TSTP Solution File: ALG271^5 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : ALG271^5 : TPTP v8.2.0. Bugfixed v5.3.0.
% 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 : n002.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 May 20 18:20:46 EDT 2024
% Result : Theorem 0.26s 0.49s
% Output : Refutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 51
% Syntax : Number of formulae : 235 ( 37 unt; 28 typ; 0 def)
% Number of atoms : 1719 ( 841 equ; 0 cnn)
% Maximal formula atoms : 8 ( 8 avg)
% Number of connectives : 4150 ( 223 ~; 379 |; 160 &;2957 @)
% ( 17 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 136 ( 136 >; 0 *; 0 +; 0 <<)
% Number of symbols : 45 ( 40 usr; 29 con; 0-2 aty)
% ( 313 !!; 100 ??; 0 @@+; 0 @@-)
% Number of variables : 707 ( 519 ^ 180 !; 8 ?; 707 :)
% 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,
cGROUP3: ( 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_RIGHT_INVERSE: ( g > g > g ) > g > $o ).
thf(func_def_6,type,
cGRP_RIGHT_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 ).
thf(func_def_31,type,
sK11: g ).
thf(func_def_32,type,
sK12: g ).
thf(func_def_33,type,
sK13: g > g ).
thf(func_def_34,type,
sK14: g > g ).
thf(func_def_35,type,
sK15: g > g ).
thf(func_def_36,type,
sK16: g > g ).
thf(func_def_37,type,
sK17: g > g ).
thf(func_def_38,type,
sK18: g > g ).
thf(func_def_39,type,
sK19: g > g ).
thf(f692,plain,
$false,
inference(avatar_sat_refutation,[],[f223,f224,f226,f246,f250,f285,f288,f290,f292,f294,f406,f432,f451,f654,f686,f691]) ).
thf(f691,plain,
( ~ spl2_11
| ~ spl2_17 ),
inference(avatar_contradiction_clause,[],[f690]) ).
thf(f690,plain,
( $false
| ~ spl2_11
| ~ spl2_17 ),
inference(trivial_inequality_removal,[],[f689]) ).
thf(f689,plain,
( ( sK1 != sK1 )
| ~ spl2_11
| ~ spl2_17 ),
inference(superposition,[],[f273,f249]) ).
thf(f249,plain,
( ! [X2: g] :
( sK1
= ( sK0 @ X2 @ ( sK15 @ X2 ) ) )
| ~ spl2_11 ),
inference(avatar_component_clause,[],[f248]) ).
thf(f248,plain,
( spl2_11
<=> ! [X2: g] :
( sK1
= ( sK0 @ X2 @ ( sK15 @ X2 ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_11])]) ).
thf(f273,plain,
( ! [X2: g] :
( ( sK0 @ sK11 @ X2 )
!= sK1 )
| ~ spl2_17 ),
inference(avatar_component_clause,[],[f272]) ).
thf(f272,plain,
( spl2_17
<=> ! [X2: g] :
( ( sK0 @ sK11 @ X2 )
!= sK1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_17])]) ).
thf(f686,plain,
( ~ spl2_9
| ~ spl2_11
| ~ spl2_18 ),
inference(avatar_contradiction_clause,[],[f685]) ).
thf(f685,plain,
( $false
| ~ spl2_9
| ~ spl2_11
| ~ spl2_18 ),
inference(subsumption_resolution,[],[f681,f242]) ).
thf(f242,plain,
( ! [X2: g] :
( sK1
= ( sK0 @ ( sK15 @ X2 ) @ X2 ) )
| ~ spl2_9 ),
inference(avatar_component_clause,[],[f241]) ).
thf(f241,plain,
( spl2_9
<=> ! [X2: g] :
( sK1
= ( sK0 @ ( sK15 @ X2 ) @ X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_9])]) ).
thf(f681,plain,
( ( sK1
!= ( sK0 @ ( sK15 @ sK3 ) @ sK3 ) )
| ~ spl2_11
| ~ spl2_18 ),
inference(trivial_inequality_removal,[],[f680]) ).
thf(f680,plain,
( ( sK1 != sK1 )
| ( sK1
!= ( sK0 @ ( sK15 @ sK3 ) @ sK3 ) )
| ~ spl2_11
| ~ spl2_18 ),
inference(superposition,[],[f276,f249]) ).
thf(f276,plain,
( ! [X1: g] :
( ( sK1
!= ( sK0 @ sK3 @ X1 ) )
| ( ( sK0 @ X1 @ sK3 )
!= sK1 ) )
| ~ spl2_18 ),
inference(avatar_component_clause,[],[f275]) ).
thf(f275,plain,
( spl2_18
<=> ! [X1: g] :
( ( sK1
!= ( sK0 @ sK3 @ X1 ) )
| ( ( sK0 @ X1 @ sK3 )
!= sK1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_18])]) ).
thf(f654,plain,
( ~ spl2_1
| ~ spl2_2
| ~ spl2_3
| ~ spl2_10
| ~ spl2_18 ),
inference(avatar_contradiction_clause,[],[f653]) ).
thf(f653,plain,
( $false
| ~ spl2_1
| ~ spl2_2
| ~ spl2_3
| ~ spl2_10
| ~ spl2_18 ),
inference(trivial_inequality_removal,[],[f646]) ).
thf(f646,plain,
( ( sK1 != sK1 )
| ~ spl2_1
| ~ spl2_2
| ~ spl2_3
| ~ spl2_10
| ~ spl2_18 ),
inference(superposition,[],[f473,f595]) ).
thf(f595,plain,
( ! [X0: g] :
( ( sK0 @ ( sK14 @ X0 ) @ X0 )
= sK1 )
| ~ spl2_1
| ~ spl2_2
| ~ spl2_3
| ~ spl2_10 ),
inference(superposition,[],[f245,f576]) ).
thf(f576,plain,
( ! [X0: g] :
( ( sK14 @ ( sK14 @ X0 ) )
= X0 )
| ~ spl2_1
| ~ spl2_2
| ~ spl2_3
| ~ spl2_10 ),
inference(superposition,[],[f214,f513]) ).
thf(f513,plain,
( ! [X0: g] :
( ( sK0 @ sK1 @ ( sK14 @ ( sK14 @ X0 ) ) )
= X0 )
| ~ spl2_1
| ~ spl2_2
| ~ spl2_10 ),
inference(forward_demodulation,[],[f502,f207]) ).
thf(f207,plain,
( ! [X1: g] :
( ( sK0 @ X1 @ sK1 )
= X1 )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f206]) ).
thf(f206,plain,
( spl2_1
<=> ! [X1: g] :
( ( sK0 @ X1 @ sK1 )
= X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).
thf(f502,plain,
( ! [X0: g] :
( ( sK0 @ sK1 @ ( sK14 @ ( sK14 @ X0 ) ) )
= ( sK0 @ X0 @ sK1 ) )
| ~ spl2_2
| ~ spl2_10 ),
inference(superposition,[],[f314,f245]) ).
thf(f314,plain,
( ! [X0: g,X1: g] :
( ( sK0 @ X0 @ ( sK0 @ ( sK14 @ X0 ) @ X1 ) )
= ( sK0 @ sK1 @ X1 ) )
| ~ spl2_2
| ~ spl2_10 ),
inference(superposition,[],[f210,f245]) ).
thf(f210,plain,
( ! [X2: g,X3: g,X4: g] :
( ( sK0 @ X2 @ ( sK0 @ X4 @ X3 ) )
= ( sK0 @ ( sK0 @ X2 @ X4 ) @ X3 ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f209]) ).
thf(f209,plain,
( spl2_2
<=> ! [X4: g,X2: g,X3: g] :
( ( sK0 @ X2 @ ( sK0 @ X4 @ X3 ) )
= ( sK0 @ ( sK0 @ X2 @ X4 ) @ X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).
thf(f214,plain,
( ! [X1: g] :
( ( sK0 @ sK1 @ X1 )
= X1 )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f213]) ).
thf(f213,plain,
( spl2_3
<=> ! [X1: g] :
( ( sK0 @ sK1 @ X1 )
= X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).
thf(f245,plain,
( ! [X1: g] :
( ( sK0 @ X1 @ ( sK14 @ X1 ) )
= sK1 )
| ~ spl2_10 ),
inference(avatar_component_clause,[],[f244]) ).
thf(f244,plain,
( spl2_10
<=> ! [X1: g] :
( ( sK0 @ X1 @ ( sK14 @ X1 ) )
= sK1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_10])]) ).
thf(f473,plain,
( ( sK1
!= ( sK0 @ ( sK14 @ sK3 ) @ sK3 ) )
| ~ spl2_10
| ~ spl2_18 ),
inference(trivial_inequality_removal,[],[f470]) ).
thf(f470,plain,
( ( sK1
!= ( sK0 @ ( sK14 @ sK3 ) @ sK3 ) )
| ( sK1 != sK1 )
| ~ spl2_10
| ~ spl2_18 ),
inference(superposition,[],[f276,f245]) ).
thf(f451,plain,
( ~ spl2_10
| ~ spl2_17 ),
inference(avatar_contradiction_clause,[],[f450]) ).
thf(f450,plain,
( $false
| ~ spl2_10
| ~ spl2_17 ),
inference(trivial_inequality_removal,[],[f446]) ).
thf(f446,plain,
( ( sK1 != sK1 )
| ~ spl2_10
| ~ spl2_17 ),
inference(superposition,[],[f273,f245]) ).
thf(f432,plain,
( ~ spl2_3
| spl2_19 ),
inference(avatar_contradiction_clause,[],[f431]) ).
thf(f431,plain,
( $false
| ~ spl2_3
| spl2_19 ),
inference(trivial_inequality_removal,[],[f417]) ).
thf(f417,plain,
( ( sK4 != sK4 )
| ~ spl2_3
| spl2_19 ),
inference(superposition,[],[f280,f214]) ).
thf(f280,plain,
( ( ( sK0 @ sK1 @ sK4 )
!= sK4 )
| spl2_19 ),
inference(avatar_component_clause,[],[f278]) ).
thf(f278,plain,
( spl2_19
<=> ( ( sK0 @ sK1 @ sK4 )
= sK4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_19])]) ).
thf(f406,plain,
( spl2_3
| ~ spl2_1
| ~ spl2_2
| ~ spl2_5 ),
inference(avatar_split_clause,[],[f405,f221,f209,f206,f213]) ).
