TSTP Solution File: SEV063^5 by Vampire---4.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEV063^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 16:01:40 EDT 2024
% Result : Theorem 0.14s 0.39s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 5
% Syntax : Number of formulae : 112 ( 51 unt; 0 typ; 0 def)
% Number of atoms : 924 ( 105 equ; 0 cnn)
% Maximal formula atoms : 3 ( 8 avg)
% Number of connectives : 2942 ( 68 ~; 58 |; 192 &;1942 @)
% ( 4 <=>; 259 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 248 ( 248 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 22 usr; 22 con; 0-2 aty)
% ( 419 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 536 ( 441 ^ 95 !; 0 ?; 536 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_16,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
sK2: a ).
thf(func_def_18,type,
sK3: a > a > $o ).
thf(func_def_19,type,
sK4: a ).
thf(func_def_20,type,
sK5: a ).
thf(func_def_21,type,
sK6: a ).
thf(func_def_22,type,
sK7: a > a > $o ).
thf(func_def_23,type,
sK8: a ).
thf(func_def_24,type,
sK9: a ).
thf(func_def_25,type,
sK10: a ).
thf(func_def_26,type,
sK11: a ).
thf(func_def_27,type,
sK12: a ).
thf(func_def_28,type,
sK13: a ).
thf(func_def_29,type,
sK14: a ).
thf(func_def_30,type,
sK15: a ).
thf(func_def_31,type,
sK16: a ).
thf(func_def_32,type,
sK17: a ).
thf(func_def_33,type,
sK18: a ).
thf(f548,plain,
$false,
inference(avatar_sat_refutation,[],[f108,f266,f458,f498,f524]) ).
thf(f524,plain,
~ spl0_7,
inference(avatar_contradiction_clause,[],[f523]) ).
thf(f523,plain,
( $false
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f519]) ).
thf(f519,plain,
( ( $true = $false )
| ~ spl0_7 ),
inference(superposition,[],[f82,f512]) ).
thf(f512,plain,
( ( $false
= ( ( ( sK7 @ sK18 @ sK16 )
& ( sK7 @ sK17 @ sK18 ) )
=> ( sK7 @ sK17 @ sK16 ) ) )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f511]) ).
thf(f511,plain,
( ( ( ^ [Y0: a] :
( ( ( sK7 @ Y0 @ sK16 )
& ( sK7 @ sK17 @ Y0 ) )
=> ( sK7 @ sK17 @ sK16 ) )
@ sK18 )
= $false )
| ~ spl0_7 ),
inference(sigma_clausification,[],[f510]) ).
thf(f510,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK7 @ Y0 @ sK16 )
& ( sK7 @ sK17 @ Y0 ) )
=> ( sK7 @ sK17 @ sK16 ) ) )
= $false )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f509]) ).
thf(f509,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK7 @ Y1 @ sK16 )
& ( sK7 @ Y0 @ Y1 ) )
=> ( sK7 @ Y0 @ sK16 ) ) )
@ sK17 )
= $false )
| ~ spl0_7 ),
inference(sigma_clausification,[],[f506]) ).
thf(f506,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK7 @ Y1 @ sK16 )
& ( sK7 @ Y0 @ Y1 ) )
=> ( sK7 @ Y0 @ sK16 ) ) ) )
= $false )
| ~ spl0_7 ),
inference(beta_eta_normalization,[],[f501]) ).
thf(f501,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK7 @ Y2 @ Y0 )
& ( sK7 @ Y1 @ Y2 ) )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
@ sK16 )
= $false )
| ~ spl0_7 ),
inference(sigma_clausification,[],[f457]) ).
thf(f457,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK7 @ Y2 @ Y0 )
& ( sK7 @ Y1 @ Y2 ) )
=> ( sK7 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f456]) ).
thf(f456,plain,
( spl0_7
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK7 @ Y2 @ Y0 )
& ( sK7 @ Y1 @ Y2 ) )
=> ( sK7 @ Y1 @ Y0 ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
thf(f82,plain,
! [X2: a,X3: a,X1: a] :
( $true
= ( ( ( sK7 @ X1 @ X2 )
& ( sK7 @ X3 @ X1 ) )
=> ( sK7 @ X3 @ X2 ) ) ),
inference(beta_eta_normalization,[],[f81]) ).
thf(f81,plain,
! [X2: a,X3: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK7 @ X1 @ X2 )
& ( sK7 @ Y0 @ X1 ) )
=> ( sK7 @ Y0 @ X2 ) )
@ X3 )
= $true ),
inference(pi_clausification,[],[f77]) ).
thf(f77,plain,
! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK7 @ X1 @ X2 )
& ( sK7 @ Y0 @ X1 ) )
=> ( sK7 @ Y0 @ X2 ) ) ) ),
inference(beta_eta_normalization,[],[f76]) ).
