TSTP Solution File: ALG272^5 by Vampire---4.9
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : ALG272^5 : TPTP v8.2.0. Bugfixed v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 04:09:07 EDT 2024
% Result : Theorem 0.14s 0.33s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 45
% Syntax : Number of formulae : 211 ( 45 unt; 23 typ; 0 def)
% Number of atoms : 1429 ( 697 equ; 0 cnn)
% Maximal formula atoms : 7 ( 7 avg)
% Number of connectives : 3324 ( 194 ~; 291 |; 167 &;2315 @)
% ( 16 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 132 ( 132 >; 0 *; 0 +; 0 <<)
% Number of symbols : 39 ( 34 usr; 25 con; 0-2 aty)
% ( 292 !!; 48 ??; 0 @@+; 0 @@-)
% Number of variables : 613 ( 439 ^ 166 !; 8 ?; 613 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
g: $tType ).
thf(func_def_0,type,
g: $tType ).
thf(func_def_1,type,
cGROUP1: ( g > g > g ) > g > $o ).
thf(func_def_2,type,
cGROUP2: ( g > g > g ) > g > $o ).
thf(func_def_3,type,
cGRP_ASSOC: ( g > g > g ) > $o ).
thf(func_def_4,type,
cGRP_INVERSE: ( g > g > g ) > g > $o ).
thf(func_def_5,type,
cGRP_LEFT_INVERSE: ( g > g > g ) > g > $o ).
thf(func_def_6,type,
cGRP_LEFT_UNIT: ( g > g > g ) > g > $o ).
thf(func_def_7,type,
cGRP_UNIT: ( g > g > g ) > g > $o ).
thf(func_def_20,type,
sK0: g > g > g ).
thf(func_def_21,type,
sK1: g ).
thf(func_def_23,type,
sK3: g ).
thf(func_def_24,type,
sK4: g ).
thf(func_def_25,type,
sK5: g ).
thf(func_def_26,type,
sK6: g ).
thf(func_def_27,type,
sK7: g ).
thf(func_def_28,type,
sK8: g ).
thf(func_def_29,type,
sK9: g ).
thf(func_def_30,type,
sK10: g > g ).
thf(func_def_31,type,
sK11: g > g ).
thf(func_def_32,type,
sK12: g > g ).
thf(func_def_33,type,
sK13: g > g ).
thf(func_def_34,type,
sK14: g > g ).
thf(f497,plain,
$false,
inference(avatar_sat_refutation,[],[f203,f207,f218,f231,f244,f267,f270,f272,f274,f342,f380,f400,f477,f488,f496]) ).
thf(f496,plain,
( ~ spl2_1
| ~ spl2_12 ),
inference(avatar_contradiction_clause,[],[f495]) ).
thf(f495,plain,
( $false
| ~ spl2_1
| ~ spl2_12 ),
inference(trivial_inequality_removal,[],[f493]) ).
thf(f493,plain,
( ( sK1 != sK1 )
| ~ spl2_1
| ~ spl2_12 ),
inference(superposition,[],[f247,f199]) ).
thf(f199,plain,
( ! [X2: g] :
( sK1
= ( sK0 @ ( sK14 @ X2 ) @ X2 ) )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f198]) ).
thf(f198,plain,
( spl2_1
<=> ! [X2: g] :
( sK1
= ( sK0 @ ( sK14 @ X2 ) @ X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).
thf(f247,plain,
( ! [X1: g] :
( sK1
!= ( sK0 @ X1 @ sK3 ) )
| ~ spl2_12 ),
inference(avatar_component_clause,[],[f246]) ).
thf(f246,plain,
( spl2_12
<=> ! [X1: g] :
( sK1
!= ( sK0 @ X1 @ sK3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_12])]) ).
thf(f488,plain,
( ~ spl2_1
| ~ spl2_3
| ~ spl2_15 ),
inference(avatar_contradiction_clause,[],[f487]) ).
thf(f487,plain,
( $false
| ~ spl2_1
| ~ spl2_3
| ~ spl2_15 ),
inference(subsumption_resolution,[],[f486,f206]) ).
thf(f206,plain,
( ! [X2: g] :
( sK1
= ( sK0 @ X2 @ ( sK14 @ X2 ) ) )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f205]) ).
thf(f205,plain,
( spl2_3
<=> ! [X2: g] :
( sK1
= ( sK0 @ X2 @ ( sK14 @ X2 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).
thf(f486,plain,
( ( sK1
!= ( sK0 @ sK4 @ ( sK14 @ sK4 ) ) )
| ~ spl2_1
| ~ spl2_15 ),
inference(trivial_inequality_removal,[],[f484]) ).
thf(f484,plain,
( ( sK1 != sK1 )
| ( sK1
!= ( sK0 @ sK4 @ ( sK14 @ sK4 ) ) )
| ~ spl2_1
| ~ spl2_15 ),
inference(superposition,[],[f258,f199]) ).
thf(f258,plain,
( ! [X2: g] :
( ( sK1
!= ( sK0 @ X2 @ sK4 ) )
| ( ( sK0 @ sK4 @ X2 )
!= sK1 ) )
| ~ spl2_15 ),
inference(avatar_component_clause,[],[f257]) ).
thf(f257,plain,
( spl2_15
<=> ! [X2: g] :
( ( sK1
!= ( sK0 @ X2 @ sK4 ) )
| ( ( sK0 @ sK4 @ X2 )
!= sK1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_15])]) ).
thf(f477,plain,
( ~ spl2_2
| ~ spl2_4
| ~ spl2_6
| ~ spl2_7
| ~ spl2_15 ),
inference(avatar_contradiction_clause,[],[f476]) ).
thf(f476,plain,
( $false
| ~ spl2_2
| ~ spl2_4
| ~ spl2_6
| ~ spl2_7
| ~ spl2_15 ),
inference(trivial_inequality_removal,[],[f469]) ).
thf(f469,plain,
( ( sK1 != sK1 )
| ~ spl2_2
| ~ spl2_4
| ~ spl2_6
| ~ spl2_7
| ~ spl2_15 ),
inference(superposition,[],[f416,f439]) ).
thf(f439,plain,
( ! [X0: g] :
( sK1
= ( sK0 @ X0 @ ( sK13 @ X0 ) ) )
| ~ spl2_2
| ~ spl2_4
| ~ spl2_6
| ~ spl2_7 ),
inference(superposition,[],[f202,f367]) ).
thf(f367,plain,
( ! [X0: g] :
( ( sK13 @ ( sK13 @ X0 ) )
= X0 )
| ~ spl2_2
| ~ spl2_4
| ~ spl2_6
| ~ spl2_7 ),
inference(superposition,[],[f290,f217]) ).
thf(f217,plain,
( ! [X2: g] :
( ( sK0 @ X2 @ sK1 )
= X2 )
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f216]) ).
thf(f216,plain,
( spl2_6
<=> ! [X2: g] :
( ( sK0 @ X2 @ sK1 )
= X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_6])]) ).
thf(f290,plain,
( ! [X0: g] :
( ( sK0 @ ( sK13 @ ( sK13 @ X0 ) ) @ sK1 )
= X0 )
| ~ spl2_2
| ~ spl2_4
| ~ spl2_7 ),
inference(superposition,[],[f282,f202]) ).
