TSTP Solution File: SEV046^5 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEV046^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n021.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 : Tue May 21 04:11:50 EDT 2024
% Result : Theorem 0.18s 0.46s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 20
% Syntax : Number of formulae : 181 ( 41 unt; 17 typ; 0 def)
% Number of atoms : 1473 ( 179 equ; 0 cnn)
% Maximal formula atoms : 2 ( 8 avg)
% Number of connectives : 4236 ( 132 ~; 121 |; 160 &;2963 @)
% ( 2 <=>; 350 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 230 ( 230 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 15 usr; 9 con; 0-3 aty)
% ( 508 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 715 ( 539 ^ 175 !; 0 ?; 715 :)
% ( 1 !>; 0 ?*; 0 @-; 0 @+)
% 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 > b > b > $o ).
thf(func_def_21,type,
sK3: a > a > $o ).
thf(func_def_22,type,
sK4: a > b ).
thf(func_def_23,type,
sK5: a > b ).
thf(func_def_24,type,
sK6: a > b ).
thf(func_def_25,type,
sK7: a ).
thf(func_def_26,type,
sK8: a > b ).
thf(func_def_27,type,
sK9: a ).
thf(func_def_28,type,
sK10: a > b ).
thf(func_def_29,type,
sK11: a > b ).
thf(func_def_30,type,
sK12: a ).
thf(func_def_31,type,
sK13: a ).
thf(f829,plain,
$false,
inference(avatar_sat_refutation,[],[f25,f577,f828]) ).
thf(f828,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f827]) ).
thf(f827,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f826]) ).
thf(f826,plain,
( ( $false = $true )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f825]) ).
thf(f825,plain,
( ( $true = ~ $true )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f815,f662]) ).
thf(f662,plain,
( ( ( sK2 @ sK12 @ ( sK11 @ sK12 ) @ ( sK10 @ sK13 ) )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f660]) ).
thf(f660,plain,
( ( $true
= ( $true
=> ( sK2 @ sK12 @ ( sK11 @ sK12 ) @ ( sK10 @ sK13 ) ) ) )
| ~ spl0_1 ),
inference(superposition,[],[f636,f608]) ).
thf(f608,plain,
( ( $true
= ( sK3 @ sK12 @ sK13 ) )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f600]) ).
thf(f600,plain,
( ( $true
= ( $true
=> ( sK3 @ sK12 @ sK13 ) ) )
| ~ spl0_1 ),
inference(superposition,[],[f103,f595]) ).
thf(f595,plain,
( ( $true
= ( sK3 @ sK13 @ sK12 ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f593]) ).
thf(f593,plain,
( ( $false
= ( ( sK3 @ sK13 @ sK12 )
=> ( sK2 @ sK13 @ ( sK10 @ sK13 ) @ ( sK11 @ sK12 ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f592]) ).
thf(f592,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK3 @ Y0 @ sK12 )
=> ( sK2 @ Y0 @ ( sK10 @ Y0 ) @ ( sK11 @ sK12 ) ) )
@ sK13 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f591]) ).
thf(f591,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ sK12 )
=> ( sK2 @ Y0 @ ( sK10 @ Y0 ) @ ( sK11 @ sK12 ) ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f590]) ).
thf(f590,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK2 @ Y1 @ ( sK10 @ Y1 ) @ ( sK11 @ Y0 ) ) ) )
@ sK12 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f584]) ).
thf(f584,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK2 @ Y1 @ ( sK10 @ Y1 ) @ ( sK11 @ Y0 ) ) ) ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f583]) ).
thf(f583,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK2 @ Y0 @ ( sK11 @ Y0 ) @ ( sK10 @ Y1 ) ) ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK2 @ Y1 @ ( sK10 @ Y1 ) @ ( sK11 @ Y0 ) ) ) ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f582]) ).
thf(f582,plain,
( ( $false
= ( ^ [Y0: a > b] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( sK2 @ Y1 @ ( Y0 @ Y1 ) @ ( sK10 @ Y2 ) ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( sK2 @ Y2 @ ( sK10 @ Y2 ) @ ( Y0 @ Y1 ) ) ) ) ) )
@ sK11 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f581]) ).
thf(f581,plain,
( ( $false
= ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( sK2 @ Y1 @ ( Y0 @ Y1 ) @ ( sK10 @ Y2 ) ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( sK2 @ Y2 @ ( sK10 @ Y2 ) @ ( Y0 @ Y1 ) ) ) ) ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f580]) ).
thf(f580,plain,
( ( $false
= ( ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( sK2 @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y3 @ Y2 )
=> ( sK2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y2 ) ) ) ) ) ) )
@ sK10 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f21]) ).
thf(f21,plain,
( ( $false
= ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( sK2 @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y3 @ Y2 )
=> ( sK2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y2 ) ) ) ) ) ) ) ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f20]) ).
thf(f20,plain,
( spl0_1
<=> ( $false
= ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( sK2 @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y3 @ Y2 )
=> ( sK2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y2 ) ) ) ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f103,plain,
! [X2: a,X1: a] :
( $true
= ( ( sK3 @ X2 @ X1 )
=> ( sK3 @ X1 @ X2 ) ) ),
inference(beta_eta_normalization,[],[f102]) ).
thf(f102,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK3 @ Y0 @ X1 )
=> ( sK3 @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_clausification,[],[f101]) ).
thf(f101,plain,
! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ X1 )
=> ( sK3 @ X1 @ Y0 ) ) )
= $true ),
inference(beta_eta_normalization,[],[f100]) ).
thf(f100,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK3 @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_clausification,[],[f99]) ).
thf(f99,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK3 @ Y0 @ Y1 ) ) ) )
= $true ),
inference(boolean_simplification,[],[f98]) ).
thf(f98,plain,
( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK3 @ Y0 @ Y1 ) ) ) ) ) ),
inference(backward_demodulation,[],[f93,f97]) ).
thf(f97,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ Y0 )
=> ( ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( ( sK2 @ Y0 @ Y2 @ Y3 )
& ( sK2 @ Y0 @ Y1 @ Y2 ) )
=> ( sK2 @ Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( sK2 @ Y0 @ Y2 @ Y1 )
=> ( sK2 @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f93]) ).
thf(f93,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ Y0 )
=> ( ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( ( sK2 @ Y0 @ Y2 @ Y3 )
& ( sK2 @ Y0 @ Y1 @ Y2 ) )
=> ( sK2 @ Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( sK2 @ Y0 @ Y2 @ Y1 )
=> ( sK2 @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK3 @ Y0 @ Y1 ) ) ) ) ) ),
inference(boolean_simplification,[],[f92]) ).
thf(f92,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ Y0 )
=> ( ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( ( sK2 @ Y0 @ Y2 @ Y3 )
& ( sK2 @ Y0 @ Y1 @ Y2 ) )
=> ( sK2 @ Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( sK2 @ Y0 @ Y2 @ Y1 )
=> ( sK2 @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK3 @ Y0 @ Y1 ) ) ) )
& $true ) ),
inference(backward_demodulation,[],[f15,f90]) ).
thf(f90,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y0 )
& ( sK3 @ Y2 @ Y1 ) )
=> ( sK3 @ Y2 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f15]) ).
thf(f15,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ Y0 )
=> ( ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( ( sK2 @ Y0 @ Y2 @ Y3 )
& ( sK2 @ Y0 @ Y1 @ Y2 ) )
=> ( sK2 @ Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( sK2 @ Y0 @ Y2 @ Y1 )
=> ( sK2 @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK3 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y0 )
& ( sK3 @ Y2 @ Y1 ) )
=> ( sK3 @ Y2 @ Y0 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f13]) ).
thf(f13,plain,
( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ Y0 )
=> ( ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( ( sK2 @ Y0 @ Y2 @ Y3 )
& ( sK2 @ Y0 @ Y1 @ Y2 ) )
=> ( sK2 @ Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( sK2 @ Y0 @ Y2 @ Y1 )
=> ( sK2 @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK3 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y0 )
& ( sK3 @ Y2 @ Y1 ) )
=> ( sK3 @ Y2 @ Y0 ) ) ) ) ) )
=> ( ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( sK2 @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y3 @ Y2 )
=> ( sK2 @ 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] :
( ( sK3 @ Y3 @ Y4 )
=> ( sK2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( sK2 @ Y3 @ ( Y2 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( sK2 @ Y4 @ ( Y0 @ Y4 ) @ ( Y1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f12]) ).
