TSTP Solution File: SEV146^5 by Vampire---4.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEV146^5 : 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 16:01:59 EDT 2024
% Result : Theorem 0.21s 0.44s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 5
% Syntax : Number of formulae : 111 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 961 ( 101 equ; 0 cnn)
% Maximal formula atoms : 3 ( 8 avg)
% Number of connectives : 2760 ( 119 ~; 107 |; 228 &;1609 @)
% ( 4 <=>; 329 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 166 ( 166 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 17 usr; 16 con; 0-2 aty)
% ( 364 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 459 ( 381 ^ 78 !; 0 ?; 459 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_17,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
sK2: a > a > $o ).
thf(func_def_19,type,
sK3: a ).
thf(func_def_20,type,
sK4: a ).
thf(func_def_21,type,
sK5: a ).
thf(func_def_22,type,
sK6: a > $o ).
thf(func_def_23,type,
sK7: a ).
thf(func_def_24,type,
sK8: a ).
thf(func_def_25,type,
sK9: a ).
thf(func_def_26,type,
sK10: a ).
thf(func_def_27,type,
sK11: a ).
thf(func_def_28,type,
sK12: a ).
thf(func_def_29,type,
sK13: a > $o ).
thf(f261,plain,
$false,
inference(avatar_sat_refutation,[],[f19,f137,f219,f222,f260]) ).
thf(f260,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f259]) ).
thf(f259,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f258]) ).
thf(f258,plain,
( ( $true = $false )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f257]) ).
thf(f257,plain,
( ( $true = ~ $true )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f252,f232]) ).
thf(f232,plain,
( ( $true
= ( sK2 @ sK11 @ sK12 ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f230]) ).
thf(f230,plain,
( ( $false
= ( ( sK2 @ sK11 @ sK12 )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK11 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f229]) ).
thf(f229,plain,
( ( ( ^ [Y0: a] :
( ( sK2 @ sK11 @ Y0 )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK11 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
@ sK12 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f228]) ).
thf(f228,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK11 @ Y0 )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK11 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f227]) ).
thf(f227,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
@ sK11 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f15]) ).
thf(f15,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f14]) ).
thf(f14,plain,
( spl0_1
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f252,plain,
( ( $true
= ( ~ ( sK2 @ sK11 @ sK12 ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f250]) ).
thf(f250,plain,
( ( $true
= ( ( sK2 @ sK11 @ sK12 )
=> $false ) )
| ~ spl0_1 ),
inference(superposition,[],[f246,f240]) ).
thf(f240,plain,
( ( $false
= ( sK13 @ sK12 ) )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f239]) ).
thf(f239,plain,
( ( $false
= ( $true
=> ( sK13 @ sK12 ) ) )
| ~ spl0_1 ),
inference(backward_demodulation,[],[f236,f238]) ).
thf(f238,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK13 @ Y1 ) )
=> ( sK13 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK11 @ Y0 )
=> ( sK13 @ Y0 ) ) ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f236]) ).
thf(f236,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK13 @ Y1 ) )
=> ( sK13 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK11 @ Y0 )
=> ( sK13 @ Y0 ) ) ) )
=> ( sK13 @ sK12 ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f235]) ).
thf(f235,plain,
( ( $false
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK11 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) )
@ sK13 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f234]) ).
thf(f234,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK11 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) ) )
= $false )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f233]) ).
thf(f233,plain,
( ( $false
= ( $true
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK11 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) ) ) ) )
| ~ spl0_1 ),
inference(backward_demodulation,[],[f230,f232]) ).
thf(f246,plain,
( ! [X1: a] :
( $true
= ( ( sK2 @ sK11 @ X1 )
=> ( sK13 @ X1 ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f245]) ).
thf(f245,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK2 @ sK11 @ Y0 )
=> ( sK13 @ Y0 ) )
@ X1 ) )
| ~ spl0_1 ),
inference(pi_clausification,[],[f241]) ).
thf(f241,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK11 @ Y0 )
=> ( sK13 @ Y0 ) ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f238]) ).
thf(f222,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f221]) ).
thf(f221,plain,
( $false
| ~ spl0_2
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f220]) ).
thf(f220,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_demodulation,[],[f136,f140]) ).
thf(f140,plain,
( ( $false
= ( sK6 @ sK4 ) )
| ~ spl0_2 ),
inference(not_proxy_clausification,[],[f129]) ).