thf(f76,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK7 @ X1 @ Y0 )
& ( sK7 @ Y1 @ X1 ) )
=> ( sK7 @ Y1 @ Y0 ) ) )
@ X2 ) ),
inference(pi_clausification,[],[f73]) ).
thf(f73,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK7 @ X1 @ Y0 )
& ( sK7 @ Y1 @ X1 ) )
=> ( sK7 @ Y1 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[],[f72]) ).
thf(f72,plain,
! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK7 @ Y0 @ Y1 )
& ( sK7 @ Y2 @ Y0 ) )
=> ( sK7 @ Y2 @ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[],[f44]) ).
thf(f44,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK7 @ Y0 @ Y1 )
& ( sK7 @ Y2 @ Y0 ) )
=> ( sK7 @ Y2 @ Y1 ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f34]) ).
thf(f34,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK7 @ Y0 @ Y1 )
& ( sK7 @ Y2 @ Y0 ) )
=> ( sK7 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK7 @ Y0 @ Y1 ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f29]) ).
thf(f29,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK7 @ Y0 @ Y1 )
& ( sK7 @ Y2 @ Y0 ) )
=> ( sK7 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK7 @ Y0 @ Y1 ) ) ) ) )
=> ( sK7 @ sK4 @ sK2 ) )
= $false ),
inference(beta_eta_normalization,[],[f28]) ).
thf(f28,plain,
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK2 ) )
@ sK7 )
= $false ),
inference(sigma_clausification,[],[f18]) ).
thf(f18,plain,
( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK2 ) ) ) ),
inference(binary_proxy_clausification,[],[f17]) ).
thf(f17,plain,
( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK5 @ sK2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK2 ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f16]) ).
thf(f16,plain,
( ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 @ sK2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK4 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK4 @ sK2 ) ) ) )
@ sK5 )
= $false ),
inference(sigma_clausification,[],[f15]) ).
thf(f15,plain,
( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 @ sK2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK4 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK4 @ sK2 ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f14]) ).
thf(f14,plain,
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ sK2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ sK2 ) ) ) ) )
@ sK4 )
= $false ),
inference(sigma_clausification,[],[f13]) ).
thf(f13,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ sK2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ sK2 ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f12]) ).
thf(f12,plain,
( ( ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ sK2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ sK2 ) ) ) ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[],[f11]) ).
thf(f11,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ sK2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ sK2 ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f10]) ).
thf(f10,plain,
( $false
= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y0 ) ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_clausification,[],[f7]) ).
thf(f7,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y0 ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
~ ! [X0: a,X1: a,X2: a > a > $o,X3: a] :
( ( ! [X4: a > a > $o] :
( ( ! [X5: a,X6: a] :
( ( X2 @ X6 @ X5 )
=> ( X4 @ X6 @ X5 ) )
& ! [X7: a,X8: a,X9: a] :
( ( ( X4 @ X7 @ X8 )
& ( X4 @ X9 @ X7 ) )
=> ( X4 @ X9 @ X8 ) ) )
=> ( X4 @ X1 @ X0 ) )
& ! [X10: a > a > $o] :
( ( ! [X11: a,X12: a] :
( ( X2 @ X11 @ X12 )
=> ( X10 @ X11 @ X12 ) )
& ! [X13: a,X14: a,X15: a] :
( ( ( X10 @ X14 @ X13 )
& ( X10 @ X13 @ X15 ) )
=> ( X10 @ X14 @ X15 ) ) )
=> ( X10 @ X0 @ X3 ) ) )
=> ! [X16: a > a > $o] :
( ( ! [X17: a,X18: a] :
( ( X2 @ X18 @ X17 )
=> ( X16 @ X18 @ X17 ) )
& ! [X19: a,X20: a,X21: a] :
( ( ( X16 @ X19 @ X21 )
& ( X16 @ X21 @ X20 ) )
=> ( X16 @ X19 @ X20 ) ) )
=> ( X16 @ X1 @ X3 ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X2: a,X1: a,X0: a > a > $o,X3: a] :
( ( ! [X4: a > a > $o] :
( ( ! [X6: a,X5: a] :
( ( X0 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) )
& ! [X6: a,X7: a,X5: a] :
( ( ( X4 @ X6 @ X7 )
& ( X4 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X1 @ X2 ) )
& ! [X4: a > a > $o] :
( ( ! [X5: a,X6: a] :
( ( X0 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) )
& ! [X6: a,X5: a,X7: a] :
( ( ( X4 @ X5 @ X6 )
& ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
=> ! [X4: a > a > $o] :
( ( ! [X6: a,X5: a] :
( ( X0 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) )
& ! [X5: a,X7: a,X6: a] :
( ( ( X4 @ X5 @ X6 )
& ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X1 @ X3 ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
! [X2: a,X1: a,X0: a > a > $o,X3: a] :
( ( ! [X4: a > a > $o] :
( ( ! [X6: a,X5: a] :
( ( X0 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) )
& ! [X6: a,X7: a,X5: a] :
( ( ( X4 @ X6 @ X7 )
& ( X4 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X1 @ X2 ) )
& ! [X4: a > a > $o] :
( ( ! [X5: a,X6: a] :
( ( X0 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) )
& ! [X6: a,X5: a,X7: a] :
( ( ( X4 @ X5 @ X6 )
& ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
=> ! [X4: a > a > $o] :
( ( ! [X6: a,X5: a] :
( ( X0 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) )
& ! [X5: a,X7: a,X6: a] :
( ( ( X4 @ X5 @ X6 )
& ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM136_pme) ).
