TSTP Solution File: SEV046^5 by Vampire---4.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEV046^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n023.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 16:01:36 EDT 2024
% Result : Theorem 0.17s 0.45s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 3
% Syntax : Number of formulae : 153 ( 40 unt; 0 typ; 0 def)
% Number of atoms : 1341 ( 168 equ; 0 cnn)
% Maximal formula atoms : 2 ( 8 avg)
% Number of connectives : 3881 ( 119 ~; 111 |; 147 &;2720 @)
% ( 2 <=>; 321 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 208 ( 208 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 14 usr; 9 con; 0-3 aty)
% ( 461 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 663 ( 491 ^ 172 !; 0 ?; 663 :)
% 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 > b ).
thf(func_def_23,type,
sK5: a > b ).
thf(func_def_24,type,
sK6: a ).
thf(func_def_25,type,
sK7: a ).
thf(func_def_26,type,
sK8: a > b ).
thf(func_def_27,type,
sK9: a > b ).
thf(func_def_28,type,
sK10: a > b ).
thf(func_def_29,type,
sK11: a ).
thf(func_def_30,type,
sK12: a ).
thf(f832,plain,
$false,
inference(avatar_sat_refutation,[],[f36,f287,f831]) ).
thf(f831,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f830]) ).
thf(f830,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f829]) ).
thf(f829,plain,
( ( $true = $false )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f828]) ).
thf(f828,plain,
( ( $true = ~ $true )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f818,f540]) ).
thf(f540,plain,
( ( $true
= ( sK3 @ sK11 @ ( sK9 @ sK12 ) @ ( sK8 @ sK12 ) ) )
| ~ spl0_1 ),
inference(superposition,[],[f423,f511]) ).
thf(f511,plain,
( ! [X2: b,X1: b] :
( ( sK3 @ sK11 @ X1 @ X2 )
= ( sK3 @ sK12 @ X1 @ X2 ) )
| ~ spl0_1 ),
inference(argument_congruence,[],[f474]) ).
thf(f474,plain,
( ! [X1: b] :
( ( sK3 @ sK11 @ X1 )
= ( sK3 @ sK12 @ X1 ) )
| ~ spl0_1 ),
inference(argument_congruence,[],[f467]) ).
thf(f467,plain,
( ( ( sK3 @ sK12 )
= ( sK3 @ sK11 ) )
| ~ spl0_1 ),
inference(equality_proxy_clausification,[],[f319]) ).
thf(f319,plain,
( ( $true
= ( ( sK3 @ sK11 )
= ( sK3 @ sK12 ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f317]) ).
thf(f317,plain,
( ( $true
= ( $true
=> ( ( sK3 @ sK11 )
= ( sK3 @ sK12 ) ) ) )
| ~ spl0_1 ),
inference(superposition,[],[f129,f307]) ).
thf(f307,plain,
( ( $true
= ( sK2 @ sK12 @ sK11 ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f305]) ).
thf(f305,plain,
( ( ( ( sK2 @ sK12 @ sK11 )
=> ( sK3 @ sK12 @ ( sK9 @ sK12 ) @ ( sK10 @ sK11 ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f304]) ).
thf(f304,plain,
( ( ( ^ [Y0: a] :
( ( sK2 @ Y0 @ sK11 )
=> ( sK3 @ Y0 @ ( sK9 @ Y0 ) @ ( sK10 @ sK11 ) ) )
@ sK12 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f303]) ).
thf(f303,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ sK11 )
=> ( sK3 @ Y0 @ ( sK9 @ Y0 ) @ ( sK10 @ sK11 ) ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f302]) ).
thf(f302,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK3 @ Y1 @ ( sK9 @ Y1 ) @ ( sK10 @ Y0 ) ) ) )
@ sK11 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f296]) ).
thf(f296,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK3 @ Y1 @ ( sK9 @ Y1 ) @ ( sK10 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f295]) ).
thf(f295,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK3 @ Y0 @ ( sK8 @ Y0 ) @ ( sK10 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK3 @ Y0 @ ( sK9 @ Y0 ) @ ( sK8 @ Y1 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK3 @ Y1 @ ( sK9 @ Y1 ) @ ( sK10 @ Y0 ) ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f294]) ).
thf(f294,plain,
( ( ( ^ [Y0: a > b] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( sK3 @ Y1 @ ( sK8 @ Y1 ) @ ( Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( sK3 @ Y1 @ ( sK9 @ Y1 ) @ ( sK8 @ Y2 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( sK3 @ Y2 @ ( sK9 @ Y2 ) @ ( Y0 @ Y1 ) ) ) ) ) )
@ sK10 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f293]) ).
thf(f293,plain,
( ( ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( sK3 @ Y1 @ ( sK8 @ Y1 ) @ ( Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( sK3 @ Y1 @ ( sK9 @ Y1 ) @ ( sK8 @ Y2 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( sK3 @ Y2 @ ( sK9 @ Y2 ) @ ( Y0 @ Y1 ) ) ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f292]) ).
thf(f292,plain,
( ( ( ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( sK3 @ Y2 @ ( sK8 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( sK3 @ Y2 @ ( Y0 @ Y2 ) @ ( sK8 @ Y3 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( sK3 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y2 ) ) ) ) ) ) )
@ sK9 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f291]) ).
thf(f291,plain,
( ( ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( sK3 @ Y2 @ ( sK8 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( sK3 @ Y2 @ ( Y0 @ Y2 ) @ ( sK8 @ Y3 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( sK3 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y2 ) ) ) ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f290]) ).
thf(f290,plain,
( ( ( ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y1 @ Y3 ) @ ( Y0 @ Y4 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( sK3 @ Y4 @ ( Y1 @ Y4 ) @ ( Y2 @ Y3 ) ) ) ) ) ) ) )
@ sK8 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f32]) ).
thf(f32,plain,
( ( ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y1 @ Y3 ) @ ( Y0 @ Y4 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( sK3 @ Y4 @ ( Y1 @ Y4 ) @ ( Y2 @ Y3 ) ) ) ) ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f31]) ).
thf(f31,plain,
( spl0_1
<=> ( ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y1 @ Y3 ) @ ( Y0 @ Y4 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( sK3 @ Y4 @ ( Y1 @ Y4 ) @ ( Y2 @ Y3 ) ) ) ) ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f129,plain,
! [X2: a,X1: a] :
( $true
= ( ( sK2 @ X2 @ X1 )
=> ( ( sK3 @ X1 )
= ( sK3 @ X2 ) ) ) ),
inference(beta_eta_normalization,[],[f128]) ).
thf(f128,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK2 @ Y0 @ X1 )
=> ( ( sK3 @ X1 )
= ( sK3 @ Y0 ) ) )
@ X2 ) ),
inference(pi_clausification,[],[f111]) ).
thf(f111,plain,
! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ X1 )
=> ( ( sK3 @ X1 )
= ( sK3 @ Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[],[f110]) ).
thf(f110,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( ( sK3 @ Y0 )
= ( sK3 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[],[f104]) ).
thf(f104,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( ( sK3 @ Y0 )
= ( sK3 @ Y1 ) ) ) ) )
= $true ),
inference(boolean_simplification,[],[f103]) ).
thf(f103,plain,
( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( ( sK3 @ Y0 )
= ( sK3 @ Y1 ) ) ) ) ) ) ),
inference(backward_demodulation,[],[f77,f102]) ).
thf(f102,plain,
( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ Y0 )
=> ( ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( sK3 @ Y0 @ Y1 @ Y2 )
=> ( sK3 @ Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( ( sK3 @ Y0 @ Y3 @ Y1 )
& ( sK3 @ Y0 @ Y2 @ Y3 ) )
=> ( sK3 @ Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f77]) ).
thf(f77,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ Y0 )
=> ( ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( sK3 @ Y0 @ Y1 @ Y2 )
=> ( sK3 @ Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( ( sK3 @ Y0 @ Y3 @ Y1 )
& ( sK3 @ Y0 @ Y2 @ Y3 ) )
=> ( sK3 @ Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( ( sK3 @ Y0 )
= ( sK3 @ Y1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f21]) ).
