TSTP Solution File: SEV140^5 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEV140^5 : TPTP v8.1.2. 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/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n018.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 : Sun May 5 09:41:29 EDT 2024
% Result : Theorem 0.21s 0.47s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 32
% Syntax : Number of formulae : 157 ( 43 unt; 23 typ; 0 def)
% Number of atoms : 1345 ( 120 equ; 0 cnn)
% Maximal formula atoms : 4 ( 10 avg)
% Number of connectives : 4657 ( 106 ~; 154 |; 256 &;3043 @)
% ( 8 <=>; 405 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 438 ( 438 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 29 usr; 28 con; 0-2 aty)
% ( 685 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 821 ( 712 ^ 108 !; 0 ?; 821 :)
% ( 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 ).
thf(func_def_21,type,
sK3: a > a > $o ).
thf(func_def_22,type,
sK4: a > a > $o ).
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(f381,plain,
$false,
inference(avatar_sat_refutation,[],[f96,f127,f167,f225,f244,f276,f314,f342,f379]) ).
thf(f379,plain,
~ spl0_10,
inference(avatar_contradiction_clause,[],[f378]) ).
thf(f378,plain,
( $false
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f375]) ).
thf(f375,plain,
( ( $false = $true )
| ~ spl0_10 ),
inference(superposition,[],[f35,f372]) ).
thf(f372,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ sK19 @ sK20 )
& ( sK6 @ sK20 @ Y0 ) )
=> ( sK6 @ sK19 @ Y0 ) ) ) )
| ~ spl0_10 ),
inference(beta_eta_normalization,[],[f371]) ).
thf(f371,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ sK19 @ Y0 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ sK19 @ Y1 ) ) )
@ sK20 ) )
| ~ spl0_10 ),
inference(sigma_clausification,[],[f368]) ).
thf(f368,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ sK19 @ Y0 )
& ( sK6 @ Y0 @ Y1 ) )
=> ( sK6 @ sK19 @ Y1 ) ) ) ) )
| ~ spl0_10 ),
inference(beta_eta_normalization,[],[f366]) ).
thf(f366,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y1 @ Y2 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) )
@ sK19 ) )
| ~ spl0_10 ),
inference(sigma_clausification,[],[f313]) ).
thf(f313,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y1 @ Y2 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) ) )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f312]) ).
thf(f312,plain,
( spl0_10
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y1 @ Y2 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
thf(f35,plain,
! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ X2 @ X1 )
& ( sK6 @ X1 @ Y0 ) )
=> ( sK6 @ X2 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[],[f34]) ).
thf(f34,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 @ X1 )
& ( sK6 @ X1 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) )
@ X2 ) ),
inference(pi_clausification,[],[f33]) ).
thf(f33,plain,
! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 @ X1 )
& ( sK6 @ X1 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[],[f32]) ).
thf(f32,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y0 )
& ( sK6 @ Y0 @ Y2 ) )
=> ( sK6 @ Y1 @ Y2 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[],[f31]) ).
thf(f31,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y0 )
& ( sK6 @ Y0 @ Y2 ) )
=> ( sK6 @ Y1 @ Y2 ) ) ) ) ) ),
inference(boolean_simplification,[],[f30]) ).
thf(f30,plain,
( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y0 )
& ( sK6 @ Y0 @ Y2 ) )
=> ( sK6 @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(backward_demodulation,[],[f25,f29]) ).
thf(f29,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f25]) ).
thf(f25,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y0 )
& ( sK6 @ Y0 @ Y2 ) )
=> ( sK6 @ Y1 @ Y2 ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[],[f23]) ).
thf(f23,plain,
( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y0 )
& ( sK6 @ Y0 @ Y2 ) )
=> ( sK6 @ Y1 @ Y2 ) ) ) ) ) )
=> ( sK6 @ sK5 @ sK2 ) ) ),
inference(beta_eta_normalization,[],[f22]) ).
thf(f22,plain,
( $false
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK5 @ sK2 ) )
@ sK6 ) ),
inference(sigma_clausification,[],[f21]) ).
thf(f21,plain,
( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK5 @ sK2 ) ) ) ),
inference(boolean_simplification,[],[f20]) ).
thf(f20,plain,
( $false
= ( $true
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK5 @ sK2 ) ) ) ) ),
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 @ Y5 @ Y6 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK4 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
| ( !! @ ( 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] :
( ( 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 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK5 @ sK2 ) ) ) ),
inference(binary_proxy_clausification,[],[f17]) ).
thf(f17,plain,
( $false
= ( ( !! @ ( 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 @ Y5 @ Y6 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK4 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
| ( !! @ ( 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] :
( ( 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 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK5 @ sK2 ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y1 @ Y2 )
| ( sK3 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK5 @ sK2 ) ) ) ) ),
inference(beta_eta_normalization,[],[f16]) ).
thf(f16,plain,
( $false
= ( ^ [Y0: a] :
( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y7 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK4 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) )
| ( !! @ ( 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] :
( ( 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 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK2 ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y2 @ Y3 )
| ( sK3 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK2 ) ) ) )
@ sK5 ) ),
inference(sigma_clausification,[],[f15]) ).
thf(f15,plain,
( $false
= ( !! @ 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 @ Y6 @ Y7 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK4 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) )
| ( !! @ ( 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] :
( ( 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 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK2 ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK4 @ Y2 @ Y3 )
| ( sK3 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK2 ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f14]) ).
