TSTP Solution File: SEV140^5 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEV140^5 : 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 : n014.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 04:12:07 EDT 2024
% Result : Theorem 0.19s 0.48s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 31
% Syntax : Number of formulae : 170 ( 41 unt; 24 typ; 0 def)
% Number of atoms : 1400 ( 134 equ; 0 cnn)
% Maximal formula atoms : 4 ( 9 avg)
% Number of connectives : 4674 ( 141 ~; 181 |; 258 &;3018 @)
% ( 6 <=>; 403 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 422 ( 422 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 28 usr; 27 con; 0-2 aty)
% ( 667 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 806 ( 693 ^ 112 !; 0 ?; 806 :)
% ( 1 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_19,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
sK2: a > a > $o ).
thf(func_def_21,type,
sK3: a > a > $o ).
thf(func_def_22,type,
sK4: a ).
thf(func_def_23,type,
sK5: a ).
thf(func_def_24,type,
sK6: a > a > $o ).
thf(func_def_25,type,
sK7: a ).
thf(func_def_26,type,
sK8: a ).
thf(func_def_27,type,
sK9: a ).
thf(func_def_28,type,
sK10: a ).
thf(func_def_29,type,
sK11: a ).
thf(func_def_30,type,
sK12: a ).
thf(func_def_31,type,
sK13: a ).
thf(func_def_32,type,
sK14: a ).
thf(func_def_33,type,
sK15: a ).
thf(func_def_34,type,
sK16: a ).
thf(func_def_35,type,
sK17: a ).
thf(func_def_36,type,
sK18: a ).
thf(func_def_37,type,
sK19: a ).
thf(func_def_38,type,
sK20: a ).
thf(func_def_39,type,
sK21: a ).
thf(func_def_40,type,
sK22: a ).
thf(f534,plain,
$false,
inference(avatar_sat_refutation,[],[f96,f172,f200,f247,f327,f447,f533]) ).
thf(f533,plain,
~ spl0_5,
inference(avatar_contradiction_clause,[],[f532]) ).
thf(f532,plain,
( $false
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f531]) ).
thf(f531,plain,
( ( $true = $false )
| ~ spl0_5 ),
inference(boolean_simplification,[],[f530]) ).
thf(f530,plain,
( ( $true = ~ $true )
| ~ spl0_5 ),
inference(forward_demodulation,[],[f525,f492]) ).
thf(f492,plain,
( ( $true
= ( sK6 @ sK17 @ sK18 ) )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f461]) ).
thf(f461,plain,
( ( $true
= ( ( sK6 @ sK17 @ sK18 )
& ( sK6 @ sK19 @ sK17 ) ) )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f459]) ).
thf(f459,plain,
( ( ( ( ( sK6 @ sK17 @ sK18 )
& ( sK6 @ sK19 @ sK17 ) )
=> ( sK6 @ sK19 @ sK18 ) )
= $false )
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f458]) ).
thf(f458,plain,
( ( ( ^ [Y0: a] :
( ( ( sK6 @ sK17 @ sK18 )
& ( sK6 @ Y0 @ sK17 ) )
=> ( sK6 @ Y0 @ sK18 ) )
@ sK19 )
= $false )
| ~ spl0_5 ),
inference(sigma_clausification,[],[f457]) ).
thf(f457,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ sK17 @ sK18 )
& ( sK6 @ Y0 @ sK17 ) )
=> ( sK6 @ Y0 @ sK18 ) ) )
= $false )
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f456]) ).
thf(f456,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ sK17 @ Y0 )
& ( sK6 @ Y1 @ sK17 ) )
=> ( sK6 @ Y1 @ Y0 ) ) )
@ sK18 )
= $false )
| ~ spl0_5 ),
inference(sigma_clausification,[],[f453]) ).
thf(f453,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ sK17 @ Y0 )
& ( sK6 @ Y1 @ sK17 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f451]) ).
thf(f451,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) )
@ sK17 )
= $false )
| ~ spl0_5 ),
inference(sigma_clausification,[],[f196]) ).
thf(f196,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) ) ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f195]) ).
thf(f195,plain,
( spl0_5
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
thf(f525,plain,
( ( $true
= ( ~ ( sK6 @ sK17 @ sK18 ) ) )
| ~ spl0_5 ),
inference(boolean_simplification,[],[f522]) ).
thf(f522,plain,
( ( $true
= ( ( sK6 @ sK17 @ sK18 )
=> $false ) )
| ~ spl0_5 ),
inference(superposition,[],[f504,f460]) ).
thf(f460,plain,
( ( ( sK6 @ sK19 @ sK18 )
= $false )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[],[f459]) ).
thf(f504,plain,
( ! [X0: a] :
( ( ( sK6 @ sK17 @ X0 )
=> ( sK6 @ sK19 @ X0 ) )
= $true )
| ~ spl0_5 ),
inference(boolean_simplification,[],[f501]) ).
thf(f501,plain,
( ! [X0: a] :
( $true
= ( ( $true
& ( sK6 @ sK17 @ X0 ) )
=> ( sK6 @ sK19 @ X0 ) ) )
| ~ spl0_5 ),
inference(superposition,[],[f37,f494]) ).
thf(f494,plain,
( ( $true
= ( sK6 @ sK19 @ sK17 ) )
| ~ spl0_5 ),
inference(boolean_simplification,[],[f493]) ).
thf(f493,plain,
( ( $true
= ( $true
& ( sK6 @ sK19 @ sK17 ) ) )
| ~ spl0_5 ),
inference(backward_demodulation,[],[f461,f492]) ).
thf(f37,plain,
! [X2: a,X3: a,X1: a] :
( $true
= ( ( ( sK6 @ X1 @ X2 )
& ( sK6 @ X2 @ X3 ) )
=> ( sK6 @ X1 @ X3 ) ) ),
inference(beta_eta_normalization,[],[f36]) ).