thf(f21,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ Y0 )
=> ( ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( sK3 @ Y0 @ Y1 @ Y2 )
=> ( sK3 @ Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( ( sK3 @ Y0 @ Y3 @ Y1 )
& ( sK3 @ Y0 @ Y2 @ Y3 ) )
=> ( sK3 @ Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( ( sK3 @ Y0 )
= ( sK3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( sK2 @ Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f15]) ).
thf(f15,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ Y0 )
=> ( ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( sK3 @ Y0 @ Y1 @ Y2 )
=> ( sK3 @ Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( ( sK3 @ Y0 @ Y3 @ Y1 )
& ( sK3 @ Y0 @ Y2 @ Y3 ) )
=> ( sK3 @ Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( ( sK3 @ Y0 )
= ( sK3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( sK2 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK2 @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f13]) ).
thf(f13,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ Y0 )
=> ( ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( sK3 @ Y0 @ Y1 @ Y2 )
=> ( sK3 @ Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( ( sK3 @ Y0 @ Y3 @ Y1 )
& ( sK3 @ Y0 @ Y2 @ Y3 ) )
=> ( sK3 @ Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( ( sK3 @ Y0 )
= ( sK3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( sK2 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK2 @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( sK3 @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( sK3 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y1 @ Y3 ) @ ( Y0 @ Y4 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( sK3 @ Y4 @ ( Y1 @ Y4 ) @ ( Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f12]) ).
thf(f12,plain,
( ( ^ [Y0: a > b > b > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y1 )
=> ( ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( Y0 @ Y1 @ Y2 @ Y3 )
=> ( Y0 @ Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( ( ( Y0 @ Y1 @ Y4 @ Y2 )
& ( Y0 @ Y1 @ Y3 @ Y4 ) )
=> ( Y0 @ Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( ( Y0 @ Y1 )
= ( Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y1 @ Y3 )
& ( sK2 @ Y3 @ Y2 ) )
=> ( sK2 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( sK2 @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y0 @ Y3 @ ( Y2 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) )
=> ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y0 @ Y4 @ ( Y1 @ Y4 ) @ ( Y2 @ Y3 ) ) ) ) ) ) ) )
& ( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( !! @ ( a > b )
@ ^ [Y3: a > b] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y4 @ Y5 )
=> ( Y0 @ Y4 @ ( Y1 @ Y4 ) @ ( Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y4 @ Y5 )
=> ( Y0 @ Y4 @ ( Y2 @ Y4 ) @ ( Y1 @ Y5 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y0 @ Y5 @ ( Y2 @ Y5 ) @ ( Y3 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[],[f11]) ).
thf(f11,plain,
( ( !! @ ( a > b > b > $o )
@ ^ [Y0: a > b > b > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y1 )
=> ( ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( Y0 @ Y1 @ Y2 @ Y3 )
=> ( Y0 @ Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( ( ( Y0 @ Y1 @ Y4 @ Y2 )
& ( Y0 @ Y1 @ Y3 @ Y4 ) )
=> ( Y0 @ Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( ( Y0 @ Y1 )
= ( Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y1 @ Y3 )
& ( sK2 @ Y3 @ Y2 ) )
=> ( sK2 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( sK2 @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y0 @ Y3 @ ( Y2 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) )
=> ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( Y0 @ Y4 @ ( Y1 @ Y4 ) @ ( Y2 @ Y3 ) ) ) ) ) ) ) )
& ( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( !! @ ( a > b )
@ ^ [Y3: a > b] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y4 @ Y5 )
=> ( Y0 @ Y4 @ ( Y1 @ Y4 ) @ ( Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y4 @ Y5 )
=> ( Y0 @ Y4 @ ( Y2 @ Y4 ) @ ( Y1 @ Y5 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y5 @ Y4 )
=> ( Y0 @ Y5 @ ( Y2 @ Y5 ) @ ( Y3 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: a > a > $o] :
( !! @ ( a > b > b > $o )
@ ^ [Y1: a > b > b > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y2 )
=> ( ( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( ( Y1 @ Y2 @ Y3 @ Y4 )
=> ( Y1 @ Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( !! @ b
@ ^ [Y5: b] :
( ( ( Y1 @ Y2 @ Y5 @ Y3 )
& ( Y1 @ Y2 @ Y4 @ Y5 ) )
=> ( Y1 @ Y2 @ Y4 @ Y3 ) ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( ( Y1 @ Y2 )
= ( Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y2 @ Y4 )
& ( Y0 @ Y4 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
=> ( ( !! @ ( a > b )
@ ^ [Y2: a > b] :
( !! @ ( a > b )
@ ^ [Y3: a > b] :
( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y1 @ Y4 @ ( Y3 @ Y4 ) @ ( Y2 @ Y5 ) ) ) ) )
=> ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y1 @ Y5 @ ( Y2 @ Y5 ) @ ( Y3 @ Y4 ) ) ) ) ) ) ) )
& ( !! @ ( a > b )
@ ^ [Y2: a > b] :
( !! @ ( a > b )
@ ^ [Y3: a > b] :
( !! @ ( a > b )
@ ^ [Y4: a > b] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y5 @ Y6 )
=> ( Y1 @ Y5 @ ( Y2 @ Y5 ) @ ( Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y5 @ Y6 )
=> ( Y1 @ Y5 @ ( Y3 @ Y5 ) @ ( Y2 @ Y6 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y6 @ Y5 )
=> ( Y1 @ Y6 @ ( Y3 @ Y6 ) @ ( Y4 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[],[f7]) ).
thf(f7,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > b > b > $o )
@ ^ [Y1: a > b > b > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y2 )
=> ( ( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( ( Y1 @ Y2 @ Y3 @ Y4 )
=> ( Y1 @ Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( !! @ b
@ ^ [Y5: b] :
( ( ( Y1 @ Y2 @ Y5 @ Y3 )
& ( Y1 @ Y2 @ Y4 @ Y5 ) )
=> ( Y1 @ Y2 @ Y4 @ Y3 ) ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( ( Y1 @ Y2 )
= ( Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y2 @ Y4 )
& ( Y0 @ Y4 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
=> ( ( !! @ ( a > b )
@ ^ [Y2: a > b] :
( !! @ ( a > b )
@ ^ [Y3: a > b] :
( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y1 @ Y4 @ ( Y3 @ Y4 ) @ ( Y2 @ Y5 ) ) ) ) )
=> ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y1 @ Y5 @ ( Y2 @ Y5 ) @ ( Y3 @ Y4 ) ) ) ) ) ) ) )
& ( !! @ ( a > b )
@ ^ [Y2: a > b] :
( !! @ ( a > b )
@ ^ [Y3: a > b] :
( !! @ ( a > b )
@ ^ [Y4: a > b] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y5 @ Y6 )
=> ( Y1 @ Y5 @ ( Y2 @ Y5 ) @ ( Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y5 @ Y6 )
=> ( Y1 @ Y5 @ ( Y3 @ Y5 ) @ ( Y2 @ Y6 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y6 @ Y5 )
=> ( Y1 @ Y6 @ ( Y3 @ Y6 ) @ ( Y4 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > b > b > $o )
@ ^ [Y1: a > b > b > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y2 )
=> ( ( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( ( Y1 @ Y2 @ Y3 @ Y4 )
=> ( Y1 @ Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( !! @ b
@ ^ [Y5: b] :
( ( ( Y1 @ Y2 @ Y5 @ Y3 )
& ( Y1 @ Y2 @ Y4 @ Y5 ) )
=> ( Y1 @ Y2 @ Y4 @ Y3 ) ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( ( Y1 @ Y2 )
= ( Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y2 @ Y4 )
& ( Y0 @ Y4 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
=> ( ( !! @ ( a > b )
@ ^ [Y2: a > b] :
( !! @ ( a > b )
@ ^ [Y3: a > b] :
( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y1 @ Y4 @ ( Y3 @ Y4 ) @ ( Y2 @ Y5 ) ) ) ) )
=> ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y1 @ Y5 @ ( Y2 @ Y5 ) @ ( Y3 @ Y4 ) ) ) ) ) ) ) )
& ( !! @ ( a > b )
@ ^ [Y2: a > b] :
( !! @ ( a > b )
@ ^ [Y3: a > b] :
( !! @ ( a > b )
@ ^ [Y4: a > b] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y5 @ Y6 )
=> ( Y1 @ Y5 @ ( Y2 @ Y5 ) @ ( Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y5 @ Y6 )
=> ( Y1 @ Y5 @ ( Y3 @ Y5 ) @ ( Y2 @ Y6 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y6 @ Y5 )
=> ( Y1 @ Y6 @ ( Y3 @ Y6 ) @ ( Y4 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > b > b > $o )
@ ^ [Y1: a > b > b > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y2 )
=> ( ( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( ( Y1 @ Y2 @ Y3 @ Y4 )
=> ( Y1 @ Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( !! @ b
@ ^ [Y5: b] :
( ( ( Y1 @ Y2 @ Y5 @ Y3 )
& ( Y1 @ Y2 @ Y4 @ Y5 ) )
=> ( Y1 @ Y2 @ Y4 @ Y3 ) ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( ( Y1 @ Y2 )
= ( Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y2 @ Y4 )
& ( Y0 @ Y4 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
=> ( ( !! @ ( a > b )
@ ^ [Y2: a > b] :
( !! @ ( a > b )
@ ^ [Y3: a > b] :
( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( Y1 @ Y4 @ ( Y3 @ Y4 ) @ ( Y2 @ Y5 ) ) ) ) )
=> ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y1 @ Y5 @ ( Y2 @ Y5 ) @ ( Y3 @ Y4 ) ) ) ) ) ) ) )
& ( !! @ ( a > b )
@ ^ [Y2: a > b] :
( !! @ ( a > b )
@ ^ [Y3: a > b] :
( !! @ ( a > b )
@ ^ [Y4: a > b] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y5 @ Y6 )
=> ( Y1 @ Y5 @ ( Y2 @ Y5 ) @ ( Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y5 @ Y6 )
=> ( Y1 @ Y5 @ ( Y3 @ Y5 ) @ ( Y2 @ Y6 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y6 @ Y5 )
=> ( Y1 @ Y6 @ ( Y3 @ Y6 ) @ ( Y4 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
~ ! [X0: a > b > b > $o,X1: a > a > $o] :
( ( ! [X2: a,X3: a] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) )
& ! [X4: a,X5: a,X6: a] :
( ( ( X1 @ X4 @ X5 )
& ( X1 @ X6 @ X4 ) )
=> ( X1 @ X6 @ X5 ) )
& ! [X7: a,X8: a] :
( ( X1 @ X7 @ X8 )
=> ( ( X0 @ X8 )
= ( X0 @ X7 ) ) )
& ! [X9: a] :
( ( X1 @ X9 @ X9 )
=> ( ! [X10: b,X11: b,X12: b] :
( ( ( X0 @ X9 @ X11 @ X10 )
& ( X0 @ X9 @ X10 @ X12 ) )
=> ( X0 @ X9 @ X11 @ X12 ) )
& ! [X13: b,X14: b] :
( ( X0 @ X9 @ X14 @ X13 )
=> ( X0 @ X9 @ X13 @ X14 ) ) ) ) )
=> ( ! [X15: a > b,X16: a > b,X17: a > b] :
( ( ! [X18: a,X19: a] :
( ( X1 @ X19 @ X18 )
=> ( X0 @ X19 @ ( X16 @ X19 ) @ ( X17 @ X18 ) ) )
& ! [X20: a,X21: a] :
( ( X1 @ X21 @ X20 )
=> ( X0 @ X21 @ ( X17 @ X21 ) @ ( X15 @ X20 ) ) ) )
=> ! [X22: a,X23: a] :
( ( X1 @ X22 @ X23 )
=> ( X0 @ X22 @ ( X16 @ X22 ) @ ( X15 @ X23 ) ) ) )
& ! [X24: a > b,X25: a > b] :
( ! [X26: a,X27: a] :
( ( X1 @ X27 @ X26 )
=> ( X0 @ X27 @ ( X24 @ X27 ) @ ( X25 @ X26 ) ) )
=> ! [X28: a,X29: a] :
( ( X1 @ X28 @ X29 )
=> ( X0 @ X28 @ ( X25 @ X28 ) @ ( X24 @ X29 ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a > b > b > $o,X0: a > a > $o] :
( ( ! [X2: a,X3: a] :
( ( X0 @ X2 @ X3 )
=> ( X0 @ X3 @ X2 ) )
& ! [X3: a,X4: a,X2: a] :
( ( ( X0 @ X3 @ X4 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X2 @ X4 ) )
& ! [X2: a,X3: a] :
( ( X0 @ X2 @ X3 )
=> ( ( X1 @ X2 )
= ( X1 @ X3 ) ) )
& ! [X2: a] :
( ( X0 @ X2 @ X2 )
=> ( ! [X3: b,X5: b,X4: b] :
( ( ( X1 @ X2 @ X5 @ X3 )
& ( X1 @ X2 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X5 @ X4 ) )
& ! [X3: b,X5: b] :
( ( X1 @ X2 @ X5 @ X3 )
=> ( X1 @ X2 @ X3 @ X5 ) ) ) ) )
=> ( ! [X4: a > b,X2: a > b,X3: a > b] :
( ( ! [X6: a,X5: a] :
( ( X0 @ X5 @ X6 )
=> ( X1 @ X5 @ ( X2 @ X5 ) @ ( X3 @ X6 ) ) )
& ! [X6: a,X5: a] :
( ( X0 @ X5 @ X6 )
=> ( X1 @ X5 @ ( X3 @ X5 ) @ ( X4 @ X6 ) ) ) )
=> ! [X5: a,X6: a] :
( ( X0 @ X5 @ X6 )
=> ( X1 @ X5 @ ( X2 @ X5 ) @ ( X4 @ X6 ) ) ) )
& ! [X2: a > b,X3: a > b] :
( ! [X6: a,X5: a] :
( ( X0 @ X5 @ X6 )
=> ( X1 @ X5 @ ( X2 @ X5 ) @ ( X3 @ X6 ) ) )
=> ! [X5: a,X6: a] :
( ( X0 @ X5 @ X6 )
=> ( X1 @ X5 @ ( X3 @ X5 ) @ ( X2 @ X6 ) ) ) ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
! [X1: a > b > b > $o,X0: a > a > $o] :
( ( ! [X2: a,X3: a] :
( ( X0 @ X2 @ X3 )
=> ( X0 @ X3 @ X2 ) )
& ! [X3: a,X4: a,X2: a] :
( ( ( X0 @ X3 @ X4 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X2 @ X4 ) )
& ! [X2: a,X3: a] :
( ( X0 @ X2 @ X3 )
=> ( ( X1 @ X2 )
= ( X1 @ X3 ) ) )
& ! [X2: a] :
( ( X0 @ X2 @ X2 )
=> ( ! [X3: b,X5: b,X4: b] :
( ( ( X1 @ X2 @ X5 @ X3 )
& ( X1 @ X2 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X5 @ X4 ) )
& ! [X3: b,X5: b] :
( ( X1 @ X2 @ X5 @ X3 )
=> ( X1 @ X2 @ X3 @ X5 ) ) ) ) )
=> ( ! [X4: a > b,X2: a > b,X3: a > b] :
( ( ! [X6: a,X5: a] :
( ( X0 @ X5 @ X6 )
=> ( X1 @ X5 @ ( X2 @ X5 ) @ ( X3 @ X6 ) ) )
& ! [X6: a,X5: a] :
( ( X0 @ X5 @ X6 )
=> ( X1 @ X5 @ ( X3 @ X5 ) @ ( X4 @ X6 ) ) ) )
=> ! [X5: a,X6: a] :
( ( X0 @ X5 @ X6 )
=> ( X1 @ X5 @ ( X2 @ X5 ) @ ( X4 @ X6 ) ) ) )
& ! [X2: a > b,X3: a > b] :
( ! [X6: a,X5: a] :
( ( X0 @ X5 @ X6 )
=> ( X1 @ X5 @ ( X2 @ X5 ) @ ( X3 @ X6 ) ) )
=> ! [X5: a,X6: a] :
( ( X0 @ X5 @ X6 )
=> ( X1 @ X5 @ ( X3 @ X5 ) @ ( X2 @ X6 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM507_pme) ).
