4 @ Y3))))) => (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (((sK3 @ Y2 @ Y5) | (sK2 @ Y2 @ Y5)) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((((sK2 @ Y6 @ Y5) | (sK3 @ Y6 @ Y5)) & (Y4 @ Y6)) => (Y4 @ Y5))))))) => (Y4 @ Y3))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (((sK3 @ Y4 @ Y6) | (sK2 @ Y4 @ Y6)) => (Y5 @ Y6)))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y5 @ Y6) & ((sK2 @ Y6 @ Y7) | (sK3 @ Y6 @ Y7))) => (Y5 @ Y7))))))) => (Y5 @ Y2)))) & (!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y5 @ Y6) & ((sK3 @ Y6 @ Y7) | (sK2 @ Y6 @ Y7))) => (Y5 @ Y7)))))) & (!! @ a @ (^[Y6 : a]: (((sK3 @ Y2 @ Y6) | (sK2 @ Y2 @ Y6)) => (Y5 @ Y6))))) => (Y5 @ Y3))))) => (!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y5 @ Y6) & ((sK3 @ Y6 @ Y7) | (sK2 @ Y6 @ Y7))) => (Y5 @ Y7)))))) & (!! @ a @ (^[Y6 : a]: (((sK3 @ Y4 @ Y6) | (sK2 @ Y4 @ Y6)) => (Y5 @ Y6))))) => (Y5 @ Y3)))))))))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK2 @ Y1 @ Y3) | (sK3 @ Y1 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & ((sK2 @ Y4 @ Y3) | (sK3 @ Y4 @ Y3))) => (Y2 @ Y3))))))) => (Y2 @ Y0))))))))))))),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.35/1.28 thf(f12,plain,(
% 1.35/1.28 ($false = ((^[Y0 : a > a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((Y0 @ Y2 @ Y4) | (sK2 @ Y2 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & ((Y0 @ Y5 @ Y4) | (sK2 @ Y5 @ Y4))) => (Y3 @ Y4))))))) => (Y3 @ Y1)))) | (~ (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: ((Y0 @ Y3 @ Y6) => (Y5 @ Y6)))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y0 @ Y6 @ Y7) & (Y5 @ Y6)) => (Y5 @ Y7))))))) => (Y5 @ Y4)))) | (!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y5 @ Y7) & (sK2 @ Y7 @ Y6)) => (Y5 @ Y6)))))) & (!! @ a @ (^[Y6 : a]: ((sK2 @ Y3 @ Y6) => (Y5 @ Y6))))) => (Y5 @ Y4))))) => (!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (((Y0 @ Y3 @ Y6) | (sK2 @ Y3 @ Y6)) => (Y5 @ Y6)))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((((sK2 @ Y7 @ Y6) | (Y0 @ Y7 @ Y6)) & (Y5 @ Y7)) => (Y5 @ Y6))))))) => (Y5 @ Y4))))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (((Y0 @ Y5 @ Y7) | (sK2 @ Y5 @ Y7)) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y7) & ((sK2 @ Y7 @ Y8) | (Y0 @ Y7 @ Y8))) => (Y6 @ Y8))))))) => (Y6 @ Y3)))) & (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y7) & ((Y0 @ Y7 @ Y8) | (sK2 @ Y7 @ Y8))) => (Y6 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: (((Y0 @ Y3 @ Y7) | (sK2 @ Y3 @ Y7)) => (Y6 @ Y7))))) => (Y6 @ Y4))))) => (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y7) & ((Y0 @ Y7 @ Y8) | (sK2 @ Y7 @ Y8))) => (Y6 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: (((Y0 @ Y5 @ Y7) | (sK2 @ Y5 @ Y7)) => (Y6 @ Y7))))) => (Y6 @ Y4)))))))))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK2 @ Y2 @ Y4) | (Y0 @ Y2 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & ((sK2 @ Y5 @ Y4) | (Y0 @ Y5 @ Y4))) => (Y3 @ Y4))))))) => (Y3 @ Y1)))))))))))) @ sK3))),
% 1.35/1.28 inference(sigma_clausification,[status(thm)],[f11])).
% 1.35/1.28 thf(f11,plain,(
% 1.35/1.28 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((Y0 @ Y2 @ Y4) | (sK2 @ Y2 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & ((Y0 @ Y5 @ Y4) | (sK2 @ Y5 @ Y4))) => (Y3 @ Y4))))))) => (Y3 @ Y1)))) | (~ (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: ((Y0 @ Y3 @ Y6) => (Y5 @ Y6)))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y0 @ Y6 @ Y7) & (Y5 @ Y6)) => (Y5 @ Y7))))))) => (Y5 @ Y4)))) | (!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y5 @ Y7) & (sK2 @ Y7 @ Y6)) => (Y5 @ Y6)))))) & (!! @ a @ (^[Y6 : a]: ((sK2 @ Y3 @ Y6) => (Y5 @ Y6))))) => (Y5 @ Y4))))) => (!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (((Y0 @ Y3 @ Y6) | (sK2 @ Y3 @ Y6)) => (Y5 @ Y6)))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((((sK2 @ Y7 @ Y6) | (Y0 @ Y7 @ Y6)) & (Y5 @ Y7)) => (Y5 @ Y6))))))) => (Y5 @ Y4))))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (((Y0 @ Y5 @ Y7) | (sK2 @ Y5 @ Y7)) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y7) & ((sK2 @ Y7 @ Y8) | (Y0 @ Y7 @ Y8))) => (Y6 @ Y8))))))) => (Y6 @ Y3)))) & (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y7) & ((Y0 @ Y7 @ Y8) | (sK2 @ Y7 @ Y8))) => (Y6 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: (((Y0 @ Y3 @ Y7) | (sK2 @ Y3 @ Y7)) => (Y6 @ Y7))))) => (Y6 @ Y4))))) => (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y7) & ((Y0 @ Y7 @ Y8) | (sK2 @ Y7 @ Y8))) => (Y6 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: (((Y0 @ Y5 @ Y7) | (sK2 @ Y5 @ Y7)) => (Y6 @ Y7))))) => (Y6 @ Y4)))))))))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK2 @ Y2 @ Y4) | (Y0 @ Y2 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & ((sK2 @ Y5 @ Y4) | (Y0 @ Y5 @ Y4))) => (Y3 @ Y4))))))) => (Y3 @ Y1))))))))))))) = $false)),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.35/1.28 thf(f10,plain,(
% 1.35/1.28 ($false = ((^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (((Y1 @ Y3 @ Y5) | (Y0 @ Y3 @ Y5)) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & ((Y1 @ Y6 @ Y5) | (Y0 @ Y6 @ Y5))) => (Y4 @ Y5))))))) => (Y4 @ Y2)))) | (~ (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: ((Y1 @ Y4 @ Y7) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y1 @ Y7 @ Y8) & (Y6 @ Y7)) => (Y6 @ Y8))))))) => (Y6 @ Y5)))) | (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y8) & (Y0 @ Y8 @ Y7)) => (Y6 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: ((Y0 @ Y4 @ Y7) => (Y6 @ Y7))))) => (Y6 @ Y5))))) => (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (((Y1 @ Y4 @ Y7) | (Y0 @ Y4 @ Y7)) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((((Y0 @ Y8 @ Y7) | (Y1 @ Y8 @ Y7)) & (Y6 @ Y8)) => (Y6 @ Y7))))))) => (Y6 @ Y5))))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (((Y1 @ Y6 @ Y8) | (Y0 @ Y6 @ Y8)) => (Y7 @ Y8)))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y8) & ((Y0 @ Y8 @ Y9) | (Y1 @ Y8 @ Y9))) => (Y7 @ Y9))))))) => (Y7 @ Y4)))) & (!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y8) & ((Y1 @ Y8 @ Y9) | (Y0 @ Y8 @ Y9))) => (Y7 @ Y9)))))) & (!! @ a @ (^[Y8 : a]: (((Y1 @ Y4 @ Y8) | (Y0 @ Y4 @ Y8)) => (Y7 @ Y8))))) => (Y7 @ Y5))))) => (!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y8) & ((Y1 @ Y8 @ Y9) | (Y0 @ Y8 @ Y9))) => (Y7 @ Y9)))))) & (!! @ a @ (^[Y8 : a]: (((Y1 @ Y6 @ Y8) | (Y0 @ Y6 @ Y8)) => (Y7 @ Y8))))) => (Y7 @ Y5)))))))))))) => (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (((Y0 @ Y3 @ Y5) | (Y1 @ Y3 @ Y5)) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & ((Y0 @ Y6 @ Y5) | (Y1 @ Y6 @ Y5))) => (Y4 @ Y5))))))) => (Y4 @ Y2)))))))))))))) @ sK2))),
% 1.35/1.28 inference(sigma_clausification,[status(thm)],[f7])).