thf(f221,plain,
( spl2_5
<=> ! [X2: g] :
( ( sK0 @ X2 @ ( sK18 @ X2 ) )
= sK1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_5])]) ).
thf(f405,plain,
( ! [X0: g] :
( ( sK0 @ sK1 @ X0 )
= X0 )
| ~ spl2_1
| ~ spl2_2
| ~ spl2_5 ),
inference(forward_demodulation,[],[f404,f342]) ).
thf(f342,plain,
( ! [X0: g] :
( ( sK0 @ sK1 @ ( sK18 @ ( sK18 @ X0 ) ) )
= X0 )
| ~ spl2_1
| ~ spl2_2
| ~ spl2_5 ),
inference(forward_demodulation,[],[f329,f207]) ).
thf(f329,plain,
( ! [X0: g] :
( ( sK0 @ sK1 @ ( sK18 @ ( sK18 @ X0 ) ) )
= ( sK0 @ X0 @ sK1 ) )
| ~ spl2_2
| ~ spl2_5 ),
inference(superposition,[],[f302,f222]) ).
thf(f222,plain,
( ! [X2: g] :
( ( sK0 @ X2 @ ( sK18 @ X2 ) )
= sK1 )
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f221]) ).
thf(f302,plain,
( ! [X0: g,X1: g] :
( ( sK0 @ X0 @ ( sK0 @ ( sK18 @ X0 ) @ X1 ) )
= ( sK0 @ sK1 @ X1 ) )
| ~ spl2_2
| ~ spl2_5 ),
inference(superposition,[],[f210,f222]) ).
thf(f404,plain,
( ! [X0: g] :
( ( sK0 @ sK1 @ ( sK0 @ sK1 @ ( sK18 @ ( sK18 @ X0 ) ) ) )
= X0 )
| ~ spl2_1
| ~ spl2_2
| ~ spl2_5 ),
inference(forward_demodulation,[],[f398,f207]) ).
thf(f398,plain,
( ! [X0: g] :
( ( sK0 @ sK1 @ ( sK0 @ sK1 @ ( sK18 @ ( sK18 @ X0 ) ) ) )
= ( sK0 @ X0 @ sK1 ) )
| ~ spl2_1
| ~ spl2_2
| ~ spl2_5 ),
inference(superposition,[],[f302,f351]) ).
thf(f351,plain,
( ! [X0: g] :
( ( sK0 @ X0 @ ( sK0 @ sK1 @ ( sK18 @ X0 ) ) )
= sK1 )
| ~ spl2_1
| ~ spl2_2
| ~ spl2_5 ),
inference(superposition,[],[f303,f207]) ).
thf(f303,plain,
( ! [X0: g,X1: g] :
( sK1
= ( sK0 @ X0 @ ( sK0 @ X1 @ ( sK18 @ ( sK0 @ X0 @ X1 ) ) ) ) )
| ~ spl2_2
| ~ spl2_5 ),
inference(superposition,[],[f210,f222]) ).
thf(f294,plain,
( ~ spl2_2
| spl2_16 ),
inference(avatar_contradiction_clause,[],[f293]) ).
thf(f293,plain,
( $false
| ~ spl2_2
| spl2_16 ),
inference(subsumption_resolution,[],[f270,f210]) ).
thf(f270,plain,
( ( ( sK0 @ sK5 @ ( sK0 @ sK12 @ sK9 ) )
!= ( sK0 @ ( sK0 @ sK5 @ sK12 ) @ sK9 ) )
| spl2_16 ),
inference(avatar_component_clause,[],[f268]) ).
thf(f268,plain,
( spl2_16
<=> ( ( sK0 @ sK5 @ ( sK0 @ sK12 @ sK9 ) )
= ( sK0 @ ( sK0 @ sK5 @ sK12 ) @ sK9 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_16])]) ).
thf(f292,plain,
( ~ spl2_2
| spl2_15 ),
inference(avatar_contradiction_clause,[],[f291]) ).
thf(f291,plain,
( $false
| ~ spl2_2
| spl2_15 ),
inference(subsumption_resolution,[],[f266,f210]) ).
thf(f266,plain,
( ( ( sK0 @ sK6 @ ( sK0 @ sK8 @ sK7 ) )
!= ( sK0 @ ( sK0 @ sK6 @ sK8 ) @ sK7 ) )
| spl2_15 ),
inference(avatar_component_clause,[],[f264]) ).
thf(f264,plain,
( spl2_15
<=> ( ( sK0 @ sK6 @ ( sK0 @ sK8 @ sK7 ) )
= ( sK0 @ ( sK0 @ sK6 @ sK8 ) @ sK7 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_15])]) ).
thf(f290,plain,
( ~ spl2_1
| spl2_14 ),
inference(avatar_contradiction_clause,[],[f289]) ).
thf(f289,plain,
( $false
| ~ spl2_1
| spl2_14 ),
inference(subsumption_resolution,[],[f262,f207]) ).
thf(f262,plain,
( ( ( sK0 @ sK10 @ sK1 )
!= sK10 )
| spl2_14 ),
inference(avatar_component_clause,[],[f260]) ).
thf(f260,plain,
( spl2_14
<=> ( ( sK0 @ sK10 @ sK1 )
= sK10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_14])]) ).
thf(f288,plain,
( ~ spl2_1
| spl2_20 ),
inference(avatar_contradiction_clause,[],[f287]) ).
thf(f287,plain,
( $false
| ~ spl2_1
| spl2_20 ),
inference(trivial_inequality_removal,[],[f286]) ).
thf(f286,plain,
( ( sK4 != sK4 )
| ~ spl2_1
| spl2_20 ),
inference(superposition,[],[f284,f207]) ).
thf(f284,plain,
( ( ( sK0 @ sK4 @ sK1 )
!= sK4 )
| spl2_20 ),
inference(avatar_component_clause,[],[f282]) ).
thf(f282,plain,
( spl2_20
<=> ( ( sK0 @ sK4 @ sK1 )
= sK4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_20])]) ).
thf(f285,plain,
( ~ spl2_14
| ~ spl2_15
| ~ spl2_16
| spl2_17
| spl2_18
| ~ spl2_19
| ~ spl2_20 ),
inference(avatar_split_clause,[],[f81,f282,f278,f275,f272,f268,f264,f260]) ).
thf(f81,plain,
! [X2: g,X1: g] :
( ( ( sK0 @ sK1 @ sK4 )
!= sK4 )
| ( ( sK0 @ sK6 @ ( sK0 @ sK8 @ sK7 ) )
!= ( sK0 @ ( sK0 @ sK6 @ sK8 ) @ sK7 ) )
| ( ( sK0 @ sK11 @ X2 )
!= sK1 )
| ( sK1
!= ( sK0 @ sK3 @ X1 ) )
| ( ( sK0 @ X1 @ sK3 )
!= sK1 )
| ( ( sK0 @ sK10 @ sK1 )
!= sK10 )
| ( ( sK0 @ sK5 @ ( sK0 @ sK12 @ sK9 ) )
!= ( sK0 @ ( sK0 @ sK5 @ sK12 ) @ sK9 ) )
| ( ( sK0 @ sK4 @ sK1 )
!= sK4 ) ),
inference(equality_proxy_clausification,[],[f80]) ).
thf(f80,plain,
! [X2: g,X1: g] :
( ( ( sK0 @ sK10 @ sK1 )
!= sK10 )
| ( ( sK0 @ X1 @ sK3 )
!= sK1 )
| ( ( sK0 @ sK1 @ sK4 )
!= sK4 )
| ( ( ( sK0 @ sK11 @ X2 )
= sK1 )
= $false )
| ( ( sK0 @ sK4 @ sK1 )
!= sK4 )
| ( ( sK0 @ sK6 @ ( sK0 @ sK8 @ sK7 ) )
!= ( sK0 @ ( sK0 @ sK6 @ sK8 ) @ sK7 ) )
| ( ( sK0 @ sK5 @ ( sK0 @ sK12 @ sK9 ) )
!= ( sK0 @ ( sK0 @ sK5 @ sK12 ) @ sK9 ) )
| ( sK1
!= ( sK0 @ sK3 @ X1 ) ) ),
inference(equality_proxy_clausification,[],[f79]) ).
thf(f79,plain,
! [X2: g,X1: g] :
( ( ( sK0 @ sK5 @ ( sK0 @ sK12 @ sK9 ) )
!= ( sK0 @ ( sK0 @ sK5 @ sK12 ) @ sK9 ) )
| ( ( sK0 @ sK1 @ sK4 )
!= sK4 )
| ( $false
= ( ( sK0 @ sK3 @ X1 )
= sK1 ) )
| ( ( sK0 @ sK4 @ sK1 )
!= sK4 )
| ( ( sK0 @ sK10 @ sK1 )
!= sK10 )
| ( ( sK0 @ X1 @ sK3 )
!= sK1 )
| ( ( ( sK0 @ sK11 @ X2 )
= sK1 )
= $false )
| ( ( sK0 @ sK6 @ ( sK0 @ sK8 @ sK7 ) )
!= ( sK0 @ ( sK0 @ sK6 @ sK8 ) @ sK7 ) ) ),
inference(beta_eta_normalization,[],[f78]) ).
thf(f78,plain,
! [X2: g,X1: g] :
( ( ( sK0 @ sK10 @ sK1 )
!= sK10 )
| ( $false
= ( ^ [Y0: g] :
( ( sK0 @ sK11 @ Y0 )
= sK1 )
@ X2 ) )
| ( ( sK0 @ X1 @ sK3 )
!= sK1 )
| ( ( sK0 @ sK4 @ sK1 )
!= sK4 )
| ( ( sK0 @ sK6 @ ( sK0 @ sK8 @ sK7 ) )
!= ( sK0 @ ( sK0 @ sK6 @ sK8 ) @ sK7 ) )
| ( $false
= ( ( sK0 @ sK3 @ X1 )
= sK1 ) )
| ( ( sK0 @ sK5 @ ( sK0 @ sK12 @ sK9 ) )
!= ( sK0 @ ( sK0 @ sK5 @ sK12 ) @ sK9 ) )
| ( ( sK0 @ sK1 @ sK4 )
!= sK4 ) ),
inference(pi_clausification,[],[f77]) ).