thf(f423,plain,
( ( $true
= ( sK3 @ sK12 @ ( sK9 @ sK12 ) @ ( sK8 @ sK12 ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f421]) ).
thf(f421,plain,
( ( $true
= ( $true
=> ( sK3 @ sK12 @ ( sK9 @ sK12 ) @ ( sK8 @ sK12 ) ) ) )
| ~ spl0_1 ),
inference(superposition,[],[f414,f377]) ).
thf(f377,plain,
( ( ( sK2 @ sK12 @ sK12 )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f373]) ).
thf(f373,plain,
( ( $true
= ( $true
=> ( sK2 @ sK12 @ sK12 ) ) )
| ~ spl0_1 ),
inference(superposition,[],[f318,f320]) ).
thf(f320,plain,
( ( $true
= ( sK2 @ sK11 @ sK12 ) )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f313]) ).
thf(f313,plain,
( ( $true
= ( $true
=> ( sK2 @ sK11 @ sK12 ) ) )
| ~ spl0_1 ),
inference(superposition,[],[f27,f307]) ).
thf(f27,plain,
! [X2: a,X1: a] :
( $true
= ( ( sK2 @ X2 @ X1 )
=> ( sK2 @ X1 @ X2 ) ) ),
inference(beta_eta_normalization,[],[f26]) ).
thf(f26,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK2 @ Y0 @ X1 )
=> ( sK2 @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_clausification,[],[f25]) ).
thf(f25,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ X1 )
=> ( sK2 @ X1 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[],[f24]) ).
thf(f24,plain,
! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK2 @ Y0 @ Y1 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[],[f23]) ).
thf(f23,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK2 @ Y0 @ Y1 ) ) ) ) ),
inference(boolean_simplification,[],[f22]) ).
thf(f22,plain,
( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK2 @ Y0 @ Y1 ) ) ) ) ) ),
inference(backward_demodulation,[],[f15,f21]) ).
thf(f318,plain,
( ! [X0: a] :
( $true
= ( ( sK2 @ sK11 @ X0 )
=> ( sK2 @ sK12 @ X0 ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f315]) ).
thf(f315,plain,
( ! [X0: a] :
( $true
= ( ( $true
& ( sK2 @ sK11 @ X0 ) )
=> ( sK2 @ sK12 @ X0 ) ) )
| ~ spl0_1 ),
inference(superposition,[],[f87,f307]) ).
thf(f87,plain,
! [X2: a,X3: a,X1: a] :
( $true
= ( ( ( sK2 @ X1 @ X3 )
& ( sK2 @ X3 @ X2 ) )
=> ( sK2 @ X1 @ X2 ) ) ),
inference(beta_eta_normalization,[],[f86]) ).
thf(f86,plain,
! [X2: a,X3: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK2 @ X1 @ Y0 )
& ( sK2 @ Y0 @ X2 ) )
=> ( sK2 @ X1 @ X2 ) )
@ X3 ) ),
inference(pi_clausification,[],[f85]) ).
thf(f85,plain,
! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ X1 @ Y0 )
& ( sK2 @ Y0 @ X2 ) )
=> ( sK2 @ X1 @ X2 ) ) ) ),
inference(beta_eta_normalization,[],[f84]) ).
thf(f84,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ X1 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK2 @ X1 @ Y0 ) ) )
@ X2 ) ),
inference(pi_clausification,[],[f83]) ).
thf(f83,plain,
! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ X1 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK2 @ X1 @ Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[],[f82]) ).
thf(f82,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( sK2 @ Y0 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[],[f79]) ).
thf(f79,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( sK2 @ Y0 @ Y1 ) ) ) ) ) ),
inference(boolean_simplification,[],[f78]) ).
thf(f78,plain,
( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( sK2 @ Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(backward_demodulation,[],[f21,f77]) ).
thf(f414,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( sK2 @ X1 @ X2 )
=> ( sK3 @ X1 @ ( sK9 @ X1 ) @ ( sK8 @ X2 ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f413]) ).
thf(f413,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK2 @ X1 @ Y0 )
=> ( sK3 @ X1 @ ( sK9 @ X1 ) @ ( sK8 @ Y0 ) ) )
@ X2 ) )
| ~ spl0_1 ),
inference(pi_clausification,[],[f410]) ).
thf(f410,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ X1 @ Y0 )
=> ( sK3 @ X1 @ ( sK9 @ X1 ) @ ( sK8 @ Y0 ) ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f409]) ).
thf(f409,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK3 @ Y0 @ ( sK9 @ Y0 ) @ ( sK8 @ Y1 ) ) ) )
@ X1 ) )
| ~ spl0_1 ),
inference(pi_clausification,[],[f324]) ).
thf(f324,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK3 @ Y0 @ ( sK9 @ Y0 ) @ ( sK8 @ Y1 ) ) ) ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f297]) ).
thf(f297,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK3 @ Y0 @ ( sK8 @ Y0 ) @ ( sK10 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK3 @ Y0 @ ( sK9 @ Y0 ) @ ( sK8 @ Y1 ) ) ) ) ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f295]) ).
thf(f818,plain,
( ( $true
= ( ~ ( sK3 @ sK11 @ ( sK9 @ sK12 ) @ ( sK8 @ sK12 ) ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f813]) ).
thf(f813,plain,
( ( $true
= ( ( sK3 @ sK11 @ ( sK9 @ sK12 ) @ ( sK8 @ sK12 ) )
=> $false ) )
| ~ spl0_1 ),
inference(superposition,[],[f754,f534]) ).
thf(f534,plain,
( ( ( sK3 @ sK11 @ ( sK9 @ sK12 ) @ ( sK10 @ sK11 ) )
= $false )
| ~ spl0_1 ),
inference(superposition,[],[f306,f511]) ).
thf(f306,plain,
( ( ( sK3 @ sK12 @ ( sK9 @ sK12 ) @ ( sK10 @ sK11 ) )
= $false )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f305]) ).
thf(f754,plain,
( ! [X0: b] :
( ( ( sK3 @ sK11 @ X0 @ ( sK8 @ sK12 ) )
=> ( sK3 @ sK11 @ X0 @ ( sK10 @ sK11 ) ) )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f735]) ).
thf(f735,plain,
( ! [X0: b] :
( $true
= ( ( $true
& ( sK3 @ sK11 @ X0 @ ( sK8 @ sK12 ) ) )
=> ( sK3 @ sK11 @ X0 @ ( sK10 @ sK11 ) ) ) )
| ~ spl0_1 ),
inference(superposition,[],[f690,f535]) ).
thf(f535,plain,
( ( $true
= ( sK3 @ sK11 @ ( sK8 @ sK12 ) @ ( sK10 @ sK11 ) ) )
| ~ spl0_1 ),
inference(superposition,[],[f382,f511]) ).
thf(f382,plain,
( ( ( sK3 @ sK12 @ ( sK8 @ sK12 ) @ ( sK10 @ sK11 ) )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f380]) ).
thf(f380,plain,
( ( $true
= ( $true
=> ( sK3 @ sK12 @ ( sK8 @ sK12 ) @ ( sK10 @ sK11 ) ) ) )
| ~ spl0_1 ),
inference(superposition,[],[f368,f307]) ).
thf(f368,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( sK2 @ X1 @ X2 )
=> ( sK3 @ X1 @ ( sK8 @ X1 ) @ ( sK10 @ X2 ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f367]) ).
thf(f367,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK2 @ X1 @ Y0 )
=> ( sK3 @ X1 @ ( sK8 @ X1 ) @ ( sK10 @ Y0 ) ) )
@ X2 ) )
| ~ spl0_1 ),
inference(pi_clausification,[],[f366]) ).
thf(f366,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ X1 @ Y0 )
=> ( sK3 @ X1 @ ( sK8 @ X1 ) @ ( sK10 @ Y0 ) ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f365]) ).
thf(f365,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK3 @ Y0 @ ( sK8 @ Y0 ) @ ( sK10 @ Y1 ) ) ) )
@ X1 ) )
| ~ spl0_1 ),
inference(pi_clausification,[],[f327]) ).
thf(f327,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK3 @ Y0 @ ( sK8 @ Y0 ) @ ( sK10 @ Y1 ) ) ) ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f326]) ).