thf(f36,plain,
! [X2: a,X3: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK6 @ X1 @ X2 )
& ( sK6 @ X2 @ Y0 ) )
=> ( sK6 @ X1 @ Y0 ) )
@ X3 ) ),
inference(pi_clausification,[],[f35]) ).
thf(f35,plain,
! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ X1 @ X2 )
& ( sK6 @ X2 @ Y0 ) )
=> ( sK6 @ X1 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[],[f34]) ).
thf(f34,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ X1 @ Y0 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ X1 @ Y1 ) ) )
@ X2 ) ),
inference(pi_clausification,[],[f33]) ).
thf(f33,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ X1 @ Y0 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ X1 @ Y1 ) ) ) ) ),
inference(beta_eta_normalization,[],[f32]) ).
thf(f32,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y1 @ Y2 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[],[f31]) ).
thf(f31,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y1 @ Y2 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) ) ),
inference(boolean_simplification,[],[f30]) ).
thf(f30,plain,
( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y1 @ Y2 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(backward_demodulation,[],[f25,f29]) ).
thf(f29,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f25]) ).
thf(f25,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y1 @ Y2 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f23]) ).
thf(f23,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y1 @ Y2 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) ) )
=> ( sK6 @ sK4 @ sK5 ) )
= $false ),
inference(beta_eta_normalization,[],[f22]) ).
thf(f22,plain,
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) )
@ sK6 )
= $false ),
inference(sigma_clausification,[],[f21]) ).
thf(f21,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) )
= $false ),
inference(boolean_simplification,[],[f20]) ).
thf(f20,plain,
( ( $true
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) ) )
= $false ),
inference(backward_demodulation,[],[f17,f19]) ).
thf(f19,plain,
( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) ) ),
inference(binary_proxy_clausification,[],[f17]) ).
thf(f17,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK3 @ Y2 @ Y1 )
| ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f16]) ).
thf(f16,plain,
( ( ^ [Y0: a] :
( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK3 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK4 @ Y0 ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y3 @ Y2 )
| ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK4 @ Y0 ) ) ) )
@ sK5 )
= $false ),
inference(sigma_clausification,[],[f15]) ).
thf(f15,plain,
( ( !! @ a
@ ^ [Y0: a] :
( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK2 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK3 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK4 @ Y0 ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK3 @ Y3 @ Y2 )
| ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) ) )
=> ( Y1 @ sK4 @ Y0 ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f14]) ).
thf(f14,plain,
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y7 )
& ( Y5 @ Y7 @ Y8 ) )
=> ( Y5 @ Y6 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK2 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y7 )
& ( Y5 @ Y8 @ Y6 ) )
=> ( Y5 @ Y8 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK3 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
@ sK4 )
= $false ),
inference(sigma_clausification,[],[f13]) ).
thf(f13,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y7 )
& ( Y5 @ Y7 @ Y8 ) )
=> ( Y5 @ Y6 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK2 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y7 )
& ( Y5 @ Y8 @ Y6 ) )
=> ( Y5 @ Y8 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( sK3 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK3 @ Y4 @ Y3 )
| ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f12]) ).
thf(f12,plain,
( ( ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y8 )
& ( Y6 @ Y8 @ Y9 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( sK2 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y8 )
& ( Y6 @ Y9 @ Y7 ) )
=> ( Y6 @ Y9 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[],[f11]) ).
thf(f11,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y8 )
& ( Y6 @ Y8 @ Y9 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( sK2 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y8 )
& ( Y6 @ Y9 @ Y7 ) )
=> ( Y6 @ Y9 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y0 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y5 @ Y4 )
| ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y9 )
& ( Y7 @ Y9 @ Y10 ) )
=> ( Y7 @ Y8 @ Y10 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y0 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y9 )
& ( Y7 @ Y10 @ Y8 ) )
=> ( Y7 @ Y10 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y1 @ Y9 @ Y8 )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y5 @ Y7 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y1 @ Y6 @ Y5 )
| ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[],[f7]) ).