thf(f12,plain,
( $false
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y1 )
=> ( ( sK2 @ Y2 )
= ( sK2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 @ Y1 )
=> ( ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( ( ( sK2 @ Y1 @ Y3 @ Y4 )
& ( sK2 @ Y1 @ Y2 @ Y3 ) )
=> ( sK2 @ Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( sK2 @ Y1 @ Y3 @ Y2 )
=> ( sK2 @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( ( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y3 @ Y4 )
=> ( sK2 @ Y3 @ ( Y2 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) )
=> ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 @ Y3 )
=> ( sK2 @ 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] :
( ( Y0 @ Y4 @ Y5 )
=> ( sK2 @ Y4 @ ( Y1 @ Y4 ) @ ( Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( sK2 @ Y4 @ ( Y3 @ Y4 ) @ ( Y2 @ Y5 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y5 @ Y4 )
=> ( sK2 @ Y5 @ ( Y1 @ Y5 ) @ ( Y2 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ sK3 ) ),
inference(sigma_clausification,[],[f11]) ).
thf(f11,plain,
( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y1 )
=> ( ( sK2 @ Y2 )
= ( sK2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 @ Y1 )
=> ( ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( ( ( sK2 @ Y1 @ Y3 @ Y4 )
& ( sK2 @ Y1 @ Y2 @ Y3 ) )
=> ( sK2 @ Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( sK2 @ Y1 @ Y3 @ Y2 )
=> ( sK2 @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( ( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y3 @ Y4 )
=> ( sK2 @ Y3 @ ( Y2 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) )
=> ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y4 @ Y3 )
=> ( sK2 @ 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] :
( ( Y0 @ Y4 @ Y5 )
=> ( sK2 @ Y4 @ ( Y1 @ Y4 ) @ ( Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y4 @ Y5 )
=> ( sK2 @ Y4 @ ( Y3 @ Y4 ) @ ( Y2 @ Y5 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y5 @ Y4 )
=> ( sK2 @ Y5 @ ( Y1 @ Y5 ) @ ( Y2 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f10]) ).
thf(f10,plain,
( $false
= ( ^ [Y0: a > b > b > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 @ Y2 )
=> ( ( Y0 @ Y3 )
= ( Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 @ Y2 )
=> ( ( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( !! @ b
@ ^ [Y5: b] :
( ( ( Y0 @ Y2 @ Y4 @ Y5 )
& ( Y0 @ Y2 @ Y3 @ Y4 ) )
=> ( Y0 @ Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( ( Y0 @ Y2 @ Y4 @ Y3 )
=> ( Y0 @ Y2 @ Y3 @ Y4 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 @ Y2 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( a > b )
@ ^ [Y2: a > b] :
( !! @ ( a > b )
@ ^ [Y3: a > b] :
( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y1 @ Y4 @ Y5 )
=> ( Y0 @ Y4 @ ( Y3 @ Y4 ) @ ( Y2 @ Y5 ) ) ) ) )
=> ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y1 @ Y5 @ Y4 )
=> ( Y0 @ 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] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y0 @ Y5 @ ( Y2 @ Y5 ) @ ( Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y0 @ Y5 @ ( Y4 @ Y5 ) @ ( Y3 @ Y6 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y6 @ Y5 )
=> ( Y0 @ Y6 @ ( Y2 @ Y6 ) @ ( Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_clausification,[],[f7]) ).
thf(f7,plain,
( $false
= ( !! @ ( a > b > b > $o )
@ ^ [Y0: a > b > b > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 @ Y2 )
=> ( ( Y0 @ Y3 )
= ( Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 @ Y2 )
=> ( ( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( !! @ b
@ ^ [Y5: b] :
( ( ( Y0 @ Y2 @ Y4 @ Y5 )
& ( Y0 @ Y2 @ Y3 @ Y4 ) )
=> ( Y0 @ Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( ( Y0 @ Y2 @ Y4 @ Y3 )
=> ( Y0 @ Y2 @ Y3 @ Y4 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 @ Y2 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( a > b )
@ ^ [Y2: a > b] :
( !! @ ( a > b )
@ ^ [Y3: a > b] :
( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y1 @ Y4 @ Y5 )
=> ( Y0 @ Y4 @ ( Y3 @ Y4 ) @ ( Y2 @ Y5 ) ) ) ) )
=> ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y1 @ Y5 @ Y4 )
=> ( Y0 @ 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] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y0 @ Y5 @ ( Y2 @ Y5 ) @ ( Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y0 @ Y5 @ ( Y4 @ Y5 ) @ ( Y3 @ Y6 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y6 @ Y5 )
=> ( Y0 @ Y6 @ ( Y2 @ Y6 ) @ ( Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( !! @ ( a > b > b > $o )
@ ^ [Y0: a > b > b > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 @ Y2 )
=> ( ( Y0 @ Y3 )
= ( Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 @ Y2 )
=> ( ( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( !! @ b
@ ^ [Y5: b] :
( ( ( Y0 @ Y2 @ Y4 @ Y5 )
& ( Y0 @ Y2 @ Y3 @ Y4 ) )
=> ( Y0 @ Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( ( Y0 @ Y2 @ Y4 @ Y3 )
=> ( Y0 @ Y2 @ Y3 @ Y4 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 @ Y2 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( a > b )
@ ^ [Y2: a > b] :
( !! @ ( a > b )
@ ^ [Y3: a > b] :
( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y1 @ Y4 @ Y5 )
=> ( Y0 @ Y4 @ ( Y3 @ Y4 ) @ ( Y2 @ Y5 ) ) ) ) )
=> ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y1 @ Y5 @ Y4 )
=> ( Y0 @ 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] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y0 @ Y5 @ ( Y2 @ Y5 ) @ ( Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y0 @ Y5 @ ( Y4 @ Y5 ) @ ( Y3 @ Y6 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y6 @ Y5 )
=> ( Y0 @ Y6 @ ( Y2 @ Y6 ) @ ( Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( !! @ ( a > b > b > $o )
@ ^ [Y0: a > b > b > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 @ Y2 )
=> ( ( Y0 @ Y3 )
= ( Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( Y1 @ Y2 @ Y2 )
=> ( ( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( !! @ b
@ ^ [Y5: b] :
( ( ( Y0 @ Y2 @ Y4 @ Y5 )
& ( Y0 @ Y2 @ Y3 @ Y4 ) )
=> ( Y0 @ Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ b
@ ^ [Y3: b] :
( !! @ b
@ ^ [Y4: b] :
( ( Y0 @ Y2 @ Y4 @ Y3 )
=> ( Y0 @ Y2 @ Y3 @ Y4 ) ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y1 @ Y3 @ Y2 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) ) )
=> ( ( !! @ ( a > b )
@ ^ [Y2: a > b] :
( !! @ ( a > b )
@ ^ [Y3: a > b] :
( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y1 @ Y4 @ Y5 )
=> ( Y0 @ Y4 @ ( Y3 @ Y4 ) @ ( Y2 @ Y5 ) ) ) ) )
=> ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y1 @ Y5 @ Y4 )