thf(f498,plain,
~ spl0_6,
inference(avatar_contradiction_clause,[],[f497]) ).
thf(f497,plain,
( $false
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f496]) ).
thf(f496,plain,
( ( $true = $false )
| ~ spl0_6 ),
inference(forward_demodulation,[],[f480,f485]) ).
thf(f485,plain,
( ( ( sK3 @ sK15 @ sK13 )
= $false )
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f484]) ).
thf(f484,plain,
( ( ( sK3 @ sK15 @ sK13 )
= $false )
| ( $true = $false )
| ~ spl0_6 ),
inference(boolean_simplification,[],[f481]) ).
thf(f481,plain,
( ( ( ( sK3 @ sK15 @ sK13 )
=> $true )
= $false )
| ( ( sK3 @ sK15 @ sK13 )
= $false )
| ~ spl0_6 ),
inference(superposition,[],[f478,f57]) ).
thf(f57,plain,
! [X2: a,X1: a] :
( ( $true
= ( sK7 @ X1 @ X2 ) )
| ( ( sK3 @ X1 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[],[f53]) ).
thf(f53,plain,
! [X2: a,X1: a] :
( $true
= ( ( sK3 @ X1 @ X2 )
=> ( sK7 @ X1 @ X2 ) ) ),
inference(beta_eta_normalization,[],[f52]) ).
thf(f52,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK3 @ X1 @ Y0 )
=> ( sK7 @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_clausification,[],[f49]) ).
thf(f49,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ X1 @ Y0 )
=> ( sK7 @ X1 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[],[f48]) ).
thf(f48,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK7 @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_clausification,[],[f46]) ).
thf(f46,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK7 @ Y0 @ Y1 ) ) ) ) ),
inference(boolean_simplification,[],[f45]) ).
thf(f45,plain,
( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK7 @ Y0 @ Y1 ) ) ) ) ) ),
inference(backward_demodulation,[],[f34,f44]) ).
thf(f478,plain,
( ( ( ( sK3 @ sK15 @ sK13 )
=> ( sK7 @ sK15 @ sK13 ) )
= $false )
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f477]) ).
thf(f477,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK3 @ Y0 @ sK13 )
=> ( sK7 @ Y0 @ sK13 ) )
@ sK15 ) )
| ~ spl0_6 ),
inference(sigma_clausification,[],[f470]) ).
thf(f470,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ sK13 )
=> ( sK7 @ Y0 @ sK13 ) ) )
= $false )
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f463]) ).
thf(f463,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK7 @ Y1 @ Y0 ) ) )
@ sK13 )
= $false )
| ~ spl0_6 ),
inference(sigma_clausification,[],[f454]) ).
thf(f454,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f453]) ).
thf(f453,plain,
( spl0_6
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
thf(f480,plain,
( ( $true
= ( sK3 @ sK15 @ sK13 ) )
| ~ spl0_6 ),
inference(binary_proxy_clausification,[],[f478]) ).
thf(f458,plain,
( spl0_6
| spl0_7
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f447,f106,f456,f453]) ).
thf(f106,plain,
( spl0_2
<=> ( ( sK7 @ sK4 @ sK6 )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f447,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK7 @ Y1 @ Y0 ) ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK7 @ Y2 @ Y0 )
& ( sK7 @ Y1 @ Y2 ) )
=> ( sK7 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f434]) ).
thf(f434,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK7 @ Y2 @ Y0 )
& ( sK7 @ Y1 @ Y2 ) )
=> ( sK7 @ Y1 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK7 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(not_proxy_clausification,[],[f154]) ).
thf(f154,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK7 @ Y2 @ Y0 )
& ( sK7 @ Y1 @ Y2 ) )
=> ( sK7 @ Y1 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK7 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f150]) ).
thf(f150,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK7 @ Y2 @ Y0 )
& ( sK7 @ Y1 @ Y2 ) )
=> ( sK7 @ Y1 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK7 @ Y1 @ Y0 ) ) ) ) )
=> $false ) )
| ~ spl0_2 ),
inference(superposition,[],[f42,f133]) ).