thf(f77,plain,
! [X1: g] :
( ( ( sK0 @ X1 @ sK3 )
!= sK1 )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ sK11 @ Y0 )
= sK1 ) ) )
| ( ( sK0 @ sK1 @ sK4 )
!= sK4 )
| ( ( sK0 @ sK4 @ sK1 )
!= sK4 )
| ( ( sK0 @ sK5 @ ( sK0 @ sK12 @ sK9 ) )
!= ( sK0 @ ( sK0 @ sK5 @ sK12 ) @ sK9 ) )
| ( ( sK0 @ sK6 @ ( sK0 @ sK8 @ sK7 ) )
!= ( sK0 @ ( sK0 @ sK6 @ sK8 ) @ sK7 ) )
| ( ( sK0 @ sK10 @ sK1 )
!= sK10 )
| ( $false
= ( ( sK0 @ sK3 @ X1 )
= sK1 ) ) ),
inference(equality_proxy_clausification,[],[f76]) ).
thf(f76,plain,
! [X1: g] :
( ( ( sK0 @ X1 @ sK3 )
!= sK1 )
| ( ( ( sK0 @ sK5 @ ( sK0 @ sK12 @ sK9 ) )
= ( sK0 @ ( sK0 @ sK5 @ sK12 ) @ sK9 ) )
= $false )
| ( ( sK0 @ sK1 @ sK4 )
!= sK4 )
| ( ( sK0 @ sK6 @ ( sK0 @ sK8 @ sK7 ) )
!= ( sK0 @ ( sK0 @ sK6 @ sK8 ) @ sK7 ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ sK11 @ Y0 )
= sK1 ) ) )
| ( ( sK0 @ sK4 @ sK1 )
!= sK4 )
| ( ( sK0 @ sK10 @ sK1 )
!= sK10 )
| ( $false
= ( ( sK0 @ sK3 @ X1 )
= sK1 ) ) ),
inference(equality_proxy_clausification,[],[f75]) ).
thf(f75,plain,
! [X1: g] :
( ( ( sK0 @ sK4 @ sK1 )
!= sK4 )
| ( ( sK0 @ sK1 @ sK4 )
!= sK4 )
| ( $false
= ( ( sK0 @ sK10 @ sK1 )
= sK10 ) )
| ( ( ( sK0 @ sK5 @ ( sK0 @ sK12 @ sK9 ) )
= ( sK0 @ ( sK0 @ sK5 @ sK12 ) @ sK9 ) )
= $false )
| ( ( sK0 @ X1 @ sK3 )
!= sK1 )
| ( ( sK0 @ sK6 @ ( sK0 @ sK8 @ sK7 ) )
!= ( sK0 @ ( sK0 @ sK6 @ sK8 ) @ sK7 ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ sK11 @ Y0 )
= sK1 ) ) )
| ( $false
= ( ( sK0 @ sK3 @ X1 )
= sK1 ) ) ),
inference(equality_proxy_clausification,[],[f74]) ).
thf(f74,plain,
! [X1: g] :
( ( ( sK0 @ sK1 @ sK4 )
!= sK4 )
| ( ( sK0 @ sK4 @ sK1 )
!= sK4 )
| ( ( ( sK0 @ X1 @ sK3 )
= sK1 )
= $false )
| ( ( ( sK0 @ sK5 @ ( sK0 @ sK12 @ sK9 ) )
= ( sK0 @ ( sK0 @ sK5 @ sK12 ) @ sK9 ) )
= $false )
| ( $false
= ( ( sK0 @ sK3 @ X1 )
= sK1 ) )
| ( ( sK0 @ sK6 @ ( sK0 @ sK8 @ sK7 ) )
!= ( sK0 @ ( sK0 @ sK6 @ sK8 ) @ sK7 ) )
| ( $false
= ( ( sK0 @ sK10 @ sK1 )
= sK10 ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ sK11 @ Y0 )
= sK1 ) ) ) ),
inference(binary_proxy_clausification,[],[f73]) ).
thf(f73,plain,
! [X1: g] :
( ( ( sK0 @ sK4 @ sK1 )
!= sK4 )
| ( ( sK0 @ sK6 @ ( sK0 @ sK8 @ sK7 ) )
!= ( sK0 @ ( sK0 @ sK6 @ sK8 ) @ sK7 ) )
| ( $false
= ( ( ( sK0 @ sK3 @ X1 )
= sK1 )
& ( ( sK0 @ X1 @ sK3 )
= sK1 ) ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ sK11 @ Y0 )
= sK1 ) ) )
| ( ( ( sK0 @ sK5 @ ( sK0 @ sK12 @ sK9 ) )
= ( sK0 @ ( sK0 @ sK5 @ sK12 ) @ sK9 ) )
= $false )
| ( $false
= ( ( sK0 @ sK10 @ sK1 )
= sK10 ) )
| ( ( sK0 @ sK1 @ sK4 )
!= sK4 ) ),
inference(beta_eta_normalization,[],[f72]) ).
thf(f72,plain,
! [X1: g] :
( ( $false
= ( ( ( sK0 @ sK3 @ X1 )
= sK1 )
& ( ( sK0 @ X1 @ sK3 )
= sK1 ) ) )
| ( ( sK0 @ sK1 @ sK4 )
!= sK4 )
| ( $false
= ( ( sK0 @ sK10 @ sK1 )
= sK10 ) )
| ( $false
= ( ^ [Y0: g] :
( ( sK0 @ sK5 @ ( sK0 @ Y0 @ sK9 ) )
= ( sK0 @ ( sK0 @ sK5 @ Y0 ) @ sK9 ) )
@ sK12 ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ sK11 @ Y0 )
= sK1 ) ) )
| ( ( sK0 @ sK6 @ ( sK0 @ sK8 @ sK7 ) )
!= ( sK0 @ ( sK0 @ sK6 @ sK8 ) @ sK7 ) )
| ( ( sK0 @ sK4 @ sK1 )
!= sK4 ) ),
inference(sigma_clausification,[],[f71]) ).
thf(f71,plain,
! [X1: g] :
( ( ( sK0 @ sK6 @ ( sK0 @ sK8 @ sK7 ) )
!= ( sK0 @ ( sK0 @ sK6 @ sK8 ) @ sK7 ) )
| ( ( sK0 @ sK1 @ sK4 )
!= sK4 )
| ( ( sK0 @ sK4 @ sK1 )
!= sK4 )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK5 @ ( sK0 @ Y0 @ sK9 ) )
= ( sK0 @ ( sK0 @ sK5 @ Y0 ) @ sK9 ) ) ) )
| ( $false
= ( ( sK0 @ sK10 @ sK1 )
= sK10 ) )
| ( $false
= ( ( ( sK0 @ sK3 @ X1 )
= sK1 )
& ( ( sK0 @ X1 @ sK3 )
= sK1 ) ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ sK11 @ Y0 )
= sK1 ) ) ) ),
inference(beta_eta_normalization,[],[f70]) ).
thf(f70,plain,
! [X1: g] :
( ( ( sK0 @ sK4 @ sK1 )
!= sK4 )
| ( ( sK0 @ sK1 @ sK4 )
!= sK4 )
| ( $false
= ( ( ( sK0 @ sK3 @ X1 )
= sK1 )
& ( ( sK0 @ X1 @ sK3 )
= sK1 ) ) )
| ( ( sK0 @ sK6 @ ( sK0 @ sK8 @ sK7 ) )
!= ( sK0 @ ( sK0 @ sK6 @ sK8 ) @ sK7 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK5 @ ( sK0 @ Y0 @ sK9 ) )
= ( sK0 @ ( sK0 @ sK5 @ Y0 ) @ sK9 ) ) ) )
| ( $false
= ( ( sK0 @ sK10 @ sK1 )
= sK10 ) )
| ( $false
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) )
@ sK11 ) ) ),
inference(sigma_clausification,[],[f69]) ).
thf(f69,plain,
! [X1: g] :
( ( ( sK0 @ sK6 @ ( sK0 @ sK8 @ sK7 ) )
!= ( sK0 @ ( sK0 @ sK6 @ sK8 ) @ sK7 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) )
| ( ( sK0 @ sK4 @ sK1 )
!= sK4 )
| ( $false
= ( ( ( sK0 @ sK3 @ X1 )
= sK1 )
& ( ( sK0 @ X1 @ sK3 )
= sK1 ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK5 @ ( sK0 @ Y0 @ sK9 ) )
= ( sK0 @ ( sK0 @ sK5 @ Y0 ) @ sK9 ) ) ) )
| ( $false
= ( ( sK0 @ sK10 @ sK1 )
= sK10 ) )
| ( ( sK0 @ sK1 @ sK4 )
!= sK4 ) ),
inference(beta_eta_normalization,[],[f68]) ).
thf(f68,plain,
! [X1: g] :
( ( ( sK0 @ sK6 @ ( sK0 @ sK8 @ sK7 ) )
!= ( sK0 @ ( sK0 @ sK6 @ sK8 ) @ sK7 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) )
| ( $false
= ( ( ( sK0 @ sK3 @ X1 )
= sK1 )
& ( ( sK0 @ X1 @ sK3 )
= sK1 ) ) )
| ( ( ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 )
@ sK10 )
= $false )
| ( ( sK0 @ sK4 @ sK1 )
!= sK4 )
| ( ( sK0 @ sK1 @ sK4 )
!= sK4 )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK5 @ ( sK0 @ Y0 @ sK9 ) )
= ( sK0 @ ( sK0 @ sK5 @ Y0 ) @ sK9 ) ) ) ) ),
inference(sigma_clausification,[],[f67]) ).
thf(f67,plain,
! [X1: g] :
( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
= $false )
| ( ( sK0 @ sK1 @ sK4 )
!= sK4 )
| ( ( sK0 @ sK4 @ sK1 )
!= sK4 )
| ( $false
= ( ( ( sK0 @ sK3 @ X1 )
= sK1 )
& ( ( sK0 @ X1 @ sK3 )
= sK1 ) ) )
| ( ( sK0 @ sK6 @ ( sK0 @ sK8 @ sK7 ) )
!= ( sK0 @ ( sK0 @ sK6 @ sK8 ) @ sK7 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK5 @ ( sK0 @ Y0 @ sK9 ) )
= ( sK0 @ ( sK0 @ sK5 @ Y0 ) @ sK9 ) ) ) ) ),
inference(beta_eta_normalization,[],[f66]) ).