thf(f129,plain,
( ( $true
= ( ~ ( sK6 @ sK4 ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f128]) ).
thf(f128,plain,
( ( $true
= ( ( sK6 @ sK4 )
=> $false ) )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f127,f106]) ).
thf(f106,plain,
( ( $false
= ( sK6 @ sK7 ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f103]) ).
thf(f103,plain,
( ( $false
= ( ( sK2 @ sK4 @ sK7 )
=> ( sK6 @ sK7 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f101]) ).
thf(f101,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) )
@ sK7 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f98]) ).
thf(f98,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) )
= $false )
| ~ spl0_2 ),
inference(not_proxy_clausification,[],[f95]) ).
thf(f95,plain,
( ( $true
= ( ~ ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f94]) ).
thf(f94,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) )
& $true ) ) )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f92,f41]) ).
thf(f41,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f40]) ).
thf(f40,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) )
& $true ) )
| ~ spl0_2 ),
inference(backward_demodulation,[],[f35,f38]) ).
thf(f38,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK3 @ Y0 )
=> ( sK6 @ Y0 ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f35]) ).
thf(f35,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK3 @ Y0 )
=> ( sK6 @ Y0 ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f33]) ).
thf(f33,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK3 @ Y0 )
=> ( sK6 @ Y0 ) ) ) )
=> ( sK6 @ sK5 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f32]) ).
thf(f32,plain,
( ( $false
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) )
@ sK6 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f31]) ).
thf(f31,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f30]) ).
thf(f30,plain,
( ( ( $true
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) ) ) )
= $false )
| ~ spl0_2 ),
inference(backward_demodulation,[],[f27,f29]) ).
thf(f29,plain,
( ( $true
= ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK5 ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f27]) ).
thf(f27,plain,
( ( $false
= ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK5 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK5 ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f26]) ).
thf(f26,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK3 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ sK4 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK3 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
@ sK5 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f25]) ).
thf(f25,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK3 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ sK4 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK3 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f24]) ).
thf(f24,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ sK3 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ sK3 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
@ sK4 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f23]) ).
thf(f23,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ sK3 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ sK3 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f22]) ).
thf(f22,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) )
@ sK3 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f18]) ).
thf(f18,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f17]) ).
thf(f17,plain,
( spl0_2
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f92,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f88]) ).
thf(f88,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) ) )
=> $false ) )
| ~ spl0_2 ),
inference(superposition,[],[f79,f37]) ).
thf(f37,plain,
( ( $false
= ( sK6 @ sK5 ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f36]) ).
thf(f36,plain,
( ( $false
= ( $true
=> ( sK6 @ sK5 ) ) )
| ~ spl0_2 ),
inference(backward_demodulation,[],[f33,f35]) ).
thf(f79,plain,
( ! [X1: a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( X1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( X1 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( X1 @ Y0 ) ) ) ) )
=> ( X1 @ sK5 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f78]) ).
thf(f78,plain,
( ! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK5 ) )
@ X1 ) )
| ~ spl0_2 ),
inference(pi_clausification,[],[f68]) ).
thf(f68,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK5 ) ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f67]) ).
thf(f67,plain,
( ( $true
= ( $true
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK5 ) ) ) ) )
| ~ spl0_2 ),
inference(backward_demodulation,[],[f29,f66]) ).
thf(f66,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f29]) ).
thf(f127,plain,
( ( $true
= ( ( sK6 @ sK4 )
=> ( sK6 @ sK7 ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f126]) ).
thf(f126,plain,
( ( $true
= ( ( ( sK6 @ sK4 )
& $true )
=> ( sK6 @ sK7 ) ) )
| ~ spl0_2 ),
inference(superposition,[],[f50,f107]) ).
thf(f107,plain,
( ( $true
= ( sK2 @ sK4 @ sK7 ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f103]) ).
thf(f50,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( ( sK6 @ X2 )
& ( sK2 @ X2 @ X1 ) )
=> ( sK6 @ X1 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f49]) ).
thf(f49,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK6 @ Y0 )
& ( sK2 @ Y0 @ X1 ) )
=> ( sK6 @ X1 ) )
@ X2 ) )
| ~ spl0_2 ),
inference(pi_clausification,[],[f45]) ).
thf(f45,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ Y0 )
& ( sK2 @ Y0 @ X1 ) )
=> ( sK6 @ X1 ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f44]) ).
thf(f44,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
@ X1 ) )
| ~ spl0_2 ),
inference(pi_clausification,[],[f41]) ).