thf(f133,plain,
( ( $false
= ( sK7 @ sK6 @ sK2 ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f130]) ).
thf(f130,plain,
( ( ( ( sK7 @ sK6 @ sK2 )
& $true )
= $false )
| ~ spl0_2 ),
inference(superposition,[],[f92,f107]) ).
thf(f107,plain,
( ( ( sK7 @ sK4 @ sK6 )
= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f106]) ).
thf(f92,plain,
! [X0: a] :
( ( ( sK7 @ X0 @ sK2 )
& ( sK7 @ sK4 @ X0 ) )
= $false ),
inference(not_proxy_clausification,[],[f89]) ).
thf(f89,plain,
! [X0: a] :
( $true
= ( ~ ( ( sK7 @ X0 @ sK2 )
& ( sK7 @ sK4 @ X0 ) ) ) ),
inference(boolean_simplification,[],[f84]) ).
thf(f84,plain,
! [X0: a] :
( $true
= ( ( ( sK7 @ X0 @ sK2 )
& ( sK7 @ sK4 @ X0 ) )
=> $false ) ),
inference(superposition,[],[f82,f36]) ).
thf(f36,plain,
( $false
= ( sK7 @ sK4 @ sK2 ) ),
inference(boolean_simplification,[],[f35]) ).
thf(f35,plain,
( ( $true
=> ( sK7 @ sK4 @ sK2 ) )
= $false ),
inference(backward_demodulation,[],[f29,f34]) ).
thf(f42,plain,
! [X1: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y2 @ Y0 )
& ( X1 @ Y1 @ Y2 ) )
=> ( X1 @ Y1 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( X1 @ Y1 @ Y0 ) ) ) ) )
=> ( X1 @ sK6 @ sK2 ) )
= $true ),
inference(beta_eta_normalization,[],[f41]) ).
thf(f41,plain,
! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK6 @ sK2 ) )
@ X1 ) ),
inference(pi_clausification,[],[f40]) ).
thf(f40,plain,
( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK6 @ sK2 ) ) ) ),
inference(boolean_simplification,[],[f39]) ).
thf(f39,plain,
( $true
= ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK6 @ sK2 ) ) )
& $true ) ),
inference(backward_demodulation,[],[f30,f37]) ).
thf(f37,plain,
( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK6 ) ) ) ),
inference(binary_proxy_clausification,[],[f30]) ).
thf(f30,plain,
( $true
= ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK6 @ sK2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK6 ) ) ) ) ),
inference(not_proxy_clausification,[],[f27]) ).
thf(f27,plain,
( ( ~ ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK6 @ sK2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK6 ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f26]) ).
thf(f26,plain,
( ( ^ [Y0: a] :
~ ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 @ sK2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK4 @ Y0 ) ) ) )
@ sK6 )
= $false ),
inference(sigma_clausification,[],[f22]) ).
thf(f22,plain,
( ( !! @ a
@ ^ [Y0: a] :
~ ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 @ sK2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK4 @ Y0 ) ) ) ) )
= $false ),
inference(boolean_simplification,[],[f21]) ).
thf(f21,plain,
( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 @ sK2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK4 @ Y0 ) ) ) )
=> $false ) )
= $false ),
inference(backward_demodulation,[],[f15,f18]) ).
thf(f266,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f265]) ).
thf(f265,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f264]) ).
thf(f264,plain,
( ( $true = $false )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f263]) ).
thf(f263,plain,
( ( $true = ~ $true )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f256,f200]) ).
thf(f200,plain,
( ( $true
= ( sK7 @ sK8 @ sK11 ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f194]) ).
thf(f194,plain,
( ( $true
= ( ( sK7 @ sK8 @ sK11 )
& ( sK7 @ sK11 @ sK9 ) ) )
| ~ spl0_1 ),
inference(not_proxy_clausification,[],[f190]) ).
thf(f190,plain,
( ( ( ~ ( ( sK7 @ sK8 @ sK11 )
& ( sK7 @ sK11 @ sK9 ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f189]) ).
thf(f189,plain,
( ( ( ^ [Y0: a] :
~ ( ( sK7 @ sK8 @ Y0 )
& ( sK7 @ Y0 @ sK9 ) )
@ sK11 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f175]) ).
thf(f175,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
~ ( ( sK7 @ sK8 @ Y0 )
& ( sK7 @ Y0 @ sK9 ) ) )
= $false )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f174]) ).
thf(f174,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK7 @ sK8 @ Y0 )
& ( sK7 @ Y0 @ sK9 ) )
=> $false ) )
= $false )
| ~ spl0_1 ),
inference(backward_demodulation,[],[f160,f171]) ).
thf(f171,plain,
( ( ( sK7 @ sK8 @ sK9 )
= $false )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f165]) ).