thf(f7,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y9 )
& ( Y7 @ Y9 @ Y10 ) )
=> ( Y7 @ Y8 @ Y10 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y0 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y9 )
& ( Y7 @ Y10 @ Y8 ) )
=> ( Y7 @ Y10 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y1 @ Y9 @ Y8 )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y5 @ Y7 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y1 @ Y6 @ Y5 )
| ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y9 )
& ( Y7 @ Y9 @ Y10 ) )
=> ( Y7 @ Y8 @ Y10 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y0 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y9 )
& ( Y7 @ Y10 @ Y8 ) )
=> ( Y7 @ Y10 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y1 @ Y9 @ Y8 )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y5 @ Y7 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y1 @ Y6 @ Y5 )
| ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y9 )
& ( Y7 @ Y9 @ Y10 ) )
=> ( Y7 @ Y8 @ Y10 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y0 @ Y8 @ Y9 )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y9 )
& ( Y7 @ Y10 @ Y8 ) )
=> ( Y7 @ Y10 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y1 @ Y9 @ Y8 )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y5 @ Y7 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y1 @ Y6 @ Y5 )
| ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
~ ! [X0: a,X1: a,X2: a > a > $o,X3: a > a > $o] :
( ! [X4: a > a > $o] :
( ( ! [X5: a,X6: a,X7: a] :
( ( ( X4 @ X7 @ X5 )
& ( X4 @ X5 @ X6 ) )
=> ( X4 @ X7 @ X6 ) )
& ! [X8: a,X9: a] :
( ( ! [X10: a > a > $o] :
( ( ! [X11: a,X12: a] :
( ( X2 @ X11 @ X12 )
=> ( X10 @ X11 @ X12 ) )
& ! [X13: a,X14: a,X15: a] :
( ( ( X10 @ X13 @ X15 )
& ( X10 @ X15 @ X14 ) )
=> ( X10 @ X13 @ X14 ) ) )
=> ( X10 @ X9 @ X8 ) )
| ! [X16: a > a > $o] :
( ( ! [X17: a,X18: a] :
( ( X3 @ X18 @ X17 )
=> ( X16 @ X18 @ X17 ) )
& ! [X19: a,X20: a,X21: a] :
( ( ( X16 @ X20 @ X19 )
& ( X16 @ X21 @ X20 ) )
=> ( X16 @ X21 @ X19 ) ) )
=> ( X16 @ X9 @ X8 ) ) )
=> ( X4 @ X9 @ X8 ) ) )
=> ( X4 @ X1 @ X0 ) )
=> ! [X22: a > a > $o] :
( ( ! [X23: a,X24: a,X25: a] :
( ( ( X22 @ X24 @ X23 )
& ( X22 @ X25 @ X24 ) )
=> ( X22 @ X25 @ X23 ) )
& ! [X26: a,X27: a] :
( ( ( X3 @ X26 @ X27 )
| ( X2 @ X26 @ X27 ) )
=> ( X22 @ X26 @ X27 ) ) )
=> ( X22 @ X1 @ X0 ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X3: a,X2: a,X1: a > a > $o,X0: a > a > $o] :
( ! [X4: a > a > $o] :
( ( ! [X6: a,X10: a,X5: a] :
( ( ( X4 @ X5 @ X6 )
& ( X4 @ X6 @ X10 ) )
=> ( X4 @ X5 @ X10 ) )
& ! [X6: a,X5: a] :
( ( ! [X7: a > a > $o] :
( ( ! [X8: a,X9: a] :
( ( X1 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) )
& ! [X8: a,X10: a,X9: a] :
( ( ( X7 @ X8 @ X9 )
& ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) ) )
=> ( X7 @ X5 @ X6 ) )
| ! [X7: a > a > $o] :
( ( ! [X9: a,X8: a] :
( ( X0 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) )
& ! [X10: a,X9: a,X8: a] :
( ( ( X7 @ X9 @ X10 )
& ( X7 @ X8 @ X9 ) )
=> ( X7 @ X8 @ X10 ) ) )
=> ( X7 @ X5 @ X6 ) ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) )
=> ! [X4: a > a > $o] :
( ( ! [X10: a,X6: a,X5: a] :
( ( ( X4 @ X6 @ X10 )
& ( X4 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X10 ) )
& ! [X5: a,X6: a] :
( ( ( X0 @ X5 @ X6 )
| ( X1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
! [X3: a,X2: a,X1: a > a > $o,X0: a > a > $o] :
( ! [X4: a > a > $o] :
( ( ! [X6: a,X10: a,X5: a] :
( ( ( X4 @ X5 @ X6 )
& ( X4 @ X6 @ X10 ) )
=> ( X4 @ X5 @ X10 ) )
& ! [X6: a,X5: a] :
( ( ! [X7: a > a > $o] :
( ( ! [X8: a,X9: a] :
( ( X1 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) )
& ! [X8: a,X10: a,X9: a] :
( ( ( X7 @ X8 @ X9 )
& ( X7 @ X9 @ X10 ) )
=> ( X7 @ X8 @ X10 ) ) )
=> ( X7 @ X5 @ X6 ) )
| ! [X7: a > a > $o] :
( ( ! [X9: a,X8: a] :
( ( X0 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) )
& ! [X10: a,X9: a,X8: a] :
( ( ( X7 @ X9 @ X10 )
& ( X7 @ X8 @ X9 ) )
=> ( X7 @ X8 @ X10 ) ) )
=> ( X7 @ X5 @ X6 ) ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) )
=> ! [X4: a > a > $o] :
( ( ! [X10: a,X6: a,X5: a] :
( ( ( X4 @ X6 @ X10 )
& ( X4 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X10 ) )
& ! [X5: a,X6: a] :
( ( ( X0 @ X5 @ X6 )
| ( X1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM250C_pme) ).
thf(f447,plain,
~ spl0_6,
inference(avatar_contradiction_clause,[],[f446]) ).
thf(f446,plain,
( $false
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f445]) ).
thf(f445,plain,
( ( $true = $false )
| ~ spl0_6 ),
inference(boolean_simplification,[],[f444]) ).
thf(f444,plain,
( ( $true = ~ $true )
| ~ spl0_6 ),
inference(boolean_simplification,[],[f443]) ).
thf(f443,plain,
( ( $true
= ( ~ ( $true
| ( sK2 @ sK16 @ sK15 ) ) ) )
| ~ spl0_6 ),
inference(forward_demodulation,[],[f438,f414]) ).
thf(f414,plain,
( ( $true
= ( sK3 @ sK16 @ sK15 ) )
| ~ spl0_6 ),
inference(binary_proxy_clausification,[],[f357]) ).
thf(f357,plain,
( ( ( ( sK3 @ sK16 @ sK15 )
=> ( sK6 @ sK16 @ sK15 ) )
= $false )
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f356]) ).
thf(f356,plain,
( ( ( ^ [Y0: a] :
( ( sK3 @ Y0 @ sK15 )
=> ( sK6 @ Y0 @ sK15 ) )
@ sK16 )
= $false )
| ~ spl0_6 ),
inference(sigma_clausification,[],[f331]) ).
thf(f331,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ sK15 )
=> ( sK6 @ Y0 @ sK15 ) ) )
= $false )
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f330]) ).
thf(f330,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) )
@ sK15 )
= $false )
| ~ spl0_6 ),
inference(sigma_clausification,[],[f199]) ).
thf(f199,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f198]) ).