=> ( Y0 @ 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] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y0 @ Y5 @ ( Y2 @ Y5 ) @ ( Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y5 @ Y6 )
=> ( Y0 @ Y5 @ ( Y4 @ Y5 ) @ ( Y3 @ Y6 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y6 @ Y5 )
=> ( Y0 @ Y6 @ ( Y2 @ Y6 ) @ ( Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
~ ! [X0: a > a > $o,X1: a > b > b > $o] :
( ( ! [X2: a,X3: a,X4: a] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X3 @ X4 ) )
=> ( X0 @ X2 @ X4 ) )
& ! [X5: a,X6: a] :
( ( X0 @ X5 @ X6 )
=> ( X0 @ X6 @ X5 ) )
& ! [X7: a] :
( ( X0 @ X7 @ X7 )
=> ( ! [X8: b,X9: b] :
( ( X1 @ X7 @ X8 @ X9 )
=> ( X1 @ X7 @ X9 @ X8 ) )
& ! [X10: b,X11: b,X12: b] :
( ( ( X1 @ X7 @ X12 @ X11 )
& ( X1 @ X7 @ X11 @ X10 ) )
=> ( X1 @ X7 @ X12 @ X10 ) ) ) )
& ! [X13: a,X14: a] :
( ( X0 @ X13 @ X14 )
=> ( ( X1 @ X13 )
= ( X1 @ X14 ) ) ) )
=> ( ! [X15: a > b,X16: a > b,X17: a > b] :
( ( ! [X18: a,X19: a] :
( ( X0 @ X19 @ X18 )
=> ( X1 @ X19 @ ( X15 @ X19 ) @ ( X16 @ X18 ) ) )
& ! [X20: a,X21: a] :
( ( X0 @ X21 @ X20 )
=> ( X1 @ X21 @ ( X17 @ X21 ) @ ( X15 @ X20 ) ) ) )
=> ! [X22: a,X23: a] :
( ( X0 @ X22 @ X23 )
=> ( X1 @ X22 @ ( X17 @ X22 ) @ ( X16 @ X23 ) ) ) )
& ! [X24: a > b,X25: a > b] :
( ! [X26: a,X27: a] :
( ( X0 @ X27 @ X26 )
=> ( X1 @ X27 @ ( X24 @ X27 ) @ ( X25 @ X26 ) ) )
=> ! [X28: a,X29: a] :
( ( X0 @ X28 @ X29 )
=> ( X1 @ X28 @ ( X25 @ X28 ) @ ( X24 @ X29 ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > a > $o,X1: a > b > b > $o] :
( ( ! [X2: a,X3: a,X4: a] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X3 @ X4 ) )
=> ( X0 @ X2 @ X4 ) )
& ! [X2: a,X3: a] :
( ( X0 @ X2 @ X3 )
=> ( X0 @ X3 @ X2 ) )
& ! [X2: a] :
( ( X0 @ X2 @ X2 )
=> ( ! [X5: b,X3: b] :
( ( X1 @ X2 @ X5 @ X3 )
=> ( X1 @ X2 @ X3 @ X5 ) )
& ! [X4: b,X3: b,X5: b] :
( ( ( X1 @ X2 @ X5 @ X3 )
& ( X1 @ X2 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X5 @ X4 ) ) ) )
& ! [X2: a,X3: a] :
( ( X0 @ X2 @ X3 )
=> ( ( X1 @ X2 )
= ( X1 @ X3 ) ) ) )
=> ( ! [X3: a > b,X4: a > b,X2: a > b] :
( ( ! [X6: a,X5: a] :
( ( X0 @ X5 @ X6 )
=> ( X1 @ X5 @ ( X3 @ X5 ) @ ( X4 @ X6 ) ) )
& ! [X6: a,X5: a] :
( ( X0 @ X5 @ X6 )
=> ( X1 @ X5 @ ( X2 @ X5 ) @ ( X3 @ 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,
! [X0: a > a > $o,X1: a > b > b > $o] :
( ( ! [X2: a,X3: a,X4: a] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X3 @ X4 ) )
=> ( X0 @ X2 @ X4 ) )
& ! [X2: a,X3: a] :
( ( X0 @ X2 @ X3 )
=> ( X0 @ X3 @ X2 ) )
& ! [X2: a] :
( ( X0 @ X2 @ X2 )
=> ( ! [X5: b,X3: b] :
( ( X1 @ X2 @ X5 @ X3 )
=> ( X1 @ X2 @ X3 @ X5 ) )
& ! [X4: b,X3: b,X5: b] :
( ( ( X1 @ X2 @ X5 @ X3 )
& ( X1 @ X2 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X5 @ X4 ) ) ) )
& ! [X2: a,X3: a] :
( ( X0 @ X2 @ X3 )
=> ( ( X1 @ X2 )
= ( X1 @ X3 ) ) ) )
=> ( ! [X3: a > b,X4: a > b,X2: a > b] :
( ( ! [X6: a,X5: a] :
( ( X0 @ X5 @ X6 )
=> ( X1 @ X5 @ ( X3 @ X5 ) @ ( X4 @ X6 ) ) )
& ! [X6: a,X5: a] :
( ( X0 @ X5 @ X6 )
=> ( X1 @ X5 @ ( X2 @ X5 ) @ ( X3 @ 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/sandbox/benchmark/theBenchmark.p',cTHM507_pme) ).
thf(f636,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( sK3 @ X1 @ X2 )
=> ( sK2 @ X1 @ ( sK11 @ X1 ) @ ( sK10 @ X2 ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f635]) ).
thf(f635,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK3 @ X1 @ Y0 )
=> ( sK2 @ X1 @ ( sK11 @ X1 ) @ ( sK10 @ Y0 ) ) )
@ X2 ) )
| ~ spl0_1 ),
inference(pi_clausification,[],[f625]) ).
thf(f625,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ X1 @ Y0 )
=> ( sK2 @ X1 @ ( sK11 @ X1 ) @ ( sK10 @ Y0 ) ) ) )
= $true )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f624]) ).
thf(f624,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK2 @ Y0 @ ( sK11 @ Y0 ) @ ( sK10 @ Y1 ) ) ) )
@ X1 ) )
| ~ spl0_1 ),
inference(pi_clausification,[],[f585]) ).
thf(f585,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK2 @ Y0 @ ( sK11 @ Y0 ) @ ( sK10 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f583]) ).
thf(f815,plain,
( ( $true
= ( ~ ( sK2 @ sK12 @ ( sK11 @ sK12 ) @ ( sK10 @ sK13 ) ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f800]) ).
thf(f800,plain,
( ( $true
= ( ( sK2 @ sK12 @ ( sK11 @ sK12 ) @ ( sK10 @ sK13 ) )
=> $false ) )
| ~ spl0_1 ),
inference(superposition,[],[f796,f759]) ).
thf(f759,plain,
( ( $false
= ( sK2 @ sK12 @ ( sK10 @ sK13 ) @ ( sK11 @ sK12 ) ) )
| ~ spl0_1 ),
inference(superposition,[],[f743,f599]) ).
thf(f599,plain,
( ( $false
= ( sK2 @ sK13 @ ( sK10 @ sK13 ) @ ( sK11 @ sK12 ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f598]) ).
thf(f598,plain,
( ( $false
= ( $true
=> ( sK2 @ sK13 @ ( sK10 @ sK13 ) @ ( sK11 @ sK12 ) ) ) )
| ~ spl0_1 ),
inference(backward_demodulation,[],[f593,f595]) ).
thf(f743,plain,
( ! [X2: b,X1: b] :
( ( sK2 @ sK12 @ X1 @ X2 )
= ( sK2 @ sK13 @ X1 @ X2 ) )
| ~ spl0_1 ),
inference(argument_congruence,[],[f740]) ).
thf(f740,plain,
( ! [X1: b] :
( ( sK2 @ sK13 @ X1 )
= ( sK2 @ sK12 @ X1 ) )
| ~ spl0_1 ),
inference(argument_congruence,[],[f733]) ).
thf(f733,plain,
( ( ( sK2 @ sK12 )
= ( sK2 @ sK13 ) )
| ~ spl0_1 ),
inference(equality_proxy_clausification,[],[f607]) ).
thf(f607,plain,
( ( $true
= ( ( sK2 @ sK13 )
= ( sK2 @ sK12 ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f605]) ).
thf(f605,plain,
( ( ( $true
=> ( ( sK2 @ sK13 )
= ( sK2 @ sK12 ) ) )
= $true )
| ~ spl0_1 ),
inference(superposition,[],[f231,f595]) ).
thf(f231,plain,
! [X2: a,X1: a] :
( $true
= ( ( sK3 @ X2 @ X1 )
=> ( ( sK2 @ X2 )
= ( sK2 @ X1 ) ) ) ),
inference(beta_eta_normalization,[],[f230]) ).
thf(f230,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK3 @ Y0 @ X1 )
=> ( ( sK2 @ Y0 )
= ( sK2 @ X1 ) ) )
@ X2 ) ),
inference(pi_clausification,[],[f227]) ).
thf(f227,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ X1 )
=> ( ( sK2 @ Y0 )
= ( sK2 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[],[f226]) ).
thf(f226,plain,
! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[],[f156]) ).
thf(f156,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( ( sK2 @ Y1 )
= ( sK2 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f97]) ).
thf(f796,plain,
( ! [X2: b,X1: b] :
( ( ( sK2 @ sK12 @ X2 @ X1 )
=> ( sK2 @ sK12 @ X1 @ X2 ) )
= $true )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f795]) ).
thf(f795,plain,
( ! [X2: b,X1: b] :
( $true
= ( ^ [Y0: b] :
( ( sK2 @ sK12 @ Y0 @ X1 )
=> ( sK2 @ sK12 @ X1 @ Y0 ) )
@ X2 ) )
| ~ spl0_1 ),
inference(pi_clausification,[],[f787]) ).
thf(f787,plain,
( ! [X1: b] :
( $true
= ( !! @ b
@ ^ [Y0: b] :
( ( sK2 @ sK12 @ Y0 @ X1 )
=> ( sK2 @ sK12 @ X1 @ Y0 ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f785]) ).