thf(f165,plain,
( ( ( ( ( sK7 @ sK8 @ sK10 )
& ( sK7 @ sK10 @ sK9 ) )
=> ( sK7 @ sK8 @ sK9 ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f164]) ).
thf(f164,plain,
( ( ( ^ [Y0: a] :
( ( ( sK7 @ sK8 @ Y0 )
& ( sK7 @ Y0 @ sK9 ) )
=> ( sK7 @ sK8 @ sK9 ) )
@ sK10 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f160]) ).
thf(f160,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK7 @ sK8 @ Y0 )
& ( sK7 @ Y0 @ sK9 ) )
=> ( sK7 @ sK8 @ sK9 ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f159]) ).
thf(f159,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK7 @ sK8 @ Y1 )
& ( sK7 @ Y1 @ Y0 ) )
=> ( sK7 @ sK8 @ Y0 ) ) )
@ sK9 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f140]) ).
thf(f140,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK7 @ sK8 @ Y1 )
& ( sK7 @ Y1 @ Y0 ) )
=> ( sK7 @ sK8 @ Y0 ) ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f137]) ).
thf(f137,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK7 @ Y0 @ Y2 )
& ( sK7 @ Y2 @ Y1 ) )
=> ( sK7 @ Y0 @ Y1 ) ) ) )
@ sK8 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f104]) ).
thf(f104,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK7 @ Y0 @ Y2 )
& ( sK7 @ Y2 @ Y1 ) )
=> ( sK7 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f103]) ).
thf(f103,plain,
( spl0_1
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK7 @ Y0 @ Y2 )
& ( sK7 @ Y2 @ Y1 ) )
=> ( sK7 @ Y0 @ Y1 ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f256,plain,
( ( $true
= ( ~ ( sK7 @ sK8 @ sK11 ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f252]) ).
thf(f252,plain,
( ( $true
= ( ( sK7 @ sK8 @ sK11 )
=> $false ) )
| ~ spl0_1 ),
inference(superposition,[],[f208,f171]) ).
thf(f208,plain,
( ! [X0: a] :
( $true
= ( ( sK7 @ X0 @ sK11 )
=> ( sK7 @ X0 @ sK9 ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f203]) ).
thf(f203,plain,
( ! [X0: a] :
( $true
= ( ( $true
& ( sK7 @ X0 @ sK11 ) )
=> ( sK7 @ X0 @ sK9 ) ) )
| ~ spl0_1 ),
inference(superposition,[],[f82,f202]) ).
thf(f202,plain,
( ( $true
= ( sK7 @ sK11 @ sK9 ) )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f201]) ).
thf(f201,plain,
( ( $true
= ( $true
& ( sK7 @ sK11 @ sK9 ) ) )
| ~ spl0_1 ),
inference(backward_demodulation,[],[f194,f200]) ).
thf(f108,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f101,f106,f103]) ).
thf(f101,plain,
( ( ( sK7 @ sK4 @ sK6 )
= $true )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK7 @ Y0 @ Y2 )
& ( sK7 @ Y2 @ Y1 ) )
=> ( sK7 @ Y0 @ Y1 ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f56]) ).
thf(f56,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK7 @ Y0 @ Y2 )
& ( sK7 @ Y2 @ Y1 ) )
=> ( sK7 @ Y0 @ Y1 ) ) ) ) )
=> ( sK7 @ sK4 @ sK6 ) ) ),
inference(boolean_simplification,[],[f55]) ).
thf(f55,plain,
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK7 @ Y0 @ Y2 )
& ( sK7 @ Y2 @ Y1 ) )
=> ( sK7 @ Y0 @ Y1 ) ) ) ) )
& $true )
=> ( sK7 @ sK4 @ sK6 ) ) ),
inference(superposition,[],[f51,f46]) ).
thf(f51,plain,
! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y0 @ Y2 )
& ( X1 @ Y2 @ Y1 ) )
=> ( X1 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( X1 @ Y0 @ Y1 ) ) ) ) )
=> ( X1 @ sK4 @ sK6 ) ) ),
inference(beta_eta_normalization,[],[f50]) ).
thf(f50,plain,
! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 @ sK6 ) )
@ X1 ) ),
inference(pi_clausification,[],[f37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09 % Problem : SEV063^5 : TPTP v8.2.0. Released v4.0.0.
% 0.04/0.09 % Command : run_vampire %s %d THM
% 0.07/0.28 % Computer : n025.cluster.edu
% 0.07/0.28 % Model : x86_64 x86_64
% 0.07/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.28 % Memory : 8042.1875MB
% 0.07/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.28 % CPULimit : 300
% 0.07/0.28 % WCLimit : 300
% 0.07/0.28 % DateTime : Fri Jun 21 19:31:09 EDT 2024
% 0.07/0.28 % CPUTime :
% 0.07/0.30 This is a TH0_THM_NEQ_NAR problem
% 0.07/0.30 Running higher-order theorem proving
% 0.07/0.30 Running /export/starexec/sandbox2/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox2/benchmark/theBenchmark.p -m 16384 -t 300
% 0.14/0.31 % (31971)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.31 % (31972)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.14/0.31 % (31972)Instruction limit reached!