thf(f282,plain,
( ! [X0: g,X1: g] :
( ( sK0 @ ( sK13 @ X0 ) @ ( sK0 @ X0 @ X1 ) )
= X1 )
| ~ spl2_2
| ~ spl2_4
| ~ spl2_7 ),
inference(forward_demodulation,[],[f275,f221]) ).
thf(f221,plain,
( ! [X2: g] :
( ( sK0 @ sK1 @ X2 )
= X2 )
| ~ spl2_7 ),
inference(avatar_component_clause,[],[f220]) ).
thf(f220,plain,
( spl2_7
<=> ! [X2: g] :
( ( sK0 @ sK1 @ X2 )
= X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_7])]) ).
thf(f275,plain,
( ! [X0: g,X1: g] :
( ( sK0 @ sK1 @ X1 )
= ( sK0 @ ( sK13 @ X0 ) @ ( sK0 @ X0 @ X1 ) ) )
| ~ spl2_2
| ~ spl2_4 ),
inference(superposition,[],[f210,f202]) ).
thf(f210,plain,
( ! [X2: g,X3: g,X4: g] :
( ( sK0 @ X4 @ ( sK0 @ X3 @ X2 ) )
= ( sK0 @ ( sK0 @ X4 @ X3 ) @ X2 ) )
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f209]) ).
thf(f209,plain,
( spl2_4
<=> ! [X2: g,X4: g,X3: g] :
( ( sK0 @ X4 @ ( sK0 @ X3 @ X2 ) )
= ( sK0 @ ( sK0 @ X4 @ X3 ) @ X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).
thf(f202,plain,
( ! [X1: g] :
( sK1
= ( sK0 @ ( sK13 @ X1 ) @ X1 ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f201]) ).
thf(f201,plain,
( spl2_2
<=> ! [X1: g] :
( sK1
= ( sK0 @ ( sK13 @ X1 ) @ X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).
thf(f416,plain,
( ( sK1
!= ( sK0 @ sK4 @ ( sK13 @ sK4 ) ) )
| ~ spl2_2
| ~ spl2_15 ),
inference(trivial_inequality_removal,[],[f407]) ).
thf(f407,plain,
( ( sK1 != sK1 )
| ( sK1
!= ( sK0 @ sK4 @ ( sK13 @ sK4 ) ) )
| ~ spl2_2
| ~ spl2_15 ),
inference(superposition,[],[f258,f202]) ).
thf(f400,plain,
( ~ spl2_2
| ~ spl2_12 ),
inference(avatar_contradiction_clause,[],[f399]) ).
thf(f399,plain,
( $false
| ~ spl2_2
| ~ spl2_12 ),
inference(trivial_inequality_removal,[],[f389]) ).
thf(f389,plain,
( ( sK1 != sK1 )
| ~ spl2_2
| ~ spl2_12 ),
inference(superposition,[],[f247,f202]) ).
thf(f380,plain,
( ~ spl2_6
| spl2_16 ),
inference(avatar_contradiction_clause,[],[f379]) ).
thf(f379,plain,
( $false
| ~ spl2_6
| spl2_16 ),
inference(trivial_inequality_removal,[],[f364]) ).
thf(f364,plain,
( ( sK5 != sK5 )
| ~ spl2_6
| spl2_16 ),
inference(superposition,[],[f262,f217]) ).
thf(f262,plain,
( ( sK5
!= ( sK0 @ sK5 @ sK1 ) )
| spl2_16 ),
inference(avatar_component_clause,[],[f260]) ).
thf(f260,plain,
( spl2_16
<=> ( sK5
= ( sK0 @ sK5 @ sK1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_16])]) ).
thf(f342,plain,
( spl2_6
| ~ spl2_4
| ~ spl2_5
| ~ spl2_7 ),
inference(avatar_split_clause,[],[f340,f220,f212,f209,f216]) ).
thf(f212,plain,
( spl2_5
<=> ! [X1: g] :
( sK1
= ( sK0 @ ( sK12 @ X1 ) @ X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_5])]) ).
thf(f340,plain,
( ! [X0: g] :
( ( sK0 @ X0 @ sK1 )
= X0 )
| ~ spl2_4
| ~ spl2_5
| ~ spl2_7 ),
inference(superposition,[],[f284,f287]) ).
thf(f287,plain,
( ! [X0: g,X1: g] :
( ( sK0 @ X0 @ X1 )
= ( sK0 @ ( sK12 @ ( sK12 @ X0 ) ) @ X1 ) )
| ~ spl2_4
| ~ spl2_5
| ~ spl2_7 ),
inference(superposition,[],[f281,f281]) ).
thf(f281,plain,
( ! [X0: g,X1: g] :
( ( sK0 @ ( sK12 @ X0 ) @ ( sK0 @ X0 @ X1 ) )
= X1 )
| ~ spl2_4
| ~ spl2_5
| ~ spl2_7 ),
inference(forward_demodulation,[],[f276,f221]) ).
thf(f276,plain,
( ! [X0: g,X1: g] :
( ( sK0 @ sK1 @ X1 )
= ( sK0 @ ( sK12 @ X0 ) @ ( sK0 @ X0 @ X1 ) ) )
| ~ spl2_4
| ~ spl2_5 ),
inference(superposition,[],[f210,f213]) ).
thf(f213,plain,
( ! [X1: g] :
( sK1
= ( sK0 @ ( sK12 @ X1 ) @ X1 ) )
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f212]) ).
thf(f284,plain,
( ! [X0: g] :
( ( sK0 @ ( sK12 @ ( sK12 @ X0 ) ) @ sK1 )
= X0 )
| ~ spl2_4
| ~ spl2_5
| ~ spl2_7 ),
inference(superposition,[],[f281,f213]) ).
thf(f274,plain,
( ~ spl2_4
| spl2_14 ),
inference(avatar_contradiction_clause,[],[f273]) ).
thf(f273,plain,
( $false
| ~ spl2_4
| spl2_14 ),
inference(subsumption_resolution,[],[f255,f210]) ).
thf(f255,plain,
( ( ( sK0 @ sK9 @ ( sK0 @ sK8 @ sK7 ) )
!= ( sK0 @ ( sK0 @ sK9 @ sK8 ) @ sK7 ) )
| spl2_14 ),
inference(avatar_component_clause,[],[f253]) ).
thf(f253,plain,
( spl2_14
<=> ( ( sK0 @ sK9 @ ( sK0 @ sK8 @ sK7 ) )
= ( sK0 @ ( sK0 @ sK9 @ sK8 ) @ sK7 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_14])]) ).
thf(f272,plain,
( ~ spl2_7
| spl2_13 ),
inference(avatar_contradiction_clause,[],[f271]) ).
thf(f271,plain,
( $false
| ~ spl2_7
| spl2_13 ),
inference(subsumption_resolution,[],[f251,f221]) ).
thf(f251,plain,
( ( sK6
!= ( sK0 @ sK1 @ sK6 ) )
| spl2_13 ),
inference(avatar_component_clause,[],[f249]) ).
thf(f249,plain,
( spl2_13
<=> ( sK6
= ( sK0 @ sK1 @ sK6 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_13])]) ).
thf(f270,plain,
( ~ spl2_7
| spl2_17 ),
inference(avatar_contradiction_clause,[],[f269]) ).
thf(f269,plain,
( $false
| ~ spl2_7
| spl2_17 ),
inference(trivial_inequality_removal,[],[f268]) ).
thf(f268,plain,
( ( sK5 != sK5 )
| ~ spl2_7
| spl2_17 ),
inference(superposition,[],[f266,f221]) ).