thf(f136,plain,
( ( $true
= ( sK6 @ sK4 ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f135]) ).
thf(f135,plain,
( spl0_4
<=> ( $true
= ( sK6 @ sK4 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
thf(f219,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f218]) ).
thf(f218,plain,
( $false
| ~ spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f217]) ).
thf(f217,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f216,f171]) ).
thf(f171,plain,
( ( $false
= ( sK6 @ sK8 ) )
| ~ spl0_3 ),
inference(boolean_simplification,[],[f170]) ).
thf(f170,plain,
( ( ( $true
=> ( sK6 @ sK8 ) )
= $false )
| ~ spl0_3 ),
inference(backward_demodulation,[],[f164,f169]) ).
thf(f169,plain,
( ( $true
= ( ( sK2 @ sK9 @ sK8 )
& ( sK6 @ sK9 ) ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f164]) ).
thf(f164,plain,
( ( $false
= ( ( ( sK2 @ sK9 @ sK8 )
& ( sK6 @ sK9 ) )
=> ( sK6 @ sK8 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f163]) ).
thf(f163,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK2 @ Y0 @ sK8 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ sK8 ) )
@ sK9 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f147]) ).
thf(f147,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ Y0 @ sK8 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ sK8 ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f143]) ).
thf(f143,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) )
@ sK8 )
= $false )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f133]) ).
thf(f133,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f132]) ).
thf(f132,plain,
( spl0_3
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
thf(f216,plain,
( ( $true
= ( sK6 @ sK8 ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(boolean_simplification,[],[f215]) ).
thf(f215,plain,
( ( $true
= ( $true
=> ( sK6 @ sK8 ) ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f214,f199]) ).
thf(f199,plain,
( ( $true
= ( sK6 @ sK10 ) )
| ~ spl0_3 ),
inference(boolean_simplification,[],[f198]) ).
thf(f198,plain,
( ( $true
= ( $true
& ( sK6 @ sK10 ) ) )
| ~ spl0_3 ),
inference(backward_demodulation,[],[f190,f197]) ).
thf(f197,plain,
( ( $true
= ( sK2 @ sK10 @ sK8 ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f190]) ).
thf(f190,plain,
( ( $true
= ( ( sK2 @ sK10 @ sK8 )
& ( sK6 @ sK10 ) ) )
| ~ spl0_3 ),
inference(not_proxy_clausification,[],[f184]) ).
thf(f184,plain,
( ( $false
= ( ~ ( ( sK2 @ sK10 @ sK8 )
& ( sK6 @ sK10 ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f183]) ).
thf(f183,plain,
( ( $false
= ( ^ [Y0: a] :
~ ( ( sK2 @ Y0 @ sK8 )
& ( sK6 @ Y0 ) )
@ sK10 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f173]) ).
thf(f173,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
~ ( ( sK2 @ Y0 @ sK8 )
& ( sK6 @ Y0 ) ) ) )
| ~ spl0_3 ),
inference(boolean_simplification,[],[f172]) ).
thf(f172,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ Y0 @ sK8 )
& ( sK6 @ Y0 ) )
=> $false ) ) )
| ~ spl0_3 ),
inference(backward_demodulation,[],[f147,f171]) ).
thf(f214,plain,
( ( $true
= ( ( sK6 @ sK10 )
=> ( sK6 @ sK8 ) ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(boolean_simplification,[],[f213]) ).
thf(f213,plain,
( ( $true
= ( ( ( sK6 @ sK10 )
& $true )
=> ( sK6 @ sK8 ) ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[],[f50,f197]) ).
thf(f137,plain,
( spl0_3
| spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f130,f17,f135,f132]) ).
thf(f130,plain,
( ( $true
= ( sK6 @ sK4 ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f125]) ).
thf(f125,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) )
=> ( sK6 @ sK4 ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f124]) ).
thf(f124,plain,
( ( $true
= ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) ) )
=> ( sK6 @ sK4 ) ) )
| ~ spl0_2 ),
inference(superposition,[],[f113,f38]) ).
thf(f113,plain,
( ! [X1: a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK3 @ Y0 )
=> ( X1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( X1 @ Y1 ) )
=> ( X1 @ Y0 ) ) ) ) )
=> ( X1 @ sK4 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f112]) ).
thf(f112,plain,
( ! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK3 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK4 ) )
@ X1 ) )
| ~ spl0_2 ),
inference(pi_clausification,[],[f66]) ).