% 1.35/1.28 thf(f7,plain,(
% 1.35/1.28 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (((Y1 @ Y3 @ Y5) | (Y0 @ Y3 @ Y5)) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & ((Y1 @ Y6 @ Y5) | (Y0 @ Y6 @ Y5))) => (Y4 @ Y5))))))) => (Y4 @ Y2)))) | (~ (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: ((Y1 @ Y4 @ Y7) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y1 @ Y7 @ Y8) & (Y6 @ Y7)) => (Y6 @ Y8))))))) => (Y6 @ Y5)))) | (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y8) & (Y0 @ Y8 @ Y7)) => (Y6 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: ((Y0 @ Y4 @ Y7) => (Y6 @ Y7))))) => (Y6 @ Y5))))) => (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (((Y1 @ Y4 @ Y7) | (Y0 @ Y4 @ Y7)) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((((Y0 @ Y8 @ Y7) | (Y1 @ Y8 @ Y7)) & (Y6 @ Y8)) => (Y6 @ Y7))))))) => (Y6 @ Y5))))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (((Y1 @ Y6 @ Y8) | (Y0 @ Y6 @ Y8)) => (Y7 @ Y8)))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y8) & ((Y0 @ Y8 @ Y9) | (Y1 @ Y8 @ Y9))) => (Y7 @ Y9))))))) => (Y7 @ Y4)))) & (!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y8) & ((Y1 @ Y8 @ Y9) | (Y0 @ Y8 @ Y9))) => (Y7 @ Y9)))))) & (!! @ a @ (^[Y8 : a]: (((Y1 @ Y4 @ Y8) | (Y0 @ Y4 @ Y8)) => (Y7 @ Y8))))) => (Y7 @ Y5))))) => (!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y8) & ((Y1 @ Y8 @ Y9) | (Y0 @ Y8 @ Y9))) => (Y7 @ Y9)))))) & (!! @ a @ (^[Y8 : a]: (((Y1 @ Y6 @ Y8) | (Y0 @ Y6 @ Y8)) => (Y7 @ Y8))))) => (Y7 @ Y5)))))))))))) => (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (((Y0 @ Y3 @ Y5) | (Y1 @ Y3 @ Y5)) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & ((Y0 @ Y6 @ Y5) | (Y1 @ Y6 @ Y5))) => (Y4 @ Y5))))))) => (Y4 @ Y2))))))))))))))) = $false)),
% 1.35/1.28 inference(not_proxy_clausification,[status(thm)],[f6])).
% 1.35/1.28 thf(f6,plain,(
% 1.35/1.28 ($true = (~ (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (((Y1 @ Y3 @ Y5) | (Y0 @ Y3 @ Y5)) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & ((Y1 @ Y6 @ Y5) | (Y0 @ Y6 @ Y5))) => (Y4 @ Y5))))))) => (Y4 @ Y2)))) | (~ (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: ((Y1 @ Y4 @ Y7) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y1 @ Y7 @ Y8) & (Y6 @ Y7)) => (Y6 @ Y8))))))) => (Y6 @ Y5)))) | (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y8) & (Y0 @ Y8 @ Y7)) => (Y6 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: ((Y0 @ Y4 @ Y7) => (Y6 @ Y7))))) => (Y6 @ Y5))))) => (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (((Y1 @ Y4 @ Y7) | (Y0 @ Y4 @ Y7)) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((((Y0 @ Y8 @ Y7) | (Y1 @ Y8 @ Y7)) & (Y6 @ Y8)) => (Y6 @ Y7))))))) => (Y6 @ Y5))))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (((Y1 @ Y6 @ Y8) | (Y0 @ Y6 @ Y8)) => (Y7 @ Y8)))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y8) & ((Y0 @ Y8 @ Y9) | (Y1 @ Y8 @ Y9))) => (Y7 @ Y9))))))) => (Y7 @ Y4)))) & (!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y8) & ((Y1 @ Y8 @ Y9) | (Y0 @ Y8 @ Y9))) => (Y7 @ Y9)))))) & (!! @ a @ (^[Y8 : a]: (((Y1 @ Y4 @ Y8) | (Y0 @ Y4 @ Y8)) => (Y7 @ Y8))))) => (Y7 @ Y5))))) => (!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y8) & ((Y1 @ Y8 @ Y9) | (Y0 @ Y8 @ Y9))) => (Y7 @ Y9)))))) & (!! @ a @ (^[Y8 : a]: (((Y1 @ Y6 @ Y8) | (Y0 @ Y6 @ Y8)) => (Y7 @ Y8))))) => (Y7 @ Y5)))))))))))) => (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (((Y0 @ Y3 @ Y5) | (Y1 @ Y3 @ Y5)) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & ((Y0 @ Y6 @ Y5) | (Y1 @ Y6 @ Y5))) => (Y4 @ Y5))))))) => (Y4 @ Y2)))))))))))))))))),
% 1.35/1.28 inference(cnf_transformation,[status(thm)],[f5])).
% 1.35/1.28 thf(f5,plain,(
% 1.35/1.28 ($true = (~ (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (((Y1 @ Y3 @ Y5) | (Y0 @ Y3 @ Y5)) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & ((Y1 @ Y6 @ Y5) | (Y0 @ Y6 @ Y5))) => (Y4 @ Y5))))))) => (Y4 @ Y2)))) | (~ (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: ((Y1 @ Y4 @ Y7) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y1 @ Y7 @ Y8) & (Y6 @ Y7)) => (Y6 @ Y8))))))) => (Y6 @ Y5)))) | (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y8) & (Y0 @ Y8 @ Y7)) => (Y6 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: ((Y0 @ Y4 @ Y7) => (Y6 @ Y7))))) => (Y6 @ Y5))))) => (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (((Y1 @ Y4 @ Y7) | (Y0 @ Y4 @ Y7)) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((((Y0 @ Y8 @ Y7) | (Y1 @ Y8 @ Y7)) & (Y6 @ Y8)) => (Y6 @ Y7))))))) => (Y6 @ Y5))))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (((Y1 @ Y6 @ Y8) | (Y0 @ Y6 @ Y8)) => (Y7 @ Y8)))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y8) & ((Y0 @ Y8 @ Y9) | (Y1 @ Y8 @ Y9))) => (Y7 @ Y9))))))) => (Y7 @ Y4)))) & (!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y8) & ((Y1 @ Y8 @ Y9) | (Y0 @ Y8 @ Y9))) => (Y7 @ Y9)))))) & (!! @ a @ (^[Y8 : a]: (((Y1 @ Y4 @ Y8) | (Y0 @ Y4 @ Y8)) => (Y7 @ Y8))))) => (Y7 @ Y5))))) => (!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y8) & ((Y1 @ Y8 @ Y9) | (Y0 @ Y8 @ Y9))) => (Y7 @ Y9)))))) & (!! @ a @ (^[Y8 : a]: (((Y1 @ Y6 @ Y8) | (Y0 @ Y6 @ Y8)) => (Y7 @ Y8))))) => (Y7 @ Y5)))))))))))) => (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (((Y0 @ Y3 @ Y5) | (Y1 @ Y3 @ Y5)) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & ((Y0 @ Y6 @ Y5) | (Y1 @ Y6 @ Y5))) => (Y4 @ Y5))))))) => (Y4 @ Y2)))))))))))))))))),
% 1.35/1.28 inference(fool_elimination,[status(thm)],[f4])).