thf(f198,plain,
( spl0_6
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
thf(f438,plain,
( ( $true
= ( ~ ( ( sK3 @ sK16 @ sK15 )
| ( sK2 @ sK16 @ sK15 ) ) ) )
| ~ spl0_6 ),
inference(boolean_simplification,[],[f433]) ).
thf(f433,plain,
( ( $true
= ( ( ( sK3 @ sK16 @ sK15 )
| ( sK2 @ sK16 @ sK15 ) )
=> $false ) )
| ~ spl0_6 ),
inference(superposition,[],[f71,f413]) ).
thf(f413,plain,
( ( $false
= ( sK6 @ sK16 @ sK15 ) )
| ~ spl0_6 ),
inference(binary_proxy_clausification,[],[f357]) ).
thf(f71,plain,
! [X2: a,X1: a] :
( $true
= ( ( ( sK3 @ X2 @ X1 )
| ( sK2 @ X2 @ X1 ) )
=> ( sK6 @ X2 @ X1 ) ) ),
inference(beta_eta_normalization,[],[f70]) ).
thf(f70,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK3 @ Y0 @ X1 )
| ( sK2 @ Y0 @ X1 ) )
=> ( sK6 @ Y0 @ X1 ) )
@ X2 ) ),
inference(pi_clausification,[],[f69]) ).
thf(f69,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK3 @ Y0 @ X1 )
| ( sK2 @ Y0 @ X1 ) )
=> ( sK6 @ Y0 @ X1 ) ) ) ),
inference(beta_eta_normalization,[],[f68]) ).
thf(f68,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK3 @ Y1 @ Y0 )
| ( sK2 @ Y1 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[],[f29]) ).
thf(f327,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f326]) ).
thf(f326,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f325]) ).
thf(f325,plain,
( ( $true = $false )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f319,f259]) ).
thf(f259,plain,
( ( $false
= ( sK6 @ sK11 @ sK12 ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f258]) ).
thf(f258,plain,
( ( ( ( ( sK6 @ sK13 @ sK12 )
& ( sK6 @ sK11 @ sK13 ) )
=> ( sK6 @ sK11 @ sK12 ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f257]) ).
thf(f257,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK6 @ Y0 @ sK12 )
& ( sK6 @ sK11 @ Y0 ) )
=> ( sK6 @ sK11 @ sK12 ) )
@ sK13 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f256]) ).
thf(f256,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ Y0 @ sK12 )
& ( sK6 @ sK11 @ Y0 ) )
=> ( sK6 @ sK11 @ sK12 ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f255]) ).
thf(f255,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 @ Y0 )
& ( sK6 @ sK11 @ Y1 ) )
=> ( sK6 @ sK11 @ Y0 ) ) )
@ sK12 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f254]) ).
thf(f254,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 @ Y0 )
& ( sK6 @ sK11 @ Y1 ) )
=> ( sK6 @ sK11 @ Y0 ) ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f250]) ).
thf(f250,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y1 )
& ( sK6 @ Y0 @ Y2 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
@ sK11 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f92]) ).
thf(f92,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y1 )
& ( sK6 @ Y0 @ Y2 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f91]) ).
thf(f91,plain,
( spl0_1
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y1 )
& ( sK6 @ Y0 @ Y2 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f319,plain,
( ( $true
= ( sK6 @ sK11 @ sK12 ) )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f317]) ).
thf(f317,plain,
( ( ( $true
=> ( sK6 @ sK11 @ sK12 ) )
= $true )
| ~ spl0_1 ),
inference(superposition,[],[f292,f282]) ).
thf(f282,plain,
( ( $true
= ( sK6 @ sK11 @ sK14 ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f279]) ).
thf(f279,plain,
( ( $true
= ( ( sK6 @ sK14 @ sK12 )
& ( sK6 @ sK11 @ sK14 ) ) )
| ~ spl0_1 ),
inference(not_proxy_clausification,[],[f268]) ).
thf(f268,plain,
( ( ( ~ ( ( sK6 @ sK14 @ sK12 )
& ( sK6 @ sK11 @ sK14 ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f267]) ).
thf(f267,plain,
( ( ( ^ [Y0: a] :
~ ( ( sK6 @ Y0 @ sK12 )
& ( sK6 @ sK11 @ Y0 ) )
@ sK14 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f264]) ).
thf(f264,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
~ ( ( sK6 @ Y0 @ sK12 )
& ( sK6 @ sK11 @ Y0 ) ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f262]) ).
thf(f262,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ Y0 @ sK12 )
& ( sK6 @ sK11 @ Y0 ) )
=> $false ) ) )
| ~ spl0_1 ),
inference(backward_demodulation,[],[f256,f259]) ).
thf(f292,plain,
( ! [X0: a] :
( $true
= ( ( sK6 @ X0 @ sK14 )
=> ( sK6 @ X0 @ sK12 ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f288]) ).
thf(f288,plain,
( ! [X0: a] :
( $true
= ( ( ( sK6 @ X0 @ sK14 )
& $true )
=> ( sK6 @ X0 @ sK12 ) ) )
| ~ spl0_1 ),
inference(superposition,[],[f37,f285]) ).
thf(f285,plain,
( ( $true
= ( sK6 @ sK14 @ sK12 ) )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f284]) ).
thf(f284,plain,
( ( $true
= ( ( sK6 @ sK14 @ sK12 )
& $true ) )
| ~ spl0_1 ),
inference(backward_demodulation,[],[f279,f282]) ).
thf(f247,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f246]) ).
thf(f246,plain,
( $false
| ~ spl0_2
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f245]) ).
thf(f245,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_4 ),
inference(boolean_simplification,[],[f244]) ).
thf(f244,plain,
( ( $true = ~ $true )
| ~ spl0_2
| ~ spl0_4 ),
inference(boolean_simplification,[],[f243]) ).