thf(f14,plain,
( $false
= ( ^ [Y0: a > a > $o] :
( !! @ 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 @ Y7 @ Y8 )
& ( Y5 @ Y8 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y0 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) )
| ( !! @ ( 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] :
( ( 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 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ sK2 ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ sK2 ) ) ) ) )
@ sK4 ) ),
inference(sigma_clausification,[],[f13]) ).
thf(f13,plain,
( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ 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 @ Y7 @ Y8 )
& ( Y5 @ Y8 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y0 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) )
| ( !! @ ( 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] :
( ( 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 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ sK2 ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y4 )
| ( sK3 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ sK2 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f12]) ).
thf(f12,plain,
( $false
= ( ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ 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 @ Y8 @ Y9 )
& ( Y6 @ Y9 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y1 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) )
| ( !! @ ( 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] :
( ( 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 @ Y5 @ Y4 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y2 @ sK2 ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y4 @ Y5 )
| ( Y0 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y2 @ sK2 ) ) ) ) ) )
@ sK3 ) ),
inference(sigma_clausification,[],[f11]) ).
thf(f11,plain,
( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ 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 @ Y8 @ Y9 )
& ( Y6 @ Y9 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y1 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) )
| ( !! @ ( 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] :
( ( 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 @ Y5 @ Y4 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y2 @ sK2 ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y4 @ Y5 )
| ( Y0 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y2 @ sK2 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f10]) ).
thf(f10,plain,
( $false
= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ 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 @ Y9 @ Y10 )
& ( Y7 @ Y10 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y2 @ Y9 @ Y8 )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) )
| ( !! @ ( 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] :
( ( 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 @ Y6 @ Y5 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y0 ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y2 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y5 )
& ( Y4 @ Y5 @ Y7 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y0 ) ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_clausification,[],[f7]) ).
thf(f7,plain,
( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ 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 @ Y9 @ Y10 )
& ( Y7 @ Y10 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y2 @ Y9 @ Y8 )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) )
| ( !! @ ( 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] :
( ( 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 @ Y6 @ Y5 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y0 ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y2 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y5 )
& ( Y4 @ Y5 @ Y7 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y0 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f6]) ).
thf(f6,plain,
( ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ 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 @ Y9 @ Y10 )
& ( Y7 @ Y10 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y2 @ Y9 @ Y8 )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) )
| ( !! @ ( 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] :
( ( 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 @ Y6 @ Y5 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y0 ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y2 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y5 )
& ( Y4 @ Y5 @ Y7 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y0 ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f5]) ).
thf(f5,plain,
( ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ 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 @ Y9 @ Y10 )
& ( Y7 @ Y10 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y2 @ Y9 @ Y8 )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) )
| ( !! @ ( 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] :
( ( 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 @ Y6 @ Y5 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y0 ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y2 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y5 )
& ( Y4 @ Y5 @ Y7 ) )
=> ( Y4 @ Y6 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y0 ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
~ ! [X0: a,X1: a > a > $o,X2: a > a > $o,X3: a] :
( ! [X4: a > a > $o] :
( ( ! [X5: a,X6: a,X7: a] :
( ( ( X4 @ X6 @ X7 )
& ( X4 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X7 ) )
& ! [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 @ X14 @ X13 )
& ( X10 @ X15 @ X14 ) )
=> ( X10 @ X15 @ X13 ) ) )
=> ( X10 @ X9 @ X8 ) )
| ! [X16: a > a > $o] :
( ( ! [X17: a,X18: a] :
( ( X1 @ X17 @ X18 )
=> ( X16 @ X17 @ X18 ) )
& ! [X19: a,X20: a,X21: a] :
( ( ( X16 @ X19 @ X21 )
& ( X16 @ X20 @ X19 ) )
=> ( X16 @ X20 @ X21 ) ) )
=> ( X16 @ X9 @ X8 ) ) )
=> ( X4 @ X9 @ X8 ) ) )
=> ( X4 @ X0 @ X3 ) )
=> ! [X22: a > a > $o] :
( ( ! [X23: a,X24: a,X25: a] :
( ( ( X22 @ X25 @ X23 )
& ( X22 @ X24 @ X25 ) )
=> ( X22 @ X24 @ X23 ) )
& ! [X26: a,X27: a] :
( ( ( X2 @ X27 @ X26 )
| ( X1 @ X27 @ X26 ) )
=> ( X22 @ X27 @ X26 ) ) )
=> ( X22 @ X0 @ X3 ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X2: a,X1: a > a > $o,X0: a > a > $o,X3: a] :
( ! [X4: a > a > $o] :
( ( ! [X5: a,X6: a,X10: a] :
( ( ( X4 @ X6 @ X10 )
& ( X4 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X10 ) )
& ! [X6: a,X5: a] :
( ( ! [X7: a > a > $o] :
( ( ! [X8: a,X9: 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 ) )
| ! [X7: a > a > $o] :
( ( ! [X8: a,X9: a] :
( ( X1 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) )
& ! [X9: a,X8: a,X10: 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,X5: a,X6: a] :
( ( ( X4 @ X6 @ X10 )
& ( X4 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X10 ) )
& ! [X6: a,X5: a] :
( ( ( X0 @ X5 @ X6 )
| ( X1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
! [X2: a,X1: a > a > $o,X0: a > a > $o,X3: a] :
( ! [X4: a > a > $o] :
( ( ! [X5: a,X6: a,X10: a] :
( ( ( X4 @ X6 @ X10 )
& ( X4 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X10 ) )
& ! [X6: a,X5: a] :
( ( ! [X7: a > a > $o] :
( ( ! [X8: a,X9: 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 ) )
| ! [X7: a > a > $o] :
( ( ! [X8: a,X9: a] :
( ( X1 @ X8 @ X9 )
=> ( X7 @ X8 @ X9 ) )
& ! [X9: a,X8: a,X10: 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,X5: a,X6: a] :
( ( ( X4 @ X6 @ X10 )
& ( X4 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X10 ) )
& ! [X6: a,X5: a] :
( ( ( X0 @ X5 @ X6 )
| ( X1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.aHb9lTsZOS/Vampire---4.8_19544',cTHM250C_pme) ).