thf(f785,plain,
( ! [X1: b] :
( $true
= ( ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK2 @ sK12 @ Y1 @ Y0 )
=> ( sK2 @ sK12 @ Y0 @ Y1 ) ) )
@ X1 ) )
| ~ spl0_1 ),
inference(pi_clausification,[],[f784]) ).
thf(f784,plain,
( ( ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK2 @ sK12 @ Y1 @ Y0 )
=> ( sK2 @ sK12 @ Y0 @ Y1 ) ) ) )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f783]) ).
thf(f783,plain,
( ( $true
= ( $true
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK2 @ sK12 @ Y1 @ Y0 )
=> ( sK2 @ sK12 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_1 ),
inference(backward_demodulation,[],[f652,f780]) ).
thf(f780,plain,
( ( $true
= ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK2 @ sK12 @ Y1 @ Y2 )
& ( sK2 @ sK12 @ Y0 @ Y1 ) )
=> ( sK2 @ sK12 @ Y0 @ Y2 ) ) ) ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f652]) ).
thf(f652,plain,
( ( ( ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK2 @ sK12 @ Y1 @ Y2 )
& ( sK2 @ sK12 @ Y0 @ Y1 ) )
=> ( sK2 @ sK12 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK2 @ sK12 @ Y1 @ Y0 )
=> ( sK2 @ sK12 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f638]) ).
thf(f638,plain,
( ( $true
= ( $true
=> ( ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK2 @ sK12 @ Y1 @ Y2 )
& ( sK2 @ sK12 @ Y0 @ Y1 ) )
=> ( sK2 @ sK12 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK2 @ sK12 @ Y1 @ Y0 )
=> ( sK2 @ sK12 @ Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_1 ),
inference(superposition,[],[f165,f634]) ).
thf(f634,plain,
( ( $true
= ( sK3 @ sK12 @ sK12 ) )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f629]) ).
thf(f629,plain,
( ( $true
= ( $true
=> ( sK3 @ sK12 @ sK12 ) ) )
| ~ spl0_1 ),
inference(superposition,[],[f609,f608]) ).
thf(f609,plain,
( ! [X0: a] :
( $true
= ( ( sK3 @ X0 @ sK13 )
=> ( sK3 @ X0 @ sK12 ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f602]) ).
thf(f602,plain,
( ! [X0: a] :
( $true
= ( ( $true
& ( sK3 @ X0 @ sK13 ) )
=> ( sK3 @ X0 @ sK12 ) ) )
| ~ spl0_1 ),
inference(superposition,[],[f137,f595]) ).
thf(f137,plain,
! [X2: a,X3: a,X1: a] :
( ( ( ( sK3 @ X2 @ X1 )
& ( sK3 @ X3 @ X2 ) )
=> ( sK3 @ X3 @ X1 ) )
= $true ),
inference(beta_eta_normalization,[],[f136]) ).
thf(f136,plain,
! [X2: a,X3: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK3 @ X2 @ X1 )
& ( sK3 @ Y0 @ X2 ) )
=> ( sK3 @ Y0 @ X1 ) )
@ X3 )
= $true ),
inference(pi_clausification,[],[f133]) ).
thf(f133,plain,
! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ X2 @ X1 )
& ( sK3 @ Y0 @ X2 ) )
=> ( sK3 @ Y0 @ X1 ) ) ) ),
inference(beta_eta_normalization,[],[f132]) ).
thf(f132,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ X1 )
& ( sK3 @ Y1 @ Y0 ) )
=> ( sK3 @ Y1 @ X1 ) ) )
@ X2 ) ),
inference(pi_clausification,[],[f129]) ).
thf(f129,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y0 @ X1 )
& ( sK3 @ Y1 @ Y0 ) )
=> ( sK3 @ Y1 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[],[f128]) ).
thf(f128,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y1 @ Y0 )
& ( sK3 @ Y2 @ Y1 ) )
=> ( sK3 @ Y2 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[],[f90]) ).
thf(f165,plain,
! [X1: a] :
( ( ( sK3 @ X1 @ X1 )
=> ( ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK2 @ X1 @ Y1 @ Y2 )
& ( sK2 @ X1 @ Y0 @ Y1 ) )
=> ( sK2 @ X1 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK2 @ X1 @ Y1 @ Y0 )
=> ( sK2 @ X1 @ Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[],[f164]) ).
thf(f164,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK3 @ Y0 @ Y0 )
=> ( ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( ( sK2 @ Y0 @ Y2 @ Y3 )
& ( sK2 @ Y0 @ Y1 @ Y2 ) )
=> ( sK2 @ Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( sK2 @ Y0 @ Y2 @ Y1 )
=> ( sK2 @ Y0 @ Y1 @ Y2 ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[],[f158]) ).
thf(f158,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ Y0 )
=> ( ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( ( sK2 @ Y0 @ Y2 @ Y3 )
& ( sK2 @ Y0 @ Y1 @ Y2 ) )
=> ( sK2 @ Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( sK2 @ Y0 @ Y2 @ Y1 )
=> ( sK2 @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f157]) ).
thf(f157,plain,
( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ Y0 )
=> ( ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( !! @ b
@ ^ [Y3: b] :
( ( ( sK2 @ Y0 @ Y2 @ Y3 )
& ( sK2 @ Y0 @ Y1 @ Y2 ) )
=> ( sK2 @ Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( sK2 @ Y0 @ Y2 @ Y1 )
=> ( sK2 @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) ) ) ),
inference(backward_demodulation,[],[f97,f156]) ).
thf(f577,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f576]) ).
thf(f576,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f575]) ).
thf(f575,plain,
( ( $false = $true )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f574]) ).
thf(f574,plain,
( ( $true = ~ $true )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f565,f328]) ).
thf(f328,plain,
( ( $true
= ( sK2 @ sK7 @ ( sK4 @ sK9 ) @ ( sK8 @ sK7 ) ) )
| ~ spl0_2 ),
inference(superposition,[],[f322,f74]) ).
thf(f74,plain,
( ( ( sK2 @ sK9 @ ( sK4 @ sK9 ) @ ( sK8 @ sK7 ) )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f73]) ).
thf(f73,plain,
( ( $true
= ( $true
=> ( sK2 @ sK9 @ ( sK4 @ sK9 ) @ ( sK8 @ sK7 ) ) ) )
| ~ spl0_2 ),
inference(superposition,[],[f71,f52]) ).
thf(f52,plain,
( ( ( sK3 @ sK9 @ sK7 )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f47]) ).
thf(f47,plain,
( ( ( ( sK3 @ sK9 @ sK7 )
=> ( sK2 @ sK9 @ ( sK4 @ sK9 ) @ ( sK5 @ sK7 ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f46]) ).
thf(f46,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK3 @ Y0 @ sK7 )
=> ( sK2 @ Y0 @ ( sK4 @ Y0 ) @ ( sK5 @ sK7 ) ) )
@ sK9 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f43]) ).
thf(f43,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ sK7 )
=> ( sK2 @ Y0 @ ( sK4 @ Y0 ) @ ( sK5 @ sK7 ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f42]) ).
thf(f42,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK2 @ Y1 @ ( sK4 @ Y1 ) @ ( sK5 @ Y0 ) ) ) )
@ sK7 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f34]) ).
thf(f34,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK2 @ Y1 @ ( sK4 @ Y1 ) @ ( sK5 @ Y0 ) ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f33]) ).
thf(f33,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK2 @ Y0 @ ( sK4 @ Y0 ) @ ( sK6 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK2 @ Y0 @ ( sK6 @ Y0 ) @ ( sK5 @ Y1 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK2 @ Y1 @ ( sK4 @ Y1 ) @ ( sK5 @ Y0 ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f32]) ).
thf(f32,plain,
( ( $false
= ( ^ [Y0: a > b] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( sK2 @ Y1 @ ( sK4 @ Y1 ) @ ( Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( sK2 @ Y1 @ ( Y0 @ Y1 ) @ ( sK5 @ Y2 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( sK2 @ Y2 @ ( sK4 @ Y2 ) @ ( sK5 @ Y1 ) ) ) ) ) )
@ sK6 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f31]) ).
thf(f31,plain,
( ( $false
= ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( sK2 @ Y1 @ ( sK4 @ Y1 ) @ ( Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( sK2 @ Y1 @ ( Y0 @ Y1 ) @ ( sK5 @ Y2 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( sK2 @ Y2 @ ( sK4 @ Y2 ) @ ( sK5 @ Y1 ) ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f30]) ).