thf(f66,plain,
! [X1: g] :
( ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
= $false )
| ( ( sK0 @ sK4 @ sK1 )
!= sK4 )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK5 @ ( sK0 @ Y0 @ sK9 ) )
= ( sK0 @ ( sK0 @ sK5 @ Y0 ) @ sK9 ) ) ) )
| ( $false
= ( ^ [Y0: g] :
( ( ( sK0 @ sK3 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ sK3 )
= sK1 ) )
@ X1 ) )
| ( ( sK0 @ sK1 @ sK4 )
!= sK4 )
| ( ( sK0 @ sK6 @ ( sK0 @ sK8 @ sK7 ) )
!= ( sK0 @ ( sK0 @ sK6 @ sK8 ) @ sK7 ) ) ),
inference(pi_clausification,[],[f65]) ).
thf(f65,plain,
( ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK3 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ sK3 )
= sK1 ) ) ) )
| ( ( sK0 @ sK6 @ ( sK0 @ sK8 @ sK7 ) )
!= ( sK0 @ ( sK0 @ sK6 @ sK8 ) @ sK7 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK5 @ ( sK0 @ Y0 @ sK9 ) )
= ( sK0 @ ( sK0 @ sK5 @ Y0 ) @ sK9 ) ) ) )
| ( ( sK0 @ sK4 @ sK1 )
!= sK4 )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
= $false )
| ( ( sK0 @ sK1 @ sK4 )
!= sK4 ) ),
inference(equality_proxy_clausification,[],[f64]) ).
thf(f64,plain,
( ( $false
= ( ( sK0 @ sK6 @ ( sK0 @ sK8 @ sK7 ) )
= ( sK0 @ ( sK0 @ sK6 @ sK8 ) @ sK7 ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
= $false )
| ( ( sK0 @ sK1 @ sK4 )
!= sK4 )
| ( ( sK0 @ sK4 @ sK1 )
!= sK4 )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK3 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ sK3 )
= sK1 ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK5 @ ( sK0 @ Y0 @ sK9 ) )
= ( sK0 @ ( sK0 @ sK5 @ Y0 ) @ sK9 ) ) ) ) ),
inference(beta_eta_normalization,[],[f63]) ).
thf(f63,plain,
( ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ sK5 @ ( sK0 @ Y1 @ Y0 ) )
= ( sK0 @ ( sK0 @ sK5 @ Y1 ) @ Y0 ) ) )
@ sK9 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) )
| ( $false
= ( ( sK0 @ sK6 @ ( sK0 @ sK8 @ sK7 ) )
= ( sK0 @ ( sK0 @ sK6 @ sK8 ) @ sK7 ) ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK3 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ sK3 )
= sK1 ) ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
= $false )
| ( ( sK0 @ sK4 @ sK1 )
!= sK4 )
| ( ( sK0 @ sK1 @ sK4 )
!= sK4 ) ),
inference(sigma_clausification,[],[f62]) ).
thf(f62,plain,
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ sK5 @ ( sK0 @ Y1 @ Y0 ) )
= ( sK0 @ ( sK0 @ sK5 @ Y1 ) @ Y0 ) ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) )
| ( $false
= ( ( sK0 @ sK6 @ ( sK0 @ sK8 @ sK7 ) )
= ( sK0 @ ( sK0 @ sK6 @ sK8 ) @ sK7 ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
= $false )
| ( ( sK0 @ sK4 @ sK1 )
!= sK4 )
| ( ( sK0 @ sK1 @ sK4 )
!= sK4 )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK3 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ sK3 )
= sK1 ) ) ) ) ),
inference(beta_eta_normalization,[],[f61]) ).
thf(f61,plain,
( ( ( sK0 @ sK4 @ sK1 )
!= sK4 )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
= $false )
| ( $false
= ( ^ [Y0: g] :
( ( sK0 @ sK6 @ ( sK0 @ Y0 @ sK7 ) )
= ( sK0 @ ( sK0 @ sK6 @ Y0 ) @ sK7 ) )
@ sK8 ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK3 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ sK3 )
= sK1 ) ) ) )
| ( ( sK0 @ sK1 @ sK4 )
!= sK4 )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ sK5 @ ( sK0 @ Y1 @ Y0 ) )
= ( sK0 @ ( sK0 @ sK5 @ Y1 ) @ Y0 ) ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) ) ),
inference(sigma_clausification,[],[f60]) ).
thf(f60,plain,
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK6 @ ( sK0 @ Y0 @ sK7 ) )
= ( sK0 @ ( sK0 @ sK6 @ Y0 ) @ sK7 ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ sK5 @ ( sK0 @ Y1 @ Y0 ) )
= ( sK0 @ ( sK0 @ sK5 @ Y1 ) @ Y0 ) ) ) ) )
| ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
= $false )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK3 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ sK3 )
= sK1 ) ) ) )
| ( ( sK0 @ sK1 @ sK4 )
!= sK4 )
| ( ( sK0 @ sK4 @ sK1 )
!= sK4 ) ),
inference(binary_proxy_clausification,[],[f59]) ).
thf(f59,plain,
( ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK3 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ sK3 )
= sK1 ) ) ) )
| ( ( sK0 @ sK1 @ sK4 )
!= sK4 )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK6 @ ( sK0 @ Y0 @ sK7 ) )
= ( sK0 @ ( sK0 @ sK6 @ Y0 ) @ sK7 ) ) ) )
| ( ( sK0 @ sK4 @ sK1 )
!= sK4 )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ sK5 @ ( sK0 @ Y1 @ Y0 ) )
= ( sK0 @ ( sK0 @ sK5 @ Y1 ) @ Y0 ) ) ) ) ) ),
inference(equality_proxy_clausification,[],[f58]) ).
thf(f58,plain,
( ( $false
= ( ( sK0 @ sK1 @ sK4 )
= sK4 ) )
| ( ( sK0 @ sK4 @ sK1 )
!= sK4 )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK3 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ sK3 )
= sK1 ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ sK5 @ ( sK0 @ Y1 @ Y0 ) )
= ( sK0 @ ( sK0 @ sK5 @ Y1 ) @ Y0 ) ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK6 @ ( sK0 @ Y0 @ sK7 ) )
= ( sK0 @ ( sK0 @ sK6 @ Y0 ) @ sK7 ) ) ) ) ),
inference(equality_proxy_clausification,[],[f57]) ).
thf(f57,plain,
( ( $false
= ( ( sK0 @ sK4 @ sK1 )
= sK4 ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK6 @ ( sK0 @ Y0 @ sK7 ) )
= ( sK0 @ ( sK0 @ sK6 @ Y0 ) @ sK7 ) ) ) )
| ( $false
= ( ( sK0 @ sK1 @ sK4 )
= sK4 ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK3 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ sK3 )
= sK1 ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ sK5 @ ( sK0 @ Y1 @ Y0 ) )
= ( sK0 @ ( sK0 @ sK5 @ Y1 ) @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f56]) ).
thf(f56,plain,
( ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK3 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ sK3 )
= sK1 ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ sK5 @ ( sK0 @ Y1 @ Y0 ) )
= ( sK0 @ ( sK0 @ sK5 @ Y1 ) @ Y0 ) ) ) ) )
| ( $false
= ( ( sK0 @ sK4 @ sK1 )
= sK4 ) )
| ( $false
= ( ( sK0 @ sK1 @ sK4 )
= sK4 ) )
| ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ sK6 @ ( sK0 @ Y1 @ Y0 ) )
= ( sK0 @ ( sK0 @ sK6 @ Y1 ) @ Y0 ) ) )
@ sK7 ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) ) ) ),
inference(sigma_clausification,[],[f55]) ).
thf(f55,plain,
( ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ sK6 @ ( sK0 @ Y1 @ Y0 ) )
= ( sK0 @ ( sK0 @ sK6 @ Y1 ) @ Y0 ) ) ) )
= $false )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ sK5 @ ( sK0 @ Y1 @ Y0 ) )
= ( sK0 @ ( sK0 @ sK5 @ Y1 ) @ Y0 ) ) ) ) )
| ( $false
= ( ( sK0 @ sK1 @ sK4 )
= sK4 ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK3 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ sK3 )
= sK1 ) ) ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) ) )
| ( $false
= ( ( sK0 @ sK4 @ sK1 )
= sK4 ) ) ),
inference(beta_eta_normalization,[],[f54]) ).
thf(f54,plain,
( ( $false
= ( ( sK0 @ sK1 @ sK4 )
= sK4 ) )
| ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y0 @ ( sK0 @ Y2 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ Y2 ) @ Y1 ) ) ) )
@ sK6 ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK3 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ sK3 )
= sK1 ) ) ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) ) )
| ( $false
= ( ( sK0 @ sK4 @ sK1 )
= sK4 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ sK5 @ ( sK0 @ Y1 @ Y0 ) )
= ( sK0 @ ( sK0 @ sK5 @ Y1 ) @ Y0 ) ) ) ) ) ),
inference(sigma_clausification,[],[f53]) ).
thf(f53,plain,
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y0 @ ( sK0 @ Y2 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ Y2 ) @ Y1 ) ) ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ sK5 @ ( sK0 @ Y1 @ Y0 ) )
= ( sK0 @ ( sK0 @ sK5 @ Y1 ) @ Y0 ) ) ) ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) ) )
| ( $false
= ( ( sK0 @ sK1 @ sK4 )
= sK4 ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK3 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ sK3 )
= sK1 ) ) ) )
| ( $false
= ( ( sK0 @ sK4 @ sK1 )
= sK4 ) ) ),
inference(binary_proxy_clausification,[],[f52]) ).
thf(f52,plain,
( ( ( ( ( sK0 @ sK1 @ sK4 )
= sK4 )
& ( ( sK0 @ sK4 @ sK1 )
= sK4 ) )
= $false )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y0 @ ( sK0 @ Y2 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ Y2 ) @ Y1 ) ) ) ) ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ sK5 @ ( sK0 @ Y1 @ Y0 ) )
= ( sK0 @ ( sK0 @ sK5 @ Y1 ) @ Y0 ) ) ) ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK3 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ sK3 )
= sK1 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f51]) ).
thf(f51,plain,
( ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y0 @ ( sK0 @ Y2 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ Y2 ) @ Y1 ) ) ) ) ) ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK3 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ sK3 )
= sK1 ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ sK5 @ ( sK0 @ Y1 @ Y0 ) )
= ( sK0 @ ( sK0 @ sK5 @ Y1 ) @ Y0 ) ) ) ) )
| ( ( ( ( sK0 @ sK1 @ sK4 )
= sK4 )
& ( ( sK0 @ sK4 @ sK1 )
= sK4 ) )
= $false ) ),
inference(beta_eta_normalization,[],[f50]) ).