thf(f243,plain,
( ( $true
= ( ~ ( ( sK3 @ sK9 @ sK10 )
| $true ) ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_demodulation,[],[f237,f230]) ).
thf(f230,plain,
( ( $true
= ( sK2 @ sK9 @ sK10 ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f228]) ).
thf(f228,plain,
( ( ( ( sK2 @ sK9 @ sK10 )
=> ( sK6 @ sK9 @ sK10 ) )
= $false )
| ~ spl0_2
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f227]) ).
thf(f227,plain,
( ( ( ^ [Y0: a] :
( ( sK2 @ sK9 @ Y0 )
=> ( sK6 @ sK9 @ Y0 ) )
@ sK10 )
= $false )
| ~ spl0_2
| ~ spl0_4 ),
inference(sigma_clausification,[],[f224]) ).
thf(f224,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK9 @ Y0 )
=> ( sK6 @ sK9 @ Y0 ) ) )
= $false )
| ~ spl0_2
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f222]) ).
thf(f222,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK6 @ Y0 @ Y1 ) ) )
@ sK9 )
= $false )
| ~ spl0_2
| ~ spl0_4 ),
inference(sigma_clausification,[],[f219]) ).
thf(f219,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
= $false )
| ~ spl0_2
| ~ spl0_4 ),
inference(not_proxy_clausification,[],[f216]) ).
thf(f216,plain,
( ( $true
= ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(boolean_simplification,[],[f215]) ).
thf(f215,plain,
( ( $true
= ( ~ ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_demodulation,[],[f214,f31]) ).
thf(f214,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y1 @ Y2 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(boolean_simplification,[],[f206]) ).
thf(f206,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y1 @ Y2 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
=> $false ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(superposition,[],[f204,f121]) ).
thf(f121,plain,
( ( ( sK6 @ sK7 @ sK8 )
= $false )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f120]) ).
thf(f120,plain,
( ( ( $true
=> ( sK6 @ sK7 @ sK8 ) )
= $false )
| ~ spl0_2 ),
inference(backward_demodulation,[],[f117,f119]) ).
thf(f119,plain,
( ( $true
= ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f117]) ).
thf(f117,plain,
( ( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) ) )
=> ( sK6 @ sK7 @ sK8 ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f116]) ).
thf(f116,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK7 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK7 @ Y0 ) ) ) )
=> ( sK6 @ sK7 @ Y0 ) )
@ sK8 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f109]) ).
thf(f109,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK7 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK3 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK7 @ Y0 ) ) ) )
=> ( sK6 @ sK7 @ Y0 ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f105]) ).
thf(f105,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( sK6 @ Y0 @ Y1 ) ) )
@ sK7 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f95]) ).
thf(f95,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
= $false )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f94]) ).
thf(f94,plain,
( spl0_2
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f204,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y0 @ Y1 )
& ( X1 @ Y1 @ Y2 ) )
=> ( X1 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( X1 @ Y0 @ Y1 ) ) ) ) )
=> ( X1 @ sK7 @ sK8 ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f203]) ).
thf(f203,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) )
@ X1 ) )
| ~ spl0_4 ),
inference(pi_clausification,[],[f171]) ).
thf(f171,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f170]) ).
thf(f170,plain,
( spl0_4
<=> ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
thf(f237,plain,
( ( $true
= ( ~ ( ( sK3 @ sK9 @ sK10 )
| ( sK2 @ sK9 @ sK10 ) ) ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(boolean_simplification,[],[f233]) ).
thf(f233,plain,
( ( $true
= ( ( ( sK3 @ sK9 @ sK10 )
| ( sK2 @ sK9 @ sK10 ) )
=> $false ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(superposition,[],[f71,f232]) ).
thf(f232,plain,
( ( ( sK6 @ sK9 @ sK10 )
= $false )
| ~ spl0_2
| ~ spl0_4 ),
inference(boolean_simplification,[],[f231]) ).
thf(f231,plain,
( ( ( $true
=> ( sK6 @ sK9 @ sK10 ) )
= $false )
| ~ spl0_2
| ~ spl0_4 ),
inference(backward_demodulation,[],[f228,f230]) ).
thf(f200,plain,
( spl0_5
| spl0_6
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f191,f167,f94,f198,f195]) ).
thf(f167,plain,
( spl0_3
<=> ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
thf(f191,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
= $false )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f185]) ).
thf(f185,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_2
| ~ spl0_3 ),
inference(not_proxy_clausification,[],[f181]) ).
thf(f181,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(boolean_simplification,[],[f178]) ).
thf(f178,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
=> $false ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[],[f176,f121]) ).
thf(f176,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y0 @ Y1 )
& ( X1 @ Y2 @ Y0 ) )
=> ( X1 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( X1 @ Y1 @ Y0 ) ) ) ) )
=> ( X1 @ sK7 @ sK8 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f175]) ).
thf(f175,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) )
@ X1 ) )
| ~ spl0_3 ),
inference(pi_clausification,[],[f168]) ).
thf(f168,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) )
= $true )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f167]) ).
thf(f172,plain,
( spl0_3
| spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f165,f94,f170,f167]) ).
thf(f165,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) )
= $true )
| ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK7 @ sK8 ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f119]) ).
thf(f96,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f87,f94,f91]) ).
thf(f87,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y1 )
& ( sK6 @ Y0 @ Y2 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f78]) ).
thf(f78,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y1 )
& ( sK6 @ Y0 @ Y2 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f60]) ).
thf(f60,plain,
( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y1 )
& ( sK6 @ Y0 @ Y2 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f59]) ).
thf(f59,plain,
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y1 )
& ( sK6 @ Y0 @ Y2 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) ) )
=> $false ) ),
inference(superposition,[],[f48,f27]) ).
thf(f27,plain,
( ( sK6 @ sK4 @ sK5 )
= $false ),
inference(boolean_simplification,[],[f26]) ).
thf(f26,plain,
( ( $true
=> ( sK6 @ sK4 @ sK5 ) )
= $false ),
inference(backward_demodulation,[],[f23,f25]) ).
thf(f48,plain,
! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( X1 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y2 @ Y1 )
& ( X1 @ Y0 @ Y2 ) )
=> ( X1 @ Y0 @ Y1 ) ) ) ) ) )
=> ( X1 @ sK4 @ sK5 ) ) ),
inference(beta_eta_normalization,[],[f47]) ).
thf(f47,plain,
! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK3 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK4 @ sK5 ) )
@ X1 ) ),
inference(pi_clausification,[],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEV140^5 : TPTP v8.2.0. Released v4.0.0.