thf(f30,plain,
( ( $false
= ( ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( sK2 @ Y2 @ ( sK4 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( sK2 @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y3 @ Y2 )
=> ( sK2 @ Y3 @ ( sK4 @ Y3 ) @ ( Y0 @ Y2 ) ) ) ) ) ) )
@ sK5 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f29]) ).
thf(f29,plain,
( ( $false
= ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( sK2 @ Y2 @ ( sK4 @ Y2 ) @ ( Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( sK2 @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y3 @ Y2 )
=> ( sK2 @ Y3 @ ( sK4 @ Y3 ) @ ( Y0 @ Y2 ) ) ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f28]) ).
thf(f28,plain,
( ( ( ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( sK2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( sK2 @ Y3 @ ( Y2 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( sK2 @ Y4 @ ( Y0 @ Y4 ) @ ( Y1 @ Y3 ) ) ) ) ) ) ) )
@ sK4 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f24]) ).
thf(f24,plain,
( ( $false
= ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( sK2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( sK2 @ Y3 @ ( Y2 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( sK2 @ Y4 @ ( Y0 @ Y4 ) @ ( Y1 @ Y3 ) ) ) ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f23]) ).
thf(f23,plain,
( spl0_2
<=> ( $false
= ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( sK2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( sK2 @ Y3 @ ( Y2 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( sK2 @ Y4 @ ( Y0 @ Y4 ) @ ( Y1 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f71,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( sK3 @ X1 @ X2 )
=> ( sK2 @ X1 @ ( sK4 @ X1 ) @ ( sK8 @ X2 ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f70]) ).
thf(f70,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK3 @ X1 @ Y0 )
=> ( sK2 @ X1 @ ( sK4 @ X1 ) @ ( sK8 @ Y0 ) ) )
@ X2 ) )
| ~ spl0_2 ),
inference(pi_clausification,[],[f67]) ).
thf(f67,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ X1 @ Y0 )
=> ( sK2 @ X1 @ ( sK4 @ X1 ) @ ( sK8 @ Y0 ) ) ) )
= $true )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f66]) ).
thf(f66,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK2 @ Y0 @ ( sK4 @ Y0 ) @ ( sK8 @ Y1 ) ) ) )
@ X1 ) )
| ~ spl0_2 ),
inference(pi_clausification,[],[f56]) ).
thf(f56,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK2 @ Y0 @ ( sK4 @ Y0 ) @ ( sK8 @ Y1 ) ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f48]) ).
thf(f48,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK2 @ Y0 @ ( sK4 @ Y0 ) @ ( sK8 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK2 @ Y0 @ ( sK8 @ Y0 ) @ ( sK5 @ Y1 ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(not_proxy_clausification,[],[f45]) ).
thf(f45,plain,
( ( $false
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK2 @ Y0 @ ( sK4 @ Y0 ) @ ( sK8 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK2 @ Y0 @ ( sK8 @ Y0 ) @ ( sK5 @ Y1 ) ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f44]) ).
thf(f44,plain,
( ( $false
= ( ^ [Y0: a > b] :
~ ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( sK2 @ Y1 @ ( sK4 @ Y1 ) @ ( Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( sK2 @ Y1 @ ( Y0 @ Y1 ) @ ( sK5 @ Y2 ) ) ) ) ) )
@ sK8 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f38]) ).
thf(f38,plain,
( ( $false
= ( !! @ ( a > b )
@ ^ [Y0: a > b] :
~ ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( sK2 @ Y1 @ ( sK4 @ Y1 ) @ ( Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( sK2 @ Y1 @ ( Y0 @ Y1 ) @ ( sK5 @ Y2 ) ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f37]) ).
thf(f37,plain,
( ( $false
= ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( sK2 @ Y1 @ ( sK4 @ Y1 ) @ ( Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y1 @ Y2 )
=> ( sK2 @ Y1 @ ( Y0 @ Y1 ) @ ( sK5 @ Y2 ) ) ) ) ) )
=> $false ) ) )
| ~ spl0_2 ),
inference(backward_demodulation,[],[f31,f34]) ).
thf(f322,plain,
( ! [X2: b,X1: b] :
( ( sK2 @ sK7 @ X1 @ X2 )
= ( sK2 @ sK9 @ X1 @ X2 ) )
| ~ spl0_2 ),
inference(argument_congruence,[],[f315]) ).
thf(f315,plain,
( ! [X1: b] :
( ( sK2 @ sK7 @ X1 )
= ( sK2 @ sK9 @ X1 ) )
| ~ spl0_2 ),
inference(argument_congruence,[],[f308]) ).
thf(f308,plain,
( ( ( sK2 @ sK7 )
= ( sK2 @ sK9 ) )
| ~ spl0_2 ),
inference(equality_proxy_clausification,[],[f241]) ).
thf(f241,plain,
( ( $true
= ( ( sK2 @ sK9 )
= ( sK2 @ sK7 ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f235]) ).
thf(f235,plain,
( ( $true
= ( $true
=> ( ( sK2 @ sK9 )
= ( sK2 @ sK7 ) ) ) )
| ~ spl0_2 ),
inference(superposition,[],[f231,f52]) ).
thf(f565,plain,
( ( $true
= ( ~ ( sK2 @ sK7 @ ( sK4 @ sK9 ) @ ( sK8 @ sK7 ) ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f560]) ).
thf(f560,plain,
( ( $true
= ( ( sK2 @ sK7 @ ( sK4 @ sK9 ) @ ( sK8 @ sK7 ) )
=> $false ) )
| ~ spl0_2 ),
inference(superposition,[],[f442,f334]) ).
thf(f334,plain,
( ( $false
= ( sK2 @ sK7 @ ( sK4 @ sK9 ) @ ( sK5 @ sK7 ) ) )
| ~ spl0_2 ),
inference(superposition,[],[f54,f322]) ).
thf(f54,plain,
( ( $false
= ( sK2 @ sK9 @ ( sK4 @ sK9 ) @ ( sK5 @ sK7 ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f53]) ).
thf(f53,plain,
( ( $false
= ( $true
=> ( sK2 @ sK9 @ ( sK4 @ sK9 ) @ ( sK5 @ sK7 ) ) ) )
| ~ spl0_2 ),
inference(backward_demodulation,[],[f47,f52]) ).
thf(f442,plain,
( ! [X0: b] :
( $true
= ( ( sK2 @ sK7 @ X0 @ ( sK8 @ sK7 ) )
=> ( sK2 @ sK7 @ X0 @ ( sK5 @ sK7 ) ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f422]) ).
thf(f422,plain,
( ! [X0: b] :
( $true
= ( ( $true
& ( sK2 @ sK7 @ X0 @ ( sK8 @ sK7 ) ) )
=> ( sK2 @ sK7 @ X0 @ ( sK5 @ sK7 ) ) ) )
| ~ spl0_2 ),
inference(superposition,[],[f391,f215]) ).
thf(f215,plain,
( ( $true
= ( sK2 @ sK7 @ ( sK8 @ sK7 ) @ ( sK5 @ sK7 ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f203]) ).
thf(f203,plain,
( ( $true
= ( $true
=> ( sK2 @ sK7 @ ( sK8 @ sK7 ) @ ( sK5 @ sK7 ) ) ) )
| ~ spl0_2 ),
inference(superposition,[],[f62,f197]) ).
thf(f197,plain,
( ( $true
= ( sK3 @ sK7 @ sK7 ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f195]) ).
thf(f195,plain,
( ( ( $true
=> ( sK3 @ sK7 @ sK7 ) )
= $true )
| ~ spl0_2 ),
inference(superposition,[],[f151,f108]) ).
thf(f108,plain,
( ( $true
= ( sK3 @ sK7 @ sK9 ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f106]) ).
thf(f106,plain,
( ( $true
= ( $true
=> ( sK3 @ sK7 @ sK9 ) ) )
| ~ spl0_2 ),
inference(superposition,[],[f103,f52]) ).
thf(f151,plain,
( ! [X0: a] :
( ( ( sK3 @ X0 @ sK9 )
=> ( sK3 @ X0 @ sK7 ) )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f145]) ).
thf(f145,plain,
( ! [X0: a] :
( ( ( $true
& ( sK3 @ X0 @ sK9 ) )
=> ( sK3 @ X0 @ sK7 ) )
= $true )
| ~ spl0_2 ),
inference(superposition,[],[f137,f52]) ).
thf(f62,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( sK3 @ X1 @ X2 )
=> ( sK2 @ X1 @ ( sK8 @ X1 ) @ ( sK5 @ X2 ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f61]) ).