thf(f19,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f12,f17,f14]) ).
thf(f12,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f11]) ).
thf(f11,plain,
( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f10]) ).
thf(f10,plain,
( $false
= ( ^ [Y0: a > a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y1 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y5 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y1 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_clausification,[],[f7]) ).
thf(f7,plain,
( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y1 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y5 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y1 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y1 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y5 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y1 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y1 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y5 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y1 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y3 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
~ ! [X0: a > a > $o] :
( ! [X1: a,X2: a] :
( ( X0 @ X2 @ X1 )
=> ! [X3: a > $o] :
( ( ! [X4: a] :
( ( X0 @ X2 @ X4 )
=> ( X3 @ X4 ) )
& ! [X5: a,X6: a] :
( ( ( X3 @ X5 )
& ( X0 @ X5 @ X6 ) )
=> ( X3 @ X6 ) ) )
=> ( X3 @ X1 ) ) )
& ! [X7: a,X8: a,X9: a] :
( ( ! [X10: a > $o] :
( ( ! [X11: a,X12: a] :
( ( ( X0 @ X11 @ X12 )
& ( X10 @ X11 ) )
=> ( X10 @ X12 ) )
& ! [X13: a] :
( ( X0 @ X8 @ X13 )
=> ( X10 @ X13 ) ) )
=> ( X10 @ X7 ) )
& ! [X14: a > $o] :
( ( ! [X15: a,X16: a] :
( ( ( X14 @ X15 )
& ( X0 @ X15 @ X16 ) )
=> ( X14 @ X16 ) )
& ! [X17: a] :
( ( X0 @ X9 @ X17 )
=> ( X14 @ X17 ) ) )
=> ( X14 @ X8 ) ) )
=> ! [X18: a > $o] :
( ( ! [X19: a] :
( ( X0 @ X9 @ X19 )
=> ( X18 @ X19 ) )
& ! [X20: a,X21: a] :
( ( ( X0 @ X20 @ X21 )
& ( X18 @ X20 ) )
=> ( X18 @ X21 ) ) )
=> ( X18 @ X7 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > a > $o] :
( ! [X2: a,X1: a] :
( ( X0 @ X1 @ X2 )
=> ! [X3: a > $o] :
( ( ! [X4: a] :
( ( X0 @ X1 @ X4 )
=> ( X3 @ X4 ) )
& ! [X5: a,X4: a] :
( ( ( X3 @ X5 )
& ( X0 @ X5 @ X4 ) )
=> ( X3 @ X4 ) ) )
=> ( X3 @ X2 ) ) )
& ! [X6: a,X2: a,X1: a] :
( ( ! [X3: a > $o] :
( ( ! [X5: a,X4: a] :
( ( ( X0 @ X5 @ X4 )
& ( X3 @ X5 ) )
=> ( X3 @ X4 ) )
& ! [X4: a] :
( ( X0 @ X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ( X3 @ X6 ) )
& ! [X3: a > $o] :
( ( ! [X5: a,X4: a] :
( ( ( X3 @ X5 )
& ( X0 @ X5 @ X4 ) )
=> ( X3 @ X4 ) )
& ! [X4: a] :
( ( X0 @ X1 @ X4 )
=> ( X3 @ X4 ) ) )
=> ( X3 @ X2 ) ) )
=> ! [X3: a > $o] :
( ( ! [X4: a] :
( ( X0 @ X1 @ X4 )
=> ( X3 @ X4 ) )
& ! [X5: a,X4: a] :
( ( ( X0 @ X5 @ X4 )
& ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) )
=> ( X3 @ X6 ) ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
! [X0: a > a > $o] :
( ! [X2: a,X1: a] :
( ( X0 @ X1 @ X2 )
=> ! [X3: a > $o] :
( ( ! [X4: a] :
( ( X0 @ X1 @ X4 )
=> ( X3 @ X4 ) )
& ! [X5: a,X4: a] :
( ( ( X3 @ X5 )
& ( X0 @ X5 @ X4 ) )
=> ( X3 @ X4 ) ) )
=> ( X3 @ X2 ) ) )
& ! [X6: a,X2: a,X1: a] :
( ( ! [X3: a > $o] :
( ( ! [X5: a,X4: a] :
( ( ( X0 @ X5 @ X4 )
& ( X3 @ X5 ) )
=> ( X3 @ X4 ) )
& ! [X4: a] :
( ( X0 @ X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ( X3 @ X6 ) )
& ! [X3: a > $o] :
( ( ! [X5: a,X4: a] :
( ( ( X3 @ X5 )
& ( X0 @ X5 @ X4 ) )
=> ( X3 @ X4 ) )
& ! [X4: a] :
( ( X0 @ X1 @ X4 )
=> ( X3 @ X4 ) ) )
=> ( X3 @ X2 ) ) )
=> ! [X3: a > $o] :
( ( ! [X4: a] :
( ( X0 @ X1 @ X4 )
=> ( X3 @ X4 ) )
& ! [X5: a,X4: a] :
( ( ( X0 @ X5 @ X4 )
& ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) )
=> ( X3 @ X6 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM525_pme) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEV146^5 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.12 % Command : run_vampire %s %d THM