% 1.35/1.28 thf(f4,plain,(
% 1.35/1.28 ~! [X0 : a,X1 : a,X2 : a > a > $o,X3 : a > a > $o] : (~((! [X4 : a,X5 : a,X6 : a] : ((! [X7 : a > $o] : ((! [X8 : a] : (((X3 @ X6 @ X8) | (X2 @ X6 @ X8)) => (X7 @ X8)) & ! [X9 : a,X10 : a] : ((((X3 @ X10 @ X9) | (X2 @ X10 @ X9)) & (X7 @ X10)) => (X7 @ X9))) => (X7 @ X5)) & ! [X11 : a > $o] : ((! [X12 : a,X13 : a] : ((((X2 @ X13 @ X12) | (X3 @ X13 @ X12)) & (X11 @ X13)) => (X11 @ X12)) & ! [X14 : a] : (((X3 @ X4 @ X14) | (X2 @ X4 @ X14)) => (X11 @ X14))) => (X11 @ X6))) => ! [X15 : a > $o] : ((! [X16 : a] : (((X3 @ X4 @ X16) | (X2 @ X4 @ X16)) => (X15 @ X16)) & ! [X17 : a,X18 : a] : ((((X3 @ X18 @ X17) | (X2 @ X18 @ X17)) & (X15 @ X18)) => (X15 @ X17))) => (X15 @ X5))) & ! [X19 : a,X20 : a] : ((! [X21 : a > $o] : ((! [X22 : a] : ((X3 @ X20 @ X22) => (X21 @ X22)) & ! [X23 : a,X24 : a] : (((X3 @ X23 @ X24) & (X21 @ X23)) => (X21 @ X24))) => (X21 @ X19)) | ! [X25 : a > $o] : ((! [X26 : a,X27 : a] : (((X25 @ X27) & (X2 @ X27 @ X26)) => (X25 @ X26)) & ! [X28 : a] : ((X2 @ X20 @ X28) => (X25 @ X28))) => (X25 @ X19))) => ! [X29 : a > $o] : ((! [X30 : a,X31 : a] : (((X29 @ X30) & ((X2 @ X30 @ X31) | (X3 @ X30 @ X31))) => (X29 @ X31)) & ! [X32 : a] : (((X3 @ X20 @ X32) | (X2 @ X20 @ X32)) => (X29 @ X32))) => (X29 @ X19)))) => ! [X33 : a > $o] : ((! [X34 : a,X35 : a] : ((((X2 @ X34 @ X35) | (X3 @ X34 @ X35)) & (X33 @ X34)) => (X33 @ X35)) & ! [X36 : a] : (((X2 @ X0 @ X36) | (X3 @ X0 @ X36)) => (X33 @ X36))) => (X33 @ X1))) | ! [X37 : a > $o] : ((! [X38 : a,X39 : a] : ((((X3 @ X38 @ X39) | (X2 @ X38 @ X39)) & (X37 @ X38)) => (X37 @ X39)) & ! [X40 : a] : (((X3 @ X0 @ X40) | (X2 @ X0 @ X40)) => (X37 @ X40))) => (X37 @ X1)))),
% 1.35/1.28 inference(rectify,[status(thm)],[f2])).
% 1.35/1.28 thf(f2,negated_conjecture,(
% 1.35/1.28 ~! [X2 : a,X3 : a,X0 : a > a > $o,X1 : a > a > $o] : (~((! [X8 : a,X10 : a,X9 : a] : ((! [X4 : a > $o] : ((! [X5 : a] : (((X1 @ X9 @ X5) | (X0 @ X9 @ X5)) => (X4 @ X5)) & ! [X7 : a,X6 : a] : ((((X1 @ X6 @ X7) | (X0 @ X6 @ X7)) & (X4 @ X6)) => (X4 @ X7))) => (X4 @ X10)) & ! [X4 : a > $o] : ((! [X7 : a,X6 : a] : ((((X0 @ X6 @ X7) | (X1 @ X6 @ X7)) & (X4 @ X6)) => (X4 @ X7)) & ! [X5 : a] : (((X1 @ X8 @ X5) | (X0 @ X8 @ X5)) => (X4 @ X5))) => (X4 @ X9))) => ! [X4 : a > $o] : ((! [X5 : a] : (((X1 @ X8 @ X5) | (X0 @ X8 @ X5)) => (X4 @ X5)) & ! [X7 : a,X6 : a] : ((((X1 @ X6 @ X7) | (X0 @ X6 @ X7)) & (X4 @ X6)) => (X4 @ X7))) => (X4 @ X10))) & ! [X9 : a,X8 : a] : ((! [X4 : a > $o] : ((! [X5 : a] : ((X1 @ X8 @ X5) => (X4 @ X5)) & ! [X6 : a,X7 : a] : (((X1 @ X6 @ X7) & (X4 @ X6)) => (X4 @ X7))) => (X4 @ X9)) | ! [X4 : a > $o] : ((! [X7 : a,X6 : a] : (((X4 @ X6) & (X0 @ X6 @ X7)) => (X4 @ X7)) & ! [X5 : a] : ((X0 @ X8 @ X5) => (X4 @ X5))) => (X4 @ X9))) => ! [X4 : a > $o] : ((! [X6 : a,X7 : a] : (((X4 @ X6) & ((X0 @ X6 @ X7) | (X1 @ X6 @ X7))) => (X4 @ X7)) & ! [X5 : a] : (((X1 @ X8 @ X5) | (X0 @ X8 @ X5)) => (X4 @ X5))) => (X4 @ X9)))) => ! [X4 : a > $o] : ((! [X6 : a,X7 : a] : ((((X0 @ X6 @ X7) | (X1 @ X6 @ X7)) & (X4 @ X6)) => (X4 @ X7)) & ! [X5 : a] : (((X0 @ X2 @ X5) | (X1 @ X2 @ X5)) => (X4 @ X5))) => (X4 @ X3))) | ! [X4 : a > $o] : ((! [X6 : a,X7 : a] : ((((X1 @ X6 @ X7) | (X0 @ X6 @ X7)) & (X4 @ X6)) => (X4 @ X7)) & ! [X5 : a] : (((X1 @ X2 @ X5) | (X0 @ X2 @ X5)) => (X4 @ X5))) => (X4 @ X3)))),
% 1.35/1.28 inference(negated_conjecture,[status(cth)],[f1])).
% 1.35/1.28 thf(f1,conjecture,(
% 1.35/1.28 ! [X2 : a,X3 : a,X0 : a > a > $o,X1 : a > a > $o] : (~((! [X8 : a,X10 : a,X9 : a] : ((! [X4 : a > $o] : ((! [X5 : a] : (((X1 @ X9 @ X5) | (X0 @ X9 @ X5)) => (X4 @ X5)) & ! [X7 : a,X6 : a] : ((((X1 @ X6 @ X7) | (X0 @ X6 @ X7)) & (X4 @ X6)) => (X4 @ X7))) => (X4 @ X10)) & ! [X4 : a > $o] : ((! [X7 : a,X6 : a] : ((((X0 @ X6 @ X7) | (X1 @ X6 @ X7)) & (X4 @ X6)) => (X4 @ X7)) & ! [X5 : a] : (((X1 @ X8 @ X5) | (X0 @ X8 @ X5)) => (X4 @ X5))) => (X4 @ X9))) => ! [X4 : a > $o] : ((! [X5 : a] : (((X1 @ X8 @ X5) | (X0 @ X8 @ X5)) => (X4 @ X5)) & ! [X7 : a,X6 : a] : ((((X1 @ X6 @ X7) | (X0 @ X6 @ X7)) & (X4 @ X6)) => (X4 @ X7))) => (X4 @ X10))) & ! [X9 : a,X8 : a] : ((! [X4 : a > $o] : ((! [X5 : a] : ((X1 @ X8 @ X5) => (X4 @ X5)) & ! [X6 : a,X7 : a] : (((X1 @ X6 @ X7) & (X4 @ X6)) => (X4 @ X7))) => (X4 @ X9)) | ! [X4 : a > $o] : ((! [X7 : a,X6 : a] : (((X4 @ X6) & (X0 @ X6 @ X7)) => (X4 @ X7)) & ! [X5 : a] : ((X0 @ X8 @ X5) => (X4 @ X5))) => (X4 @ X9))) => ! [X4 : a > $o] : ((! [X6 : a,X7 : a] : (((X4 @ X6) & ((X0 @ X6 @ X7) | (X1 @ X6 @ X7))) => (X4 @ X7)) & ! [X5 : a] : (((X1 @ X8 @ X5) | (X0 @ X8 @ X5)) => (X4 @ X5))) => (X4 @ X9)))) => ! [X4 : a > $o] : ((! [X6 : a,X7 : a] : ((((X0 @ X6 @ X7) | (X1 @ X6 @ X7)) & (X4 @ X6)) => (X4 @ X7)) & ! [X5 : a] : (((X0 @ X2 @ X5) | (X1 @ X2 @ X5)) => (X4 @ X5))) => (X4 @ X3))) | ! [X4 : a > $o] : ((! [X6 : a,X7 : a] : ((((X1 @ X6 @ X7) | (X0 @ X6 @ X7)) & (X4 @ X6)) => (X4 @ X7)) & ! [X5 : a] : (((X1 @ X2 @ X5) | (X0 @ X2 @ X5)) => (X4 @ X5))) => (X4 @ X3)))),
% 1.35/1.28 file('/export/starexec/sandbox2/tmp/tmp.MNEUYGSWeg/DTF2THF_13164.p',cTHM251G_pme)).
