%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV037^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n019.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 09:40:07 AM UTC 2026
% Result : Theorem 1.55s 1.40s
% Output : Refutation 1.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 9
% Syntax : Number of formulae : 243 ( 46 unt; 0 typ; 8 def)
% Number of atoms : 2275 ( 301 equ; 0 cnn)
% Maximal formula atoms : 3 ( 9 avg)
% Number of connectives : 6395 ( 211 ~; 206 |; 234 &;4474 @)
% ( 8 <=>; 501 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 398 ( 398 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 28 usr; 19 con; 0-3 aty)
% ( 761 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 1107 ( 885 ^; 222 !; 0 ?;1107 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_7,type,
b: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
b: $tType ).
thf(func_def_19,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
sK2: a > a > $o ).
thf(func_def_21,type,
sK3: a > b > b > $o ).
thf(func_def_22,type,
sK4: a > a > $o ).
thf(func_def_23,type,
sK5: a > b ).
thf(func_def_24,type,
sK6: a > b ).
thf(func_def_25,type,
sK7: a > b ).
thf(func_def_26,type,
sK8: a ).
thf(func_def_27,type,
sK9: a > b ).
thf(func_def_28,type,
sK10: a ).
thf(func_def_29,type,
sK11: a > b ).
thf(func_def_30,type,
sK12: a > b ).
thf(func_def_31,type,
sK13: a ).
thf(func_def_32,type,
sK14: a ).
thf(func_def_33,type,
sK15: a > b ).
thf(func_def_34,type,
sK16: a > b ).
thf(func_def_35,type,
sK17: a ).
thf(func_def_36,type,
sK18: a ).
thf(func_def_37,type,
sK19: a ).
thf(func_def_38,type,
sK20: a ).
thf(f1343,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f81,f92,f940,f1259,f1275,f1282,f1307,f1315,f1338]) ).
thf(f1338,plain,
( ~ spl0_5
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f1337]) ).
thf(f1337,plain,
( $false
| ~ spl0_5
| ~ spl0_8 ),
inference(trivial_inequality_removal,[status(thm)],[f1333]) ).
thf(f1333,plain,
( ( $false = $true )
| ~ spl0_5
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f1329,f1321]) ).
thf(f1321,plain,
( ! [X2: a,X1: a] :
( ( ( sK2 @ X2 @ X1 )
=> ( sK3 @ X2 @ ( sK15 @ X2 ) @ ( sK16 @ X1 ) ) )
= $true )
| ~ spl0_5 ),
inference(beta_eta_normalization,[status(thm)],[f1320]) ).
thf(f1320,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( sK2 @ Y0 @ X1 )
=> ( sK3 @ Y0 @ ( sK15 @ Y0 ) @ ( sK16 @ X1 ) ) )
@ X2 )
= $true )
| ~ spl0_5 ),
inference(pi_clausification,[status(thm)],[f1319]) ).
thf(f1319,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ X1 )
=> ( sK3 @ Y0 @ ( sK15 @ Y0 ) @ ( sK16 @ X1 ) ) ) ) )
| ~ spl0_5 ),
inference(beta_eta_normalization,[status(thm)],[f1318]) ).
thf(f1318,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK3 @ Y1 @ ( sK15 @ Y1 ) @ ( sK16 @ Y0 ) ) ) )
@ X1 )
= $true )
| ~ spl0_5 ),
inference(pi_clausification,[status(thm)],[f1271]) ).
thf(f1271,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK3 @ Y1 @ ( sK15 @ Y1 ) @ ( sK16 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f1270]) ).
thf(f1270,definition,
( spl0_5
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK3 @ Y1 @ ( sK15 @ Y1 ) @ ( sK16 @ Y0 ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f1329,plain,
( ( $false
= ( ( sK2 @ sK19 @ sK20 )
=> ( sK3 @ sK19 @ ( sK15 @ sK19 ) @ ( sK16 @ sK20 ) ) ) )
| ~ spl0_8 ),
inference(forward_demodulation,[status(thm)],[f1328,f50]) ).
thf(f50,plain,
! [X2: a,X1: a] :
( ( sK2 @ X1 @ X2 )
= ( sK4 @ X1 @ X2 ) ),
inference(argument_congruence,[status(thm)],[f48]) ).
thf(f48,plain,
! [X1: a] :
( ( sK4 @ X1 )
= ( sK2 @ X1 ) ),
inference(argument_congruence,[status(thm)],[f43]) ).
thf(f43,plain,
sK4 = sK2,
inference(equality_proxy_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
( ( sK4 = sK2 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( $true
= ( ( sK4 = sK2 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK4 @ Y1 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( $true
= ( ( sK4 = sK2 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK4 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y0 )
& ( sK4 @ Y1 @ Y2 ) )
=> ( sK4 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( $false
= ( ( ( sK4 = sK2 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK4 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y0 )
& ( sK4 @ Y1 @ Y2 ) )
=> ( sK4 @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 @ Y0 )
=> ( ( ( sK3 @ Y1 )
= ( sK3 @ Y0 ) )
& ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( ( ( sK3 @ Y1 @ Y4 @ Y3 )
& ( sK3 @ Y1 @ Y3 @ Y2 ) )
=> ( sK3 @ Y1 @ Y4 @ Y2 ) ) ) ) )
& ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( sK3 @ Y1 @ Y3 @ Y2 )
=> ( sK3 @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) )
=> ( ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y2 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) ) ) ) )
& ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y3 @ Y2 )
=> ( sK3 @ Y3 @ ( Y1 @ Y3 ) @ ( Y0 @ Y2 ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y2 @ Y3 )
=> ( sK3 @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) ) ) ) )
& ( ( ^ [Y0: a > b,Y1: a > b] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( sK3 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y2 ) ) ) ) ) )
= ( ^ [Y0: a > b,Y1: a > b] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y2 @ Y3 )
=> ( sK3 @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
( $false
= ( ^ [Y0: a > a > $o] :
( ( ( Y0 = sK2 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y1 )
=> ( ( ( sK3 @ Y2 )
= ( sK3 @ Y1 ) )
& ( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( !! @ b
@ ^ [Y5: b] :
( ( ( sK3 @ Y2 @ Y5 @ Y4 )
& ( sK3 @ Y2 @ Y4 @ Y3 ) )
=> ( sK3 @ Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( ( sK3 @ Y2 @ Y4 @ Y3 )
=> ( sK3 @ Y2 @ Y3 @ Y4 ) ) ) ) ) ) ) )
=> ( ( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( !! @ ( a > b )
@ ^ [Y3: a > b] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( sK3 @ Y4 @ ( Y1 @ Y4 ) @ ( Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( sK3 @ Y4 @ ( Y3 @ Y4 ) @ ( Y2 @ Y5 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( sK3 @ Y4 @ ( Y1 @ Y4 ) @ ( Y2 @ Y5 ) ) ) ) ) ) ) ) )
& ( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 @ Y3 )
=> ( sK3 @ Y4 @ ( Y2 @ Y4 ) @ ( Y1 @ Y3 ) ) ) ) )
=> ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y1 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) ) ) ) )
& ( ( ^ [Y1: a > b,Y2: a > b] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( sK3 @ Y4 @ ( Y1 @ Y4 ) @ ( Y2 @ Y3 ) ) ) ) ) )
= ( ^ [Y1: a > b,Y2: a > b] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y1 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) ) ) ) ) ) )
@ sK4 ) ),
inference(sigma_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( Y0 = sK2 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y1 )
=> ( ( ( sK3 @ Y2 )
= ( sK3 @ Y1 ) )
& ( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( !! @ b
@ ^ [Y5: b] :
( ( ( sK3 @ Y2 @ Y5 @ Y4 )
& ( sK3 @ Y2 @ Y4 @ Y3 ) )
=> ( sK3 @ Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( ( sK3 @ Y2 @ Y4 @ Y3 )
=> ( sK3 @ Y2 @ Y3 @ Y4 ) ) ) ) ) ) ) )
=> ( ( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( !! @ ( a > b )
@ ^ [Y3: a > b] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( sK3 @ Y4 @ ( Y1 @ Y4 ) @ ( Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( sK3 @ Y4 @ ( Y3 @ Y4 ) @ ( Y2 @ Y5 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( sK3 @ Y4 @ ( Y1 @ Y4 ) @ ( Y2 @ Y5 ) ) ) ) ) ) ) ) )
& ( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 @ Y3 )
=> ( sK3 @ Y4 @ ( Y2 @ Y4 ) @ ( Y1 @ Y3 ) ) ) ) )
=> ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y1 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) ) ) ) )
& ( ( ^ [Y1: a > b,Y2: a > b] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( sK3 @ Y4 @ ( Y1 @ Y4 ) @ ( Y2 @ Y3 ) ) ) ) ) )
= ( ^ [Y1: a > b,Y2: a > b] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y1 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
( $false
= ( ^ [Y0: a > b > b > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( Y1 = sK2 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y2 @ Y3 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 @ Y2 )
=> ( ( ( Y0 @ Y3 )
= ( Y0 @ Y2 ) )
& ( !! @ b
@ ^ [Y4: b] :
( !! @ b
@ ^ [Y5: b] :
( !! @ b
@ ^ [Y6: b] :
( ( ( Y0 @ Y3 @ Y6 @ Y5 )
& ( Y0 @ Y3 @ Y5 @ Y4 ) )
=> ( Y0 @ Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ b
@ ^ [Y4: b] :
( !! @ b
@ ^ [Y5: b] :
( ( Y0 @ Y3 @ Y5 @ Y4 )
=> ( Y0 @ Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) )
=> ( ( !! @ ( a > b )
@ ^ [Y2: a > b] :
( !! @ ( a > b )
@ ^ [Y3: a > b] :
( !! @ ( a > b )
@ ^ [Y4: a > b] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y0 @ Y5 @ ( Y2 @ Y5 ) @ ( Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y0 @ Y5 @ ( Y4 @ Y5 ) @ ( Y3 @ Y6 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y0 @ Y5 @ ( Y2 @ Y5 ) @ ( Y3 @ Y6 ) ) ) ) ) ) ) ) )
& ( !! @ ( a > b )
@ ^ [Y2: a > b] :
( !! @ ( a > b )
@ ^ [Y3: a > b] :
( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y1 @ Y5 @ Y4 )
=> ( Y0 @ Y5 @ ( Y3 @ Y5 ) @ ( Y2 @ Y4 ) ) ) ) )
=> ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y1 @ Y4 @ Y5 )
=> ( Y0 @ Y4 @ ( Y2 @ Y4 ) @ ( Y3 @ Y5 ) ) ) ) ) ) ) )
& ( ( ^ [Y2: a > b,Y3: a > b] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y0 @ Y5 @ ( Y2 @ Y5 ) @ ( Y3 @ Y4 ) ) ) ) ) )
= ( ^ [Y2: a > b,Y3: a > b] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y1 @ Y4 @ Y5 )
=> ( Y0 @ Y4 @ ( Y2 @ Y4 ) @ ( Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) )
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( $false
= ( !! @ ( a > b > b > $o )
@ ^ [Y0: a > b > b > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( Y1 = sK2 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y2 @ Y3 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 @ Y2 )
=> ( ( ( Y0 @ Y3 )
= ( Y0 @ Y2 ) )
& ( !! @ b
@ ^ [Y4: b] :
( !! @ b
@ ^ [Y5: b] :
( !! @ b
@ ^ [Y6: b] :
( ( ( Y0 @ Y3 @ Y6 @ Y5 )
& ( Y0 @ Y3 @ Y5 @ Y4 ) )
=> ( Y0 @ Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ b
@ ^ [Y4: b] :
( !! @ b
@ ^ [Y5: b] :
( ( Y0 @ Y3 @ Y5 @ Y4 )
=> ( Y0 @ Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) )
=> ( ( !! @ ( a > b )
@ ^ [Y2: a > b] :
( !! @ ( a > b )
@ ^ [Y3: a > b] :
( !! @ ( a > b )
@ ^ [Y4: a > b] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y0 @ Y5 @ ( Y2 @ Y5 ) @ ( Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y0 @ Y5 @ ( Y4 @ Y5 ) @ ( Y3 @ Y6 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y0 @ Y5 @ ( Y2 @ Y5 ) @ ( Y3 @ Y6 ) ) ) ) ) ) ) ) )
& ( !! @ ( a > b )
@ ^ [Y2: a > b] :
( !! @ ( a > b )
@ ^ [Y3: a > b] :
( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y1 @ Y5 @ Y4 )
=> ( Y0 @ Y5 @ ( Y3 @ Y5 ) @ ( Y2 @ Y4 ) ) ) ) )
=> ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y1 @ Y4 @ Y5 )
=> ( Y0 @ Y4 @ ( Y2 @ Y4 ) @ ( Y3 @ Y5 ) ) ) ) ) ) ) )
& ( ( ^ [Y2: a > b,Y3: a > b] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y0 @ Y5 @ ( Y2 @ Y5 ) @ ( Y3 @ Y4 ) ) ) ) ) )
= ( ^ [Y2: a > b,Y3: a > b] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y1 @ Y4 @ Y5 )
=> ( Y0 @ Y4 @ ( Y2 @ Y4 ) @ ( Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f10]) ).
thf(f10,plain,
( $false
= ( ^ [Y0: a > a > $o] :
( !! @ ( a > b > b > $o )
@ ^ [Y1: a > b > b > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( Y2 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y3 @ Y4 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 @ Y3 )
=> ( ( ( Y1 @ Y4 )
= ( Y1 @ Y3 ) )
& ( !! @ b
@ ^ [Y5: b] :
( !! @ b
@ ^ [Y6: b] :
( !! @ b
@ ^ [Y7: b] :
( ( ( Y1 @ Y4 @ Y7 @ Y6 )
& ( Y1 @ Y4 @ Y6 @ Y5 ) )
=> ( Y1 @ Y4 @ Y7 @ Y5 ) ) ) ) )
& ( !! @ b
@ ^ [Y5: b] :
( !! @ b
@ ^ [Y6: b] :
( ( Y1 @ Y4 @ Y6 @ Y5 )
=> ( Y1 @ Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) )
=> ( ( !! @ ( a > b )
@ ^ [Y3: a > b] :
( !! @ ( a > b )
@ ^ [Y4: a > b] :
( !! @ ( a > b )
@ ^ [Y5: a > b] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y6 @ Y7 )
=> ( Y1 @ Y6 @ ( Y3 @ Y6 ) @ ( Y5 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y6 @ Y7 )
=> ( Y1 @ Y6 @ ( Y5 @ Y6 ) @ ( Y4 @ Y7 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y6 @ Y7 )
=> ( Y1 @ Y6 @ ( Y3 @ Y6 ) @ ( Y4 @ Y7 ) ) ) ) ) ) ) ) )
& ( !! @ ( a > b )
@ ^ [Y3: a > b] :
( !! @ ( a > b )
@ ^ [Y4: a > b] :
( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y2 @ Y6 @ Y5 )
=> ( Y1 @ Y6 @ ( Y4 @ Y6 ) @ ( Y3 @ Y5 ) ) ) ) )
=> ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y2 @ Y5 @ Y6 )
=> ( Y1 @ Y5 @ ( Y3 @ Y5 ) @ ( Y4 @ Y6 ) ) ) ) ) ) ) )
& ( ( ^ [Y3: a > b,Y4: a > b] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y6 @ Y5 )
=> ( Y1 @ Y6 @ ( Y3 @ Y6 ) @ ( Y4 @ Y5 ) ) ) ) ) )
= ( ^ [Y3: a > b,Y4: a > b] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y2 @ Y5 @ Y6 )
=> ( Y1 @ Y5 @ ( Y3 @ Y5 ) @ ( Y4 @ Y6 ) ) ) ) ) ) ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > b > b > $o )
@ ^ [Y1: a > b > b > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( Y2 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y3 @ Y4 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 @ Y3 )
=> ( ( ( Y1 @ Y4 )
= ( Y1 @ Y3 ) )
& ( !! @ b
@ ^ [Y5: b] :
( !! @ b
@ ^ [Y6: b] :
( !! @ b
@ ^ [Y7: b] :
( ( ( Y1 @ Y4 @ Y7 @ Y6 )
& ( Y1 @ Y4 @ Y6 @ Y5 ) )
=> ( Y1 @ Y4 @ Y7 @ Y5 ) ) ) ) )
& ( !! @ b
@ ^ [Y5: b] :
( !! @ b
@ ^ [Y6: b] :
( ( Y1 @ Y4 @ Y6 @ Y5 )
=> ( Y1 @ Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) )
=> ( ( !! @ ( a > b )
@ ^ [Y3: a > b] :
( !! @ ( a > b )
@ ^ [Y4: a > b] :
( !! @ ( a > b )
@ ^ [Y5: a > b] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y6 @ Y7 )
=> ( Y1 @ Y6 @ ( Y3 @ Y6 ) @ ( Y5 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y6 @ Y7 )
=> ( Y1 @ Y6 @ ( Y5 @ Y6 ) @ ( Y4 @ Y7 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y6 @ Y7 )
=> ( Y1 @ Y6 @ ( Y3 @ Y6 ) @ ( Y4 @ Y7 ) ) ) ) ) ) ) ) )
& ( !! @ ( a > b )
@ ^ [Y3: a > b] :
( !! @ ( a > b )
@ ^ [Y4: a > b] :
( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y2 @ Y6 @ Y5 )
=> ( Y1 @ Y6 @ ( Y4 @ Y6 ) @ ( Y3 @ Y5 ) ) ) ) )
=> ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y2 @ Y5 @ Y6 )
=> ( Y1 @ Y5 @ ( Y3 @ Y5 ) @ ( Y4 @ Y6 ) ) ) ) ) ) ) )
& ( ( ^ [Y3: a > b,Y4: a > b] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y6 @ Y5 )
=> ( Y1 @ Y6 @ ( Y3 @ Y6 ) @ ( Y4 @ Y5 ) ) ) ) ) )
= ( ^ [Y3: a > b,Y4: a > b] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y2 @ Y5 @ Y6 )
=> ( Y1 @ Y5 @ ( Y3 @ Y5 ) @ ( Y4 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > b > b > $o )
@ ^ [Y1: a > b > b > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( Y2 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y3 @ Y4 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 @ Y3 )
=> ( ( ( Y1 @ Y4 )
= ( Y1 @ Y3 ) )
& ( !! @ b
@ ^ [Y5: b] :
( !! @ b
@ ^ [Y6: b] :
( !! @ b
@ ^ [Y7: b] :
( ( ( Y1 @ Y4 @ Y7 @ Y6 )
& ( Y1 @ Y4 @ Y6 @ Y5 ) )
=> ( Y1 @ Y4 @ Y7 @ Y5 ) ) ) ) )
& ( !! @ b
@ ^ [Y5: b] :
( !! @ b
@ ^ [Y6: b] :
( ( Y1 @ Y4 @ Y6 @ Y5 )
=> ( Y1 @ Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) )
=> ( ( !! @ ( a > b )
@ ^ [Y3: a > b] :
( !! @ ( a > b )
@ ^ [Y4: a > b] :
( !! @ ( a > b )
@ ^ [Y5: a > b] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y6 @ Y7 )
=> ( Y1 @ Y6 @ ( Y3 @ Y6 ) @ ( Y5 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y6 @ Y7 )
=> ( Y1 @ Y6 @ ( Y5 @ Y6 ) @ ( Y4 @ Y7 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y6 @ Y7 )
=> ( Y1 @ Y6 @ ( Y3 @ Y6 ) @ ( Y4 @ Y7 ) ) ) ) ) ) ) ) )
& ( !! @ ( a > b )
@ ^ [Y3: a > b] :
( !! @ ( a > b )
@ ^ [Y4: a > b] :
( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y2 @ Y6 @ Y5 )
=> ( Y1 @ Y6 @ ( Y4 @ Y6 ) @ ( Y3 @ Y5 ) ) ) ) )
=> ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y2 @ Y5 @ Y6 )
=> ( Y1 @ Y5 @ ( Y3 @ Y5 ) @ ( Y4 @ Y6 ) ) ) ) ) ) ) )
& ( ( ^ [Y3: a > b,Y4: a > b] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y6 @ Y5 )
=> ( Y1 @ Y6 @ ( Y3 @ Y6 ) @ ( Y4 @ Y5 ) ) ) ) ) )
= ( ^ [Y3: a > b,Y4: a > b] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y2 @ Y5 @ Y6 )
=> ( Y1 @ Y5 @ ( Y3 @ Y5 ) @ ( Y4 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > b > b > $o )
@ ^ [Y1: a > b > b > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( Y2 = Y0 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y3 @ Y4 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y2 @ Y4 @ Y3 )
=> ( ( ( Y1 @ Y4 )
= ( Y1 @ Y3 ) )
& ( !! @ b
@ ^ [Y5: b] :
( !! @ b
@ ^ [Y6: b] :
( !! @ b
@ ^ [Y7: b] :
( ( ( Y1 @ Y4 @ Y7 @ Y6 )
& ( Y1 @ Y4 @ Y6 @ Y5 ) )
=> ( Y1 @ Y4 @ Y7 @ Y5 ) ) ) ) )
& ( !! @ b
@ ^ [Y5: b] :
( !! @ b
@ ^ [Y6: b] :
( ( Y1 @ Y4 @ Y6 @ Y5 )
=> ( Y1 @ Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) )
=> ( ( !! @ ( a > b )
@ ^ [Y3: a > b] :
( !! @ ( a > b )
@ ^ [Y4: a > b] :
( !! @ ( a > b )
@ ^ [Y5: a > b] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y6 @ Y7 )
=> ( Y1 @ Y6 @ ( Y3 @ Y6 ) @ ( Y5 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y6 @ Y7 )
=> ( Y1 @ Y6 @ ( Y5 @ Y6 ) @ ( Y4 @ Y7 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y6 @ Y7 )
=> ( Y1 @ Y6 @ ( Y3 @ Y6 ) @ ( Y4 @ Y7 ) ) ) ) ) ) ) ) )
& ( !! @ ( a > b )
@ ^ [Y3: a > b] :
( !! @ ( a > b )
@ ^ [Y4: a > b] :
( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y2 @ Y6 @ Y5 )
=> ( Y1 @ Y6 @ ( Y4 @ Y6 ) @ ( Y3 @ Y5 ) ) ) ) )
=> ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y2 @ Y5 @ Y6 )
=> ( Y1 @ Y5 @ ( Y3 @ Y5 ) @ ( Y4 @ Y6 ) ) ) ) ) ) ) )
& ( ( ^ [Y3: a > b,Y4: a > b] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y6 @ Y5 )
=> ( Y1 @ Y6 @ ( Y3 @ Y6 ) @ ( Y4 @ Y5 ) ) ) ) ) )
= ( ^ [Y3: a > b,Y4: a > b] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y2 @ Y5 @ Y6 )
=> ( Y1 @ Y5 @ ( Y3 @ Y5 ) @ ( Y4 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > a > $o,X1: a > b > b > $o,X2: a > a > $o] :
( ( ! [X3: a,X4: a,X5: a] :
( ( ( X0 @ X4 @ X3 )
& ( X0 @ X3 @ X5 ) )
=> ( X0 @ X4 @ X5 ) )
& ! [X6: a,X7: a] :
( ( X0 @ X7 @ X6 )
=> ( X0 @ X6 @ X7 ) )
& ( X0 = X2 ) )
=> ( ! [X8: a,X9: a] :
( ( X0 @ X8 @ X9 )
=> ( ! [X10: b,X11: b] :
( ( X1 @ X8 @ X10 @ X11 )
=> ( X1 @ X8 @ X11 @ X10 ) )
& ! [X12: b,X13: b,X14: b] :
( ( ( X1 @ X8 @ X13 @ X14 )
& ( X1 @ X8 @ X12 @ X13 ) )
=> ( X1 @ X8 @ X12 @ X14 ) )
& ( ( X1 @ X8 )
= ( X1 @ X9 ) ) ) )
=> ( ( ( ^ [X15: a > b,X16: a > b] :
! [X17: a,X18: a] :
( ( X2 @ X17 @ X18 )
=> ( X1 @ X17 @ ( X15 @ X17 ) @ ( X16 @ X18 ) ) ) )
= ( ^ [X19: a > b,X20: a > b] :
! [X21: a,X22: a] :
( ( X0 @ X22 @ X21 )
=> ( X1 @ X22 @ ( X19 @ X22 ) @ ( X20 @ X21 ) ) ) ) )
& ! [X23: a > b,X24: a > b] :
( ! [X25: a,X26: a] :
( ( X0 @ X25 @ X26 )
=> ( X1 @ X25 @ ( X23 @ X25 ) @ ( X24 @ X26 ) ) )
=> ! [X27: a,X28: a] :
( ( X0 @ X28 @ X27 )
=> ( X1 @ X28 @ ( X24 @ X28 ) @ ( X23 @ X27 ) ) ) )
& ! [X29: a > b,X30: a > b,X31: a > b] :
( ( ! [X32: a,X33: a] :
( ( X0 @ X33 @ X32 )
=> ( X1 @ X33 @ ( X29 @ X33 ) @ ( X30 @ X32 ) ) )
& ! [X34: a,X35: a] :
( ( X0 @ X35 @ X34 )
=> ( X1 @ X35 @ ( X31 @ X35 ) @ ( X29 @ X34 ) ) ) )
=> ! [X36: a,X37: a] :
( ( X0 @ X37 @ X36 )
=> ( X1 @ X37 @ ( X31 @ X37 ) @ ( X30 @ X36 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > a > $o,X2: a > b > b > $o,X1: a > a > $o] :
( ( ! [X4: a,X3: a,X5: a] :
( ( ( X0 @ X3 @ X4 )
& ( X0 @ X4 @ X5 ) )
=> ( X0 @ X3 @ X5 ) )
& ! [X4: a,X3: a] :
( ( X0 @ X3 @ X4 )
=> ( X0 @ X4 @ X3 ) )
& ( X0 = X1 ) )
=> ( ! [X3: a,X4: a] :
( ( X0 @ X3 @ X4 )
=> ( ! [X6: b,X7: b] :
( ( X2 @ X3 @ X6 @ X7 )
=> ( X2 @ X3 @ X7 @ X6 ) )
& ! [X6: b,X7: b,X5: b] :
( ( ( X2 @ X3 @ X7 @ X5 )
& ( X2 @ X3 @ X6 @ X7 ) )
=> ( X2 @ X3 @ X6 @ X5 ) )
& ( ( X2 @ X3 )
= ( X2 @ X4 ) ) ) )
=> ( ( ( ^ [X8: a > b,X9: a > b] :
! [X3: a,X4: a] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ ( X8 @ X3 ) @ ( X9 @ X4 ) ) ) )
= ( ^ [X8: a > b,X9: a > b] :
! [X4: a,X3: a] :
( ( X0 @ X3 @ X4 )
=> ( X2 @ X3 @ ( X8 @ X3 ) @ ( X9 @ X4 ) ) ) ) )
& ! [X3: a > b,X4: a > b] :
( ! [X6: a,X7: a] :
( ( X0 @ X6 @ X7 )
=> ( X2 @ X6 @ ( X3 @ X6 ) @ ( X4 @ X7 ) ) )
=> ! [X7: a,X6: a] :
( ( X0 @ X6 @ X7 )
=> ( X2 @ X6 @ ( X4 @ X6 ) @ ( X3 @ X7 ) ) ) )
& ! [X4: a > b,X5: a > b,X3: a > b] :
( ( ! [X7: a,X6: a] :
( ( X0 @ X6 @ X7 )
=> ( X2 @ X6 @ ( X4 @ X6 ) @ ( X5 @ X7 ) ) )
& ! [X7: a,X6: a] :
( ( X0 @ X6 @ X7 )
=> ( X2 @ X6 @ ( X3 @ X6 ) @ ( X4 @ X7 ) ) ) )
=> ! [X7: a,X6: a] :
( ( X0 @ X6 @ X7 )
=> ( X2 @ X6 @ ( X3 @ X6 ) @ ( X5 @ X7 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a > a > $o,X2: a > b > b > $o,X1: a > a > $o] :
( ( ! [X4: a,X3: a,X5: a] :
( ( ( X0 @ X3 @ X4 )
& ( X0 @ X4 @ X5 ) )
=> ( X0 @ X3 @ X5 ) )
& ! [X4: a,X3: a] :
( ( X0 @ X3 @ X4 )
=> ( X0 @ X4 @ X3 ) )
& ( X0 = X1 ) )
=> ( ! [X3: a,X4: a] :
( ( X0 @ X3 @ X4 )
=> ( ! [X6: b,X7: b] :
( ( X2 @ X3 @ X6 @ X7 )
=> ( X2 @ X3 @ X7 @ X6 ) )
& ! [X6: b,X7: b,X5: b] :
( ( ( X2 @ X3 @ X7 @ X5 )
& ( X2 @ X3 @ X6 @ X7 ) )
=> ( X2 @ X3 @ X6 @ X5 ) )
& ( ( X2 @ X3 )
= ( X2 @ X4 ) ) ) )
=> ( ( ( ^ [X8: a > b,X9: a > b] :
! [X3: a,X4: a] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ ( X8 @ X3 ) @ ( X9 @ X4 ) ) ) )
= ( ^ [X8: a > b,X9: a > b] :
! [X4: a,X3: a] :
( ( X0 @ X3 @ X4 )
=> ( X2 @ X3 @ ( X8 @ X3 ) @ ( X9 @ X4 ) ) ) ) )
& ! [X3: a > b,X4: a > b] :
( ! [X6: a,X7: a] :
( ( X0 @ X6 @ X7 )
=> ( X2 @ X6 @ ( X3 @ X6 ) @ ( X4 @ X7 ) ) )
=> ! [X7: a,X6: a] :
( ( X0 @ X6 @ X7 )
=> ( X2 @ X6 @ ( X4 @ X6 ) @ ( X3 @ X7 ) ) ) )
& ! [X4: a > b,X5: a > b,X3: a > b] :
( ( ! [X7: a,X6: a] :
( ( X0 @ X6 @ X7 )
=> ( X2 @ X6 @ ( X4 @ X6 ) @ ( X5 @ X7 ) ) )
& ! [X7: a,X6: a] :
( ( X0 @ X6 @ X7 )
=> ( X2 @ X6 @ ( X3 @ X6 ) @ ( X4 @ X7 ) ) ) )
=> ! [X7: a,X6: a] :
( ( X0 @ X6 @ X7 )
=> ( X2 @ X6 @ ( X3 @ X6 ) @ ( X5 @ X7 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.DsRAyE7nCA/DTF2THF_14528.p',cTHM516_pme) ).