% 0.14/0.31 % (31972)------------------------------
% 0.14/0.31 % (31972)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.14/0.31 % (31972)Termination reason: Unknown
% 0.14/0.31 % (31972)Termination phase: Saturation
% 0.14/0.31
% 0.14/0.31 % (31972)Memory used [KB]: 5500
% 0.14/0.31 % (31972)Time elapsed: 0.004 s
% 0.14/0.31 % (31972)Instructions burned: 6 (million)
% 0.14/0.31 % (31972)------------------------------
% 0.14/0.31 % (31972)------------------------------
% 0.14/0.31 % (31974)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.31 % (31974)Instruction limit reached!
% 0.14/0.31 % (31974)------------------------------
% 0.14/0.31 % (31974)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.14/0.31 % (31974)Termination reason: Unknown
% 0.14/0.31 % (31974)Termination phase: Property scanning
% 0.14/0.31
% 0.14/0.31 % (31974)Memory used [KB]: 1023
% 0.14/0.31 % (31974)Time elapsed: 0.002 s
% 0.14/0.31 % (31974)Instructions burned: 2 (million)
% 0.14/0.31 % (31974)------------------------------
% 0.14/0.31 % (31974)------------------------------
% 0.14/0.31 % (31975)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.32 % (31976)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.14/0.32 % (31977)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.32 % (31973)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.14/0.32 % (31975)Instruction limit reached!
% 0.14/0.32 % (31975)------------------------------
% 0.14/0.32 % (31975)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.14/0.32 % (31975)Termination reason: Unknown
% 0.14/0.32 % (31975)Termination phase: Property scanning
% 0.14/0.32
% 0.14/0.32 % (31975)Memory used [KB]: 1023
% 0.14/0.32 % (31975)Time elapsed: 0.003 s
% 0.14/0.32 % (31975)Instructions burned: 3 (million)
% 0.14/0.32 % (31975)------------------------------
% 0.14/0.32 % (31975)------------------------------
% 0.14/0.32 % (31978)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.14/0.32 % (31979)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.14/0.32 % (31978)Instruction limit reached!
% 0.14/0.32 % (31978)------------------------------
% 0.14/0.32 % (31978)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.14/0.32 % (31978)Termination reason: Unknown
% 0.14/0.32 % (31978)Termination phase: Saturation
% 0.14/0.32
% 0.14/0.32 % (31978)Memory used [KB]: 5500
% 0.14/0.32 % (31978)Time elapsed: 0.003 s
% 0.14/0.32 % (31978)Instructions burned: 5 (million)
% 0.14/0.32 % (31978)------------------------------
% 0.14/0.32 % (31978)------------------------------
% 0.14/0.32 % (31977)Instruction limit reached!
% 0.14/0.32 % (31977)------------------------------
% 0.14/0.32 % (31977)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.14/0.32 % (31977)Termination reason: Unknown
% 0.14/0.33 % (31977)Termination phase: Saturation
% 0.14/0.33
% 0.14/0.33 % (31977)Memory used [KB]: 5628
% 0.14/0.33 % (31977)Time elapsed: 0.011 s
% 0.14/0.33 % (31977)Instructions burned: 19 (million)
% 0.14/0.33 % (31977)------------------------------
% 0.14/0.33 % (31977)------------------------------
% 0.14/0.33 % (31973)Instruction limit reached!
% 0.14/0.33 % (31973)------------------------------
% 0.14/0.33 % (31973)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.14/0.33 % (31973)Termination reason: Unknown
% 0.14/0.33 % (31973)Termination phase: Saturation
% 0.14/0.33
% 0.14/0.33 % (31973)Memory used [KB]: 5628
% 0.14/0.33 % (31973)Time elapsed: 0.017 s
% 0.14/0.33 % (31973)Instructions burned: 27 (million)
% 0.14/0.33 % (31973)------------------------------
% 0.14/0.33 % (31973)------------------------------
% 0.14/0.33 % (31981)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.14/0.33 % (31980)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.14/0.33 % (31981)Instruction limit reached!
% 0.14/0.33 % (31981)------------------------------
% 0.14/0.33 % (31981)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.14/0.33 % (31981)Termination reason: Unknown
% 0.14/0.33 % (31981)Termination phase: Saturation
% 0.14/0.33
% 0.14/0.33 % (31981)Memory used [KB]: 5500
% 0.14/0.33 % (31981)Time elapsed: 0.003 s
% 0.14/0.33 % (31981)Instructions burned: 3 (million)
% 0.14/0.33 % (31981)------------------------------
% 0.14/0.33 % (31981)------------------------------
% 0.14/0.34 % (31979)Instruction limit reached!