thf(f326,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK3 @ Y0 @ ( sK8 @ Y0 ) @ ( sK10 @ Y1 ) ) ) ) )
& $true ) )
| ~ spl0_1 ),
inference(backward_demodulation,[],[f297,f324]) ).
thf(f690,plain,
( ! [X2: b,X3: b,X1: b] :
( $true
= ( ( ( sK3 @ sK11 @ X3 @ X1 )
& ( sK3 @ sK11 @ X2 @ X3 ) )
=> ( sK3 @ sK11 @ X2 @ X1 ) ) )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f689,f511]) ).
thf(f689,plain,
( ! [X2: b,X3: b,X1: b] :
( $true
= ( ( ( sK3 @ sK11 @ X3 @ X1 )
& ( sK3 @ sK12 @ X2 @ X3 ) )
=> ( sK3 @ sK11 @ X2 @ X1 ) ) )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f688,f511]) ).
thf(f688,plain,
( ! [X2: b,X3: b,X1: b] :
( $true
= ( ( ( sK3 @ sK12 @ X3 @ X1 )
& ( sK3 @ sK12 @ X2 @ X3 ) )
=> ( sK3 @ sK11 @ X2 @ X1 ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f687]) ).
thf(f687,plain,
( ! [X2: b,X3: b,X1: b] :
( ( ^ [Y0: b] :
( ( ( sK3 @ sK12 @ Y0 @ X1 )
& ( sK3 @ sK12 @ X2 @ Y0 ) )
=> ( sK3 @ sK11 @ X2 @ X1 ) )
@ X3 )
= $true )
| ~ spl0_1 ),
inference(pi_clausification,[],[f683]) ).
thf(f683,plain,
( ! [X2: b,X1: b] :
( ( !! @ b
@ ^ [Y0: b] :
( ( ( sK3 @ sK12 @ Y0 @ X1 )
& ( sK3 @ sK12 @ X2 @ Y0 ) )
=> ( sK3 @ sK11 @ X2 @ X1 ) ) )
= $true )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f682,f511]) ).
thf(f682,plain,
( ! [X2: b,X1: b] :
( $true
= ( !! @ b
@ ^ [Y0: b] :
( ( ( sK3 @ sK12 @ Y0 @ X1 )
& ( sK3 @ sK12 @ X2 @ Y0 ) )
=> ( sK3 @ sK12 @ X2 @ X1 ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f681]) ).
thf(f681,plain,
( ! [X2: b,X1: b] :
( $true
= ( ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( ( sK3 @ sK12 @ Y1 @ X1 )
& ( sK3 @ sK12 @ Y0 @ Y1 ) )
=> ( sK3 @ sK12 @ Y0 @ X1 ) ) )
@ X2 ) )
| ~ spl0_1 ),
inference(pi_clausification,[],[f673]) ).
thf(f673,plain,
( ! [X1: b] :
( ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( ( sK3 @ sK12 @ Y1 @ X1 )
& ( sK3 @ sK12 @ Y0 @ Y1 ) )
=> ( sK3 @ sK12 @ Y0 @ X1 ) ) ) )
= $true )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f671]) ).
thf(f671,plain,
( ! [X1: b] :
( $true
= ( ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK3 @ sK12 @ Y2 @ Y0 )
& ( sK3 @ sK12 @ Y1 @ Y2 ) )
=> ( sK3 @ sK12 @ Y1 @ Y0 ) ) ) )
@ X1 ) )
| ~ spl0_1 ),
inference(pi_clausification,[],[f554]) ).
thf(f554,plain,
( ( $true
= ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK3 @ sK12 @ Y2 @ Y0 )
& ( sK3 @ sK12 @ Y1 @ Y2 ) )
=> ( sK3 @ sK12 @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f399]) ).
thf(f399,plain,
( ( $true
= ( ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK3 @ sK12 @ Y0 @ Y1 )
=> ( sK3 @ sK12 @ Y1 @ Y0 ) ) ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK3 @ sK12 @ Y2 @ Y0 )
& ( sK3 @ sK12 @ Y1 @ Y2 ) )
=> ( sK3 @ sK12 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f387]) ).
thf(f387,plain,
( ( $true
= ( $true
=> ( ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK3 @ sK12 @ Y0 @ Y1 )
=> ( sK3 @ sK12 @ Y1 @ Y0 ) ) ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK3 @ sK12 @ Y2 @ Y0 )
& ( sK3 @ sK12 @ Y1 @ Y2 ) )
=> ( sK3 @ sK12 @ Y1 @ Y0 ) ) ) ) ) ) ) )
| ~ spl0_1 ),
inference(superposition,[],[f181,f377]) ).
thf(f181,plain,
! [X1: a] :
( $true
= ( ( sK2 @ X1 @ X1 )
=> ( ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK3 @ X1 @ Y0 @ Y1 )
=> ( sK3 @ X1 @ Y1 @ Y0 ) ) ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK3 @ X1 @ Y2 @ Y0 )
& ( sK3 @ X1 @ Y1 @ Y2 ) )
=> ( sK3 @ X1 @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f180]) ).
thf(f180,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK2 @ Y0 @ Y0 )
=> ( ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( sK3 @ Y0 @ Y1 @ Y2 )
=> ( sK3 @ Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( ( sK3 @ Y0 @ Y3 @ Y1 )
& ( sK3 @ Y0 @ Y2 @ Y3 ) )
=> ( sK3 @ Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[],[f102]) ).
thf(f287,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f286]) ).
thf(f286,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f285]) ).
thf(f285,plain,
( ( $true = $false )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f284]) ).
thf(f284,plain,
( ( $true = ~ $true )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f274,f72]) ).
thf(f72,plain,
( ( $true
= ( sK3 @ sK6 @ ( sK5 @ sK6 ) @ ( sK4 @ sK7 ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f71]) ).
thf(f71,plain,
( ( ( $true
=> ( sK3 @ sK6 @ ( sK5 @ sK6 ) @ ( sK4 @ sK7 ) ) )
= $true )
| ~ spl0_2 ),
inference(superposition,[],[f68,f60]) ).
thf(f60,plain,
( ( $true
= ( sK2 @ sK6 @ sK7 ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f57]) ).
thf(f57,plain,
( ( $true
= ( $true
=> ( sK2 @ sK6 @ sK7 ) ) )
| ~ spl0_2 ),
inference(superposition,[],[f27,f54]) ).
thf(f54,plain,
( ( $true
= ( sK2 @ sK7 @ sK6 ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f52]) ).
thf(f52,plain,
( ( ( ( sK2 @ sK7 @ sK6 )
=> ( sK3 @ sK7 @ ( sK4 @ sK7 ) @ ( sK5 @ sK6 ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f51]) ).
thf(f51,plain,
( ( ( ^ [Y0: a] :
( ( sK2 @ Y0 @ sK6 )
=> ( sK3 @ Y0 @ ( sK4 @ Y0 ) @ ( sK5 @ sK6 ) ) )
@ sK7 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f50]) ).
thf(f50,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ sK6 )
=> ( sK3 @ Y0 @ ( sK4 @ Y0 ) @ ( sK5 @ sK6 ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f49]) ).
thf(f49,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK3 @ Y1 @ ( sK4 @ Y1 ) @ ( sK5 @ Y0 ) ) ) )
@ sK6 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f43]) ).
thf(f43,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK3 @ Y1 @ ( sK4 @ Y1 ) @ ( sK5 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f42]) ).
thf(f42,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK3 @ Y0 @ ( sK5 @ Y0 ) @ ( sK4 @ Y1 ) ) ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK3 @ Y1 @ ( sK4 @ Y1 ) @ ( sK5 @ Y0 ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f41]) ).
thf(f41,plain,
( ( ( ^ [Y0: a > b] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( sK3 @ Y1 @ ( Y0 @ Y1 ) @ ( sK4 @ Y2 ) ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( sK3 @ Y2 @ ( sK4 @ Y2 ) @ ( Y0 @ Y1 ) ) ) ) ) )
@ sK5 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f40]) ).