thf(f1328,plain,
( ( ( ( sK4 @ sK19 @ sK20 )
=> ( sK3 @ sK19 @ ( sK15 @ sK19 ) @ ( sK16 @ sK20 ) ) )
= $false )
| ~ spl0_8 ),
inference(beta_eta_normalization,[status(thm)],[f1327]) ).
thf(f1327,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK4 @ sK19 @ Y0 )
=> ( sK3 @ sK19 @ ( sK15 @ sK19 ) @ ( sK16 @ Y0 ) ) )
@ sK20 ) )
| ~ spl0_8 ),
inference(sigma_clausification,[status(thm)],[f1326]) ).
thf(f1326,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ sK19 @ Y0 )
=> ( sK3 @ sK19 @ ( sK15 @ sK19 ) @ ( sK16 @ Y0 ) ) ) ) )
| ~ spl0_8 ),
inference(beta_eta_normalization,[status(thm)],[f1325]) ).
thf(f1325,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK3 @ Y0 @ ( sK15 @ Y0 ) @ ( sK16 @ Y1 ) ) ) )
@ sK19 ) )
| ~ spl0_8 ),
inference(sigma_clausification,[status(thm)],[f1281]) ).
thf(f1281,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK3 @ Y0 @ ( sK15 @ Y0 ) @ ( sK16 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f1280]) ).
thf(f1280,definition,
( spl0_8
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK3 @ Y0 @ ( sK15 @ Y0 ) @ ( sK16 @ Y1 ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition]) ).
thf(f1315,plain,
( ~ spl0_6
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f1314]) ).
thf(f1314,plain,
( $false
| ~ spl0_6
| ~ spl0_8 ),
inference(trivial_inequality_removal,[status(thm)],[f1313]) ).
thf(f1313,plain,
( ( $false = $true )
| ~ spl0_6
| ~ spl0_8 ),
inference(backward_demodulation,[status(thm)],[f1274,f1281]) ).
thf(f1274,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK3 @ Y0 @ ( sK15 @ Y0 ) @ ( sK16 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f1273]) ).
thf(f1273,definition,
( spl0_6
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK3 @ Y0 @ ( sK15 @ Y0 ) @ ( sK16 @ Y1 ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f1307,plain,
( ~ spl0_1
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f1306]) ).
thf(f1306,plain,
( $false
| ~ spl0_1
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f1302]) ).
thf(f1302,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_7 ),
inference(superposition,[status(thm)],[f1298,f1288]) ).
thf(f1288,plain,
( ! [X2: a,X1: a] :
( ( ( sK2 @ X1 @ X2 )
=> ( sK3 @ X1 @ ( sK15 @ X1 ) @ ( sK16 @ X2 ) ) )
= $true )
| ~ spl0_1
| ~ spl0_7 ),
inference(forward_demodulation,[status(thm)],[f1287,f50]) ).
thf(f1287,plain,
( ! [X2: a,X1: a] :
( ( ( sK4 @ X1 @ X2 )
=> ( sK3 @ X1 @ ( sK15 @ X1 ) @ ( sK16 @ X2 ) ) )
= $true )
| ~ spl0_1
| ~ spl0_7 ),
inference(beta_eta_normalization,[status(thm)],[f1286]) ).
thf(f1286,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( sK4 @ X1 @ Y0 )
=> ( sK3 @ X1 @ ( sK15 @ X1 ) @ ( sK16 @ Y0 ) ) )
@ X2 )
= $true )
| ~ spl0_1
| ~ spl0_7 ),
inference(pi_clausification,[status(thm)],[f1285]) ).
thf(f1285,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ X1 @ Y0 )
=> ( sK3 @ X1 @ ( sK15 @ X1 ) @ ( sK16 @ Y0 ) ) ) )
= $true )
| ~ spl0_1
| ~ spl0_7 ),
inference(beta_eta_normalization,[status(thm)],[f1284]) ).
thf(f1284,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK3 @ Y0 @ ( sK15 @ Y0 ) @ ( sK16 @ Y1 ) ) ) )
@ X1 )
= $true )
| ~ spl0_1
| ~ spl0_7 ),
inference(pi_clausification,[status(thm)],[f1283]) ).
thf(f1283,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK3 @ Y0 @ ( sK15 @ Y0 ) @ ( sK16 @ Y1 ) ) ) ) )
!= $false )
| ~ spl0_1
| ~ spl0_7 ),
inference(backward_demodulation,[status(thm)],[f1266,f1278]) ).
thf(f1278,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK3 @ Y1 @ ( sK15 @ Y1 ) @ ( sK16 @ Y0 ) ) ) ) ) )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f1277]) ).
thf(f1277,definition,
( spl0_7
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK3 @ Y1 @ ( sK15 @ Y1 ) @ ( sK16 @ Y0 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f1266,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK3 @ Y0 @ ( sK15 @ Y0 ) @ ( sK16 @ Y1 ) ) ) ) )
!= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK3 @ Y1 @ ( sK15 @ Y1 ) @ ( sK16 @ Y0 ) ) ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f1265]) ).
thf(f1265,plain,
( ( ( ^ [Y0: a > b] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( sK3 @ Y2 @ ( sK15 @ Y2 ) @ ( Y0 @ Y1 ) ) ) ) )
@ sK16 )
!= ( ^ [Y0: a > b] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( sK3 @ Y1 @ ( sK15 @ Y1 ) @ ( Y0 @ Y2 ) ) ) ) )
@ sK16 ) )
| ~ spl0_1 ),
inference(negative_extensionality,[status(thm)],[f1264]) ).
thf(f1264,plain,
( ( ( ^ [Y0: a > b] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( sK3 @ Y1 @ ( sK15 @ Y1 ) @ ( Y0 @ Y2 ) ) ) ) ) )
!= ( ^ [Y0: a > b] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( sK3 @ Y2 @ ( sK15 @ Y2 ) @ ( Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f1263]) ).
thf(f1263,plain,
( ( ( ^ [Y0: a > b,Y1: a > b] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( sK3 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y2 ) ) ) ) )
@ sK15 )
!= ( ^ [Y0: a > b,Y1: a > b] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y2 @ Y3 )
=> ( sK3 @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
@ sK15 ) )
| ~ spl0_1 ),
inference(negative_extensionality,[status(thm)],[f1262]) ).
thf(f1262,plain,
( ( ( ^ [Y0: a > b,Y1: a > b] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y2 @ Y3 )
=> ( sK3 @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) ) )
!= ( ^ [Y0: a > b,Y1: a > b] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( sK3 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y2 ) ) ) ) ) ) )
| ~ spl0_1 ),
inference(equality_proxy_clausification,[status(thm)],[f77]) ).
thf(f77,plain,
( ( $false
= ( ( ^ [Y0: a > b,Y1: a > b] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( sK3 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y2 ) ) ) ) ) )
= ( ^ [Y0: a > b,Y1: a > b] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y2 @ Y3 )
=> ( sK3 @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) ) ) ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f76]) ).
thf(f76,definition,
( spl0_1
<=> ( $false
= ( ( ^ [Y0: a > b,Y1: a > b] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( sK3 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y2 ) ) ) ) ) )
= ( ^ [Y0: a > b,Y1: a > b] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y2 @ Y3 )
=> ( sK3 @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f1298,plain,
( ( $false
= ( ( sK2 @ sK18 @ sK17 )
=> ( sK3 @ sK18 @ ( sK15 @ sK18 ) @ ( sK16 @ sK17 ) ) ) )
| ~ spl0_7 ),
inference(beta_eta_normalization,[status(thm)],[f1297]) ).
thf(f1297,plain,
( ( ( ^ [Y0: a] :
( ( sK2 @ Y0 @ sK17 )
=> ( sK3 @ Y0 @ ( sK15 @ Y0 ) @ ( sK16 @ sK17 ) ) )
@ sK18 )
= $false )
| ~ spl0_7 ),
inference(sigma_clausification,[status(thm)],[f1296]) ).
thf(f1296,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ sK17 )
=> ( sK3 @ Y0 @ ( sK15 @ Y0 ) @ ( sK16 @ sK17 ) ) ) ) )
| ~ spl0_7 ),
inference(beta_eta_normalization,[status(thm)],[f1295]) ).
thf(f1295,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK3 @ Y1 @ ( sK15 @ Y1 ) @ ( sK16 @ Y0 ) ) ) )
@ sK17 ) )
| ~ spl0_7 ),
inference(sigma_clausification,[status(thm)],[f1278]) ).
thf(f1282,plain,
( spl0_7
| spl0_8
| ~ spl0_1 ),
inference(avatar_split_clause,[status(thm)],[f1268,f76,f1280,f1277]) ).
thf(f1268,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK3 @ Y1 @ ( sK15 @ Y1 ) @ ( sK16 @ Y0 ) ) ) ) ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK3 @ Y0 @ ( sK15 @ Y0 ) @ ( sK16 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f1266]) ).
thf(f1275,plain,
( spl0_5
| spl0_6
| ~ spl0_1 ),
inference(avatar_split_clause,[status(thm)],[f1267,f76,f1273,f1270]) ).
thf(f1267,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK3 @ Y0 @ ( sK15 @ Y0 ) @ ( sK16 @ Y1 ) ) ) ) )
= $true )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK3 @ Y1 @ ( sK15 @ Y1 ) @ ( sK16 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f1266]) ).
thf(f1259,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[status(thm)],[f1258]) ).
thf(f1258,plain,
( $false
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f1257]) ).
thf(f1257,plain,
( ( $false = $true )
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f1245,f964]) ).
thf(f964,plain,
( ( $false
= ( sK3 @ sK13 @ ( sK11 @ sK13 ) @ ( sK12 @ sK14 ) ) )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f963]) ).
thf(f963,plain,
( ( $false
= ( $true
=> ( sK3 @ sK13 @ ( sK11 @ sK13 ) @ ( sK12 @ sK14 ) ) ) )
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f957,f959]) ).
thf(f959,plain,
( ( ( sK2 @ sK13 @ sK14 )
= $true )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f957]) ).
thf(f957,plain,
( ( ( ( sK2 @ sK13 @ sK14 )
=> ( sK3 @ sK13 @ ( sK11 @ sK13 ) @ ( sK12 @ sK14 ) ) )
= $false )
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f956,f50]) ).
thf(f956,plain,
( ( $false
= ( ( sK4 @ sK13 @ sK14 )
=> ( sK3 @ sK13 @ ( sK11 @ sK13 ) @ ( sK12 @ sK14 ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f955]) ).
thf(f955,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK4 @ sK13 @ Y0 )
=> ( sK3 @ sK13 @ ( sK11 @ sK13 ) @ ( sK12 @ Y0 ) ) )
@ sK14 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f954]) ).
thf(f954,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ sK13 @ Y0 )
=> ( sK3 @ sK13 @ ( sK11 @ sK13 ) @ ( sK12 @ Y0 ) ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f953]) ).
thf(f953,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK3 @ Y0 @ ( sK11 @ Y0 ) @ ( sK12 @ Y1 ) ) ) )
@ sK13 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f947]) ).
thf(f947,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK3 @ Y0 @ ( sK11 @ Y0 ) @ ( sK12 @ Y1 ) ) ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f946]) ).
thf(f946,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 @ Y0 )
=> ( sK3 @ Y1 @ ( sK12 @ Y1 ) @ ( sK11 @ Y0 ) ) ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK3 @ Y0 @ ( sK11 @ Y0 ) @ ( sK12 @ Y1 ) ) ) ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f945]) ).
thf(f945,plain,
( ( $false
= ( ^ [Y0: a > b] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y2 @ Y1 )
=> ( sK3 @ Y2 @ ( Y0 @ Y2 ) @ ( sK11 @ Y1 ) ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( sK3 @ Y1 @ ( sK11 @ Y1 ) @ ( Y0 @ Y2 ) ) ) ) ) )
@ sK12 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f944]) ).
thf(f944,plain,
( ( ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y2 @ Y1 )
=> ( sK3 @ Y2 @ ( Y0 @ Y2 ) @ ( sK11 @ Y1 ) ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( sK3 @ Y1 @ ( sK11 @ Y1 ) @ ( Y0 @ Y2 ) ) ) ) ) ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f943]) ).
thf(f943,plain,
( ( $false
= ( ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y3 @ Y2 )
=> ( sK3 @ Y3 @ ( Y1 @ Y3 ) @ ( Y0 @ Y2 ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y2 @ Y3 )
=> ( sK3 @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) ) ) )
@ sK11 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f91]) ).
thf(f91,plain,
( ( $false
= ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y3 @ Y2 )
=> ( sK3 @ Y3 @ ( Y1 @ Y3 ) @ ( Y0 @ Y2 ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y2 @ Y3 )
=> ( sK3 @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) ) ) ) ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f90]) ).
thf(f90,definition,
( spl0_4
<=> ( $false
= ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y3 @ Y2 )
=> ( sK3 @ Y3 @ ( Y1 @ Y3 ) @ ( Y0 @ Y2 ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y2 @ Y3 )
=> ( sK3 @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f1245,plain,
( ( $true
= ( sK3 @ sK13 @ ( sK11 @ sK13 ) @ ( sK12 @ sK14 ) ) )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f1242]) ).
thf(f1242,plain,
( ( ( $true
=> ( sK3 @ sK13 @ ( sK11 @ sK13 ) @ ( sK12 @ sK14 ) ) )
= $true )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f1231,f1170]) ).
thf(f1170,plain,
( ( ( sK3 @ sK13 @ ( sK12 @ sK14 ) @ ( sK11 @ sK13 ) )
= $true )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f1058,f1163]) ).
thf(f1163,plain,
( ! [X2: b,X1: b] :
( ( sK3 @ sK13 @ X1 @ X2 )
= ( sK3 @ sK14 @ X1 @ X2 ) )
| ~ spl0_4 ),
inference(argument_congruence,[status(thm)],[f1156]) ).
thf(f1156,plain,
( ! [X1: b] :
( ( sK3 @ sK14 @ X1 )
= ( sK3 @ sK13 @ X1 ) )
| ~ spl0_4 ),
inference(argument_congruence,[status(thm)],[f1142]) ).
thf(f1142,plain,
( ( ( sK3 @ sK13 )
= ( sK3 @ sK14 ) )
| ~ spl0_4 ),
inference(equality_proxy_clausification,[status(thm)],[f1141]) ).
thf(f1141,plain,
( ( ( ( sK3 @ sK13 )
= ( sK3 @ sK14 ) )
= $true )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f1140]) ).
thf(f1140,plain,
( ( ( ( ( sK3 @ sK13 )
= ( sK3 @ sK14 ) )
& $true )
= $true )
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f1139,f1138]) ).
thf(f1138,plain,
( ( ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK3 @ sK13 @ Y1 @ Y0 )
=> ( sK3 @ sK13 @ Y0 @ Y1 ) ) ) )
= $true )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f1136]) ).
thf(f1136,plain,
( ( ( $true
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK3 @ sK13 @ Y1 @ Y0 )
=> ( sK3 @ sK13 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f1049,f1135]) ).
thf(f1135,plain,
( ( $true
= ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK3 @ sK13 @ Y2 @ Y1 )
& ( sK3 @ sK13 @ Y1 @ Y0 ) )
=> ( sK3 @ sK13 @ Y2 @ Y0 ) ) ) ) ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f1049]) ).
thf(f1049,plain,
( ( ( ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK3 @ sK13 @ Y2 @ Y1 )
& ( sK3 @ sK13 @ Y1 @ Y0 ) )
=> ( sK3 @ sK13 @ Y2 @ Y0 ) ) ) ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK3 @ sK13 @ Y1 @ Y0 )
=> ( sK3 @ sK13 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f1048]) ).
thf(f1048,plain,
( ( ( $true
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK3 @ sK13 @ Y2 @ Y1 )
& ( sK3 @ sK13 @ Y1 @ Y0 ) )
=> ( sK3 @ sK13 @ Y2 @ Y0 ) ) ) ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK3 @ sK13 @ Y1 @ Y0 )
=> ( sK3 @ sK13 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f1047]) ).
thf(f1047,plain,
( ( ( ( ( sK3 @ sK13 )
= ( sK3 @ sK13 ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK3 @ sK13 @ Y2 @ Y1 )
& ( sK3 @ sK13 @ Y1 @ Y0 ) )
=> ( sK3 @ sK13 @ Y2 @ Y0 ) ) ) ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK3 @ sK13 @ Y1 @ Y0 )
=> ( sK3 @ sK13 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f1028]) ).
thf(f1028,plain,
( ( ( $true
=> ( ( ( sK3 @ sK13 )
= ( sK3 @ sK13 ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK3 @ sK13 @ Y2 @ Y1 )
& ( sK3 @ sK13 @ Y1 @ Y0 ) )
=> ( sK3 @ sK13 @ Y2 @ Y0 ) ) ) ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK3 @ sK13 @ Y1 @ Y0 )
=> ( sK3 @ sK13 @ Y0 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f54,f1019]) ).
thf(f1019,plain,
( ( ( sK2 @ sK13 @ sK13 )
= $true )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f1018]) ).
thf(f1018,plain,
( ( $true
= ( $true
=> ( sK2 @ sK13 @ sK13 ) ) )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f973,f962]) ).
thf(f962,plain,
( ( ( sK2 @ sK14 @ sK13 )
= $true )
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f961]) ).
thf(f961,plain,
( ( ( sK2 @ sK14 @ sK13 )
= $true )
| ( $false = $true )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f960]) ).
thf(f960,plain,
( ( $false
= ( $false
=> ( sK3 @ sK13 @ ( sK11 @ sK13 ) @ ( sK12 @ sK14 ) ) ) )
| ( ( sK2 @ sK14 @ sK13 )
= $true )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f957,f84]) ).
thf(f84,plain,
! [X2: a,X1: a] :
( ( $false
= ( sK2 @ X1 @ X2 ) )
| ( ( sK2 @ X2 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f73]) ).
thf(f73,plain,
! [X2: a,X1: a] :
( ( ( sK2 @ X1 @ X2 )
=> ( sK2 @ X2 @ X1 ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f72,f50]) ).
thf(f72,plain,
! [X2: a,X1: a] :
( ( ( sK2 @ X1 @ X2 )
=> ( sK4 @ X2 @ X1 ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f71,f50]) ).
thf(f71,plain,
! [X2: a,X1: a] :
( ( ( sK4 @ X1 @ X2 )
=> ( sK4 @ X2 @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f70]) ).
thf(f70,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK4 @ X1 @ Y0 )
=> ( sK4 @ Y0 @ X1 ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f68]) ).
thf(f68,plain,
! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ X1 @ Y0 )
=> ( sK4 @ Y0 @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f67]) ).
thf(f67,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK4 @ Y1 @ Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK4 @ Y1 @ Y0 ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f39]) ).
thf(f39,plain,
( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK4 @ Y1 @ Y0 ) ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f21,f38]) ).
thf(f973,plain,
( ! [X0: a] :
( ( ( sK2 @ sK14 @ X0 )
=> ( sK2 @ sK13 @ X0 ) )
= $true )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f967]) ).
thf(f967,plain,
( ! [X0: a] :
( $true
= ( ( ( sK2 @ sK14 @ X0 )
& $true )
=> ( sK2 @ sK13 @ X0 ) ) )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f59,f959]) ).
thf(f59,plain,
! [X2: a,X3: a,X1: a] :
( ( ( ( sK2 @ X3 @ X1 )
& ( sK2 @ X2 @ X3 ) )
=> ( sK2 @ X2 @ X1 ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f58,f50]) ).
thf(f58,plain,
! [X2: a,X3: a,X1: a] :
( ( ( ( sK2 @ X3 @ X1 )
& ( sK2 @ X2 @ X3 ) )
=> ( sK4 @ X2 @ X1 ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f52,f50]) ).
thf(f52,plain,
! [X2: a,X3: a,X1: a] :
( ( ( ( sK4 @ X3 @ X1 )
& ( sK2 @ X2 @ X3 ) )
=> ( sK4 @ X2 @ X1 ) )
= $true ),
inference(backward_demodulation,[status(thm)],[f35,f50]) ).
thf(f35,plain,
! [X2: a,X3: a,X1: a] :
( ( ( ( sK4 @ X3 @ X1 )
& ( sK4 @ X2 @ X3 ) )
=> ( sK4 @ X2 @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f34]) ).
thf(f34,plain,
! [X2: a,X3: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK4 @ Y0 @ X1 )
& ( sK4 @ X2 @ Y0 ) )
=> ( sK4 @ X2 @ X1 ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
! [X2: a,X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ Y0 @ X1 )
& ( sK4 @ X2 @ Y0 ) )
=> ( sK4 @ X2 @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f32]) ).
thf(f32,plain,
! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ X1 )
& ( sK4 @ Y0 @ Y1 ) )
=> ( sK4 @ Y0 @ X1 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ X1 )
& ( sK4 @ Y0 @ Y1 ) )
=> ( sK4 @ Y0 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f30]) ).
thf(f30,plain,
! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y0 )
& ( sK4 @ Y1 @ Y2 ) )
=> ( sK4 @ Y1 @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y0 )
& ( sK4 @ Y1 @ Y2 ) )
=> ( sK4 @ Y1 @ Y0 ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f22]) ).
thf(f22,plain,
( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y0 )
& ( sK4 @ Y1 @ Y2 ) )
=> ( sK4 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f17,f21]) ).
thf(f54,plain,
! [X2: a,X1: a] :
( $true
= ( ( sK2 @ X2 @ X1 )
=> ( ( ( sK3 @ X2 )
= ( sK3 @ X1 ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK3 @ X2 @ Y2 @ Y1 )
& ( sK3 @ X2 @ Y1 @ Y0 ) )
=> ( sK3 @ X2 @ Y2 @ Y0 ) ) ) ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK3 @ X2 @ Y1 @ Y0 )
=> ( sK3 @ X2 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f47,f50]) ).
thf(f47,plain,
! [X2: a,X1: a] :
( $true
= ( ( sK4 @ X2 @ X1 )
=> ( ( ( sK3 @ X2 )
= ( sK3 @ X1 ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK3 @ X2 @ Y2 @ Y1 )
& ( sK3 @ X2 @ Y1 @ Y0 ) )
=> ( sK3 @ X2 @ Y2 @ Y0 ) ) ) ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK3 @ X2 @ Y1 @ Y0 )
=> ( sK3 @ X2 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f46]) ).
thf(f46,plain,
! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( sK4 @ Y0 @ X1 )
=> ( ( ( sK3 @ Y0 )
= ( sK3 @ X1 ) )
& ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( ( sK3 @ Y0 @ Y3 @ Y2 )
& ( sK3 @ Y0 @ Y2 @ Y1 ) )
=> ( sK3 @ Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( sK3 @ Y0 @ Y2 @ Y1 )
=> ( sK3 @ Y0 @ Y1 @ Y2 ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ Y0 @ X1 )
=> ( ( ( sK3 @ Y0 )
= ( sK3 @ X1 ) )
& ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( ( sK3 @ Y0 @ Y3 @ Y2 )
& ( sK3 @ Y0 @ Y2 @ Y1 ) )
=> ( sK3 @ Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( sK3 @ Y0 @ Y2 @ Y1 )
=> ( sK3 @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f41]) ).
thf(f41,plain,
! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 @ Y0 )
=> ( ( ( sK3 @ Y1 )
= ( sK3 @ Y0 ) )
& ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( ( ( sK3 @ Y1 @ Y4 @ Y3 )
& ( sK3 @ Y1 @ Y3 @ Y2 ) )
=> ( sK3 @ Y1 @ Y4 @ Y2 ) ) ) ) )
& ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( sK3 @ Y1 @ Y3 @ Y2 )
=> ( sK3 @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 @ Y0 )
=> ( ( ( sK3 @ Y1 )
= ( sK3 @ Y0 ) )
& ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( ( ( sK3 @ Y1 @ Y4 @ Y3 )
& ( sK3 @ Y1 @ Y3 @ Y2 ) )
=> ( sK3 @ Y1 @ Y4 @ Y2 ) ) ) ) )
& ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( sK3 @ Y1 @ Y3 @ Y2 )
=> ( sK3 @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 @ Y0 )
=> ( ( ( sK3 @ Y1 )
= ( sK3 @ Y0 ) )
& ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( ( ( sK3 @ Y1 @ Y4 @ Y3 )
& ( sK3 @ Y1 @ Y3 @ Y2 ) )
=> ( sK3 @ Y1 @ Y4 @ Y2 ) ) ) ) )
& ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( sK3 @ Y1 @ Y3 @ Y2 )
=> ( sK3 @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) )
=> ( ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y2 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) ) ) ) )
& ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y3 @ Y2 )
=> ( sK3 @ Y3 @ ( Y1 @ Y3 ) @ ( Y0 @ Y2 ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y2 @ Y3 )
=> ( sK3 @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) ) ) ) )
& ( ( ^ [Y0: a > b,Y1: a > b] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( sK3 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y2 ) ) ) ) ) )
= ( ^ [Y0: a > b,Y1: a > b] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y2 @ Y3 )
=> ( sK3 @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f18]) ).
thf(f18,plain,
( $false
= ( $true
=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 @ Y0 )
=> ( ( ( sK3 @ Y1 )
= ( sK3 @ Y0 ) )
& ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( ( ( sK3 @ Y1 @ Y4 @ Y3 )
& ( sK3 @ Y1 @ Y3 @ Y2 ) )
=> ( sK3 @ Y1 @ Y4 @ Y2 ) ) ) ) )
& ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( sK3 @ Y1 @ Y3 @ Y2 )
=> ( sK3 @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) )
=> ( ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y2 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) ) ) ) )
& ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y3 @ Y2 )
=> ( sK3 @ Y3 @ ( Y1 @ Y3 ) @ ( Y0 @ Y2 ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y2 @ Y3 )
=> ( sK3 @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) ) ) ) )
& ( ( ^ [Y0: a > b,Y1: a > b] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( sK3 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y2 ) ) ) ) ) )
= ( ^ [Y0: a > b,Y1: a > b] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y2 @ Y3 )
=> ( sK3 @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f15,f17]) ).
thf(f1139,plain,
( ( $true
= ( ( ( sK3 @ sK13 )
= ( sK3 @ sK14 ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK3 @ sK13 @ Y1 @ Y0 )
=> ( sK3 @ sK13 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f1137]) ).
thf(f1137,plain,
( ( ( ( ( sK3 @ sK13 )
= ( sK3 @ sK14 ) )
& $true
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK3 @ sK13 @ Y1 @ Y0 )
=> ( sK3 @ sK13 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f978,f1135]) ).
thf(f978,plain,
( ( ( ( ( sK3 @ sK13 )
= ( sK3 @ sK14 ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK3 @ sK13 @ Y2 @ Y1 )
& ( sK3 @ sK13 @ Y1 @ Y0 ) )
=> ( sK3 @ sK13 @ Y2 @ Y0 ) ) ) ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK3 @ sK13 @ Y1 @ Y0 )
=> ( sK3 @ sK13 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f966]) ).
thf(f966,plain,
( ( ( $true
=> ( ( ( sK3 @ sK13 )
= ( sK3 @ sK14 ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK3 @ sK13 @ Y2 @ Y1 )
& ( sK3 @ sK13 @ Y1 @ Y0 ) )
=> ( sK3 @ sK13 @ Y2 @ Y0 ) ) ) ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK3 @ sK13 @ Y1 @ Y0 )
=> ( sK3 @ sK13 @ Y0 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f54,f959]) ).
thf(f1058,plain,
( ( ( sK3 @ sK14 @ ( sK12 @ sK14 ) @ ( sK11 @ sK13 ) )
= $true )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f1053]) ).
thf(f1053,plain,
( ( ( $true
=> ( sK3 @ sK14 @ ( sK12 @ sK14 ) @ ( sK11 @ sK13 ) ) )
= $true )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f1025,f962]) ).
thf(f1025,plain,
( ! [X2: a,X1: a] :
( ( ( sK2 @ X2 @ X1 )
=> ( sK3 @ X2 @ ( sK12 @ X2 ) @ ( sK11 @ X1 ) ) )
= $true )
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f1024,f50]) ).
thf(f1024,plain,
( ! [X2: a,X1: a] :
( ( ( sK4 @ X2 @ X1 )
=> ( sK3 @ X2 @ ( sK12 @ X2 ) @ ( sK11 @ X1 ) ) )
= $true )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f1023]) ).
thf(f1023,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( sK4 @ Y0 @ X1 )
=> ( sK3 @ Y0 @ ( sK12 @ Y0 ) @ ( sK11 @ X1 ) ) )
@ X2 )
= $true )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f1013]) ).
thf(f1013,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ Y0 @ X1 )
=> ( sK3 @ Y0 @ ( sK12 @ Y0 ) @ ( sK11 @ X1 ) ) ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f1012]) ).
thf(f1012,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 @ Y0 )
=> ( sK3 @ Y1 @ ( sK12 @ Y1 ) @ ( sK11 @ Y0 ) ) ) )
@ X1 )
= $true )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f948]) ).
thf(f948,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 @ Y0 )
=> ( sK3 @ Y1 @ ( sK12 @ Y1 ) @ ( sK11 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f946]) ).
thf(f1231,plain,
( ! [X2: b,X1: b] :
( ( ( sK3 @ sK13 @ X2 @ X1 )
=> ( sK3 @ sK13 @ X1 @ X2 ) )
= $true )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f1230]) ).