thf(f342,plain,
~ spl0_9,
inference(avatar_contradiction_clause,[],[f341]) ).
thf(f341,plain,
( $false
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f340]) ).
thf(f340,plain,
( ( $false = $true )
| ~ spl0_9 ),
inference(boolean_simplification,[],[f339]) ).
thf(f339,plain,
( ( $true = ~ $true )
| ~ spl0_9 ),
inference(boolean_simplification,[],[f338]) ).
thf(f338,plain,
( ( $true
= ( ~ ( ( sK4 @ sK18 @ sK17 )
| $true ) ) )
| ~ spl0_9 ),
inference(forward_demodulation,[],[f332,f325]) ).
thf(f325,plain,
( ( ( sK3 @ sK18 @ sK17 )
= $true )
| ~ spl0_9 ),
inference(binary_proxy_clausification,[],[f323]) ).
thf(f323,plain,
( ( $false
= ( ( sK3 @ sK18 @ sK17 )
=> ( sK6 @ sK18 @ sK17 ) ) )
| ~ spl0_9 ),
inference(beta_eta_normalization,[],[f322]) ).
thf(f322,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK3 @ Y0 @ sK17 )
=> ( sK6 @ Y0 @ sK17 ) )
@ sK18 ) )
| ~ spl0_9 ),
inference(sigma_clausification,[],[f319]) ).
thf(f319,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK3 @ Y0 @ sK17 )
=> ( sK6 @ Y0 @ sK17 ) ) ) )
| ~ spl0_9 ),
inference(beta_eta_normalization,[],[f317]) ).
thf(f317,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) )
@ sK17 ) )
| ~ spl0_9 ),
inference(sigma_clausification,[],[f310]) ).
thf(f310,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f309]) ).
thf(f309,plain,
( spl0_9
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
thf(f332,plain,
( ( $true
= ( ~ ( ( sK4 @ sK18 @ sK17 )
| ( sK3 @ sK18 @ sK17 ) ) ) )
| ~ spl0_9 ),
inference(boolean_simplification,[],[f328]) ).
thf(f328,plain,
( ( ( ( ( sK4 @ sK18 @ sK17 )
| ( sK3 @ sK18 @ sK17 ) )
=> $false )
= $true )
| ~ spl0_9 ),
inference(superposition,[],[f71,f327]) ).
thf(f327,plain,
( ( $false
= ( sK6 @ sK18 @ sK17 ) )
| ~ spl0_9 ),
inference(boolean_simplification,[],[f326]) ).
thf(f326,plain,
( ( $false
= ( $true
=> ( sK6 @ sK18 @ sK17 ) ) )
| ~ spl0_9 ),
inference(backward_demodulation,[],[f323,f325]) ).
thf(f71,plain,
! [X2: a,X1: a] :
( $true
= ( ( ( sK4 @ X1 @ X2 )
| ( sK3 @ X1 @ X2 ) )
=> ( sK6 @ X1 @ X2 ) ) ),
inference(beta_eta_normalization,[],[f70]) ).
thf(f70,plain,
! [X2: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK4 @ X1 @ Y0 )
| ( sK3 @ X1 @ Y0 ) )
=> ( sK6 @ X1 @ Y0 ) )
@ X2 )
= $true ),
inference(pi_clausification,[],[f69]) ).
thf(f69,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ X1 @ Y0 )
| ( sK3 @ X1 @ Y0 ) )
=> ( sK6 @ X1 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[],[f68]) ).
thf(f68,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y0 @ Y1 )
| ( sK3 @ Y0 @ Y1 ) )
=> ( sK6 @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_clausification,[],[f29]) ).
thf(f314,plain,
( spl0_9
| spl0_10
| ~ spl0_1
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f305,f162,f91,f312,f309]) ).
thf(f91,plain,
( spl0_1
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( 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] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f162,plain,
( spl0_3
<=> ( ( !! @ ( 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] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) ) )
= $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
thf(f305,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y1 @ Y2 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) ) )
| ~ spl0_1
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f292]) ).
thf(f292,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y1 @ Y2 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_1
| ~ spl0_3 ),
inference(not_proxy_clausification,[],[f285]) ).
thf(f285,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] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl0_1
| ~ spl0_3 ),
inference(boolean_simplification,[],[f282]) ).
thf(f282,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y1 @ Y2 ) )
=> ( sK6 @ Y0 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK3 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
=> $false )
= $true )
| ~ spl0_1
| ~ spl0_3 ),
inference(superposition,[],[f280,f141]) ).