thf(f40,plain,
( ( ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( sK3 @ Y1 @ ( Y0 @ Y1 ) @ ( sK4 @ Y2 ) ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y2 @ Y1 )
=> ( sK3 @ Y2 @ ( sK4 @ Y2 ) @ ( Y0 @ Y1 ) ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f39]) ).
thf(f39,plain,
( ( ( ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( sK3 @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( sK3 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y2 ) ) ) ) ) ) )
@ sK4 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f35]) ).
thf(f35,plain,
( ( ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( sK3 @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( sK3 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y2 ) ) ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f34]) ).
thf(f34,plain,
( spl0_2
<=> ( ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( sK3 @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( sK3 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y2 ) ) ) ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f68,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( sK2 @ X1 @ X2 )
=> ( sK3 @ X1 @ ( sK5 @ X1 ) @ ( sK4 @ X2 ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f67]) ).
thf(f67,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK2 @ X1 @ Y0 )
=> ( sK3 @ X1 @ ( sK5 @ X1 ) @ ( sK4 @ Y0 ) ) )
@ X2 ) )
| ~ spl0_2 ),
inference(pi_clausification,[],[f66]) ).
thf(f66,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ X1 @ Y0 )
=> ( sK3 @ X1 @ ( sK5 @ X1 ) @ ( sK4 @ Y0 ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f65]) ).
thf(f65,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK3 @ Y0 @ ( sK5 @ Y0 ) @ ( sK4 @ Y1 ) ) ) )
@ X1 ) )
| ~ spl0_2 ),
inference(pi_clausification,[],[f44]) ).
thf(f44,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK3 @ Y0 @ ( sK5 @ Y0 ) @ ( sK4 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f42]) ).
thf(f274,plain,
( ( $true
= ( ~ ( sK3 @ sK6 @ ( sK5 @ sK6 ) @ ( sK4 @ sK7 ) ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f263]) ).
thf(f263,plain,
( ( $true
= ( ( sK3 @ sK6 @ ( sK5 @ sK6 ) @ ( sK4 @ sK7 ) )
=> $false ) )
| ~ spl0_2 ),
inference(superposition,[],[f259,f211]) ).
thf(f211,plain,
( ( ( sK3 @ sK6 @ ( sK4 @ sK7 ) @ ( sK5 @ sK6 ) )
= $false )
| ~ spl0_2 ),
inference(superposition,[],[f56,f205]) ).
thf(f205,plain,
( ! [X2: b,X1: b] :
( ( sK3 @ sK7 @ X1 @ X2 )
= ( sK3 @ sK6 @ X1 @ X2 ) )
| ~ spl0_2 ),
inference(argument_congruence,[],[f175]) ).
thf(f175,plain,
( ! [X1: b] :
( ( sK3 @ sK6 @ X1 )
= ( sK3 @ sK7 @ X1 ) )
| ~ spl0_2 ),
inference(argument_congruence,[],[f147]) ).
thf(f147,plain,
( ( ( sK3 @ sK7 )
= ( sK3 @ sK6 ) )
| ~ spl0_2 ),
inference(equality_proxy_clausification,[],[f138]) ).
thf(f138,plain,
( ( $true
= ( ( sK3 @ sK6 )
= ( sK3 @ sK7 ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f133]) ).
thf(f133,plain,
( ( $true
= ( $true
=> ( ( sK3 @ sK6 )
= ( sK3 @ sK7 ) ) ) )
| ~ spl0_2 ),
inference(superposition,[],[f129,f54]) ).
thf(f56,plain,
( ( ( sK3 @ sK7 @ ( sK4 @ sK7 ) @ ( sK5 @ sK6 ) )
= $false )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f55]) ).
thf(f55,plain,
( ( ( $true
=> ( sK3 @ sK7 @ ( sK4 @ sK7 ) @ ( sK5 @ sK6 ) ) )
= $false )
| ~ spl0_2 ),
inference(backward_demodulation,[],[f52,f54]) ).
thf(f259,plain,
( ! [X2: b,X1: b] :
( $true
= ( ( sK3 @ sK6 @ X1 @ X2 )
=> ( sK3 @ sK6 @ X2 @ X1 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f258]) ).
thf(f258,plain,
( ! [X2: b,X1: b] :
( $true
= ( ^ [Y0: b] :
( ( sK3 @ sK6 @ X1 @ Y0 )
=> ( sK3 @ sK6 @ Y0 @ X1 ) )
@ X2 ) )
| ~ spl0_2 ),
inference(pi_clausification,[],[f246]) ).
thf(f246,plain,
( ! [X1: b] :
( $true
= ( !! @ b
@ ^ [Y0: b] :
( ( sK3 @ sK6 @ X1 @ Y0 )
=> ( sK3 @ sK6 @ Y0 @ X1 ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f243]) ).
thf(f243,plain,
( ! [X1: b] :
( $true
= ( ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK3 @ sK6 @ Y0 @ Y1 )
=> ( sK3 @ sK6 @ Y1 @ Y0 ) ) )
@ X1 ) )
| ~ spl0_2 ),
inference(pi_clausification,[],[f242]) ).
thf(f242,plain,
( ( $true
= ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK3 @ sK6 @ Y0 @ Y1 )
=> ( sK3 @ sK6 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f241]) ).
thf(f241,plain,
( ( $true
= ( ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK3 @ sK6 @ Y0 @ Y1 )
=> ( sK3 @ sK6 @ Y1 @ Y0 ) ) ) )
& $true ) )
| ~ spl0_2 ),
inference(backward_demodulation,[],[f194,f237]) ).
thf(f237,plain,
( ( ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK3 @ sK6 @ Y2 @ Y0 )
& ( sK3 @ sK6 @ Y1 @ Y2 ) )
=> ( sK3 @ sK6 @ Y1 @ Y0 ) ) ) ) )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f194]) ).
thf(f194,plain,
( ( ( ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK3 @ sK6 @ Y0 @ Y1 )
=> ( sK3 @ sK6 @ Y1 @ Y0 ) ) ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK3 @ sK6 @ Y2 @ Y0 )
& ( sK3 @ sK6 @ Y1 @ Y2 ) )
=> ( sK3 @ sK6 @ Y1 @ Y0 ) ) ) ) ) )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f192]) ).
thf(f192,plain,
( ( $true
= ( $true
=> ( ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK3 @ sK6 @ Y0 @ Y1 )
=> ( sK3 @ sK6 @ Y1 @ Y0 ) ) ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK3 @ sK6 @ Y2 @ Y0 )
& ( sK3 @ sK6 @ Y1 @ Y2 ) )
=> ( sK3 @ sK6 @ Y1 @ Y0 ) ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(superposition,[],[f181,f146]) ).
thf(f146,plain,
( ( $true
= ( sK2 @ sK6 @ sK6 ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f142]) ).
thf(f142,plain,
( ( $true
= ( $true
=> ( sK2 @ sK6 @ sK6 ) ) )
| ~ spl0_2 ),
inference(superposition,[],[f98,f60]) ).
thf(f98,plain,
( ! [X0: a] :
( ( ( sK2 @ X0 @ sK7 )
=> ( sK2 @ X0 @ sK6 ) )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f91]) ).
thf(f91,plain,
( ! [X0: a] :
( ( ( ( sK2 @ X0 @ sK7 )
& $true )
=> ( sK2 @ X0 @ sK6 ) )
= $true )
| ~ spl0_2 ),
inference(superposition,[],[f87,f54]) ).
thf(f36,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f29,f34,f31]) ).
thf(f29,plain,
( ( ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y1 @ Y3 ) @ ( Y0 @ Y4 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( sK3 @ Y4 @ ( Y1 @ Y4 ) @ ( Y2 @ Y3 ) ) ) ) ) ) ) ) )
= $false )
| ( ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( sK3 @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( sK3 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y2 ) ) ) ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f14]) ).
thf(f14,plain,
( ( ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( sK3 @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y3 @ Y2 )
=> ( sK3 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y2 ) ) ) ) ) ) ) )
& ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( sK3 @ Y3 @ ( Y1 @ Y3 ) @ ( Y0 @ Y4 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y4 @ Y3 )
=> ( sK3 @ Y4 @ ( Y1 @ Y4 ) @ ( Y2 @ Y3 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : SEV046^5 : TPTP v8.2.0. Released v4.0.0.