thf(f61,plain,
( ! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( sK3 @ X1 @ Y0 )
=> ( sK2 @ X1 @ ( sK8 @ X1 ) @ ( sK5 @ Y0 ) ) )
@ X2 )
= $true )
| ~ spl0_2 ),
inference(pi_clausification,[],[f60]) ).
thf(f60,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ X1 @ Y0 )
=> ( sK2 @ X1 @ ( sK8 @ X1 ) @ ( sK5 @ Y0 ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f59]) ).
thf(f59,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK2 @ Y0 @ ( sK8 @ Y0 ) @ ( sK5 @ Y1 ) ) ) )
@ X1 ) )
| ~ spl0_2 ),
inference(pi_clausification,[],[f58]) ).
thf(f58,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK2 @ Y0 @ ( sK8 @ Y0 ) @ ( sK5 @ Y1 ) ) ) ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f57]) ).
thf(f57,plain,
( ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y0 @ Y1 )
=> ( sK2 @ Y0 @ ( sK8 @ Y0 ) @ ( sK5 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_2 ),
inference(backward_demodulation,[],[f48,f56]) ).
thf(f391,plain,
( ! [X2: b,X3: b,X1: b] :
( $true
= ( ( ( sK2 @ sK7 @ X2 @ X3 )
& ( sK2 @ sK7 @ X1 @ X2 ) )
=> ( sK2 @ sK7 @ X1 @ X3 ) ) )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f390,f322]) ).
thf(f390,plain,
( ! [X2: b,X3: b,X1: b] :
( $true
= ( ( ( sK2 @ sK7 @ X2 @ X3 )
& ( sK2 @ sK7 @ X1 @ X2 ) )
=> ( sK2 @ sK9 @ X1 @ X3 ) ) )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f389,f322]) ).
thf(f389,plain,
( ! [X2: b,X3: b,X1: b] :
( $true
= ( ( ( sK2 @ sK7 @ X2 @ X3 )
& ( sK2 @ sK9 @ X1 @ X2 ) )
=> ( sK2 @ sK9 @ X1 @ X3 ) ) )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f388,f322]) ).
thf(f388,plain,
( ! [X2: b,X3: b,X1: b] :
( $true
= ( ( ( sK2 @ sK9 @ X2 @ X3 )
& ( sK2 @ sK9 @ X1 @ X2 ) )
=> ( sK2 @ sK9 @ X1 @ X3 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f387]) ).
thf(f387,plain,
( ! [X2: b,X3: b,X1: b] :
( ( ^ [Y0: b] :
( ( ( sK2 @ sK9 @ X2 @ Y0 )
& ( sK2 @ sK9 @ X1 @ X2 ) )
=> ( sK2 @ sK9 @ X1 @ Y0 ) )
@ X3 )
= $true )
| ~ spl0_2 ),
inference(pi_clausification,[],[f386]) ).
thf(f386,plain,
( ! [X2: b,X1: b] :
( ( !! @ b
@ ^ [Y0: b] :
( ( ( sK2 @ sK9 @ X2 @ Y0 )
& ( sK2 @ sK9 @ X1 @ X2 ) )
=> ( sK2 @ sK9 @ X1 @ Y0 ) ) )
= $true )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f385]) ).
thf(f385,plain,
( ! [X2: b,X1: b] :
( ( ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( ( sK2 @ sK9 @ Y0 @ Y1 )
& ( sK2 @ sK9 @ X1 @ Y0 ) )
=> ( sK2 @ sK9 @ X1 @ Y1 ) ) )
@ X2 )
= $true )
| ~ spl0_2 ),
inference(pi_clausification,[],[f381]) ).
thf(f381,plain,
( ! [X1: b] :
( $true
= ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( ( sK2 @ sK9 @ Y0 @ Y1 )
& ( sK2 @ sK9 @ X1 @ Y0 ) )
=> ( sK2 @ sK9 @ X1 @ Y1 ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f379]) ).
thf(f379,plain,
( ! [X1: b] :
( $true
= ( ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK2 @ sK9 @ Y1 @ Y2 )
& ( sK2 @ sK9 @ Y0 @ Y1 ) )
=> ( sK2 @ sK9 @ Y0 @ Y2 ) ) ) )
@ X1 ) )
| ~ spl0_2 ),
inference(pi_clausification,[],[f378]) ).
thf(f378,plain,
( ( $true
= ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK2 @ sK9 @ Y1 @ Y2 )
& ( sK2 @ sK9 @ Y0 @ Y1 ) )
=> ( sK2 @ sK9 @ Y0 @ Y2 ) ) ) ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f377]) ).
thf(f377,plain,
( ( $true
= ( ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK2 @ sK9 @ Y1 @ Y2 )
& ( sK2 @ sK9 @ Y0 @ Y1 ) )
=> ( sK2 @ sK9 @ Y0 @ Y2 ) ) ) ) )
& $true ) )
| ~ spl0_2 ),
inference(backward_demodulation,[],[f190,f373]) ).
thf(f373,plain,
( ( ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK2 @ sK9 @ Y1 @ Y0 )
=> ( sK2 @ sK9 @ Y0 @ Y1 ) ) ) )
= $true )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f190]) ).
thf(f190,plain,
( ( ( ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK2 @ sK9 @ Y1 @ Y2 )
& ( sK2 @ sK9 @ Y0 @ Y1 ) )
=> ( sK2 @ sK9 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK2 @ sK9 @ Y1 @ Y0 )
=> ( sK2 @ sK9 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f189]) ).
thf(f189,plain,
( ( $true
= ( $true
=> ( ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( !! @ b
@ ^ [Y2: b] :
( ( ( sK2 @ sK9 @ Y1 @ Y2 )
& ( sK2 @ sK9 @ Y0 @ Y1 ) )
=> ( sK2 @ sK9 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ b
@ ^ [Y0: b] :
( !! @ b
@ ^ [Y1: b] :
( ( sK2 @ sK9 @ Y1 @ Y0 )
=> ( sK2 @ sK9 @ Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(superposition,[],[f165,f163]) ).
thf(f163,plain,
( ( $true
= ( sK3 @ sK9 @ sK9 ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f161]) ).
thf(f161,plain,
( ( $true
= ( $true
=> ( sK3 @ sK9 @ sK9 ) ) )
| ~ spl0_2 ),
inference(superposition,[],[f147,f108]) ).
thf(f147,plain,
( ! [X0: a] :
( ( ( sK3 @ sK7 @ X0 )
=> ( sK3 @ sK9 @ X0 ) )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f143]) ).
thf(f143,plain,
( ! [X0: a] :
( $true
= ( ( ( sK3 @ sK7 @ X0 )
& $true )
=> ( sK3 @ sK9 @ X0 ) ) )
| ~ spl0_2 ),
inference(superposition,[],[f137,f52]) ).
thf(f25,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f18,f23,f20]) ).
thf(f18,plain,
( ( $false
= ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( sK2 @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y3 @ Y2 )
=> ( sK2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y1 @ Y2 ) ) ) ) ) ) ) ) )
| ( $false
= ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( !! @ ( a > b )
@ ^ [Y2: a > b] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( sK2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( sK2 @ Y3 @ ( Y2 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( sK2 @ Y4 @ ( Y0 @ Y4 ) @ ( Y1 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f17]) ).
thf(f17,plain,
( $false
= ( ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( sK2 @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y3 @ Y2 )
=> ( sK2 @ 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] :
( ( sK3 @ Y3 @ Y4 )
=> ( sK2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( sK2 @ Y3 @ ( Y2 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( sK2 @ Y4 @ ( Y0 @ Y4 ) @ ( Y1 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f16]) ).
thf(f16,plain,
( $false
= ( $true
=> ( ( !! @ ( a > b )
@ ^ [Y0: a > b] :
( !! @ ( a > b )
@ ^ [Y1: a > b] :
( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y2 @ Y3 )
=> ( sK2 @ Y2 @ ( Y1 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) )
=> ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y3 @ Y2 )
=> ( sK2 @ 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] :
( ( sK3 @ Y3 @ Y4 )
=> ( sK2 @ Y3 @ ( Y0 @ Y3 ) @ ( Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y3 @ Y4 )
=> ( sK2 @ Y3 @ ( Y2 @ Y3 ) @ ( Y1 @ Y4 ) ) ) ) ) )
=> ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( sK2 @ Y4 @ ( Y0 @ Y4 ) @ ( Y1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(backward_demodulation,[],[f13,f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : SEV046^5 : TPTP v8.2.0. Released v4.0.0.
