%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV146^5 : 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 : n015.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 09:40:23 AM UTC 2026
% Result : Theorem 1.59s 1.41s
% Output : Refutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 6
% Syntax : Number of formulae : 111 ( 7 unt; 0 typ; 5 def)
% Number of atoms : 1131 ( 101 equ; 0 cnn)
% Maximal formula atoms : 4 ( 10 avg)
% Number of connectives : 3461 ( 111 ~; 109 |; 287 &;2053 @)
% ( 5 <=>; 416 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 213 ( 213 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 21 usr; 20 con; 0-2 aty)
% ( 480 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 588 ( 502 ^; 86 !; 0 ?; 588 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_17,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
sK2: a > a > $o ).
thf(func_def_19,type,
sK3: a ).
thf(func_def_20,type,
sK4: a ).
thf(func_def_21,type,
sK5: a ).
thf(func_def_22,type,
sK6: a > $o ).
thf(func_def_23,type,
sK7: a ).
thf(func_def_24,type,
sK8: a ).
thf(func_def_25,type,
sK9: a ).
thf(func_def_26,type,
sK10: a ).
thf(func_def_27,type,
sK11: a > $o ).
thf(func_def_28,type,
sK12: a ).
thf(func_def_29,type,
sK13: a ).
thf(func_def_30,type,
sK14: a ).
thf(func_def_31,type,
sK15: a ).
thf(func_def_32,type,
sK16: a ).
thf(f475,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f19,f90,f169,f213,f443,f472]) ).
thf(f472,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f471]) ).
thf(f471,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f467]) ).
thf(f467,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7 ),
inference(superposition,[status(thm)],[f455,f316]) ).
thf(f316,plain,
( ! [X0: a] :
( $true
= ( ( sK2 @ sK4 @ X0 )
=> ( sK6 @ X0 ) ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f304]) ).
thf(f304,plain,
( ! [X0: a] :
( ( ( $true
& ( sK2 @ sK4 @ X0 ) )
=> ( sK6 @ X0 ) )
= $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f292,f86]) ).
thf(f86,plain,
( ( ( sK6 @ sK4 )
= $true )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f85]) ).
thf(f85,definition,
( spl0_3
<=> ( ( sK6 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f292,plain,
( ! [X2: a,X1: a] :
( ( ( ( sK6 @ X1 )
& ( sK2 @ X1 @ X2 ) )
=> ( sK6 @ X2 ) )
= $true )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f291]) ).
thf(f291,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK6 @ X1 )
& ( sK2 @ X1 @ Y0 ) )
=> ( sK6 @ Y0 ) )
@ X2 )
= $true )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f287]) ).
thf(f287,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ X1 )
& ( sK2 @ X1 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
= $true )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f286]) ).
thf(f286,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( sK2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y1 ) ) )
@ X1 )
= $true )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f248]) ).
thf(f248,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( sK2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y1 ) ) ) )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f245]) ).
thf(f245,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK3 @ Y0 )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( sK2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y1 ) ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f243]) ).
thf(f243,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK3 @ Y0 )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( sK2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y1 ) ) ) ) )
=> ( sK6 @ sK5 ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f242]) ).
thf(f242,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK5 ) )
@ sK6 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f233]) ).
thf(f233,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK5 ) ) )
= $false )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f232]) ).
thf(f232,plain,
( ( ( $true
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK5 ) ) ) )
= $false )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f227,f231]) ).
thf(f231,plain,
( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK5 ) ) ) )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f227]) ).
thf(f227,plain,
( ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK5 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK5 ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f226]) ).
thf(f226,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK3 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ sK4 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK3 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
@ sK5 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f223]) ).
thf(f223,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK3 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ sK4 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK3 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f222]) ).
thf(f222,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ sK3 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ sK3 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
@ sK4 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f217]) ).
thf(f217,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ sK3 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ sK3 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f216]) ).
thf(f216,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) )
@ sK3 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f17]) ).
thf(f17,definition,
( spl0_2
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f455,plain,
( ( ( ( sK2 @ sK4 @ sK16 )
=> ( sK6 @ sK16 ) )
= $false )
| ~ spl0_7 ),
inference(beta_eta_normalization,[status(thm)],[f453]) ).
thf(f453,plain,
( ( ( ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) )
@ sK16 )
= $false )
| ~ spl0_7 ),
inference(sigma_clausification,[status(thm)],[f442]) ).
thf(f442,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) )
= $false )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f441]) ).
thf(f441,definition,
( spl0_7
<=> ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f443,plain,
( spl0_4
| spl0_7
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f437,f17,f441,f88]) ).
thf(f88,definition,
( spl0_4
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f437,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) )
= $false )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f427]) ).
thf(f427,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(not_proxy_clausification,[status(thm)],[f339]) ).
thf(f339,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) ) ) )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f336]) ).
thf(f336,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) ) )
=> $false )
= $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f328,f247]) ).
thf(f247,plain,
( ( ( sK6 @ sK5 )
= $false )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f246]) ).
thf(f246,plain,
( ( ( $true
=> ( sK6 @ sK5 ) )
= $false )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f243,f245]) ).
thf(f328,plain,
( ! [X1: a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( X1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( X1 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( X1 @ Y0 ) ) ) ) )
=> ( X1 @ sK5 ) )
= $true )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f327]) ).
thf(f327,plain,
( ! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK5 ) )
@ X1 )
= $true )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f263]) ).
thf(f263,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK5 ) ) )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f231]) ).
thf(f213,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f212]) ).
thf(f212,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f211]) ).
thf(f211,plain,
( ( $true = $false )
| ~ spl0_1 ),
inference(forward_demodulation,[status(thm)],[f205,f190]) ).
thf(f190,plain,
( ( ( sK11 @ sK9 )
= $false )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f189]) ).
thf(f189,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK11 @ Y0 )
& ( sK2 @ Y0 @ Y1 ) )
=> ( sK11 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK10 @ Y0 )
=> ( sK11 @ Y0 ) ) ) )
=> ( sK11 @ sK9 ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f188]) ).
thf(f188,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK10 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) )
@ sK11 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f187]) ).
thf(f187,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK10 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) )
= $false )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f186]) ).
thf(f186,plain,
( ( ( $true
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK10 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) ) )
= $false )
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f183,f185]) ).
thf(f185,plain,
( ( ( sK2 @ sK10 @ sK9 )
= $true )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f183]) ).
thf(f183,plain,
( ( ( ( sK2 @ sK10 @ sK9 )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK10 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f182]) ).
thf(f182,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK2 @ Y0 @ sK9 )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK9 ) ) ) )
@ sK10 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f177]) ).
thf(f177,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ sK9 )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK9 ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f176]) ).
thf(f176,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) )
@ sK9 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f14]) ).
thf(f14,definition,
( spl0_1
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f205,plain,
( ( ( sK11 @ sK9 )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f204]) ).
thf(f204,plain,
( ( ( $true
=> ( sK11 @ sK9 ) )
= $true )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f201,f185]) ).
thf(f201,plain,
( ! [X1: a] :
( $true
= ( ( sK2 @ sK10 @ X1 )
=> ( sK11 @ X1 ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f200]) ).
thf(f200,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( ( sK2 @ sK10 @ Y0 )
=> ( sK11 @ Y0 ) )
@ X1 )
= $true )
| ~ spl0_1 ),
inference(pi_clausification,[status(thm)],[f199]) ).
thf(f199,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK10 @ Y0 )
=> ( sK11 @ Y0 ) ) )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f198]) ).
thf(f198,plain,
( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK10 @ Y0 )
=> ( sK11 @ Y0 ) ) ) )
= $true )
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f191,f197]) ).
thf(f197,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK11 @ Y0 )
& ( sK2 @ Y0 @ Y1 ) )
=> ( sK11 @ Y1 ) ) ) )
= $true )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f191]) ).
thf(f191,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK11 @ Y0 )
& ( sK2 @ Y0 @ Y1 ) )
=> ( sK11 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK10 @ Y0 )
=> ( sK11 @ Y0 ) ) ) )
= $true )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f189]) ).
thf(f169,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f168]) ).
thf(f168,plain,
( $false
| ~ spl0_2
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f164]) ).
thf(f164,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f161,f64]) ).
thf(f64,plain,
( ! [X2: a,X1: a] :
( ( ( ( sK6 @ X1 )
& ( sK2 @ X1 @ X2 ) )
=> ( sK6 @ X2 ) )
= $true )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f63]) ).
thf(f63,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK6 @ X1 )
& ( sK2 @ X1 @ Y0 ) )
=> ( sK6 @ Y0 ) )
@ X2 )
= $true )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ X1 )
& ( sK2 @ X1 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
= $true )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f58]) ).
thf(f58,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( sK2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y1 ) ) )
@ X1 )
= $true )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( sK2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y1 ) ) ) )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK3 @ Y0 )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( sK2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y1 ) ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK3 @ Y0 )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 )
& ( sK2 @ Y0 @ Y1 ) )
=> ( sK6 @ Y1 ) ) ) ) )
=> ( sK6 @ sK5 ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f32]) ).
thf(f32,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK5 ) )
@ sK6 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK5 ) ) )
= $false )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ( $true
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK5 ) ) ) )
= $false )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f27,f29]) ).
thf(f29,plain,
( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK5 ) ) ) )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK5 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK5 ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK3 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ sK4 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK3 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
@ sK5 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK3 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ sK4 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK3 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ sK3 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ sK3 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
@ sK4 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ sK3 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ sK3 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) )
@ sK3 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f18]) ).
thf(f161,plain,
( ( $false
= ( ( ( sK6 @ sK8 )
& ( sK2 @ sK8 @ sK7 ) )
=> ( sK6 @ sK7 ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f160]) ).
thf(f160,plain,
( ( ( ^ [Y0: a] :
( ( ( sK6 @ Y0 )
& ( sK2 @ Y0 @ sK7 ) )
=> ( sK6 @ sK7 ) )
@ sK8 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f159]) ).
thf(f159,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ Y0 )
& ( sK2 @ Y0 @ sK7 ) )
=> ( sK6 @ sK7 ) ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f152]) ).
thf(f152,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
@ sK7 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f89]) ).
thf(f89,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) )
= $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f88]) ).
thf(f90,plain,
( spl0_3
| spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f83,f17,f88,f85]) ).
thf(f83,plain,
( ( ( sK6 @ sK4 )
= $true )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) )
= $false )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f62]) ).
thf(f62,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) )
=> ( sK6 @ sK4 ) )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f61]) ).
thf(f61,plain,
( ( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) ) )
=> ( sK6 @ sK4 ) )
= $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f57,f41]) ).