thf(f266,plain,
( ( ( sK0 @ sK1 @ sK5 )
!= sK5 )
| spl2_17 ),
inference(avatar_component_clause,[],[f264]) ).
thf(f264,plain,
( spl2_17
<=> ( ( sK0 @ sK1 @ sK5 )
= sK5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_17])]) ).
thf(f267,plain,
( spl2_12
| ~ spl2_13
| ~ spl2_14
| spl2_15
| ~ spl2_16
| ~ spl2_17 ),
inference(avatar_split_clause,[],[f74,f264,f260,f257,f253,f249,f246]) ).
thf(f74,plain,
! [X2: g,X1: g] :
( ( ( sK0 @ sK9 @ ( sK0 @ sK8 @ sK7 ) )
!= ( sK0 @ ( sK0 @ sK9 @ sK8 ) @ sK7 ) )
| ( sK1
!= ( sK0 @ X1 @ sK3 ) )
| ( sK1
!= ( sK0 @ X2 @ sK4 ) )
| ( sK5
!= ( sK0 @ sK5 @ sK1 ) )
| ( sK6
!= ( sK0 @ sK1 @ sK6 ) )
| ( ( sK0 @ sK1 @ sK5 )
!= sK5 )
| ( ( sK0 @ sK4 @ X2 )
!= sK1 ) ),
inference(equality_proxy_clausification,[],[f73]) ).
thf(f73,plain,
! [X2: g,X1: g] :
( ( $false
= ( ( sK0 @ ( sK0 @ sK9 @ sK8 ) @ sK7 )
= ( sK0 @ sK9 @ ( sK0 @ sK8 @ sK7 ) ) ) )
| ( sK1
!= ( sK0 @ X1 @ sK3 ) )
| ( ( sK0 @ sK4 @ X2 )
!= sK1 )
| ( sK1
!= ( sK0 @ X2 @ sK4 ) )
| ( ( sK0 @ sK1 @ sK5 )
!= sK5 )
| ( sK5
!= ( sK0 @ sK5 @ sK1 ) )
| ( sK6
!= ( sK0 @ sK1 @ sK6 ) ) ),
inference(beta_eta_normalization,[],[f72]) ).
thf(f72,plain,
! [X2: g,X1: g] :
( ( sK6
!= ( sK0 @ sK1 @ sK6 ) )
| ( ( sK0 @ sK4 @ X2 )
!= sK1 )
| ( sK1
!= ( sK0 @ X2 @ sK4 ) )
| ( sK5
!= ( sK0 @ sK5 @ sK1 ) )
| ( $false
= ( ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ sK8 ) @ sK7 )
= ( sK0 @ Y0 @ ( sK0 @ sK8 @ sK7 ) ) )
@ sK9 ) )
| ( ( sK0 @ sK1 @ sK5 )
!= sK5 )
| ( sK1
!= ( sK0 @ X1 @ sK3 ) ) ),
inference(sigma_clausification,[],[f71]) ).
thf(f71,plain,
! [X2: g,X1: g] :
( ( sK1
!= ( sK0 @ X1 @ sK3 ) )
| ( sK5
!= ( sK0 @ sK5 @ sK1 ) )
| ( sK1
!= ( sK0 @ X2 @ sK4 ) )
| ( sK6
!= ( sK0 @ sK1 @ sK6 ) )
| ( ( sK0 @ sK4 @ X2 )
!= sK1 )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ sK8 ) @ sK7 )
= ( sK0 @ Y0 @ ( sK0 @ sK8 @ sK7 ) ) ) )
= $false )
| ( ( sK0 @ sK1 @ sK5 )
!= sK5 ) ),
inference(beta_eta_normalization,[],[f70]) ).
thf(f70,plain,
! [X2: g,X1: g] :
( ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ sK7 )
= ( sK0 @ Y1 @ ( sK0 @ Y0 @ sK7 ) ) ) )
@ sK8 ) )
| ( sK6
!= ( sK0 @ sK1 @ sK6 ) )
| ( ( sK0 @ sK1 @ sK5 )
!= sK5 )
| ( sK5
!= ( sK0 @ sK5 @ sK1 ) )
| ( sK1
!= ( sK0 @ X2 @ sK4 ) )
| ( ( sK0 @ sK4 @ X2 )
!= sK1 )
| ( sK1
!= ( sK0 @ X1 @ sK3 ) ) ),
inference(sigma_clausification,[],[f69]) ).
thf(f69,plain,
! [X2: g,X1: g] :
( ( sK5
!= ( sK0 @ sK5 @ sK1 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ sK7 )
= ( sK0 @ Y1 @ ( sK0 @ Y0 @ sK7 ) ) ) ) ) )
| ( ( sK0 @ sK4 @ X2 )
!= sK1 )
| ( ( sK0 @ sK1 @ sK5 )
!= sK5 )
| ( sK6
!= ( sK0 @ sK1 @ sK6 ) )
| ( sK1
!= ( sK0 @ X2 @ sK4 ) )
| ( sK1
!= ( sK0 @ X1 @ sK3 ) ) ),
inference(equality_proxy_clausification,[],[f68]) ).
thf(f68,plain,
! [X2: g,X1: g] :
( ( $false
= ( ( sK0 @ sK5 @ sK1 )
= sK5 ) )
| ( ( sK0 @ sK1 @ sK5 )
!= sK5 )
| ( sK6
!= ( sK0 @ sK1 @ sK6 ) )
| ( sK1
!= ( sK0 @ X2 @ sK4 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ sK7 )
= ( sK0 @ Y1 @ ( sK0 @ Y0 @ sK7 ) ) ) ) ) )
| ( sK1
!= ( sK0 @ X1 @ sK3 ) )
| ( ( sK0 @ sK4 @ X2 )
!= sK1 ) ),
inference(equality_proxy_clausification,[],[f67]) ).
thf(f67,plain,
! [X2: g,X1: g] :
( ( $false
= ( ( sK0 @ sK1 @ sK5 )
= sK5 ) )
| ( sK1
!= ( sK0 @ X1 @ sK3 ) )
| ( sK1
!= ( sK0 @ X2 @ sK4 ) )
| ( $false
= ( ( sK0 @ sK5 @ sK1 )
= sK5 ) )
| ( ( sK0 @ sK4 @ X2 )
!= sK1 )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ sK7 )
= ( sK0 @ Y1 @ ( sK0 @ Y0 @ sK7 ) ) ) ) ) )
| ( sK6
!= ( sK0 @ sK1 @ sK6 ) ) ),
inference(binary_proxy_clausification,[],[f66]) ).
thf(f66,plain,
! [X2: g,X1: g] :
( ( $false
= ( ( ( sK0 @ sK1 @ sK5 )
= sK5 )
& ( ( sK0 @ sK5 @ sK1 )
= sK5 ) ) )
| ( sK1
!= ( sK0 @ X1 @ sK3 ) )
| ( ( sK0 @ sK4 @ X2 )
!= sK1 )
| ( sK6
!= ( sK0 @ sK1 @ sK6 ) )
| ( sK1
!= ( sK0 @ X2 @ sK4 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ sK7 )
= ( sK0 @ Y1 @ ( sK0 @ Y0 @ sK7 ) ) ) ) ) ) ),
inference(equality_proxy_clausification,[],[f65]) ).