% 0.02/0.11 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.11/0.32 % Computer : n021.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sun May 19 19:07:52 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.32 This is a TH0_THM_EQU_NAR problem
% 0.11/0.32 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.34 % (8983)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)
% 0.11/0.34 % (8984)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)
% 0.11/0.34 % (8982)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.11/0.34 % (8987)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)
% 0.11/0.34 % (8985)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.11/0.34 % (8986)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)
% 0.11/0.34 % (8988)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.18/0.34 % (8989)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)
% 0.18/0.34 % (8985)Instruction limit reached!
% 0.18/0.34 % (8985)------------------------------
% 0.18/0.34 % (8985)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.34 % (8985)Termination reason: Unknown
% 0.18/0.34 % (8985)Termination phase: Preprocessing 3
% 0.18/0.34 % (8986)Instruction limit reached!
% 0.18/0.34 % (8986)------------------------------
% 0.18/0.34 % (8986)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.34 % (8986)Termination reason: Unknown
% 0.18/0.34 % (8986)Termination phase: Property scanning
% 0.18/0.34
% 0.18/0.34 % (8986)Memory used [KB]: 1023
% 0.18/0.34 % (8986)Time elapsed: 0.003 s
% 0.18/0.34 % (8986)Instructions burned: 3 (million)
% 0.18/0.34 % (8986)------------------------------
% 0.18/0.34 % (8986)------------------------------
% 0.18/0.34
% 0.18/0.34 % (8985)Memory used [KB]: 1023
% 0.18/0.34 % (8985)Time elapsed: 0.003 s
% 0.18/0.34 % (8985)Instructions burned: 3 (million)
% 0.18/0.34 % (8985)------------------------------
% 0.18/0.34 % (8985)------------------------------
% 0.18/0.34 % (8983)Instruction limit reached!
% 0.18/0.34 % (8983)------------------------------
% 0.18/0.34 % (8983)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.34 % (8983)Termination reason: Unknown
% 0.18/0.34 % (8983)Termination phase: Saturation
% 0.18/0.34
% 0.18/0.34 % (8983)Memory used [KB]: 5500
% 0.18/0.34 % (8983)Time elapsed: 0.004 s
% 0.18/0.34 % (8983)Instructions burned: 4 (million)
% 0.18/0.34 % (8983)------------------------------
% 0.18/0.34 % (8983)------------------------------
% 0.18/0.34 % (8989)Instruction limit reached!
% 0.18/0.34 % (8989)------------------------------
% 0.18/0.34 % (8989)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.34 % (8989)Termination reason: Unknown
% 0.18/0.34 % (8989)Termination phase: Saturation
% 0.18/0.34
% 0.18/0.34 % (8989)Memory used [KB]: 5500
% 0.18/0.34 % (8989)Time elapsed: 0.004 s
% 0.18/0.34 % (8989)Instructions burned: 4 (million)
% 0.18/0.34 % (8989)------------------------------
% 0.18/0.34 % (8989)------------------------------
% 0.18/0.35 % (8988)Instruction limit reached!
% 0.18/0.35 % (8988)------------------------------
% 0.18/0.35 % (8988)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.35 % (8988)Termination reason: Unknown
% 0.18/0.35 % (8988)Termination phase: Saturation
% 0.18/0.35
% 0.18/0.35 % (8988)Memory used [KB]: 5628
% 0.18/0.35 % (8988)Time elapsed: 0.013 s
% 0.18/0.35 % (8988)Instructions burned: 19 (million)
% 0.18/0.35 % (8988)------------------------------
% 0.18/0.35 % (8988)------------------------------
% 0.18/0.35 % (8990)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)
% 0.18/0.35 % (8991)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)
% 0.18/0.35 % (8993)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)
% 0.18/0.35 % (8992)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)
% 0.18/0.35 % (8984)Instruction limit reached!
% 0.18/0.35 % (8984)------------------------------
% 0.18/0.35 % (8984)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.35 % (8984)Termination reason: Unknown
% 0.18/0.35 % (8984)Termination phase: Saturation
% 0.18/0.35
% 0.18/0.35 % (8984)Memory used [KB]: 5756
% 0.18/0.35 % (8984)Time elapsed: 0.018 s
% 0.18/0.35 % (8984)Instructions burned: 28 (million)
% 0.18/0.35 % (8984)------------------------------
% 0.18/0.35 % (8984)------------------------------
% 0.18/0.35 % (8992)Instruction limit reached!
% 0.18/0.35 % (8992)------------------------------
% 0.18/0.35 % (8992)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.35 % (8992)Termination reason: Unknown
% 0.18/0.35 % (8992)Termination phase: Preprocessing 3
% 0.18/0.35
% 0.18/0.35 % (8992)Memory used [KB]: 1023
% 0.18/0.35 % (8992)Time elapsed: 0.003 s
% 0.18/0.35 % (8992)Instructions burned: 3 (million)
% 0.18/0.35 % (8992)------------------------------
% 0.18/0.35 % (8992)------------------------------
% 0.18/0.36 % (8991)Instruction limit reached!
% 0.18/0.36 % (8991)------------------------------
% 0.18/0.36 % (8991)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.36 % (8991)Termination reason: Unknown
% 0.18/0.36 % (8991)Termination phase: Saturation
% 0.18/0.36
% 0.18/0.36 % (8991)Memory used [KB]: 5756
% 0.18/0.36 % (8991)Time elapsed: 0.010 s
% 0.18/0.36 % (8991)Instructions burned: 16 (million)
% 0.18/0.36 % (8991)------------------------------
% 0.18/0.36 % (8991)------------------------------
% 0.18/0.36 % (8994)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.18/0.37 % (8994)Instruction limit reached!
% 0.18/0.37 % (8994)------------------------------
% 0.18/0.37 % (8994)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.37 % (8994)Termination reason: Unknown
% 0.18/0.37 % (8994)Termination phase: Saturation
% 0.18/0.37
% 0.18/0.37 % (8994)Memory used [KB]: 1023
% 0.18/0.37 % (8994)Time elapsed: 0.005 s
% 0.18/0.37 % (8994)Instructions burned: 7 (million)
% 0.18/0.37 % (8994)------------------------------
% 0.18/0.37 % (8994)------------------------------
% 0.18/0.37 % (8995)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.18/0.37 % (8996)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)
% 0.18/0.37 % (8996)Instruction limit reached!
% 0.18/0.37 % (8996)------------------------------
% 0.18/0.37 % (8996)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.37 % (8996)Termination reason: Unknown
% 0.18/0.37 % (8996)Termination phase: Preprocessing 3
% 0.18/0.37
% 0.18/0.37 % (8996)Memory used [KB]: 1023
% 0.18/0.37 % (8996)Time elapsed: 0.003 s
% 0.18/0.37 % (8996)Instructions burned: 3 (million)
% 0.18/0.37 % (8996)------------------------------
% 0.18/0.37 % (8996)------------------------------
% 0.18/0.37 % (8990)Instruction limit reached!
% 0.18/0.37 % (8990)------------------------------
% 0.18/0.37 % (8990)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.37 % (8990)Termination reason: Unknown
% 0.18/0.37 % (8990)Termination phase: Saturation
% 0.18/0.37
% 0.18/0.37 % (8990)Memory used [KB]: 5628
% 0.18/0.37 % (8990)Time elapsed: 0.020 s
% 0.18/0.37 % (8990)Instructions burned: 37 (million)
% 0.18/0.37 % (8990)------------------------------
% 0.18/0.37 % (8990)------------------------------
% 0.18/0.37 % (8997)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)
% 0.18/0.38 % (8997)Instruction limit reached!
% 0.18/0.38 % (8997)------------------------------
% 0.18/0.38 % (8997)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.38 % (8997)Termination reason: Unknown
% 0.18/0.38 % (8997)Termination phase: Preprocessing 3
% 0.18/0.38
% 0.18/0.38 % (8997)Memory used [KB]: 1023
% 0.18/0.38 % (8997)Time elapsed: 0.003 s
% 0.18/0.38 % (8995)Instruction limit reached!
% 0.18/0.38 % (8995)------------------------------
% 0.18/0.38 % (8995)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.38 % (8995)Termination reason: Unknown
% 0.18/0.38 % (8995)Termination phase: Saturation
% 0.18/0.38
% 0.18/0.38 % (8995)Memory used [KB]: 5756
% 0.18/0.38 % (8995)Time elapsed: 0.010 s
% 0.18/0.38 % (8995)Instructions burned: 16 (million)
% 0.18/0.38 % (8995)------------------------------
% 0.18/0.38 % (8995)------------------------------
% 0.18/0.38 % (8997)Instructions burned: 3 (million)
% 0.18/0.38 % (8997)------------------------------
% 0.18/0.38 % (8997)------------------------------
% 0.18/0.38 % (8998)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)
% 0.18/0.38 % (8999)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)
% 0.18/0.38 % (8998)Instruction limit reached!