thf(f1230,plain,
( ! [X2: b,X1: b] :
( ( ^ [Y0: b] :
( ( sK3 @ sK13 @ Y0 @ X1 )
=> ( sK3 @ sK13 @ X1 @ Y0 ) )
@ X2 )
= $true )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f1214]) ).
thf(f1214,plain,
( ! [X1: b] :
( ( !! @ b
@ ^ [Y0: b] :
( ( sK3 @ sK13 @ Y0 @ X1 )
=> ( sK3 @ sK13 @ X1 @ Y0 ) ) )
= $true )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f1207]) ).
thf(f1207,plain,
( ! [X1: b] :
( $true
= ( ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK3 @ sK13 @ Y1 @ Y0 )
=> ( sK3 @ sK13 @ Y0 @ Y1 ) ) )
@ X1 ) )
| ~ spl0_4 ),
inference(pi_clausification,[status(thm)],[f1138]) ).
thf(f940,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[status(thm)],[f939]) ).
thf(f939,plain,
( $false
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f938]) ).
thf(f938,plain,
( ( $false = $true )
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f926,f501]) ).
thf(f501,plain,
( ( $false
= ( sK3 @ sK8 @ ( sK6 @ sK10 ) @ ( sK5 @ sK8 ) ) )
| ~ spl0_3 ),
inference(not_proxy_clausification,[status(thm)],[f452]) ).
thf(f452,plain,
( ( ( ~ ( sK3 @ sK8 @ ( sK6 @ sK10 ) @ ( sK5 @ sK8 ) ) )
= $true )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f420]) ).
thf(f420,plain,
( ( $true
= ( ( sK3 @ sK8 @ ( sK6 @ sK10 ) @ ( sK5 @ sK8 ) )
=> $false ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f416,f122]) ).
thf(f122,plain,
( ( ( sK3 @ sK8 @ ( sK5 @ sK8 ) @ ( sK6 @ sK10 ) )
= $false )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f121]) ).
thf(f121,plain,
( ( $false
= ( $true
=> ( sK3 @ sK8 @ ( sK5 @ sK8 ) @ ( sK6 @ sK10 ) ) ) )
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f115,f120]) ).
thf(f120,plain,
( ( ( sK2 @ sK8 @ sK10 )
= $true )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f115]) ).
thf(f115,plain,
( ( ( ( sK2 @ sK8 @ sK10 )
=> ( sK3 @ sK8 @ ( sK5 @ sK8 ) @ ( sK6 @ sK10 ) ) )
= $false )
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f114,f50]) ).
thf(f114,plain,
( ( $false
= ( ( sK4 @ sK8 @ sK10 )
=> ( sK3 @ sK8 @ ( sK5 @ sK8 ) @ ( sK6 @ sK10 ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f113]) ).
thf(f113,plain,
( ( ( ^ [Y0: a] :
( ( sK4 @ sK8 @ Y0 )
=> ( sK3 @ sK8 @ ( sK5 @ sK8 ) @ ( sK6 @ Y0 ) ) )
@ sK10 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f110]) ).
thf(f110,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ sK8 @ Y0 )
=> ( sK3 @ sK8 @ ( sK5 @ sK8 ) @ ( sK6 @ Y0 ) ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f109]) ).
thf(f109,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK3 @ Y0 @ ( sK5 @ Y0 ) @ ( sK6 @ Y1 ) ) ) )
@ sK8 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f101]) ).
thf(f101,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK3 @ Y0 @ ( sK5 @ Y0 ) @ ( sK6 @ Y1 ) ) ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f100]) ).
thf(f100,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK3 @ Y0 @ ( sK5 @ Y0 ) @ ( sK7 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK3 @ Y0 @ ( sK7 @ Y0 ) @ ( sK6 @ Y1 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK3 @ Y0 @ ( sK5 @ Y0 ) @ ( sK6 @ Y1 ) ) ) ) ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f99]) ).
thf(f99,plain,
( ( $false
= ( ^ [Y0: a > b] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( sK3 @ Y1 @ ( sK5 @ Y1 ) @ ( Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( sK3 @ Y1 @ ( Y0 @ Y1 ) @ ( sK6 @ Y2 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( sK3 @ Y1 @ ( sK5 @ Y1 ) @ ( sK6 @ Y2 ) ) ) ) ) )
@ sK7 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f98]) ).
thf(f98,plain,
( ( $false
= ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( sK3 @ Y1 @ ( sK5 @ Y1 ) @ ( Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( sK3 @ Y1 @ ( Y0 @ Y1 ) @ ( sK6 @ Y2 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y1 @ Y2 )
=> ( sK3 @ Y1 @ ( sK5 @ Y1 ) @ ( sK6 @ Y2 ) ) ) ) ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f97]) ).
thf(f97,plain,
( ( ( ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y2 @ Y3 )
=> ( sK3 @ Y2 @ ( sK5 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y2 @ Y3 )
=> ( sK3 @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y2 @ Y3 )
=> ( sK3 @ Y2 @ ( sK5 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) )
@ sK6 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f96]) ).
thf(f96,plain,
( ( $false
= ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y2 @ Y3 )
=> ( sK3 @ Y2 @ ( sK5 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y2 @ Y3 )
=> ( sK3 @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y2 @ Y3 )
=> ( sK3 @ Y2 @ ( sK5 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f95]) ).
thf(f95,plain,
( ( $false
= ( ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y2 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) ) ) )
@ sK5 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[status(thm)],[f88]) ).
thf(f88,plain,
( ( $false
= ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y2 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) ) ) ) ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f87]) ).
thf(f87,definition,
( spl0_3
<=> ( $false
= ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y2 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f416,plain,
( ! [X2: b,X1: b] :
( ( ( sK3 @ sK8 @ X2 @ X1 )
=> ( sK3 @ sK8 @ X1 @ X2 ) )
= $true )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f415]) ).
thf(f415,plain,
( ! [X2: b,X1: b] :
( ( ^ [Y0: b] :
( ( sK3 @ sK8 @ Y0 @ X1 )
=> ( sK3 @ sK8 @ X1 @ Y0 ) )
@ X2 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f409]) ).
thf(f409,plain,
( ! [X1: b] :
( ( !! @ b
@ ^ [Y0: b] :
( ( sK3 @ sK8 @ Y0 @ X1 )
=> ( sK3 @ sK8 @ X1 @ Y0 ) ) )
= $true )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f407]) ).
thf(f407,plain,
( ! [X1: b] :
( $true
= ( ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK3 @ sK8 @ Y1 @ Y0 )
=> ( sK3 @ sK8 @ Y0 @ Y1 ) ) )
@ X1 ) )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f324]) ).
thf(f324,plain,
( ( ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK3 @ sK8 @ Y1 @ Y0 )
=> ( sK3 @ sK8 @ Y0 @ Y1 ) ) ) )
= $true )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f134]) ).
thf(f134,plain,
( ( ( ( ( sK3 @ sK8 )
= ( sK3 @ sK10 ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK3 @ sK8 @ Y2 @ Y1 )
& ( sK3 @ sK8 @ Y1 @ Y0 ) )
=> ( sK3 @ sK8 @ Y2 @ Y0 ) ) ) ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK3 @ sK8 @ Y1 @ Y0 )
=> ( sK3 @ sK8 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f129]) ).
thf(f129,plain,
( ( ( $true
=> ( ( ( sK3 @ sK8 )
= ( sK3 @ sK10 ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK3 @ sK8 @ Y2 @ Y1 )
& ( sK3 @ sK8 @ Y1 @ Y0 ) )
=> ( sK3 @ sK8 @ Y2 @ Y0 ) ) ) ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK3 @ sK8 @ Y1 @ Y0 )
=> ( sK3 @ sK8 @ Y0 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f54,f120]) ).
thf(f926,plain,
( ( ( sK3 @ sK8 @ ( sK6 @ sK10 ) @ ( sK5 @ sK8 ) )
= $true )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f923]) ).
thf(f923,plain,
( ( $true
= ( $true
=> ( sK3 @ sK8 @ ( sK6 @ sK10 ) @ ( sK5 @ sK8 ) ) ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f642,f722]) ).
thf(f722,plain,
( ( ( sK3 @ sK8 @ ( sK6 @ sK10 ) @ ( sK7 @ sK10 ) )
= $true )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f717]) ).
thf(f717,plain,
( ( ( $true
=> ( sK3 @ sK8 @ ( sK6 @ sK10 ) @ ( sK7 @ sK10 ) ) )
= $true )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f416,f520]) ).
thf(f520,plain,
( ( ( sK3 @ sK8 @ ( sK7 @ sK10 ) @ ( sK6 @ sK10 ) )
= $true )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f310,f389]) ).
thf(f389,plain,
( ! [X2: b,X1: b] :
( ( sK3 @ sK10 @ X1 @ X2 )
= ( sK3 @ sK8 @ X1 @ X2 ) )
| ~ spl0_3 ),
inference(argument_congruence,[status(thm)],[f352]) ).
thf(f352,plain,
( ! [X1: b] :
( ( sK3 @ sK10 @ X1 )
= ( sK3 @ sK8 @ X1 ) )
| ~ spl0_3 ),
inference(argument_congruence,[status(thm)],[f338]) ).
thf(f338,plain,
( ( ( sK3 @ sK10 )
= ( sK3 @ sK8 ) )
| ~ spl0_3 ),
inference(equality_proxy_clausification,[status(thm)],[f333]) ).
thf(f333,plain,
( ( ( ( sK3 @ sK8 )
= ( sK3 @ sK10 ) )
= $true )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f332]) ).
thf(f332,plain,
( ( ( ( ( sK3 @ sK8 )
= ( sK3 @ sK10 ) )
& $true )
= $true )
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f330,f331]) ).
thf(f331,plain,
( ( ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK3 @ sK8 @ Y2 @ Y1 )
& ( sK3 @ sK8 @ Y1 @ Y0 ) )
=> ( sK3 @ sK8 @ Y2 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f328]) ).
thf(f328,plain,
( ( ( ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK3 @ sK8 @ Y2 @ Y1 )
& ( sK3 @ sK8 @ Y1 @ Y0 ) )
=> ( sK3 @ sK8 @ Y2 @ Y0 ) ) ) ) )
& $true )
= $true )
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f198,f324]) ).
thf(f198,plain,
( ( $true
= ( ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK3 @ sK8 @ Y2 @ Y1 )
& ( sK3 @ sK8 @ Y1 @ Y0 ) )
=> ( sK3 @ sK8 @ Y2 @ Y0 ) ) ) ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK3 @ sK8 @ Y1 @ Y0 )
=> ( sK3 @ sK8 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f197]) ).
thf(f197,plain,
( ( ( $true
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK3 @ sK8 @ Y2 @ Y1 )
& ( sK3 @ sK8 @ Y1 @ Y0 ) )
=> ( sK3 @ sK8 @ Y2 @ Y0 ) ) ) ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK3 @ sK8 @ Y1 @ Y0 )
=> ( sK3 @ sK8 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f196]) ).
thf(f196,plain,
( ( ( ( ( sK3 @ sK8 )
= ( sK3 @ sK8 ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK3 @ sK8 @ Y2 @ Y1 )
& ( sK3 @ sK8 @ Y1 @ Y0 ) )
=> ( sK3 @ sK8 @ Y2 @ Y0 ) ) ) ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK3 @ sK8 @ Y1 @ Y0 )
=> ( sK3 @ sK8 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f181]) ).
thf(f181,plain,
( ( ( $true
=> ( ( ( sK3 @ sK8 )
= ( sK3 @ sK8 ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK3 @ sK8 @ Y2 @ Y1 )
& ( sK3 @ sK8 @ Y1 @ Y0 ) )
=> ( sK3 @ sK8 @ Y2 @ Y0 ) ) ) ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK3 @ sK8 @ Y1 @ Y0 )
=> ( sK3 @ sK8 @ Y0 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f54,f174]) ).
thf(f174,plain,
( ( ( sK2 @ sK8 @ sK8 )
= $true )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f172]) ).
thf(f172,plain,
( ( $true
= ( $true
=> ( sK2 @ sK8 @ sK8 ) ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f135,f133]) ).
thf(f133,plain,
( ( ( sK2 @ sK10 @ sK8 )
= $true )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f127]) ).
thf(f127,plain,
( ( ( $true
=> ( sK2 @ sK10 @ sK8 ) )
= $true )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f73,f120]) ).
thf(f135,plain,
( ! [X0: a] :
( $true
= ( ( sK2 @ sK10 @ X0 )
=> ( sK2 @ sK8 @ X0 ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f131]) ).
thf(f131,plain,
( ! [X0: a] :
( ( ( ( sK2 @ sK10 @ X0 )
& $true )
=> ( sK2 @ sK8 @ X0 ) )
= $true )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f59,f120]) ).
thf(f330,plain,
( ( ( ( ( sK3 @ sK8 )
= ( sK3 @ sK10 ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK3 @ sK8 @ Y2 @ Y1 )
& ( sK3 @ sK8 @ Y1 @ Y0 ) )
=> ( sK3 @ sK8 @ Y2 @ Y0 ) ) ) ) ) )
= $true )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f329]) ).
thf(f329,plain,
( ( ( ( ( sK3 @ sK8 )
= ( sK3 @ sK10 ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK3 @ sK8 @ Y2 @ Y1 )
& ( sK3 @ sK8 @ Y1 @ Y0 ) )
=> ( sK3 @ sK8 @ Y2 @ Y0 ) ) ) ) )
& $true )
= $true )
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f134,f324]) ).
thf(f310,plain,
( ( ( sK3 @ sK10 @ ( sK7 @ sK10 ) @ ( sK6 @ sK10 ) )
= $true )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f305]) ).
thf(f305,plain,
( ( $true
= ( $true
=> ( sK3 @ sK10 @ ( sK7 @ sK10 ) @ ( sK6 @ sK10 ) ) ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f214,f250]) ).
thf(f250,plain,
( ( ( sK2 @ sK10 @ sK10 )
= $true )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f246]) ).
thf(f246,plain,
( ( ( $true
=> ( sK2 @ sK10 @ sK10 ) )
= $true )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f136,f133]) ).
thf(f136,plain,
( ! [X0: a] :
( ( ( sK2 @ X0 @ sK8 )
=> ( sK2 @ X0 @ sK10 ) )
= $true )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f130]) ).
thf(f130,plain,
( ! [X0: a] :
( ( ( $true
& ( sK2 @ X0 @ sK8 ) )
=> ( sK2 @ X0 @ sK10 ) )
= $true )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f59,f120]) ).
thf(f214,plain,
( ! [X2: a,X1: a] :
( ( ( sK2 @ X1 @ X2 )
=> ( sK3 @ X1 @ ( sK7 @ X1 ) @ ( sK6 @ X2 ) ) )
= $true )
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f213,f50]) ).
thf(f213,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( sK4 @ X1 @ X2 )
=> ( sK3 @ X1 @ ( sK7 @ X1 ) @ ( sK6 @ X2 ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f212]) ).
thf(f212,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK4 @ X1 @ Y0 )
=> ( sK3 @ X1 @ ( sK7 @ X1 ) @ ( sK6 @ Y0 ) ) )
@ X2 ) )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f209]) ).
thf(f209,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ X1 @ Y0 )
=> ( sK3 @ X1 @ ( sK7 @ X1 ) @ ( sK6 @ Y0 ) ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f208]) ).
thf(f208,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK3 @ Y0 @ ( sK7 @ Y0 ) @ ( sK6 @ Y1 ) ) ) )
@ X1 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f205]) ).
thf(f205,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK3 @ Y0 @ ( sK7 @ Y0 ) @ ( sK6 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f204]) ).
thf(f204,plain,
( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK3 @ Y0 @ ( sK7 @ Y0 ) @ ( sK6 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f102,f203]) ).
thf(f203,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK3 @ Y0 @ ( sK5 @ Y0 ) @ ( sK7 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f102]) ).
thf(f102,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK3 @ Y0 @ ( sK5 @ Y0 ) @ ( sK7 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK3 @ Y0 @ ( sK7 @ Y0 ) @ ( sK6 @ Y1 ) ) ) ) ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f100]) ).
thf(f642,plain,
( ! [X0: b] :
( $true
= ( ( sK3 @ sK8 @ X0 @ ( sK7 @ sK10 ) )
=> ( sK3 @ sK8 @ X0 @ ( sK5 @ sK8 ) ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f602]) ).
thf(f602,plain,
( ! [X0: b] :
( ( ( ( sK3 @ sK8 @ X0 @ ( sK7 @ sK10 ) )
& $true )
=> ( sK3 @ sK8 @ X0 @ ( sK5 @ sK8 ) ) )
= $true )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f576,f449]) ).
thf(f449,plain,
( ( ( sK3 @ sK8 @ ( sK7 @ sK10 ) @ ( sK5 @ sK8 ) )
= $true )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f436]) ).
thf(f436,plain,
( ( ( $true
=> ( sK3 @ sK8 @ ( sK7 @ sK10 ) @ ( sK5 @ sK8 ) ) )
= $true )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f416,f240]) ).
thf(f240,plain,
( ( ( sK3 @ sK8 @ ( sK5 @ sK8 ) @ ( sK7 @ sK10 ) )
= $true )
| ~ spl0_3 ),
inference(boolean_simplification,[status(thm)],[f238]) ).
thf(f238,plain,
( ( ( $true
=> ( sK3 @ sK8 @ ( sK5 @ sK8 ) @ ( sK7 @ sK10 ) ) )
= $true )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f232,f120]) ).
thf(f232,plain,
( ! [X2: a,X1: a] :
( ( ( sK2 @ X1 @ X2 )
=> ( sK3 @ X1 @ ( sK5 @ X1 ) @ ( sK7 @ X2 ) ) )
= $true )
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f231,f50]) ).
thf(f231,plain,
( ! [X2: a,X1: a] :
( ( ( sK4 @ X1 @ X2 )
=> ( sK3 @ X1 @ ( sK5 @ X1 ) @ ( sK7 @ X2 ) ) )
= $true )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f230]) ).
thf(f230,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( sK4 @ X1 @ Y0 )
=> ( sK3 @ X1 @ ( sK5 @ X1 ) @ ( sK7 @ Y0 ) ) )
@ X2 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f227]) ).
thf(f227,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ X1 @ Y0 )
=> ( sK3 @ X1 @ ( sK5 @ X1 ) @ ( sK7 @ Y0 ) ) ) )
= $true )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f226]) ).
thf(f226,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y0 @ Y1 )
=> ( sK3 @ Y0 @ ( sK5 @ Y0 ) @ ( sK7 @ Y1 ) ) ) )
@ X1 ) )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f203]) ).
thf(f576,plain,
( ! [X2: b,X3: b,X1: b] :
( ( ( ( sK3 @ sK8 @ X3 @ X2 )
& ( sK3 @ sK8 @ X2 @ X1 ) )
=> ( sK3 @ sK8 @ X3 @ X1 ) )
= $true )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f575]) ).
thf(f575,plain,
( ! [X2: b,X3: b,X1: b] :
( ( ^ [Y0: b] :
( ( ( sK3 @ sK8 @ Y0 @ X2 )
& ( sK3 @ sK8 @ X2 @ X1 ) )
=> ( sK3 @ sK8 @ Y0 @ X1 ) )
@ X3 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f570]) ).
thf(f570,plain,
( ! [X2: b,X1: b] :
( ( !! @ b
@ ^ [Y0: b] :
( ( ( sK3 @ sK8 @ Y0 @ X2 )
& ( sK3 @ sK8 @ X2 @ X1 ) )
=> ( sK3 @ sK8 @ Y0 @ X1 ) ) )
= $true )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f569]) ).
thf(f569,plain,
( ! [X2: b,X1: b] :
( ( ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( ( sK3 @ sK8 @ Y1 @ Y0 )
& ( sK3 @ sK8 @ Y0 @ X1 ) )
=> ( sK3 @ sK8 @ Y1 @ X1 ) ) )
@ X2 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f556]) ).
thf(f556,plain,
( ! [X1: b] :
( ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( ( sK3 @ sK8 @ Y1 @ Y0 )
& ( sK3 @ sK8 @ Y0 @ X1 ) )
=> ( sK3 @ sK8 @ Y1 @ X1 ) ) ) )
= $true )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f553]) ).
thf(f553,plain,
( ! [X1: b] :
( $true
= ( ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK3 @ sK8 @ Y2 @ Y1 )
& ( sK3 @ sK8 @ Y1 @ Y0 ) )
=> ( sK3 @ sK8 @ Y2 @ Y0 ) ) ) )
@ X1 ) )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f331]) ).
thf(f92,plain,
( spl0_3
| spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f85,f79,f90,f87]) ).
thf(f79,definition,
( spl0_2
<=> ( $false
= ( ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y2 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) ) ) ) )
& ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y3 @ Y2 )
=> ( sK3 @ Y3 @ ( Y1 @ Y3 ) @ ( Y0 @ Y2 ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y2 @ Y3 )
=> ( sK3 @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f85,plain,
( ( $false
= ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y3 @ Y2 )
=> ( sK3 @ Y3 @ ( Y1 @ Y3 ) @ ( Y0 @ Y2 ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y2 @ Y3 )
=> ( sK3 @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) ) ) ) ) )
| ( $false
= ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y2 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f80]) ).
thf(f80,plain,
( ( $false
= ( ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y2 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) ) ) ) )
& ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y3 @ Y2 )
=> ( sK3 @ Y3 @ ( Y1 @ Y3 ) @ ( Y0 @ Y2 ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y2 @ Y3 )
=> ( sK3 @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f79]) ).
thf(f81,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f74,f79,f76]) ).
thf(f74,plain,
( ( $false
= ( ( ^ [Y0: a > b,Y1: a > b] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( sK3 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y2 ) ) ) ) ) )
= ( ^ [Y0: a > b,Y1: a > b] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y2 @ Y3 )
=> ( sK3 @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) ) ) ) )
| ( $false
= ( ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y2 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) ) ) ) )
& ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y3 @ Y2 )
=> ( sK3 @ Y3 @ ( Y1 @ Y3 ) @ ( Y0 @ Y2 ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y2 @ Y3 )
=> ( sK3 @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( $false
= ( ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y2 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) ) ) ) )
& ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y3 @ Y2 )
=> ( sK3 @ Y3 @ ( Y1 @ Y3 ) @ ( Y0 @ Y2 ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y2 @ Y3 )
=> ( sK3 @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) ) ) ) )
& ( ( ^ [Y0: a > b,Y1: a > b] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( sK3 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y2 ) ) ) ) ) )
= ( ^ [Y0: a > b,Y1: a > b] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y2 @ Y3 )
=> ( sK3 @ Y2 @ ( Y0 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV037^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n019.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 12:39:09 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.47 ---- Original DTF file ---
% 0.18/0.47 thf(spec,logic,$$dhol).
% 0.18/0.47 %------------------------------------------------------------------------------
% 0.18/0.47 % File : SEV037^5 : TPTP v9.2.1. Released v4.0.0.
% 0.18/0.47 % Domain : Set Theory (Relations)
% 0.18/0.47 % Problem : TPS problem from EQUIVALENCE-RELATIONS-THMS
% 0.18/0.47 % Version : Especial.
% 0.18/0.47 % English :
% 0.18/0.47
% 0.18/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.18/0.47 % Source : [Bro09]
% 0.18/0.47 % Names : tps_1202 [Bro09]
% 0.18/0.47
% 0.18/0.47 % Status : Theorem
% 0.18/0.47 % Rating : 0.33 v9.1.0, 0.38 v9.0.0, 0.30 v8.2.0, 0.38 v8.1.0, 0.45 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.20 v6.2.0, 0.43 v6.1.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.33 v4.0.1, 1.00 v4.0.0
% 0.18/0.47 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.18/0.47 % Number of atoms : 3 ( 3 equ; 0 cnn)
% 0.18/0.47 % Maximal formula atoms : 3 ( 3 avg)
% 0.18/0.47 % Number of connectives : 103 ( 0 ~; 0 |; 9 &; 78 @)
% 0.18/0.47 % ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% 0.18/0.47 % Maximal formula depth : 19 ( 19 avg)
% 0.18/0.47 % Number of types : 3 ( 2 usr)
% 0.18/0.47 % Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% 0.18/0.47 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.18/0.47 % Number of variables : 38 ( 4 ^; 34 !; 0 ?; 38 :)
% 0.18/0.47 % SPC : TH0_THM_EQU_NAR
% 0.18/0.47
% 0.18/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.18/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.18/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.18/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.18/0.47 %------------------------------------------------------------------------------
% 0.18/0.47 thf(a_type,type,
% 0.18/0.47 a: $tType ).
% 0.18/0.47
% 0.18/0.47 thf(b_type,type,
% 0.18/0.47 b: $tType ).
% 0.18/0.47
% 0.18/0.47 thf(cTHM516_pme,conjecture,
% 0.18/0.47 ! [Xp: a > a > $o,Xq: a > a > $o,Xr: a > b > b > $o] :
% 0.18/0.47 ( ( ! [Xx: a,Xy: a] :
% 0.18/0.47 ( ( Xp @ Xx @ Xy )
% 0.18/0.47 => ( Xp @ Xy @ Xx ) )
% 0.18/0.47 & ! [Xx: a,Xy: a,Xz: a] :
% 0.18/0.47 ( ( ( Xp @ Xx @ Xy )
% 0.18/0.47 & ( Xp @ Xy @ Xz ) )
% 0.18/0.47 => ( Xp @ Xx @ Xz ) )
% 0.18/0.47 & ( Xp = Xq ) )
% 0.18/0.47 => ( ! [Xx: a,Xy: a] :
% 0.18/0.47 ( ( Xp @ Xx @ Xy )
% 0.18/0.47 => ( ! [Xx0: b,Xy0: b] :
% 0.18/0.47 ( ( Xr @ Xx @ Xx0 @ Xy0 )
% 0.18/0.47 => ( Xr @ Xx @ Xy0 @ Xx0 ) )
% 0.18/0.47 & ! [Xx0: b,Xy0: b,Xz: b] :
% 0.18/0.47 ( ( ( Xr @ Xx @ Xx0 @ Xy0 )
% 0.18/0.47 & ( Xr @ Xx @ Xy0 @ Xz ) )
% 0.18/0.47 => ( Xr @ Xx @ Xx0 @ Xz ) )
% 0.18/0.47 & ( ( Xr @ Xx )
% 0.18/0.47 = ( Xr @ Xy ) ) ) )
% 0.18/0.47 => ( ! [Xx: a > b,Xy: a > b] :
% 0.18/0.47 ( ! [Xx0: a,Xy0: a] :
% 0.18/0.47 ( ( Xp @ Xx0 @ Xy0 )
% 0.18/0.47 => ( Xr @ Xx0 @ ( Xx @ Xx0 ) @ ( Xy @ Xy0 ) ) )
% 0.18/0.47 => ! [Xx0: a,Xy0: a] :
% 0.18/0.47 ( ( Xp @ Xx0 @ Xy0 )
% 0.18/0.47 => ( Xr @ Xx0 @ ( Xy @ Xx0 ) @ ( Xx @ Xy0 ) ) ) )
% 0.18/0.47 & ! [Xx: a > b,Xy: a > b,Xz: a > b] :
% 0.18/0.47 ( ( ! [Xx0: a,Xy0: a] :
% 0.18/0.47 ( ( Xp @ Xx0 @ Xy0 )
% 0.18/0.47 => ( Xr @ Xx0 @ ( Xx @ Xx0 ) @ ( Xy @ Xy0 ) ) )
% 0.18/0.47 & ! [Xx0: a,Xy0: a] :
% 0.18/0.47 ( ( Xp @ Xx0 @ Xy0 )
% 0.18/0.47 => ( Xr @ Xx0 @ ( Xy @ Xx0 ) @ ( Xz @ Xy0 ) ) ) )
% 0.18/0.47 => ! [Xx0: a,Xy0: a] :
% 0.18/0.47 ( ( Xp @ Xx0 @ Xy0 )
% 0.18/0.47 => ( Xr @ Xx0 @ ( Xx @ Xx0 ) @ ( Xz @ Xy0 ) ) ) )
% 0.18/0.47 & ( ( ^ [Xf: a > b,Xg: a > b] :
% 0.18/0.47 ! [Xx: a,Xy: a] :
% 0.18/0.47 ( ( Xp @ Xx @ Xy )
% 0.18/0.47 => ( Xr @ Xx @ ( Xf @ Xx ) @ ( Xg @ Xy ) ) ) )
% 0.18/0.47 = ( ^ [Xf: a > b,Xg: a > b] :
% 0.18/0.47 ! [Xx: a,Xy: a] :
% 0.18/0.47 ( ( Xq @ Xx @ Xy )
% 0.18/0.47 => ( Xr @ Xx @ ( Xf @ Xx ) @ ( Xg @ Xy ) ) ) ) ) ) ) ) ).
% 0.18/0.47
% 0.18/0.47 %------------------------------------------------------------------------------
% 0.18/0.47 ------------------------
% 1.52/1.20 ---- Embedded in THF ---
% 1.52/1.20 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.52/1.20 %%% Generated on Tue Feb 24 12:39:10 EST 2026
% 1.52/1.20 %%% using '$$dhol' embedding, version 1.3.0.
% 1.52/1.20 %%% Logic specification used:
% 1.52/1.20 %%% thf(spec, logic, $$dhol).
% 1.52/1.20
% 1.52/1.20 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.DsRAyE7nCA/DTF2DTF14528.p
% See solution above
% 1.52/1.20 ------------------------
% 1.52/1.21 ---- Cleaned THF ---
% 1.52/1.21 thf(a_type,type,
% 1.52/1.21 a: $tType ).
% 1.52/1.21
% 1.52/1.21 thf(b_type,type,
% 1.52/1.21 b: $tType ).