% 1.35/1.28 thf(f610,plain,(
% 1.35/1.28 ~spl0_14 | ~spl0_17),
% 1.35/1.28 inference(avatar_contradiction_clause,[status(thm)],[f609])).
% 1.35/1.28 thf(f609,plain,(
% 1.35/1.28 $false | (~spl0_14 | ~spl0_17)),
% 1.35/1.28 inference(trivial_inequality_removal,[status(thm)],[f608])).
% 1.35/1.28 thf(f608,plain,(
% 1.35/1.28 ($true = $false) | (~spl0_14 | ~spl0_17)),
% 1.35/1.28 inference(forward_demodulation,[status(thm)],[f607,f547])).
% 1.35/1.28 thf(f607,plain,(
% 1.35/1.28 ((sK6 @ sK16) = $true) | (~spl0_14 | ~spl0_17)),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f606])).
% 1.35/1.28 thf(f606,plain,(
% 1.35/1.28 (($true => (sK6 @ sK16)) = $true) | (~spl0_14 | ~spl0_17)),
% 1.35/1.28 inference(forward_demodulation,[status(thm)],[f605,f584])).
% 1.35/1.28 thf(f605,plain,(
% 1.35/1.28 (((sK6 @ sK18) => (sK6 @ sK16)) = $true) | ~spl0_17),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f604])).
% 1.35/1.28 thf(f604,plain,(
% 1.35/1.28 ($true = (((sK6 @ sK18) & $true) => (sK6 @ sK16))) | ~spl0_17),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f603])).
% 1.35/1.28 thf(f603,plain,(
% 1.35/1.28 ($true = (((sK6 @ sK18) & ((sK3 @ sK18 @ sK16) | $true)) => (sK6 @ sK16))) | ~spl0_17),
% 1.35/1.28 inference(superposition,[status(thm)],[f223,f596])).
% 1.35/1.28 thf(f596,plain,(
% 1.35/1.28 ((sK2 @ sK18 @ sK16) = $true) | ~spl0_17),
% 1.35/1.28 inference(avatar_component_clause,[status(thm)],[f595])).
% 1.35/1.28 thf(f595,definition,(
% 1.35/1.28 spl0_17 <=> ((sK2 @ sK18 @ sK16) = $true)),
% 1.35/1.28 introduced(definition,[new_symbols(naming,[spl0_17])],[avatar_definition])).
% 1.35/1.28 thf(f600,plain,(
% 1.35/1.28 spl0_17 | spl0_18 | ~spl0_14),
% 1.35/1.28 inference(avatar_split_clause,[status(thm)],[f593,f491,f598,f595])).
% 1.35/1.28 thf(f593,plain,(
% 1.35/1.28 ($true = (sK3 @ sK18 @ sK16)) | ((sK2 @ sK18 @ sK16) = $true) | ~spl0_14),
% 1.35/1.28 inference(binary_proxy_clausification,[status(thm)],[f581])).
% 1.35/1.28 thf(f536,plain,(
% 1.35/1.28 ~spl0_13 | ~spl0_15),
% 1.35/1.28 inference(avatar_contradiction_clause,[status(thm)],[f535])).
% 1.35/1.28 thf(f535,plain,(
% 1.35/1.28 $false | (~spl0_13 | ~spl0_15)),
% 1.35/1.28 inference(trivial_inequality_removal,[status(thm)],[f534])).
% 1.35/1.28 thf(f534,plain,(
% 1.35/1.28 ($true = $false) | (~spl0_13 | ~spl0_15)),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f533])).
% 1.35/1.28 thf(f533,plain,(
% 1.35/1.28 ($true = (~ $true)) | (~spl0_13 | ~spl0_15)),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f531])).
% 1.35/1.28 thf(f531,plain,(
% 1.35/1.28 ($true = (~ ((sK3 @ sK5 @ sK15) | $true))) | (~spl0_13 | ~spl0_15)),
% 1.35/1.28 inference(backward_demodulation,[status(thm)],[f512,f519])).
% 1.35/1.28 thf(f519,plain,(
% 1.35/1.28 ((sK2 @ sK5 @ sK15) = $true) | ~spl0_15),
% 1.35/1.28 inference(avatar_component_clause,[status(thm)],[f518])).
% 1.35/1.28 thf(f518,definition,(
% 1.35/1.28 spl0_15 <=> ((sK2 @ sK5 @ sK15) = $true)),
% 1.35/1.28 introduced(definition,[new_symbols(naming,[spl0_15])],[avatar_definition])).
% 1.35/1.28 thf(f512,plain,(
% 1.35/1.28 ((~ ((sK3 @ sK5 @ sK15) | (sK2 @ sK5 @ sK15))) = $true) | ~spl0_13),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f510])).
% 1.35/1.28 thf(f510,plain,(
% 1.35/1.28 ($true = (((sK3 @ sK5 @ sK15) | (sK2 @ sK5 @ sK15)) => $false)) | ~spl0_13),
% 1.35/1.28 inference(superposition,[status(thm)],[f60,f501])).
% 1.35/1.28 thf(f501,plain,(
% 1.35/1.28 ((sK6 @ sK15) = $false) | ~spl0_13),
% 1.35/1.28 inference(binary_proxy_clausification,[status(thm)],[f500])).
% 1.35/1.28 thf(f500,plain,(
% 1.35/1.28 ((((sK2 @ sK5 @ sK15) | (sK3 @ sK5 @ sK15)) => (sK6 @ sK15)) = $false) | ~spl0_13),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f496])).
% 1.35/1.28 thf(f496,plain,(
% 1.35/1.28 (((^[Y0 : a]: (((sK2 @ sK5 @ Y0) | (sK3 @ sK5 @ Y0)) => (sK6 @ Y0))) @ sK15) = $false) | ~spl0_13),
% 1.35/1.28 inference(sigma_clausification,[status(thm)],[f489])).
% 1.35/1.28 thf(f489,plain,(
% 1.35/1.28 ((!! @ a @ (^[Y0 : a]: (((sK2 @ sK5 @ Y0) | (sK3 @ sK5 @ Y0)) => (sK6 @ Y0)))) = $false) | ~spl0_13),
% 1.35/1.28 inference(avatar_component_clause,[status(thm)],[f488])).
% 1.35/1.28 thf(f488,definition,(
% 1.35/1.28 spl0_13 <=> ((!! @ a @ (^[Y0 : a]: (((sK2 @ sK5 @ Y0) | (sK3 @ sK5 @ Y0)) => (sK6 @ Y0)))) = $false)),
% 1.35/1.28 introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition])).
% 1.35/1.28 thf(f60,plain,(
% 1.35/1.28 ( ! [X1 : a] : (((((sK3 @ sK5 @ X1) | (sK2 @ sK5 @ X1)) => (sK6 @ X1)) = $true)) )),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f59])).
% 1.35/1.28 thf(f59,plain,(
% 1.35/1.28 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (((sK3 @ sK5 @ Y0) | (sK2 @ sK5 @ Y0)) => (sK6 @ Y0))) @ X1))) )),
% 1.35/1.28 inference(pi_clausification,[status(thm)],[f54])).
% 1.35/1.28 thf(f529,plain,(
% 1.35/1.28 ~spl0_13 | ~spl0_16),
% 1.35/1.28 inference(avatar_contradiction_clause,[status(thm)],[f528])).
% 1.35/1.28 thf(f528,plain,(
% 1.35/1.28 $false | (~spl0_13 | ~spl0_16)),
% 1.35/1.28 inference(trivial_inequality_removal,[status(thm)],[f527])).