% 0.11/0.33 % Computer : n025.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 21 19:23:24 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.11/0.35 This is a TH0_THM_NEQ_NAR problem
% 0.11/0.35 Running higher-order theorem proving
% 0.11/0.35 Running /export/starexec/sandbox/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox/benchmark/theBenchmark.p -m 16384 -t 300
% 0.21/0.37 % (7694)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)
% 0.21/0.37 % (7692)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)
% 0.21/0.37 % (7691)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)
% 0.21/0.37 % (7695)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)
% 0.21/0.37 % (7690)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.21/0.37 % (7693)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.21/0.37 % (7693)Instruction limit reached!
% 0.21/0.37 % (7693)------------------------------
% 0.21/0.37 % (7693)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.37 % (7693)Termination reason: Unknown
% 0.21/0.37 % (7694)Instruction limit reached!
% 0.21/0.37 % (7694)------------------------------
% 0.21/0.37 % (7694)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.37 % (7694)Termination reason: Unknown
% 0.21/0.37 % (7694)Termination phase: Property scanning
% 0.21/0.37
% 0.21/0.37 % (7694)Memory used [KB]: 1023
% 0.21/0.37 % (7694)Time elapsed: 0.004 s
% 0.21/0.37 % (7694)Instructions burned: 3 (million)
% 0.21/0.37 % (7694)------------------------------
% 0.21/0.37 % (7694)------------------------------
% 0.21/0.37 % (7693)Termination phase: Preprocessing 3
% 0.21/0.37
% 0.21/0.37 % (7693)Memory used [KB]: 1023
% 0.21/0.37 % (7693)Time elapsed: 0.004 s
% 0.21/0.37 % (7693)Instructions burned: 2 (million)
% 0.21/0.37 % (7693)------------------------------
% 0.21/0.37 % (7693)------------------------------
% 0.21/0.37 % (7691)Instruction limit reached!
% 0.21/0.37 % (7691)------------------------------
% 0.21/0.37 % (7691)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.37 % (7691)Termination reason: Unknown
% 0.21/0.37 % (7691)Termination phase: Saturation
% 0.21/0.37
% 0.21/0.37 % (7691)Memory used [KB]: 1023
% 0.21/0.37 % (7691)Time elapsed: 0.005 s
% 0.21/0.37 % (7691)Instructions burned: 4 (million)
% 0.21/0.37 % (7691)------------------------------
% 0.21/0.37 % (7691)------------------------------
% 0.21/0.38 % (7695)Refutation not found, incomplete strategy
% 0.21/0.38 % (7695)------------------------------
% 0.21/0.38 % (7695)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.38 % (7695)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.38
% 0.21/0.38
% 0.21/0.38 % (7695)Memory used [KB]: 5500
% 0.21/0.38 % (7695)Time elapsed: 0.007 s
% 0.21/0.38 % (7695)Instructions burned: 5 (million)
% 0.21/0.38 % (7695)------------------------------
% 0.21/0.38 % (7695)------------------------------
% 0.21/0.38 % (7696)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.21/0.39 % (7696)Instruction limit reached!
% 0.21/0.39 % (7696)------------------------------
% 0.21/0.39 % (7696)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.39 % (7696)Termination reason: Unknown
% 0.21/0.39 % (7696)Termination phase: Saturation
% 0.21/0.39
% 0.21/0.39 % (7696)Memory used [KB]: 5756
% 0.21/0.39 % (7698)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)
% 0.21/0.39 % (7696)Time elapsed: 0.015 s
% 0.21/0.39 % (7696)Instructions burned: 19 (million)
% 0.21/0.39 % (7696)------------------------------
% 0.21/0.39 % (7696)------------------------------
% 0.21/0.39 % (7699)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)
% 0.21/0.39 % (7697)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)
% 0.21/0.39 % (7692)Instruction limit reached!