% 1.52/1.21
% 1.52/1.21 thf(cTHM516_pme,conjecture,
% 1.52/1.21 ! [Xp: a > a > $o,Xq: a > a > $o,Xr: a > b > b > $o] :
% 1.52/1.21 ( ( ! [Xx: a,Xy: a] :
% 1.52/1.21 ( ( Xp @ Xx @ Xy )
% 1.52/1.21 => ( Xp @ Xy @ Xx ) )
% 1.52/1.21 & ! [Xx: a,Xy: a,Xz: a] :
% 1.52/1.21 ( ( ( Xp @ Xx @ Xy )
% 1.52/1.21 & ( Xp @ Xy @ Xz ) )
% 1.52/1.21 => ( Xp @ Xx @ Xz ) )
% 1.52/1.21 & ( Xp = Xq ) )
% 1.52/1.21 => ( ! [Xx: a,Xy: a] :
% 1.52/1.21 ( ( Xp @ Xx @ Xy )
% 1.52/1.21 => ( ! [Xx0: b,Xy0: b] :
% 1.52/1.21 ( ( Xr @ Xx @ Xx0 @ Xy0 )
% 1.52/1.21 => ( Xr @ Xx @ Xy0 @ Xx0 ) )
% 1.52/1.21 & ! [Xx0: b,Xy0: b,Xz: b] :
% 1.52/1.21 ( ( ( Xr @ Xx @ Xx0 @ Xy0 )
% 1.52/1.21 & ( Xr @ Xx @ Xy0 @ Xz ) )
% 1.52/1.21 => ( Xr @ Xx @ Xx0 @ Xz ) )
% 1.52/1.21 & ( ( Xr @ Xx )
% 1.52/1.21 = ( Xr @ Xy ) ) ) )
% 1.52/1.21 => ( ! [Xx: a > b,Xy: a > b] :
% 1.52/1.21 ( ! [Xx0: a,Xy0: a] :
% 1.52/1.21 ( ( Xp @ Xx0 @ Xy0 )
% 1.52/1.21 => ( Xr @ Xx0 @ ( Xx @ Xx0 ) @ ( Xy @ Xy0 ) ) )
% 1.52/1.21 => ! [Xx0: a,Xy0: a] :
% 1.52/1.21 ( ( Xp @ Xx0 @ Xy0 )
% 1.52/1.21 => ( Xr @ Xx0 @ ( Xy @ Xx0 ) @ ( Xx @ Xy0 ) ) ) )
% 1.52/1.21 & ! [Xx: a > b,Xy: a > b,Xz: a > b] :
% 1.52/1.21 ( ( ! [Xx0: a,Xy0: a] :
% 1.52/1.21 ( ( Xp @ Xx0 @ Xy0 )
% 1.52/1.21 => ( Xr @ Xx0 @ ( Xx @ Xx0 ) @ ( Xy @ Xy0 ) ) )
% 1.52/1.21 & ! [Xx0: a,Xy0: a] :
% 1.52/1.21 ( ( Xp @ Xx0 @ Xy0 )
% 1.52/1.21 => ( Xr @ Xx0 @ ( Xy @ Xx0 ) @ ( Xz @ Xy0 ) ) ) )
% 1.52/1.21 => ! [Xx0: a,Xy0: a] :
% 1.52/1.21 ( ( Xp @ Xx0 @ Xy0 )
% 1.52/1.21 => ( Xr @ Xx0 @ ( Xx @ Xx0 ) @ ( Xz @ Xy0 ) ) ) )
% 1.52/1.21 & ( ( ^ [Xf: a > b,Xg: a > b] :
% 1.52/1.21 ! [Xx: a,Xy: a] :
% 1.52/1.21 ( ( Xp @ Xx @ Xy )
% 1.52/1.21 => ( Xr @ Xx @ ( Xf @ Xx ) @ ( Xg @ Xy ) ) ) )
% 1.52/1.21 = ( ^ [Xf: a > b,Xg: a > b] :
% 1.52/1.21 ! [Xx: a,Xy: a] :
% 1.52/1.21 ( ( Xq @ Xx @ Xy )
% 1.52/1.21 => ( Xr @ Xx @ ( Xf @ Xx ) @ ( Xg @ Xy ) ) ) ) ) ) ) ) ).
% 1.52/1.21 ------------------------
% 1.52/1.23 % (14641)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_14528 for (2999ds/4Mi)
% 1.52/1.23 % (14641)Instruction limit reached!
% 1.52/1.23 % (14641)------------------------------
% 1.52/1.23 % (14641)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.23 % (14641)Termination reason: Unknown
% 1.52/1.23 % (14641)Termination phase: Property scanning
% 1.52/1.23
% 1.52/1.23 % (14641)Memory used [KB]: 1023
% 1.52/1.23 % (14641)Time elapsed: 0.003 s
% 1.52/1.23 % (14641)Instructions burned: 5 (million)
% 1.52/1.23 % (14643)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_14528 for (2999ds/2Mi)
% 1.52/1.23 % (14641)------------------------------
% 1.52/1.23 % (14641)------------------------------
% 1.52/1.23 % (14643)Instruction limit reached!
% 1.52/1.23 % (14643)------------------------------
% 1.52/1.23 % (14643)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.23 % (14643)Termination reason: Unknown
% 1.52/1.23 % (14643)Termination phase: Preprocessing 3
% 1.52/1.23
% 1.52/1.23 % (14643)Memory used [KB]: 1023
% 1.52/1.23 % (14643)Time elapsed: 0.003 s
% 1.52/1.23 % (14643)Instructions burned: 3 (million)
% 1.52/1.23 % (14643)------------------------------
% 1.52/1.23 % (14643)------------------------------
% 1.52/1.24 % (14645)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_14528 for (2999ds/275Mi)
% 1.52/1.24 % (14646)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_14528 for (2999ds/18Mi)
% 1.52/1.24 % (14642)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_14528 for (2999ds/27Mi)
% 1.52/1.24 % (14640)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_14528 for (2999ds/183Mi)
% 1.52/1.25 % (14646)Instruction limit reached!
% 1.52/1.25 % (14646)------------------------------
% 1.52/1.25 % (14646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.25 % (14646)Termination reason: Unknown
% 1.52/1.25 % (14646)Termination phase: Saturation
% 1.52/1.25
% 1.52/1.25 % (14646)Memory used [KB]: 5756
% 1.52/1.25 % (14646)Time elapsed: 0.012 s
% 1.52/1.25 % (14646)Instructions burned: 18 (million)
% 1.52/1.25 % (14646)------------------------------
% 1.52/1.25 % (14646)------------------------------
% 1.52/1.25 % (14647)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_14528 for (2999ds/3Mi)
% 1.52/1.25 % (14648)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_14528 for (2999ds/37Mi)
% 1.52/1.25 % (14644)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_14528 for (2999ds/2Mi)
% 1.52/1.25 % (14644)Instruction limit reached!
% 1.52/1.25 % (14644)------------------------------
% 1.52/1.25 % (14644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.25 % (14644)Termination reason: Unknown
% 1.52/1.25 % (14644)Termination phase: shuffling
% 1.52/1.25
% 1.52/1.25 % (14644)Memory used [KB]: 1023
% 1.52/1.25 % (14644)Time elapsed: 0.004 s
% 1.52/1.25 % (14644)Instructions burned: 2 (million)
% 1.52/1.25 % (14644)------------------------------
% 1.52/1.25 % (14644)------------------------------
% 1.52/1.25 % (14647)Instruction limit reached!
% 1.52/1.25 % (14647)------------------------------
% 1.52/1.25 % (14647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.25 % (14647)Termination reason: Unknown
% 1.52/1.25 % (14647)Termination phase: Preprocessing 3
% 1.52/1.25
% 1.52/1.25 % (14647)Memory used [KB]: 1023
% 1.52/1.25 % (14647)Time elapsed: 0.003 s
% 1.52/1.25 % (14647)Instructions burned: 4 (million)
% 1.52/1.25 % (14647)------------------------------
% 1.52/1.25 % (14647)------------------------------
% 1.52/1.25 % (14642)Instruction limit reached!
% 1.52/1.25 % (14642)------------------------------
% 1.52/1.25 % (14642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.25 % (14642)Termination reason: Unknown
% 1.52/1.25 % (14642)Termination phase: Saturation
% 1.52/1.25
% 1.52/1.25 % (14642)Memory used [KB]: 5756
% 1.52/1.25 % (14642)Time elapsed: 0.011 s
% 1.52/1.25 % (14642)Instructions burned: 29 (million)
% 1.52/1.25 % (14642)------------------------------
% 1.52/1.25 % (14642)------------------------------
% 1.52/1.26 % (14652)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_14528 for (2999ds/7Mi)
% 1.52/1.26 % (14652)Instruction limit reached!
% 1.52/1.26 % (14652)------------------------------
% 1.52/1.26 % (14652)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.26 % (14652)Termination reason: Unknown
% 1.52/1.26 % (14652)Termination phase: Saturation
% 1.52/1.26
% 1.52/1.26 % (14652)Memory used [KB]: 1023
% 1.52/1.26 % (14652)Time elapsed: 0.004 s
% 1.52/1.26 % (14652)Instructions burned: 8 (million)
% 1.52/1.26 % (14652)------------------------------
% 1.52/1.26 % (14652)------------------------------
% 1.52/1.26 % (14648)Instruction limit reached!
% 1.52/1.26 % (14648)------------------------------
% 1.52/1.26 % (14648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.26 % (14648)Termination reason: Unknown
% 1.52/1.26 % (14648)Termination phase: Saturation
% 1.52/1.26
% 1.52/1.26 % (14648)Memory used [KB]: 5628
% 1.52/1.26 % (14648)Time elapsed: 0.019 s
% 1.52/1.26 % (14648)Instructions burned: 37 (million)
% 1.52/1.26 % (14648)------------------------------
% 1.52/1.26 % (14648)------------------------------
% 1.52/1.27 % (14649)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_14528 for (2999ds/15Mi)
% 1.52/1.27 % (14650)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_14528 for (2999ds/3Mi)
% 1.52/1.27 % (14650)Instruction limit reached!
% 1.52/1.27 % (14650)------------------------------
% 1.52/1.27 % (14650)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.27 % (14650)Termination reason: Unknown
% 1.52/1.27 % (14650)Termination phase: Preprocessing 3
% 1.52/1.27
% 1.52/1.27 % (14650)Memory used [KB]: 1023
% 1.52/1.27 % (14650)Time elapsed: 0.003 s
% 1.52/1.27 % (14650)Instructions burned: 3 (million)
% 1.52/1.27 % (14650)------------------------------
% 1.52/1.27 % (14650)------------------------------
% 1.52/1.27 % (14653)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_14528 for (2999ds/16Mi)
% 1.52/1.27 % (14649)Instruction limit reached!
% 1.52/1.27 % (14649)------------------------------
% 1.52/1.27 % (14649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.27 % (14649)Termination reason: Unknown
% 1.52/1.27 % (14649)Termination phase: Saturation
% 1.52/1.27
% 1.52/1.27 % (14649)Memory used [KB]: 5628
% 1.52/1.27 % (14649)Time elapsed: 0.010 s
% 1.52/1.27 % (14649)Instructions burned: 15 (million)
% 1.52/1.27 % (14649)------------------------------
% 1.52/1.27 % (14649)------------------------------
% 1.52/1.28 % (14653)Instruction limit reached!
% 1.52/1.28 % (14653)------------------------------
% 1.52/1.28 % (14653)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.28 % (14653)Termination reason: Unknown
% 1.52/1.28 % (14653)Termination phase: Saturation
% 1.52/1.28
% 1.52/1.28 % (14653)Memory used [KB]: 5884
% 1.52/1.28 % (14653)Time elapsed: 0.007 s
% 1.52/1.28 % (14653)Instructions burned: 17 (million)
% 1.52/1.28 % (14653)------------------------------
% 1.52/1.28 % (14653)------------------------------
% 1.52/1.28 % (14651)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_14528 for (2999ds/1041Mi)
% 1.52/1.28 % (14654)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_14528 for (2999ds/3Mi)
% 1.52/1.28 % (14654)Instruction limit reached!
% 1.52/1.28 % (14654)------------------------------
% 1.52/1.28 % (14654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.28 % (14654)Termination reason: Unknown
% 1.52/1.28 % (14654)Termination phase: SInE selection
% 1.52/1.28
% 1.52/1.28 % (14654)Memory used [KB]: 1023
% 1.52/1.28 % (14654)Time elapsed: 0.003 s
% 1.52/1.28 % (14654)Instructions burned: 3 (million)
% 1.52/1.28 % (14654)------------------------------
% 1.52/1.28 % (14654)------------------------------
% 1.52/1.29 % (14655)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_14528 for (2999ds/3Mi)
% 1.52/1.29 % (14656)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_14528 for (2999ds/7Mi)
% 1.52/1.29 % (14655)Instruction limit reached!
% 1.52/1.29 % (14655)------------------------------
% 1.52/1.29 % (14655)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.29 % (14655)Termination reason: Unknown
% 1.52/1.29 % (14655)Termination phase: Naming
% 1.52/1.29
% 1.52/1.29 % (14655)Memory used [KB]: 1023
% 1.52/1.29 % (14655)Time elapsed: 0.003 s
% 1.52/1.29 % (14655)Instructions burned: 3 (million)
% 1.52/1.29 % (14655)------------------------------
% 1.52/1.29 % (14655)------------------------------
% 1.52/1.29 % (14656)Instruction limit reached!
% 1.52/1.29 % (14656)------------------------------
% 1.52/1.29 % (14656)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.29 % (14656)Termination reason: Unknown
% 1.52/1.29 % (14656)Termination phase: Saturation
% 1.52/1.29
% 1.52/1.29 % (14656)Memory used [KB]: 5500
% 1.52/1.29 % (14656)Time elapsed: 0.003 s
% 1.52/1.29 % (14656)Instructions burned: 7 (million)
% 1.52/1.29 % (14656)------------------------------
% 1.52/1.29 % (14656)------------------------------
% 1.52/1.29 % (14657)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_14528 for (2999ds/3Mi)
% 1.52/1.29 % (14640)Instruction limit reached!
% 1.52/1.29 % (14640)------------------------------
% 1.52/1.29 % (14640)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.29 % (14640)Termination reason: Unknown
% 1.52/1.29 % (14640)Termination phase: Saturation
% 1.52/1.29
% 1.52/1.29 % (14640)Memory used [KB]: 5884
% 1.52/1.29 % (14640)Time elapsed: 0.055 s
% 1.52/1.29 % (14640)Instructions burned: 186 (million)
% 1.52/1.29 % (14640)------------------------------
% 1.52/1.29 % (14640)------------------------------
% 1.52/1.29 % (14657)Instruction limit reached!
% 1.52/1.29 % (14657)------------------------------
% 1.52/1.29 % (14657)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.29 % (14657)Termination reason: Unknown
% 1.52/1.29 % (14657)Termination phase: shuffling
% 1.52/1.29
% 1.52/1.29 % (14657)Memory used [KB]: 1023
% 1.52/1.29 % (14657)Time elapsed: 0.003 s
% 1.52/1.29 % (14657)Instructions burned: 3 (million)
% 1.52/1.29 % (14657)------------------------------
% 1.52/1.29 % (14657)------------------------------
% 1.55/1.30 % (14660)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_14528 for (2999ds/710Mi)
% 1.55/1.30 % (14658)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_14528 for (2999ds/4Mi)
% 1.55/1.30 % (14658)Instruction limit reached!
% 1.55/1.30 % (14658)------------------------------
% 1.55/1.30 % (14658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.30 % (14658)Termination reason: Unknown
% 1.55/1.30 % (14658)Termination phase: Preprocessing 3
% 1.55/1.30
% 1.55/1.30 % (14658)Memory used [KB]: 1023
% 1.55/1.30 % (14658)Time elapsed: 0.004 s
% 1.55/1.30 % (14658)Instructions burned: 4 (million)
% 1.55/1.30 % (14658)------------------------------
% 1.55/1.30 % (14658)------------------------------
% 1.55/1.30 % (14661)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_14528 for (2999ds/6Mi)
% 1.55/1.30 % (14659)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_14528 for (2999ds/18Mi)
% 1.55/1.31 % (14661)Instruction limit reached!
% 1.55/1.31 % (14661)------------------------------
% 1.55/1.31 % (14661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.31 % (14661)Termination reason: Unknown
% 1.55/1.31 % (14661)Termination phase: Saturation
% 1.55/1.31
% 1.55/1.31 % (14661)Memory used [KB]: 1023
% 1.55/1.31 % (14661)Time elapsed: 0.004 s
% 1.55/1.31 % (14661)Instructions burned: 7 (million)
% 1.55/1.31 % (14661)------------------------------
% 1.55/1.31 % (14661)------------------------------
% 1.55/1.31 % (14662)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_14528 for (2999ds/902Mi)
% 1.55/1.31 % (14659)Instruction limit reached!
% 1.55/1.31 % (14659)------------------------------
% 1.55/1.31 % (14659)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.31 % (14659)Termination reason: Unknown
% 1.55/1.31 % (14659)Termination phase: Saturation
% 1.55/1.31
% 1.55/1.31 % (14659)Memory used [KB]: 5628
% 1.55/1.31 % (14659)Time elapsed: 0.011 s
% 1.55/1.31 % (14659)Instructions burned: 18 (million)
% 1.55/1.31 % (14659)------------------------------
% 1.55/1.31 % (14659)------------------------------
% 1.55/1.32 % (14664)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_14528 for (2999ds/5Mi)
% 1.55/1.32 % (14664)Instruction limit reached!
% 1.55/1.32 % (14664)------------------------------
% 1.55/1.32 % (14664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.32 % (14664)Termination reason: Unknown
% 1.55/1.32 % (14664)Termination phase: Saturation
% 1.55/1.32
% 1.55/1.32 % (14664)Memory used [KB]: 5500
% 1.55/1.32 % (14664)Time elapsed: 0.003 s
% 1.55/1.32 % (14664)Instructions burned: 6 (million)
% 1.55/1.32 % (14664)------------------------------
% 1.55/1.32 % (14664)------------------------------
% 1.55/1.32 % (14663)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_14528 for (2999ds/21Mi)
% 1.55/1.33 % (14666)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_14528 for (2999ds/377Mi)
% 1.55/1.33 % (14663)Instruction limit reached!
% 1.55/1.33 % (14663)------------------------------
% 1.55/1.33 % (14663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.33 % (14663)Termination reason: Unknown
% 1.55/1.33 % (14663)Termination phase: Saturation
% 1.55/1.33
% 1.55/1.33 % (14663)Memory used [KB]: 5756
% 1.55/1.33 % (14663)Time elapsed: 0.013 s
% 1.55/1.33 % (14663)Instructions burned: 21 (million)
% 1.55/1.33 % (14663)------------------------------
% 1.55/1.33 % (14663)------------------------------
% 1.55/1.33 % (14665)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_14528 for (2999ds/6Mi)
% 1.55/1.33 % (14665)Instruction limit reached!
% 1.55/1.33 % (14665)------------------------------
% 1.55/1.33 % (14665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.33 % (14665)Termination reason: Unknown
% 1.55/1.33 % (14665)Termination phase: Saturation
% 1.55/1.33
% 1.55/1.33 % (14665)Memory used [KB]: 5500
% 1.55/1.33 % (14665)Time elapsed: 0.005 s
% 1.55/1.33 % (14665)Instructions burned: 7 (million)
% 1.55/1.33 % (14665)------------------------------
% 1.55/1.33 % (14665)------------------------------
% 1.55/1.35 % (14668)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_14528 for (2998ds/19Mi)
% 1.55/1.35 % (14667)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_14528 for (2999ds/779Mi)
% 1.55/1.35 % (14645)Instruction limit reached!
% 1.55/1.35 % (14645)------------------------------
% 1.55/1.35 % (14645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.35 % (14645)Termination reason: Unknown
% 1.55/1.35 % (14645)Termination phase: Saturation
% 1.55/1.35
% 1.55/1.35 % (14645)Memory used [KB]: 5756
% 1.55/1.35 % (14645)Time elapsed: 0.121 s
% 1.55/1.35 % (14645)Instructions burned: 277 (million)
% 1.55/1.35 % (14645)------------------------------
% 1.55/1.35 % (14645)------------------------------
% 1.55/1.36 % (14668)Instruction limit reached!
% 1.55/1.36 % (14668)------------------------------
% 1.55/1.36 % (14668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.36 % (14668)Termination reason: Unknown
% 1.55/1.36 % (14668)Termination phase: Saturation
% 1.55/1.36
% 1.55/1.36 % (14668)Memory used [KB]: 5500
% 1.55/1.36 % (14668)Time elapsed: 0.011 s
% 1.55/1.36 % (14668)Instructions burned: 20 (million)
% 1.55/1.36 % (14668)------------------------------
% 1.55/1.36 % (14668)------------------------------
% 1.55/1.37 % (14670)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_14528 for (2998ds/17Mi)
% 1.55/1.38 % (14670)Instruction limit reached!
% 1.55/1.38 % (14670)------------------------------
% 1.55/1.38 % (14670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.38 % (14670)Termination reason: Unknown
% 1.55/1.38 % (14670)Termination phase: Saturation
% 1.55/1.38
% 1.55/1.38 % (14670)Memory used [KB]: 5628
% 1.55/1.38 % (14670)Time elapsed: 0.007 s
% 1.55/1.38 % (14670)Instructions burned: 17 (million)
% 1.55/1.38 % (14670)------------------------------
% 1.55/1.38 % (14670)------------------------------
% 1.55/1.38 % (14669)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_14528 for (2998ds/879Mi)
% 1.55/1.39 % (14671)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_14528 for (2998ds/3Mi)
% 1.55/1.39 % (14671)Instruction limit reached!
% 1.55/1.39 % (14671)------------------------------
% 1.55/1.39 % (14671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.39 % (14671)Termination reason: Unknown
% 1.55/1.39 % (14671)Termination phase: shuffling
% 1.55/1.39
% 1.55/1.39 % (14671)Memory used [KB]: 1023
% 1.55/1.39 % (14671)Time elapsed: 0.002 s
% 1.55/1.39 % (14671)Instructions burned: 3 (million)
% 1.55/1.39 % (14671)------------------------------
% 1.55/1.39 % (14671)------------------------------
% 1.55/1.39 % (14651)First to succeed.
% 1.55/1.40 % (14672)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_14528 for (2998ds/30Mi)
% 1.55/1.40 % (14651)Refutation found. Thanks to Tanya!
% 1.55/1.40 % SZS status Theorem for DTF2THF_14528
% 1.55/1.40 % SZS output start Proof for DTF2THF_14528
% 1.55/1.40 thf(type_def_5, type, a: $tType).
% 1.55/1.40 thf(type_def_7, type, b: $tType).
% 1.55/1.40 thf(func_def_0, type, a: $tType).
% 1.55/1.40 thf(func_def_1, type, b: $tType).
% 1.55/1.40 thf(func_def_19, type, ph1: !>[X0: $tType]:(X0)).
% 1.55/1.40 thf(func_def_20, type, sK2: a > a > $o).
% 1.55/1.40 thf(func_def_21, type, sK3: a > b > b > $o).
% 1.55/1.40 thf(func_def_22, type, sK4: a > a > $o).
% 1.55/1.40 thf(func_def_23, type, sK5: a > b).
% 1.55/1.40 thf(func_def_24, type, sK6: a > b).
% 1.55/1.40 thf(func_def_25, type, sK7: a > b).
% 1.55/1.40 thf(func_def_26, type, sK8: a).
% 1.55/1.40 thf(func_def_27, type, sK9: a > b).
% 1.55/1.40 thf(func_def_28, type, sK10: a).
% 1.55/1.40 thf(func_def_29, type, sK11: a > b).
% 1.55/1.40 thf(func_def_30, type, sK12: a > b).
% 1.55/1.40 thf(func_def_31, type, sK13: a).
% 1.55/1.40 thf(func_def_32, type, sK14: a).
% 1.55/1.40 thf(func_def_33, type, sK15: a > b).
% 1.55/1.40 thf(func_def_34, type, sK16: a > b).
% 1.55/1.40 thf(func_def_35, type, sK17: a).
% 1.55/1.40 thf(func_def_36, type, sK18: a).
% 1.55/1.40 thf(func_def_37, type, sK19: a).
% 1.55/1.40 thf(func_def_38, type, sK20: a).
% 1.55/1.40 thf(f1343,plain,(
% 1.55/1.40 $false),
% 1.55/1.40 inference(avatar_sat_refutation,[status(thm)],[f81,f92,f940,f1259,f1275,f1282,f1307,f1315,f1338])).
% 1.55/1.40 thf(f1338,plain,(
% 1.55/1.40 ~spl0_5 | ~spl0_8),
% 1.55/1.40 inference(avatar_contradiction_clause,[status(thm)],[f1337])).
% 1.55/1.40 thf(f1337,plain,(
% 1.55/1.40 $false | (~spl0_5 | ~spl0_8)),
% 1.55/1.40 inference(trivial_inequality_removal,[status(thm)],[f1333])).
% 1.55/1.40 thf(f1333,plain,(
% 1.55/1.40 ($false = $true) | (~spl0_5 | ~spl0_8)),
% 1.55/1.40 inference(superposition,[status(thm)],[f1329,f1321])).
% 1.55/1.40 thf(f1321,plain,(
% 1.55/1.40 ( ! [X2 : a,X1 : a] : ((((sK2 @ X2 @ X1) => (sK3 @ X2 @ (sK15 @ X2) @ (sK16 @ X1))) = $true)) ) | ~spl0_5),
% 1.55/1.40 inference(beta_eta_normalization,[status(thm)],[f1320])).
% 1.55/1.40 thf(f1320,plain,(
% 1.55/1.40 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: ((sK2 @ Y0 @ X1) => (sK3 @ Y0 @ (sK15 @ Y0) @ (sK16 @ X1)))) @ X2) = $true)) ) | ~spl0_5),
% 1.55/1.40 inference(pi_clausification,[status(thm)],[f1319])).
% 1.55/1.40 thf(f1319,plain,(
% 1.55/1.40 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0 @ X1) => (sK3 @ Y0 @ (sK15 @ Y0) @ (sK16 @ X1))))))) ) | ~spl0_5),
% 1.55/1.40 inference(beta_eta_normalization,[status(thm)],[f1318])).
% 1.55/1.40 thf(f1318,plain,(
% 1.55/1.40 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (sK3 @ Y1 @ (sK15 @ Y1) @ (sK16 @ Y0)))))) @ X1) = $true)) ) | ~spl0_5),
% 1.55/1.40 inference(pi_clausification,[status(thm)],[f1271])).
% 1.55/1.40 thf(f1271,plain,(
% 1.55/1.40 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (sK3 @ Y1 @ (sK15 @ Y1) @ (sK16 @ Y0))))))) = $true) | ~spl0_5),
% 1.55/1.40 inference(avatar_component_clause,[status(thm)],[f1270])).
% 1.55/1.40 thf(f1270,definition,(
% 1.55/1.40 spl0_5 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (sK3 @ Y1 @ (sK15 @ Y1) @ (sK16 @ Y0))))))) = $true)),
% 1.55/1.40 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.55/1.40 thf(f1329,plain,(
% 1.55/1.40 ($false = ((sK2 @ sK19 @ sK20) => (sK3 @ sK19 @ (sK15 @ sK19) @ (sK16 @ sK20)))) | ~spl0_8),
% 1.55/1.40 inference(forward_demodulation,[status(thm)],[f1328,f50])).
% 1.55/1.40 thf(f50,plain,(
% 1.55/1.40 ( ! [X2 : a,X1 : a] : (((sK2 @ X1 @ X2) = (sK4 @ X1 @ X2))) )),
% 1.55/1.40 inference(argument_congruence,[status(thm)],[f48])).
% 1.55/1.40 thf(f48,plain,(
% 1.55/1.40 ( ! [X1 : a] : (((sK4 @ X1) = (sK2 @ X1))) )),
% 1.55/1.40 inference(argument_congruence,[status(thm)],[f43])).
% 1.55/1.40 thf(f43,plain,(
% 1.55/1.40 (sK4 = sK2)),
% 1.55/1.40 inference(equality_proxy_clausification,[status(thm)],[f38])).
% 1.55/1.40 thf(f38,plain,(
% 1.55/1.40 ((sK4 = sK2) = $true)),
% 1.55/1.40 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.55/1.40 thf(f21,plain,(
% 1.55/1.40 ($true = ((sK4 = sK2) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y0 @ Y1) => (sK4 @ Y1 @ Y0))))))))),
% 1.55/1.40 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.55/1.40 thf(f17,plain,(
% 1.55/1.40 ($true = (((sK4 = sK2) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y0 @ Y1) => (sK4 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y2 @ Y0) & (sK4 @ Y1 @ Y2)) => (sK4 @ Y1 @ Y0))))))))))),
% 1.55/1.40 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.55/1.40 thf(f15,plain,(
% 1.55/1.40 ($false = ((((sK4 = sK2) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y0 @ Y1) => (sK4 @ Y1 @ Y0))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y2 @ Y0) & (sK4 @ Y1 @ Y2)) => (sK4 @ Y1 @ Y0))))))))) => ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y1 @ Y0) => ((((sK3 @ Y1) = (sK3 @ Y0)) & (!! @ b @ (^[Y2 : b]: (!! @ b @ (^[Y3 : b]: (!! @ b @ (^[Y4 : b]: (((sK3 @ Y1 @ Y4 @ Y3) & (sK3 @ Y1 @ Y3 @ Y2)) => (sK3 @ Y1 @ Y4 @ Y2))))))))) & (!! @ b @ (^[Y2 : b]: (!! @ b @ (^[Y3 : b]: ((sK3 @ Y1 @ Y3 @ Y2) => (sK3 @ Y1 @ Y2 @ Y3)))))))))))) => (((!! @ (a > b) @ (^[Y0 : a > b]: (!! @ (a > b) @ (^[Y1 : a > b]: (!! @ (a > b) @ (^[Y2 : a > b]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y3 @ Y4) => (sK3 @ Y3 @ (Y0 @ Y3) @ (Y2 @ Y4))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y3 @ Y4) => (sK3 @ Y3 @ (Y2 @ Y3) @ (Y1 @ Y4)))))))) => (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y3 @ Y4) => (sK3 @ Y3 @ (Y0 @ Y3) @ (Y1 @ Y4)))))))))))))) & (!! @ (a > b) @ (^[Y0 : a > b]: (!! @ (a > b) @ (^[Y1 : a > b]: ((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y3 @ Y2) => (sK3 @ Y3 @ (Y1 @ Y3) @ (Y0 @ Y2))))))) => (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y2 @ Y3) => (sK3 @ Y2 @ (Y0 @ Y2) @ (Y1 @ Y3))))))))))))) & ((^[Y0 : a > b]: ((^[Y1 : a > b]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y3 @ Y2) => (sK3 @ Y3 @ (Y0 @ Y3) @ (Y1 @ Y2)))))))))) = (^[Y0 : a > b]: ((^[Y1 : a > b]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y2 @ Y3) => (sK3 @ Y2 @ (Y0 @ Y2) @ (Y1 @ Y3)))))))))))))))),
% 1.55/1.40 inference(beta_eta_normalization,[status(thm)],[f14])).