thf(f141,plain,
( ( $false
= ( sK6 @ sK10 @ sK11 ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f140]) ).
thf(f140,plain,
( ( $false
= ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) ) )
| ( !! @ ( 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] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) ) ) )
=> ( sK6 @ sK10 @ sK11 ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f139]) ).
thf(f139,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK10 @ Y0 ) ) )
| ( !! @ ( 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] :
( ( sK3 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK10 @ Y0 ) ) ) )
=> ( sK6 @ sK10 @ Y0 ) )
@ sK11 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f138]) ).
thf(f138,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK4 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK10 @ Y0 ) ) )
| ( !! @ ( 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] :
( ( sK3 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK10 @ Y0 ) ) ) )
=> ( sK6 @ sK10 @ Y0 ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f134]) ).
thf(f134,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( 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] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( sK6 @ Y0 @ Y1 ) ) )
@ sK10 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f92]) ).
thf(f92,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( 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] :
( ( sK3 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( sK6 @ Y0 @ Y1 ) ) ) ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f91]) ).
thf(f280,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] :
( ( sK3 @ Y1 @ Y0 )
=> ( X1 @ Y1 @ Y0 ) ) ) ) )
=> ( X1 @ sK10 @ sK11 ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f279]) ).
thf(f279,plain,
( ! [X1: 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] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) )
@ X1 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[],[f163]) ).
thf(f163,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] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) ) )
= $true )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f162]) ).
thf(f276,plain,
~ spl0_6,
inference(avatar_contradiction_clause,[],[f275]) ).
thf(f275,plain,
( $false
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f274]) ).
thf(f274,plain,
( ( $false = $true )
| ~ spl0_6 ),
inference(boolean_simplification,[],[f273]) ).
thf(f273,plain,
( ( $true = ~ $true )
| ~ spl0_6 ),
inference(boolean_simplification,[],[f272]) ).
thf(f272,plain,
( ( ( ~ ( $true
| ( sK3 @ sK16 @ sK15 ) ) )
= $true )
| ~ spl0_6 ),
inference(forward_demodulation,[],[f269,f259]) ).
thf(f259,plain,
( ( $true
= ( sK4 @ sK16 @ sK15 ) )
| ~ spl0_6 ),
inference(binary_proxy_clausification,[],[f257]) ).
thf(f257,plain,
( ( $false
= ( ( sK4 @ sK16 @ sK15 )
=> ( sK6 @ sK16 @ sK15 ) ) )
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f256]) ).
thf(f256,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK4 @ Y0 @ sK15 )
=> ( sK6 @ Y0 @ sK15 ) )
@ sK16 ) )
| ~ spl0_6 ),
inference(sigma_clausification,[],[f255]) ).
thf(f255,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK4 @ Y0 @ sK15 )
=> ( sK6 @ Y0 @ sK15 ) ) ) )
| ~ spl0_6 ),
inference(beta_eta_normalization,[],[f251]) ).
thf(f251,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) )
@ sK15 ) )
| ~ spl0_6 ),
inference(sigma_clausification,[],[f224]) ).
thf(f224,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f223]) ).
thf(f223,plain,
( spl0_6
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
thf(f269,plain,
( ( ( ~ ( ( sK4 @ sK16 @ sK15 )
| ( sK3 @ sK16 @ sK15 ) ) )
= $true )
| ~ spl0_6 ),
inference(boolean_simplification,[],[f262]) ).
thf(f262,plain,
( ( $true
= ( ( ( sK4 @ sK16 @ sK15 )
| ( sK3 @ sK16 @ sK15 ) )
=> $false ) )
| ~ spl0_6 ),
inference(superposition,[],[f71,f261]) ).
thf(f261,plain,
( ( $false
= ( sK6 @ sK16 @ sK15 ) )
| ~ spl0_6 ),
inference(boolean_simplification,[],[f260]) ).
thf(f260,plain,
( ( $false
= ( $true
=> ( sK6 @ sK16 @ sK15 ) ) )
| ~ spl0_6 ),
inference(backward_demodulation,[],[f257,f259]) ).
thf(f244,plain,
~ spl0_5,
inference(avatar_contradiction_clause,[],[f243]) ).
thf(f243,plain,
( $false
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f240]) ).
thf(f240,plain,
( ( $false = $true )
| ~ spl0_5 ),
inference(superposition,[],[f37,f236]) ).
thf(f236,plain,
( ( $false
= ( ( ( sK6 @ sK13 @ sK14 )
& ( sK6 @ sK14 @ sK12 ) )
=> ( sK6 @ sK13 @ sK12 ) ) )
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f235]) ).
thf(f235,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK6 @ sK13 @ Y0 )
& ( sK6 @ Y0 @ sK12 ) )
=> ( sK6 @ sK13 @ sK12 ) )
@ sK14 ) )
| ~ spl0_5 ),
inference(sigma_clausification,[],[f234]) ).
thf(f234,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ sK13 @ Y0 )
& ( sK6 @ Y0 @ sK12 ) )
=> ( sK6 @ sK13 @ sK12 ) ) ) )
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f233]) ).
thf(f233,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y1 @ sK12 ) )
=> ( sK6 @ Y0 @ sK12 ) ) )
@ sK13 ) )
| ~ spl0_5 ),
inference(sigma_clausification,[],[f232]) ).