thf(f41,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK3 @ Y0 )
=> ( sK6 @ Y0 ) ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK3 @ Y0 )
=> ( sK6 @ Y0 ) ) )
& $true )
= $true )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f35,f38]) ).
thf(f57,plain,
( ! [X1: a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK3 @ Y0 )
=> ( X1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( X1 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( X1 @ Y0 ) ) ) ) )
=> ( X1 @ sK4 ) )
= $true )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f56]) ).
thf(f56,plain,
( ! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 ) )
@ X1 )
= $true )
| ~ spl0_2 ),
inference(pi_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 ) ) )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f52]) ).
thf(f52,plain,
( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 ) ) )
& $true )
= $true )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f29,f50]) ).
thf(f50,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK5 ) ) )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f29]) ).
thf(f19,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f12,f17,f14]) ).
thf(f12,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: a > a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y1 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y1 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y1 )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( Y0 @ Y4 @ Y5 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y1 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y1 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y1 )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( Y0 @ Y4 @ Y5 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y1 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y1 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y1 )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( Y0 @ Y4 @ Y5 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y1 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y1 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y5 )
& ( Y0 @ Y5 @ Y6 ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y1 )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( Y0 @ Y4 @ Y5 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > a > $o] :
( ! [X1: a,X2: a] :
( ( X0 @ X1 @ X2 )
=> ! [X3: a > $o] :
( ( ! [X4: a] :
( ( X0 @ X1 @ X4 )
=> ( X3 @ X4 ) )
& ! [X5: a,X6: a] :
( ( ( X0 @ X6 @ X5 )
& ( X3 @ X6 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) )
& ! [X7: a,X8: a,X9: a] :
( ( ! [X10: a > $o] :
( ( ! [X11: a,X12: a] :
( ( ( X0 @ X11 @ X12 )
& ( X10 @ X11 ) )
=> ( X10 @ X12 ) )
& ! [X13: a] :
( ( X0 @ X8 @ X13 )
=> ( X10 @ X13 ) ) )
=> ( X10 @ X7 ) )
& ! [X14: a > $o] :
( ( ! [X15: a,X16: a] :
( ( ( X0 @ X15 @ X16 )
& ( X14 @ X15 ) )
=> ( X14 @ X16 ) )
& ! [X17: a] :
( ( X0 @ X9 @ X17 )
=> ( X14 @ X17 ) ) )
=> ( X14 @ X8 ) ) )
=> ! [X18: a > $o] :
( ( ! [X19: a,X20: a] :
( ( ( X0 @ X20 @ X19 )
& ( X18 @ X20 ) )
=> ( X18 @ X19 ) )
& ! [X21: a] :
( ( X0 @ X9 @ X21 )
=> ( X18 @ X21 ) ) )
=> ( X18 @ X7 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > a > $o] :
( ! [X1: a,X2: a] :
( ( X0 @ X1 @ X2 )
=> ! [X3: a > $o] :
( ( ! [X4: a] :
( ( X0 @ X1 @ X4 )
=> ( X3 @ X4 ) )
& ! [X4: a,X5: a] :
( ( ( X0 @ X5 @ X4 )
& ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) )
=> ( X3 @ X2 ) ) )
& ! [X6: a,X2: a,X1: a] :
( ( ! [X3: a > $o] :
( ( ! [X5: a,X4: a] :
( ( ( X0 @ X5 @ X4 )
& ( X3 @ X5 ) )
=> ( X3 @ X4 ) )
& ! [X4: a] :
( ( X0 @ X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ( X3 @ X6 ) )
& ! [X3: a > $o] :
( ( ! [X5: a,X4: a] :
( ( ( X0 @ X5 @ X4 )
& ( X3 @ X5 ) )
=> ( X3 @ X4 ) )
& ! [X4: a] :
( ( X0 @ X1 @ X4 )
=> ( X3 @ X4 ) ) )
=> ( X3 @ X2 ) ) )
=> ! [X3: a > $o] :
( ( ! [X4: a,X5: a] :
( ( ( X0 @ X5 @ X4 )
& ( X3 @ X5 ) )
=> ( X3 @ X4 ) )
& ! [X4: a] :
( ( X0 @ X1 @ X4 )
=> ( X3 @ X4 ) ) )
=> ( X3 @ X6 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a > a > $o] :
( ! [X1: a,X2: a] :
( ( X0 @ X1 @ X2 )
=> ! [X3: a > $o] :
( ( ! [X4: a] :
( ( X0 @ X1 @ X4 )
=> ( X3 @ X4 ) )
& ! [X4: a,X5: a] :
( ( ( X0 @ X5 @ X4 )
& ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) )
=> ( X3 @ X2 ) ) )
& ! [X6: a,X2: a,X1: a] :
( ( ! [X3: a > $o] :
( ( ! [X5: a,X4: a] :
( ( ( X0 @ X5 @ X4 )
& ( X3 @ X5 ) )
=> ( X3 @ X4 ) )
& ! [X4: a] :
( ( X0 @ X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ( X3 @ X6 ) )
& ! [X3: a > $o] :
( ( ! [X5: a,X4: a] :
( ( ( X0 @ X5 @ X4 )
& ( X3 @ X5 ) )
=> ( X3 @ X4 ) )
& ! [X4: a] :
( ( X0 @ X1 @ X4 )
=> ( X3 @ X4 ) ) )
=> ( X3 @ X2 ) ) )
=> ! [X3: a > $o] :
( ( ! [X4: a,X5: a] :
( ( ( X0 @ X5 @ X4 )
& ( X3 @ X5 ) )
=> ( X3 @ X4 ) )
& ! [X4: a] :
( ( X0 @ X1 @ X4 )
=> ( X3 @ X4 ) ) )
=> ( X3 @ X6 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.M0ffQNqfuq/DTF2THF_14972.p',cTHM525_pme) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEV146^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.29 % Computer : n015.cluster.edu
% 0.12/0.29 % Model : x86_64 x86_64
% 0.12/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.29 % Memory : 8042.1875MB
% 0.12/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.29 % CPULimit : 300
% 0.12/0.29 % WCLimit : 300
% 0.12/0.29 % DateTime : Tue Feb 24 12:41:01 EST 2026
% 0.12/0.30 % CPUTime :
% 0.12/0.30 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.39 ---- Original DTF file ---
% 0.17/0.39 thf(spec,logic,$$dhol).
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 % File : SEV146^5 : TPTP v9.2.1. Released v4.0.0.
% 0.17/0.39 % Domain : Set Theory (Relations)
% 0.17/0.39 % Problem : TPS problem from TRANSITIVE-CLOSURE
% 0.17/0.39 % Version : Especial.
% 0.17/0.39 % English :
% 0.17/0.39
% 0.17/0.39 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.17/0.39 % Source : [Bro09]
% 0.17/0.39 % Names : tps_1133 [Bro09]
% 0.17/0.39
% 0.17/0.39 % Status : Theorem
% 0.17/0.39 % Rating : 0.00 v8.1.0, 0.08 v7.4.0, 0.00 v7.3.0, 0.10 v7.2.0, 0.00 v6.2.0, 0.17 v6.0.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.1.0, 0.33 v4.0.0
% 0.17/0.39 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.17/0.39 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.17/0.39 % Maximal formula atoms : 0 ( 0 avg)
% 0.17/0.39 % Number of connectives : 58 ( 0 ~; 0 |; 10 &; 34 @)
% 0.17/0.39 % ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% 0.17/0.39 % Maximal formula depth : 17 ( 17 avg)
% 0.17/0.39 % Number of types : 2 ( 1 usr)
% 0.17/0.39 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.17/0.39 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.17/0.39 % Number of variables : 22 ( 0 ^; 22 !; 0 ?; 22 :)
% 0.17/0.39 % SPC : TH0_THM_NEQ_NAR
% 0.17/0.39
% 0.17/0.39 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.17/0.39 % project in the Department of Mathematical Sciences at Carnegie
% 0.17/0.39 % Mellon University. Distributed under the Creative Commons copyleft
% 0.17/0.39 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 thf(a_type,type,
% 0.17/0.39 a: $tType ).
% 0.17/0.39
% 0.17/0.39 thf(cTHM525_pme,conjecture,
% 0.17/0.39 ! [Xr: a > a > $o] :
% 0.17/0.39 ( ! [Xx: a,Xy: a] :
% 0.17/0.39 ( ( Xr @ Xx @ Xy )
% 0.17/0.39 => ! [Xq: a > $o] :
% 0.17/0.39 ( ( ! [Xw: a] :
% 0.17/0.39 ( ( Xr @ Xx @ Xw )
% 0.17/0.39 => ( Xq @ Xw ) )
% 0.17/0.39 & ! [Xv: a,Xw: a] :
% 0.17/0.39 ( ( ( Xq @ Xv )
% 0.17/0.39 & ( Xr @ Xv @ Xw ) )
% 0.17/0.39 => ( Xq @ Xw ) ) )
% 0.17/0.39 => ( Xq @ Xy ) ) )
% 0.17/0.39 & ! [Xx: a,Xy: a,Xz: a] :
% 0.17/0.39 ( ( ! [Xq: a > $o] :
% 0.17/0.39 ( ( ! [Xw: a] :
% 0.17/0.39 ( ( Xr @ Xx @ Xw )
% 0.17/0.39 => ( Xq @ Xw ) )
% 0.17/0.39 & ! [Xv: a,Xw: a] :
% 0.17/0.39 ( ( ( Xq @ Xv )
% 0.17/0.39 & ( Xr @ Xv @ Xw ) )
% 0.17/0.39 => ( Xq @ Xw ) ) )
% 0.17/0.39 => ( Xq @ Xy ) )
% 0.17/0.39 & ! [Xq: a > $o] :
% 0.17/0.39 ( ( ! [Xw: a] :
% 0.17/0.39 ( ( Xr @ Xy @ Xw )
% 0.17/0.39 => ( Xq @ Xw ) )
% 0.17/0.39 & ! [Xv: a,Xw: a] :
% 0.17/0.39 ( ( ( Xq @ Xv )
% 0.17/0.39 & ( Xr @ Xv @ Xw ) )
% 0.17/0.39 => ( Xq @ Xw ) ) )
% 0.17/0.39 => ( Xq @ Xz ) ) )
% 0.17/0.39 => ! [Xq: a > $o] :
% 0.17/0.39 ( ( ! [Xw: a] :
% 0.17/0.39 ( ( Xr @ Xx @ Xw )
% 0.17/0.39 => ( Xq @ Xw ) )
% 0.17/0.39 & ! [Xv: a,Xw: a] :
% 0.17/0.39 ( ( ( Xq @ Xv )
% 0.17/0.39 & ( Xr @ Xv @ Xw ) )
% 0.17/0.39 => ( Xq @ Xw ) ) )
% 0.17/0.39 => ( Xq @ Xz ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 ------------------------
% 1.39/1.29 ---- Embedded in THF ---
% 1.39/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.39/1.29 %%% Generated on Tue Feb 24 12:41:02 EST 2026
% 1.39/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.39/1.29 %%% Logic specification used:
% 1.39/1.29 %%% thf(spec, logic, $$dhol).