% 1.55/1.40 thf(f14,plain,(
% 1.55/1.40 ($false = ((^[Y0 : a > a > $o]: ((((Y0 = sK2) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y1))))))))) => ((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ Y2 @ Y1) => ((((sK3 @ Y2) = (sK3 @ Y1)) & (!! @ b @ (^[Y3 : b]: (!! @ b @ (^[Y4 : b]: (!! @ b @ (^[Y5 : b]: (((sK3 @ Y2 @ Y5 @ Y4) & (sK3 @ Y2 @ Y4 @ Y3)) => (sK3 @ Y2 @ Y5 @ Y3))))))))) & (!! @ b @ (^[Y3 : b]: (!! @ b @ (^[Y4 : b]: ((sK3 @ Y2 @ Y4 @ Y3) => (sK3 @ Y2 @ Y3 @ Y4)))))))))))) => (((!! @ (a > b) @ (^[Y1 : a > b]: (!! @ (a > b) @ (^[Y2 : a > b]: (!! @ (a > b) @ (^[Y3 : a > b]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((Y0 @ Y4 @ Y5) => (sK3 @ Y4 @ (Y1 @ Y4) @ (Y3 @ Y5))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((Y0 @ Y4 @ Y5) => (sK3 @ Y4 @ (Y3 @ Y4) @ (Y2 @ Y5)))))))) => (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((Y0 @ Y4 @ Y5) => (sK3 @ Y4 @ (Y1 @ Y4) @ (Y2 @ Y5)))))))))))))) & (!! @ (a > b) @ (^[Y1 : a > b]: (!! @ (a > b) @ (^[Y2 : a > b]: ((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y0 @ Y4 @ Y3) => (sK3 @ Y4 @ (Y2 @ Y4) @ (Y1 @ Y3))))))) => (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y0 @ Y3 @ Y4) => (sK3 @ Y3 @ (Y1 @ Y3) @ (Y2 @ Y4))))))))))))) & ((^[Y1 : a > b]: ((^[Y2 : a > b]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (sK3 @ Y4 @ (Y1 @ Y4) @ (Y2 @ Y3)))))))))) = (^[Y1 : a > b]: ((^[Y2 : a > b]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y0 @ Y3 @ Y4) => (sK3 @ Y3 @ (Y1 @ Y3) @ (Y2 @ Y4))))))))))))))) @ sK4))),
% 1.55/1.40 inference(sigma_clausification,[status(thm)],[f13])).
% 1.55/1.40 thf(f13,plain,(
% 1.55/1.40 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: ((((Y0 = sK2) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y1))))))))) => ((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((Y0 @ Y2 @ Y1) => ((((sK3 @ Y2) = (sK3 @ Y1)) & (!! @ b @ (^[Y3 : b]: (!! @ b @ (^[Y4 : b]: (!! @ b @ (^[Y5 : b]: (((sK3 @ Y2 @ Y5 @ Y4) & (sK3 @ Y2 @ Y4 @ Y3)) => (sK3 @ Y2 @ Y5 @ Y3))))))))) & (!! @ b @ (^[Y3 : b]: (!! @ b @ (^[Y4 : b]: ((sK3 @ Y2 @ Y4 @ Y3) => (sK3 @ Y2 @ Y3 @ Y4)))))))))))) => (((!! @ (a > b) @ (^[Y1 : a > b]: (!! @ (a > b) @ (^[Y2 : a > b]: (!! @ (a > b) @ (^[Y3 : a > b]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((Y0 @ Y4 @ Y5) => (sK3 @ Y4 @ (Y1 @ Y4) @ (Y3 @ Y5))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((Y0 @ Y4 @ Y5) => (sK3 @ Y4 @ (Y3 @ Y4) @ (Y2 @ Y5)))))))) => (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((Y0 @ Y4 @ Y5) => (sK3 @ Y4 @ (Y1 @ Y4) @ (Y2 @ Y5)))))))))))))) & (!! @ (a > b) @ (^[Y1 : a > b]: (!! @ (a > b) @ (^[Y2 : a > b]: ((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y0 @ Y4 @ Y3) => (sK3 @ Y4 @ (Y2 @ Y4) @ (Y1 @ Y3))))))) => (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y0 @ Y3 @ Y4) => (sK3 @ Y3 @ (Y1 @ Y3) @ (Y2 @ Y4))))))))))))) & ((^[Y1 : a > b]: ((^[Y2 : a > b]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (sK3 @ Y4 @ (Y1 @ Y4) @ (Y2 @ Y3)))))))))) = (^[Y1 : a > b]: ((^[Y2 : a > b]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y0 @ Y3 @ Y4) => (sK3 @ Y3 @ (Y1 @ Y3) @ (Y2 @ Y4)))))))))))))))))),
% 1.55/1.40 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.55/1.40 thf(f12,plain,(
% 1.55/1.40 ($false = ((^[Y0 : a > b > b > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: ((((Y1 = sK2) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ Y2 @ Y3) => (Y1 @ Y3 @ Y2))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y3 @ Y4)) => (Y1 @ Y3 @ Y2))))))))) => ((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ Y3 @ Y2) => ((((Y0 @ Y3) = (Y0 @ Y2)) & (!! @ b @ (^[Y4 : b]: (!! @ b @ (^[Y5 : b]: (!! @ b @ (^[Y6 : b]: (((Y0 @ Y3 @ Y6 @ Y5) & (Y0 @ Y3 @ Y5 @ Y4)) => (Y0 @ Y3 @ Y6 @ Y4))))))))) & (!! @ b @ (^[Y4 : b]: (!! @ b @ (^[Y5 : b]: ((Y0 @ Y3 @ Y5 @ Y4) => (Y0 @ Y3 @ Y4 @ Y5)))))))))))) => (((!! @ (a > b) @ (^[Y2 : a > b]: (!! @ (a > b) @ (^[Y3 : a > b]: (!! @ (a > b) @ (^[Y4 : a > b]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y1 @ Y5 @ Y6) => (Y0 @ Y5 @ (Y2 @ Y5) @ (Y4 @ Y6))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y1 @ Y5 @ Y6) => (Y0 @ Y5 @ (Y4 @ Y5) @ (Y3 @ Y6)))))))) => (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y1 @ Y5 @ Y6) => (Y0 @ Y5 @ (Y2 @ Y5) @ (Y3 @ Y6)))))))))))))) & (!! @ (a > b) @ (^[Y2 : a > b]: (!! @ (a > b) @ (^[Y3 : a > b]: ((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((Y1 @ Y5 @ Y4) => (Y0 @ Y5 @ (Y3 @ Y5) @ (Y2 @ Y4))))))) => (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((Y1 @ Y4 @ Y5) => (Y0 @ Y4 @ (Y2 @ Y4) @ (Y3 @ Y5))))))))))))) & ((^[Y2 : a > b]: ((^[Y3 : a > b]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK2 @ Y5 @ Y4) => (Y0 @ Y5 @ (Y2 @ Y5) @ (Y3 @ Y4)))))))))) = (^[Y2 : a > b]: ((^[Y3 : a > b]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((Y1 @ Y4 @ Y5) => (Y0 @ Y4 @ (Y2 @ Y4) @ (Y3 @ Y5))))))))))))))))) @ sK3))),
% 1.55/1.40 inference(sigma_clausification,[status(thm)],[f11])).
% 1.55/1.40 thf(f11,plain,(
% 1.55/1.40 ($false = (!! @ (a > b > b > $o) @ (^[Y0 : a > b > b > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: ((((Y1 = sK2) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ Y2 @ Y3) => (Y1 @ Y3 @ Y2))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y3 @ Y4)) => (Y1 @ Y3 @ Y2))))))))) => ((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((Y1 @ Y3 @ Y2) => ((((Y0 @ Y3) = (Y0 @ Y2)) & (!! @ b @ (^[Y4 : b]: (!! @ b @ (^[Y5 : b]: (!! @ b @ (^[Y6 : b]: (((Y0 @ Y3 @ Y6 @ Y5) & (Y0 @ Y3 @ Y5 @ Y4)) => (Y0 @ Y3 @ Y6 @ Y4))))))))) & (!! @ b @ (^[Y4 : b]: (!! @ b @ (^[Y5 : b]: ((Y0 @ Y3 @ Y5 @ Y4) => (Y0 @ Y3 @ Y4 @ Y5)))))))))))) => (((!! @ (a > b) @ (^[Y2 : a > b]: (!! @ (a > b) @ (^[Y3 : a > b]: (!! @ (a > b) @ (^[Y4 : a > b]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y1 @ Y5 @ Y6) => (Y0 @ Y5 @ (Y2 @ Y5) @ (Y4 @ Y6))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y1 @ Y5 @ Y6) => (Y0 @ Y5 @ (Y4 @ Y5) @ (Y3 @ Y6)))))))) => (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y1 @ Y5 @ Y6) => (Y0 @ Y5 @ (Y2 @ Y5) @ (Y3 @ Y6)))))))))))))) & (!! @ (a > b) @ (^[Y2 : a > b]: (!! @ (a > b) @ (^[Y3 : a > b]: ((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((Y1 @ Y5 @ Y4) => (Y0 @ Y5 @ (Y3 @ Y5) @ (Y2 @ Y4))))))) => (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((Y1 @ Y4 @ Y5) => (Y0 @ Y4 @ (Y2 @ Y4) @ (Y3 @ Y5))))))))))))) & ((^[Y2 : a > b]: ((^[Y3 : a > b]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK2 @ Y5 @ Y4) => (Y0 @ Y5 @ (Y2 @ Y5) @ (Y3 @ Y4)))))))))) = (^[Y2 : a > b]: ((^[Y3 : a > b]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((Y1 @ Y4 @ Y5) => (Y0 @ Y4 @ (Y2 @ Y4) @ (Y3 @ Y5)))))))))))))))))))),
% 1.55/1.40 inference(beta_eta_normalization,[status(thm)],[f10])).
% 1.55/1.40 thf(f10,plain,(
% 1.55/1.40 ($false = ((^[Y0 : a > a > $o]: (!! @ (a > b > b > $o) @ (^[Y1 : a > b > b > $o]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: ((((Y2 = Y0) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y2 @ Y3 @ Y4) => (Y2 @ Y4 @ Y3))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y4 @ Y3))))))))) => ((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y2 @ Y4 @ Y3) => ((((Y1 @ Y4) = (Y1 @ Y3)) & (!! @ b @ (^[Y5 : b]: (!! @ b @ (^[Y6 : b]: (!! @ b @ (^[Y7 : b]: (((Y1 @ Y4 @ Y7 @ Y6) & (Y1 @ Y4 @ Y6 @ Y5)) => (Y1 @ Y4 @ Y7 @ Y5))))))))) & (!! @ b @ (^[Y5 : b]: (!! @ b @ (^[Y6 : b]: ((Y1 @ Y4 @ Y6 @ Y5) => (Y1 @ Y4 @ Y5 @ Y6)))))))))))) => (((!! @ (a > b) @ (^[Y3 : a > b]: (!! @ (a > b) @ (^[Y4 : a > b]: (!! @ (a > b) @ (^[Y5 : a > b]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((Y2 @ Y6 @ Y7) => (Y1 @ Y6 @ (Y3 @ Y6) @ (Y5 @ Y7))))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((Y2 @ Y6 @ Y7) => (Y1 @ Y6 @ (Y5 @ Y6) @ (Y4 @ Y7)))))))) => (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((Y2 @ Y6 @ Y7) => (Y1 @ Y6 @ (Y3 @ Y6) @ (Y4 @ Y7)))))))))))))) & (!! @ (a > b) @ (^[Y3 : a > b]: (!! @ (a > b) @ (^[Y4 : a > b]: ((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y2 @ Y6 @ Y5) => (Y1 @ Y6 @ (Y4 @ Y6) @ (Y3 @ Y5))))))) => (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y2 @ Y5 @ Y6) => (Y1 @ Y5 @ (Y3 @ Y5) @ (Y4 @ Y6))))))))))))) & ((^[Y3 : a > b]: ((^[Y4 : a > b]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y0 @ Y6 @ Y5) => (Y1 @ Y6 @ (Y3 @ Y6) @ (Y4 @ Y5)))))))))) = (^[Y3 : a > b]: ((^[Y4 : a > b]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y2 @ Y5 @ Y6) => (Y1 @ Y5 @ (Y3 @ Y5) @ (Y4 @ Y6))))))))))))))))))) @ sK2))),
% 1.55/1.40 inference(sigma_clausification,[status(thm)],[f7])).
% 1.55/1.40 thf(f7,plain,(
% 1.55/1.40 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > b > b > $o) @ (^[Y1 : a > b > b > $o]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: ((((Y2 = Y0) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y2 @ Y3 @ Y4) => (Y2 @ Y4 @ Y3))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y4 @ Y3))))))))) => ((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y2 @ Y4 @ Y3) => ((((Y1 @ Y4) = (Y1 @ Y3)) & (!! @ b @ (^[Y5 : b]: (!! @ b @ (^[Y6 : b]: (!! @ b @ (^[Y7 : b]: (((Y1 @ Y4 @ Y7 @ Y6) & (Y1 @ Y4 @ Y6 @ Y5)) => (Y1 @ Y4 @ Y7 @ Y5))))))))) & (!! @ b @ (^[Y5 : b]: (!! @ b @ (^[Y6 : b]: ((Y1 @ Y4 @ Y6 @ Y5) => (Y1 @ Y4 @ Y5 @ Y6)))))))))))) => (((!! @ (a > b) @ (^[Y3 : a > b]: (!! @ (a > b) @ (^[Y4 : a > b]: (!! @ (a > b) @ (^[Y5 : a > b]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((Y2 @ Y6 @ Y7) => (Y1 @ Y6 @ (Y3 @ Y6) @ (Y5 @ Y7))))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((Y2 @ Y6 @ Y7) => (Y1 @ Y6 @ (Y5 @ Y6) @ (Y4 @ Y7)))))))) => (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((Y2 @ Y6 @ Y7) => (Y1 @ Y6 @ (Y3 @ Y6) @ (Y4 @ Y7)))))))))))))) & (!! @ (a > b) @ (^[Y3 : a > b]: (!! @ (a > b) @ (^[Y4 : a > b]: ((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y2 @ Y6 @ Y5) => (Y1 @ Y6 @ (Y4 @ Y6) @ (Y3 @ Y5))))))) => (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y2 @ Y5 @ Y6) => (Y1 @ Y5 @ (Y3 @ Y5) @ (Y4 @ Y6))))))))))))) & ((^[Y3 : a > b]: ((^[Y4 : a > b]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y0 @ Y6 @ Y5) => (Y1 @ Y6 @ (Y3 @ Y6) @ (Y4 @ Y5)))))))))) = (^[Y3 : a > b]: ((^[Y4 : a > b]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y2 @ Y5 @ Y6) => (Y1 @ Y5 @ (Y3 @ Y5) @ (Y4 @ Y6)))))))))))))))))))))),
% 1.55/1.40 inference(not_proxy_clausification,[status(thm)],[f6])).
% 1.55/1.40 thf(f6,plain,(
% 1.55/1.40 ((~ (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > b > b > $o) @ (^[Y1 : a > b > b > $o]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: ((((Y2 = Y0) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y2 @ Y3 @ Y4) => (Y2 @ Y4 @ Y3))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y4 @ Y3))))))))) => ((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y2 @ Y4 @ Y3) => ((((Y1 @ Y4) = (Y1 @ Y3)) & (!! @ b @ (^[Y5 : b]: (!! @ b @ (^[Y6 : b]: (!! @ b @ (^[Y7 : b]: (((Y1 @ Y4 @ Y7 @ Y6) & (Y1 @ Y4 @ Y6 @ Y5)) => (Y1 @ Y4 @ Y7 @ Y5))))))))) & (!! @ b @ (^[Y5 : b]: (!! @ b @ (^[Y6 : b]: ((Y1 @ Y4 @ Y6 @ Y5) => (Y1 @ Y4 @ Y5 @ Y6)))))))))))) => (((!! @ (a > b) @ (^[Y3 : a > b]: (!! @ (a > b) @ (^[Y4 : a > b]: (!! @ (a > b) @ (^[Y5 : a > b]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((Y2 @ Y6 @ Y7) => (Y1 @ Y6 @ (Y3 @ Y6) @ (Y5 @ Y7))))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((Y2 @ Y6 @ Y7) => (Y1 @ Y6 @ (Y5 @ Y6) @ (Y4 @ Y7)))))))) => (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((Y2 @ Y6 @ Y7) => (Y1 @ Y6 @ (Y3 @ Y6) @ (Y4 @ Y7)))))))))))))) & (!! @ (a > b) @ (^[Y3 : a > b]: (!! @ (a > b) @ (^[Y4 : a > b]: ((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y2 @ Y6 @ Y5) => (Y1 @ Y6 @ (Y4 @ Y6) @ (Y3 @ Y5))))))) => (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y2 @ Y5 @ Y6) => (Y1 @ Y5 @ (Y3 @ Y5) @ (Y4 @ Y6))))))))))))) & ((^[Y3 : a > b]: ((^[Y4 : a > b]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y0 @ Y6 @ Y5) => (Y1 @ Y6 @ (Y3 @ Y6) @ (Y4 @ Y5)))))))))) = (^[Y3 : a > b]: ((^[Y4 : a > b]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y2 @ Y5 @ Y6) => (Y1 @ Y5 @ (Y3 @ Y5) @ (Y4 @ Y6))))))))))))))))))))) = $true)),
% 1.55/1.40 inference(cnf_transformation,[status(thm)],[f5])).
% 1.55/1.40 thf(f5,plain,(
% 1.55/1.40 ((~ (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > b > b > $o) @ (^[Y1 : a > b > b > $o]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: ((((Y2 = Y0) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y2 @ Y3 @ Y4) => (Y2 @ Y4 @ Y3))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y4 @ Y3))))))))) => ((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((Y2 @ Y4 @ Y3) => ((((Y1 @ Y4) = (Y1 @ Y3)) & (!! @ b @ (^[Y5 : b]: (!! @ b @ (^[Y6 : b]: (!! @ b @ (^[Y7 : b]: (((Y1 @ Y4 @ Y7 @ Y6) & (Y1 @ Y4 @ Y6 @ Y5)) => (Y1 @ Y4 @ Y7 @ Y5))))))))) & (!! @ b @ (^[Y5 : b]: (!! @ b @ (^[Y6 : b]: ((Y1 @ Y4 @ Y6 @ Y5) => (Y1 @ Y4 @ Y5 @ Y6)))))))))))) => (((!! @ (a > b) @ (^[Y3 : a > b]: (!! @ (a > b) @ (^[Y4 : a > b]: (!! @ (a > b) @ (^[Y5 : a > b]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((Y2 @ Y6 @ Y7) => (Y1 @ Y6 @ (Y3 @ Y6) @ (Y5 @ Y7))))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((Y2 @ Y6 @ Y7) => (Y1 @ Y6 @ (Y5 @ Y6) @ (Y4 @ Y7)))))))) => (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((Y2 @ Y6 @ Y7) => (Y1 @ Y6 @ (Y3 @ Y6) @ (Y4 @ Y7)))))))))))))) & (!! @ (a > b) @ (^[Y3 : a > b]: (!! @ (a > b) @ (^[Y4 : a > b]: ((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y2 @ Y6 @ Y5) => (Y1 @ Y6 @ (Y4 @ Y6) @ (Y3 @ Y5))))))) => (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y2 @ Y5 @ Y6) => (Y1 @ Y5 @ (Y3 @ Y5) @ (Y4 @ Y6))))))))))))) & ((^[Y3 : a > b]: ((^[Y4 : a > b]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y0 @ Y6 @ Y5) => (Y1 @ Y6 @ (Y3 @ Y6) @ (Y4 @ Y5)))))))))) = (^[Y3 : a > b]: ((^[Y4 : a > b]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((Y2 @ Y5 @ Y6) => (Y1 @ Y5 @ (Y3 @ Y5) @ (Y4 @ Y6))))))))))))))))))))) = $true)),
% 1.55/1.40 inference(fool_elimination,[status(thm)],[f4])).
% 1.55/1.40 thf(f4,plain,(
% 1.55/1.40 ~! [X0 : a > a > $o,X1 : a > b > b > $o,X2 : a > a > $o] : ((! [X3 : a,X4 : a,X5 : a] : (((X0 @ X4 @ X3) & (X0 @ X3 @ X5)) => (X0 @ X4 @ X5)) & ! [X6 : a,X7 : a] : ((X0 @ X7 @ X6) => (X0 @ X6 @ X7)) & (X0 = X2)) => (! [X8 : a,X9 : a] : ((X0 @ X8 @ X9) => (! [X10 : b,X11 : b] : ((X1 @ X8 @ X10 @ X11) => (X1 @ X8 @ X11 @ X10)) & ! [X12 : b,X13 : b,X14 : b] : (((X1 @ X8 @ X13 @ X14) & (X1 @ X8 @ X12 @ X13)) => (X1 @ X8 @ X12 @ X14)) & ((X1 @ X8) = (X1 @ X9)))) => (((^[X15 : a > b, X16 : a > b] : (! [X17 : a,X18 : a] : ((X2 @ X17 @ X18) => (X1 @ X17 @ (X15 @ X17) @ (X16 @ X18))))) = (^[X19 : a > b, X20 : a > b] : (! [X21 : a,X22 : a] : ((X0 @ X22 @ X21) => (X1 @ X22 @ (X19 @ X22) @ (X20 @ X21)))))) & ! [X23 : a > b,X24 : a > b] : (! [X25 : a,X26 : a] : ((X0 @ X25 @ X26) => (X1 @ X25 @ (X23 @ X25) @ (X24 @ X26))) => ! [X27 : a,X28 : a] : ((X0 @ X28 @ X27) => (X1 @ X28 @ (X24 @ X28) @ (X23 @ X27)))) & ! [X29 : a > b,X30 : a > b,X31 : a > b] : ((! [X32 : a,X33 : a] : ((X0 @ X33 @ X32) => (X1 @ X33 @ (X29 @ X33) @ (X30 @ X32))) & ! [X34 : a,X35 : a] : ((X0 @ X35 @ X34) => (X1 @ X35 @ (X31 @ X35) @ (X29 @ X34)))) => ! [X36 : a,X37 : a] : ((X0 @ X37 @ X36) => (X1 @ X37 @ (X31 @ X37) @ (X30 @ X36)))))))),
% 1.55/1.40 inference(rectify,[status(thm)],[f2])).
% 1.55/1.40 thf(f2,negated_conjecture,(
% 1.55/1.40 ~! [X0 : a > a > $o,X2 : a > b > b > $o,X1 : a > a > $o] : ((! [X4 : a,X3 : a,X5 : a] : (((X0 @ X3 @ X4) & (X0 @ X4 @ X5)) => (X0 @ X3 @ X5)) & ! [X4 : a,X3 : a] : ((X0 @ X3 @ X4) => (X0 @ X4 @ X3)) & (X0 = X1)) => (! [X3 : a,X4 : a] : ((X0 @ X3 @ X4) => (! [X6 : b,X7 : b] : ((X2 @ X3 @ X6 @ X7) => (X2 @ X3 @ X7 @ X6)) & ! [X6 : b,X7 : b,X5 : b] : (((X2 @ X3 @ X7 @ X5) & (X2 @ X3 @ X6 @ X7)) => (X2 @ X3 @ X6 @ X5)) & ((X2 @ X3) = (X2 @ X4)))) => (((^[X8 : a > b, X9 : a > b] : (! [X3 : a,X4 : a] : ((X1 @ X3 @ X4) => (X2 @ X3 @ (X8 @ X3) @ (X9 @ X4))))) = (^[X8 : a > b, X9 : a > b] : (! [X4 : a,X3 : a] : ((X0 @ X3 @ X4) => (X2 @ X3 @ (X8 @ X3) @ (X9 @ X4)))))) & ! [X3 : a > b,X4 : a > b] : (! [X6 : a,X7 : a] : ((X0 @ X6 @ X7) => (X2 @ X6 @ (X3 @ X6) @ (X4 @ X7))) => ! [X7 : a,X6 : a] : ((X0 @ X6 @ X7) => (X2 @ X6 @ (X4 @ X6) @ (X3 @ X7)))) & ! [X4 : a > b,X5 : a > b,X3 : a > b] : ((! [X7 : a,X6 : a] : ((X0 @ X6 @ X7) => (X2 @ X6 @ (X4 @ X6) @ (X5 @ X7))) & ! [X7 : a,X6 : a] : ((X0 @ X6 @ X7) => (X2 @ X6 @ (X3 @ X6) @ (X4 @ X7)))) => ! [X7 : a,X6 : a] : ((X0 @ X6 @ X7) => (X2 @ X6 @ (X3 @ X6) @ (X5 @ X7)))))))),
% 1.55/1.40 inference(negated_conjecture,[status(cth)],[f1])).
% 1.55/1.40 thf(f1,conjecture,(
% 1.55/1.40 ! [X0 : a > a > $o,X2 : a > b > b > $o,X1 : a > a > $o] : ((! [X4 : a,X3 : a,X5 : a] : (((X0 @ X3 @ X4) & (X0 @ X4 @ X5)) => (X0 @ X3 @ X5)) & ! [X4 : a,X3 : a] : ((X0 @ X3 @ X4) => (X0 @ X4 @ X3)) & (X0 = X1)) => (! [X3 : a,X4 : a] : ((X0 @ X3 @ X4) => (! [X6 : b,X7 : b] : ((X2 @ X3 @ X6 @ X7) => (X2 @ X3 @ X7 @ X6)) & ! [X6 : b,X7 : b,X5 : b] : (((X2 @ X3 @ X7 @ X5) & (X2 @ X3 @ X6 @ X7)) => (X2 @ X3 @ X6 @ X5)) & ((X2 @ X3) = (X2 @ X4)))) => (((^[X8 : a > b, X9 : a > b] : (! [X3 : a,X4 : a] : ((X1 @ X3 @ X4) => (X2 @ X3 @ (X8 @ X3) @ (X9 @ X4))))) = (^[X8 : a > b, X9 : a > b] : (! [X4 : a,X3 : a] : ((X0 @ X3 @ X4) => (X2 @ X3 @ (X8 @ X3) @ (X9 @ X4)))))) & ! [X3 : a > b,X4 : a > b] : (! [X6 : a,X7 : a] : ((X0 @ X6 @ X7) => (X2 @ X6 @ (X3 @ X6) @ (X4 @ X7))) => ! [X7 : a,X6 : a] : ((X0 @ X6 @ X7) => (X2 @ X6 @ (X4 @ X6) @ (X3 @ X7)))) & ! [X4 : a > b,X5 : a > b,X3 : a > b] : ((! [X7 : a,X6 : a] : ((X0 @ X6 @ X7) => (X2 @ X6 @ (X4 @ X6) @ (X5 @ X7))) & ! [X7 : a,X6 : a] : ((X0 @ X6 @ X7) => (X2 @ X6 @ (X3 @ X6) @ (X4 @ X7)))) => ! [X7 : a,X6 : a] : ((X0 @ X6 @ X7) => (X2 @ X6 @ (X3 @ X6) @ (X5 @ X7)))))))),
% 1.55/1.40 file('/export/starexec/sandbox/tmp/tmp.DsRAyE7nCA/DTF2THF_14528.p',cTHM516_pme)).
% 1.55/1.40 thf(f1328,plain,(
% 1.55/1.40 (((sK4 @ sK19 @ sK20) => (sK3 @ sK19 @ (sK15 @ sK19) @ (sK16 @ sK20))) = $false) | ~spl0_8),
% 1.55/1.40 inference(beta_eta_normalization,[status(thm)],[f1327])).
% 1.55/1.40 thf(f1327,plain,(
% 1.55/1.40 ($false = ((^[Y0 : a]: ((sK4 @ sK19 @ Y0) => (sK3 @ sK19 @ (sK15 @ sK19) @ (sK16 @ Y0)))) @ sK20)) | ~spl0_8),
% 1.55/1.40 inference(sigma_clausification,[status(thm)],[f1326])).
% 1.55/1.40 thf(f1326,plain,(
% 1.55/1.40 ($false = (!! @ a @ (^[Y0 : a]: ((sK4 @ sK19 @ Y0) => (sK3 @ sK19 @ (sK15 @ sK19) @ (sK16 @ Y0)))))) | ~spl0_8),
% 1.55/1.40 inference(beta_eta_normalization,[status(thm)],[f1325])).