% 0.09/0.10 % Command : run_vampire %s %d THM
% 0.10/0.30 % Computer : n023.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Fri Jun 21 19:24:54 EDT 2024
% 0.10/0.30 % CPUTime :
% 0.16/0.32 This is a TH0_THM_EQU_NAR problem
% 0.16/0.32 Running higher-order theorem proving
% 0.16/0.32 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
% 0.16/0.34 % (1577)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.16/0.34 % (1580)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.16/0.34 % (1579)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)
% 0.16/0.34 % (1582)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)
% 0.16/0.34 % (1583)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.16/0.34 % (1581)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)
% 0.16/0.34 % (1578)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)
% 0.16/0.34 % (1581)Instruction limit reached!
% 0.16/0.34 % (1581)------------------------------
% 0.16/0.34 % (1581)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.16/0.34 % (1581)Termination reason: Unknown
% 0.16/0.34 % (1581)Termination phase: shuffling
% 0.16/0.34
% 0.16/0.34 % (1581)Memory used [KB]: 1023
% 0.16/0.34 % (1581)Time elapsed: 0.003 s
% 0.16/0.34 % (1581)Instructions burned: 2 (million)
% 0.16/0.34 % (1581)------------------------------
% 0.16/0.34 % (1581)------------------------------
% 0.16/0.34 % (1580)Instruction limit reached!
% 0.16/0.34 % (1580)------------------------------
% 0.16/0.34 % (1580)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.16/0.34 % (1580)Termination reason: Unknown
% 0.16/0.34 % (1580)Termination phase: Preprocessing 3
% 0.16/0.34
% 0.16/0.34 % (1580)Memory used [KB]: 1023
% 0.16/0.34 % (1580)Time elapsed: 0.004 s
% 0.16/0.34 % (1580)Instructions burned: 3 (million)
% 0.16/0.34 % (1580)------------------------------
% 0.16/0.34 % (1580)------------------------------
% 0.16/0.34 % (1578)Instruction limit reached!
% 0.16/0.34 % (1578)------------------------------
% 0.16/0.34 % (1578)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.16/0.34 % (1578)Termination reason: Unknown
% 0.16/0.34 % (1578)Termination phase: Saturation
% 0.16/0.34
% 0.16/0.34 % (1578)Memory used [KB]: 5500
% 0.16/0.34 % (1578)Time elapsed: 0.005 s
% 0.16/0.34 % (1578)Instructions burned: 4 (million)
% 0.16/0.34 % (1578)------------------------------
% 0.16/0.34 % (1578)------------------------------
% 0.16/0.35 % (1583)Instruction limit reached!
% 0.16/0.35 % (1583)------------------------------
% 0.16/0.35 % (1583)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.16/0.35 % (1583)Termination reason: Unknown
% 0.16/0.35 % (1583)Termination phase: Saturation
% 0.16/0.35
% 0.16/0.35 % (1583)Memory used [KB]: 5628
% 0.16/0.35 % (1583)Time elapsed: 0.013 s
% 0.16/0.35 % (1583)Instructions burned: 19 (million)
% 0.16/0.35 % (1583)------------------------------
% 0.16/0.35 % (1583)------------------------------
% 0.16/0.35 % (1584)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)
% 0.16/0.35 % (1579)Instruction limit reached!
% 0.16/0.35 % (1579)------------------------------
% 0.16/0.35 % (1579)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.16/0.35 % (1579)Termination reason: Unknown
% 0.16/0.35 % (1585)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)
% 0.16/0.35 % (1579)Termination phase: Saturation
% 0.16/0.35
% 0.16/0.35 % (1579)Memory used [KB]: 5756
% 0.16/0.35 % (1579)Time elapsed: 0.018 s
% 0.16/0.35 % (1579)Instructions burned: 27 (million)
% 0.16/0.35 % (1579)------------------------------
% 0.16/0.35 % (1579)------------------------------
% 0.16/0.35 % (1586)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)
% 0.16/0.35 % (1584)Instruction limit reached!
% 0.16/0.35 % (1584)------------------------------
% 0.16/0.35 % (1584)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.16/0.35 % (1584)Termination reason: Unknown
% 0.16/0.35 % (1584)Termination phase: Saturation
% 0.16/0.35
% 0.16/0.35 % (1584)Memory used [KB]: 5500
% 0.16/0.35 % (1584)Time elapsed: 0.004 s
% 0.16/0.35 % (1584)Instructions burned: 4 (million)
% 0.16/0.35 % (1584)------------------------------
% 0.16/0.35 % (1584)------------------------------
% 0.16/0.36 % (1586)Instruction limit reached!
% 0.16/0.36 % (1586)------------------------------
% 0.16/0.36 % (1586)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.16/0.36 % (1586)Termination reason: Unknown
% 0.16/0.36 % (1586)Termination phase: Saturation
% 0.16/0.36
% 0.16/0.36 % (1586)Memory used [KB]: 5628
% 0.16/0.36 % (1586)Time elapsed: 0.009 s
% 0.16/0.36 % (1586)Instructions burned: 15 (million)
% 0.16/0.36 % (1586)------------------------------
% 0.16/0.36 % (1586)------------------------------
% 0.16/0.36 % (1587)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)
% 0.16/0.36 % (1587)Instruction limit reached!
% 0.16/0.36 % (1587)------------------------------
% 0.16/0.36 % (1587)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.16/0.36 % (1587)Termination reason: Unknown
% 0.16/0.36 % (1587)Termination phase: Saturation
% 0.16/0.36
% 0.16/0.36 % (1587)Memory used [KB]: 5500
% 0.16/0.36 % (1587)Time elapsed: 0.004 s
% 0.16/0.36 % (1587)Instructions burned: 4 (million)
% 0.16/0.36 % (1587)------------------------------
% 0.16/0.36 % (1587)------------------------------
% 0.16/0.37 % (1588)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)
% 0.16/0.37 % (1589)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.16/0.37 % (1585)Instruction limit reached!
% 0.16/0.37 % (1585)------------------------------
% 0.16/0.37 % (1585)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.16/0.37 % (1585)Termination reason: Unknown
% 0.16/0.37 % (1585)Termination phase: Saturation
% 0.16/0.37
% 0.16/0.37 % (1585)Memory used [KB]: 5756
% 0.16/0.37 % (1585)Time elapsed: 0.020 s
% 0.16/0.37 % (1585)Instructions burned: 37 (million)
% 0.16/0.37 % (1585)------------------------------
% 0.16/0.37 % (1585)------------------------------
% 0.16/0.37 % (1589)Instruction limit reached!
% 0.16/0.37 % (1589)------------------------------
% 0.16/0.37 % (1589)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.16/0.37 % (1589)Termination reason: Unknown
% 0.16/0.37 % (1589)Termination phase: Saturation
% 0.16/0.37
% 0.16/0.37 % (1589)Memory used [KB]: 1151
% 0.16/0.37 % (1589)Time elapsed: 0.006 s
% 0.16/0.37 % (1589)Instructions burned: 7 (million)
% 0.16/0.37 % (1589)------------------------------
% 0.16/0.37 % (1589)------------------------------
% 0.16/0.37 % (1590)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.16/0.38 % (1591)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)
% 0.16/0.38 % (1591)Instruction limit reached!
% 0.16/0.38 % (1591)------------------------------
% 0.16/0.38 % (1591)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.16/0.38 % (1591)Termination reason: Unknown
% 0.16/0.38 % (1591)Termination phase: Preprocessing 3
% 0.16/0.38
% 0.16/0.38 % (1591)Memory used [KB]: 1023
% 0.16/0.38 % (1591)Time elapsed: 0.003 s
% 0.16/0.38 % (1591)Instructions burned: 3 (million)
% 0.16/0.38 % (1591)------------------------------
% 0.16/0.38 % (1591)------------------------------
% 0.16/0.38 % (1590)Instruction limit reached!