thf(f232,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y0 @ Y1 )
& ( sK6 @ Y1 @ sK12 ) )
=> ( sK6 @ Y0 @ sK12 ) ) ) ) )
| ~ spl0_5 ),
inference(beta_eta_normalization,[],[f228]) ).
thf(f228,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) )
@ sK12 ) )
| ~ spl0_5 ),
inference(sigma_clausification,[],[f221]) ).
thf(f221,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f220]) ).
thf(f220,plain,
( spl0_5
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
thf(f37,plain,
! [X2: a,X3: a,X1: a] :
( $true
= ( ( ( sK6 @ X2 @ X1 )
& ( sK6 @ X1 @ X3 ) )
=> ( sK6 @ X2 @ X3 ) ) ),
inference(beta_eta_normalization,[],[f36]) ).
thf(f36,plain,
! [X2: a,X3: a,X1: a] :
( ( ^ [Y0: a] :
( ( ( sK6 @ X2 @ X1 )
& ( sK6 @ X1 @ Y0 ) )
=> ( sK6 @ X2 @ Y0 ) )
@ X3 )
= $true ),
inference(pi_clausification,[],[f35]) ).
thf(f225,plain,
( spl0_5
| spl0_6
| ~ spl0_1
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f216,f165,f91,f223,f220]) ).
thf(f165,plain,
( spl0_4
<=> ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
thf(f216,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_1
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f210]) ).
thf(f210,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl0_1
| ~ spl0_4 ),
inference(not_proxy_clausification,[],[f187]) ).
thf(f187,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl0_1
| ~ spl0_4 ),
inference(boolean_simplification,[],[f183]) ).
thf(f183,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y1 @ Y2 )
& ( sK6 @ Y2 @ Y0 ) )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 @ Y0 )
=> ( sK6 @ Y1 @ Y0 ) ) ) ) )
=> $false )
= $true )
| ~ spl0_1
| ~ spl0_4 ),
inference(superposition,[],[f177,f141]) ).
thf(f177,plain,
( ! [X1: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y1 @ Y2 )
& ( X1 @ Y2 @ Y0 ) )
=> ( X1 @ Y1 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK4 @ Y1 @ Y0 )
=> ( X1 @ Y1 @ Y0 ) ) ) ) )
=> ( X1 @ sK10 @ sK11 ) )
= $true )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f176]) ).
thf(f176,plain,
( ! [X1: a > a > $o] :
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) )
@ X1 )
= $true )
| ~ spl0_4 ),
inference(pi_clausification,[],[f166]) ).
thf(f166,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) ) ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f165]) ).
thf(f167,plain,
( spl0_3
| spl0_4
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f160,f91,f165,f162]) ).
thf(f160,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) ) ) )
| ( ( !! @ ( 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] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) ) )
= $true )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f142]) ).
thf(f142,plain,
( ( $true
= ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK4 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) ) )
| ( !! @ ( 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] :
( ( sK3 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) ) ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f140]) ).
thf(f127,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f126]) ).
thf(f126,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f122]) ).
thf(f122,plain,
( ( $false = $true )
| ~ spl0_2 ),
inference(superposition,[],[f119,f37]) ).
thf(f119,plain,
( ( $false
= ( ( ( sK6 @ sK9 @ sK8 )
& ( sK6 @ sK8 @ sK7 ) )
=> ( sK6 @ sK9 @ sK7 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f118]) ).
thf(f118,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK6 @ Y0 @ sK8 )
& ( sK6 @ sK8 @ sK7 ) )
=> ( sK6 @ Y0 @ sK7 ) )
@ sK9 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f117]) ).
thf(f117,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ Y0 @ sK8 )
& ( sK6 @ sK8 @ sK7 ) )
=> ( sK6 @ Y0 @ sK7 ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f116]) ).
thf(f116,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 @ Y0 )
& ( sK6 @ Y0 @ sK7 ) )
=> ( sK6 @ Y1 @ sK7 ) ) )
@ sK8 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f107]) ).
thf(f107,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 @ Y0 )
& ( sK6 @ Y0 @ sK7 ) )
=> ( sK6 @ Y1 @ sK7 ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f105]) ).
thf(f105,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y1 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y2 @ Y0 ) ) ) )
@ sK7 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f95]) ).
thf(f95,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y1 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y2 @ Y0 ) ) ) ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f94]) ).
thf(f94,plain,
( spl0_2
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK6 @ Y2 @ Y1 )
& ( sK6 @ Y1 @ Y0 ) )
=> ( sK6 @ Y2 @ Y0 ) ) ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f96,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f87,f94,f91]) ).
thf(f87,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( 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] :
( ( 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 @ Y1 @ Y0 ) )
=> ( sK6 @ Y2 @ Y0 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f78]) ).
thf(f78,plain,
( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( 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] :
( ( 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 @ Y1 @ Y0 ) )
=> ( sK6 @ Y2 @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f60]) ).
thf(f60,plain,
( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( 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] :
( ( 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 @ Y1 @ Y0 ) )
=> ( sK6 @ Y2 @ Y0 ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[],[f59]) ).
thf(f59,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( 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] :
( ( 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 @ Y1 @ Y0 ) )
=> ( sK6 @ Y2 @ Y0 ) ) ) ) ) )
=> $false )
= $true ),
inference(superposition,[],[f48,f27]) ).
thf(f27,plain,
( $false
= ( sK6 @ sK5 @ sK2 ) ),
inference(boolean_simplification,[],[f26]) ).