% 1.55/1.40 thf(f1325,plain,(
% 1.55/1.40 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y0 @ Y1) => (sK3 @ Y0 @ (sK15 @ Y0) @ (sK16 @ Y1)))))) @ sK19)) | ~spl0_8),
% 1.55/1.40 inference(sigma_clausification,[status(thm)],[f1281])).
% 1.55/1.40 thf(f1281,plain,(
% 1.55/1.40 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y0 @ Y1) => (sK3 @ Y0 @ (sK15 @ Y0) @ (sK16 @ Y1))))))) = $false) | ~spl0_8),
% 1.55/1.40 inference(avatar_component_clause,[status(thm)],[f1280])).
% 1.55/1.40 thf(f1280,definition,(
% 1.55/1.40 spl0_8 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y0 @ Y1) => (sK3 @ Y0 @ (sK15 @ Y0) @ (sK16 @ Y1))))))) = $false)),
% 1.55/1.40 introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition])).
% 1.55/1.40 thf(f1315,plain,(
% 1.55/1.40 ~spl0_6 | ~spl0_8),
% 1.55/1.40 inference(avatar_contradiction_clause,[status(thm)],[f1314])).
% 1.55/1.40 thf(f1314,plain,(
% 1.55/1.40 $false | (~spl0_6 | ~spl0_8)),
% 1.55/1.40 inference(trivial_inequality_removal,[status(thm)],[f1313])).
% 1.55/1.40 thf(f1313,plain,(
% 1.55/1.40 ($false = $true) | (~spl0_6 | ~spl0_8)),
% 1.55/1.40 inference(backward_demodulation,[status(thm)],[f1274,f1281])).
% 1.55/1.40 thf(f1274,plain,(
% 1.55/1.40 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y0 @ Y1) => (sK3 @ Y0 @ (sK15 @ Y0) @ (sK16 @ Y1))))))) = $true) | ~spl0_6),
% 1.55/1.40 inference(avatar_component_clause,[status(thm)],[f1273])).
% 1.55/1.40 thf(f1273,definition,(
% 1.55/1.40 spl0_6 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y0 @ Y1) => (sK3 @ Y0 @ (sK15 @ Y0) @ (sK16 @ Y1))))))) = $true)),
% 1.55/1.40 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.55/1.40 thf(f1307,plain,(
% 1.55/1.40 ~spl0_1 | ~spl0_7),
% 1.55/1.40 inference(avatar_contradiction_clause,[status(thm)],[f1306])).
% 1.55/1.40 thf(f1306,plain,(
% 1.55/1.40 $false | (~spl0_1 | ~spl0_7)),
% 1.55/1.40 inference(trivial_inequality_removal,[status(thm)],[f1302])).
% 1.55/1.40 thf(f1302,plain,(
% 1.55/1.40 ($false = $true) | (~spl0_1 | ~spl0_7)),
% 1.55/1.40 inference(superposition,[status(thm)],[f1298,f1288])).
% 1.55/1.40 thf(f1288,plain,(
% 1.55/1.40 ( ! [X2 : a,X1 : a] : ((((sK2 @ X1 @ X2) => (sK3 @ X1 @ (sK15 @ X1) @ (sK16 @ X2))) = $true)) ) | (~spl0_1 | ~spl0_7)),
% 1.55/1.40 inference(forward_demodulation,[status(thm)],[f1287,f50])).
% 1.55/1.40 thf(f1287,plain,(
% 1.55/1.40 ( ! [X2 : a,X1 : a] : ((((sK4 @ X1 @ X2) => (sK3 @ X1 @ (sK15 @ X1) @ (sK16 @ X2))) = $true)) ) | (~spl0_1 | ~spl0_7)),
% 1.55/1.40 inference(beta_eta_normalization,[status(thm)],[f1286])).
% 1.55/1.40 thf(f1286,plain,(
% 1.55/1.40 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: ((sK4 @ X1 @ Y0) => (sK3 @ X1 @ (sK15 @ X1) @ (sK16 @ Y0)))) @ X2) = $true)) ) | (~spl0_1 | ~spl0_7)),
% 1.55/1.40 inference(pi_clausification,[status(thm)],[f1285])).
% 1.55/1.40 thf(f1285,plain,(
% 1.55/1.40 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: ((sK4 @ X1 @ Y0) => (sK3 @ X1 @ (sK15 @ X1) @ (sK16 @ Y0))))) = $true)) ) | (~spl0_1 | ~spl0_7)),
% 1.55/1.40 inference(beta_eta_normalization,[status(thm)],[f1284])).
% 1.55/1.40 thf(f1284,plain,(
% 1.55/1.40 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y0 @ Y1) => (sK3 @ Y0 @ (sK15 @ Y0) @ (sK16 @ Y1)))))) @ X1) = $true)) ) | (~spl0_1 | ~spl0_7)),
% 1.55/1.40 inference(pi_clausification,[status(thm)],[f1283])).
% 1.55/1.40 thf(f1283,plain,(
% 1.55/1.40 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y0 @ Y1) => (sK3 @ Y0 @ (sK15 @ Y0) @ (sK16 @ Y1))))))) != $false) | (~spl0_1 | ~spl0_7)),
% 1.55/1.40 inference(backward_demodulation,[status(thm)],[f1266,f1278])).
% 1.55/1.40 thf(f1278,plain,(
% 1.55/1.40 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (sK3 @ Y1 @ (sK15 @ Y1) @ (sK16 @ Y0)))))))) | ~spl0_7),
% 1.55/1.40 inference(avatar_component_clause,[status(thm)],[f1277])).
% 1.55/1.40 thf(f1277,definition,(
% 1.55/1.40 spl0_7 <=> ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (sK3 @ Y1 @ (sK15 @ Y1) @ (sK16 @ Y0))))))))),
% 1.55/1.40 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 1.55/1.40 thf(f1266,plain,(
% 1.55/1.40 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y0 @ Y1) => (sK3 @ Y0 @ (sK15 @ Y0) @ (sK16 @ Y1))))))) != (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (sK3 @ Y1 @ (sK15 @ Y1) @ (sK16 @ Y0)))))))) | ~spl0_1),
% 1.55/1.40 inference(beta_eta_normalization,[status(thm)],[f1265])).
% 1.55/1.40 thf(f1265,plain,(
% 1.55/1.40 (((^[Y0 : a > b]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (sK3 @ Y2 @ (sK15 @ Y2) @ (Y0 @ Y1)))))))) @ sK16) != ((^[Y0 : a > b]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK4 @ Y1 @ Y2) => (sK3 @ Y1 @ (sK15 @ Y1) @ (Y0 @ Y2)))))))) @ sK16)) | ~spl0_1),
% 1.55/1.40 inference(negative_extensionality,[status(thm)],[f1264])).
% 1.55/1.40 thf(f1264,plain,(
% 1.55/1.40 ((^[Y0 : a > b]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK4 @ Y1 @ Y2) => (sK3 @ Y1 @ (sK15 @ Y1) @ (Y0 @ Y2)))))))) != (^[Y0 : a > b]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (sK3 @ Y2 @ (sK15 @ Y2) @ (Y0 @ Y1))))))))) | ~spl0_1),
% 1.55/1.40 inference(beta_eta_normalization,[status(thm)],[f1263])).
% 1.55/1.40 thf(f1263,plain,(
% 1.55/1.40 (((^[Y0 : a > b]: ((^[Y1 : a > b]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y3 @ Y2) => (sK3 @ Y3 @ (Y0 @ Y3) @ (Y1 @ Y2)))))))))) @ sK15) != ((^[Y0 : a > b]: ((^[Y1 : a > b]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y2 @ Y3) => (sK3 @ Y2 @ (Y0 @ Y2) @ (Y1 @ Y3)))))))))) @ sK15)) | ~spl0_1),
% 1.55/1.40 inference(negative_extensionality,[status(thm)],[f1262])).
% 1.55/1.40 thf(f1262,plain,(
% 1.55/1.40 ((^[Y0 : a > b]: ((^[Y1 : a > b]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y2 @ Y3) => (sK3 @ Y2 @ (Y0 @ Y2) @ (Y1 @ Y3)))))))))) != (^[Y0 : a > b]: ((^[Y1 : a > b]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y3 @ Y2) => (sK3 @ Y3 @ (Y0 @ Y3) @ (Y1 @ Y2))))))))))) | ~spl0_1),
% 1.55/1.40 inference(equality_proxy_clausification,[status(thm)],[f77])).
% 1.55/1.40 thf(f77,plain,(
% 1.55/1.40 ($false = ((^[Y0 : a > b]: ((^[Y1 : a > b]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y3 @ Y2) => (sK3 @ Y3 @ (Y0 @ Y3) @ (Y1 @ Y2)))))))))) = (^[Y0 : a > b]: ((^[Y1 : a > b]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y2 @ Y3) => (sK3 @ Y2 @ (Y0 @ Y2) @ (Y1 @ Y3)))))))))))) | ~spl0_1),
% 1.55/1.40 inference(avatar_component_clause,[status(thm)],[f76])).
% 1.55/1.40 thf(f76,definition,(
% 1.55/1.40 spl0_1 <=> ($false = ((^[Y0 : a > b]: ((^[Y1 : a > b]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y3 @ Y2) => (sK3 @ Y3 @ (Y0 @ Y3) @ (Y1 @ Y2)))))))))) = (^[Y0 : a > b]: ((^[Y1 : a > b]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y2 @ Y3) => (sK3 @ Y2 @ (Y0 @ Y2) @ (Y1 @ Y3))))))))))))),
% 1.55/1.40 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.55/1.40 thf(f1298,plain,(
% 1.55/1.40 ($false = ((sK2 @ sK18 @ sK17) => (sK3 @ sK18 @ (sK15 @ sK18) @ (sK16 @ sK17)))) | ~spl0_7),
% 1.55/1.40 inference(beta_eta_normalization,[status(thm)],[f1297])).
% 1.55/1.40 thf(f1297,plain,(
% 1.55/1.40 (((^[Y0 : a]: ((sK2 @ Y0 @ sK17) => (sK3 @ Y0 @ (sK15 @ Y0) @ (sK16 @ sK17)))) @ sK18) = $false) | ~spl0_7),
% 1.55/1.40 inference(sigma_clausification,[status(thm)],[f1296])).
% 1.55/1.40 thf(f1296,plain,(
% 1.55/1.40 ($false = (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0 @ sK17) => (sK3 @ Y0 @ (sK15 @ Y0) @ (sK16 @ sK17)))))) | ~spl0_7),
% 1.55/1.40 inference(beta_eta_normalization,[status(thm)],[f1295])).
% 1.55/1.40 thf(f1295,plain,(
% 1.55/1.40 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (sK3 @ Y1 @ (sK15 @ Y1) @ (sK16 @ Y0)))))) @ sK17)) | ~spl0_7),
% 1.55/1.40 inference(sigma_clausification,[status(thm)],[f1278])).
% 1.55/1.40 thf(f1282,plain,(
% 1.55/1.40 spl0_7 | spl0_8 | ~spl0_1),
% 1.55/1.40 inference(avatar_split_clause,[status(thm)],[f1268,f76,f1280,f1277])).
% 1.55/1.40 thf(f1268,plain,(
% 1.55/1.40 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (sK3 @ Y1 @ (sK15 @ Y1) @ (sK16 @ Y0)))))))) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y0 @ Y1) => (sK3 @ Y0 @ (sK15 @ Y0) @ (sK16 @ Y1))))))) = $false) | ~spl0_1),
% 1.55/1.40 inference(binary_proxy_clausification,[status(thm)],[f1266])).
% 1.55/1.40 thf(f1275,plain,(
% 1.55/1.40 spl0_5 | spl0_6 | ~spl0_1),
% 1.55/1.40 inference(avatar_split_clause,[status(thm)],[f1267,f76,f1273,f1270])).
% 1.55/1.40 thf(f1267,plain,(
% 1.55/1.40 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y0 @ Y1) => (sK3 @ Y0 @ (sK15 @ Y0) @ (sK16 @ Y1))))))) = $true) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (sK3 @ Y1 @ (sK15 @ Y1) @ (sK16 @ Y0))))))) = $true) | ~spl0_1),
% 1.55/1.40 inference(binary_proxy_clausification,[status(thm)],[f1266])).
% 1.55/1.40 thf(f1259,plain,(
% 1.55/1.40 ~spl0_4),
% 1.55/1.40 inference(avatar_contradiction_clause,[status(thm)],[f1258])).
% 1.55/1.40 thf(f1258,plain,(
% 1.55/1.40 $false | ~spl0_4),
% 1.55/1.40 inference(trivial_inequality_removal,[status(thm)],[f1257])).
% 1.55/1.40 thf(f1257,plain,(
% 1.55/1.40 ($false = $true) | ~spl0_4),
% 1.55/1.40 inference(forward_demodulation,[status(thm)],[f1245,f964])).
% 1.55/1.40 thf(f964,plain,(
% 1.55/1.40 ($false = (sK3 @ sK13 @ (sK11 @ sK13) @ (sK12 @ sK14))) | ~spl0_4),
% 1.55/1.40 inference(boolean_simplification,[status(thm)],[f963])).
% 1.55/1.40 thf(f963,plain,(
% 1.55/1.40 ($false = ($true => (sK3 @ sK13 @ (sK11 @ sK13) @ (sK12 @ sK14)))) | ~spl0_4),
% 1.55/1.40 inference(backward_demodulation,[status(thm)],[f957,f959])).
% 1.55/1.40 thf(f959,plain,(
% 1.55/1.40 ((sK2 @ sK13 @ sK14) = $true) | ~spl0_4),
% 1.55/1.40 inference(binary_proxy_clausification,[status(thm)],[f957])).
% 1.55/1.40 thf(f957,plain,(
% 1.55/1.40 (((sK2 @ sK13 @ sK14) => (sK3 @ sK13 @ (sK11 @ sK13) @ (sK12 @ sK14))) = $false) | ~spl0_4),
% 1.55/1.40 inference(forward_demodulation,[status(thm)],[f956,f50])).
% 1.55/1.40 thf(f956,plain,(
% 1.55/1.40 ($false = ((sK4 @ sK13 @ sK14) => (sK3 @ sK13 @ (sK11 @ sK13) @ (sK12 @ sK14)))) | ~spl0_4),
% 1.55/1.40 inference(beta_eta_normalization,[status(thm)],[f955])).
% 1.55/1.40 thf(f955,plain,(
% 1.55/1.40 ($false = ((^[Y0 : a]: ((sK4 @ sK13 @ Y0) => (sK3 @ sK13 @ (sK11 @ sK13) @ (sK12 @ Y0)))) @ sK14)) | ~spl0_4),
% 1.55/1.40 inference(sigma_clausification,[status(thm)],[f954])).
% 1.55/1.40 thf(f954,plain,(
% 1.55/1.40 ($false = (!! @ a @ (^[Y0 : a]: ((sK4 @ sK13 @ Y0) => (sK3 @ sK13 @ (sK11 @ sK13) @ (sK12 @ Y0)))))) | ~spl0_4),
% 1.55/1.40 inference(beta_eta_normalization,[status(thm)],[f953])).
% 1.55/1.40 thf(f953,plain,(
% 1.55/1.40 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y0 @ Y1) => (sK3 @ Y0 @ (sK11 @ Y0) @ (sK12 @ Y1)))))) @ sK13) = $false) | ~spl0_4),
% 1.55/1.40 inference(sigma_clausification,[status(thm)],[f947])).
% 1.55/1.40 thf(f947,plain,(
% 1.55/1.40 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y0 @ Y1) => (sK3 @ Y0 @ (sK11 @ Y0) @ (sK12 @ Y1)))))))) | ~spl0_4),
% 1.55/1.40 inference(binary_proxy_clausification,[status(thm)],[f946])).
% 1.55/1.40 thf(f946,plain,(
% 1.55/1.40 ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y1 @ Y0) => (sK3 @ Y1 @ (sK12 @ Y1) @ (sK11 @ Y0))))))) => (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y0 @ Y1) => (sK3 @ Y0 @ (sK11 @ Y0) @ (sK12 @ Y1))))))))) | ~spl0_4),
% 1.55/1.40 inference(beta_eta_normalization,[status(thm)],[f945])).
% 1.55/1.40 thf(f945,plain,(
% 1.55/1.40 ($false = ((^[Y0 : a > b]: ((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK4 @ Y2 @ Y1) => (sK3 @ Y2 @ (Y0 @ Y2) @ (sK11 @ Y1))))))) => (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK4 @ Y1 @ Y2) => (sK3 @ Y1 @ (sK11 @ Y1) @ (Y0 @ Y2))))))))) @ sK12)) | ~spl0_4),
% 1.55/1.40 inference(sigma_clausification,[status(thm)],[f944])).
% 1.55/1.40 thf(f944,plain,(
% 1.55/1.40 ((!! @ (a > b) @ (^[Y0 : a > b]: ((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK4 @ Y2 @ Y1) => (sK3 @ Y2 @ (Y0 @ Y2) @ (sK11 @ Y1))))))) => (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK4 @ Y1 @ Y2) => (sK3 @ Y1 @ (sK11 @ Y1) @ (Y0 @ Y2)))))))))) = $false) | ~spl0_4),
% 1.55/1.40 inference(beta_eta_normalization,[status(thm)],[f943])).
% 1.55/1.40 thf(f943,plain,(
% 1.55/1.40 ($false = ((^[Y0 : a > b]: (!! @ (a > b) @ (^[Y1 : a > b]: ((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y3 @ Y2) => (sK3 @ Y3 @ (Y1 @ Y3) @ (Y0 @ Y2))))))) => (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y2 @ Y3) => (sK3 @ Y2 @ (Y0 @ Y2) @ (Y1 @ Y3))))))))))) @ sK11)) | ~spl0_4),
% 1.55/1.40 inference(sigma_clausification,[status(thm)],[f91])).
% 1.55/1.40 thf(f91,plain,(
% 1.55/1.40 ($false = (!! @ (a > b) @ (^[Y0 : a > b]: (!! @ (a > b) @ (^[Y1 : a > b]: ((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y3 @ Y2) => (sK3 @ Y3 @ (Y1 @ Y3) @ (Y0 @ Y2))))))) => (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y2 @ Y3) => (sK3 @ Y2 @ (Y0 @ Y2) @ (Y1 @ Y3))))))))))))) | ~spl0_4),
% 1.55/1.40 inference(avatar_component_clause,[status(thm)],[f90])).
% 1.55/1.40 thf(f90,definition,(
% 1.55/1.40 spl0_4 <=> ($false = (!! @ (a > b) @ (^[Y0 : a > b]: (!! @ (a > b) @ (^[Y1 : a > b]: ((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y3 @ Y2) => (sK3 @ Y3 @ (Y1 @ Y3) @ (Y0 @ Y2))))))) => (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y2 @ Y3) => (sK3 @ Y2 @ (Y0 @ Y2) @ (Y1 @ Y3)))))))))))))),
% 1.55/1.40 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.55/1.40 thf(f1245,plain,(
% 1.55/1.40 ($true = (sK3 @ sK13 @ (sK11 @ sK13) @ (sK12 @ sK14))) | ~spl0_4),
% 1.55/1.40 inference(boolean_simplification,[status(thm)],[f1242])).
% 1.55/1.40 thf(f1242,plain,(
% 1.55/1.40 (($true => (sK3 @ sK13 @ (sK11 @ sK13) @ (sK12 @ sK14))) = $true) | ~spl0_4),
% 1.55/1.40 inference(superposition,[status(thm)],[f1231,f1170])).
% 1.55/1.40 thf(f1170,plain,(
% 1.55/1.40 ((sK3 @ sK13 @ (sK12 @ sK14) @ (sK11 @ sK13)) = $true) | ~spl0_4),
% 1.55/1.40 inference(superposition,[status(thm)],[f1058,f1163])).
% 1.55/1.40 thf(f1163,plain,(
% 1.55/1.40 ( ! [X2 : b,X1 : b] : (((sK3 @ sK13 @ X1 @ X2) = (sK3 @ sK14 @ X1 @ X2))) ) | ~spl0_4),
% 1.55/1.40 inference(argument_congruence,[status(thm)],[f1156])).
% 1.55/1.40 thf(f1156,plain,(
% 1.55/1.40 ( ! [X1 : b] : (((sK3 @ sK14 @ X1) = (sK3 @ sK13 @ X1))) ) | ~spl0_4),
% 1.55/1.40 inference(argument_congruence,[status(thm)],[f1142])).
% 1.55/1.40 thf(f1142,plain,(
% 1.55/1.40 ((sK3 @ sK13) = (sK3 @ sK14)) | ~spl0_4),
% 1.55/1.40 inference(equality_proxy_clausification,[status(thm)],[f1141])).
% 1.55/1.40 thf(f1141,plain,(
% 1.55/1.40 (((sK3 @ sK13) = (sK3 @ sK14)) = $true) | ~spl0_4),
% 1.55/1.40 inference(boolean_simplification,[status(thm)],[f1140])).
% 1.55/1.40 thf(f1140,plain,(
% 1.55/1.40 ((((sK3 @ sK13) = (sK3 @ sK14)) & $true) = $true) | ~spl0_4),
% 1.55/1.40 inference(backward_demodulation,[status(thm)],[f1139,f1138])).
% 1.55/1.40 thf(f1138,plain,(
% 1.55/1.40 ((!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: ((sK3 @ sK13 @ Y1 @ Y0) => (sK3 @ sK13 @ Y0 @ Y1)))))) = $true) | ~spl0_4),
% 1.55/1.40 inference(boolean_simplification,[status(thm)],[f1136])).
% 1.55/1.40 thf(f1136,plain,(
% 1.55/1.40 (($true & (!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: ((sK3 @ sK13 @ Y1 @ Y0) => (sK3 @ sK13 @ Y0 @ Y1))))))) = $true) | ~spl0_4),
% 1.55/1.40 inference(backward_demodulation,[status(thm)],[f1049,f1135])).
% 1.55/1.40 thf(f1135,plain,(
% 1.55/1.40 ($true = (!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: (!! @ b @ (^[Y2 : b]: (((sK3 @ sK13 @ Y2 @ Y1) & (sK3 @ sK13 @ Y1 @ Y0)) => (sK3 @ sK13 @ Y2 @ Y0))))))))) | ~spl0_4),
% 1.55/1.40 inference(binary_proxy_clausification,[status(thm)],[f1049])).
% 1.55/1.40 thf(f1049,plain,(
% 1.55/1.40 (((!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: (!! @ b @ (^[Y2 : b]: (((sK3 @ sK13 @ Y2 @ Y1) & (sK3 @ sK13 @ Y1 @ Y0)) => (sK3 @ sK13 @ Y2 @ Y0)))))))) & (!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: ((sK3 @ sK13 @ Y1 @ Y0) => (sK3 @ sK13 @ Y0 @ Y1))))))) = $true) | ~spl0_4),
% 1.55/1.40 inference(boolean_simplification,[status(thm)],[f1048])).
% 1.55/1.40 thf(f1048,plain,(
% 1.55/1.40 ((($true & (!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: (!! @ b @ (^[Y2 : b]: (((sK3 @ sK13 @ Y2 @ Y1) & (sK3 @ sK13 @ Y1 @ Y0)) => (sK3 @ sK13 @ Y2 @ Y0))))))))) & (!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: ((sK3 @ sK13 @ Y1 @ Y0) => (sK3 @ sK13 @ Y0 @ Y1))))))) = $true) | ~spl0_4),
% 1.55/1.40 inference(boolean_simplification,[status(thm)],[f1047])).
% 1.55/1.40 thf(f1047,plain,(
% 1.55/1.40 (((((sK3 @ sK13) = (sK3 @ sK13)) & (!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: (!! @ b @ (^[Y2 : b]: (((sK3 @ sK13 @ Y2 @ Y1) & (sK3 @ sK13 @ Y1 @ Y0)) => (sK3 @ sK13 @ Y2 @ Y0))))))))) & (!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: ((sK3 @ sK13 @ Y1 @ Y0) => (sK3 @ sK13 @ Y0 @ Y1))))))) = $true) | ~spl0_4),
% 1.55/1.40 inference(boolean_simplification,[status(thm)],[f1028])).
% 1.55/1.40 thf(f1028,plain,(
% 1.55/1.40 (($true => ((((sK3 @ sK13) = (sK3 @ sK13)) & (!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: (!! @ b @ (^[Y2 : b]: (((sK3 @ sK13 @ Y2 @ Y1) & (sK3 @ sK13 @ Y1 @ Y0)) => (sK3 @ sK13 @ Y2 @ Y0))))))))) & (!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: ((sK3 @ sK13 @ Y1 @ Y0) => (sK3 @ sK13 @ Y0 @ Y1)))))))) = $true) | ~spl0_4),
% 1.55/1.40 inference(superposition,[status(thm)],[f54,f1019])).
% 1.55/1.40 thf(f1019,plain,(
% 1.55/1.40 ((sK2 @ sK13 @ sK13) = $true) | ~spl0_4),
% 1.55/1.40 inference(boolean_simplification,[status(thm)],[f1018])).
% 1.55/1.40 thf(f1018,plain,(
% 1.55/1.40 ($true = ($true => (sK2 @ sK13 @ sK13))) | ~spl0_4),
% 1.55/1.40 inference(superposition,[status(thm)],[f973,f962])).
% 1.55/1.40 thf(f962,plain,(
% 1.55/1.40 ((sK2 @ sK14 @ sK13) = $true) | ~spl0_4),
% 1.55/1.40 inference(trivial_inequality_removal,[status(thm)],[f961])).
% 1.55/1.40 thf(f961,plain,(
% 1.55/1.40 ((sK2 @ sK14 @ sK13) = $true) | ($false = $true) | ~spl0_4),
% 1.55/1.40 inference(boolean_simplification,[status(thm)],[f960])).
% 1.55/1.40 thf(f960,plain,(
% 1.55/1.40 ($false = ($false => (sK3 @ sK13 @ (sK11 @ sK13) @ (sK12 @ sK14)))) | ((sK2 @ sK14 @ sK13) = $true) | ~spl0_4),
% 1.55/1.40 inference(superposition,[status(thm)],[f957,f84])).
% 1.55/1.40 thf(f84,plain,(
% 1.55/1.40 ( ! [X2 : a,X1 : a] : (($false = (sK2 @ X1 @ X2)) | ((sK2 @ X2 @ X1) = $true)) )),
% 1.55/1.40 inference(binary_proxy_clausification,[status(thm)],[f73])).
% 1.55/1.40 thf(f73,plain,(
% 1.55/1.40 ( ! [X2 : a,X1 : a] : ((((sK2 @ X1 @ X2) => (sK2 @ X2 @ X1)) = $true)) )),
% 1.55/1.40 inference(forward_demodulation,[status(thm)],[f72,f50])).
% 1.55/1.40 thf(f72,plain,(
% 1.55/1.40 ( ! [X2 : a,X1 : a] : ((((sK2 @ X1 @ X2) => (sK4 @ X2 @ X1)) = $true)) )),
% 1.55/1.40 inference(forward_demodulation,[status(thm)],[f71,f50])).
% 1.55/1.40 thf(f71,plain,(
% 1.55/1.40 ( ! [X2 : a,X1 : a] : ((((sK4 @ X1 @ X2) => (sK4 @ X2 @ X1)) = $true)) )),
% 1.55/1.40 inference(beta_eta_normalization,[status(thm)],[f70])).
% 1.55/1.40 thf(f70,plain,(
% 1.55/1.40 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: ((sK4 @ X1 @ Y0) => (sK4 @ Y0 @ X1))) @ X2))) )),
% 1.55/1.40 inference(pi_clausification,[status(thm)],[f68])).
% 1.55/1.40 thf(f68,plain,(
% 1.55/1.40 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: ((sK4 @ X1 @ Y0) => (sK4 @ Y0 @ X1)))) = $true)) )),
% 1.55/1.40 inference(beta_eta_normalization,[status(thm)],[f67])).
% 1.55/1.40 thf(f67,plain,(
% 1.55/1.40 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y0 @ Y1) => (sK4 @ Y1 @ Y0))))) @ X1))) )),
% 1.55/1.40 inference(pi_clausification,[status(thm)],[f40])).
% 1.55/1.40 thf(f40,plain,(
% 1.55/1.40 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y0 @ Y1) => (sK4 @ Y1 @ Y0)))))) = $true)),
% 1.55/1.40 inference(boolean_simplification,[status(thm)],[f39])).
% 1.55/1.40 thf(f39,plain,(
% 1.55/1.40 ($true = ($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y0 @ Y1) => (sK4 @ Y1 @ Y0))))))))),
% 1.55/1.40 inference(backward_demodulation,[status(thm)],[f21,f38])).
% 1.55/1.40 thf(f973,plain,(
% 1.55/1.40 ( ! [X0 : a] : ((((sK2 @ sK14 @ X0) => (sK2 @ sK13 @ X0)) = $true)) ) | ~spl0_4),
% 1.55/1.40 inference(boolean_simplification,[status(thm)],[f967])).
% 1.55/1.40 thf(f967,plain,(
% 1.55/1.40 ( ! [X0 : a] : (($true = (((sK2 @ sK14 @ X0) & $true) => (sK2 @ sK13 @ X0)))) ) | ~spl0_4),
% 1.55/1.40 inference(superposition,[status(thm)],[f59,f959])).
% 1.55/1.40 thf(f59,plain,(
% 1.55/1.40 ( ! [X2 : a,X3 : a,X1 : a] : (((((sK2 @ X3 @ X1) & (sK2 @ X2 @ X3)) => (sK2 @ X2 @ X1)) = $true)) )),
% 1.55/1.40 inference(forward_demodulation,[status(thm)],[f58,f50])).