% 1.39/1.29
% 1.39/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.M0ffQNqfuq/DTF2DTF14972.p
% See solution above
% 1.39/1.29 ------------------------
% 1.58/1.30 ---- Cleaned THF ---
% 1.58/1.30 thf(a_type,type,
% 1.58/1.30 a: $tType ).
% 1.58/1.30
% 1.58/1.30 thf(cTHM525_pme,conjecture,
% 1.58/1.30 ! [Xr: a > a > $o] :
% 1.58/1.30 ( ! [Xx: a,Xy: a] :
% 1.58/1.30 ( ( Xr @ Xx @ Xy )
% 1.58/1.30 => ! [Xq: a > $o] :
% 1.58/1.30 ( ( ! [Xw: a] :
% 1.58/1.30 ( ( Xr @ Xx @ Xw )
% 1.58/1.30 => ( Xq @ Xw ) )
% 1.58/1.30 & ! [Xv: a,Xw: a] :
% 1.58/1.30 ( ( ( Xq @ Xv )
% 1.58/1.30 & ( Xr @ Xv @ Xw ) )
% 1.58/1.30 => ( Xq @ Xw ) ) )
% 1.58/1.30 => ( Xq @ Xy ) ) )
% 1.58/1.30 & ! [Xx: a,Xy: a,Xz: a] :
% 1.58/1.30 ( ( ! [Xq: a > $o] :
% 1.58/1.30 ( ( ! [Xw: a] :
% 1.58/1.30 ( ( Xr @ Xx @ Xw )
% 1.58/1.30 => ( Xq @ Xw ) )
% 1.58/1.30 & ! [Xv: a,Xw: a] :
% 1.58/1.30 ( ( ( Xq @ Xv )
% 1.58/1.30 & ( Xr @ Xv @ Xw ) )
% 1.58/1.30 => ( Xq @ Xw ) ) )
% 1.58/1.30 => ( Xq @ Xy ) )
% 1.58/1.30 & ! [Xq: a > $o] :
% 1.58/1.30 ( ( ! [Xw: a] :
% 1.58/1.30 ( ( Xr @ Xy @ Xw )
% 1.58/1.30 => ( Xq @ Xw ) )
% 1.58/1.30 & ! [Xv: a,Xw: a] :
% 1.58/1.30 ( ( ( Xq @ Xv )
% 1.58/1.30 & ( Xr @ Xv @ Xw ) )
% 1.58/1.30 => ( Xq @ Xw ) ) )
% 1.58/1.30 => ( Xq @ Xz ) ) )
% 1.58/1.30 => ! [Xq: a > $o] :
% 1.58/1.30 ( ( ! [Xw: a] :
% 1.58/1.30 ( ( Xr @ Xx @ Xw )
% 1.58/1.30 => ( Xq @ Xw ) )
% 1.58/1.30 & ! [Xv: a,Xw: a] :
% 1.58/1.30 ( ( ( Xq @ Xv )
% 1.58/1.30 & ( Xr @ Xv @ Xw ) )
% 1.58/1.30 => ( Xq @ Xw ) ) )
% 1.58/1.30 => ( Xq @ Xz ) ) ) ) ).
% 1.58/1.30 ------------------------
% 1.58/1.32 % (15075)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_14972 for (2999ds/275Mi)
% 1.58/1.32 % (15070)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_14972 for (2999ds/183Mi)
% 1.58/1.32 % (15076)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_14972 for (2999ds/18Mi)
% 1.58/1.32 % (15073)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_14972 for (2999ds/2Mi)
% 1.58/1.32 % (15072)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_14972 for (2999ds/27Mi)
% 1.58/1.32 % (15074)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_14972 for (2999ds/2Mi)
% 1.58/1.32 % (15071)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_14972 for (2999ds/4Mi)
% 1.58/1.32 % (15073)Instruction limit reached!
% 1.58/1.32 % (15073)------------------------------
% 1.58/1.32 % (15073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.32 % (15073)Termination reason: Unknown
% 1.58/1.32 % (15073)Termination phase: Preprocessing 3
% 1.58/1.32 % (15074)Instruction limit reached!
% 1.58/1.32 % (15074)------------------------------
% 1.58/1.32 % (15074)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.32
% 1.58/1.32 % (15073)Memory used [KB]: 1023
% 1.58/1.32 % (15073)Time elapsed: 0.003 s
% 1.58/1.32 % (15073)Instructions burned: 2 (million)
% 1.58/1.32 % (15073)------------------------------
% 1.58/1.32 % (15073)------------------------------
% 1.58/1.32 % (15074)Termination reason: Unknown
% 1.58/1.32 % (15074)Termination phase: Property scanning
% 1.58/1.32
% 1.58/1.32 % (15074)Memory used [KB]: 1023
% 1.58/1.32 % (15074)Time elapsed: 0.003 s
% 1.58/1.32 % (15074)Instructions burned: 3 (million)
% 1.58/1.32 % (15074)------------------------------
% 1.58/1.32 % (15074)------------------------------
% 1.58/1.32 % (15071)Instruction limit reached!
% 1.58/1.32 % (15071)------------------------------
% 1.58/1.32 % (15071)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.32 % (15071)Termination reason: Unknown
% 1.58/1.32 % (15071)Termination phase: Saturation
% 1.58/1.32
% 1.58/1.32 % (15071)Memory used [KB]: 1023
% 1.58/1.32 % (15071)Time elapsed: 0.004 s
% 1.58/1.32 % (15071)Instructions burned: 4 (million)
% 1.58/1.32 % (15071)------------------------------
% 1.58/1.32 % (15071)------------------------------
% 1.58/1.33 % (15076)Instruction limit reached!
% 1.58/1.33 % (15076)------------------------------
% 1.58/1.33 % (15076)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.33 % (15076)Termination reason: Unknown
% 1.58/1.33 % (15076)Termination phase: Saturation
% 1.58/1.33
% 1.58/1.33 % (15076)Memory used [KB]: 5628
% 1.58/1.33 % (15076)Time elapsed: 0.012 s
% 1.58/1.33 % (15076)Instructions burned: 19 (million)
% 1.58/1.33 % (15076)------------------------------
% 1.58/1.33 % (15076)------------------------------
% 1.58/1.34 % (15072)Instruction limit reached!
% 1.58/1.34 % (15072)------------------------------
% 1.58/1.34 % (15072)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.34 % (15072)Termination reason: Unknown
% 1.58/1.34 % (15072)Termination phase: Saturation
% 1.58/1.34
% 1.58/1.34 % (15072)Memory used [KB]: 5756
% 1.58/1.34 % (15072)Time elapsed: 0.017 s
% 1.58/1.34 % (15072)Instructions burned: 28 (million)
% 1.58/1.34 % (15072)------------------------------
% 1.58/1.34 % (15072)------------------------------
% 1.58/1.34 % (15077)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_14972 for (2999ds/3Mi)
% 1.58/1.34 % (15078)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_14972 for (2999ds/37Mi)
% 1.58/1.34 % (15079)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_14972 for (2999ds/15Mi)
% 1.58/1.34 % (15077)Instruction limit reached!
% 1.58/1.34 % (15077)------------------------------
% 1.58/1.34 % (15077)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.34 % (15077)Termination reason: Unknown
% 1.58/1.34 % (15077)Termination phase: Property scanning
% 1.58/1.34
% 1.58/1.34 % (15077)Memory used [KB]: 1023
% 1.58/1.34 % (15077)Time elapsed: 0.003 s
% 1.58/1.34 % (15077)Instructions burned: 3 (million)
% 1.58/1.34 % (15077)------------------------------
% 1.58/1.34 % (15077)------------------------------
% 1.58/1.35 % (15079)Instruction limit reached!
% 1.58/1.35 % (15079)------------------------------
% 1.58/1.35 % (15079)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.35 % (15079)Termination reason: Unknown
% 1.58/1.35 % (15079)Termination phase: Saturation
% 1.58/1.35
% 1.58/1.35 % (15079)Memory used [KB]: 5756
% 1.58/1.35 % (15079)Time elapsed: 0.009 s
% 1.58/1.35 % (15079)Instructions burned: 15 (million)
% 1.58/1.35 % (15079)------------------------------
% 1.58/1.35 % (15079)------------------------------
% 1.58/1.35 % (15080)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_14972 for (2999ds/3Mi)
% 1.58/1.35 % (15080)Instruction limit reached!
% 1.58/1.35 % (15080)------------------------------
% 1.58/1.35 % (15080)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.35 % (15080)Termination reason: Unknown
% 1.58/1.35 % (15080)Termination phase: Property scanning
% 1.58/1.35
% 1.58/1.35 % (15080)Memory used [KB]: 1023
% 1.58/1.35 % (15080)Time elapsed: 0.003 s
% 1.58/1.35 % (15080)Instructions burned: 3 (million)
% 1.58/1.35 % (15080)------------------------------
% 1.58/1.35 % (15080)------------------------------
% 1.58/1.35 % (15081)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_14972 for (2999ds/1041Mi)
% 1.58/1.36 % (15082)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_14972 for (2999ds/7Mi)
% 1.58/1.36 % (15078)Instruction limit reached!
% 1.58/1.36 % (15078)------------------------------
% 1.58/1.36 % (15078)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.36 % (15078)Termination reason: Unknown
% 1.58/1.36 % (15078)Termination phase: Saturation
% 1.58/1.36
% 1.58/1.36 % (15078)Memory used [KB]: 5628
% 1.58/1.36 % (15078)Time elapsed: 0.019 s
% 1.58/1.36 % (15078)Instructions burned: 37 (million)
% 1.58/1.36 % (15078)------------------------------
% 1.58/1.36 % (15078)------------------------------
% 1.58/1.36 % (15082)Instruction limit reached!
% 1.58/1.36 % (15082)------------------------------
% 1.58/1.36 % (15082)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.36 % (15082)Termination reason: Unknown
% 1.58/1.36 % (15082)Termination phase: Saturation
% 1.58/1.36
% 1.58/1.36 % (15082)Memory used [KB]: 1023
% 1.58/1.36 % (15082)Time elapsed: 0.005 s
% 1.58/1.36 % (15082)Instructions burned: 7 (million)
% 1.58/1.36 % (15082)------------------------------
% 1.58/1.36 % (15082)------------------------------
% 1.58/1.36 % (15083)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_14972 for (2999ds/16Mi)
% 1.58/1.36 % (15084)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_14972 for (2999ds/3Mi)
% 1.58/1.37 % (15084)Instruction limit reached!