thf(f26,plain,
( $false
= ( $true
=> ( sK6 @ sK5 @ sK2 ) ) ),
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 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK4 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
| ( !! @ ( 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] :
( ( 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 @ Y1 @ Y0 ) )
=> ( X1 @ Y2 @ Y0 ) ) ) ) ) )
=> ( X1 @ sK5 @ sK2 ) ) ),
inference(beta_eta_normalization,[],[f47]) ).
thf(f47,plain,
! [X1: 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 @ Y5 @ Y6 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK4 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
| ( !! @ ( 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] :
( ( 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 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK5 @ sK2 ) )
@ X1 )
= $true ),
inference(pi_clausification,[],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEV140^5 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.35 % Computer : n018.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 3 12:04:46 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 This is a TH0_THM_NEQ_NAR problem
% 0.14/0.36 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/sandbox2/tmp/tmp.aHb9lTsZOS/Vampire---4.8_19544
% 0.21/0.38 % (19737)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 Vampire---4 for (2999ds/27Mi)
% 0.21/0.39 % (19736)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 Vampire---4 for (2999ds/4Mi)
% 0.21/0.39 % (19739)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.21/0.39 % (19738)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.21/0.39 % (19735)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on Vampire---4 for (2999ds/183Mi)
% 0.21/0.39 % (19741)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.21/0.39 % (19740)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on Vampire---4 for (2999ds/275Mi)
% 0.21/0.39 % (19738)Instruction limit reached!
% 0.21/0.39 % (19738)------------------------------
% 0.21/0.39 % (19738)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (19738)Termination reason: Unknown
% 0.21/0.39 % (19738)Termination phase: Naming
% 0.21/0.39 % (19739)Instruction limit reached!
% 0.21/0.39 % (19739)------------------------------
% 0.21/0.39 % (19739)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (19739)Termination reason: Unknown
% 0.21/0.39 % (19739)Termination phase: Property scanning
% 0.21/0.39
% 0.21/0.39 % (19739)Memory used [KB]: 1023
% 0.21/0.39 % (19739)Time elapsed: 0.004 s
% 0.21/0.39 % (19739)Instructions burned: 3 (million)
% 0.21/0.39 % (19739)------------------------------
% 0.21/0.39 % (19739)------------------------------
% 0.21/0.39
% 0.21/0.39 % (19738)Memory used [KB]: 1023
% 0.21/0.39 % (19738)Time elapsed: 0.004 s
% 0.21/0.39 % (19738)Instructions burned: 2 (million)
% 0.21/0.39 % (19738)------------------------------
% 0.21/0.39 % (19738)------------------------------
% 0.21/0.39 % (19736)Instruction limit reached!
% 0.21/0.39 % (19736)------------------------------
% 0.21/0.39 % (19736)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (19736)Termination reason: Unknown
% 0.21/0.39 % (19736)Termination phase: Property scanning
% 0.21/0.39
% 0.21/0.39 % (19736)Memory used [KB]: 1023
% 0.21/0.39 % (19736)Time elapsed: 0.005 s
% 0.21/0.39 % (19736)Instructions burned: 5 (million)
% 0.21/0.39 % (19742)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.21/0.39 % (19736)------------------------------
% 0.21/0.39 % (19736)------------------------------
% 0.21/0.39 % (19742)Instruction limit reached!
% 0.21/0.39 % (19742)------------------------------
% 0.21/0.39 % (19742)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (19742)Termination reason: Unknown
% 0.21/0.39 % (19742)Termination phase: Property scanning
% 0.21/0.39
% 0.21/0.39 % (19742)Memory used [KB]: 1023
% 0.21/0.39 % (19742)Time elapsed: 0.005 s
% 0.21/0.39 % (19742)Instructions burned: 4 (million)
% 0.21/0.39 % (19742)------------------------------
% 0.21/0.39 % (19742)------------------------------
% 0.21/0.40 % (19741)Instruction limit reached!
% 0.21/0.40 % (19741)------------------------------
% 0.21/0.40 % (19741)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (19741)Termination reason: Unknown
% 0.21/0.40 % (19741)Termination phase: Saturation
% 0.21/0.40
% 0.21/0.40 % (19741)Memory used [KB]: 5628
% 0.21/0.40 % (19741)Time elapsed: 0.018 s
% 0.21/0.40 % (19741)Instructions burned: 19 (million)
% 0.21/0.40 % (19741)------------------------------
% 0.21/0.40 % (19741)------------------------------
% 0.21/0.41 % (19737)Instruction limit reached!
% 0.21/0.41 % (19737)------------------------------
% 0.21/0.41 % (19737)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (19737)Termination reason: Unknown
% 0.21/0.41 % (19737)Termination phase: Saturation
% 0.21/0.41
% 0.21/0.41 % (19737)Memory used [KB]: 5628
% 0.21/0.41 % (19737)Time elapsed: 0.025 s
% 0.21/0.41 % (19737)Instructions burned: 28 (million)
% 0.21/0.41 % (19737)------------------------------
% 0.21/0.41 % (19737)------------------------------
% 0.21/0.41 % (19747)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 Vampire---4 for (2999ds/37Mi)
% 0.21/0.41 % (19749)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.21/0.41 % (19748)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 Vampire---4 for (2999ds/15Mi)
% 0.21/0.41 % (19749)Instruction limit reached!