thf(f50,plain,
( ( $false
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y0 @ ( sK0 @ Y2 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ Y2 ) @ Y1 ) ) ) )
@ sK5 ) )
| ( ( ( ( sK0 @ sK1 @ sK4 )
= sK4 )
& ( ( sK0 @ sK4 @ sK1 )
= sK4 ) )
= $false )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y0 @ ( sK0 @ Y2 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ Y2 ) @ Y1 ) ) ) ) ) ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK3 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ sK3 )
= sK1 ) ) ) ) ),
inference(sigma_clausification,[],[f49]) ).
thf(f49,plain,
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y0 @ ( sK0 @ Y2 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ Y2 ) @ Y1 ) ) ) ) ) )
| ( ( ( ( sK0 @ sK1 @ sK4 )
= sK4 )
& ( ( sK0 @ sK4 @ sK1 )
= sK4 ) )
= $false )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK3 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ sK3 )
= sK1 ) ) ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y0 @ ( sK0 @ Y2 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ Y2 ) @ Y1 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f48]) ).
thf(f48,plain,
( ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK3 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ sK3 )
= sK1 ) ) ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y0 @ ( sK0 @ Y2 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ Y2 ) @ Y1 ) ) ) ) ) ) )
| ( $false
= ( ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
@ sK4 ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y0 @ ( sK0 @ Y2 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ Y2 ) @ Y1 ) ) ) ) ) ) ),
inference(sigma_clausification,[],[f47]) ).
thf(f47,plain,
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y0 @ ( sK0 @ Y2 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ Y2 ) @ Y1 ) ) ) ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y0 @ ( sK0 @ Y2 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ Y2 ) @ Y1 ) ) ) ) ) )
| ( $false
= ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK3 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ sK3 )
= sK1 ) ) ) ) ),
inference(beta_eta_normalization,[],[f46]) ).
thf(f46,plain,
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y0 @ ( sK0 @ Y2 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ Y2 ) @ Y1 ) ) ) ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y0 @ ( sK0 @ Y2 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ Y2 ) @ Y1 ) ) ) ) ) )
| ( $false
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) )
@ sK3 ) ) ),
inference(sigma_clausification,[],[f45]) ).
thf(f45,plain,
( ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y0 @ ( sK0 @ Y2 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ Y2 ) @ Y1 ) ) ) ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y0 @ ( sK0 @ Y2 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ Y2 ) @ Y1 ) ) ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f44]) ).
thf(f44,plain,
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y0 @ ( sK0 @ Y2 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ Y2 ) @ Y1 ) ) ) ) ) )
= $false )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y0 @ ( sK0 @ Y2 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ Y2 ) @ Y1 ) ) ) ) ) ) )
| ( $false
= ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f43]) ).
thf(f43,plain,
( ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y0 @ ( sK0 @ Y2 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) ) ) )
| ( $false
= ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y0 @ ( sK0 @ Y2 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ Y2 ) @ Y1 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f41]) ).
thf(f41,plain,
( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y0 @ ( sK0 @ Y2 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) ) )
!= ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y0 @ ( sK0 @ Y2 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ Y2 ) @ Y1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f40]) ).
thf(f40,plain,
( ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( ( Y2 @ Y4 @ Y5 )
= Y3 )
& ( ( Y2 @ Y5 @ Y4 )
= Y3 ) ) ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ Y3 @ ( Y2 @ Y5 @ Y4 ) )
= ( Y2 @ ( Y2 @ Y3 @ Y5 ) @ Y4 ) ) ) ) )
@ Y0 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( ( Y2 @ Y3 @ Y4 )
= Y4 )
& ( ( Y2 @ Y4 @ Y3 )
= Y4 ) ) )
@ Y0
@ Y1 ) )
@ sK0
@ sK1 )
!= ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y2 @ Y4 @ Y3 )
= Y4 ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( Y2 @ Y4 @ Y5 )
= Y3 ) ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ Y3 @ ( Y2 @ Y5 @ Y4 ) )
= ( Y2 @ ( Y2 @ Y3 @ Y5 ) @ Y4 ) ) ) ) )
@ Y0 ) )
@ sK0
@ sK1 ) ),
inference(definition_unfolding,[],[f30,f39,f38]) ).
thf(f38,plain,
( cGROUP1
= ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( ( Y2 @ Y4 @ Y5 )
= Y3 )
& ( ( Y2 @ Y5 @ Y4 )
= Y3 ) ) ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ Y3 @ ( Y2 @ Y5 @ Y4 ) )
= ( Y2 @ ( Y2 @ Y3 @ Y5 ) @ Y4 ) ) ) ) )
@ Y0 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( ( Y2 @ Y3 @ Y4 )
= Y4 )
& ( ( Y2 @ Y4 @ Y3 )
= Y4 ) ) )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f32,f37,f33,f35]) ).
thf(f35,plain,
( cGRP_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( ( Y0 @ Y1 @ Y2 )
= Y2 )
& ( ( Y0 @ Y2 @ Y1 )
= Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f14,plain,
( cGRP_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( ( Y0 @ Y1 @ Y2 )
= Y2 )
& ( ( Y0 @ Y2 @ Y1 )
= Y2 ) ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f13,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/sandbox2/benchmark/theBenchmark.p',cGRP_UNIT_def) ).
thf(f33,plain,
( cGRP_ASSOC
= ( ^ [Y0: g > g > g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( Y0 @ Y1 @ ( Y0 @ Y3 @ Y2 ) )
= ( Y0 @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f20,plain,
( cGRP_ASSOC
= ( ^ [Y0: g > g > g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( Y0 @ Y1 @ ( Y0 @ Y3 @ Y2 ) )
= ( Y0 @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f19,plain,
( ( ^ [X0: g > g > g] :
! [X1: g,X2: g,X3: g] :
( ( X0 @ X3 @ ( X0 @ X1 @ X2 ) )
= ( X0 @ ( X0 @ X3 @ X1 ) @ X2 ) ) )
= cGRP_ASSOC ),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: g > g > g] :
! [X2: g,X3: g,X1: g] :
( ( X0 @ ( X0 @ X1 @ X2 ) @ X3 )
= ( X0 @ X1 @ ( X0 @ X2 @ X3 ) ) ) )
= cGRP_ASSOC ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGRP_ASSOC_def) ).
thf(f37,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,[],[f16]) ).
thf(f16,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,[],[f15]) ).
thf(f15,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/sandbox2/benchmark/theBenchmark.p',cGRP_INVERSE_def) ).
thf(f32,plain,
( cGROUP1
= ( ^ [Y0: g > g > g,Y1: g] :
( ( cGRP_INVERSE @ Y0 @ Y1 )
& ( cGRP_ASSOC @ Y0 )
& ( cGRP_UNIT @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f22,plain,
( cGROUP1
= ( ^ [Y0: g > g > g,Y1: g] :
( ( cGRP_INVERSE @ Y0 @ Y1 )
& ( cGRP_ASSOC @ Y0 )
& ( cGRP_UNIT @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f21]) ).
thf(f21,plain,
( ( ^ [X0: g > g > g,X1: g] :
( ( cGRP_UNIT @ X0 @ X1 )
& ( cGRP_ASSOC @ X0 )
& ( cGRP_INVERSE @ X0 @ X1 ) ) )
= cGROUP1 ),
inference(rectify,[],[f6]) ).
thf(f6,axiom,
( ( ^ [X0: g > g > g,X4: g] :
( ( cGRP_UNIT @ X0 @ X4 )
& ( cGRP_ASSOC @ X0 )
& ( cGRP_INVERSE @ X0 @ X4 ) ) )
= cGROUP1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGROUP1_def) ).
thf(f39,plain,
( cGROUP3
= ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y2 @ Y4 @ Y3 )
= Y4 ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( Y2 @ Y4 @ Y5 )
= Y3 ) ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ Y3 @ ( Y2 @ Y5 @ Y4 ) )
= ( Y2 @ ( Y2 @ Y3 @ Y5 ) @ Y4 ) ) ) ) )
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f31,f36,f34,f33]) ).
thf(f34,plain,
( cGRP_RIGHT_INVERSE
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y2 @ Y3 )
= Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f24,plain,
( cGRP_RIGHT_INVERSE
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y2 @ Y3 )
= Y1 ) ) ) ) ),
inference(fool_elimination,[],[f23]) ).
thf(f23,plain,
( ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
? [X3: g] :
( ( X0 @ X2 @ X3 )
= X1 ) )
= cGRP_RIGHT_INVERSE ),
inference(rectify,[],[f3]) ).
thf(f3,axiom,
( ( ^ [X0: g > g > g,X4: g] :
! [X1: g] :
? [X2: g] :
( ( X0 @ X1 @ X2 )
= X4 ) )
= cGRP_RIGHT_INVERSE ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGRP_RIGHT_INVERSE_def) ).
thf(f36,plain,
( cGRP_RIGHT_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y2 @ Y1 )
= Y2 ) ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f12,plain,
( cGRP_RIGHT_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y2 @ Y1 )
= Y2 ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f11,plain,
( ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
( ( X0 @ X2 @ X1 )
= X2 ) )
= cGRP_RIGHT_UNIT ),
inference(rectify,[],[f4]) ).
thf(f4,axiom,
( ( ^ [X0: g > g > g,X4: g] :
! [X1: g] :
( ( X0 @ X1 @ X4 )
= X1 ) )
= cGRP_RIGHT_UNIT ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGRP_RIGHT_UNIT_def) ).
thf(f31,plain,
( cGROUP3
= ( ^ [Y0: g > g > g,Y1: g] :
( ( cGRP_RIGHT_UNIT @ Y0 @ Y1 )
& ( cGRP_RIGHT_INVERSE @ Y0 @ Y1 )
& ( cGRP_ASSOC @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f26,plain,
( cGROUP3
= ( ^ [Y0: g > g > g,Y1: g] :
( ( cGRP_RIGHT_UNIT @ Y0 @ Y1 )
& ( cGRP_RIGHT_INVERSE @ Y0 @ Y1 )
& ( cGRP_ASSOC @ Y0 ) ) ) ),
inference(fool_elimination,[],[f25]) ).
thf(f25,plain,
( ( ^ [X0: g > g > g,X1: g] :
( ( cGRP_ASSOC @ X0 )
& ( cGRP_RIGHT_INVERSE @ X0 @ X1 )
& ( cGRP_RIGHT_UNIT @ X0 @ X1 ) ) )
= cGROUP3 ),
inference(rectify,[],[f7]) ).