% 1.58/1.37 % (15084)------------------------------
% 1.58/1.37 % (15084)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.37 % (15084)Termination reason: Unknown
% 1.58/1.37 % (15084)Termination phase: Property scanning
% 1.58/1.37
% 1.58/1.37 % (15084)Memory used [KB]: 1023
% 1.58/1.37 % (15084)Time elapsed: 0.003 s
% 1.58/1.37 % (15084)Instructions burned: 4 (million)
% 1.58/1.37 % (15084)------------------------------
% 1.58/1.37 % (15084)------------------------------
% 1.58/1.37 % (15083)Instruction limit reached!
% 1.58/1.37 % (15083)------------------------------
% 1.58/1.37 % (15083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.37 % (15083)Termination reason: Unknown
% 1.58/1.37 % (15083)Termination phase: Saturation
% 1.58/1.37
% 1.58/1.37 % (15083)Memory used [KB]: 5628
% 1.58/1.37 % (15083)Time elapsed: 0.010 s
% 1.58/1.37 % (15083)Instructions burned: 17 (million)
% 1.58/1.37 % (15083)------------------------------
% 1.58/1.37 % (15083)------------------------------
% 1.58/1.37 % (15085)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_14972 for (2999ds/3Mi)
% 1.58/1.37 % (15085)Instruction limit reached!
% 1.58/1.37 % (15085)------------------------------
% 1.58/1.37 % (15085)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.37 % (15085)Termination reason: Unknown
% 1.58/1.37 % (15085)Termination phase: Property scanning
% 1.58/1.37
% 1.58/1.37 % (15085)Memory used [KB]: 1023
% 1.58/1.37 % (15085)Time elapsed: 0.003 s
% 1.58/1.37 % (15085)Instructions burned: 3 (million)
% 1.58/1.37 % (15085)------------------------------
% 1.58/1.37 % (15085)------------------------------
% 1.58/1.37 % (15086)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_14972 for (2999ds/7Mi)
% 1.58/1.38 % (15086)Instruction limit reached!
% 1.58/1.38 % (15086)------------------------------
% 1.58/1.38 % (15086)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.38 % (15086)Termination reason: Unknown
% 1.58/1.38 % (15086)Termination phase: Saturation
% 1.58/1.38
% 1.58/1.38 % (15086)Memory used [KB]: 5500
% 1.58/1.38 % (15086)Time elapsed: 0.005 s
% 1.58/1.38 % (15086)Instructions burned: 7 (million)
% 1.58/1.38 % (15086)------------------------------
% 1.58/1.38 % (15086)------------------------------
% 1.58/1.38 % (15087)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_14972 for (2999ds/3Mi)
% 1.58/1.38 % (15087)Instruction limit reached!
% 1.58/1.38 % (15087)------------------------------
% 1.58/1.38 % (15087)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.38 % (15087)Termination reason: Unknown
% 1.58/1.38 % (15087)Termination phase: Saturation
% 1.58/1.38
% 1.58/1.38 % (15087)Memory used [KB]: 5500
% 1.58/1.38 % (15087)Time elapsed: 0.003 s
% 1.58/1.38 % (15087)Instructions burned: 4 (million)
% 1.58/1.38 % (15087)------------------------------
% 1.58/1.38 % (15087)------------------------------
% 1.58/1.39 % (15088)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_14972 for (2999ds/4Mi)
% 1.58/1.39 % (15088)Instruction limit reached!
% 1.58/1.39 % (15088)------------------------------
% 1.58/1.39 % (15088)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.39 % (15088)Termination reason: Unknown
% 1.58/1.39 % (15088)Termination phase: Property scanning
% 1.58/1.39
% 1.58/1.39 % (15088)Memory used [KB]: 1023
% 1.58/1.39 % (15088)Time elapsed: 0.003 s
% 1.58/1.39 % (15088)Instructions burned: 4 (million)
% 1.58/1.39 % (15088)------------------------------
% 1.58/1.39 % (15088)------------------------------
% 1.58/1.39 % (15089)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_14972 for (2999ds/18Mi)
% 1.58/1.39 % (15090)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_14972 for (2999ds/710Mi)
% 1.59/1.40 % (15089)Instruction limit reached!
% 1.59/1.40 % (15089)------------------------------
% 1.59/1.40 % (15089)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.40 % (15089)Termination reason: Unknown
% 1.59/1.40 % (15089)Termination phase: Saturation
% 1.59/1.40
% 1.59/1.40 % (15089)Memory used [KB]: 5628
% 1.59/1.40 % (15089)Time elapsed: 0.011 s
% 1.59/1.40 % (15089)Instructions burned: 19 (million)
% 1.59/1.40 % (15089)------------------------------
% 1.59/1.40 % (15089)------------------------------
% 1.59/1.40 % (15091)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_14972 for (2999ds/6Mi)
% 1.59/1.40 % (15081)First to succeed.
% 1.59/1.40 % (15091)Instruction limit reached!
% 1.59/1.40 % (15091)------------------------------
% 1.59/1.40 % (15091)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.40 % (15091)Termination reason: Unknown
% 1.59/1.40 % (15091)Termination phase: Saturation
% 1.59/1.40
% 1.59/1.40 % (15091)Memory used [KB]: 5500
% 1.59/1.40 % (15091)Time elapsed: 0.005 s
% 1.59/1.40 % (15091)Instructions burned: 7 (million)
% 1.59/1.40 % (15091)------------------------------
% 1.59/1.40 % (15091)------------------------------
% 1.59/1.40 % (15092)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_14972 for (2999ds/902Mi)
% 1.59/1.41 % (15081)Refutation found. Thanks to Tanya!
% 1.59/1.41 % SZS status Theorem for DTF2THF_14972
% 1.59/1.41 % SZS output start Proof for DTF2THF_14972
% 1.59/1.41 thf(type_def_5, type, a: $tType).
% 1.59/1.41 thf(func_def_0, type, a: $tType).
% 1.59/1.41 thf(func_def_17, type, ph1: !>[X0: $tType]:(X0)).
% 1.59/1.41 thf(func_def_18, type, sK2: a > a > $o).
% 1.59/1.41 thf(func_def_19, type, sK3: a).
% 1.59/1.41 thf(func_def_20, type, sK4: a).
% 1.59/1.41 thf(func_def_21, type, sK5: a).
% 1.59/1.41 thf(func_def_22, type, sK6: a > $o).
% 1.59/1.41 thf(func_def_23, type, sK7: a).
% 1.59/1.41 thf(func_def_24, type, sK8: a).
% 1.59/1.41 thf(func_def_25, type, sK9: a).
% 1.59/1.41 thf(func_def_26, type, sK10: a).
% 1.59/1.41 thf(func_def_27, type, sK11: a > $o).
% 1.59/1.41 thf(func_def_28, type, sK12: a).
% 1.59/1.41 thf(func_def_29, type, sK13: a).
% 1.59/1.41 thf(func_def_30, type, sK14: a).
% 1.59/1.41 thf(func_def_31, type, sK15: a).
% 1.59/1.41 thf(func_def_32, type, sK16: a).
% 1.59/1.41 thf(f475,plain,(
% 1.59/1.41 $false),
% 1.59/1.41 inference(avatar_sat_refutation,[status(thm)],[f19,f90,f169,f213,f443,f472])).
% 1.59/1.41 thf(f472,plain,(
% 1.59/1.41 ~spl0_2 | ~spl0_3 | ~spl0_7),
% 1.59/1.41 inference(avatar_contradiction_clause,[status(thm)],[f471])).
% 1.59/1.41 thf(f471,plain,(
% 1.59/1.41 $false | (~spl0_2 | ~spl0_3 | ~spl0_7)),
% 1.59/1.41 inference(trivial_inequality_removal,[status(thm)],[f467])).
% 1.59/1.41 thf(f467,plain,(
% 1.59/1.41 ($true = $false) | (~spl0_2 | ~spl0_3 | ~spl0_7)),
% 1.59/1.41 inference(superposition,[status(thm)],[f455,f316])).
% 1.59/1.41 thf(f316,plain,(
% 1.59/1.41 ( ! [X0 : a] : (($true = ((sK2 @ sK4 @ X0) => (sK6 @ X0)))) ) | (~spl0_2 | ~spl0_3)),
% 1.59/1.41 inference(boolean_simplification,[status(thm)],[f304])).
% 1.59/1.41 thf(f304,plain,(
% 1.59/1.41 ( ! [X0 : a] : (((($true & (sK2 @ sK4 @ X0)) => (sK6 @ X0)) = $true)) ) | (~spl0_2 | ~spl0_3)),
% 1.59/1.41 inference(superposition,[status(thm)],[f292,f86])).
% 1.59/1.41 thf(f86,plain,(
% 1.59/1.41 ((sK6 @ sK4) = $true) | ~spl0_3),
% 1.59/1.41 inference(avatar_component_clause,[status(thm)],[f85])).
% 1.59/1.41 thf(f85,definition,(
% 1.59/1.41 spl0_3 <=> ((sK6 @ sK4) = $true)),
% 1.59/1.41 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.59/1.41 thf(f292,plain,(
% 1.59/1.41 ( ! [X2 : a,X1 : a] : (((((sK6 @ X1) & (sK2 @ X1 @ X2)) => (sK6 @ X2)) = $true)) ) | ~spl0_2),
% 1.59/1.41 inference(beta_eta_normalization,[status(thm)],[f291])).
% 1.59/1.41 thf(f291,plain,(
% 1.59/1.41 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: (((sK6 @ X1) & (sK2 @ X1 @ Y0)) => (sK6 @ Y0))) @ X2) = $true)) ) | ~spl0_2),
% 1.59/1.41 inference(pi_clausification,[status(thm)],[f287])).
% 1.59/1.41 thf(f287,plain,(
% 1.59/1.41 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: (((sK6 @ X1) & (sK2 @ X1 @ Y0)) => (sK6 @ Y0)))) = $true)) ) | ~spl0_2),
% 1.59/1.41 inference(beta_eta_normalization,[status(thm)],[f286])).
% 1.59/1.41 thf(f286,plain,(
% 1.59/1.41 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0) & (sK2 @ Y0 @ Y1)) => (sK6 @ Y1))))) @ X1) = $true)) ) | ~spl0_2),
% 1.59/1.41 inference(pi_clausification,[status(thm)],[f248])).