% 0.06/0.13 % 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
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun May 19 18:24:52 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.34 This is a TH0_THM_NEQ_NAR problem
% 0.13/0.34 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
% 0.13/0.36 % (13013)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.13/0.36 % (13015)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)
% 0.13/0.36 % (13014)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)
% 0.13/0.36 % (13016)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.13/0.36 % (13017)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)
% 0.13/0.36 % (13019)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.13/0.36 % (13016)Instruction limit reached!
% 0.13/0.36 % (13016)------------------------------
% 0.13/0.36 % (13016)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.36 % (13016)Termination reason: Unknown
% 0.13/0.36 % (13016)Termination phase: Unused predicate definition removal
% 0.13/0.36 % (13017)Instruction limit reached!
% 0.13/0.36 % (13017)------------------------------
% 0.13/0.36 % (13017)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.36 % (13017)Termination reason: Unknown
% 0.13/0.36 % (13017)Termination phase: shuffling
% 0.13/0.36
% 0.13/0.36 % (13017)Memory used [KB]: 1023
% 0.13/0.36 % (13017)Time elapsed: 0.003 s
% 0.13/0.36 % (13017)Instructions burned: 3 (million)
% 0.13/0.36 % (13017)------------------------------
% 0.13/0.36 % (13017)------------------------------
% 0.13/0.36
% 0.13/0.36 % (13016)Memory used [KB]: 895
% 0.13/0.36 % (13016)Time elapsed: 0.003 s
% 0.13/0.36 % (13016)Instructions burned: 2 (million)
% 0.13/0.36 % (13016)------------------------------
% 0.13/0.36 % (13016)------------------------------
% 0.13/0.36 % (13014)Instruction limit reached!
% 0.13/0.36 % (13014)------------------------------
% 0.13/0.36 % (13014)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.36 % (13014)Termination reason: Unknown
% 0.13/0.36 % (13014)Termination phase: Property scanning
% 0.13/0.36
% 0.13/0.36 % (13014)Memory used [KB]: 1023
% 0.13/0.36 % (13014)Time elapsed: 0.004 s
% 0.13/0.36 % (13014)Instructions burned: 4 (million)
% 0.13/0.36 % (13014)------------------------------
% 0.13/0.36 % (13014)------------------------------
% 0.13/0.36 % (13018)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)
% 0.13/0.37 % (13019)Instruction limit reached!
% 0.13/0.37 % (13019)------------------------------
% 0.13/0.37 % (13019)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (13019)Termination reason: Unknown
% 0.13/0.37 % (13019)Termination phase: Saturation
% 0.13/0.37
% 0.13/0.37 % (13019)Memory used [KB]: 5628
% 0.13/0.37 % (13019)Time elapsed: 0.013 s
% 0.13/0.37 % (13019)Instructions burned: 19 (million)
% 0.13/0.37 % (13019)------------------------------
% 0.13/0.37 % (13019)------------------------------
% 0.13/0.37 % (13020)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)
% 0.13/0.37 % (13020)Instruction limit reached!
% 0.13/0.37 % (13020)------------------------------
% 0.13/0.37 % (13020)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (13022)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)
% 0.13/0.37 % (13020)Termination reason: Unknown
% 0.13/0.37 % (13020)Termination phase: Property scanning
% 0.13/0.37
% 0.13/0.37 % (13020)Memory used [KB]: 1023
% 0.13/0.37 % (13020)Time elapsed: 0.004 s
% 0.13/0.37 % (13020)Instructions burned: 4 (million)
% 0.13/0.37 % (13020)------------------------------
% 0.13/0.37 % (13020)------------------------------
% 0.13/0.37 % (13015)Instruction limit reached!
% 0.13/0.37 % (13015)------------------------------
% 0.13/0.37 % (13015)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (13015)Termination reason: Unknown
% 0.13/0.37 % (13015)Termination phase: Saturation
% 0.13/0.37
% 0.13/0.37 % (13015)Memory used [KB]: 5628
% 0.13/0.37 % (13015)Time elapsed: 0.017 s
% 0.13/0.37 % (13015)Instructions burned: 28 (million)
% 0.13/0.37 % (13015)------------------------------
% 0.13/0.37 % (13015)------------------------------
% 0.13/0.37 % (13021)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)
% 0.13/0.37 % (13023)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)
% 0.13/0.38 % (13023)Instruction limit reached!
% 0.13/0.38 % (13023)------------------------------
% 0.13/0.38 % (13023)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38 % (13023)Termination reason: Unknown
% 0.13/0.38 % (13023)Termination phase: Property scanning
% 0.13/0.38
% 0.13/0.38 % (13023)Memory used [KB]: 1023
% 0.13/0.38 % (13023)Time elapsed: 0.004 s
% 0.13/0.38 % (13023)Instructions burned: 4 (million)
% 0.13/0.38 % (13023)------------------------------
% 0.13/0.38 % (13023)------------------------------
% 0.13/0.38 % (13022)Instruction limit reached!