thf(f7,axiom,
( ( ^ [X0: g > g > g,X4: g] :
( ( cGRP_ASSOC @ X0 )
& ( cGRP_RIGHT_INVERSE @ X0 @ X4 )
& ( cGRP_RIGHT_UNIT @ X0 @ X4 ) ) )
= cGROUP3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGROUP3_def) ).
thf(f30,plain,
( ( cGROUP3 @ sK0 @ sK1 )
!= ( cGROUP1 @ sK0 @ sK1 ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f29,plain,
( ( cGROUP3 @ sK0 @ sK1 )
!= ( cGROUP1 @ sK0 @ sK1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f27,f28]) ).
thf(f28,plain,
( ? [X0: g > g > g,X1: g] :
( ( cGROUP1 @ X0 @ X1 )
!= ( cGROUP3 @ X0 @ X1 ) )
=> ( ( cGROUP3 @ sK0 @ sK1 )
!= ( cGROUP1 @ sK0 @ sK1 ) ) ),
introduced(choice_axiom,[]) ).
thf(f27,plain,
? [X0: g > g > g,X1: g] :
( ( cGROUP1 @ X0 @ X1 )
!= ( cGROUP3 @ X0 @ X1 ) ),
inference(ennf_transformation,[],[f18]) ).
thf(f18,plain,
~ ! [X0: g > g > g,X1: g] :
( ( cGROUP1 @ X0 @ X1 )
= ( cGROUP3 @ X0 @ X1 ) ),
inference(fool_elimination,[],[f17]) ).
thf(f17,plain,
~ ! [X0: g > g > g,X1: g] :
( ( cGROUP1 @ X0 @ X1 )
<=> ( cGROUP3 @ X0 @ X1 ) ),
inference(rectify,[],[f9]) ).
thf(f9,negated_conjecture,
~ ! [X0: g > g > g,X4: g] :
( ( cGROUP1 @ X0 @ X4 )
<=> ( cGROUP3 @ X0 @ X4 ) ),
inference(negated_conjecture,[],[f8]) ).
thf(f8,conjecture,
! [X0: g > g > g,X4: g] :
( ( cGROUP1 @ X0 @ X4 )
<=> ( cGROUP3 @ X0 @ X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cEQUIV_01_03) ).
thf(f250,plain,
( spl2_11
| spl2_10 ),
inference(avatar_split_clause,[],[f113,f244,f248]) ).
thf(f113,plain,
! [X2: g,X1: g] :
( ( ( sK0 @ X1 @ ( sK14 @ X1 ) )
= sK1 )
| ( sK1
= ( sK0 @ X2 @ ( sK15 @ X2 ) ) ) ),
inference(equality_proxy_clausification,[],[f112]) ).
thf(f112,plain,
! [X2: g,X1: g] :
( ( ( ( sK0 @ X2 @ ( sK15 @ X2 ) )
= sK1 )
= $true )
| ( ( sK0 @ X1 @ ( sK14 @ X1 ) )
= sK1 ) ),
inference(binary_proxy_clausification,[],[f110]) ).
thf(f110,plain,
! [X2: g,X1: g] :
( ( $true
= ( ( ( sK0 @ X2 @ ( sK15 @ X2 ) )
= sK1 )
& ( ( sK0 @ ( sK15 @ X2 ) @ X2 )
= sK1 ) ) )
| ( ( sK0 @ X1 @ ( sK14 @ X1 ) )
= sK1 ) ),
inference(beta_eta_normalization,[],[f109]) ).
thf(f109,plain,
! [X2: g,X1: g] :
( ( ( sK0 @ X1 @ ( sK14 @ X1 ) )
= sK1 )
| ( $true
= ( ^ [Y0: g] :
( ( ( sK0 @ X2 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ X2 )
= sK1 ) )
@ ( sK15 @ X2 ) ) ) ),
inference(sigma_clausification,[],[f108]) ).
thf(f108,plain,
! [X2: g,X1: g] :
( ( $true
= ( ?? @ g
@ ^ [Y0: g] :
( ( ( sK0 @ X2 @ Y0 )
= sK1 )
& ( ( sK0 @ Y0 @ X2 )
= sK1 ) ) ) )
| ( ( sK0 @ X1 @ ( sK14 @ X1 ) )
= sK1 ) ),
inference(beta_eta_normalization,[],[f107]) ).
thf(f107,plain,
! [X2: g,X1: g] :
( ( ( sK0 @ X1 @ ( sK14 @ X1 ) )
= sK1 )
| ( $true
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) )
@ X2 ) ) ),
inference(pi_clausification,[],[f106]) ).
thf(f106,plain,
! [X1: g] :
( ( ( sK0 @ X1 @ ( sK14 @ X1 ) )
= sK1 )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) ) ) ),
inference(equality_proxy_clausification,[],[f105]) ).
thf(f105,plain,
! [X1: g] :
( ( $true
= ( ( sK0 @ X1 @ ( sK14 @ X1 ) )
= sK1 ) )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f104]) ).
thf(f104,plain,
! [X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ( sK0 @ X1 @ Y0 )
= sK1 )
@ ( sK14 @ X1 ) ) )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) ) ) ),
inference(sigma_clausification,[],[f103]) ).
thf(f103,plain,
! [X1: g] :
( ( ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ X1 @ Y0 )
= sK1 ) )
= $true )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f102]) ).
thf(f102,plain,
! [X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) )
@ X1 ) )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) ) ) ),
inference(pi_clausification,[],[f88]) ).
thf(f88,plain,
( ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f87]) ).
thf(f87,plain,
( ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) ) )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f85]) ).
thf(f85,plain,
( ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y0 @ ( sK0 @ Y2 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ Y2 ) @ Y1 ) ) ) ) ) ) )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f83]) ).
thf(f83,plain,
( ( ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y0 @ ( sK0 @ Y2 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ Y2 ) @ Y1 ) ) ) ) ) )
= $true )
| ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y0 @ ( sK0 @ Y2 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ Y2 ) @ Y1 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f42]) ).
thf(f42,plain,
( ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( ( sK0 @ Y0 @ Y1 )
= sK1 )
& ( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y0 @ ( sK0 @ Y2 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) ) ) )
| ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y0 @ ( sK0 @ Y2 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ Y2 ) @ Y1 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f41]) ).
thf(f246,plain,
( spl2_9
| spl2_10 ),
inference(avatar_split_clause,[],[f114,f244,f241]) ).
thf(f114,plain,
! [X2: g,X1: g] :
( ( sK1
= ( sK0 @ ( sK15 @ X2 ) @ X2 ) )
| ( ( sK0 @ X1 @ ( sK14 @ X1 ) )
= sK1 ) ),
inference(equality_proxy_clausification,[],[f111]) ).
thf(f111,plain,
! [X2: g,X1: g] :
( ( ( ( sK0 @ ( sK15 @ X2 ) @ X2 )
= sK1 )
= $true )
| ( ( sK0 @ X1 @ ( sK14 @ X1 ) )
= sK1 ) ),
inference(binary_proxy_clausification,[],[f110]) ).
thf(f226,plain,
( spl2_2
| spl2_2 ),
inference(avatar_split_clause,[],[f158,f209,f209]) ).
thf(f158,plain,
! [X2: g,X3: g,X1: g,X6: g,X4: g,X5: g] :
( ( ( sK0 @ ( sK0 @ X4 @ X6 ) @ X5 )
= ( sK0 @ X4 @ ( sK0 @ X6 @ X5 ) ) )
| ( ( sK0 @ ( sK0 @ X1 @ X3 ) @ X2 )
= ( sK0 @ X1 @ ( sK0 @ X3 @ X2 ) ) ) ),
inference(equality_proxy_clausification,[],[f157]) ).
thf(f157,plain,
! [X2: g,X3: g,X1: g,X6: g,X4: g,X5: g] :
( ( $true
= ( ( sK0 @ X4 @ ( sK0 @ X6 @ X5 ) )
= ( sK0 @ ( sK0 @ X4 @ X6 ) @ X5 ) ) )
| ( ( sK0 @ ( sK0 @ X1 @ X3 ) @ X2 )
= ( sK0 @ X1 @ ( sK0 @ X3 @ X2 ) ) ) ),
inference(beta_eta_normalization,[],[f156]) ).
thf(f156,plain,
! [X2: g,X3: g,X1: g,X6: g,X4: g,X5: g] :
( ( ( sK0 @ ( sK0 @ X1 @ X3 ) @ X2 )
= ( sK0 @ X1 @ ( sK0 @ X3 @ X2 ) ) )
| ( ( ^ [Y0: g] :
( ( sK0 @ X4 @ ( sK0 @ Y0 @ X5 ) )
= ( sK0 @ ( sK0 @ X4 @ Y0 ) @ X5 ) )
@ X6 )
= $true ) ),
inference(pi_clausification,[],[f155]) ).
thf(f155,plain,
! [X2: g,X3: g,X1: g,X4: g,X5: g] :
( ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ X4 @ ( sK0 @ Y0 @ X5 ) )
= ( sK0 @ ( sK0 @ X4 @ Y0 ) @ X5 ) ) ) )
| ( ( sK0 @ ( sK0 @ X1 @ X3 ) @ X2 )
= ( sK0 @ X1 @ ( sK0 @ X3 @ X2 ) ) ) ),
inference(beta_eta_normalization,[],[f154]) ).
thf(f154,plain,
! [X2: g,X3: g,X1: g,X4: g,X5: g] :
( ( ( sK0 @ ( sK0 @ X1 @ X3 ) @ X2 )
= ( sK0 @ X1 @ ( sK0 @ X3 @ X2 ) ) )
| ( $true
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ X4 @ ( sK0 @ Y1 @ Y0 ) )
= ( sK0 @ ( sK0 @ X4 @ Y1 ) @ Y0 ) ) )
@ X5 ) ) ),
inference(pi_clausification,[],[f153]) ).
thf(f153,plain,
! [X2: g,X3: g,X1: g,X4: g] :
( ( ( sK0 @ ( sK0 @ X1 @ X3 ) @ X2 )
= ( sK0 @ X1 @ ( sK0 @ X3 @ X2 ) ) )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ X4 @ ( sK0 @ Y1 @ Y0 ) )
= ( sK0 @ ( sK0 @ X4 @ Y1 ) @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f152]) ).