% 1.59/1.41 thf(f248,plain,(
% 1.59/1.41 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0) & (sK2 @ Y0 @ Y1)) => (sK6 @ Y1)))))) = $true) | ~spl0_2),
% 1.59/1.41 inference(binary_proxy_clausification,[status(thm)],[f245])).
% 1.59/1.41 thf(f245,plain,(
% 1.59/1.41 ($true = ((!! @ a @ (^[Y0 : a]: ((sK2 @ sK3 @ Y0) => (sK6 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0) & (sK2 @ Y0 @ Y1)) => (sK6 @ Y1)))))))) | ~spl0_2),
% 1.59/1.41 inference(binary_proxy_clausification,[status(thm)],[f243])).
% 1.59/1.41 thf(f243,plain,(
% 1.59/1.41 ((((!! @ a @ (^[Y0 : a]: ((sK2 @ sK3 @ Y0) => (sK6 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0) & (sK2 @ Y0 @ Y1)) => (sK6 @ Y1))))))) => (sK6 @ sK5)) = $false) | ~spl0_2),
% 1.59/1.41 inference(beta_eta_normalization,[status(thm)],[f242])).
% 1.59/1.41 thf(f242,plain,(
% 1.59/1.41 (((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK2 @ sK3 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK2 @ Y1 @ Y2)) => (Y0 @ Y2))))))) => (Y0 @ sK5))) @ sK6) = $false) | ~spl0_2),
% 1.59/1.41 inference(sigma_clausification,[status(thm)],[f233])).
% 1.59/1.41 thf(f233,plain,(
% 1.59/1.41 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK2 @ sK3 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK2 @ Y1 @ Y2)) => (Y0 @ Y2))))))) => (Y0 @ sK5)))) = $false) | ~spl0_2),
% 1.59/1.41 inference(boolean_simplification,[status(thm)],[f232])).
% 1.59/1.41 thf(f232,plain,(
% 1.59/1.41 (($true => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK2 @ sK3 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK2 @ Y1 @ Y2)) => (Y0 @ Y2))))))) => (Y0 @ sK5))))) = $false) | ~spl0_2),
% 1.59/1.41 inference(backward_demodulation,[status(thm)],[f227,f231])).
% 1.59/1.41 thf(f231,plain,(
% 1.59/1.41 (((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK2 @ sK3 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1))))))) => (Y0 @ sK4)))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK2 @ sK4 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1))))))) => (Y0 @ sK5))))) = $true) | ~spl0_2),
% 1.59/1.41 inference(binary_proxy_clausification,[status(thm)],[f227])).
% 1.59/1.41 thf(f227,plain,(
% 1.59/1.41 ((((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK2 @ sK3 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1))))))) => (Y0 @ sK4)))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK2 @ sK4 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1))))))) => (Y0 @ sK5))))) => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK2 @ sK3 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK2 @ Y1 @ Y2)) => (Y0 @ Y2))))))) => (Y0 @ sK5))))) = $false) | ~spl0_2),
% 1.59/1.41 inference(beta_eta_normalization,[status(thm)],[f226])).
% 1.59/1.41 thf(f226,plain,(
% 1.59/1.41 (((^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK2 @ sK3 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & (sK2 @ Y3 @ Y2)) => (Y1 @ Y2))))))) => (Y1 @ sK4)))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK2 @ sK4 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & (sK2 @ Y3 @ Y2)) => (Y1 @ Y2))))))) => (Y1 @ Y0))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK2 @ sK3 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & (sK2 @ Y2 @ Y3)) => (Y1 @ Y3))))))) => (Y1 @ Y0)))))) @ sK5) = $false) | ~spl0_2),
% 1.59/1.41 inference(sigma_clausification,[status(thm)],[f223])).
% 1.59/1.41 thf(f223,plain,(
% 1.59/1.41 ((!! @ a @ (^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK2 @ sK3 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & (sK2 @ Y3 @ Y2)) => (Y1 @ Y2))))))) => (Y1 @ sK4)))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK2 @ sK4 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & (sK2 @ Y3 @ Y2)) => (Y1 @ Y2))))))) => (Y1 @ Y0))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK2 @ sK3 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & (sK2 @ Y2 @ Y3)) => (Y1 @ Y3))))))) => (Y1 @ Y0))))))) = $false) | ~spl0_2),
% 1.59/1.41 inference(beta_eta_normalization,[status(thm)],[f222])).
% 1.59/1.41 thf(f222,plain,(
% 1.59/1.41 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK2 @ sK3 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & (sK2 @ Y4 @ Y3)) => (Y2 @ Y3))))))) => (Y2 @ Y0)))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & (sK2 @ Y4 @ Y3)) => (Y2 @ Y3))))))) => (Y2 @ Y1))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK2 @ sK3 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK2 @ Y3 @ Y4)) => (Y2 @ Y4))))))) => (Y2 @ Y1)))))))) @ sK4) = $false) | ~spl0_2),
% 1.59/1.41 inference(sigma_clausification,[status(thm)],[f217])).
% 1.59/1.41 thf(f217,plain,(
% 1.59/1.41 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK2 @ sK3 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & (sK2 @ Y4 @ Y3)) => (Y2 @ Y3))))))) => (Y2 @ Y0)))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & (sK2 @ Y4 @ Y3)) => (Y2 @ Y3))))))) => (Y2 @ Y1))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK2 @ sK3 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK2 @ Y3 @ Y4)) => (Y2 @ Y4))))))) => (Y2 @ Y1))))))))) = $false) | ~spl0_2),
% 1.59/1.41 inference(beta_eta_normalization,[status(thm)],[f216])).
% 1.59/1.41 thf(f216,plain,(
% 1.59/1.41 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((sK2 @ Y0 @ Y4) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & (sK2 @ Y5 @ Y4)) => (Y3 @ Y4))))))) => (Y3 @ Y1)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((sK2 @ Y1 @ Y4) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & (sK2 @ Y5 @ Y4)) => (Y3 @ Y4))))))) => (Y3 @ Y2))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((sK2 @ Y0 @ Y4) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & (sK2 @ Y4 @ Y5)) => (Y3 @ Y5))))))) => (Y3 @ Y2)))))))))) @ sK3) = $false) | ~spl0_2),
% 1.59/1.41 inference(sigma_clausification,[status(thm)],[f18])).
% 1.59/1.41 thf(f18,plain,(
% 1.59/1.41 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((sK2 @ Y0 @ Y4) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & (sK2 @ Y5 @ Y4)) => (Y3 @ Y4))))))) => (Y3 @ Y1)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((sK2 @ Y1 @ Y4) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & (sK2 @ Y5 @ Y4)) => (Y3 @ Y4))))))) => (Y3 @ Y2))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((sK2 @ Y0 @ Y4) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & (sK2 @ Y4 @ Y5)) => (Y3 @ Y5))))))) => (Y3 @ Y2))))))))))) = $false) | ~spl0_2),
% 1.59/1.41 inference(avatar_component_clause,[status(thm)],[f17])).
% 1.59/1.41 thf(f17,definition,(
% 1.59/1.41 spl0_2 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((sK2 @ Y0 @ Y4) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & (sK2 @ Y5 @ Y4)) => (Y3 @ Y4))))))) => (Y3 @ Y1)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((sK2 @ Y1 @ Y4) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & (sK2 @ Y5 @ Y4)) => (Y3 @ Y4))))))) => (Y3 @ Y2))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((sK2 @ Y0 @ Y4) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & (sK2 @ Y4 @ Y5)) => (Y3 @ Y5))))))) => (Y3 @ Y2))))))))))) = $false)),
% 1.59/1.41 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.59/1.41 thf(f455,plain,(
% 1.59/1.41 (((sK2 @ sK4 @ sK16) => (sK6 @ sK16)) = $false) | ~spl0_7),
% 1.59/1.41 inference(beta_eta_normalization,[status(thm)],[f453])).
% 1.59/1.41 thf(f453,plain,(
% 1.59/1.41 (((^[Y0 : a]: ((sK2 @ sK4 @ Y0) => (sK6 @ Y0))) @ sK16) = $false) | ~spl0_7),
% 1.59/1.41 inference(sigma_clausification,[status(thm)],[f442])).
% 1.59/1.41 thf(f442,plain,(
% 1.59/1.41 ((!! @ a @ (^[Y0 : a]: ((sK2 @ sK4 @ Y0) => (sK6 @ Y0)))) = $false) | ~spl0_7),
% 1.59/1.41 inference(avatar_component_clause,[status(thm)],[f441])).
% 1.59/1.41 thf(f441,definition,(
% 1.59/1.41 spl0_7 <=> ((!! @ a @ (^[Y0 : a]: ((sK2 @ sK4 @ Y0) => (sK6 @ Y0)))) = $false)),
% 1.59/1.41 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 1.59/1.41 thf(f443,plain,(
% 1.59/1.41 spl0_4 | spl0_7 | ~spl0_2),
% 1.59/1.41 inference(avatar_split_clause,[status(thm)],[f437,f17,f441,f88])).
% 1.59/1.41 thf(f88,definition,(
% 1.59/1.41 spl0_4 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & (sK2 @ Y1 @ Y0)) => (sK6 @ Y0)))))) = $false)),
% 1.59/1.41 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.59/1.41 thf(f437,plain,(
% 1.59/1.41 ((!! @ a @ (^[Y0 : a]: ((sK2 @ sK4 @ Y0) => (sK6 @ Y0)))) = $false) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & (sK2 @ Y1 @ Y0)) => (sK6 @ Y0)))))) = $false) | ~spl0_2),
% 1.59/1.41 inference(binary_proxy_clausification,[status(thm)],[f427])).
% 1.59/1.41 thf(f427,plain,(
% 1.59/1.41 (((!! @ a @ (^[Y0 : a]: ((sK2 @ sK4 @ Y0) => (sK6 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & (sK2 @ Y1 @ Y0)) => (sK6 @ Y0))))))) = $false) | ~spl0_2),
% 1.59/1.41 inference(not_proxy_clausification,[status(thm)],[f339])).
% 1.59/1.41 thf(f339,plain,(
% 1.59/1.41 ((~ ((!! @ a @ (^[Y0 : a]: ((sK2 @ sK4 @ Y0) => (sK6 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & (sK2 @ Y1 @ Y0)) => (sK6 @ Y0)))))))) = $true) | ~spl0_2),
% 1.59/1.41 inference(boolean_simplification,[status(thm)],[f336])).
% 1.59/1.41 thf(f336,plain,(
% 1.59/1.41 ((((!! @ a @ (^[Y0 : a]: ((sK2 @ sK4 @ Y0) => (sK6 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & (sK2 @ Y1 @ Y0)) => (sK6 @ Y0))))))) => $false) = $true) | ~spl0_2),
% 1.59/1.41 inference(superposition,[status(thm)],[f328,f247])).