% 1.55/1.40 thf(f58,plain,(
% 1.55/1.40 ( ! [X2 : a,X3 : a,X1 : a] : (((((sK2 @ X3 @ X1) & (sK2 @ X2 @ X3)) => (sK4 @ X2 @ X1)) = $true)) )),
% 1.55/1.40 inference(forward_demodulation,[status(thm)],[f52,f50])).
% 1.55/1.40 thf(f52,plain,(
% 1.55/1.40 ( ! [X2 : a,X3 : a,X1 : a] : (((((sK4 @ X3 @ X1) & (sK2 @ X2 @ X3)) => (sK4 @ X2 @ X1)) = $true)) )),
% 1.55/1.40 inference(backward_demodulation,[status(thm)],[f35,f50])).
% 1.55/1.40 thf(f35,plain,(
% 1.55/1.40 ( ! [X2 : a,X3 : a,X1 : a] : (((((sK4 @ X3 @ X1) & (sK4 @ X2 @ X3)) => (sK4 @ X2 @ X1)) = $true)) )),
% 1.55/1.40 inference(beta_eta_normalization,[status(thm)],[f34])).
% 1.55/1.40 thf(f34,plain,(
% 1.55/1.40 ( ! [X2 : a,X3 : a,X1 : a] : (($true = ((^[Y0 : a]: (((sK4 @ Y0 @ X1) & (sK4 @ X2 @ Y0)) => (sK4 @ X2 @ X1))) @ X3))) )),
% 1.55/1.40 inference(pi_clausification,[status(thm)],[f33])).
% 1.55/1.40 thf(f33,plain,(
% 1.55/1.40 ( ! [X2 : a,X1 : a] : (((!! @ a @ (^[Y0 : a]: (((sK4 @ Y0 @ X1) & (sK4 @ X2 @ Y0)) => (sK4 @ X2 @ X1)))) = $true)) )),
% 1.55/1.40 inference(beta_eta_normalization,[status(thm)],[f32])).
% 1.55/1.40 thf(f32,plain,(
% 1.55/1.40 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y1 @ X1) & (sK4 @ Y0 @ Y1)) => (sK4 @ Y0 @ X1))))) @ X2) = $true)) )),
% 1.55/1.40 inference(pi_clausification,[status(thm)],[f31])).
% 1.55/1.40 thf(f31,plain,(
% 1.55/1.40 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK4 @ Y1 @ X1) & (sK4 @ Y0 @ Y1)) => (sK4 @ Y0 @ X1)))))))) )),
% 1.55/1.40 inference(beta_eta_normalization,[status(thm)],[f30])).
% 1.55/1.40 thf(f30,plain,(
% 1.55/1.40 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y2 @ Y0) & (sK4 @ Y1 @ Y2)) => (sK4 @ Y1 @ Y0))))))) @ X1) = $true)) )),
% 1.55/1.40 inference(pi_clausification,[status(thm)],[f23])).
% 1.55/1.40 thf(f23,plain,(
% 1.55/1.40 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y2 @ Y0) & (sK4 @ Y1 @ Y2)) => (sK4 @ Y1 @ Y0)))))))) = $true)),
% 1.55/1.40 inference(boolean_simplification,[status(thm)],[f22])).
% 1.55/1.40 thf(f22,plain,(
% 1.55/1.40 ($true = ($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK4 @ Y2 @ Y0) & (sK4 @ Y1 @ Y2)) => (sK4 @ Y1 @ Y0))))))))))),
% 1.55/1.40 inference(backward_demodulation,[status(thm)],[f17,f21])).
% 1.55/1.40 thf(f54,plain,(
% 1.55/1.40 ( ! [X2 : a,X1 : a] : (($true = ((sK2 @ X2 @ X1) => ((((sK3 @ X2) = (sK3 @ X1)) & (!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: (!! @ b @ (^[Y2 : b]: (((sK3 @ X2 @ Y2 @ Y1) & (sK3 @ X2 @ Y1 @ Y0)) => (sK3 @ X2 @ Y2 @ Y0))))))))) & (!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: ((sK3 @ X2 @ Y1 @ Y0) => (sK3 @ X2 @ Y0 @ Y1)))))))))) )),
% 1.55/1.40 inference(backward_demodulation,[status(thm)],[f47,f50])).
% 1.55/1.40 thf(f47,plain,(
% 1.55/1.40 ( ! [X2 : a,X1 : a] : (($true = ((sK4 @ X2 @ X1) => ((((sK3 @ X2) = (sK3 @ X1)) & (!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: (!! @ b @ (^[Y2 : b]: (((sK3 @ X2 @ Y2 @ Y1) & (sK3 @ X2 @ Y1 @ Y0)) => (sK3 @ X2 @ Y2 @ Y0))))))))) & (!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: ((sK3 @ X2 @ Y1 @ Y0) => (sK3 @ X2 @ Y0 @ Y1)))))))))) )),
% 1.55/1.40 inference(beta_eta_normalization,[status(thm)],[f46])).
% 1.55/1.40 thf(f46,plain,(
% 1.55/1.40 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: ((sK4 @ Y0 @ X1) => ((((sK3 @ Y0) = (sK3 @ X1)) & (!! @ b @ (^[Y1 : b]: (!! @ b @ (^[Y2 : b]: (!! @ b @ (^[Y3 : b]: (((sK3 @ Y0 @ Y3 @ Y2) & (sK3 @ Y0 @ Y2 @ Y1)) => (sK3 @ Y0 @ Y3 @ Y1))))))))) & (!! @ b @ (^[Y1 : b]: (!! @ b @ (^[Y2 : b]: ((sK3 @ Y0 @ Y2 @ Y1) => (sK3 @ Y0 @ Y1 @ Y2))))))))) @ X2) = $true)) )),
% 1.55/1.40 inference(pi_clausification,[status(thm)],[f42])).
% 1.55/1.40 thf(f42,plain,(
% 1.55/1.40 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: ((sK4 @ Y0 @ X1) => ((((sK3 @ Y0) = (sK3 @ X1)) & (!! @ b @ (^[Y1 : b]: (!! @ b @ (^[Y2 : b]: (!! @ b @ (^[Y3 : b]: (((sK3 @ Y0 @ Y3 @ Y2) & (sK3 @ Y0 @ Y2 @ Y1)) => (sK3 @ Y0 @ Y3 @ Y1))))))))) & (!! @ b @ (^[Y1 : b]: (!! @ b @ (^[Y2 : b]: ((sK3 @ Y0 @ Y2 @ Y1) => (sK3 @ Y0 @ Y1 @ Y2)))))))))) = $true)) )),
% 1.55/1.40 inference(beta_eta_normalization,[status(thm)],[f41])).
% 1.55/1.40 thf(f41,plain,(
% 1.55/1.40 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y1 @ Y0) => ((((sK3 @ Y1) = (sK3 @ Y0)) & (!! @ b @ (^[Y2 : b]: (!! @ b @ (^[Y3 : b]: (!! @ b @ (^[Y4 : b]: (((sK3 @ Y1 @ Y4 @ Y3) & (sK3 @ Y1 @ Y3 @ Y2)) => (sK3 @ Y1 @ Y4 @ Y2))))))))) & (!! @ b @ (^[Y2 : b]: (!! @ b @ (^[Y3 : b]: ((sK3 @ Y1 @ Y3 @ Y2) => (sK3 @ Y1 @ Y2 @ Y3))))))))))) @ X1) = $true)) )),
% 1.55/1.40 inference(pi_clausification,[status(thm)],[f25])).
% 1.55/1.40 thf(f25,plain,(
% 1.55/1.40 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y1 @ Y0) => ((((sK3 @ Y1) = (sK3 @ Y0)) & (!! @ b @ (^[Y2 : b]: (!! @ b @ (^[Y3 : b]: (!! @ b @ (^[Y4 : b]: (((sK3 @ Y1 @ Y4 @ Y3) & (sK3 @ Y1 @ Y3 @ Y2)) => (sK3 @ Y1 @ Y4 @ Y2))))))))) & (!! @ b @ (^[Y2 : b]: (!! @ b @ (^[Y3 : b]: ((sK3 @ Y1 @ Y3 @ Y2) => (sK3 @ Y1 @ Y2 @ Y3)))))))))))) = $true)),
% 1.55/1.40 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.55/1.40 thf(f19,plain,(
% 1.55/1.40 ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y1 @ Y0) => ((((sK3 @ Y1) = (sK3 @ Y0)) & (!! @ b @ (^[Y2 : b]: (!! @ b @ (^[Y3 : b]: (!! @ b @ (^[Y4 : b]: (((sK3 @ Y1 @ Y4 @ Y3) & (sK3 @ Y1 @ Y3 @ Y2)) => (sK3 @ Y1 @ Y4 @ Y2))))))))) & (!! @ b @ (^[Y2 : b]: (!! @ b @ (^[Y3 : b]: ((sK3 @ Y1 @ Y3 @ Y2) => (sK3 @ Y1 @ Y2 @ Y3)))))))))))) => (((!! @ (a > b) @ (^[Y0 : a > b]: (!! @ (a > b) @ (^[Y1 : a > b]: (!! @ (a > b) @ (^[Y2 : a > b]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y3 @ Y4) => (sK3 @ Y3 @ (Y0 @ Y3) @ (Y2 @ Y4))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y3 @ Y4) => (sK3 @ Y3 @ (Y2 @ Y3) @ (Y1 @ Y4)))))))) => (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y3 @ Y4) => (sK3 @ Y3 @ (Y0 @ Y3) @ (Y1 @ Y4)))))))))))))) & (!! @ (a > b) @ (^[Y0 : a > b]: (!! @ (a > b) @ (^[Y1 : a > b]: ((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y3 @ Y2) => (sK3 @ Y3 @ (Y1 @ Y3) @ (Y0 @ Y2))))))) => (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y2 @ Y3) => (sK3 @ Y2 @ (Y0 @ Y2) @ (Y1 @ Y3))))))))))))) & ((^[Y0 : a > b]: ((^[Y1 : a > b]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y3 @ Y2) => (sK3 @ Y3 @ (Y0 @ Y3) @ (Y1 @ Y2)))))))))) = (^[Y0 : a > b]: ((^[Y1 : a > b]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y2 @ Y3) => (sK3 @ Y2 @ (Y0 @ Y2) @ (Y1 @ Y3))))))))))))))),
% 1.55/1.40 inference(boolean_simplification,[status(thm)],[f18])).
% 1.55/1.40 thf(f18,plain,(
% 1.55/1.40 ($false = ($true => ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y1 @ Y0) => ((((sK3 @ Y1) = (sK3 @ Y0)) & (!! @ b @ (^[Y2 : b]: (!! @ b @ (^[Y3 : b]: (!! @ b @ (^[Y4 : b]: (((sK3 @ Y1 @ Y4 @ Y3) & (sK3 @ Y1 @ Y3 @ Y2)) => (sK3 @ Y1 @ Y4 @ Y2))))))))) & (!! @ b @ (^[Y2 : b]: (!! @ b @ (^[Y3 : b]: ((sK3 @ Y1 @ Y3 @ Y2) => (sK3 @ Y1 @ Y2 @ Y3)))))))))))) => (((!! @ (a > b) @ (^[Y0 : a > b]: (!! @ (a > b) @ (^[Y1 : a > b]: (!! @ (a > b) @ (^[Y2 : a > b]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y3 @ Y4) => (sK3 @ Y3 @ (Y0 @ Y3) @ (Y2 @ Y4))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y3 @ Y4) => (sK3 @ Y3 @ (Y2 @ Y3) @ (Y1 @ Y4)))))))) => (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y3 @ Y4) => (sK3 @ Y3 @ (Y0 @ Y3) @ (Y1 @ Y4)))))))))))))) & (!! @ (a > b) @ (^[Y0 : a > b]: (!! @ (a > b) @ (^[Y1 : a > b]: ((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y3 @ Y2) => (sK3 @ Y3 @ (Y1 @ Y3) @ (Y0 @ Y2))))))) => (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y2 @ Y3) => (sK3 @ Y2 @ (Y0 @ Y2) @ (Y1 @ Y3))))))))))))) & ((^[Y0 : a > b]: ((^[Y1 : a > b]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y3 @ Y2) => (sK3 @ Y3 @ (Y0 @ Y3) @ (Y1 @ Y2)))))))))) = (^[Y0 : a > b]: ((^[Y1 : a > b]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y2 @ Y3) => (sK3 @ Y2 @ (Y0 @ Y2) @ (Y1 @ Y3)))))))))))))))),
% 1.55/1.40 inference(backward_demodulation,[status(thm)],[f15,f17])).
% 1.55/1.40 thf(f1139,plain,(
% 1.55/1.40 ($true = (((sK3 @ sK13) = (sK3 @ sK14)) & (!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: ((sK3 @ sK13 @ Y1 @ Y0) => (sK3 @ sK13 @ Y0 @ Y1)))))))) | ~spl0_4),
% 1.55/1.40 inference(boolean_simplification,[status(thm)],[f1137])).
% 1.55/1.40 thf(f1137,plain,(
% 1.55/1.40 (((((sK3 @ sK13) = (sK3 @ sK14)) & $true) & (!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: ((sK3 @ sK13 @ Y1 @ Y0) => (sK3 @ sK13 @ Y0 @ Y1))))))) = $true) | ~spl0_4),
% 1.55/1.40 inference(backward_demodulation,[status(thm)],[f978,f1135])).
% 1.55/1.40 thf(f978,plain,(
% 1.55/1.40 (((((sK3 @ sK13) = (sK3 @ sK14)) & (!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: (!! @ b @ (^[Y2 : b]: (((sK3 @ sK13 @ Y2 @ Y1) & (sK3 @ sK13 @ Y1 @ Y0)) => (sK3 @ sK13 @ Y2 @ Y0))))))))) & (!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: ((sK3 @ sK13 @ Y1 @ Y0) => (sK3 @ sK13 @ Y0 @ Y1))))))) = $true) | ~spl0_4),
% 1.55/1.40 inference(boolean_simplification,[status(thm)],[f966])).
% 1.55/1.40 thf(f966,plain,(
% 1.55/1.40 (($true => ((((sK3 @ sK13) = (sK3 @ sK14)) & (!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: (!! @ b @ (^[Y2 : b]: (((sK3 @ sK13 @ Y2 @ Y1) & (sK3 @ sK13 @ Y1 @ Y0)) => (sK3 @ sK13 @ Y2 @ Y0))))))))) & (!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: ((sK3 @ sK13 @ Y1 @ Y0) => (sK3 @ sK13 @ Y0 @ Y1)))))))) = $true) | ~spl0_4),
% 1.55/1.40 inference(superposition,[status(thm)],[f54,f959])).
% 1.55/1.40 thf(f1058,plain,(
% 1.55/1.40 ((sK3 @ sK14 @ (sK12 @ sK14) @ (sK11 @ sK13)) = $true) | ~spl0_4),
% 1.55/1.40 inference(boolean_simplification,[status(thm)],[f1053])).
% 1.55/1.40 thf(f1053,plain,(
% 1.55/1.40 (($true => (sK3 @ sK14 @ (sK12 @ sK14) @ (sK11 @ sK13))) = $true) | ~spl0_4),
% 1.55/1.40 inference(superposition,[status(thm)],[f1025,f962])).
% 1.55/1.40 thf(f1025,plain,(
% 1.55/1.40 ( ! [X2 : a,X1 : a] : ((((sK2 @ X2 @ X1) => (sK3 @ X2 @ (sK12 @ X2) @ (sK11 @ X1))) = $true)) ) | ~spl0_4),
% 1.55/1.40 inference(forward_demodulation,[status(thm)],[f1024,f50])).
% 1.55/1.40 thf(f1024,plain,(
% 1.55/1.40 ( ! [X2 : a,X1 : a] : ((((sK4 @ X2 @ X1) => (sK3 @ X2 @ (sK12 @ X2) @ (sK11 @ X1))) = $true)) ) | ~spl0_4),
% 1.55/1.40 inference(beta_eta_normalization,[status(thm)],[f1023])).
% 1.55/1.40 thf(f1023,plain,(
% 1.55/1.40 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: ((sK4 @ Y0 @ X1) => (sK3 @ Y0 @ (sK12 @ Y0) @ (sK11 @ X1)))) @ X2) = $true)) ) | ~spl0_4),
% 1.55/1.40 inference(pi_clausification,[status(thm)],[f1013])).
% 1.55/1.40 thf(f1013,plain,(
% 1.55/1.40 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: ((sK4 @ Y0 @ X1) => (sK3 @ Y0 @ (sK12 @ Y0) @ (sK11 @ X1))))))) ) | ~spl0_4),
% 1.55/1.40 inference(beta_eta_normalization,[status(thm)],[f1012])).
% 1.55/1.40 thf(f1012,plain,(
% 1.55/1.40 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y1 @ Y0) => (sK3 @ Y1 @ (sK12 @ Y1) @ (sK11 @ Y0)))))) @ X1) = $true)) ) | ~spl0_4),
% 1.55/1.40 inference(pi_clausification,[status(thm)],[f948])).
% 1.55/1.40 thf(f948,plain,(
% 1.55/1.40 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y1 @ Y0) => (sK3 @ Y1 @ (sK12 @ Y1) @ (sK11 @ Y0))))))) = $true) | ~spl0_4),
% 1.55/1.40 inference(binary_proxy_clausification,[status(thm)],[f946])).
% 1.55/1.40 thf(f1231,plain,(
% 1.55/1.40 ( ! [X2 : b,X1 : b] : ((((sK3 @ sK13 @ X2 @ X1) => (sK3 @ sK13 @ X1 @ X2)) = $true)) ) | ~spl0_4),
% 1.55/1.40 inference(beta_eta_normalization,[status(thm)],[f1230])).
% 1.55/1.40 thf(f1230,plain,(
% 1.55/1.40 ( ! [X2 : b,X1 : b] : ((((^[Y0 : b]: ((sK3 @ sK13 @ Y0 @ X1) => (sK3 @ sK13 @ X1 @ Y0))) @ X2) = $true)) ) | ~spl0_4),
% 1.55/1.40 inference(pi_clausification,[status(thm)],[f1214])).
% 1.55/1.40 thf(f1214,plain,(
% 1.55/1.40 ( ! [X1 : b] : (((!! @ b @ (^[Y0 : b]: ((sK3 @ sK13 @ Y0 @ X1) => (sK3 @ sK13 @ X1 @ Y0)))) = $true)) ) | ~spl0_4),
% 1.55/1.40 inference(beta_eta_normalization,[status(thm)],[f1207])).
% 1.55/1.40 thf(f1207,plain,(
% 1.55/1.40 ( ! [X1 : b] : (($true = ((^[Y0 : b]: (!! @ b @ (^[Y1 : b]: ((sK3 @ sK13 @ Y1 @ Y0) => (sK3 @ sK13 @ Y0 @ Y1))))) @ X1))) ) | ~spl0_4),
% 1.55/1.40 inference(pi_clausification,[status(thm)],[f1138])).
% 1.55/1.40 thf(f940,plain,(
% 1.55/1.40 ~spl0_3),
% 1.55/1.40 inference(avatar_contradiction_clause,[status(thm)],[f939])).
% 1.55/1.40 thf(f939,plain,(
% 1.55/1.40 $false | ~spl0_3),
% 1.55/1.40 inference(trivial_inequality_removal,[status(thm)],[f938])).
% 1.55/1.40 thf(f938,plain,(
% 1.55/1.40 ($false = $true) | ~spl0_3),
% 1.55/1.40 inference(forward_demodulation,[status(thm)],[f926,f501])).
% 1.55/1.40 thf(f501,plain,(
% 1.55/1.40 ($false = (sK3 @ sK8 @ (sK6 @ sK10) @ (sK5 @ sK8))) | ~spl0_3),
% 1.55/1.40 inference(not_proxy_clausification,[status(thm)],[f452])).
% 1.55/1.40 thf(f452,plain,(
% 1.55/1.40 ((~ (sK3 @ sK8 @ (sK6 @ sK10) @ (sK5 @ sK8))) = $true) | ~spl0_3),
% 1.55/1.40 inference(boolean_simplification,[status(thm)],[f420])).
% 1.55/1.40 thf(f420,plain,(
% 1.55/1.40 ($true = ((sK3 @ sK8 @ (sK6 @ sK10) @ (sK5 @ sK8)) => $false)) | ~spl0_3),
% 1.55/1.40 inference(superposition,[status(thm)],[f416,f122])).
% 1.55/1.40 thf(f122,plain,(
% 1.55/1.40 ((sK3 @ sK8 @ (sK5 @ sK8) @ (sK6 @ sK10)) = $false) | ~spl0_3),
% 1.55/1.40 inference(boolean_simplification,[status(thm)],[f121])).
% 1.55/1.40 thf(f121,plain,(
% 1.55/1.40 ($false = ($true => (sK3 @ sK8 @ (sK5 @ sK8) @ (sK6 @ sK10)))) | ~spl0_3),
% 1.55/1.40 inference(backward_demodulation,[status(thm)],[f115,f120])).
% 1.55/1.40 thf(f120,plain,(
% 1.55/1.40 ((sK2 @ sK8 @ sK10) = $true) | ~spl0_3),
% 1.55/1.40 inference(binary_proxy_clausification,[status(thm)],[f115])).
% 1.55/1.40 thf(f115,plain,(
% 1.55/1.40 (((sK2 @ sK8 @ sK10) => (sK3 @ sK8 @ (sK5 @ sK8) @ (sK6 @ sK10))) = $false) | ~spl0_3),
% 1.55/1.40 inference(forward_demodulation,[status(thm)],[f114,f50])).
% 1.55/1.40 thf(f114,plain,(
% 1.55/1.40 ($false = ((sK4 @ sK8 @ sK10) => (sK3 @ sK8 @ (sK5 @ sK8) @ (sK6 @ sK10)))) | ~spl0_3),
% 1.55/1.40 inference(beta_eta_normalization,[status(thm)],[f113])).
% 1.55/1.40 thf(f113,plain,(
% 1.55/1.40 (((^[Y0 : a]: ((sK4 @ sK8 @ Y0) => (sK3 @ sK8 @ (sK5 @ sK8) @ (sK6 @ Y0)))) @ sK10) = $false) | ~spl0_3),
% 1.55/1.40 inference(sigma_clausification,[status(thm)],[f110])).
% 1.55/1.40 thf(f110,plain,(
% 1.55/1.40 ($false = (!! @ a @ (^[Y0 : a]: ((sK4 @ sK8 @ Y0) => (sK3 @ sK8 @ (sK5 @ sK8) @ (sK6 @ Y0)))))) | ~spl0_3),
% 1.55/1.40 inference(beta_eta_normalization,[status(thm)],[f109])).
% 1.55/1.40 thf(f109,plain,(
% 1.55/1.40 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y0 @ Y1) => (sK3 @ Y0 @ (sK5 @ Y0) @ (sK6 @ Y1)))))) @ sK8)) | ~spl0_3),
% 1.55/1.40 inference(sigma_clausification,[status(thm)],[f101])).
% 1.55/1.40 thf(f101,plain,(
% 1.55/1.40 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y0 @ Y1) => (sK3 @ Y0 @ (sK5 @ Y0) @ (sK6 @ Y1)))))))) | ~spl0_3),
% 1.55/1.40 inference(binary_proxy_clausification,[status(thm)],[f100])).
% 1.55/1.40 thf(f100,plain,(
% 1.55/1.40 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y0 @ Y1) => (sK3 @ Y0 @ (sK5 @ Y0) @ (sK7 @ Y1))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y0 @ Y1) => (sK3 @ Y0 @ (sK7 @ Y0) @ (sK6 @ Y1)))))))) => (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y0 @ Y1) => (sK3 @ Y0 @ (sK5 @ Y0) @ (sK6 @ Y1)))))))) = $false) | ~spl0_3),
% 1.55/1.40 inference(beta_eta_normalization,[status(thm)],[f99])).
% 1.55/1.40 thf(f99,plain,(
% 1.55/1.40 ($false = ((^[Y0 : a > b]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK4 @ Y1 @ Y2) => (sK3 @ Y1 @ (sK5 @ Y1) @ (Y0 @ Y2))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK4 @ Y1 @ Y2) => (sK3 @ Y1 @ (Y0 @ Y1) @ (sK6 @ Y2)))))))) => (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK4 @ Y1 @ Y2) => (sK3 @ Y1 @ (sK5 @ Y1) @ (sK6 @ Y2))))))))) @ sK7)) | ~spl0_3),
% 1.55/1.40 inference(sigma_clausification,[status(thm)],[f98])).
% 1.55/1.40 thf(f98,plain,(
% 1.55/1.40 ($false = (!! @ (a > b) @ (^[Y0 : a > b]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK4 @ Y1 @ Y2) => (sK3 @ Y1 @ (sK5 @ Y1) @ (Y0 @ Y2))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK4 @ Y1 @ Y2) => (sK3 @ Y1 @ (Y0 @ Y1) @ (sK6 @ Y2)))))))) => (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK4 @ Y1 @ Y2) => (sK3 @ Y1 @ (sK5 @ Y1) @ (sK6 @ Y2))))))))))) | ~spl0_3),
% 1.55/1.40 inference(beta_eta_normalization,[status(thm)],[f97])).
% 1.55/1.40 thf(f97,plain,(
% 1.55/1.40 (((^[Y0 : a > b]: (!! @ (a > b) @ (^[Y1 : a > b]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y2 @ Y3) => (sK3 @ Y2 @ (sK5 @ Y2) @ (Y1 @ Y3))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y2 @ Y3) => (sK3 @ Y2 @ (Y1 @ Y2) @ (Y0 @ Y3)))))))) => (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y2 @ Y3) => (sK3 @ Y2 @ (sK5 @ Y2) @ (Y0 @ Y3))))))))))) @ sK6) = $false) | ~spl0_3),
% 1.55/1.40 inference(sigma_clausification,[status(thm)],[f96])).
% 1.55/1.40 thf(f96,plain,(
% 1.55/1.40 ($false = (!! @ (a > b) @ (^[Y0 : a > b]: (!! @ (a > b) @ (^[Y1 : a > b]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y2 @ Y3) => (sK3 @ Y2 @ (sK5 @ Y2) @ (Y1 @ Y3))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y2 @ Y3) => (sK3 @ Y2 @ (Y1 @ Y2) @ (Y0 @ Y3)))))))) => (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y2 @ Y3) => (sK3 @ Y2 @ (sK5 @ Y2) @ (Y0 @ Y3))))))))))))) | ~spl0_3),
% 1.55/1.40 inference(beta_eta_normalization,[status(thm)],[f95])).
% 1.55/1.40 thf(f95,plain,(
% 1.55/1.40 ($false = ((^[Y0 : a > b]: (!! @ (a > b) @ (^[Y1 : a > b]: (!! @ (a > b) @ (^[Y2 : a > b]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y3 @ Y4) => (sK3 @ Y3 @ (Y0 @ Y3) @ (Y2 @ Y4))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y3 @ Y4) => (sK3 @ Y3 @ (Y2 @ Y3) @ (Y1 @ Y4)))))))) => (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y3 @ Y4) => (sK3 @ Y3 @ (Y0 @ Y3) @ (Y1 @ Y4))))))))))))) @ sK5)) | ~spl0_3),
% 1.55/1.40 inference(sigma_clausification,[status(thm)],[f88])).
% 1.55/1.40 thf(f88,plain,(
% 1.55/1.40 ($false = (!! @ (a > b) @ (^[Y0 : a > b]: (!! @ (a > b) @ (^[Y1 : a > b]: (!! @ (a > b) @ (^[Y2 : a > b]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y3 @ Y4) => (sK3 @ Y3 @ (Y0 @ Y3) @ (Y2 @ Y4))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y3 @ Y4) => (sK3 @ Y3 @ (Y2 @ Y3) @ (Y1 @ Y4)))))))) => (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y3 @ Y4) => (sK3 @ Y3 @ (Y0 @ Y3) @ (Y1 @ Y4))))))))))))))) | ~spl0_3),
% 1.55/1.40 inference(avatar_component_clause,[status(thm)],[f87])).
% 1.55/1.40 thf(f87,definition,(
% 1.55/1.40 spl0_3 <=> ($false = (!! @ (a > b) @ (^[Y0 : a > b]: (!! @ (a > b) @ (^[Y1 : a > b]: (!! @ (a > b) @ (^[Y2 : a > b]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y3 @ Y4) => (sK3 @ Y3 @ (Y0 @ Y3) @ (Y2 @ Y4))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y3 @ Y4) => (sK3 @ Y3 @ (Y2 @ Y3) @ (Y1 @ Y4)))))))) => (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y3 @ Y4) => (sK3 @ Y3 @ (Y0 @ Y3) @ (Y1 @ Y4)))))))))))))))),
% 1.55/1.40 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.55/1.40 thf(f416,plain,(
% 1.55/1.40 ( ! [X2 : b,X1 : b] : ((((sK3 @ sK8 @ X2 @ X1) => (sK3 @ sK8 @ X1 @ X2)) = $true)) ) | ~spl0_3),
% 1.55/1.40 inference(beta_eta_normalization,[status(thm)],[f415])).
% 1.55/1.40 thf(f415,plain,(
% 1.55/1.40 ( ! [X2 : b,X1 : b] : ((((^[Y0 : b]: ((sK3 @ sK8 @ Y0 @ X1) => (sK3 @ sK8 @ X1 @ Y0))) @ X2) = $true)) ) | ~spl0_3),
% 1.55/1.40 inference(pi_clausification,[status(thm)],[f409])).
% 1.55/1.40 thf(f409,plain,(
% 1.55/1.40 ( ! [X1 : b] : (((!! @ b @ (^[Y0 : b]: ((sK3 @ sK8 @ Y0 @ X1) => (sK3 @ sK8 @ X1 @ Y0)))) = $true)) ) | ~spl0_3),
% 1.55/1.40 inference(beta_eta_normalization,[status(thm)],[f407])).