% 0.14/0.34 % (31979)------------------------------
% 0.14/0.34 % (31979)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.14/0.34 % (31979)Termination reason: Unknown
% 0.14/0.34 % (31979)Termination phase: Saturation
% 0.14/0.34
% 0.14/0.34 % (31979)Memory used [KB]: 5884
% 0.14/0.34 % (31979)Time elapsed: 0.014 s
% 0.14/0.34 % (31979)Instructions burned: 39 (million)
% 0.14/0.34 % (31979)------------------------------
% 0.14/0.34 % (31979)------------------------------
% 0.14/0.34 % (31980)Instruction limit reached!
% 0.14/0.34 % (31980)------------------------------
% 0.14/0.34 % (31980)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.14/0.34 % (31980)Termination reason: Unknown
% 0.14/0.34 % (31980)Termination phase: Saturation
% 0.14/0.34
% 0.14/0.34 % (31980)Memory used [KB]: 5756
% 0.14/0.34 % (31980)Time elapsed: 0.009 s
% 0.14/0.34 % (31980)Instructions burned: 15 (million)
% 0.14/0.34 % (31980)------------------------------
% 0.14/0.34 % (31980)------------------------------
% 0.14/0.34 % (31982)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.14/0.34 % (31983)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.14/0.35 % (31983)Instruction limit reached!
% 0.14/0.35 % (31983)------------------------------
% 0.14/0.35 % (31983)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.14/0.35 % (31983)Termination reason: Unknown
% 0.14/0.35 % (31983)Termination phase: Saturation
% 0.14/0.35
% 0.14/0.35 % (31983)Memory used [KB]: 1023
% 0.14/0.35 % (31983)Time elapsed: 0.005 s
% 0.14/0.35 % (31983)Instructions burned: 7 (million)
% 0.14/0.35 % (31983)------------------------------
% 0.14/0.35 % (31983)------------------------------
% 0.14/0.35 % (31984)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.14/0.35 % (31986)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.14/0.35 % (31984)Instruction limit reached!
% 0.14/0.35 % (31984)------------------------------
% 0.14/0.35 % (31984)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.14/0.35 % (31984)Termination reason: Unknown
% 0.14/0.35 % (31984)Termination phase: Saturation
% 0.14/0.35 % (31985)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.14/0.35
% 0.14/0.35 % (31984)Memory used [KB]: 5628
% 0.14/0.35 % (31984)Time elapsed: 0.009 s
% 0.14/0.35 % (31984)Instructions burned: 18 (million)
% 0.14/0.35 % (31984)------------------------------
% 0.14/0.35 % (31984)------------------------------
% 0.14/0.36 % (31986)Instruction limit reached!
% 0.14/0.36 % (31986)------------------------------
% 0.14/0.36 % (31986)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.14/0.36 % (31986)Termination reason: Unknown
% 0.14/0.36 % (31986)Termination phase: Equality resolution with deletion
% 0.14/0.36
% 0.14/0.36 % (31986)Memory used [KB]: 1023
% 0.14/0.36 % (31986)Time elapsed: 0.004 s
% 0.14/0.36 % (31986)Instructions burned: 3 (million)
% 0.14/0.36 % (31986)------------------------------
% 0.14/0.36 % (31986)------------------------------
% 0.14/0.36 % (31985)Instruction limit reached!
% 0.14/0.36 % (31985)------------------------------
% 0.14/0.36 % (31985)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.14/0.36 % (31985)Termination reason: Unknown
% 0.14/0.36 % (31985)Termination phase: Twee Goal Transformation
% 0.14/0.36
% 0.14/0.36 % (31985)Memory used [KB]: 1023
% 0.14/0.36 % (31985)Time elapsed: 0.004 s
% 0.14/0.36 % (31985)Instructions burned: 4 (million)
% 0.14/0.36 % (31985)------------------------------
% 0.14/0.36 % (31985)------------------------------
% 0.14/0.36 % (31987)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.14/0.36 % (31987)Instruction limit reached!
% 0.14/0.36 % (31987)------------------------------
% 0.14/0.36 % (31987)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.14/0.36 % (31987)Termination reason: Unknown
% 0.14/0.36 % (31987)Termination phase: Saturation
% 0.14/0.36
% 0.14/0.36 % (31987)Memory used [KB]: 5500
% 0.14/0.36 % (31987)Time elapsed: 0.005 s
% 0.14/0.36 % (31987)Instructions burned: 7 (million)
% 0.14/0.36 % (31987)------------------------------
% 0.14/0.36 % (31987)------------------------------
% 0.14/0.37 % (31988)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.14/0.37 % (31988)Instruction limit reached!