% 1.35/1.28 thf(f527,plain,(
% 1.35/1.28 ($true = $false) | (~spl0_13 | ~spl0_16)),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f526])).
% 1.35/1.28 thf(f526,plain,(
% 1.35/1.28 ($true = (~ $true)) | (~spl0_13 | ~spl0_16)),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f524])).
% 1.35/1.28 thf(f524,plain,(
% 1.35/1.28 ($true = (~ ($true | (sK2 @ sK5 @ sK15)))) | (~spl0_13 | ~spl0_16)),
% 1.35/1.28 inference(backward_demodulation,[status(thm)],[f512,f522])).
% 1.35/1.28 thf(f522,plain,(
% 1.35/1.28 ($true = (sK3 @ sK5 @ sK15)) | ~spl0_16),
% 1.35/1.28 inference(avatar_component_clause,[status(thm)],[f521])).
% 1.35/1.28 thf(f521,definition,(
% 1.35/1.28 spl0_16 <=> ($true = (sK3 @ sK5 @ sK15))),
% 1.35/1.28 introduced(definition,[new_symbols(naming,[spl0_16])],[avatar_definition])).
% 1.35/1.28 thf(f523,plain,(
% 1.35/1.28 spl0_15 | spl0_16 | ~spl0_13),
% 1.35/1.28 inference(avatar_split_clause,[status(thm)],[f516,f488,f521,f518])).
% 1.35/1.28 thf(f516,plain,(
% 1.35/1.28 ($true = (sK3 @ sK5 @ sK15)) | ((sK2 @ sK5 @ sK15) = $true) | ~spl0_13),
% 1.35/1.28 inference(binary_proxy_clausification,[status(thm)],[f502])).
% 1.35/1.28 thf(f502,plain,(
% 1.35/1.28 (((sK2 @ sK5 @ sK15) | (sK3 @ sK5 @ sK15)) = $true) | ~spl0_13),
% 1.35/1.28 inference(binary_proxy_clausification,[status(thm)],[f500])).
% 1.35/1.28 thf(f493,plain,(
% 1.35/1.28 spl0_13 | spl0_14 | ~spl0_1),
% 1.35/1.28 inference(avatar_split_clause,[status(thm)],[f484,f29,f491,f488])).
% 1.35/1.28 thf(f29,definition,(
% 1.35/1.28 spl0_1 <=> ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK2 @ sK5 @ Y1) | (sK3 @ sK5 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK2 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1))) => (Y0 @ Y1))))))) => (Y0 @ sK4)))))),
% 1.35/1.28 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.35/1.28 thf(f484,plain,(
% 1.35/1.28 ((!! @ a @ (^[Y0 : a]: (((sK2 @ sK5 @ Y0) | (sK3 @ sK5 @ Y0)) => (sK6 @ Y0)))) = $false) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & ((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0))) => (sK6 @ Y0)))))) = $false) | ~spl0_1),
% 1.35/1.28 inference(binary_proxy_clausification,[status(thm)],[f481])).
% 1.35/1.28 thf(f481,plain,(
% 1.35/1.28 ($false = ((!! @ a @ (^[Y0 : a]: (((sK2 @ sK5 @ Y0) | (sK3 @ sK5 @ Y0)) => (sK6 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & ((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0))) => (sK6 @ Y0)))))))) | ~spl0_1),
% 1.35/1.28 inference(not_proxy_clausification,[status(thm)],[f478])).
% 1.35/1.28 thf(f478,plain,(
% 1.35/1.28 ($true = (~ ((!! @ a @ (^[Y0 : a]: (((sK2 @ sK5 @ Y0) | (sK3 @ sK5 @ Y0)) => (sK6 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & ((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0))) => (sK6 @ Y0))))))))) | ~spl0_1),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f475])).
% 1.35/1.28 thf(f475,plain,(
% 1.35/1.28 ((((!! @ a @ (^[Y0 : a]: (((sK2 @ sK5 @ Y0) | (sK3 @ sK5 @ Y0)) => (sK6 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & ((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0))) => (sK6 @ Y0))))))) => $false) = $true) | ~spl0_1),
% 1.35/1.28 inference(superposition,[status(thm)],[f473,f40])).
% 1.35/1.28 thf(f40,plain,(
% 1.35/1.28 ((sK6 @ sK4) = $false)),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f39])).
% 1.35/1.28 thf(f39,plain,(
% 1.35/1.28 ($false = ($true => (sK6 @ sK4)))),
% 1.35/1.28 inference(backward_demodulation,[status(thm)],[f26,f38])).
% 1.35/1.28 thf(f473,plain,(
% 1.35/1.28 ( ! [X1 : a > $o] : (($true = (((!! @ a @ (^[Y0 : a]: (((sK2 @ sK5 @ Y0) | (sK3 @ sK5 @ Y0)) => (X1 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((X1 @ Y1) & ((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0))) => (X1 @ Y0))))))) => (X1 @ sK4)))) ) | ~spl0_1),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f472])).
% 1.35/1.28 thf(f472,plain,(
% 1.35/1.28 ( ! [X1 : a > $o] : ((((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK2 @ sK5 @ Y1) | (sK3 @ sK5 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK2 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1))) => (Y0 @ Y1))))))) => (Y0 @ sK4))) @ X1) = $true)) ) | ~spl0_1),
% 1.35/1.28 inference(pi_clausification,[status(thm)],[f30])).
% 1.35/1.28 thf(f30,plain,(
% 1.35/1.28 ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK2 @ sK5 @ Y1) | (sK3 @ sK5 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK2 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1))) => (Y0 @ Y1))))))) => (Y0 @ sK4))))) | ~spl0_1),
% 1.35/1.28 inference(avatar_component_clause,[status(thm)],[f29])).
% 1.35/1.28 thf(f443,plain,(
% 1.35/1.28 spl0_9 | spl0_10 | ~spl0_4 | ~spl0_7),
% 1.35/1.28 inference(avatar_split_clause,[status(thm)],[f434,f331,f46,f441,f438])).
% 1.35/1.28 thf(f434,plain,(
% 1.35/1.28 ($false = (!! @ a @ (^[Y0 : a]: ((sK2 @ sK12 @ Y0) => (sK14 @ Y0))))) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK14 @ Y1) & (sK2 @ Y1 @ Y0)) => (sK14 @ Y0)))))) = $false) | (~spl0_4 | ~spl0_7)),
% 1.35/1.28 inference(binary_proxy_clausification,[status(thm)],[f428])).
% 1.35/1.28 thf(f428,plain,(
% 1.35/1.28 ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK14 @ Y1) & (sK2 @ Y1 @ Y0)) => (sK14 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ sK12 @ Y0) => (sK14 @ Y0)))))) | (~spl0_4 | ~spl0_7)),
% 1.35/1.28 inference(not_proxy_clausification,[status(thm)],[f380])).
% 1.35/1.28 thf(f380,plain,(
% 1.35/1.28 ((~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK14 @ Y1) & (sK2 @ Y1 @ Y0)) => (sK14 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ sK12 @ Y0) => (sK14 @ Y0)))))) = $true) | (~spl0_4 | ~spl0_7)),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f377])).
% 1.35/1.28 thf(f377,plain,(
% 1.35/1.28 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK14 @ Y1) & (sK2 @ Y1 @ Y0)) => (sK14 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ sK12 @ Y0) => (sK14 @ Y0))))) => $false) = $true) | (~spl0_4 | ~spl0_7)),
% 1.35/1.28 inference(superposition,[status(thm)],[f358,f296])).
% 1.35/1.28 thf(f296,plain,(
% 1.35/1.28 ($false = (sK14 @ sK13)) | ~spl0_4),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f295])).
% 1.35/1.28 thf(f295,plain,(
% 1.35/1.28 (($true => (sK14 @ sK13)) = $false) | ~spl0_4),
% 1.35/1.28 inference(backward_demodulation,[status(thm)],[f292,f294])).
% 1.35/1.28 thf(f294,plain,(
% 1.35/1.28 ($true = ((!! @ a @ (^[Y0 : a]: (((sK3 @ sK12 @ Y0) | (sK2 @ sK12 @ Y0)) => (sK14 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) & (sK14 @ Y1)) => (sK14 @ Y0)))))))) | ~spl0_4),
% 1.35/1.28 inference(binary_proxy_clausification,[status(thm)],[f292])).