thf(f65,plain,
! [X2: g,X1: g] :
( ( sK1
!= ( sK0 @ X1 @ sK3 ) )
| ( $false
= ( ( sK0 @ X2 @ sK4 )
= sK1 ) )
| ( ( sK0 @ sK4 @ X2 )
!= sK1 )
| ( sK6
!= ( sK0 @ sK1 @ sK6 ) )
| ( $false
= ( ( ( sK0 @ sK1 @ sK5 )
= sK5 )
& ( ( sK0 @ sK5 @ sK1 )
= sK5 ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ sK7 )
= ( sK0 @ Y1 @ ( sK0 @ Y0 @ sK7 ) ) ) ) ) ) ),
inference(equality_proxy_clausification,[],[f64]) ).
thf(f64,plain,
! [X2: g,X1: g] :
( ( sK6
!= ( sK0 @ sK1 @ sK6 ) )
| ( ( ( sK0 @ sK4 @ X2 )
= sK1 )
= $false )
| ( $false
= ( ( sK0 @ X2 @ sK4 )
= sK1 ) )
| ( sK1
!= ( sK0 @ X1 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK1 @ sK5 )
= sK5 )
& ( ( sK0 @ sK5 @ sK1 )
= sK5 ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ sK7 )
= ( sK0 @ Y1 @ ( sK0 @ Y0 @ sK7 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f63]) ).
thf(f63,plain,
! [X2: g,X1: g] :
( ( $false
= ( ( sK0 @ X2 @ sK4 )
= sK1 ) )
| ( ( ( sK0 @ sK4 @ X2 )
= sK1 )
= $false )
| ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) )
@ sK7 ) )
| ( sK1
!= ( sK0 @ X1 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK1 @ sK5 )
= sK5 )
& ( ( sK0 @ sK5 @ sK1 )
= sK5 ) ) )
| ( sK6
!= ( sK0 @ sK1 @ sK6 ) ) ),
inference(sigma_clausification,[],[f62]) ).
thf(f62,plain,
! [X2: g,X1: g] :
( ( sK1
!= ( sK0 @ X1 @ sK3 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) )
| ( $false
= ( ( sK0 @ X2 @ sK4 )
= sK1 ) )
| ( ( ( sK0 @ sK4 @ X2 )
= sK1 )
= $false )
| ( $false
= ( ( ( sK0 @ sK1 @ sK5 )
= sK5 )
& ( ( sK0 @ sK5 @ sK1 )
= sK5 ) ) )
| ( sK6
!= ( sK0 @ sK1 @ sK6 ) ) ),
inference(binary_proxy_clausification,[],[f61]) ).
thf(f61,plain,
! [X2: g,X1: g] :
( ( sK1
!= ( sK0 @ X1 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK4 @ X2 )
= sK1 )
& ( ( sK0 @ X2 @ sK4 )
= sK1 ) ) )
| ( sK6
!= ( sK0 @ sK1 @ sK6 ) )
| ( $false
= ( ( ( sK0 @ sK1 @ sK5 )
= sK5 )
& ( ( sK0 @ sK5 @ sK1 )
= sK5 ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(equality_proxy_clausification,[],[f60]) ).
thf(f60,plain,
! [X2: g,X1: g] :
( ( $false
= ( ( sK0 @ sK1 @ sK6 )
= sK6 ) )
| ( $false
= ( ( ( sK0 @ sK4 @ X2 )
= sK1 )
& ( ( sK0 @ X2 @ sK4 )
= sK1 ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) )
| ( $false
= ( ( ( sK0 @ sK1 @ sK5 )
= sK5 )
& ( ( sK0 @ sK5 @ sK1 )
= sK5 ) ) )
| ( sK1
!= ( sK0 @ X1 @ sK3 ) ) ),
inference(beta_eta_normalization,[],[f59]) ).
thf(f59,plain,
! [X2: g,X1: g] :
( ( $false
= ( ( ( sK0 @ sK1 @ sK5 )
= sK5 )
& ( ( sK0 @ sK5 @ sK1 )
= sK5 ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) )
| ( $false
= ( ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= Y0 )
@ sK6 ) )
| ( $false
= ( ( ( sK0 @ sK4 @ X2 )
= sK1 )
& ( ( sK0 @ X2 @ sK4 )
= sK1 ) ) )
| ( sK1
!= ( sK0 @ X1 @ sK3 ) ) ),
inference(sigma_clausification,[],[f58]) ).
thf(f58,plain,
! [X2: g,X1: g] :
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= Y0 ) ) )
| ( $false
= ( ( ( sK0 @ sK1 @ sK5 )
= sK5 )
& ( ( sK0 @ sK5 @ sK1 )
= sK5 ) ) )
| ( $false
= ( ( ( sK0 @ sK4 @ X2 )
= sK1 )
& ( ( sK0 @ X2 @ sK4 )
= sK1 ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) )
| ( sK1
!= ( sK0 @ X1 @ sK3 ) ) ),
inference(beta_eta_normalization,[],[f57]) ).
thf(f57,plain,
! [X2: g,X1: g] :
( ( $false
= ( ( ( sK0 @ sK1 @ sK5 )
= sK5 )
& ( ( sK0 @ sK5 @ sK1 )
= sK5 ) ) )
| ( $false
= ( ^ [Y0: g] :
( ( ( sK0 @ sK4 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ sK4 )
= sK1 ) )
@ X2 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= Y0 ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) )
| ( sK1
!= ( sK0 @ X1 @ sK3 ) ) ),
inference(pi_clausification,[],[f56]) ).
thf(f56,plain,
! [X1: g] :
( ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK4 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ sK4 )
= sK1 ) ) ) )
| ( sK1
!= ( sK0 @ X1 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK1 @ sK5 )
= sK5 )
& ( ( sK0 @ sK5 @ sK1 )
= sK5 ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= Y0 ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(equality_proxy_clausification,[],[f55]) ).
thf(f55,plain,
! [X1: g] :
( ( $false
= ( ( sK0 @ X1 @ sK3 )
= sK1 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= Y0 ) ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK4 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ sK4 )
= sK1 ) ) ) )
| ( $false
= ( ( ( sK0 @ sK1 @ sK5 )
= sK5 )
& ( ( sK0 @ sK5 @ sK1 )
= sK5 ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f54]) ).
thf(f54,plain,
! [X1: g] :
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) )
| ( $false
= ( ( sK0 @ X1 @ sK3 )
= sK1 ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK4 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ sK4 )
= sK1 ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= Y0 ) ) )
| ( $false
= ( ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
@ sK5 ) ) ),
inference(sigma_clausification,[],[f53]) ).
thf(f53,plain,
! [X1: g] :
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) ) )
| ( $false
= ( ( sK0 @ X1 @ sK3 )
= sK1 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK4 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ sK4 )
= sK1 ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= Y0 ) ) ) ),
inference(duplicate_literal_removal,[],[f52]) ).
thf(f52,plain,
! [X1: g] :
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK4 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ sK4 )
= sK1 ) ) ) )
| ( $false
= ( ( sK0 @ X1 @ sK3 )
= sK1 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= Y0 ) ) ) ),
inference(binary_proxy_clausification,[],[f51]) ).
thf(f51,plain,
! [X1: g] :
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) )
= $false )
| ( $false
= ( ( sK0 @ X1 @ sK3 )
= sK1 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK4 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ sK4 )
= sK1 ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) ) ) ),
inference(beta_eta_normalization,[],[f50]) ).
thf(f50,plain,
! [X1: g] :
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) )
= $false )
| ( $false
= ( ( sK0 @ X1 @ sK3 )
= sK1 ) )
| ( $false
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) )
@ sK4 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(sigma_clausification,[],[f49]) ).