% 0.13/0.38 % (13022)------------------------------
% 0.13/0.38 % (13022)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38 % (13022)Termination reason: Unknown
% 0.13/0.38 % (13022)Termination phase: Saturation
% 0.13/0.38
% 0.13/0.38 % (13022)Memory used [KB]: 5756
% 0.13/0.38 % (13022)Time elapsed: 0.010 s
% 0.13/0.38 % (13022)Instructions burned: 16 (million)
% 0.13/0.38 % (13022)------------------------------
% 0.13/0.38 % (13022)------------------------------
% 0.13/0.38 % (13024)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)
% 0.13/0.39 % (13025)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.13/0.39 % (13026)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.13/0.39 % (13027)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)
% 0.13/0.39 % (13025)Instruction limit reached!
% 0.13/0.39 % (13025)------------------------------
% 0.13/0.39 % (13025)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.39 % (13025)Termination reason: Unknown
% 0.13/0.39 % (13025)Termination phase: Saturation
% 0.13/0.39
% 0.13/0.39 % (13025)Memory used [KB]: 1023
% 0.13/0.39 % (13025)Time elapsed: 0.006 s
% 0.13/0.39 % (13025)Instructions burned: 7 (million)
% 0.13/0.39 % (13025)------------------------------
% 0.13/0.39 % (13025)------------------------------
% 0.13/0.39 % (13021)Instruction limit reached!
% 0.13/0.39 % (13021)------------------------------
% 0.13/0.39 % (13021)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.39 % (13021)Termination reason: Unknown
% 0.13/0.39 % (13021)Termination phase: Saturation
% 0.13/0.39
% 0.13/0.39 % (13021)Memory used [KB]: 5628
% 0.13/0.39 % (13021)Time elapsed: 0.021 s
% 0.13/0.39 % (13021)Instructions burned: 37 (million)
% 0.13/0.39 % (13021)------------------------------
% 0.13/0.39 % (13021)------------------------------
% 0.13/0.39 % (13027)Instruction limit reached!
% 0.13/0.39 % (13027)------------------------------
% 0.13/0.39 % (13027)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.39 % (13027)Termination reason: Unknown
% 0.13/0.39 % (13027)Termination phase: Property scanning
% 0.13/0.39
% 0.13/0.39 % (13027)Memory used [KB]: 1023
% 0.13/0.39 % (13027)Time elapsed: 0.004 s
% 0.13/0.39 % (13027)Instructions burned: 4 (million)
% 0.13/0.39 % (13027)------------------------------
% 0.13/0.39 % (13027)------------------------------
% 0.13/0.39 % (13028)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)
% 0.13/0.39 % (13028)Instruction limit reached!
% 0.13/0.39 % (13028)------------------------------
% 0.13/0.39 % (13028)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.39 % (13028)Termination reason: Unknown
% 0.13/0.39 % (13028)Termination phase: Preprocessing 3
% 0.13/0.39
% 0.13/0.39 % (13028)Memory used [KB]: 1023
% 0.13/0.39 % (13028)Time elapsed: 0.003 s
% 0.13/0.39 % (13028)Instructions burned: 3 (million)
% 0.13/0.39 % (13028)------------------------------
% 0.13/0.39 % (13028)------------------------------
% 0.19/0.40 % (13026)Instruction limit reached!
% 0.19/0.40 % (13026)------------------------------
% 0.19/0.40 % (13026)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.40 % (13026)Termination reason: Unknown
% 0.19/0.40 % (13026)Termination phase: Saturation
% 0.19/0.40
% 0.19/0.40 % (13026)Memory used [KB]: 5628
% 0.19/0.40 % (13026)Time elapsed: 0.011 s
% 0.19/0.40 % (13026)Instructions burned: 16 (million)
% 0.19/0.40 % (13026)------------------------------
% 0.19/0.40 % (13026)------------------------------
% 0.19/0.41 % (13029)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)
% 0.19/0.41 % (13030)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)
% 0.19/0.41 % (13031)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.19/0.41 % (13030)Instruction limit reached!
% 0.19/0.41 % (13030)------------------------------
% 0.19/0.41 % (13030)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.41 % (13030)Termination reason: Unknown
% 0.19/0.41 % (13030)Termination phase: Property scanning
% 0.19/0.41
% 0.19/0.41 % (13030)Memory used [KB]: 1023
% 0.19/0.41 % (13030)Time elapsed: 0.003 s
% 0.19/0.41 % (13030)Instructions burned: 3 (million)
% 0.19/0.41 % (13030)------------------------------
% 0.19/0.41 % (13030)------------------------------
% 0.19/0.41 % (13032)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)
% 0.19/0.41 % (13029)Instruction limit reached!
% 0.19/0.41 % (13029)------------------------------
% 0.19/0.41 % (13029)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.41 % (13029)Termination reason: Unknown
% 0.19/0.41 % (13029)Termination phase: Saturation
% 0.19/0.41
% 0.19/0.41 % (13029)Memory used [KB]: 5500
% 0.19/0.41 % (13029)Time elapsed: 0.006 s
% 0.19/0.41 % (13029)Instructions burned: 7 (million)
% 0.19/0.41 % (13029)------------------------------
% 0.19/0.41 % (13029)------------------------------
% 0.19/0.41 % (13031)Instruction limit reached!
% 0.19/0.41 % (13031)------------------------------
% 0.19/0.41 % (13031)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.41 % (13031)Termination reason: Unknown
% 0.19/0.41 % (13031)Termination phase: Saturation
% 0.19/0.41
% 0.19/0.41 % (13031)Memory used [KB]: 5500
% 0.19/0.41 % (13031)Time elapsed: 0.005 s
% 0.19/0.41 % (13031)Instructions burned: 5 (million)
% 0.19/0.41 % (13031)------------------------------
% 0.19/0.41 % (13031)------------------------------
% 0.19/0.42 % (13032)Instruction limit reached!