% 1.35/1.28 thf(f292,plain,(
% 1.35/1.28 ((((!! @ a @ (^[Y0 : a]: (((sK3 @ sK12 @ Y0) | (sK2 @ sK12 @ Y0)) => (sK14 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) & (sK14 @ Y1)) => (sK14 @ Y0))))))) => (sK14 @ sK13)) = $false) | ~spl0_4),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f291])).
% 1.35/1.28 thf(f291,plain,(
% 1.35/1.28 (((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK3 @ sK12 @ Y1) | (sK2 @ sK12 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK2 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1))))))) => (Y0 @ sK13))) @ sK14) = $false) | ~spl0_4),
% 1.35/1.28 inference(sigma_clausification,[status(thm)],[f277])).
% 1.35/1.28 thf(f277,plain,(
% 1.35/1.28 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK3 @ sK12 @ Y1) | (sK2 @ sK12 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK2 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1))))))) => (Y0 @ sK13)))) = $false) | ~spl0_4),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f276])).
% 1.35/1.28 thf(f276,plain,(
% 1.35/1.28 ($false = ($true => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK3 @ sK12 @ Y1) | (sK2 @ sK12 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK2 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1))))))) => (Y0 @ sK13)))))) | ~spl0_4),
% 1.35/1.28 inference(backward_demodulation,[status(thm)],[f257,f275])).
% 1.35/1.28 thf(f275,plain,(
% 1.35/1.28 ($true = ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK3 @ sK12 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2))))))) => (Y0 @ sK13)))) | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK12 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK13)))))) | ~spl0_4),
% 1.35/1.28 inference(binary_proxy_clausification,[status(thm)],[f257])).
% 1.35/1.28 thf(f257,plain,(
% 1.35/1.28 ((((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK3 @ sK12 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2))))))) => (Y0 @ sK13)))) | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK12 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK13))))) => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK3 @ sK12 @ Y1) | (sK2 @ sK12 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK2 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1))))))) => (Y0 @ sK13))))) = $false) | ~spl0_4),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f256])).
% 1.35/1.28 thf(f256,plain,(
% 1.35/1.28 (((^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK3 @ sK12 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y2 @ Y3) & (Y1 @ Y2)) => (Y1 @ Y3))))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & (sK2 @ Y3 @ Y2)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ sK12 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK3 @ sK12 @ Y2) | (sK2 @ sK12 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((((sK2 @ Y3 @ Y2) | (sK3 @ Y3 @ Y2)) & (Y1 @ Y3)) => (Y1 @ Y2))))))) => (Y1 @ Y0)))))) @ sK13) = $false) | ~spl0_4),
% 1.35/1.28 inference(sigma_clausification,[status(thm)],[f239])).
% 1.35/1.28 thf(f239,plain,(
% 1.35/1.28 ((!! @ a @ (^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK3 @ sK12 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y2 @ Y3) & (Y1 @ Y2)) => (Y1 @ Y3))))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & (sK2 @ Y3 @ Y2)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ sK12 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK3 @ sK12 @ Y2) | (sK2 @ sK12 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((((sK2 @ Y3 @ Y2) | (sK3 @ Y3 @ Y2)) & (Y1 @ Y3)) => (Y1 @ Y2))))))) => (Y1 @ Y0))))))) = $false) | ~spl0_4),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f238])).
% 1.35/1.28 thf(f238,plain,(
% 1.35/1.28 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK3 @ Y0 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y3 @ Y4) & (Y2 @ Y3)) => (Y2 @ Y4))))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & (sK2 @ Y4 @ Y3)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK3 @ Y0 @ Y3) | (sK2 @ Y0 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((((sK2 @ Y4 @ Y3) | (sK3 @ Y4 @ Y3)) & (Y2 @ Y4)) => (Y2 @ Y3))))))) => (Y2 @ Y1)))))))) @ sK12)) | ~spl0_4),
% 1.35/1.28 inference(sigma_clausification,[status(thm)],[f47])).
% 1.35/1.28 thf(f358,plain,(
% 1.35/1.28 ( ! [X1 : a > $o] : (($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((X1 @ Y1) & (sK2 @ Y1 @ Y0)) => (X1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ sK12 @ Y0) => (X1 @ Y0))))) => (X1 @ sK13)))) ) | ~spl0_7),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f357])).
% 1.35/1.28 thf(f357,plain,(
% 1.35/1.28 ( ! [X1 : a > $o] : (($true = ((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK12 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK13))) @ X1))) ) | ~spl0_7),
% 1.35/1.28 inference(pi_clausification,[status(thm)],[f332])).
% 1.35/1.28 thf(f336,plain,(
% 1.35/1.28 spl0_7 | spl0_8 | ~spl0_4),
% 1.35/1.28 inference(avatar_split_clause,[status(thm)],[f329,f46,f334,f331])).
% 1.35/1.28 thf(f329,plain,(
% 1.35/1.28 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK12 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK13)))) = $true) | ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK3 @ sK12 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) & (Y0 @ Y1)) => (Y0 @ Y2))))))) => (Y0 @ sK13))))) | ~spl0_4),
% 1.35/1.28 inference(binary_proxy_clausification,[status(thm)],[f275])).
% 1.35/1.28 thf(f233,plain,(
% 1.35/1.28 spl0_5 | spl0_6 | ~spl0_3),
% 1.35/1.28 inference(avatar_split_clause,[status(thm)],[f224,f43,f231,f228])).
% 1.35/1.28 thf(f224,plain,(
% 1.35/1.28 ((sK3 @ sK7 @ sK11) = $true) | ($true = (sK2 @ sK7 @ sK11)) | ~spl0_3),
% 1.35/1.28 inference(binary_proxy_clausification,[status(thm)],[f206])).
% 1.35/1.28 thf(f206,plain,(
% 1.35/1.28 ($true = ((sK3 @ sK7 @ sK11) | (sK2 @ sK7 @ sK11))) | ~spl0_3),
% 1.35/1.28 inference(binary_proxy_clausification,[status(thm)],[f204])).
% 1.35/1.28 thf(f204,plain,(
% 1.35/1.28 ((((sK3 @ sK7 @ sK11) | (sK2 @ sK7 @ sK11)) => (sK10 @ sK11)) = $false) | ~spl0_3),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f200])).
% 1.35/1.28 thf(f200,plain,(
% 1.35/1.28 (((^[Y0 : a]: (((sK3 @ sK7 @ Y0) | (sK2 @ sK7 @ Y0)) => (sK10 @ Y0))) @ sK11) = $false) | ~spl0_3),
% 1.35/1.28 inference(sigma_clausification,[status(thm)],[f197])).
% 1.35/1.28 thf(f197,plain,(
% 1.35/1.28 ($false = (!! @ a @ (^[Y0 : a]: (((sK3 @ sK7 @ Y0) | (sK2 @ sK7 @ Y0)) => (sK10 @ Y0))))) | ~spl0_3),
% 1.35/1.28 inference(not_proxy_clausification,[status(thm)],[f148])).
% 1.35/1.28 thf(f148,plain,(
% 1.35/1.28 ((~ (!! @ a @ (^[Y0 : a]: (((sK3 @ sK7 @ Y0) | (sK2 @ sK7 @ Y0)) => (sK10 @ Y0))))) = $true) | ~spl0_3),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f147])).
% 1.35/1.28 thf(f147,plain,(
% 1.35/1.28 ($true = (~ ($true & (!! @ a @ (^[Y0 : a]: (((sK3 @ sK7 @ Y0) | (sK2 @ sK7 @ Y0)) => (sK10 @ Y0))))))) | ~spl0_3),
% 1.35/1.28 inference(forward_demodulation,[status(thm)],[f146,f90])).
% 1.35/1.28 thf(f90,plain,(
% 1.35/1.28 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((sK3 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1))) => (sK10 @ Y1)))))) = $true) | ~spl0_3),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f89])).
% 1.35/1.28 thf(f89,plain,(
% 1.35/1.28 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((sK3 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1))) => (sK10 @ Y1)))))) & $true) = $true) | ~spl0_3),
% 1.35/1.28 inference(backward_demodulation,[status(thm)],[f82,f87])).