thf(f49,plain,
! [X1: g] :
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) ) )
| ( $false
= ( ( sK0 @ X1 @ sK3 )
= sK1 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f48]) ).
thf(f48,plain,
! [X1: g] :
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) )
= $false )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) ) )
| ( $false
= ( ( sK0 @ X1 @ sK3 )
= sK1 ) ) ),
inference(binary_proxy_clausification,[],[f47]) ).
thf(f47,plain,
! [X1: g] :
( ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) ) ) )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) )
= $false )
| ( $false
= ( ( sK0 @ X1 @ sK3 )
= sK1 ) ) ),
inference(beta_eta_normalization,[],[f46]) ).
thf(f46,plain,
! [X1: g] :
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) )
= $false )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) ) ) )
| ( ( ^ [Y0: g] :
( ( sK0 @ Y0 @ sK3 )
= sK1 )
@ X1 )
= $false ) ),
inference(pi_clausification,[],[f45]) ).
thf(f45,plain,
( ( ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK3 )
= sK1 ) )
= $false )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) )
= $false )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f44]) ).
thf(f44,plain,
( ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) ) ) )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) )
= $false )
| ( $false
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y1 @ Y0 )
= sK1 ) )
@ sK3 ) ) ),
inference(sigma_clausification,[],[f43]) ).
thf(f43,plain,
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) )
| ( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) )
= $false )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f42]) ).
thf(f42,plain,
( ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f40]) ).
thf(f40,plain,
( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) )
!= ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f39]) ).
thf(f39,plain,
( ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y2 @ Y3 @ Y4 )
= Y4 ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ ( Y2 @ Y5 @ Y4 ) @ Y3 )
= ( Y2 @ Y5 @ ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
@ Y0 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( Y2 @ Y5 @ Y4 )
= Y3 ) ) )
@ Y0
@ Y1 ) )
@ sK0
@ sK1 )
!= ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( ( Y2 @ Y3 @ Y4 )
= Y4 )
& ( ( Y2 @ Y4 @ Y3 )
= Y4 ) ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ ( Y2 @ Y5 @ Y4 ) @ Y3 )
= ( Y2 @ Y5 @ ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
@ Y0 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( ( Y2 @ Y4 @ Y5 )
= Y3 )
& ( ( Y2 @ Y5 @ Y4 )
= Y3 ) ) ) )
@ Y0
@ Y1 ) )
@ sK0
@ sK1 ) ),
inference(definition_unfolding,[],[f35,f37,f38]) ).
thf(f38,plain,
( cGROUP2
= ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y2 @ Y3 @ Y4 )
= Y4 ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ ( Y2 @ Y5 @ Y4 ) @ Y3 )
= ( Y2 @ Y5 @ ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
@ Y0 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( Y2 @ Y5 @ Y4 )
= Y3 ) ) )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f31,f30,f29,f34]) ).
thf(f34,plain,
( cGRP_LEFT_INVERSE
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y3 @ Y2 )
= Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f13,plain,
( cGRP_LEFT_INVERSE
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y3 @ Y2 )
= Y1 ) ) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f12,plain,
( cGRP_LEFT_INVERSE
= ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
? [X3: g] :
( ( X0 @ X3 @ X2 )
= X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f3,axiom,
( cGRP_LEFT_INVERSE
= ( ^ [X0: g > g > g,X4: g] :
! [X1: g] :
? [X2: g] :
( ( X0 @ X2 @ X1 )
= X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGRP_LEFT_INVERSE_def) ).
thf(f29,plain,
( cGRP_ASSOC
= ( ^ [Y0: g > g > g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( Y0 @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ Y3 @ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f11,plain,
( cGRP_ASSOC
= ( ^ [Y0: g > g > g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( Y0 @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ Y3 @ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: g > g > g] :
! [X1: g,X2: g,X3: g] :
( ( X0 @ ( X0 @ X1 @ X2 ) @ X3 )
= ( X0 @ X1 @ ( X0 @ X2 @ X3 ) ) ) )
= cGRP_ASSOC ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGRP_ASSOC_def) ).
thf(f30,plain,
( cGRP_LEFT_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y1 @ Y2 )
= Y2 ) ) ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f21,plain,
( cGRP_LEFT_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y1 @ Y2 )
= Y2 ) ) ) ),
inference(fool_elimination,[],[f20]) ).
thf(f20,plain,
( ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
( ( X0 @ X1 @ X2 )
= X2 ) )
= cGRP_LEFT_UNIT ),
inference(rectify,[],[f4]) ).
thf(f4,axiom,
( ( ^ [X0: g > g > g,X4: g] :
! [X1: g] :
( ( X0 @ X4 @ X1 )
= X1 ) )
= cGRP_LEFT_UNIT ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGRP_LEFT_UNIT_def) ).
thf(f31,plain,
( cGROUP2
= ( ^ [Y0: g > g > g,Y1: g] :
( ( cGRP_LEFT_UNIT @ Y0 @ Y1 )
& ( cGRP_ASSOC @ Y0 )
& ( cGRP_LEFT_INVERSE @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f19,plain,
( cGROUP2
= ( ^ [Y0: g > g > g,Y1: g] :
( ( cGRP_LEFT_UNIT @ Y0 @ Y1 )
& ( cGRP_ASSOC @ Y0 )
& ( cGRP_LEFT_INVERSE @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f18,plain,
( cGROUP2
= ( ^ [X0: g > g > g,X1: g] :
( ( cGRP_LEFT_INVERSE @ X0 @ X1 )
& ( cGRP_ASSOC @ X0 )
& ( cGRP_LEFT_UNIT @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f7,axiom,
( cGROUP2
= ( ^ [X0: g > g > g,X4: g] :
( ( cGRP_LEFT_INVERSE @ X0 @ X4 )
& ( cGRP_ASSOC @ X0 )
& ( cGRP_LEFT_UNIT @ X0 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGROUP2_def) ).
thf(f37,plain,
( cGROUP1
= ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( ( Y2 @ Y3 @ Y4 )
= Y4 )
& ( ( Y2 @ Y4 @ Y3 )
= Y4 ) ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ ( Y2 @ Y5 @ Y4 ) @ Y3 )
= ( Y2 @ Y5 @ ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
@ Y0 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( ( Y2 @ Y4 @ Y5 )
= Y3 )
& ( ( Y2 @ Y5 @ Y4 )
= Y3 ) ) ) )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f36,f33,f29,f32]) ).
thf(f32,plain,
( cGRP_INVERSE
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( ( Y0 @ Y2 @ Y3 )
= Y1 )
& ( ( Y0 @ Y3 @ Y2 )
= Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f25,plain,
( cGRP_INVERSE
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( ( Y0 @ Y2 @ Y3 )
= Y1 )
& ( ( Y0 @ Y3 @ Y2 )
= Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f24]) ).
thf(f24,plain,
( cGRP_INVERSE
= ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
? [X3: g] :
( ( ( X0 @ X3 @ X2 )
= X1 )
& ( ( X0 @ X2 @ X3 )
= X1 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
( cGRP_INVERSE
= ( ^ [X0: g > g > g,X4: g] :
! [X1: g] :
? [X2: g] :
( ( ( X0 @ X2 @ X1 )
= X4 )
& ( ( X0 @ X1 @ X2 )
= X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGRP_INVERSE_def) ).