% 0.19/0.42 % (13032)------------------------------
% 0.19/0.42 % (13032)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.42 % (13032)Termination reason: Unknown
% 0.19/0.42 % (13032)Termination phase: Saturation
% 0.19/0.42
% 0.19/0.42 % (13032)Memory used [KB]: 5628
% 0.19/0.42 % (13032)Time elapsed: 0.010 s
% 0.19/0.42 % (13032)Instructions burned: 18 (million)
% 0.19/0.42 % (13032)------------------------------
% 0.19/0.42 % (13032)------------------------------
% 0.19/0.42 % (13034)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.19/0.42 % (13035)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)
% 0.19/0.42 % (13037)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.19/0.42 % (13033)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.19/0.42 % (13036)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)
% 0.19/0.43 % (13034)Instruction limit reached!
% 0.19/0.43 % (13034)------------------------------
% 0.19/0.43 % (13034)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.43 % (13034)Termination reason: Unknown
% 0.19/0.43 % (13034)Termination phase: Saturation
% 0.19/0.43
% 0.19/0.43 % (13034)Memory used [KB]: 5500
% 0.19/0.43 % (13034)Time elapsed: 0.005 s
% 0.19/0.43 % (13034)Instructions burned: 6 (million)
% 0.19/0.43 % (13034)------------------------------
% 0.19/0.43 % (13034)------------------------------
% 0.19/0.43 % (13037)Instruction limit reached!
% 0.19/0.43 % (13037)------------------------------
% 0.19/0.43 % (13037)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.43 % (13037)Termination reason: Unknown
% 0.19/0.43 % (13037)Termination phase: Saturation
% 0.19/0.43
% 0.19/0.43 % (13037)Memory used [KB]: 5500
% 0.19/0.43 % (13037)Time elapsed: 0.003 s
% 0.19/0.43 % (13037)Instructions burned: 6 (million)
% 0.19/0.43 % (13037)------------------------------
% 0.19/0.43 % (13037)------------------------------
% 0.19/0.43 % (13039)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2999ds/377Mi)
% 0.19/0.44 % (13036)Instruction limit reached!
% 0.19/0.44 % (13036)------------------------------
% 0.19/0.44 % (13036)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.44 % (13036)Termination reason: Unknown
% 0.19/0.44 % (13036)Termination phase: Saturation
% 0.19/0.44
% 0.19/0.44 % (13036)Memory used [KB]: 5756
% 0.19/0.44 % (13036)Time elapsed: 0.015 s
% 0.19/0.44 % (13036)Instructions burned: 21 (million)
% 0.19/0.44 % (13036)------------------------------
% 0.19/0.44 % (13036)------------------------------
% 0.19/0.44 % (13038)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)
% 0.19/0.44 % (13038)Instruction limit reached!
% 0.19/0.44 % (13038)------------------------------
% 0.19/0.44 % (13038)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.44 % (13038)Termination reason: Unknown
% 0.19/0.44 % (13038)Termination phase: Saturation
% 0.19/0.44
% 0.19/0.44 % (13038)Memory used [KB]: 5500
% 0.19/0.44 % (13038)Time elapsed: 0.005 s
% 0.19/0.44 % (13038)Instructions burned: 7 (million)
% 0.19/0.44 % (13038)------------------------------
% 0.19/0.44 % (13038)------------------------------
% 0.19/0.45 % (13013)Instruction limit reached!
% 0.19/0.45 % (13013)------------------------------
% 0.19/0.45 % (13013)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.45 % (13013)Termination reason: Unknown
% 0.19/0.45 % (13013)Termination phase: Saturation
% 0.19/0.45
% 0.19/0.45 % (13013)Memory used [KB]: 6140
% 0.19/0.45 % (13013)Time elapsed: 0.090 s
% 0.19/0.45 % (13013)Instructions burned: 183 (million)
% 0.19/0.45 % (13013)------------------------------
% 0.19/0.45 % (13013)------------------------------
% 0.19/0.45 % (13040)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)
% 0.19/0.46 % (13041)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on theBenchmark for (2998ds/19Mi)
% 0.19/0.46 % (13042)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on theBenchmark for (2998ds/879Mi)
% 0.19/0.47 % (13041)Instruction limit reached!
% 0.19/0.47 % (13041)------------------------------
% 0.19/0.47 % (13041)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.47 % (13041)Termination reason: Unknown
% 0.19/0.47 % (13041)Termination phase: Saturation
% 0.19/0.47
% 0.19/0.47 % (13041)Memory used [KB]: 5500
% 0.19/0.47 % (13041)Time elapsed: 0.011 s
% 0.19/0.47 % (13041)Instructions burned: 19 (million)
% 0.19/0.47 % (13041)------------------------------
% 0.19/0.47 % (13041)------------------------------
% 0.19/0.47 % (13024)First to succeed.
% 0.19/0.48 % (13043)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2998ds/17Mi)
% 0.19/0.48 % (13024)Refutation found. Thanks to Tanya!
% 0.19/0.48 % SZS status Theorem for theBenchmark
% 0.19/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.48 % (13024)------------------------------
% 0.19/0.48 % (13024)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.48 % (13024)Termination reason: Refutation
% 0.19/0.48
% 0.19/0.48 % (13024)Memory used [KB]: 6140
% 0.19/0.48 % (13024)Time elapsed: 0.121 s
% 0.19/0.48 % (13024)Instructions burned: 117 (million)
% 0.19/0.48 % (13024)------------------------------
% 0.19/0.48 % (13024)------------------------------
% 0.19/0.48 % (13012)Success in time 0.143 s
% 0.19/0.48 % Vampire---4.8 exiting
%------------------------------------------------------------------------------