% 0.18/0.38 % (8998)------------------------------
% 0.18/0.38 % (8998)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.38 % (8998)Termination reason: Unknown
% 0.18/0.38 % (8998)Termination phase: Saturation
% 0.18/0.38
% 0.18/0.38 % (8998)Memory used [KB]: 5500
% 0.18/0.38 % (8998)Time elapsed: 0.005 s
% 0.18/0.38 % (8998)Instructions burned: 7 (million)
% 0.18/0.38 % (8998)------------------------------
% 0.18/0.38 % (8998)------------------------------
% 0.18/0.38 % (8999)Instruction limit reached!
% 0.18/0.38 % (8999)------------------------------
% 0.18/0.38 % (8999)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.38 % (8999)Termination reason: Unknown
% 0.18/0.38 % (8999)Termination phase: Property scanning
% 0.18/0.38
% 0.18/0.38 % (8999)Memory used [KB]: 1023
% 0.18/0.38 % (8999)Time elapsed: 0.003 s
% 0.18/0.38 % (8999)Instructions burned: 4 (million)
% 0.18/0.38 % (8999)------------------------------
% 0.18/0.38 % (8999)------------------------------
% 0.18/0.38 % (9000)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.18/0.39 % (9000)Instruction limit reached!
% 0.18/0.39 % (9000)------------------------------
% 0.18/0.39 % (9000)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.39 % (9000)Termination reason: Unknown
% 0.18/0.39 % (9000)Termination phase: Saturation
% 0.18/0.39
% 0.18/0.39 % (9000)Memory used [KB]: 5500
% 0.18/0.39 % (9000)Time elapsed: 0.004 s
% 0.18/0.39 % (9000)Instructions burned: 5 (million)
% 0.18/0.39 % (9000)------------------------------
% 0.18/0.39 % (9000)------------------------------
% 0.18/0.39 % (9001)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)
% 0.18/0.39 % (9002)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.18/0.40 % (9003)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.18/0.40 % (9004)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)
% 0.18/0.40 % (9001)Instruction limit reached!
% 0.18/0.40 % (9001)------------------------------
% 0.18/0.40 % (9001)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.40 % (9001)Termination reason: Unknown
% 0.18/0.40 % (9001)Termination phase: Saturation
% 0.18/0.40
% 0.18/0.40 % (9001)Memory used [KB]: 5628
% 0.18/0.40 % (9001)Time elapsed: 0.013 s
% 0.18/0.40 % (9003)Instruction limit reached!
% 0.18/0.40 % (9003)------------------------------
% 0.18/0.40 % (9003)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.40 % (9001)Instructions burned: 19 (million)
% 0.18/0.40 % (9001)------------------------------
% 0.18/0.40 % (9001)------------------------------
% 0.18/0.40 % (9003)Termination reason: Unknown
% 0.18/0.40 % (9003)Termination phase: Saturation
% 0.18/0.40
% 0.18/0.40 % (9003)Memory used [KB]: 5500
% 0.18/0.40 % (9003)Time elapsed: 0.005 s
% 0.18/0.40 % (9003)Instructions burned: 7 (million)
% 0.18/0.40 % (9003)------------------------------
% 0.18/0.40 % (9003)------------------------------
% 0.18/0.40 % (9005)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)
% 0.18/0.41 % (9005)Instruction limit reached!
% 0.18/0.41 % (9005)------------------------------
% 0.18/0.41 % (9005)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.41 % (9005)Termination reason: Unknown
% 0.18/0.41 % (9005)Termination phase: Saturation
% 0.18/0.41
% 0.18/0.41 % (9005)Memory used [KB]: 5756
% 0.18/0.41 % (9005)Time elapsed: 0.014 s
% 0.18/0.41 % (9005)Instructions burned: 22 (million)
% 0.18/0.41 % (9005)------------------------------
% 0.18/0.41 % (9005)------------------------------
% 0.18/0.41 % (9006)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.18/0.41 % (9007)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.18/0.41 % (9006)Instruction limit reached!
% 0.18/0.41 % (9006)------------------------------
% 0.18/0.41 % (9006)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.41 % (9006)Termination reason: Unknown
% 0.18/0.41 % (9006)Termination phase: Saturation
% 0.18/0.41
% 0.18/0.41 % (9006)Memory used [KB]: 5500
% 0.18/0.41 % (9006)Time elapsed: 0.004 s
% 0.18/0.41 % (9006)Instructions burned: 5 (million)
% 0.18/0.41 % (9006)------------------------------
% 0.18/0.41 % (9006)------------------------------
% 0.18/0.42 % (9007)Instruction limit reached!
% 0.18/0.42 % (9007)------------------------------
% 0.18/0.42 % (9007)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.42 % (9007)Termination reason: Unknown
% 0.18/0.42 % (9007)Termination phase: Saturation
% 0.18/0.42
% 0.18/0.42 % (9007)Memory used [KB]: 5500
% 0.18/0.42 % (9007)Time elapsed: 0.005 s
% 0.18/0.42 % (9007)Instructions burned: 7 (million)
% 0.18/0.42 % (9007)------------------------------
% 0.18/0.42 % (9007)------------------------------
% 0.18/0.42 % (8982)Instruction limit reached!
% 0.18/0.42 % (8982)------------------------------
% 0.18/0.42 % (8982)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.42 % (8982)Termination reason: Unknown
% 0.18/0.42 % (8982)Termination phase: Saturation
% 0.18/0.42
% 0.18/0.42 % (8982)Memory used [KB]: 5884
% 0.18/0.42 % (8982)Time elapsed: 0.083 s
% 0.18/0.42 % (8982)Instructions burned: 184 (million)
% 0.18/0.42 % (8982)------------------------------
% 0.18/0.42 % (8982)------------------------------
% 0.18/0.43 % (9008)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2999ds/377Mi)
% 0.18/0.43 % (9009)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 (2999ds/779Mi)
% 0.18/0.43 % (9010)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 (2999ds/19Mi)
% 0.18/0.43 % (9011)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on theBenchmark for (2999ds/879Mi)
% 0.18/0.44 % (9010)Instruction limit reached!
% 0.18/0.44 % (9010)------------------------------
% 0.18/0.44 % (9010)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.44 % (9010)Termination reason: Unknown
% 0.18/0.44 % (9010)Termination phase: Saturation
% 0.18/0.44
% 0.18/0.44 % (9010)Memory used [KB]: 5628
% 0.18/0.44 % (9010)Time elapsed: 0.010 s
% 0.18/0.44 % (9010)Instructions burned: 19 (million)
% 0.18/0.44 % (9010)------------------------------
% 0.18/0.44 % (9010)------------------------------
% 0.18/0.45 % (8993)First to succeed.
% 0.18/0.45 % (9012)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2999ds/17Mi)
% 0.18/0.45 % (8987)Instruction limit reached!
% 0.18/0.45 % (8987)------------------------------
% 0.18/0.45 % (8987)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.45 % (8987)Termination reason: Unknown
% 0.18/0.45 % (8987)Termination phase: Saturation
% 0.18/0.45
% 0.18/0.45 % (8987)Memory used [KB]: 5756
% 0.18/0.45 % (8987)Time elapsed: 0.119 s
% 0.18/0.45 % (8987)Instructions burned: 275 (million)
% 0.18/0.46 % (8987)------------------------------
% 0.18/0.46 % (8987)------------------------------
% 0.18/0.46 % (8993)Refutation found. Thanks to Tanya!
% 0.18/0.46 % SZS status Theorem for theBenchmark
% 0.18/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.46 % (8993)------------------------------
% 0.18/0.46 % (8993)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.46 % (8993)Termination reason: Refutation
% 0.18/0.46
% 0.18/0.46 % (8993)Memory used [KB]: 6396
% 0.18/0.46 % (8993)Time elapsed: 0.103 s
% 0.18/0.46 % (8993)Instructions burned: 173 (million)
% 0.18/0.46 % (8993)------------------------------
% 0.18/0.46 % (8993)------------------------------
% 0.18/0.46 % (8981)Success in time 0.118 s
% 0.18/0.46 % Vampire---4.8 exiting
%------------------------------------------------------------------------------