thf(f33,plain,
( cGRP_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( ( Y0 @ Y1 @ Y2 )
= Y2 )
& ( ( Y0 @ Y2 @ Y1 )
= Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f17,plain,
( cGRP_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( ( Y0 @ Y1 @ Y2 )
= Y2 )
& ( ( Y0 @ Y2 @ Y1 )
= Y2 ) ) ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f16,plain,
( ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
( ( ( X0 @ X2 @ X1 )
= X2 )
& ( ( X0 @ X1 @ X2 )
= X2 ) ) )
= cGRP_UNIT ),
inference(rectify,[],[f5]) ).
thf(f5,axiom,
( ( ^ [X0: g > g > g,X4: g] :
! [X1: g] :
( ( ( X0 @ X1 @ X4 )
= X1 )
& ( ( X0 @ X4 @ X1 )
= X1 ) ) )
= cGRP_UNIT ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGRP_UNIT_def) ).
thf(f36,plain,
( cGROUP1
= ( ^ [Y0: g > g > g,Y1: g] :
( ( cGRP_UNIT @ Y0 @ Y1 )
& ( cGRP_ASSOC @ Y0 )
& ( cGRP_INVERSE @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f15,plain,
( cGROUP1
= ( ^ [Y0: g > g > g,Y1: g] :
( ( cGRP_UNIT @ Y0 @ Y1 )
& ( cGRP_ASSOC @ Y0 )
& ( cGRP_INVERSE @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f14,plain,
( ( ^ [X0: g > g > g,X1: g] :
( ( cGRP_INVERSE @ X0 @ X1 )
& ( cGRP_ASSOC @ X0 )
& ( cGRP_UNIT @ X0 @ X1 ) ) )
= cGROUP1 ),
inference(rectify,[],[f6]) ).
thf(f6,axiom,
( ( ^ [X0: g > g > g,X4: g] :
( ( cGRP_INVERSE @ X0 @ X4 )
& ( cGRP_ASSOC @ X0 )
& ( cGRP_UNIT @ X0 @ X4 ) ) )
= cGROUP1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGROUP1_def) ).
thf(f35,plain,
( ( cGROUP1 @ sK0 @ sK1 )
!= ( cGROUP2 @ sK0 @ sK1 ) ),
inference(cnf_transformation,[],[f28]) ).
thf(f28,plain,
( ( cGROUP1 @ sK0 @ sK1 )
!= ( cGROUP2 @ sK0 @ sK1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f26,f27]) ).
thf(f27,plain,
( ? [X0: g > g > g,X1: g] :
( ( cGROUP2 @ X0 @ X1 )
!= ( cGROUP1 @ X0 @ X1 ) )
=> ( ( cGROUP1 @ sK0 @ sK1 )
!= ( cGROUP2 @ sK0 @ sK1 ) ) ),
introduced(choice_axiom,[]) ).
thf(f26,plain,
? [X0: g > g > g,X1: g] :
( ( cGROUP2 @ X0 @ X1 )
!= ( cGROUP1 @ X0 @ X1 ) ),
inference(ennf_transformation,[],[f23]) ).
thf(f23,plain,
~ ! [X0: g > g > g,X1: g] :
( ( cGROUP2 @ X0 @ X1 )
= ( cGROUP1 @ X0 @ X1 ) ),
inference(fool_elimination,[],[f22]) ).
thf(f22,plain,
~ ! [X0: g > g > g,X1: g] :
( ( cGROUP1 @ X0 @ X1 )
<=> ( cGROUP2 @ X0 @ X1 ) ),
inference(rectify,[],[f9]) ).
thf(f9,negated_conjecture,
~ ! [X0: g > g > g,X4: g] :
( ( cGROUP1 @ X0 @ X4 )
<=> ( cGROUP2 @ X0 @ X4 ) ),
inference(negated_conjecture,[],[f8]) ).
thf(f8,conjecture,
! [X0: g > g > g,X4: g] :
( ( cGROUP1 @ X0 @ X4 )
<=> ( cGROUP2 @ X0 @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cEQUIV_01_02) ).
thf(f244,plain,
( spl2_7
| spl2_7 ),
inference(avatar_split_clause,[],[f90,f220,f220]) ).
thf(f90,plain,
! [X2: g,X1: g] :
( ( ( sK0 @ sK1 @ X1 )
= X1 )
| ( ( sK0 @ sK1 @ X2 )
= X2 ) ),
inference(equality_proxy_clausification,[],[f89]) ).
thf(f89,plain,
! [X2: g,X1: g] :
( ( ( sK0 @ sK1 @ X2 )
= X2 )
| ( $true
= ( ( sK0 @ sK1 @ X1 )
= X1 ) ) ),
inference(equality_proxy_clausification,[],[f88]) ).
thf(f88,plain,
! [X2: g,X1: g] :
( ( $true
= ( ( sK0 @ sK1 @ X2 )
= X2 ) )
| ( $true
= ( ( sK0 @ sK1 @ X1 )
= X1 ) ) ),
inference(beta_eta_normalization,[],[f87]) ).
thf(f87,plain,
! [X2: g,X1: g] :
( ( $true
= ( ( sK0 @ sK1 @ X1 )
= X1 ) )
| ( $true
= ( ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= Y0 )
@ X2 ) ) ),
inference(pi_clausification,[],[f86]) ).
thf(f86,plain,
! [X1: g] :
( ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= Y0 ) ) )
| ( $true
= ( ( sK0 @ sK1 @ X1 )
= X1 ) ) ),
inference(binary_proxy_clausification,[],[f84]) ).
thf(f84,plain,
! [X1: g] :
( ( $true
= ( ( ( sK0 @ sK1 @ X1 )
= X1 )
& ( ( sK0 @ X1 @ sK1 )
= X1 ) ) )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= Y0 ) ) ) ),
inference(beta_eta_normalization,[],[f83]) ).
thf(f83,plain,
! [X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= Y0 ) ) ) ),
inference(pi_clausification,[],[f82]) ).
thf(f82,plain,
( ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) ) )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= Y0 ) ) ) ),
inference(binary_proxy_clausification,[],[f80]) ).
thf(f80,plain,
( ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) ) )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= Y0 ) ) ) ),
inference(binary_proxy_clausification,[],[f78]) ).
thf(f78,plain,
( ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) ) ) )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= Y0 ) ) ) ),
inference(binary_proxy_clausification,[],[f76]) ).
thf(f76,plain,
( ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) ) )
| ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f41]) ).
thf(f41,plain,
( ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) ) )
| ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f40]) ).
thf(f231,plain,
spl2_4,
inference(avatar_split_clause,[],[f140,f209]) ).
thf(f140,plain,
! [X2: g,X3: g,X1: g] :
( ( sK0 @ ( sK0 @ X3 @ X2 ) @ X1 )
= ( sK0 @ X3 @ ( sK0 @ X2 @ X1 ) ) ),
inference(equality_proxy_clausification,[],[f139]) ).
thf(f139,plain,
! [X2: g,X3: g,X1: g] :
( $true
= ( ( sK0 @ ( sK0 @ X3 @ X2 ) @ X1 )
= ( sK0 @ X3 @ ( sK0 @ X2 @ X1 ) ) ) ),
inference(beta_eta_normalization,[],[f138]) ).
thf(f138,plain,
! [X2: g,X3: g,X1: g] :
( $true
= ( ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ X2 ) @ X1 )
= ( sK0 @ Y0 @ ( sK0 @ X2 @ X1 ) ) )
@ X3 ) ),
inference(pi_clausification,[],[f137]) ).