thf(f152,plain,
! [X2: g,X3: g,X1: g,X4: g] :
( ( ( sK0 @ ( sK0 @ X1 @ X3 ) @ X2 )
= ( sK0 @ X1 @ ( sK0 @ X3 @ X2 ) ) )
| ( $true
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y0 @ ( sK0 @ Y2 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ Y2 ) @ Y1 ) ) ) )
@ X4 ) ) ),
inference(pi_clausification,[],[f151]) ).
thf(f151,plain,
! [X2: g,X3: g,X1: g] :
( ( ( sK0 @ ( sK0 @ X1 @ X3 ) @ X2 )
= ( sK0 @ X1 @ ( sK0 @ X3 @ X2 ) ) )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y0 @ ( sK0 @ Y2 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ Y2 ) @ Y1 ) ) ) ) ) ) ),
inference(equality_proxy_clausification,[],[f150]) ).
thf(f150,plain,
! [X2: g,X3: g,X1: g] :
( ( $true
= ( ( sK0 @ X1 @ ( sK0 @ X3 @ X2 ) )
= ( sK0 @ ( sK0 @ X1 @ X3 ) @ X2 ) ) )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y0 @ ( sK0 @ Y2 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ Y2 ) @ Y1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f149]) ).
thf(f149,plain,
! [X2: g,X3: g,X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ( sK0 @ X1 @ ( sK0 @ Y0 @ X2 ) )
= ( sK0 @ ( sK0 @ X1 @ Y0 ) @ X2 ) )
@ X3 ) )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y0 @ ( sK0 @ Y2 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ Y2 ) @ Y1 ) ) ) ) ) ) ),
inference(pi_clausification,[],[f134]) ).
thf(f134,plain,
! [X2: g,X1: g] :
( ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ X1 @ ( sK0 @ Y0 @ X2 ) )
= ( sK0 @ ( sK0 @ X1 @ Y0 ) @ X2 ) ) ) )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y0 @ ( sK0 @ Y2 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ Y2 ) @ Y1 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f133]) ).
thf(f133,plain,
! [X2: g,X1: g] :
( ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y0 @ ( sK0 @ Y2 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ Y2 ) @ Y1 ) ) ) ) ) ) )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ X1 @ ( sK0 @ Y0 @ X2 ) )
= ( sK0 @ ( sK0 @ X1 @ Y0 ) @ X2 ) ) ) ) ),
inference(beta_eta_normalization,[],[f132]) ).
thf(f132,plain,
! [X2: g,X1: g] :
( ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y0 @ ( sK0 @ Y2 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ Y2 ) @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ X1 @ ( sK0 @ Y1 @ Y0 ) )
= ( sK0 @ ( sK0 @ X1 @ Y1 ) @ Y0 ) ) )
@ X2 ) ) ),
inference(pi_clausification,[],[f131]) ).
thf(f131,plain,
! [X1: g] :
( ( $true
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ X1 @ ( sK0 @ Y1 @ Y0 ) )
= ( sK0 @ ( sK0 @ X1 @ Y1 ) @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y0 @ ( sK0 @ Y2 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ Y2 ) @ Y1 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[],[f130]) ).
thf(f130,plain,
! [X1: g] :
( ( $true
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y0 @ ( sK0 @ Y2 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ Y2 ) @ Y1 ) ) ) )
@ X1 ) )
| ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y0 @ ( sK0 @ Y2 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ Y2 ) @ Y1 ) ) ) ) ) ) ) ),
inference(pi_clausification,[],[f84]) ).
thf(f84,plain,
( ( $true
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y0 @ ( sK0 @ Y2 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ Y2 ) @ Y1 ) ) ) ) ) )
| ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y0 @ ( sK0 @ Y2 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ Y2 ) @ Y1 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f83]) ).
thf(f224,plain,
( spl2_1
| spl2_1 ),
inference(avatar_split_clause,[],[f174,f206,f206]) ).
thf(f174,plain,
! [X2: g,X1: g] :
( ( ( sK0 @ X1 @ sK1 )
= X1 )
| ( ( sK0 @ X2 @ sK1 )
= X2 ) ),
inference(equality_proxy_clausification,[],[f173]) ).
thf(f173,plain,
! [X2: g,X1: g] :
( ( ( ( sK0 @ X2 @ sK1 )
= X2 )
= $true )
| ( ( sK0 @ X1 @ sK1 )
= X1 ) ),
inference(beta_eta_normalization,[],[f172]) ).
thf(f172,plain,
! [X2: g,X1: g] :
( ( ( sK0 @ X1 @ sK1 )
= X1 )
| ( $true
= ( ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 )
@ X2 ) ) ),
inference(pi_clausification,[],[f171]) ).
thf(f171,plain,
! [X1: g] :
( ( ( sK0 @ X1 @ sK1 )
= X1 )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) ) ),
inference(equality_proxy_clausification,[],[f165]) ).
thf(f165,plain,
! [X1: g] :
( ( $true
= ( ( sK0 @ X1 @ sK1 )
= X1 ) )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) ) ),
inference(binary_proxy_clausification,[],[f164]) ).
thf(f164,plain,
! [X1: g] :
( ( $true
= ( ( ( sK0 @ sK1 @ X1 )
= X1 )
& ( ( sK0 @ X1 @ sK1 )
= X1 ) ) )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) ) ),
inference(binary_proxy_clausification,[],[f162]) ).
thf(f162,plain,
! [X1: g] :
( ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) ) )
| ( $true
= ( ( ( sK0 @ sK1 @ X1 )
= X1 )
& ( ( sK0 @ X1 @ sK1 )
= X1 ) ) ) ),
inference(binary_proxy_clausification,[],[f160]) ).
thf(f160,plain,
! [X1: g] :
( ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y0 @ ( sK0 @ Y2 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ Y2 ) @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ( ( sK0 @ sK1 @ X1 )
= X1 )
& ( ( sK0 @ X1 @ sK1 )
= X1 ) ) ) ),
inference(beta_eta_normalization,[],[f159]) ).
thf(f159,plain,
! [X1: g] :
( ( $true
= ( ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
@ X1 ) )
| ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y0 @ ( sK0 @ Y2 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ Y2 ) @ Y1 ) ) ) ) ) ) ) ),
inference(pi_clausification,[],[f82]) ).
thf(f82,plain,
( ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( ( sK0 @ sK1 @ Y0 )
= Y0 )
& ( ( sK0 @ Y0 @ sK1 )
= Y0 ) ) ) )
| ( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ Y0 @ ( sK0 @ Y2 @ Y1 ) )
= ( sK0 @ ( sK0 @ Y0 @ Y2 ) @ Y1 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[],[f42]) ).
thf(f223,plain,
( spl2_5
| spl2_3 ),
inference(avatar_split_clause,[],[f182,f213,f221]) ).
thf(f182,plain,
! [X2: g,X1: g] :
( ( ( sK0 @ sK1 @ X1 )
= X1 )
| ( ( sK0 @ X2 @ ( sK18 @ X2 ) )
= sK1 ) ),
inference(equality_proxy_clausification,[],[f181]) ).
thf(f181,plain,
! [X2: g,X1: g] :
( ( ( sK0 @ X2 @ ( sK18 @ X2 ) )
= sK1 )
| ( $true
= ( ( sK0 @ sK1 @ X1 )
= X1 ) ) ),
inference(equality_proxy_clausification,[],[f180]) ).
thf(f180,plain,
! [X2: g,X1: g] :
( ( $true
= ( ( sK0 @ X2 @ ( sK18 @ X2 ) )
= sK1 ) )
| ( $true
= ( ( sK0 @ sK1 @ X1 )
= X1 ) ) ),
inference(beta_eta_normalization,[],[f179]) ).
thf(f179,plain,
! [X2: g,X1: g] :
( ( $true
= ( ( sK0 @ sK1 @ X1 )
= X1 ) )
| ( $true
= ( ^ [Y0: g] :
( ( sK0 @ X2 @ Y0 )
= sK1 )
@ ( sK18 @ X2 ) ) ) ),
inference(sigma_clausification,[],[f178]) ).
thf(f178,plain,
! [X2: g,X1: g] :
( ( ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ X2 @ Y0 )
= sK1 ) )
= $true )
| ( $true
= ( ( sK0 @ sK1 @ X1 )
= X1 ) ) ),
inference(beta_eta_normalization,[],[f177]) ).
thf(f177,plain,
! [X2: g,X1: g] :
( ( $true
= ( ( sK0 @ sK1 @ X1 )
= X1 ) )
| ( $true
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) )
@ X2 ) ) ),
inference(pi_clausification,[],[f176]) ).
thf(f176,plain,
! [X1: g] :
( ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) )
| ( $true
= ( ( sK0 @ sK1 @ X1 )
= X1 ) ) ),
inference(binary_proxy_clausification,[],[f163]) ).
thf(f163,plain,
! [X1: g] :
( ( $true
= ( ( ( sK0 @ sK1 @ X1 )
= X1 )
& ( ( sK0 @ X1 @ sK1 )
= X1 ) ) )
| ( $true
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) ) ) ),
inference(binary_proxy_clausification,[],[f162]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : ALG271^5 : TPTP v8.2.0. Bugfixed v5.3.0.
% 0.08/0.16 % 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
% 0.15/0.41 % Computer : n002.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8042.1875MB
% 0.15/0.41 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sat May 18 22:55:08 EDT 2024
% 0.15/0.41 % CPUTime :
% 0.15/0.41 This is a TH0_THM_EQU_NAR problem
% 0.15/0.41 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/benchmark/theBenchmark.p
% 0.15/0.43 % (11293)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.43 % (11294)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)
% 0.15/0.43 % (11297)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)
% 0.15/0.43 % (11292)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)
% 0.15/0.43 % (11291)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)
% 0.15/0.43 % (11295)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)
% 0.15/0.43 % (11290)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.43 % (11296)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.15/0.43 % (11293)Instruction limit reached!
% 0.15/0.43 % (11293)------------------------------
% 0.15/0.43 % (11293)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.43 % (11293)Termination reason: Unknown
% 0.15/0.43 % (11294)Instruction limit reached!