% 1.59/1.41 thf(f247,plain,(
% 1.59/1.41 ((sK6 @ sK5) = $false) | ~spl0_2),
% 1.59/1.41 inference(boolean_simplification,[status(thm)],[f246])).
% 1.59/1.41 thf(f246,plain,(
% 1.59/1.41 (($true => (sK6 @ sK5)) = $false) | ~spl0_2),
% 1.59/1.41 inference(backward_demodulation,[status(thm)],[f243,f245])).
% 1.59/1.41 thf(f328,plain,(
% 1.59/1.41 ( ! [X1 : a > $o] : (((((!! @ a @ (^[Y0 : a]: ((sK2 @ sK4 @ Y0) => (X1 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((X1 @ Y1) & (sK2 @ Y1 @ Y0)) => (X1 @ Y0))))))) => (X1 @ sK5)) = $true)) ) | ~spl0_2),
% 1.59/1.41 inference(beta_eta_normalization,[status(thm)],[f327])).
% 1.59/1.41 thf(f327,plain,(
% 1.59/1.41 ( ! [X1 : a > $o] : ((((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK2 @ sK4 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1))))))) => (Y0 @ sK5))) @ X1) = $true)) ) | ~spl0_2),
% 1.59/1.41 inference(pi_clausification,[status(thm)],[f263])).
% 1.59/1.41 thf(f263,plain,(
% 1.59/1.41 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK2 @ sK4 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1))))))) => (Y0 @ sK5)))) = $true) | ~spl0_2),
% 1.59/1.41 inference(binary_proxy_clausification,[status(thm)],[f231])).
% 1.59/1.41 thf(f213,plain,(
% 1.59/1.41 ~spl0_1),
% 1.59/1.41 inference(avatar_contradiction_clause,[status(thm)],[f212])).
% 1.59/1.41 thf(f212,plain,(
% 1.59/1.41 $false | ~spl0_1),
% 1.59/1.41 inference(trivial_inequality_removal,[status(thm)],[f211])).
% 1.59/1.41 thf(f211,plain,(
% 1.59/1.41 ($true = $false) | ~spl0_1),
% 1.59/1.41 inference(forward_demodulation,[status(thm)],[f205,f190])).
% 1.59/1.41 thf(f190,plain,(
% 1.59/1.41 ((sK11 @ sK9) = $false) | ~spl0_1),
% 1.59/1.41 inference(binary_proxy_clausification,[status(thm)],[f189])).
% 1.59/1.41 thf(f189,plain,(
% 1.59/1.41 ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK11 @ Y0) & (sK2 @ Y0 @ Y1)) => (sK11 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ sK10 @ Y0) => (sK11 @ Y0))))) => (sK11 @ sK9))) | ~spl0_1),
% 1.59/1.41 inference(beta_eta_normalization,[status(thm)],[f188])).
% 1.59/1.41 thf(f188,plain,(
% 1.59/1.41 (((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK2 @ Y1 @ Y2)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK10 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK9))) @ sK11) = $false) | ~spl0_1),
% 1.59/1.41 inference(sigma_clausification,[status(thm)],[f187])).
% 1.59/1.41 thf(f187,plain,(
% 1.59/1.41 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK2 @ Y1 @ Y2)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK10 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK9)))) = $false) | ~spl0_1),
% 1.59/1.41 inference(boolean_simplification,[status(thm)],[f186])).
% 1.59/1.41 thf(f186,plain,(
% 1.59/1.41 (($true => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK2 @ Y1 @ Y2)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK10 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK9))))) = $false) | ~spl0_1),
% 1.59/1.41 inference(backward_demodulation,[status(thm)],[f183,f185])).
% 1.59/1.41 thf(f185,plain,(
% 1.59/1.41 ((sK2 @ sK10 @ sK9) = $true) | ~spl0_1),
% 1.59/1.41 inference(binary_proxy_clausification,[status(thm)],[f183])).
% 1.59/1.41 thf(f183,plain,(
% 1.59/1.41 (((sK2 @ sK10 @ sK9) => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK2 @ Y1 @ Y2)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK10 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK9))))) = $false) | ~spl0_1),
% 1.59/1.41 inference(beta_eta_normalization,[status(thm)],[f182])).
% 1.59/1.41 thf(f182,plain,(
% 1.59/1.41 ($false = ((^[Y0 : a]: ((sK2 @ Y0 @ sK9) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & (sK2 @ Y2 @ Y3)) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ Y0 @ Y2) => (Y1 @ Y2))))) => (Y1 @ sK9)))))) @ sK10)) | ~spl0_1),
% 1.59/1.41 inference(sigma_clausification,[status(thm)],[f177])).
% 1.59/1.41 thf(f177,plain,(
% 1.59/1.41 ((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0 @ sK9) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & (sK2 @ Y2 @ Y3)) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ Y0 @ Y2) => (Y1 @ Y2))))) => (Y1 @ sK9))))))) = $false) | ~spl0_1),
% 1.59/1.41 inference(beta_eta_normalization,[status(thm)],[f176])).
% 1.59/1.41 thf(f176,plain,(
% 1.59/1.41 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK2 @ Y3 @ Y4)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y1 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y0)))))))) @ sK9)) | ~spl0_1),
% 1.59/1.41 inference(sigma_clausification,[status(thm)],[f15])).
% 1.59/1.41 thf(f15,plain,(
% 1.59/1.41 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK2 @ Y3 @ Y4)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y1 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y0))))))))) = $false) | ~spl0_1),
% 1.59/1.41 inference(avatar_component_clause,[status(thm)],[f14])).
% 1.59/1.41 thf(f14,definition,(
% 1.59/1.41 spl0_1 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK2 @ Y3 @ Y4)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y1 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y0))))))))) = $false)),
% 1.59/1.41 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.59/1.41 thf(f205,plain,(
% 1.59/1.41 ((sK11 @ sK9) = $true) | ~spl0_1),
% 1.59/1.41 inference(boolean_simplification,[status(thm)],[f204])).
% 1.59/1.41 thf(f204,plain,(
% 1.59/1.41 (($true => (sK11 @ sK9)) = $true) | ~spl0_1),
% 1.59/1.41 inference(superposition,[status(thm)],[f201,f185])).
% 1.59/1.41 thf(f201,plain,(
% 1.59/1.41 ( ! [X1 : a] : (($true = ((sK2 @ sK10 @ X1) => (sK11 @ X1)))) ) | ~spl0_1),
% 1.59/1.41 inference(beta_eta_normalization,[status(thm)],[f200])).
% 1.59/1.41 thf(f200,plain,(
% 1.59/1.41 ( ! [X1 : a] : ((((^[Y0 : a]: ((sK2 @ sK10 @ Y0) => (sK11 @ Y0))) @ X1) = $true)) ) | ~spl0_1),
% 1.59/1.41 inference(pi_clausification,[status(thm)],[f199])).
% 1.59/1.41 thf(f199,plain,(
% 1.59/1.41 ((!! @ a @ (^[Y0 : a]: ((sK2 @ sK10 @ Y0) => (sK11 @ Y0)))) = $true) | ~spl0_1),
% 1.59/1.41 inference(boolean_simplification,[status(thm)],[f198])).
% 1.59/1.41 thf(f198,plain,(
% 1.59/1.41 (($true & (!! @ a @ (^[Y0 : a]: ((sK2 @ sK10 @ Y0) => (sK11 @ Y0))))) = $true) | ~spl0_1),
% 1.59/1.41 inference(backward_demodulation,[status(thm)],[f191,f197])).
% 1.59/1.41 thf(f197,plain,(
% 1.59/1.41 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK11 @ Y0) & (sK2 @ Y0 @ Y1)) => (sK11 @ Y1)))))) = $true) | ~spl0_1),
% 1.59/1.41 inference(binary_proxy_clausification,[status(thm)],[f191])).
% 1.59/1.41 thf(f191,plain,(
% 1.59/1.41 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK11 @ Y0) & (sK2 @ Y0 @ Y1)) => (sK11 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ sK10 @ Y0) => (sK11 @ Y0))))) = $true) | ~spl0_1),
% 1.59/1.41 inference(binary_proxy_clausification,[status(thm)],[f189])).
% 1.59/1.41 thf(f169,plain,(
% 1.59/1.41 ~spl0_2 | ~spl0_4),
% 1.59/1.41 inference(avatar_contradiction_clause,[status(thm)],[f168])).
% 1.59/1.41 thf(f168,plain,(
% 1.59/1.41 $false | (~spl0_2 | ~spl0_4)),
% 1.59/1.41 inference(trivial_inequality_removal,[status(thm)],[f164])).
% 1.59/1.41 thf(f164,plain,(
% 1.59/1.41 ($true = $false) | (~spl0_2 | ~spl0_4)),
% 1.59/1.41 inference(superposition,[status(thm)],[f161,f64])).
% 1.59/1.41 thf(f64,plain,(
% 1.59/1.41 ( ! [X2 : a,X1 : a] : (((((sK6 @ X1) & (sK2 @ X1 @ X2)) => (sK6 @ X2)) = $true)) ) | ~spl0_2),
% 1.59/1.41 inference(beta_eta_normalization,[status(thm)],[f63])).
% 1.59/1.41 thf(f63,plain,(
% 1.59/1.41 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: (((sK6 @ X1) & (sK2 @ X1 @ Y0)) => (sK6 @ Y0))) @ X2) = $true)) ) | ~spl0_2),
% 1.59/1.41 inference(pi_clausification,[status(thm)],[f59])).
% 1.59/1.41 thf(f59,plain,(
% 1.59/1.41 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: (((sK6 @ X1) & (sK2 @ X1 @ Y0)) => (sK6 @ Y0)))) = $true)) ) | ~spl0_2),
% 1.59/1.41 inference(beta_eta_normalization,[status(thm)],[f58])).
% 1.59/1.41 thf(f58,plain,(
% 1.59/1.41 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0) & (sK2 @ Y0 @ Y1)) => (sK6 @ Y1))))) @ X1) = $true)) ) | ~spl0_2),
% 1.59/1.41 inference(pi_clausification,[status(thm)],[f38])).
% 1.59/1.41 thf(f38,plain,(
% 1.59/1.41 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0) & (sK2 @ Y0 @ Y1)) => (sK6 @ Y1)))))) = $true) | ~spl0_2),
% 1.59/1.41 inference(binary_proxy_clausification,[status(thm)],[f35])).