thf(f137,plain,
! [X2: g,X1: g] :
( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ X2 ) @ X1 )
= ( sK0 @ Y0 @ ( sK0 @ X2 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[],[f136]) ).
thf(f136,plain,
! [X2: g,X1: g] :
( $true
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ X1 )
= ( sK0 @ Y1 @ ( sK0 @ Y0 @ X1 ) ) ) )
@ X2 ) ),
inference(pi_clausification,[],[f135]) ).
thf(f135,plain,
! [X1: g] :
( $true
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ X1 )
= ( sK0 @ Y1 @ ( sK0 @ Y0 @ X1 ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f134]) ).
thf(f134,plain,
! [X1: g] :
( $true
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[],[f133]) ).
thf(f133,plain,
( $true
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(duplicate_literal_removal,[],[f118]) ).
thf(f118,plain,
( ( $true
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f117]) ).
thf(f117,plain,
( ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) ) )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f77]) ).
thf(f77,plain,
( ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) ) ) )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f76]) ).
thf(f218,plain,
( spl2_5
| spl2_6 ),
inference(avatar_split_clause,[],[f177,f216,f212]) ).
thf(f177,plain,
! [X2: g,X1: g] :
( ( sK1
= ( sK0 @ ( sK12 @ X1 ) @ X1 ) )
| ( ( sK0 @ X2 @ sK1 )
= X2 ) ),
inference(equality_proxy_clausification,[],[f174]) ).
thf(f174,plain,
! [X2: g,X1: g] :
( ( $true
= ( ( sK0 @ X2 @ sK1 )
= X2 ) )
| ( sK1
= ( sK0 @ ( sK12 @ X1 ) @ X1 ) ) ),
inference(binary_proxy_clausification,[],[f173]) ).
thf(f173,plain,
! [X2: g,X1: g] :
( ( sK1
= ( sK0 @ ( sK12 @ X1 ) @ X1 ) )
| ( $true
= ( ( ( sK0 @ sK1 @ X2 )
= X2 )
& ( ( sK0 @ X2 @ sK1 )
= X2 ) ) ) ),
inference(equality_proxy_clausification,[],[f172]) ).
thf(f172,plain,
! [X2: g,X1: g] :
( ( $true
= ( ( sK0 @ ( sK12 @ X1 ) @ X1 )
= sK1 ) )
| ( $true
= ( ( ( sK0 @ sK1 @ X2 )
= X2 )
& ( ( sK0 @ X2 @ sK1 )
= X2 ) ) ) ),
inference(beta_eta_normalization,[],[f171]) ).
thf(f171,plain,
! [X2: g,X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
@ X2 ) )
| ( $true
= ( ( sK0 @ ( sK12 @ X1 ) @ X1 )
= sK1 ) ) ),
inference(pi_clausification,[],[f170]) ).
thf(f170,plain,
! [X1: g] :
( ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) ) )
| ( $true
= ( ( sK0 @ ( sK12 @ X1 ) @ X1 )
= sK1 ) ) ),
inference(binary_proxy_clausification,[],[f168]) ).
thf(f168,plain,
! [X1: g] :
( ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) ) )
| ( $true
= ( ( sK0 @ ( sK12 @ X1 ) @ X1 )
= sK1 ) ) ),
inference(beta_eta_normalization,[],[f167]) ).
thf(f167,plain,
! [X1: g] :
( ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) ) )
| ( $true
= ( ^ [Y0: g] :
( ( sK0 @ Y0 @ X1 )
= sK1 )
@ ( sK12 @ X1 ) ) ) ),
inference(sigma_clausification,[],[f166]) ).
thf(f166,plain,
! [X1: g] :
( ( $true
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ X1 )
= sK1 ) ) )
| ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f164]) ).
thf(f164,plain,
! [X1: g] :
( ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) ) ) )
| ( $true
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ X1 )
= sK1 ) ) ) ),
inference(beta_eta_normalization,[],[f163]) ).
thf(f163,plain,
! [X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y1 @ Y0 )
= sK1 ) )
@ X1 ) )
| ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) ) ) ) ),
inference(pi_clausification,[],[f75]) ).
thf(f75,plain,
( ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) )
| ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f41]) ).
thf(f207,plain,
( spl2_2
| spl2_3 ),
inference(avatar_split_clause,[],[f195,f205,f201]) ).
thf(f195,plain,
! [X2: g,X1: g] :
( ( sK1
= ( sK0 @ X2 @ ( sK14 @ X2 ) ) )
| ( sK1
= ( sK0 @ ( sK13 @ X1 ) @ X1 ) ) ),
inference(equality_proxy_clausification,[],[f194]) ).
thf(f194,plain,
! [X2: g,X1: g] :
( ( $true
= ( ( sK0 @ X2 @ ( sK14 @ X2 ) )
= sK1 ) )
| ( sK1
= ( sK0 @ ( sK13 @ X1 ) @ X1 ) ) ),
inference(binary_proxy_clausification,[],[f192]) ).
thf(f192,plain,
! [X2: g,X1: g] :
( ( sK1
= ( sK0 @ ( sK13 @ X1 ) @ X1 ) )
| ( $true
= ( ( ( sK0 @ X2 @ ( sK14 @ X2 ) )
= sK1 )
& ( ( sK0 @ ( sK14 @ X2 ) @ X2 )
= sK1 ) ) ) ),
inference(beta_eta_normalization,[],[f191]) ).
thf(f191,plain,
! [X2: g,X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ( ( sK0 @ X2 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ X2 )
= sK1 ) )
@ ( sK14 @ X2 ) ) )
| ( sK1
= ( sK0 @ ( sK13 @ X1 ) @ X1 ) ) ),
inference(sigma_clausification,[],[f190]) ).
thf(f190,plain,
! [X2: g,X1: g] :
( ( ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK0 @ X2 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ X2 )
= sK1 ) ) )
= $true )
| ( sK1
= ( sK0 @ ( sK13 @ X1 ) @ X1 ) ) ),
inference(equality_proxy_clausification,[],[f189]) ).
thf(f189,plain,
! [X2: g,X1: g] :
( ( $true
= ( ( sK0 @ ( sK13 @ X1 ) @ X1 )
= sK1 ) )
| ( ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK0 @ X2 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ X2 )
= sK1 ) ) )
= $true ) ),
inference(beta_eta_normalization,[],[f188]) ).
thf(f188,plain,
! [X2: g,X1: g] :
( ( ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) )
@ X2 )
= $true )
| ( $true
= ( ( sK0 @ ( sK13 @ X1 ) @ X1 )
= sK1 ) ) ),
inference(pi_clausification,[],[f187]) ).
thf(f187,plain,
! [X1: g] :
( ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) ) )
| ( $true
= ( ( sK0 @ ( sK13 @ X1 ) @ X1 )
= sK1 ) ) ),
inference(beta_eta_normalization,[],[f186]) ).
thf(f186,plain,
! [X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ( sK0 @ Y0 @ X1 )
= sK1 )
@ ( sK13 @ X1 ) ) )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) ) ) ),
inference(sigma_clausification,[],[f165]) ).
thf(f165,plain,
! [X1: g] :
( ( $true
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ X1 )
= sK1 ) ) )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f164]) ).
thf(f203,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f196,f201,f198]) ).
thf(f196,plain,
! [X2: g,X1: g] :
( ( sK1
= ( sK0 @ ( sK14 @ X2 ) @ X2 ) )
| ( sK1
= ( sK0 @ ( sK13 @ X1 ) @ X1 ) ) ),
inference(equality_proxy_clausification,[],[f193]) ).
thf(f193,plain,
! [X2: g,X1: g] :
( ( sK1
= ( sK0 @ ( sK13 @ X1 ) @ X1 ) )
| ( $true
= ( ( sK0 @ ( sK14 @ X2 ) @ X2 )
= sK1 ) ) ),
inference(binary_proxy_clausification,[],[f192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : ALG272^5 : TPTP v8.2.0. Bugfixed v5.3.0.