% 0.15/0.43 % (11294)------------------------------
% 0.15/0.43 % (11294)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.43 % (11293)Termination phase: Property scanning
% 0.15/0.43
% 0.15/0.43 % (11293)Memory used [KB]: 1023
% 0.15/0.43 % (11293)Time elapsed: 0.004 s
% 0.15/0.43 % (11293)Instructions burned: 3 (million)
% 0.15/0.43 % (11293)------------------------------
% 0.15/0.43 % (11293)------------------------------
% 0.15/0.43 % (11294)Termination reason: Unknown
% 0.15/0.43 % (11294)Termination phase: Function definition elimination
% 0.15/0.43
% 0.15/0.43 % (11294)Memory used [KB]: 1023
% 0.15/0.43 % (11294)Time elapsed: 0.004 s
% 0.15/0.43 % (11294)Instructions burned: 3 (million)
% 0.15/0.43 % (11294)------------------------------
% 0.15/0.43 % (11294)------------------------------
% 0.15/0.43 % (11297)Instruction limit reached!
% 0.15/0.43 % (11297)------------------------------
% 0.15/0.43 % (11297)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.43 % (11297)Termination reason: Unknown
% 0.15/0.43 % (11297)Termination phase: Property scanning
% 0.15/0.43
% 0.15/0.43 % (11297)Memory used [KB]: 1023
% 0.15/0.43 % (11297)Time elapsed: 0.004 s
% 0.15/0.43 % (11297)Instructions burned: 4 (million)
% 0.15/0.43 % (11297)------------------------------
% 0.15/0.43 % (11297)------------------------------
% 0.15/0.43 % (11291)Instruction limit reached!
% 0.15/0.43 % (11291)------------------------------
% 0.15/0.43 % (11291)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.43 % (11291)Termination reason: Unknown
% 0.15/0.43 % (11291)Termination phase: Saturation
% 0.15/0.43
% 0.15/0.43 % (11291)Memory used [KB]: 5500
% 0.15/0.43 % (11291)Time elapsed: 0.004 s
% 0.15/0.43 % (11291)Instructions burned: 4 (million)
% 0.15/0.43 % (11291)------------------------------
% 0.15/0.43 % (11291)------------------------------
% 0.15/0.44 % (11296)Instruction limit reached!
% 0.15/0.44 % (11296)------------------------------
% 0.15/0.44 % (11296)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.44 % (11296)Termination reason: Unknown
% 0.15/0.44 % (11296)Termination phase: Saturation
% 0.15/0.44
% 0.15/0.44 % (11296)Memory used [KB]: 5628
% 0.15/0.44 % (11296)Time elapsed: 0.012 s
% 0.15/0.44 % (11296)Instructions burned: 18 (million)
% 0.15/0.44 % (11296)------------------------------
% 0.15/0.44 % (11296)------------------------------
% 0.15/0.45 % (11292)Instruction limit reached!
% 0.15/0.45 % (11292)------------------------------
% 0.15/0.45 % (11292)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.45 % (11292)Termination reason: Unknown
% 0.15/0.45 % (11292)Termination phase: Saturation
% 0.15/0.45
% 0.15/0.45 % (11292)Memory used [KB]: 5756
% 0.15/0.45 % (11292)Time elapsed: 0.019 s
% 0.15/0.45 % (11292)Instructions burned: 28 (million)
% 0.15/0.45 % (11292)------------------------------
% 0.15/0.45 % (11292)------------------------------
% 0.15/0.45 % (11301)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)
% 0.15/0.45 % (11300)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)
% 0.15/0.45 % (11298)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)
% 0.15/0.45 % (11299)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)
% 0.15/0.45 % (11300)Instruction limit reached!
% 0.15/0.45 % (11300)------------------------------
% 0.15/0.45 % (11300)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.45 % (11300)Termination reason: Unknown
% 0.15/0.45 % (11300)Termination phase: Saturation
% 0.15/0.45
% 0.15/0.45 % (11300)Memory used [KB]: 5500
% 0.15/0.45 % (11300)Time elapsed: 0.004 s
% 0.15/0.45 % (11300)Instructions burned: 4 (million)
% 0.15/0.45 % (11300)------------------------------
% 0.15/0.45 % (11300)------------------------------
% 0.15/0.46 % (11299)Instruction limit reached!
% 0.15/0.46 % (11299)------------------------------
% 0.15/0.46 % (11299)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.46 % (11299)Termination reason: Unknown
% 0.15/0.46 % (11299)Termination phase: Saturation
% 0.15/0.46
% 0.15/0.46 % (11299)Memory used [KB]: 5500
% 0.15/0.46 % (11299)Time elapsed: 0.010 s
% 0.15/0.46 % (11299)Instructions burned: 15 (million)
% 0.15/0.46 % (11299)------------------------------
% 0.15/0.46 % (11299)------------------------------
% 0.15/0.46 % (11302)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.15/0.46 % (11302)Instruction limit reached!
% 0.15/0.46 % (11302)------------------------------
% 0.15/0.46 % (11302)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.46 % (11302)Termination reason: Unknown
% 0.15/0.46 % (11302)Termination phase: Saturation
% 0.15/0.46
% 0.15/0.46 % (11302)Memory used [KB]: 1023
% 0.15/0.46 % (11302)Time elapsed: 0.007 s
% 0.15/0.46 % (11302)Instructions burned: 9 (million)
% 0.15/0.46 % (11302)------------------------------
% 0.15/0.46 % (11302)------------------------------
% 0.15/0.46 % (11303)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.15/0.47 % (11304)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.15/0.47 % (11304)Instruction limit reached!
% 0.15/0.47 % (11304)------------------------------
% 0.15/0.47 % (11304)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.47 % (11304)Termination reason: Unknown
% 0.15/0.47 % (11304)Termination phase: Preprocessing 3
% 0.15/0.47
% 0.15/0.47 % (11304)Memory used [KB]: 1023
% 0.15/0.47 % (11304)Time elapsed: 0.004 s
% 0.15/0.47 % (11304)Instructions burned: 3 (million)
% 0.15/0.47 % (11304)------------------------------
% 0.15/0.47 % (11304)------------------------------
% 0.15/0.47 % (11298)Instruction limit reached!
% 0.15/0.47 % (11298)------------------------------
% 0.15/0.47 % (11298)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.47 % (11298)Termination reason: Unknown
% 0.15/0.47 % (11298)Termination phase: Saturation
% 0.15/0.47
% 0.15/0.47 % (11298)Memory used [KB]: 5628
% 0.15/0.47 % (11298)Time elapsed: 0.023 s
% 0.15/0.47 % (11298)Instructions burned: 37 (million)
% 0.15/0.47 % (11298)------------------------------
% 0.15/0.47 % (11298)------------------------------
% 0.26/0.47 % (11305)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.26/0.47 % (11305)Instruction limit reached!
% 0.26/0.47 % (11305)------------------------------
% 0.26/0.47 % (11305)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.26/0.47 % (11305)Termination reason: Unknown
% 0.26/0.47 % (11305)Termination phase: Property scanning
% 0.26/0.47
% 0.26/0.47 % (11305)Memory used [KB]: 1023
% 0.26/0.47 % (11305)Time elapsed: 0.004 s
% 0.26/0.47 % (11305)Instructions burned: 3 (million)
% 0.26/0.47 % (11305)------------------------------
% 0.26/0.47 % (11305)------------------------------
% 0.26/0.48 % (11303)Instruction limit reached!
% 0.26/0.48 % (11303)------------------------------
% 0.26/0.48 % (11303)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.26/0.48 % (11303)Termination reason: Unknown
% 0.26/0.48 % (11303)Termination phase: Saturation
% 0.26/0.48
% 0.26/0.48 % (11303)Memory used [KB]: 5756
% 0.26/0.48 % (11303)Time elapsed: 0.014 s
% 0.26/0.48 % (11303)Instructions burned: 17 (million)
% 0.26/0.48 % (11303)------------------------------
% 0.26/0.48 % (11303)------------------------------
% 0.26/0.48 % (11295)First to succeed.
% 0.26/0.48 % (11306)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.26/0.48 % (11306)Instruction limit reached!
% 0.26/0.48 % (11306)------------------------------
% 0.26/0.48 % (11306)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.26/0.48 % (11306)Termination reason: Unknown
% 0.26/0.48 % (11306)Termination phase: Saturation
% 0.26/0.48
% 0.26/0.48 % (11306)Memory used [KB]: 5500
% 0.26/0.48 % (11306)Time elapsed: 0.006 s
% 0.26/0.48 % (11306)Instructions burned: 8 (million)
% 0.26/0.48 % (11306)------------------------------
% 0.26/0.48 % (11306)------------------------------
% 0.26/0.48 % (11307)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.26/0.48 % (11308)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.26/0.49 % (11307)Instruction limit reached!
% 0.26/0.49 % (11307)------------------------------
% 0.26/0.49 % (11307)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.26/0.49 % (11307)Termination reason: Unknown
% 0.26/0.49 % (11307)Termination phase: Function definition elimination
% 0.26/0.49
% 0.26/0.49 % (11307)Memory used [KB]: 1023
% 0.26/0.49 % (11307)Time elapsed: 0.004 s
% 0.26/0.49 % (11307)Instructions burned: 3 (million)
% 0.26/0.49 % (11307)------------------------------
% 0.26/0.49 % (11307)------------------------------
% 0.26/0.49 % (11308)Instruction limit reached!
% 0.26/0.49 % (11308)------------------------------
% 0.26/0.49 % (11308)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.26/0.49 % (11308)Termination reason: Unknown
% 0.26/0.49 % (11308)Termination phase: Saturation
% 0.26/0.49
% 0.26/0.49 % (11308)Memory used [KB]: 5500
% 0.26/0.49 % (11308)Time elapsed: 0.004 s
% 0.26/0.49 % (11308)Instructions burned: 4 (million)
% 0.26/0.49 % (11308)------------------------------
% 0.26/0.49 % (11308)------------------------------
% 0.26/0.49 % (11295)Refutation found. Thanks to Tanya!
% 0.26/0.49 % SZS status Theorem for theBenchmark
% 0.26/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.26/0.49 % (11295)------------------------------
% 0.26/0.49 % (11295)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.26/0.49 % (11295)Termination reason: Refutation
% 0.26/0.49
% 0.26/0.49 % (11295)Memory used [KB]: 6140
% 0.26/0.49 % (11295)Time elapsed: 0.060 s
% 0.26/0.49 % (11295)Instructions burned: 80 (million)
% 0.26/0.49 % (11295)------------------------------
% 0.26/0.49 % (11295)------------------------------
% 0.26/0.49 % (11289)Success in time 0.066 s
% 0.26/0.49 % Vampire---4.8 exiting
%------------------------------------------------------------------------------