% 0.16/0.38 % (1590)------------------------------
% 0.16/0.38 % (1590)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.16/0.38 % (1590)Termination reason: Unknown
% 0.16/0.38 % (1590)Termination phase: Saturation
% 0.16/0.38
% 0.16/0.38 % (1590)Memory used [KB]: 5756
% 0.16/0.38 % (1590)Time elapsed: 0.011 s
% 0.16/0.38 % (1590)Instructions burned: 16 (million)
% 0.16/0.38 % (1590)------------------------------
% 0.16/0.38 % (1590)------------------------------
% 0.16/0.38 % (1592)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)
% 0.16/0.39 % (1593)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)
% 0.16/0.39 % (1592)Instruction limit reached!
% 0.16/0.39 % (1592)------------------------------
% 0.16/0.39 % (1592)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.16/0.39 % (1592)Termination reason: Unknown
% 0.16/0.39 % (1592)Termination phase: Property scanning
% 0.16/0.39
% 0.16/0.39 % (1592)Memory used [KB]: 1023
% 0.16/0.39 % (1592)Time elapsed: 0.004 s
% 0.16/0.39 % (1592)Instructions burned: 4 (million)
% 0.16/0.39 % (1592)------------------------------
% 0.16/0.39 % (1592)------------------------------
% 0.17/0.39 % (1593)Instruction limit reached!
% 0.17/0.39 % (1593)------------------------------
% 0.17/0.39 % (1593)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.17/0.39 % (1593)Termination reason: Unknown
% 0.17/0.39 % (1593)Termination phase: Saturation
% 0.17/0.39
% 0.17/0.39 % (1593)Memory used [KB]: 5628
% 0.17/0.39 % (1593)Time elapsed: 0.006 s
% 0.17/0.39 % (1593)Instructions burned: 8 (million)
% 0.17/0.39 % (1593)------------------------------
% 0.17/0.39 % (1593)------------------------------
% 0.17/0.39 % (1594)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)
% 0.17/0.40 % (1594)Instruction limit reached!
% 0.17/0.40 % (1594)------------------------------
% 0.17/0.40 % (1594)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.17/0.40 % (1594)Termination reason: Unknown
% 0.17/0.40 % (1594)Termination phase: Property scanning
% 0.17/0.40
% 0.17/0.40 % (1594)Memory used [KB]: 1023
% 0.17/0.40 % (1594)Time elapsed: 0.003 s
% 0.17/0.40 % (1594)Instructions burned: 4 (million)
% 0.17/0.40 % (1594)------------------------------
% 0.17/0.40 % (1594)------------------------------
% 0.17/0.40 % (1595)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.17/0.40 % (1595)Instruction limit reached!
% 0.17/0.40 % (1595)------------------------------
% 0.17/0.40 % (1595)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.17/0.40 % (1595)Termination reason: Unknown
% 0.17/0.40 % (1595)Termination phase: Property scanning
% 0.17/0.40
% 0.17/0.40 % (1595)Memory used [KB]: 1023
% 0.17/0.40 % (1595)Time elapsed: 0.003 s
% 0.17/0.40 % (1595)Instructions burned: 4 (million)
% 0.17/0.40 % (1595)------------------------------
% 0.17/0.40 % (1595)------------------------------
% 0.17/0.40 % (1596)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)
% 0.17/0.40 % (1597)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.17/0.41 % (1598)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.17/0.41 % (1596)Instruction limit reached!
% 0.17/0.41 % (1596)------------------------------
% 0.17/0.41 % (1596)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.17/0.41 % (1596)Termination reason: Unknown
% 0.17/0.41 % (1596)Termination phase: Saturation
% 0.17/0.41
% 0.17/0.41 % (1596)Memory used [KB]: 5628
% 0.17/0.41 % (1596)Time elapsed: 0.012 s
% 0.17/0.41 % (1596)Instructions burned: 19 (million)
% 0.17/0.41 % (1596)------------------------------
% 0.17/0.41 % (1596)------------------------------
% 0.17/0.41 % (1599)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)
% 0.17/0.41 % (1598)Instruction limit reached!
% 0.17/0.41 % (1598)------------------------------
% 0.17/0.41 % (1598)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.17/0.41 % (1598)Termination reason: Unknown
% 0.17/0.41 % (1598)Termination phase: Saturation
% 0.17/0.41
% 0.17/0.41 % (1598)Memory used [KB]: 5500
% 0.17/0.41 % (1598)Time elapsed: 0.005 s
% 0.17/0.41 % (1598)Instructions burned: 7 (million)
% 0.17/0.41 % (1598)------------------------------
% 0.17/0.41 % (1598)------------------------------
% 0.17/0.42 % (1577)Instruction limit reached!
% 0.17/0.42 % (1577)------------------------------
% 0.17/0.42 % (1577)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.17/0.42 % (1577)Termination reason: Unknown
% 0.17/0.42 % (1577)Termination phase: Saturation
% 0.17/0.42
% 0.17/0.42 % (1577)Memory used [KB]: 5884
% 0.17/0.42 % (1577)Time elapsed: 0.084 s
% 0.17/0.42 % (1577)Instructions burned: 184 (million)
% 0.17/0.42 % (1577)------------------------------
% 0.17/0.42 % (1577)------------------------------
% 0.17/0.42 % (1600)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)
% 0.17/0.43 % (1601)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2998ds/5Mi)
% 0.17/0.43 % (1601)Instruction limit reached!
% 0.17/0.43 % (1601)------------------------------
% 0.17/0.43 % (1601)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.17/0.43 % (1601)Termination reason: Unknown
% 0.17/0.43 % (1601)Termination phase: Saturation
% 0.17/0.43
% 0.17/0.43 % (1601)Memory used [KB]: 5500
% 0.17/0.43 % (1601)Time elapsed: 0.004 s
% 0.17/0.43 % (1601)Instructions burned: 5 (million)
% 0.17/0.43 % (1601)------------------------------
% 0.17/0.43 % (1601)------------------------------
% 0.17/0.43 % (1602)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on theBenchmark for (2998ds/6Mi)
% 0.17/0.43 % (1602)Instruction limit reached!
% 0.17/0.43 % (1602)------------------------------
% 0.17/0.43 % (1602)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.17/0.43 % (1602)Termination reason: Unknown
% 0.17/0.43 % (1602)Termination phase: Saturation
% 0.17/0.43
% 0.17/0.43 % (1602)Memory used [KB]: 5500
% 0.17/0.43 % (1602)Time elapsed: 0.005 s
% 0.17/0.43 % (1602)Instructions burned: 6 (million)
% 0.17/0.43 % (1602)------------------------------
% 0.17/0.43 % (1602)------------------------------
% 0.17/0.44 % (1600)Instruction limit reached!
% 0.17/0.44 % (1600)------------------------------
% 0.17/0.44 % (1600)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.17/0.44 % (1600)Termination reason: Unknown
% 0.17/0.44 % (1600)Termination phase: Saturation
% 0.17/0.44
% 0.17/0.44 % (1600)Memory used [KB]: 5756
% 0.17/0.44 % (1600)Time elapsed: 0.013 s
% 0.17/0.44 % (1600)Instructions burned: 21 (million)
% 0.17/0.44 % (1600)------------------------------
% 0.17/0.44 % (1600)------------------------------
% 0.17/0.44 % (1603)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2998ds/377Mi)
% 0.17/0.44 % (1588)First to succeed.
% 0.17/0.45 % (1604)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on theBenchmark for (2998ds/779Mi)
% 0.17/0.45 % (1605)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on theBenchmark for (2998ds/19Mi)
% 0.17/0.45 % (1588)Refutation found. Thanks to Tanya!
% 0.17/0.45 % SZS status Theorem for theBenchmark
% 0.17/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.45 % (1588)------------------------------
% 0.17/0.45 % (1588)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.17/0.45 % (1588)Termination reason: Refutation
% 0.17/0.45
% 0.17/0.45 % (1588)Memory used [KB]: 6524
% 0.17/0.45 % (1588)Time elapsed: 0.087 s
% 0.17/0.45 % (1588)Instructions burned: 147 (million)
% 0.17/0.45 % (1588)------------------------------
% 0.17/0.45 % (1588)------------------------------
% 0.17/0.45 % (1576)Success in time 0.138 s
%------------------------------------------------------------------------------