% 0.05/0.09 % Command : run_vampire %s %d THM
% 0.08/0.28 % Computer : n032.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 300
% 0.08/0.28 % DateTime : Wed Jun 19 14:54:53 EDT 2024
% 0.08/0.28 % CPUTime :
% 0.08/0.29 This is a TH0_THM_EQU_NAR problem
% 0.08/0.29 Running higher-order theorem proving
% 0.08/0.29 Running /export/starexec/sandbox/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox/benchmark/theBenchmark.p -m 16384 -t 300
% 0.08/0.31 % (9953)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.08/0.31 % (9954)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)
% 0.08/0.31 % (9956)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.08/0.31 % (9958)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)
% 0.08/0.31 % (9957)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)
% 0.08/0.31 % (9956)Instruction limit reached!
% 0.08/0.31 % (9956)------------------------------
% 0.08/0.31 % (9956)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.08/0.31 % (9956)Termination reason: Unknown
% 0.08/0.31 % (9956)Termination phase: Property scanning
% 0.08/0.31 % (9957)Instruction limit reached!
% 0.08/0.31 % (9957)------------------------------
% 0.08/0.31 % (9957)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.08/0.31 % (9957)Termination reason: Unknown
% 0.08/0.31 % (9957)Termination phase: Property scanning
% 0.08/0.31
% 0.08/0.31 % (9957)Memory used [KB]: 1023
% 0.08/0.31 % (9957)Time elapsed: 0.002 s
% 0.08/0.31 % (9957)Instructions burned: 2 (million)
% 0.08/0.31 % (9957)------------------------------
% 0.08/0.31 % (9957)------------------------------
% 0.08/0.31 % (9959)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.08/0.31
% 0.08/0.31 % (9956)Memory used [KB]: 1023
% 0.08/0.31 % (9956)Time elapsed: 0.003 s
% 0.08/0.31 % (9956)Instructions burned: 3 (million)
% 0.08/0.31 % (9956)------------------------------
% 0.08/0.31 % (9956)------------------------------
% 0.08/0.31 % (9954)Instruction limit reached!
% 0.08/0.31 % (9954)------------------------------
% 0.08/0.31 % (9954)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.08/0.31 % (9954)Termination reason: Unknown
% 0.08/0.31 % (9954)Termination phase: Saturation
% 0.08/0.31
% 0.08/0.31 % (9954)Memory used [KB]: 5500
% 0.08/0.31 % (9954)Time elapsed: 0.004 s
% 0.08/0.31 % (9954)Instructions burned: 6 (million)
% 0.08/0.31 % (9954)------------------------------
% 0.08/0.31 % (9954)------------------------------
% 0.14/0.31 % (9955)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)
% 0.14/0.32 % (9959)Instruction limit reached!
% 0.14/0.32 % (9959)------------------------------
% 0.14/0.32 % (9959)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.14/0.32 % (9959)Termination reason: Unknown
% 0.14/0.32 % (9959)Termination phase: Saturation
% 0.14/0.32
% 0.14/0.32 % (9959)Memory used [KB]: 5628
% 0.14/0.32 % (9959)Time elapsed: 0.009 s
% 0.14/0.32 % (9959)Instructions burned: 19 (million)
% 0.14/0.32 % (9959)------------------------------
% 0.14/0.32 % (9959)------------------------------
% 0.14/0.32 % (9960)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)
% 0.14/0.32 % (9961)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)
% 0.14/0.32 % (9962)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)
% 0.14/0.32 % (9960)Instruction limit reached!
% 0.14/0.32 % (9960)------------------------------
% 0.14/0.32 % (9960)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.14/0.32 % (9960)Termination reason: Unknown
% 0.14/0.32 % (9960)Termination phase: Saturation
% 0.14/0.32
% 0.14/0.32 % (9960)Memory used [KB]: 5500
% 0.14/0.32 % (9960)Time elapsed: 0.003 s
% 0.14/0.32 % (9960)Instructions burned: 4 (million)
% 0.14/0.32 % (9960)------------------------------
% 0.14/0.32 % (9960)------------------------------
% 0.14/0.32 % (9962)Instruction limit reached!
% 0.14/0.32 % (9962)------------------------------
% 0.14/0.32 % (9962)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.14/0.32 % (9962)Termination reason: Unknown
% 0.14/0.32 % (9962)Termination phase: Saturation
% 0.14/0.32
% 0.14/0.32 % (9962)Memory used [KB]: 5628
% 0.14/0.32 % (9962)Time elapsed: 0.007 s
% 0.14/0.32 % (9962)Instructions burned: 16 (million)
% 0.14/0.32 % (9962)------------------------------
% 0.14/0.32 % (9962)------------------------------
% 0.14/0.32 % (9958)First to succeed.
% 0.14/0.33 % (9963)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)
% 0.14/0.33 % (9963)Instruction limit reached!
% 0.14/0.33 % (9963)------------------------------
% 0.14/0.33 % (9963)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.14/0.33 % (9963)Termination reason: Unknown
% 0.14/0.33 % (9963)Termination phase: Saturation
% 0.14/0.33
% 0.14/0.33 % (9963)Memory used [KB]: 5500
% 0.14/0.33 % (9963)Time elapsed: 0.003 s
% 0.14/0.33 % (9963)Instructions burned: 4 (million)
% 0.14/0.33 % (9963)------------------------------
% 0.14/0.33 % (9963)------------------------------
% 0.14/0.33 % (9964)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)
% 0.14/0.33 % (9955)Instruction limit reached!
% 0.14/0.33 % (9955)------------------------------
% 0.14/0.33 % (9955)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.14/0.33 % (9955)Termination reason: Unknown
% 0.14/0.33 % (9955)Termination phase: Saturation
% 0.14/0.33
% 0.14/0.33 % (9955)Memory used [KB]: 5756
% 0.14/0.33 % (9955)Time elapsed: 0.018 s
% 0.14/0.33 % (9955)Instructions burned: 28 (million)
% 0.14/0.33 % (9955)------------------------------
% 0.14/0.33 % (9955)------------------------------
% 0.14/0.33 % (9958)Refutation found. Thanks to Tanya!
% 0.14/0.33 % SZS status Theorem for theBenchmark
% 0.14/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.33 % (9958)------------------------------
% 0.14/0.33 % (9958)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.14/0.33 % (9958)Termination reason: Refutation
% 0.14/0.33
% 0.14/0.33 % (9958)Memory used [KB]: 5884
% 0.14/0.33 % (9958)Time elapsed: 0.023 s
% 0.14/0.33 % (9958)Instructions burned: 44 (million)
% 0.14/0.33 % (9958)------------------------------
% 0.14/0.33 % (9958)------------------------------
% 0.14/0.33 % (9952)Success in time 0.022 s
%------------------------------------------------------------------------------