% 0.21/0.39 % (7692)------------------------------
% 0.21/0.39 % (7692)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.39 % (7692)Termination reason: Unknown
% 0.21/0.39 % (7692)Termination phase: Saturation
% 0.21/0.39
% 0.21/0.39 % (7692)Memory used [KB]: 5756
% 0.21/0.39 % (7692)Time elapsed: 0.022 s
% 0.21/0.39 % (7692)Instructions burned: 27 (million)
% 0.21/0.39 % (7692)------------------------------
% 0.21/0.39 % (7692)------------------------------
% 0.21/0.39 % (7697)Instruction limit reached!
% 0.21/0.39 % (7697)------------------------------
% 0.21/0.39 % (7697)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.39 % (7697)Termination reason: Unknown
% 0.21/0.39 % (7697)Termination phase: Property scanning
% 0.21/0.39
% 0.21/0.39 % (7697)Memory used [KB]: 1023
% 0.21/0.39 % (7697)Time elapsed: 0.004 s
% 0.21/0.39 % (7697)Instructions burned: 3 (million)
% 0.21/0.39 % (7697)------------------------------
% 0.21/0.39 % (7697)------------------------------
% 0.21/0.39 % (7700)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)
% 0.21/0.39 % (7700)Instruction limit reached!
% 0.21/0.39 % (7700)------------------------------
% 0.21/0.39 % (7700)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.39 % (7700)Termination reason: Unknown
% 0.21/0.39 % (7700)Termination phase: Preprocessing 3
% 0.21/0.39
% 0.21/0.39 % (7700)Memory used [KB]: 1023
% 0.21/0.39 % (7700)Time elapsed: 0.004 s
% 0.21/0.39 % (7700)Instructions burned: 3 (million)
% 0.21/0.39 % (7700)------------------------------
% 0.21/0.39 % (7700)------------------------------
% 0.21/0.40 % (7699)Instruction limit reached!
% 0.21/0.40 % (7699)------------------------------
% 0.21/0.40 % (7699)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.40 % (7699)Termination reason: Unknown
% 0.21/0.40 % (7699)Termination phase: Saturation
% 0.21/0.40
% 0.21/0.40 % (7699)Memory used [KB]: 5756
% 0.21/0.40 % (7699)Time elapsed: 0.013 s
% 0.21/0.40 % (7699)Instructions burned: 15 (million)
% 0.21/0.40 % (7699)------------------------------
% 0.21/0.40 % (7699)------------------------------
% 0.21/0.41 % (7701)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)
% 0.21/0.41 % (7702)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.41 % (7703)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.21/0.41 % (7704)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)
% 0.21/0.41 % (7702)Instruction limit reached!
% 0.21/0.41 % (7702)------------------------------
% 0.21/0.41 % (7702)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.41 % (7702)Termination reason: Unknown
% 0.21/0.41 % (7702)Termination phase: Saturation
% 0.21/0.41
% 0.21/0.41 % (7702)Memory used [KB]: 1023
% 0.21/0.41 % (7702)Time elapsed: 0.007 s
% 0.21/0.41 % (7702)Instructions burned: 7 (million)
% 0.21/0.41 % (7702)------------------------------
% 0.21/0.41 % (7702)------------------------------
% 0.21/0.41 % (7698)Instruction limit reached!
% 0.21/0.41 % (7698)------------------------------
% 0.21/0.41 % (7698)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.41 % (7698)Termination reason: Unknown
% 0.21/0.41 % (7698)Termination phase: Saturation
% 0.21/0.41 % (7704)Instruction limit reached!
% 0.21/0.41 % (7704)------------------------------
% 0.21/0.41 % (7704)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.41 % (7704)Termination reason: Unknown
% 0.21/0.41 % (7704)Termination phase: Preprocessing 3
% 0.21/0.41
% 0.21/0.41 % (7704)Memory used [KB]: 1023
% 0.21/0.41 % (7704)Time elapsed: 0.004 s
% 0.21/0.41 % (7704)Instructions burned: 3 (million)
% 0.21/0.41 % (7704)------------------------------
% 0.21/0.41 % (7704)------------------------------
% 0.21/0.41
% 0.21/0.41 % (7698)Memory used [KB]: 5628
% 0.21/0.41 % (7698)Time elapsed: 0.025 s
% 0.21/0.41 % (7698)Instructions burned: 37 (million)
% 0.21/0.41 % (7698)------------------------------
% 0.21/0.41 % (7698)------------------------------
% 0.21/0.42 % (7705)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)
% 0.21/0.42 % (7705)Instruction limit reached!