% 1.59/1.41 thf(f35,plain,(
% 1.59/1.41 ($true = ((!! @ a @ (^[Y0 : a]: ((sK2 @ sK3 @ Y0) => (sK6 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0) & (sK2 @ Y0 @ Y1)) => (sK6 @ Y1)))))))) | ~spl0_2),
% 1.59/1.41 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.59/1.41 thf(f33,plain,(
% 1.59/1.41 ((((!! @ a @ (^[Y0 : a]: ((sK2 @ sK3 @ Y0) => (sK6 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0) & (sK2 @ Y0 @ Y1)) => (sK6 @ Y1))))))) => (sK6 @ sK5)) = $false) | ~spl0_2),
% 1.59/1.41 inference(beta_eta_normalization,[status(thm)],[f32])).
% 1.59/1.41 thf(f32,plain,(
% 1.59/1.41 (((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK2 @ sK3 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK2 @ Y1 @ Y2)) => (Y0 @ Y2))))))) => (Y0 @ sK5))) @ sK6) = $false) | ~spl0_2),
% 1.59/1.41 inference(sigma_clausification,[status(thm)],[f31])).
% 1.59/1.41 thf(f31,plain,(
% 1.59/1.41 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK2 @ sK3 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK2 @ Y1 @ Y2)) => (Y0 @ Y2))))))) => (Y0 @ sK5)))) = $false) | ~spl0_2),
% 1.59/1.41 inference(boolean_simplification,[status(thm)],[f30])).
% 1.59/1.41 thf(f30,plain,(
% 1.59/1.41 (($true => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK2 @ sK3 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK2 @ Y1 @ Y2)) => (Y0 @ Y2))))))) => (Y0 @ sK5))))) = $false) | ~spl0_2),
% 1.59/1.41 inference(backward_demodulation,[status(thm)],[f27,f29])).
% 1.59/1.41 thf(f29,plain,(
% 1.59/1.41 (((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK2 @ sK3 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1))))))) => (Y0 @ sK4)))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK2 @ sK4 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1))))))) => (Y0 @ sK5))))) = $true) | ~spl0_2),
% 1.59/1.41 inference(binary_proxy_clausification,[status(thm)],[f27])).
% 1.59/1.41 thf(f27,plain,(
% 1.59/1.41 ((((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK2 @ sK3 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1))))))) => (Y0 @ sK4)))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK2 @ sK4 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1))))))) => (Y0 @ sK5))))) => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK2 @ sK3 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK2 @ Y1 @ Y2)) => (Y0 @ Y2))))))) => (Y0 @ sK5))))) = $false) | ~spl0_2),
% 1.59/1.41 inference(beta_eta_normalization,[status(thm)],[f26])).
% 1.59/1.41 thf(f26,plain,(
% 1.59/1.41 (((^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK2 @ sK3 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & (sK2 @ Y3 @ Y2)) => (Y1 @ Y2))))))) => (Y1 @ sK4)))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK2 @ sK4 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & (sK2 @ Y3 @ Y2)) => (Y1 @ Y2))))))) => (Y1 @ Y0))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK2 @ sK3 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & (sK2 @ Y2 @ Y3)) => (Y1 @ Y3))))))) => (Y1 @ Y0)))))) @ sK5) = $false) | ~spl0_2),
% 1.59/1.41 inference(sigma_clausification,[status(thm)],[f25])).
% 1.59/1.41 thf(f25,plain,(
% 1.59/1.41 ((!! @ a @ (^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK2 @ sK3 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & (sK2 @ Y3 @ Y2)) => (Y1 @ Y2))))))) => (Y1 @ sK4)))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK2 @ sK4 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & (sK2 @ Y3 @ Y2)) => (Y1 @ Y2))))))) => (Y1 @ Y0))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK2 @ sK3 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & (sK2 @ Y2 @ Y3)) => (Y1 @ Y3))))))) => (Y1 @ Y0))))))) = $false) | ~spl0_2),
% 1.59/1.41 inference(beta_eta_normalization,[status(thm)],[f24])).
% 1.59/1.41 thf(f24,plain,(
% 1.59/1.41 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK2 @ sK3 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & (sK2 @ Y4 @ Y3)) => (Y2 @ Y3))))))) => (Y2 @ Y0)))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & (sK2 @ Y4 @ Y3)) => (Y2 @ Y3))))))) => (Y2 @ Y1))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK2 @ sK3 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK2 @ Y3 @ Y4)) => (Y2 @ Y4))))))) => (Y2 @ Y1)))))))) @ sK4) = $false) | ~spl0_2),
% 1.59/1.41 inference(sigma_clausification,[status(thm)],[f23])).
% 1.59/1.41 thf(f23,plain,(
% 1.59/1.41 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK2 @ sK3 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & (sK2 @ Y4 @ Y3)) => (Y2 @ Y3))))))) => (Y2 @ Y0)))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & (sK2 @ Y4 @ Y3)) => (Y2 @ Y3))))))) => (Y2 @ Y1))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK2 @ sK3 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK2 @ Y3 @ Y4)) => (Y2 @ Y4))))))) => (Y2 @ Y1))))))))) = $false) | ~spl0_2),
% 1.59/1.41 inference(beta_eta_normalization,[status(thm)],[f22])).
% 1.59/1.41 thf(f22,plain,(
% 1.59/1.41 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((sK2 @ Y0 @ Y4) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & (sK2 @ Y5 @ Y4)) => (Y3 @ Y4))))))) => (Y3 @ Y1)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((sK2 @ Y1 @ Y4) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & (sK2 @ Y5 @ Y4)) => (Y3 @ Y4))))))) => (Y3 @ Y2))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((sK2 @ Y0 @ Y4) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & (sK2 @ Y4 @ Y5)) => (Y3 @ Y5))))))) => (Y3 @ Y2)))))))))) @ sK3) = $false) | ~spl0_2),
% 1.59/1.41 inference(sigma_clausification,[status(thm)],[f18])).
% 1.59/1.41 thf(f161,plain,(
% 1.59/1.41 ($false = (((sK6 @ sK8) & (sK2 @ sK8 @ sK7)) => (sK6 @ sK7))) | ~spl0_4),
% 1.59/1.41 inference(beta_eta_normalization,[status(thm)],[f160])).
% 1.59/1.41 thf(f160,plain,(
% 1.59/1.41 (((^[Y0 : a]: (((sK6 @ Y0) & (sK2 @ Y0 @ sK7)) => (sK6 @ sK7))) @ sK8) = $false) | ~spl0_4),
% 1.59/1.41 inference(sigma_clausification,[status(thm)],[f159])).
% 1.59/1.41 thf(f159,plain,(
% 1.59/1.41 ((!! @ a @ (^[Y0 : a]: (((sK6 @ Y0) & (sK2 @ Y0 @ sK7)) => (sK6 @ sK7)))) = $false) | ~spl0_4),
% 1.59/1.41 inference(beta_eta_normalization,[status(thm)],[f152])).
% 1.59/1.41 thf(f152,plain,(
% 1.59/1.41 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & (sK2 @ Y1 @ Y0)) => (sK6 @ Y0))))) @ sK7) = $false) | ~spl0_4),
% 1.59/1.41 inference(sigma_clausification,[status(thm)],[f89])).
% 1.59/1.41 thf(f89,plain,(
% 1.59/1.41 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & (sK2 @ Y1 @ Y0)) => (sK6 @ Y0)))))) = $false) | ~spl0_4),
% 1.59/1.41 inference(avatar_component_clause,[status(thm)],[f88])).
% 1.59/1.41 thf(f90,plain,(
% 1.59/1.41 spl0_3 | spl0_4 | ~spl0_2),
% 1.59/1.41 inference(avatar_split_clause,[status(thm)],[f83,f17,f88,f85])).
% 1.59/1.41 thf(f83,plain,(
% 1.59/1.41 ((sK6 @ sK4) = $true) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & (sK2 @ Y1 @ Y0)) => (sK6 @ Y0)))))) = $false) | ~spl0_2),
% 1.59/1.41 inference(binary_proxy_clausification,[status(thm)],[f62])).
% 1.59/1.41 thf(f62,plain,(
% 1.59/1.41 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & (sK2 @ Y1 @ Y0)) => (sK6 @ Y0)))))) => (sK6 @ sK4)) = $true) | ~spl0_2),
% 1.59/1.41 inference(boolean_simplification,[status(thm)],[f61])).
% 1.59/1.41 thf(f61,plain,(
% 1.59/1.41 ((($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & (sK2 @ Y1 @ Y0)) => (sK6 @ Y0))))))) => (sK6 @ sK4)) = $true) | ~spl0_2),
% 1.59/1.41 inference(superposition,[status(thm)],[f57,f41])).
% 1.59/1.41 thf(f41,plain,(
% 1.59/1.41 ($true = (!! @ a @ (^[Y0 : a]: ((sK2 @ sK3 @ Y0) => (sK6 @ Y0))))) | ~spl0_2),
% 1.59/1.41 inference(boolean_simplification,[status(thm)],[f40])).
% 1.59/1.41 thf(f40,plain,(
% 1.59/1.41 (((!! @ a @ (^[Y0 : a]: ((sK2 @ sK3 @ Y0) => (sK6 @ Y0)))) & $true) = $true) | ~spl0_2),
% 1.59/1.41 inference(backward_demodulation,[status(thm)],[f35,f38])).
% 1.59/1.41 thf(f57,plain,(
% 1.59/1.41 ( ! [X1 : a > $o] : (((((!! @ a @ (^[Y0 : a]: ((sK2 @ sK3 @ Y0) => (X1 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((X1 @ Y1) & (sK2 @ Y1 @ Y0)) => (X1 @ Y0))))))) => (X1 @ sK4)) = $true)) ) | ~spl0_2),
% 1.59/1.41 inference(beta_eta_normalization,[status(thm)],[f56])).
% 1.59/1.41 thf(f56,plain,(
% 1.59/1.41 ( ! [X1 : a > $o] : ((((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK2 @ sK3 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1))))))) => (Y0 @ sK4))) @ X1) = $true)) ) | ~spl0_2),
% 1.59/1.41 inference(pi_clausification,[status(thm)],[f53])).
% 1.59/1.41 thf(f53,plain,(
% 1.59/1.41 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK2 @ sK3 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1))))))) => (Y0 @ sK4)))) = $true) | ~spl0_2),
% 1.59/1.41 inference(boolean_simplification,[status(thm)],[f52])).
% 1.59/1.41 thf(f52,plain,(
% 1.59/1.41 (((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK2 @ sK3 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1))))))) => (Y0 @ sK4)))) & $true) = $true) | ~spl0_2),
% 1.59/1.41 inference(backward_demodulation,[status(thm)],[f29,f50])).