% 1.35/1.28 thf(f87,plain,(
% 1.35/1.28 ((!! @ a @ (^[Y0 : a]: (((sK3 @ sK9 @ Y0) | (sK2 @ sK9 @ Y0)) => (sK10 @ Y0)))) = $true) | ~spl0_3),
% 1.35/1.28 inference(binary_proxy_clausification,[status(thm)],[f82])).
% 1.35/1.28 thf(f82,plain,(
% 1.35/1.28 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((sK3 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1))) => (sK10 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (((sK3 @ sK9 @ Y0) | (sK2 @ sK9 @ Y0)) => (sK10 @ Y0)))))) | ~spl0_3),
% 1.35/1.28 inference(binary_proxy_clausification,[status(thm)],[f74])).
% 1.35/1.28 thf(f74,plain,(
% 1.35/1.28 ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((sK3 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1))) => (sK10 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (((sK3 @ sK9 @ Y0) | (sK2 @ sK9 @ Y0)) => (sK10 @ Y0))))) => (sK10 @ sK8))) | ~spl0_3),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f73])).
% 1.35/1.28 thf(f73,plain,(
% 1.35/1.28 (((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK3 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2))) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK3 @ sK9 @ Y1) | (sK2 @ sK9 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK8))) @ sK10) = $false) | ~spl0_3),
% 1.35/1.28 inference(sigma_clausification,[status(thm)],[f69])).
% 1.35/1.28 thf(f69,plain,(
% 1.35/1.28 ($false = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK3 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2))) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK3 @ sK9 @ Y1) | (sK2 @ sK9 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK8))))) | ~spl0_3),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f68])).
% 1.35/1.28 thf(f68,plain,(
% 1.35/1.28 (($true => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK3 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2))) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK3 @ sK9 @ Y1) | (sK2 @ sK9 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK8))))) = $false) | ~spl0_3),
% 1.35/1.28 inference(backward_demodulation,[status(thm)],[f62,f67])).
% 1.35/1.28 thf(f67,plain,(
% 1.35/1.28 ($true = ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK3 @ sK9 @ Y1) | (sK2 @ sK9 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK2 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK7)))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK3 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2))) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK3 @ sK7 @ Y1) | (sK2 @ sK7 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK8)))))) | ~spl0_3),
% 1.35/1.28 inference(binary_proxy_clausification,[status(thm)],[f62])).
% 1.35/1.28 thf(f62,plain,(
% 1.35/1.28 ((((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK3 @ sK9 @ Y1) | (sK2 @ sK9 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK2 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK7)))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK3 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2))) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK3 @ sK7 @ Y1) | (sK2 @ sK7 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK8))))) => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK3 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2))) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK3 @ sK9 @ Y1) | (sK2 @ sK9 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK8))))) = $false) | ~spl0_3),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f61])).
% 1.35/1.28 thf(f61,plain,(
% 1.35/1.28 (((^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK3 @ Y0 @ Y2) | (sK2 @ Y0 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((sK2 @ Y2 @ Y3) | (sK3 @ Y2 @ Y3))) => (Y1 @ Y3))))))) => (Y1 @ sK7)))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((sK3 @ Y2 @ Y3) | (sK2 @ Y2 @ Y3))) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (((sK3 @ sK7 @ Y2) | (sK2 @ sK7 @ Y2)) => (Y1 @ Y2))))) => (Y1 @ sK8))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((sK3 @ Y2 @ Y3) | (sK2 @ Y2 @ Y3))) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (((sK3 @ Y0 @ Y2) | (sK2 @ Y0 @ Y2)) => (Y1 @ Y2))))) => (Y1 @ sK8)))))) @ sK9) = $false) | ~spl0_3),
% 1.35/1.28 inference(sigma_clausification,[status(thm)],[f58])).
% 1.35/1.28 thf(f58,plain,(
% 1.35/1.28 ((!! @ a @ (^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK3 @ Y0 @ Y2) | (sK2 @ Y0 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((sK2 @ Y2 @ Y3) | (sK3 @ Y2 @ Y3))) => (Y1 @ Y3))))))) => (Y1 @ sK7)))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((sK3 @ Y2 @ Y3) | (sK2 @ Y2 @ Y3))) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (((sK3 @ sK7 @ Y2) | (sK2 @ sK7 @ Y2)) => (Y1 @ Y2))))) => (Y1 @ sK8))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((sK3 @ Y2 @ Y3) | (sK2 @ Y2 @ Y3))) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (((sK3 @ Y0 @ Y2) | (sK2 @ Y0 @ Y2)) => (Y1 @ Y2))))) => (Y1 @ sK8))))))) = $false) | ~spl0_3),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f57])).
% 1.35/1.28 thf(f57,plain,(
% 1.35/1.28 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK3 @ Y1 @ Y3) | (sK2 @ Y1 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK2 @ Y3 @ Y4) | (sK3 @ Y3 @ Y4))) => (Y2 @ Y4))))))) => (Y2 @ sK7)))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK3 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4))) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (((sK3 @ sK7 @ Y3) | (sK2 @ sK7 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ Y0))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK3 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4))) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (((sK3 @ Y1 @ Y3) | (sK2 @ Y1 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ Y0)))))))) @ sK8) = $false) | ~spl0_3),
% 1.35/1.28 inference(sigma_clausification,[status(thm)],[f52])).
% 1.35/1.28 thf(f52,plain,(
% 1.35/1.28 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK3 @ Y1 @ Y3) | (sK2 @ Y1 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK2 @ Y3 @ Y4) | (sK3 @ Y3 @ Y4))) => (Y2 @ Y4))))))) => (Y2 @ sK7)))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK3 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4))) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (((sK3 @ sK7 @ Y3) | (sK2 @ sK7 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ Y0))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK3 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4))) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (((sK3 @ Y1 @ Y3) | (sK2 @ Y1 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ Y0))))))))) = $false) | ~spl0_3),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f51])).
% 1.35/1.28 thf(f51,plain,(
% 1.35/1.28 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK3 @ Y2 @ Y4) | (sK2 @ Y2 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK2 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y0)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK3 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5))) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y0 @ Y4) | (sK2 @ Y0 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y1))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK3 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5))) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y2 @ Y4) | (sK2 @ Y2 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y1)))))))))) @ sK7) = $false) | ~spl0_3),
% 1.35/1.28 inference(sigma_clausification,[status(thm)],[f44])).
% 1.35/1.28 thf(f146,plain,(
% 1.35/1.28 ((~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((sK3 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1))) => (sK10 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (((sK3 @ sK7 @ Y0) | (sK2 @ sK7 @ Y0)) => (sK10 @ Y0)))))) = $true) | ~spl0_3),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f143])).
% 1.35/1.28 thf(f143,plain,(
% 1.35/1.28 ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK10 @ Y0) & ((sK3 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1))) => (sK10 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (((sK3 @ sK7 @ Y0) | (sK2 @ sK7 @ Y0)) => (sK10 @ Y0))))) => $false)) | ~spl0_3),
% 1.35/1.28 inference(superposition,[status(thm)],[f132,f81])).
% 1.35/1.28 thf(f81,plain,(
% 1.35/1.28 ($false = (sK10 @ sK8)) | ~spl0_3),
% 1.35/1.28 inference(binary_proxy_clausification,[status(thm)],[f74])).
% 1.35/1.28 thf(f132,plain,(
% 1.35/1.28 ( ! [X1 : a > $o] : (($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((X1 @ Y0) & ((sK3 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1))) => (X1 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (((sK3 @ sK7 @ Y0) | (sK2 @ sK7 @ Y0)) => (X1 @ Y0))))) => (X1 @ sK8)))) ) | ~spl0_3),
% 1.35/1.28 inference(beta_eta_normalization,[status(thm)],[f131])).
% 1.35/1.28 thf(f131,plain,(
% 1.35/1.28 ( ! [X1 : a > $o] : ((((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK3 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2))) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK3 @ sK7 @ Y1) | (sK2 @ sK7 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK8))) @ X1) = $true)) ) | ~spl0_3),
% 1.35/1.28 inference(pi_clausification,[status(thm)],[f127])).
% 1.35/1.28 thf(f127,plain,(
% 1.35/1.28 ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK3 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2))) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK3 @ sK7 @ Y1) | (sK2 @ sK7 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK8))))) | ~spl0_3),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f126])).