% 1.55/1.40 thf(f407,plain,(
% 1.55/1.40 ( ! [X1 : b] : (($true = ((^[Y0 : b]: (!! @ b @ (^[Y1 : b]: ((sK3 @ sK8 @ Y1 @ Y0) => (sK3 @ sK8 @ Y0 @ Y1))))) @ X1))) ) | ~spl0_3),
% 1.55/1.40 inference(pi_clausification,[status(thm)],[f324])).
% 1.55/1.40 thf(f324,plain,(
% 1.55/1.40 ((!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: ((sK3 @ sK8 @ Y1 @ Y0) => (sK3 @ sK8 @ Y0 @ Y1)))))) = $true) | ~spl0_3),
% 1.55/1.40 inference(binary_proxy_clausification,[status(thm)],[f134])).
% 1.55/1.40 thf(f134,plain,(
% 1.55/1.40 (((((sK3 @ sK8) = (sK3 @ sK10)) & (!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: (!! @ b @ (^[Y2 : b]: (((sK3 @ sK8 @ Y2 @ Y1) & (sK3 @ sK8 @ Y1 @ Y0)) => (sK3 @ sK8 @ Y2 @ Y0))))))))) & (!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: ((sK3 @ sK8 @ Y1 @ Y0) => (sK3 @ sK8 @ Y0 @ Y1))))))) = $true) | ~spl0_3),
% 1.55/1.40 inference(boolean_simplification,[status(thm)],[f129])).
% 1.55/1.40 thf(f129,plain,(
% 1.55/1.40 (($true => ((((sK3 @ sK8) = (sK3 @ sK10)) & (!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: (!! @ b @ (^[Y2 : b]: (((sK3 @ sK8 @ Y2 @ Y1) & (sK3 @ sK8 @ Y1 @ Y0)) => (sK3 @ sK8 @ Y2 @ Y0))))))))) & (!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: ((sK3 @ sK8 @ Y1 @ Y0) => (sK3 @ sK8 @ Y0 @ Y1)))))))) = $true) | ~spl0_3),
% 1.55/1.40 inference(superposition,[status(thm)],[f54,f120])).
% 1.55/1.40 thf(f926,plain,(
% 1.55/1.40 ((sK3 @ sK8 @ (sK6 @ sK10) @ (sK5 @ sK8)) = $true) | ~spl0_3),
% 1.55/1.40 inference(boolean_simplification,[status(thm)],[f923])).
% 1.55/1.40 thf(f923,plain,(
% 1.55/1.40 ($true = ($true => (sK3 @ sK8 @ (sK6 @ sK10) @ (sK5 @ sK8)))) | ~spl0_3),
% 1.55/1.40 inference(superposition,[status(thm)],[f642,f722])).
% 1.55/1.40 thf(f722,plain,(
% 1.55/1.40 ((sK3 @ sK8 @ (sK6 @ sK10) @ (sK7 @ sK10)) = $true) | ~spl0_3),
% 1.55/1.40 inference(boolean_simplification,[status(thm)],[f717])).
% 1.55/1.40 thf(f717,plain,(
% 1.55/1.40 (($true => (sK3 @ sK8 @ (sK6 @ sK10) @ (sK7 @ sK10))) = $true) | ~spl0_3),
% 1.55/1.40 inference(superposition,[status(thm)],[f416,f520])).
% 1.55/1.40 thf(f520,plain,(
% 1.55/1.40 ((sK3 @ sK8 @ (sK7 @ sK10) @ (sK6 @ sK10)) = $true) | ~spl0_3),
% 1.55/1.40 inference(superposition,[status(thm)],[f310,f389])).
% 1.55/1.40 thf(f389,plain,(
% 1.55/1.40 ( ! [X2 : b,X1 : b] : (((sK3 @ sK10 @ X1 @ X2) = (sK3 @ sK8 @ X1 @ X2))) ) | ~spl0_3),
% 1.55/1.40 inference(argument_congruence,[status(thm)],[f352])).
% 1.55/1.40 thf(f352,plain,(
% 1.55/1.40 ( ! [X1 : b] : (((sK3 @ sK10 @ X1) = (sK3 @ sK8 @ X1))) ) | ~spl0_3),
% 1.55/1.40 inference(argument_congruence,[status(thm)],[f338])).
% 1.55/1.40 thf(f338,plain,(
% 1.55/1.40 ((sK3 @ sK10) = (sK3 @ sK8)) | ~spl0_3),
% 1.55/1.40 inference(equality_proxy_clausification,[status(thm)],[f333])).
% 1.55/1.40 thf(f333,plain,(
% 1.55/1.40 (((sK3 @ sK8) = (sK3 @ sK10)) = $true) | ~spl0_3),
% 1.55/1.40 inference(boolean_simplification,[status(thm)],[f332])).
% 1.55/1.40 thf(f332,plain,(
% 1.55/1.40 ((((sK3 @ sK8) = (sK3 @ sK10)) & $true) = $true) | ~spl0_3),
% 1.55/1.40 inference(forward_demodulation,[status(thm)],[f330,f331])).
% 1.55/1.40 thf(f331,plain,(
% 1.55/1.40 ((!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: (!! @ b @ (^[Y2 : b]: (((sK3 @ sK8 @ Y2 @ Y1) & (sK3 @ sK8 @ Y1 @ Y0)) => (sK3 @ sK8 @ Y2 @ Y0)))))))) = $true) | ~spl0_3),
% 1.55/1.40 inference(boolean_simplification,[status(thm)],[f328])).
% 1.55/1.40 thf(f328,plain,(
% 1.55/1.40 (((!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: (!! @ b @ (^[Y2 : b]: (((sK3 @ sK8 @ Y2 @ Y1) & (sK3 @ sK8 @ Y1 @ Y0)) => (sK3 @ sK8 @ Y2 @ Y0)))))))) & $true) = $true) | ~spl0_3),
% 1.55/1.40 inference(backward_demodulation,[status(thm)],[f198,f324])).
% 1.55/1.40 thf(f198,plain,(
% 1.55/1.40 ($true = ((!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: (!! @ b @ (^[Y2 : b]: (((sK3 @ sK8 @ Y2 @ Y1) & (sK3 @ sK8 @ Y1 @ Y0)) => (sK3 @ sK8 @ Y2 @ Y0)))))))) & (!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: ((sK3 @ sK8 @ Y1 @ Y0) => (sK3 @ sK8 @ Y0 @ Y1)))))))) | ~spl0_3),
% 1.55/1.40 inference(boolean_simplification,[status(thm)],[f197])).
% 1.55/1.40 thf(f197,plain,(
% 1.55/1.40 ((($true & (!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: (!! @ b @ (^[Y2 : b]: (((sK3 @ sK8 @ Y2 @ Y1) & (sK3 @ sK8 @ Y1 @ Y0)) => (sK3 @ sK8 @ Y2 @ Y0))))))))) & (!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: ((sK3 @ sK8 @ Y1 @ Y0) => (sK3 @ sK8 @ Y0 @ Y1))))))) = $true) | ~spl0_3),
% 1.55/1.40 inference(boolean_simplification,[status(thm)],[f196])).
% 1.55/1.40 thf(f196,plain,(
% 1.55/1.40 (((((sK3 @ sK8) = (sK3 @ sK8)) & (!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: (!! @ b @ (^[Y2 : b]: (((sK3 @ sK8 @ Y2 @ Y1) & (sK3 @ sK8 @ Y1 @ Y0)) => (sK3 @ sK8 @ Y2 @ Y0))))))))) & (!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: ((sK3 @ sK8 @ Y1 @ Y0) => (sK3 @ sK8 @ Y0 @ Y1))))))) = $true) | ~spl0_3),
% 1.55/1.40 inference(boolean_simplification,[status(thm)],[f181])).
% 1.55/1.40 thf(f181,plain,(
% 1.55/1.40 (($true => ((((sK3 @ sK8) = (sK3 @ sK8)) & (!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: (!! @ b @ (^[Y2 : b]: (((sK3 @ sK8 @ Y2 @ Y1) & (sK3 @ sK8 @ Y1 @ Y0)) => (sK3 @ sK8 @ Y2 @ Y0))))))))) & (!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: ((sK3 @ sK8 @ Y1 @ Y0) => (sK3 @ sK8 @ Y0 @ Y1)))))))) = $true) | ~spl0_3),
% 1.55/1.40 inference(superposition,[status(thm)],[f54,f174])).
% 1.55/1.40 thf(f174,plain,(
% 1.55/1.40 ((sK2 @ sK8 @ sK8) = $true) | ~spl0_3),
% 1.55/1.40 inference(boolean_simplification,[status(thm)],[f172])).
% 1.55/1.40 thf(f172,plain,(
% 1.55/1.40 ($true = ($true => (sK2 @ sK8 @ sK8))) | ~spl0_3),
% 1.55/1.40 inference(superposition,[status(thm)],[f135,f133])).
% 1.55/1.40 thf(f133,plain,(
% 1.55/1.40 ((sK2 @ sK10 @ sK8) = $true) | ~spl0_3),
% 1.55/1.40 inference(boolean_simplification,[status(thm)],[f127])).
% 1.55/1.40 thf(f127,plain,(
% 1.55/1.40 (($true => (sK2 @ sK10 @ sK8)) = $true) | ~spl0_3),
% 1.55/1.40 inference(superposition,[status(thm)],[f73,f120])).
% 1.55/1.40 thf(f135,plain,(
% 1.55/1.40 ( ! [X0 : a] : (($true = ((sK2 @ sK10 @ X0) => (sK2 @ sK8 @ X0)))) ) | ~spl0_3),
% 1.55/1.40 inference(boolean_simplification,[status(thm)],[f131])).
% 1.55/1.40 thf(f131,plain,(
% 1.55/1.40 ( ! [X0 : a] : (((((sK2 @ sK10 @ X0) & $true) => (sK2 @ sK8 @ X0)) = $true)) ) | ~spl0_3),
% 1.55/1.40 inference(superposition,[status(thm)],[f59,f120])).
% 1.55/1.40 thf(f330,plain,(
% 1.55/1.40 ((((sK3 @ sK8) = (sK3 @ sK10)) & (!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: (!! @ b @ (^[Y2 : b]: (((sK3 @ sK8 @ Y2 @ Y1) & (sK3 @ sK8 @ Y1 @ Y0)) => (sK3 @ sK8 @ Y2 @ Y0))))))))) = $true) | ~spl0_3),
% 1.55/1.40 inference(boolean_simplification,[status(thm)],[f329])).
% 1.55/1.40 thf(f329,plain,(
% 1.55/1.40 (((((sK3 @ sK8) = (sK3 @ sK10)) & (!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: (!! @ b @ (^[Y2 : b]: (((sK3 @ sK8 @ Y2 @ Y1) & (sK3 @ sK8 @ Y1 @ Y0)) => (sK3 @ sK8 @ Y2 @ Y0))))))))) & $true) = $true) | ~spl0_3),
% 1.55/1.40 inference(backward_demodulation,[status(thm)],[f134,f324])).
% 1.55/1.40 thf(f310,plain,(
% 1.55/1.40 ((sK3 @ sK10 @ (sK7 @ sK10) @ (sK6 @ sK10)) = $true) | ~spl0_3),
% 1.55/1.40 inference(boolean_simplification,[status(thm)],[f305])).
% 1.55/1.40 thf(f305,plain,(
% 1.55/1.40 ($true = ($true => (sK3 @ sK10 @ (sK7 @ sK10) @ (sK6 @ sK10)))) | ~spl0_3),
% 1.55/1.40 inference(superposition,[status(thm)],[f214,f250])).
% 1.55/1.40 thf(f250,plain,(
% 1.55/1.40 ((sK2 @ sK10 @ sK10) = $true) | ~spl0_3),
% 1.55/1.40 inference(boolean_simplification,[status(thm)],[f246])).
% 1.55/1.40 thf(f246,plain,(
% 1.55/1.40 (($true => (sK2 @ sK10 @ sK10)) = $true) | ~spl0_3),
% 1.55/1.40 inference(superposition,[status(thm)],[f136,f133])).
% 1.55/1.40 thf(f136,plain,(
% 1.55/1.40 ( ! [X0 : a] : ((((sK2 @ X0 @ sK8) => (sK2 @ X0 @ sK10)) = $true)) ) | ~spl0_3),
% 1.55/1.40 inference(boolean_simplification,[status(thm)],[f130])).
% 1.55/1.40 thf(f130,plain,(
% 1.55/1.40 ( ! [X0 : a] : (((($true & (sK2 @ X0 @ sK8)) => (sK2 @ X0 @ sK10)) = $true)) ) | ~spl0_3),
% 1.55/1.40 inference(superposition,[status(thm)],[f59,f120])).
% 1.55/1.40 thf(f214,plain,(
% 1.55/1.40 ( ! [X2 : a,X1 : a] : ((((sK2 @ X1 @ X2) => (sK3 @ X1 @ (sK7 @ X1) @ (sK6 @ X2))) = $true)) ) | ~spl0_3),
% 1.55/1.40 inference(forward_demodulation,[status(thm)],[f213,f50])).
% 1.55/1.40 thf(f213,plain,(
% 1.55/1.40 ( ! [X2 : a,X1 : a] : (($true = ((sK4 @ X1 @ X2) => (sK3 @ X1 @ (sK7 @ X1) @ (sK6 @ X2))))) ) | ~spl0_3),
% 1.55/1.40 inference(beta_eta_normalization,[status(thm)],[f212])).
% 1.55/1.40 thf(f212,plain,(
% 1.55/1.40 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: ((sK4 @ X1 @ Y0) => (sK3 @ X1 @ (sK7 @ X1) @ (sK6 @ Y0)))) @ X2))) ) | ~spl0_3),
% 1.55/1.40 inference(pi_clausification,[status(thm)],[f209])).
% 1.55/1.40 thf(f209,plain,(
% 1.55/1.40 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: ((sK4 @ X1 @ Y0) => (sK3 @ X1 @ (sK7 @ X1) @ (sK6 @ Y0))))))) ) | ~spl0_3),
% 1.55/1.40 inference(beta_eta_normalization,[status(thm)],[f208])).
% 1.55/1.40 thf(f208,plain,(
% 1.55/1.40 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y0 @ Y1) => (sK3 @ Y0 @ (sK7 @ Y0) @ (sK6 @ Y1)))))) @ X1) = $true)) ) | ~spl0_3),
% 1.55/1.40 inference(pi_clausification,[status(thm)],[f205])).
% 1.55/1.40 thf(f205,plain,(
% 1.55/1.40 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y0 @ Y1) => (sK3 @ Y0 @ (sK7 @ Y0) @ (sK6 @ Y1))))))) = $true) | ~spl0_3),
% 1.55/1.40 inference(boolean_simplification,[status(thm)],[f204])).
% 1.55/1.40 thf(f204,plain,(
% 1.55/1.40 (($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y0 @ Y1) => (sK3 @ Y0 @ (sK7 @ Y0) @ (sK6 @ Y1)))))))) = $true) | ~spl0_3),
% 1.55/1.40 inference(backward_demodulation,[status(thm)],[f102,f203])).
% 1.55/1.40 thf(f203,plain,(
% 1.55/1.40 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y0 @ Y1) => (sK3 @ Y0 @ (sK5 @ Y0) @ (sK7 @ Y1))))))) = $true) | ~spl0_3),
% 1.55/1.40 inference(binary_proxy_clausification,[status(thm)],[f102])).
% 1.55/1.40 thf(f102,plain,(
% 1.55/1.40 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y0 @ Y1) => (sK3 @ Y0 @ (sK5 @ Y0) @ (sK7 @ Y1))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y0 @ Y1) => (sK3 @ Y0 @ (sK7 @ Y0) @ (sK6 @ Y1))))))))) | ~spl0_3),
% 1.55/1.40 inference(binary_proxy_clausification,[status(thm)],[f100])).
% 1.55/1.40 thf(f642,plain,(
% 1.55/1.40 ( ! [X0 : b] : (($true = ((sK3 @ sK8 @ X0 @ (sK7 @ sK10)) => (sK3 @ sK8 @ X0 @ (sK5 @ sK8))))) ) | ~spl0_3),
% 1.55/1.40 inference(boolean_simplification,[status(thm)],[f602])).
% 1.55/1.40 thf(f602,plain,(
% 1.55/1.40 ( ! [X0 : b] : (((((sK3 @ sK8 @ X0 @ (sK7 @ sK10)) & $true) => (sK3 @ sK8 @ X0 @ (sK5 @ sK8))) = $true)) ) | ~spl0_3),
% 1.55/1.40 inference(superposition,[status(thm)],[f576,f449])).
% 1.55/1.40 thf(f449,plain,(
% 1.55/1.40 ((sK3 @ sK8 @ (sK7 @ sK10) @ (sK5 @ sK8)) = $true) | ~spl0_3),
% 1.55/1.40 inference(boolean_simplification,[status(thm)],[f436])).
% 1.55/1.40 thf(f436,plain,(
% 1.55/1.40 (($true => (sK3 @ sK8 @ (sK7 @ sK10) @ (sK5 @ sK8))) = $true) | ~spl0_3),
% 1.55/1.40 inference(superposition,[status(thm)],[f416,f240])).
% 1.55/1.40 thf(f240,plain,(
% 1.55/1.40 ((sK3 @ sK8 @ (sK5 @ sK8) @ (sK7 @ sK10)) = $true) | ~spl0_3),
% 1.55/1.40 inference(boolean_simplification,[status(thm)],[f238])).
% 1.55/1.40 thf(f238,plain,(
% 1.55/1.40 (($true => (sK3 @ sK8 @ (sK5 @ sK8) @ (sK7 @ sK10))) = $true) | ~spl0_3),
% 1.55/1.40 inference(superposition,[status(thm)],[f232,f120])).
% 1.55/1.40 thf(f232,plain,(
% 1.55/1.40 ( ! [X2 : a,X1 : a] : ((((sK2 @ X1 @ X2) => (sK3 @ X1 @ (sK5 @ X1) @ (sK7 @ X2))) = $true)) ) | ~spl0_3),
% 1.55/1.40 inference(forward_demodulation,[status(thm)],[f231,f50])).
% 1.55/1.40 thf(f231,plain,(
% 1.55/1.40 ( ! [X2 : a,X1 : a] : ((((sK4 @ X1 @ X2) => (sK3 @ X1 @ (sK5 @ X1) @ (sK7 @ X2))) = $true)) ) | ~spl0_3),
% 1.55/1.40 inference(beta_eta_normalization,[status(thm)],[f230])).
% 1.55/1.40 thf(f230,plain,(
% 1.55/1.40 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: ((sK4 @ X1 @ Y0) => (sK3 @ X1 @ (sK5 @ X1) @ (sK7 @ Y0)))) @ X2) = $true)) ) | ~spl0_3),
% 1.55/1.40 inference(pi_clausification,[status(thm)],[f227])).
% 1.55/1.40 thf(f227,plain,(
% 1.55/1.40 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: ((sK4 @ X1 @ Y0) => (sK3 @ X1 @ (sK5 @ X1) @ (sK7 @ Y0))))) = $true)) ) | ~spl0_3),
% 1.55/1.40 inference(beta_eta_normalization,[status(thm)],[f226])).
% 1.55/1.40 thf(f226,plain,(
% 1.55/1.40 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK4 @ Y0 @ Y1) => (sK3 @ Y0 @ (sK5 @ Y0) @ (sK7 @ Y1)))))) @ X1))) ) | ~spl0_3),
% 1.55/1.40 inference(pi_clausification,[status(thm)],[f203])).
% 1.55/1.40 thf(f576,plain,(
% 1.55/1.40 ( ! [X2 : b,X3 : b,X1 : b] : (((((sK3 @ sK8 @ X3 @ X2) & (sK3 @ sK8 @ X2 @ X1)) => (sK3 @ sK8 @ X3 @ X1)) = $true)) ) | ~spl0_3),
% 1.55/1.40 inference(beta_eta_normalization,[status(thm)],[f575])).
% 1.55/1.40 thf(f575,plain,(
% 1.55/1.40 ( ! [X2 : b,X3 : b,X1 : b] : ((((^[Y0 : b]: (((sK3 @ sK8 @ Y0 @ X2) & (sK3 @ sK8 @ X2 @ X1)) => (sK3 @ sK8 @ Y0 @ X1))) @ X3) = $true)) ) | ~spl0_3),
% 1.55/1.40 inference(pi_clausification,[status(thm)],[f570])).
% 1.55/1.40 thf(f570,plain,(
% 1.55/1.40 ( ! [X2 : b,X1 : b] : (((!! @ b @ (^[Y0 : b]: (((sK3 @ sK8 @ Y0 @ X2) & (sK3 @ sK8 @ X2 @ X1)) => (sK3 @ sK8 @ Y0 @ X1)))) = $true)) ) | ~spl0_3),
% 1.55/1.40 inference(beta_eta_normalization,[status(thm)],[f569])).
% 1.55/1.40 thf(f569,plain,(
% 1.55/1.40 ( ! [X2 : b,X1 : b] : ((((^[Y0 : b]: (!! @ b @ (^[Y1 : b]: (((sK3 @ sK8 @ Y1 @ Y0) & (sK3 @ sK8 @ Y0 @ X1)) => (sK3 @ sK8 @ Y1 @ X1))))) @ X2) = $true)) ) | ~spl0_3),
% 1.55/1.40 inference(pi_clausification,[status(thm)],[f556])).
% 1.55/1.40 thf(f556,plain,(
% 1.55/1.40 ( ! [X1 : b] : (((!! @ b @ (^[Y0 : b]: (!! @ b @ (^[Y1 : b]: (((sK3 @ sK8 @ Y1 @ Y0) & (sK3 @ sK8 @ Y0 @ X1)) => (sK3 @ sK8 @ Y1 @ X1)))))) = $true)) ) | ~spl0_3),
% 1.55/1.40 inference(beta_eta_normalization,[status(thm)],[f553])).
% 1.55/1.40 thf(f553,plain,(
% 1.55/1.40 ( ! [X1 : b] : (($true = ((^[Y0 : b]: (!! @ b @ (^[Y1 : b]: (!! @ b @ (^[Y2 : b]: (((sK3 @ sK8 @ Y2 @ Y1) & (sK3 @ sK8 @ Y1 @ Y0)) => (sK3 @ sK8 @ Y2 @ Y0))))))) @ X1))) ) | ~spl0_3),
% 1.55/1.40 inference(pi_clausification,[status(thm)],[f331])).
% 1.55/1.40 thf(f92,plain,(
% 1.55/1.40 spl0_3 | spl0_4 | ~spl0_2),
% 1.55/1.40 inference(avatar_split_clause,[status(thm)],[f85,f79,f90,f87])).
% 1.55/1.40 thf(f79,definition,(
% 1.55/1.40 spl0_2 <=> ($false = ((!! @ (a > b) @ (^[Y0 : a > b]: (!! @ (a > b) @ (^[Y1 : a > b]: (!! @ (a > b) @ (^[Y2 : a > b]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y3 @ Y4) => (sK3 @ Y3 @ (Y0 @ Y3) @ (Y2 @ Y4))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y3 @ Y4) => (sK3 @ Y3 @ (Y2 @ Y3) @ (Y1 @ Y4)))))))) => (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y3 @ Y4) => (sK3 @ Y3 @ (Y0 @ Y3) @ (Y1 @ Y4)))))))))))))) & (!! @ (a > b) @ (^[Y0 : a > b]: (!! @ (a > b) @ (^[Y1 : a > b]: ((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y3 @ Y2) => (sK3 @ Y3 @ (Y1 @ Y3) @ (Y0 @ Y2))))))) => (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y2 @ Y3) => (sK3 @ Y2 @ (Y0 @ Y2) @ (Y1 @ Y3))))))))))))))),
% 1.55/1.40 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.55/1.40 thf(f85,plain,(
% 1.55/1.40 ($false = (!! @ (a > b) @ (^[Y0 : a > b]: (!! @ (a > b) @ (^[Y1 : a > b]: ((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y3 @ Y2) => (sK3 @ Y3 @ (Y1 @ Y3) @ (Y0 @ Y2))))))) => (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y2 @ Y3) => (sK3 @ Y2 @ (Y0 @ Y2) @ (Y1 @ Y3))))))))))))) | ($false = (!! @ (a > b) @ (^[Y0 : a > b]: (!! @ (a > b) @ (^[Y1 : a > b]: (!! @ (a > b) @ (^[Y2 : a > b]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y3 @ Y4) => (sK3 @ Y3 @ (Y0 @ Y3) @ (Y2 @ Y4))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y3 @ Y4) => (sK3 @ Y3 @ (Y2 @ Y3) @ (Y1 @ Y4)))))))) => (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y3 @ Y4) => (sK3 @ Y3 @ (Y0 @ Y3) @ (Y1 @ Y4))))))))))))))) | ~spl0_2),
% 1.55/1.40 inference(binary_proxy_clausification,[status(thm)],[f80])).
% 1.55/1.40 thf(f80,plain,(
% 1.55/1.40 ($false = ((!! @ (a > b) @ (^[Y0 : a > b]: (!! @ (a > b) @ (^[Y1 : a > b]: (!! @ (a > b) @ (^[Y2 : a > b]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y3 @ Y4) => (sK3 @ Y3 @ (Y0 @ Y3) @ (Y2 @ Y4))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y3 @ Y4) => (sK3 @ Y3 @ (Y2 @ Y3) @ (Y1 @ Y4)))))))) => (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y3 @ Y4) => (sK3 @ Y3 @ (Y0 @ Y3) @ (Y1 @ Y4)))))))))))))) & (!! @ (a > b) @ (^[Y0 : a > b]: (!! @ (a > b) @ (^[Y1 : a > b]: ((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y3 @ Y2) => (sK3 @ Y3 @ (Y1 @ Y3) @ (Y0 @ Y2))))))) => (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y2 @ Y3) => (sK3 @ Y2 @ (Y0 @ Y2) @ (Y1 @ Y3)))))))))))))) | ~spl0_2),
% 1.55/1.40 inference(avatar_component_clause,[status(thm)],[f79])).
% 1.55/1.40 thf(f81,plain,(
% 1.55/1.40 spl0_1 | spl0_2),
% 1.55/1.40 inference(avatar_split_clause,[status(thm)],[f74,f79,f76])).
% 1.55/1.40 thf(f74,plain,(
% 1.55/1.40 ($false = ((^[Y0 : a > b]: ((^[Y1 : a > b]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y3 @ Y2) => (sK3 @ Y3 @ (Y0 @ Y3) @ (Y1 @ Y2)))))))))) = (^[Y0 : a > b]: ((^[Y1 : a > b]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y2 @ Y3) => (sK3 @ Y2 @ (Y0 @ Y2) @ (Y1 @ Y3)))))))))))) | ($false = ((!! @ (a > b) @ (^[Y0 : a > b]: (!! @ (a > b) @ (^[Y1 : a > b]: (!! @ (a > b) @ (^[Y2 : a > b]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y3 @ Y4) => (sK3 @ Y3 @ (Y0 @ Y3) @ (Y2 @ Y4))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y3 @ Y4) => (sK3 @ Y3 @ (Y2 @ Y3) @ (Y1 @ Y4)))))))) => (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y3 @ Y4) => (sK3 @ Y3 @ (Y0 @ Y3) @ (Y1 @ Y4)))))))))))))) & (!! @ (a > b) @ (^[Y0 : a > b]: (!! @ (a > b) @ (^[Y1 : a > b]: ((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y3 @ Y2) => (sK3 @ Y3 @ (Y1 @ Y3) @ (Y0 @ Y2))))))) => (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y2 @ Y3) => (sK3 @ Y2 @ (Y0 @ Y2) @ (Y1 @ Y3))))))))))))))),
% 1.55/1.40 inference(binary_proxy_clausification,[status(thm)],[f24])).
% 1.55/1.40 thf(f24,plain,(
% 1.55/1.40 ($false = (((!! @ (a > b) @ (^[Y0 : a > b]: (!! @ (a > b) @ (^[Y1 : a > b]: (!! @ (a > b) @ (^[Y2 : a > b]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y3 @ Y4) => (sK3 @ Y3 @ (Y0 @ Y3) @ (Y2 @ Y4))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y3 @ Y4) => (sK3 @ Y3 @ (Y2 @ Y3) @ (Y1 @ Y4)))))))) => (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK4 @ Y3 @ Y4) => (sK3 @ Y3 @ (Y0 @ Y3) @ (Y1 @ Y4)))))))))))))) & (!! @ (a > b) @ (^[Y0 : a > b]: (!! @ (a > b) @ (^[Y1 : a > b]: ((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y3 @ Y2) => (sK3 @ Y3 @ (Y1 @ Y3) @ (Y0 @ Y2))))))) => (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y2 @ Y3) => (sK3 @ Y2 @ (Y0 @ Y2) @ (Y1 @ Y3))))))))))))) & ((^[Y0 : a > b]: ((^[Y1 : a > b]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y3 @ Y2) => (sK3 @ Y3 @ (Y0 @ Y3) @ (Y1 @ Y2)))))))))) = (^[Y0 : a > b]: ((^[Y1 : a > b]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK4 @ Y2 @ Y3) => (sK3 @ Y2 @ (Y0 @ Y2) @ (Y1 @ Y3)))))))))))))),
% 1.55/1.40 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.55/1.40 % SZS output end Proof for DTF2THF_14528
% 1.55/1.40 % (14651)------------------------------
% 1.55/1.40 % (14651)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.40 % (14651)Termination reason: Refutation
% 1.55/1.40
% 1.55/1.40 % (14651)Memory used [KB]: 6780
% 1.55/1.40 % (14651)Time elapsed: 0.124 s
% 1.55/1.40 % (14651)Instructions burned: 317 (million)
% 1.55/1.40 % (14651)------------------------------
% 1.55/1.40 % (14651)------------------------------
% 1.55/1.40 % (14639)Success in time 0.166 s
%------------------------------------------------------------------------------