% 0.21/0.41 % (19749)------------------------------
% 0.21/0.41 % (19749)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (19749)Termination reason: Unknown
% 0.21/0.41 % (19749)Termination phase: Preprocessing 3
% 0.21/0.41
% 0.21/0.41 % (19749)Memory used [KB]: 1023
% 0.21/0.41 % (19749)Time elapsed: 0.003 s
% 0.21/0.41 % (19749)Instructions burned: 3 (million)
% 0.21/0.41 % (19749)------------------------------
% 0.21/0.41 % (19749)------------------------------
% 0.21/0.41 % (19750)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 Vampire---4 for (2999ds/1041Mi)
% 0.21/0.42 % (19748)Instruction limit reached!
% 0.21/0.42 % (19748)------------------------------
% 0.21/0.42 % (19748)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (19748)Termination reason: Unknown
% 0.21/0.42 % (19748)Termination phase: Saturation
% 0.21/0.42
% 0.21/0.42 % (19748)Memory used [KB]: 5756
% 0.21/0.42 % (19748)Time elapsed: 0.011 s
% 0.21/0.42 % (19748)Instructions burned: 16 (million)
% 0.21/0.42 % (19748)------------------------------
% 0.21/0.42 % (19748)------------------------------
% 0.21/0.42 % (19752)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on Vampire---4 for (2999ds/7Mi)
% 0.21/0.42 % (19754)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 Vampire---4 for (2999ds/3Mi)
% 0.21/0.42 % (19753)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on Vampire---4 for (2999ds/16Mi)
% 0.21/0.42 % (19754)Instruction limit reached!
% 0.21/0.42 % (19754)------------------------------
% 0.21/0.42 % (19754)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (19754)Termination reason: Unknown
% 0.21/0.42 % (19754)Termination phase: Preprocessing 3
% 0.21/0.42
% 0.21/0.42 % (19752)Instruction limit reached!
% 0.21/0.42 % (19752)------------------------------
% 0.21/0.42 % (19752)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (19754)Memory used [KB]: 1023
% 0.21/0.42 % (19754)Time elapsed: 0.003 s
% 0.21/0.42 % (19754)Instructions burned: 3 (million)
% 0.21/0.42 % (19754)------------------------------
% 0.21/0.42 % (19754)------------------------------
% 0.21/0.42 % (19752)Termination reason: Unknown
% 0.21/0.42 % (19752)Termination phase: Saturation
% 0.21/0.42
% 0.21/0.42 % (19752)Memory used [KB]: 1023
% 0.21/0.42 % (19752)Time elapsed: 0.006 s
% 0.21/0.42 % (19752)Instructions burned: 8 (million)
% 0.21/0.42 % (19752)------------------------------
% 0.21/0.42 % (19752)------------------------------
% 0.21/0.42 % (19747)Instruction limit reached!
% 0.21/0.42 % (19747)------------------------------
% 0.21/0.42 % (19747)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (19747)Termination reason: Unknown
% 0.21/0.42 % (19747)Termination phase: Saturation
% 0.21/0.42
% 0.21/0.42 % (19747)Memory used [KB]: 5628
% 0.21/0.42 % (19747)Time elapsed: 0.019 s
% 0.21/0.42 % (19747)Instructions burned: 37 (million)
% 0.21/0.42 % (19747)------------------------------
% 0.21/0.42 % (19747)------------------------------
% 0.21/0.43 % (19756)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 Vampire---4 for (2999ds/3Mi)
% 0.21/0.43 % (19753)Instruction limit reached!
% 0.21/0.43 % (19753)------------------------------
% 0.21/0.43 % (19753)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43 % (19753)Termination reason: Unknown
% 0.21/0.43 % (19753)Termination phase: Saturation
% 0.21/0.43
% 0.21/0.43 % (19753)Memory used [KB]: 5628
% 0.21/0.43 % (19753)Time elapsed: 0.010 s
% 0.21/0.43 % (19753)Instructions burned: 16 (million)
% 0.21/0.43 % (19753)------------------------------
% 0.21/0.43 % (19753)------------------------------
% 0.21/0.43 % (19756)Instruction limit reached!
% 0.21/0.43 % (19756)------------------------------
% 0.21/0.43 % (19756)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43 % (19756)Termination reason: Unknown
% 0.21/0.43 % (19756)Termination phase: Preprocessing 3
% 0.21/0.43
% 0.21/0.43 % (19756)Memory used [KB]: 1023
% 0.21/0.43 % (19756)Time elapsed: 0.003 s
% 0.21/0.43 % (19756)Instructions burned: 3 (million)
% 0.21/0.43 % (19756)------------------------------
% 0.21/0.43 % (19756)------------------------------
% 0.21/0.44 % (19757)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on Vampire---4 for (2999ds/7Mi)
% 0.21/0.44 % (19758)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.21/0.44 % (19760)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on Vampire---4 for (2999ds/4Mi)
% 0.21/0.44 % (19758)Instruction limit reached!
% 0.21/0.44 % (19758)------------------------------
% 0.21/0.44 % (19758)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.44 % (19758)Termination reason: Unknown
% 0.21/0.44 % (19758)Termination phase: shuffling
% 0.21/0.44
% 0.21/0.44 % (19758)Memory used [KB]: 1023
% 0.21/0.44 % (19758)Time elapsed: 0.003 s
% 0.21/0.44 % (19758)Instructions burned: 3 (million)
% 0.21/0.44 % (19758)------------------------------
% 0.21/0.44 % (19758)------------------------------
% 0.21/0.44 % (19757)Instruction limit reached!