% 1.59/1.41 thf(f50,plain,(
% 1.59/1.41 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK2 @ sK4 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1))))))) => (Y0 @ sK5)))) = $true) | ~spl0_2),
% 1.59/1.41 inference(binary_proxy_clausification,[status(thm)],[f29])).
% 1.59/1.41 thf(f19,plain,(
% 1.59/1.41 spl0_1 | spl0_2),
% 1.59/1.41 inference(avatar_split_clause,[status(thm)],[f12,f17,f14])).
% 1.59/1.41 thf(f12,plain,(
% 1.59/1.41 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK2 @ Y3 @ Y4)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y1 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y0))))))))) = $false) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((sK2 @ Y0 @ Y4) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & (sK2 @ Y5 @ Y4)) => (Y3 @ Y4))))))) => (Y3 @ Y1)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((sK2 @ Y1 @ Y4) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & (sK2 @ Y5 @ Y4)) => (Y3 @ Y4))))))) => (Y3 @ Y2))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((sK2 @ Y0 @ Y4) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & (sK2 @ Y4 @ Y5)) => (Y3 @ Y5))))))) => (Y3 @ Y2))))))))))) = $false)),
% 1.59/1.41 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.59/1.41 thf(f11,plain,(
% 1.59/1.41 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((sK2 @ Y0 @ Y4) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & (sK2 @ Y5 @ Y4)) => (Y3 @ Y4))))))) => (Y3 @ Y1)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((sK2 @ Y1 @ Y4) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & (sK2 @ Y5 @ Y4)) => (Y3 @ Y4))))))) => (Y3 @ Y2))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((sK2 @ Y0 @ Y4) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & (sK2 @ Y4 @ Y5)) => (Y3 @ Y5))))))) => (Y3 @ Y2))))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK2 @ Y3 @ Y4)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y1 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y0)))))))))) = $false)),
% 1.59/1.41 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.59/1.41 thf(f10,plain,(
% 1.59/1.41 (((^[Y0 : a > a > $o]: ((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y0 @ Y1 @ Y5) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & (Y0 @ Y6 @ Y5)) => (Y4 @ Y5))))))) => (Y4 @ Y2)))) & (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y0 @ Y2 @ Y5) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & (Y0 @ Y6 @ Y5)) => (Y4 @ Y5))))))) => (Y4 @ Y3))))) => (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y0 @ Y1 @ Y5) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & (Y0 @ Y5 @ Y6)) => (Y4 @ Y6))))))) => (Y4 @ Y3))))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ Y2 @ Y1) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & (Y0 @ Y4 @ Y5)) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: ((Y0 @ Y2 @ Y4) => (Y3 @ Y4))))) => (Y3 @ Y1))))))))))) @ sK2) = $false)),
% 1.59/1.41 inference(sigma_clausification,[status(thm)],[f7])).
% 1.59/1.41 thf(f7,plain,(
% 1.59/1.41 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: ((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y0 @ Y1 @ Y5) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & (Y0 @ Y6 @ Y5)) => (Y4 @ Y5))))))) => (Y4 @ Y2)))) & (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y0 @ Y2 @ Y5) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & (Y0 @ Y6 @ Y5)) => (Y4 @ Y5))))))) => (Y4 @ Y3))))) => (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y0 @ Y1 @ Y5) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & (Y0 @ Y5 @ Y6)) => (Y4 @ Y6))))))) => (Y4 @ Y3))))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ Y2 @ Y1) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & (Y0 @ Y4 @ Y5)) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: ((Y0 @ Y2 @ Y4) => (Y3 @ Y4))))) => (Y3 @ Y1)))))))))))))),
% 1.59/1.41 inference(not_proxy_clausification,[status(thm)],[f6])).
% 1.59/1.41 thf(f6,plain,(
% 1.59/1.41 ($true = (~ (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: ((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y0 @ Y1 @ Y5) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & (Y0 @ Y6 @ Y5)) => (Y4 @ Y5))))))) => (Y4 @ Y2)))) & (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y0 @ Y2 @ Y5) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & (Y0 @ Y6 @ Y5)) => (Y4 @ Y5))))))) => (Y4 @ Y3))))) => (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y0 @ Y1 @ Y5) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & (Y0 @ Y5 @ Y6)) => (Y4 @ Y6))))))) => (Y4 @ Y3))))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ Y2 @ Y1) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & (Y0 @ Y4 @ Y5)) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: ((Y0 @ Y2 @ Y4) => (Y3 @ Y4))))) => (Y3 @ Y1))))))))))))))),
% 1.59/1.41 inference(cnf_transformation,[status(thm)],[f5])).
% 1.59/1.41 thf(f5,plain,(
% 1.59/1.41 ($true = (~ (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: ((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y0 @ Y1 @ Y5) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & (Y0 @ Y6 @ Y5)) => (Y4 @ Y5))))))) => (Y4 @ Y2)))) & (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y0 @ Y2 @ Y5) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & (Y0 @ Y6 @ Y5)) => (Y4 @ Y5))))))) => (Y4 @ Y3))))) => (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y0 @ Y1 @ Y5) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & (Y0 @ Y5 @ Y6)) => (Y4 @ Y6))))))) => (Y4 @ Y3))))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ Y2 @ Y1) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & (Y0 @ Y4 @ Y5)) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: ((Y0 @ Y2 @ Y4) => (Y3 @ Y4))))) => (Y3 @ Y1))))))))))))))),
% 1.59/1.41 inference(fool_elimination,[status(thm)],[f4])).
% 1.59/1.41 thf(f4,plain,(
% 1.59/1.41 ~! [X0 : a > a > $o] : (! [X1 : a,X2 : a] : ((X0 @ X1 @ X2) => ! [X3 : a > $o] : ((! [X4 : a] : ((X0 @ X1 @ X4) => (X3 @ X4)) & ! [X5 : a,X6 : a] : (((X0 @ X6 @ X5) & (X3 @ X6)) => (X3 @ X5))) => (X3 @ X2))) & ! [X7 : a,X8 : a,X9 : a] : ((! [X10 : a > $o] : ((! [X11 : a,X12 : a] : (((X0 @ X11 @ X12) & (X10 @ X11)) => (X10 @ X12)) & ! [X13 : a] : ((X0 @ X8 @ X13) => (X10 @ X13))) => (X10 @ X7)) & ! [X14 : a > $o] : ((! [X15 : a,X16 : a] : (((X0 @ X15 @ X16) & (X14 @ X15)) => (X14 @ X16)) & ! [X17 : a] : ((X0 @ X9 @ X17) => (X14 @ X17))) => (X14 @ X8))) => ! [X18 : a > $o] : ((! [X19 : a,X20 : a] : (((X0 @ X20 @ X19) & (X18 @ X20)) => (X18 @ X19)) & ! [X21 : a] : ((X0 @ X9 @ X21) => (X18 @ X21))) => (X18 @ X7))))),
% 1.59/1.41 inference(rectify,[status(thm)],[f2])).
% 1.59/1.41 thf(f2,negated_conjecture,(
% 1.59/1.41 ~! [X0 : a > a > $o] : (! [X1 : a,X2 : a] : ((X0 @ X1 @ X2) => ! [X3 : a > $o] : ((! [X4 : a] : ((X0 @ X1 @ X4) => (X3 @ X4)) & ! [X4 : a,X5 : a] : (((X0 @ X5 @ X4) & (X3 @ X5)) => (X3 @ X4))) => (X3 @ X2))) & ! [X6 : a,X2 : a,X1 : a] : ((! [X3 : a > $o] : ((! [X5 : a,X4 : a] : (((X0 @ X5 @ X4) & (X3 @ X5)) => (X3 @ X4)) & ! [X4 : a] : ((X0 @ X2 @ X4) => (X3 @ X4))) => (X3 @ X6)) & ! [X3 : a > $o] : ((! [X5 : a,X4 : a] : (((X0 @ X5 @ X4) & (X3 @ X5)) => (X3 @ X4)) & ! [X4 : a] : ((X0 @ X1 @ X4) => (X3 @ X4))) => (X3 @ X2))) => ! [X3 : a > $o] : ((! [X4 : a,X5 : a] : (((X0 @ X5 @ X4) & (X3 @ X5)) => (X3 @ X4)) & ! [X4 : a] : ((X0 @ X1 @ X4) => (X3 @ X4))) => (X3 @ X6))))),
% 1.59/1.41 inference(negated_conjecture,[status(cth)],[f1])).
% 1.59/1.41 thf(f1,conjecture,(
% 1.59/1.41 ! [X0 : a > a > $o] : (! [X1 : a,X2 : a] : ((X0 @ X1 @ X2) => ! [X3 : a > $o] : ((! [X4 : a] : ((X0 @ X1 @ X4) => (X3 @ X4)) & ! [X4 : a,X5 : a] : (((X0 @ X5 @ X4) & (X3 @ X5)) => (X3 @ X4))) => (X3 @ X2))) & ! [X6 : a,X2 : a,X1 : a] : ((! [X3 : a > $o] : ((! [X5 : a,X4 : a] : (((X0 @ X5 @ X4) & (X3 @ X5)) => (X3 @ X4)) & ! [X4 : a] : ((X0 @ X2 @ X4) => (X3 @ X4))) => (X3 @ X6)) & ! [X3 : a > $o] : ((! [X5 : a,X4 : a] : (((X0 @ X5 @ X4) & (X3 @ X5)) => (X3 @ X4)) & ! [X4 : a] : ((X0 @ X1 @ X4) => (X3 @ X4))) => (X3 @ X2))) => ! [X3 : a > $o] : ((! [X4 : a,X5 : a] : (((X0 @ X5 @ X4) & (X3 @ X5)) => (X3 @ X4)) & ! [X4 : a] : ((X0 @ X1 @ X4) => (X3 @ X4))) => (X3 @ X6))))),
% 1.59/1.41 file('/export/starexec/sandbox2/tmp/tmp.M0ffQNqfuq/DTF2THF_14972.p',cTHM525_pme)).
% 1.59/1.41 % SZS output end Proof for DTF2THF_14972
% 1.59/1.41 % (15081)------------------------------
% 1.59/1.41 % (15081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.41 % (15081)Termination reason: Refutation
% 1.59/1.41
% 1.59/1.41 % (15081)Memory used [KB]: 5884
% 1.59/1.41 % (15081)Time elapsed: 0.056 s
% 1.59/1.41 % (15081)Instructions burned: 91 (million)
% 1.59/1.41 % (15081)------------------------------
% 1.59/1.41 % (15081)------------------------------
% 1.59/1.41 % (15069)Success in time 0.103 s
%------------------------------------------------------------------------------