% 1.35/1.28 thf(f126,plain,(
% 1.35/1.28 ($true = ($true & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK3 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2))) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK3 @ sK7 @ Y1) | (sK2 @ sK7 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK8)))))) | ~spl0_3),
% 1.35/1.28 inference(backward_demodulation,[status(thm)],[f67,f125])).
% 1.35/1.28 thf(f125,plain,(
% 1.35/1.28 ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK3 @ sK9 @ Y1) | (sK2 @ sK9 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK2 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK7))))) | ~spl0_3),
% 1.35/1.28 inference(binary_proxy_clausification,[status(thm)],[f67])).
% 1.35/1.28 thf(f48,plain,(
% 1.35/1.28 spl0_3 | spl0_4 | ~spl0_2),
% 1.35/1.28 inference(avatar_split_clause,[status(thm)],[f41,f32,f46,f43])).
% 1.35/1.28 thf(f32,definition,(
% 1.35/1.28 spl0_2 <=> (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK3 @ Y0 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y3 @ Y4) & (Y2 @ Y3)) => (Y2 @ Y4))))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & (sK2 @ Y4 @ Y3)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK3 @ Y0 @ Y3) | (sK2 @ Y0 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((((sK2 @ Y4 @ Y3) | (sK3 @ Y4 @ Y3)) & (Y2 @ Y4)) => (Y2 @ Y3))))))) => (Y2 @ Y1))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK3 @ Y2 @ Y4) | (sK2 @ Y2 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK2 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y0)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK3 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5))) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y0 @ Y4) | (sK2 @ Y0 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y1))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK3 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5))) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y2 @ Y4) | (sK2 @ Y2 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y1)))))))))))) = $false)),
% 1.35/1.28 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.35/1.28 thf(f41,plain,(
% 1.35/1.28 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK3 @ Y0 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y3 @ Y4) & (Y2 @ Y3)) => (Y2 @ Y4))))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & (sK2 @ Y4 @ Y3)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK3 @ Y0 @ Y3) | (sK2 @ Y0 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((((sK2 @ Y4 @ Y3) | (sK3 @ Y4 @ Y3)) & (Y2 @ Y4)) => (Y2 @ Y3))))))) => (Y2 @ Y1))))))))) = $false) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK3 @ Y2 @ Y4) | (sK2 @ Y2 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK2 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y0)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK3 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5))) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y0 @ Y4) | (sK2 @ Y0 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y1))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK3 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5))) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y2 @ Y4) | (sK2 @ Y2 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y1))))))))))) = $false) | ~spl0_2),
% 1.35/1.28 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.35/1.28 thf(f33,plain,(
% 1.35/1.28 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK3 @ Y0 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y3 @ Y4) & (Y2 @ Y3)) => (Y2 @ Y4))))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & (sK2 @ Y4 @ Y3)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK3 @ Y0 @ Y3) | (sK2 @ Y0 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((((sK2 @ Y4 @ Y3) | (sK3 @ Y4 @ Y3)) & (Y2 @ Y4)) => (Y2 @ Y3))))))) => (Y2 @ Y1))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK3 @ Y2 @ Y4) | (sK2 @ Y2 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK2 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y0)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK3 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5))) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y0 @ Y4) | (sK2 @ Y0 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y1))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK3 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5))) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y2 @ Y4) | (sK2 @ Y2 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y1)))))))))))) = $false) | ~spl0_2),
% 1.35/1.28 inference(avatar_component_clause,[status(thm)],[f32])).
% 1.35/1.28 thf(f34,plain,(
% 1.35/1.28 spl0_1 | spl0_2),
% 1.35/1.28 inference(avatar_split_clause,[status(thm)],[f27,f32,f29])).
% 1.35/1.28 thf(f27,plain,(
% 1.35/1.28 ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK2 @ sK5 @ Y1) | (sK3 @ sK5 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK2 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1))) => (Y0 @ Y1))))))) => (Y0 @ sK4))))) | (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK3 @ Y0 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y3 @ Y4) & (Y2 @ Y3)) => (Y2 @ Y4))))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & (sK2 @ Y4 @ Y3)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK3 @ Y0 @ Y3) | (sK2 @ Y0 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((((sK2 @ Y4 @ Y3) | (sK3 @ Y4 @ Y3)) & (Y2 @ Y4)) => (Y2 @ Y3))))))) => (Y2 @ Y1))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK3 @ Y2 @ Y4) | (sK2 @ Y2 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK2 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y0)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK3 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5))) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y0 @ Y4) | (sK2 @ Y0 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y1))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK3 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5))) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y2 @ Y4) | (sK2 @ Y2 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y1)))))))))))) = $false)),
% 1.35/1.28 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 1.35/1.28 thf(f22,plain,(
% 1.35/1.28 ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK3 @ Y0 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y3 @ Y4) & (Y2 @ Y3)) => (Y2 @ Y4))))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & (sK2 @ Y4 @ Y3)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK3 @ Y0 @ Y3) | (sK2 @ Y0 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((((sK2 @ Y4 @ Y3) | (sK3 @ Y4 @ Y3)) & (Y2 @ Y4)) => (Y2 @ Y3))))))) => (Y2 @ Y1))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK3 @ Y2 @ Y4) | (sK2 @ Y2 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK2 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y0)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK3 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5))) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y0 @ Y4) | (sK2 @ Y0 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y1))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK3 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5))) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y2 @ Y4) | (sK2 @ Y2 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y1)))))))))))) => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK2 @ sK5 @ Y1) | (sK3 @ sK5 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK2 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1))) => (Y0 @ Y1))))))) => (Y0 @ sK4))))))),
% 1.35/1.28 inference(not_proxy_clausification,[status(thm)],[f21])).
% 1.35/1.28 thf(f21,plain,(
% 1.35/1.28 ((~ (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK3 @ Y0 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y3 @ Y4) & (Y2 @ Y3)) => (Y2 @ Y4))))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & (sK2 @ Y4 @ Y3)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK3 @ Y0 @ Y3) | (sK2 @ Y0 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((((sK2 @ Y4 @ Y3) | (sK3 @ Y4 @ Y3)) & (Y2 @ Y4)) => (Y2 @ Y3))))))) => (Y2 @ Y1))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK3 @ Y2 @ Y4) | (sK2 @ Y2 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK2 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y0)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK3 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5))) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y0 @ Y4) | (sK2 @ Y0 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y1))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK3 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5))) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y2 @ Y4) | (sK2 @ Y2 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y1)))))))))))) => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK2 @ sK5 @ Y1) | (sK3 @ sK5 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK2 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1))) => (Y0 @ Y1))))))) => (Y0 @ sK4)))))) = $false)),
% 1.35/1.28 inference(boolean_simplification,[status(thm)],[f20])).
% 1.35/1.28 thf(f20,plain,(
% 1.35/1.28 (($false | (~ (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK3 @ Y0 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y3 @ Y4) & (Y2 @ Y3)) => (Y2 @ Y4))))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & (sK2 @ Y4 @ Y3)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK3 @ Y0 @ Y3) | (sK2 @ Y0 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((((sK2 @ Y4 @ Y3) | (sK3 @ Y4 @ Y3)) & (Y2 @ Y4)) => (Y2 @ Y3))))))) => (Y2 @ Y1))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK3 @ Y2 @ Y4) | (sK2 @ Y2 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK2 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y0)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK3 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5))) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y0 @ Y4) | (sK2 @ Y0 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y1))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK3 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5))) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (((sK3 @ Y2 @ Y4) | (sK2 @ Y2 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y1)))))))))))) => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK2 @ sK5 @ Y1) | (sK3 @ sK5 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK2 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1))) => (Y0 @ Y1))))))) => (Y0 @ sK4))))))) = $false)),
% 1.35/1.28 inference(backward_demodulation,[status(thm)],[f17,f19])).
% 1.35/1.28 % SZS output end Proof for DTF2THF_13164
% 1.35/1.28 % (13346)------------------------------
% 1.35/1.28 % (13346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.35/1.28 % (13346)Termination reason: Refutation
% 1.35/1.28
% 1.35/1.28 % (13346)Memory used [KB]: 7036
% 1.35/1.28 % (13346)Time elapsed: 0.124 s
% 1.35/1.28 % (13346)Instructions burned: 345 (million)
% 1.35/1.28 % (13346)------------------------------
% 1.35/1.28 % (13346)------------------------------
% 1.35/1.28 % (13326)Success in time 0.141 s
%------------------------------------------------------------------------------