% 0.14/0.37 % (31988)------------------------------
% 0.14/0.37 % (31988)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.14/0.37 % (31988)Termination reason: Unknown
% 0.14/0.37 % (31988)Termination phase: Saturation
% 0.14/0.37
% 0.14/0.37 % (31988)Memory used [KB]: 5500
% 0.14/0.37 % (31988)Time elapsed: 0.003 s
% 0.14/0.37 % (31988)Instructions burned: 3 (million)
% 0.14/0.37 % (31988)------------------------------
% 0.14/0.37 % (31988)------------------------------
% 0.14/0.37 % (31989)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.14/0.37 % (31990)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.37 % (31971)Instruction limit reached!
% 0.14/0.37 % (31971)------------------------------
% 0.14/0.37 % (31971)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.14/0.37 % (31971)Termination reason: Unknown
% 0.14/0.37 % (31971)Termination phase: Saturation
% 0.14/0.37
% 0.14/0.37 % (31971)Memory used [KB]: 6396
% 0.14/0.37 % (31971)Time elapsed: 0.062 s
% 0.14/0.37 % (31971)Instructions burned: 184 (million)
% 0.14/0.37 % (31971)------------------------------
% 0.14/0.37 % (31971)------------------------------
% 0.14/0.37 % (31989)Instruction limit reached!
% 0.14/0.37 % (31989)------------------------------
% 0.14/0.37 % (31989)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.14/0.37 % (31989)Termination reason: Unknown
% 0.14/0.37 % (31989)Termination phase: Saturation
% 0.14/0.37
% 0.14/0.37 % (31989)Memory used [KB]: 5500
% 0.14/0.37 % (31989)Time elapsed: 0.004 s
% 0.14/0.37 % (31989)Instructions burned: 4 (million)
% 0.14/0.37 % (31989)------------------------------
% 0.14/0.37 % (31989)------------------------------
% 0.14/0.37 % (31991)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.14/0.38 % (31990)Instruction limit reached!
% 0.14/0.38 % (31990)------------------------------
% 0.14/0.38 % (31990)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.14/0.38 % (31990)Termination reason: Unknown
% 0.14/0.38 % (31990)Termination phase: Saturation
% 0.14/0.38
% 0.14/0.38 % (31990)Memory used [KB]: 5628
% 0.14/0.38 % (31990)Time elapsed: 0.008 s
% 0.14/0.38 % (31990)Instructions burned: 18 (million)
% 0.14/0.38 % (31990)------------------------------
% 0.14/0.38 % (31990)------------------------------
% 0.14/0.38 % (31992)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.14/0.38 % (31992)Instruction limit reached!
% 0.14/0.38 % (31992)------------------------------
% 0.14/0.38 % (31992)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.14/0.38 % (31992)Termination reason: Unknown
% 0.14/0.38 % (31992)Termination phase: Saturation
% 0.14/0.38
% 0.14/0.38 % (31992)Memory used [KB]: 5500
% 0.14/0.38 % (31992)Time elapsed: 0.004 s
% 0.14/0.38 % (31992)Instructions burned: 8 (million)
% 0.14/0.38 % (31992)------------------------------
% 0.14/0.38 % (31992)------------------------------
% 0.14/0.38 % (31995)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.14/0.38 % (31993)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on theBenchmark for (2999ds/902Mi)
% 0.14/0.38 % (31994)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on theBenchmark for (2999ds/21Mi)
% 0.14/0.39 % (31995)Instruction limit reached!
% 0.14/0.39 % (31995)------------------------------
% 0.14/0.39 % (31995)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.14/0.39 % (31995)Termination reason: Unknown
% 0.14/0.39 % (31995)Termination phase: Saturation
% 0.14/0.39
% 0.14/0.39 % (31995)Memory used [KB]: 5500
% 0.14/0.39 % (31995)Time elapsed: 0.003 s
% 0.14/0.39 % (31995)Instructions burned: 5 (million)
% 0.14/0.39 % (31995)------------------------------
% 0.14/0.39 % (31995)------------------------------
% 0.14/0.39 % (31982)First to succeed.
% 0.14/0.39 % (31996)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.14/0.39 % (31982)Refutation found. Thanks to Tanya!
% 0.14/0.39 % SZS status Theorem for theBenchmark
% 0.14/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.39 % (31982)------------------------------
% 0.14/0.39 % (31982)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.14/0.39 % (31982)Termination reason: Refutation
% 0.14/0.39
% 0.14/0.39 % (31982)Memory used [KB]: 6012
% 0.14/0.39 % (31982)Time elapsed: 0.051 s
% 0.14/0.39 % (31982)Instructions burned: 90 (million)
% 0.14/0.39 % (31982)------------------------------
% 0.14/0.39 % (31982)------------------------------
% 0.14/0.39 % (31970)Success in time 0.081 s
%------------------------------------------------------------------------------