% 0.21/0.42 % (7705)------------------------------
% 0.21/0.42 % (7705)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.42 % (7705)Termination reason: Unknown
% 0.21/0.42 % (7705)Termination phase: Preprocessing 3
% 0.21/0.42
% 0.21/0.42 % (7705)Memory used [KB]: 1023
% 0.21/0.42 % (7705)Time elapsed: 0.004 s
% 0.21/0.42 % (7705)Instructions burned: 3 (million)
% 0.21/0.42 % (7705)------------------------------
% 0.21/0.42 % (7705)------------------------------
% 0.21/0.42 % (7703)Instruction limit reached!
% 0.21/0.42 % (7703)------------------------------
% 0.21/0.42 % (7703)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.42 % (7703)Termination reason: Unknown
% 0.21/0.42 % (7703)Termination phase: Saturation
% 0.21/0.42
% 0.21/0.42 % (7703)Memory used [KB]: 5628
% 0.21/0.42 % (7703)Time elapsed: 0.035 s
% 0.21/0.42 % (7703)Instructions burned: 16 (million)
% 0.21/0.42 % (7703)------------------------------
% 0.21/0.42 % (7703)------------------------------
% 0.21/0.43 % (7706)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)
% 0.21/0.43 % (7707)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)
% 0.21/0.43 % (7708)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.21/0.43 % (7707)Instruction limit reached!
% 0.21/0.43 % (7707)------------------------------
% 0.21/0.43 % (7707)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.43 % (7707)Termination reason: Unknown
% 0.21/0.43 % (7707)Termination phase: Saturation
% 0.21/0.43
% 0.21/0.43 % (7707)Memory used [KB]: 5500
% 0.21/0.43 % (7707)Time elapsed: 0.004 s
% 0.21/0.43 % (7707)Instructions burned: 3 (million)
% 0.21/0.43 % (7707)------------------------------
% 0.21/0.43 % (7707)------------------------------
% 0.21/0.43 % (7708)Instruction limit reached!
% 0.21/0.43 % (7708)------------------------------
% 0.21/0.43 % (7708)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.43 % (7708)Termination reason: Unknown
% 0.21/0.43 % (7708)Termination phase: Saturation
% 0.21/0.43
% 0.21/0.43 % (7708)Memory used [KB]: 5500
% 0.21/0.43 % (7708)Time elapsed: 0.005 s
% 0.21/0.43 % (7708)Instructions burned: 4 (million)
% 0.21/0.43 % (7708)------------------------------
% 0.21/0.43 % (7708)------------------------------
% 0.21/0.43 % (7706)Instruction limit reached!
% 0.21/0.43 % (7706)------------------------------
% 0.21/0.43 % (7706)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.43 % (7706)Termination reason: Unknown
% 0.21/0.43 % (7706)Termination phase: Saturation
% 0.21/0.43
% 0.21/0.43 % (7706)Memory used [KB]: 5500
% 0.21/0.43 % (7706)Time elapsed: 0.007 s
% 0.21/0.43 % (7706)Instructions burned: 7 (million)
% 0.21/0.43 % (7706)------------------------------
% 0.21/0.43 % (7706)------------------------------
% 0.21/0.43 % (7709)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)
% 0.21/0.43 % (7710)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.21/0.44 % (7701)First to succeed.
% 0.21/0.44 % (7701)Refutation found. Thanks to Tanya!
% 0.21/0.44 % SZS status Theorem for theBenchmark
% 0.21/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.45 % (7701)------------------------------
% 0.21/0.45 % (7701)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.45 % (7701)Termination reason: Refutation
% 0.21/0.45
% 0.21/0.45 % (7701)Memory used [KB]: 5884
% 0.21/0.45 % (7701)Time elapsed: 0.060 s
% 0.21/0.45 % (7701)Instructions burned: 47 (million)
% 0.21/0.45 % (7701)------------------------------
% 0.21/0.45 % (7701)------------------------------
% 0.21/0.45 % (7689)Success in time 0.094 s
%------------------------------------------------------------------------------