% 0.21/0.44 % (19757)------------------------------
% 0.21/0.44 % (19757)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.44 % (19760)Instruction limit reached!
% 0.21/0.44 % (19760)------------------------------
% 0.21/0.44 % (19760)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.44 % (19757)Termination reason: Unknown
% 0.21/0.44 % (19757)Termination phase: Saturation
% 0.21/0.44
% 0.21/0.44 % (19757)Memory used [KB]: 5500
% 0.21/0.44 % (19757)Time elapsed: 0.005 s
% 0.21/0.44 % (19757)Instructions burned: 7 (million)
% 0.21/0.44 % (19757)------------------------------
% 0.21/0.44 % (19757)------------------------------
% 0.21/0.44 % (19760)Termination reason: Unknown
% 0.21/0.44 % (19760)Termination phase: Property scanning
% 0.21/0.44
% 0.21/0.44 % (19760)Memory used [KB]: 1023
% 0.21/0.44 % (19760)Time elapsed: 0.004 s
% 0.21/0.44 % (19760)Instructions burned: 5 (million)
% 0.21/0.44 % (19760)------------------------------
% 0.21/0.44 % (19760)------------------------------
% 0.21/0.45 % (19762)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.21/0.45 % (19763)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on Vampire---4 for (2999ds/710Mi)
% 0.21/0.45 % (19764)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on Vampire---4 for (2999ds/6Mi)
% 0.21/0.46 % (19765)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 Vampire---4 for (2999ds/902Mi)
% 0.21/0.46 % (19766)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 Vampire---4 for (2999ds/21Mi)
% 0.21/0.46 % (19762)Instruction limit reached!
% 0.21/0.46 % (19762)------------------------------
% 0.21/0.46 % (19762)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.46 % (19762)Termination reason: Unknown
% 0.21/0.46 % (19762)Termination phase: Saturation
% 0.21/0.46
% 0.21/0.46 % (19762)Memory used [KB]: 5628
% 0.21/0.46 % (19762)Time elapsed: 0.033 s
% 0.21/0.46 % (19762)Instructions burned: 19 (million)
% 0.21/0.46 % (19762)------------------------------
% 0.21/0.46 % (19762)------------------------------
% 0.21/0.46 % (19764)Instruction limit reached!
% 0.21/0.46 % (19764)------------------------------
% 0.21/0.46 % (19764)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.46 % (19764)Termination reason: Unknown
% 0.21/0.46 % (19764)Termination phase: Saturation
% 0.21/0.46
% 0.21/0.46 % (19764)Memory used [KB]: 5500
% 0.21/0.46 % (19764)Time elapsed: 0.005 s
% 0.21/0.46 % (19764)Instructions burned: 7 (million)
% 0.21/0.46 % (19764)------------------------------
% 0.21/0.46 % (19764)------------------------------
% 0.21/0.46 % (19750)First to succeed.
% 0.21/0.47 % (19766)Instruction limit reached!
% 0.21/0.47 % (19766)------------------------------
% 0.21/0.47 % (19766)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.47 % (19766)Termination reason: Unknown
% 0.21/0.47 % (19766)Termination phase: Saturation
% 0.21/0.47
% 0.21/0.47 % (19766)Memory used [KB]: 5756
% 0.21/0.47 % (19766)Time elapsed: 0.014 s
% 0.21/0.47 % (19766)Instructions burned: 21 (million)
% 0.21/0.47 % (19766)------------------------------
% 0.21/0.47 % (19766)------------------------------
% 0.21/0.47 % (19768)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on Vampire---4 for (2999ds/5Mi)
% 0.21/0.47 % (19769)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 Vampire---4 for (2999ds/6Mi)
% 0.21/0.47 % (19768)Instruction limit reached!
% 0.21/0.47 % (19768)------------------------------
% 0.21/0.47 % (19768)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.47 % (19768)Termination reason: Unknown
% 0.21/0.47 % (19768)Termination phase: Saturation
% 0.21/0.47
% 0.21/0.47 % (19768)Memory used [KB]: 5500
% 0.21/0.47 % (19768)Time elapsed: 0.004 s
% 0.21/0.47 % (19768)Instructions burned: 5 (million)
% 0.21/0.47 % (19768)------------------------------
% 0.21/0.47 % (19768)------------------------------
% 0.21/0.47 % (19750)Refutation found. Thanks to Tanya!
% 0.21/0.47 % SZS status Theorem for Vampire---4
% 0.21/0.47 % SZS output start Proof for Vampire---4
% See solution above
% 0.21/0.47 % (19750)------------------------------
% 0.21/0.47 % (19750)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.47 % (19750)Termination reason: Refutation
% 0.21/0.47
% 0.21/0.47 % (19750)Memory used [KB]: 6140
% 0.21/0.47 % (19750)Time elapsed: 0.063 s
% 0.21/0.47 % (19750)Instructions burned: 93 (million)
% 0.21/0.47 % (19750)------------------------------
% 0.21/0.47 % (19750)------------------------------
% 0.21/0.47 % (19734)Success in time 0.108 s
% 0.21/0.47 % Vampire---4.8 exiting
%------------------------------------------------------------------------------