TSTP Solution File: LCL176-3 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : LCL176-3 : TPTP v8.1.2. Released v2.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n025.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Apr 30 13:40:44 EDT 2024

% Result   : Unsatisfiable 0.15s 0.39s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   45
% Syntax   : Number of formulae    :  140 (  22 unt;   0 def)
%            Number of atoms       :  351 (   1 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  388 ( 177   ~; 175   |;   0   &)
%                                         (  36 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :   40 (  38 usr;  37 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   1 con; 0-2 aty)
%            Number of variables   :  204 ( 204   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f249,plain,
    $false,
    inference(avatar_sat_refutation,[],[f21,f25,f29,f33,f39,f43,f48,f52,f57,f62,f68,f73,f77,f82,f87,f94,f104,f115,f119,f126,f135,f139,f143,f151,f159,f163,f171,f179,f183,f187,f191,f216,f220,f229,f233,f237,f248]) ).

fof(f248,plain,
    ( spl0_1
    | ~ spl0_35 ),
    inference(avatar_contradiction_clause,[],[f243]) ).

fof(f243,plain,
    ( $false
    | spl0_1
    | ~ spl0_35 ),
    inference(resolution,[],[f232,f20]) ).

fof(f20,plain,
    ( ~ theorem(or(not(p),p))
    | spl0_1 ),
    inference(avatar_component_clause,[],[f18]) ).

fof(f18,plain,
    ( spl0_1
  <=> theorem(or(not(p),p)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f232,plain,
    ( ! [X0] : theorem(or(not(X0),X0))
    | ~ spl0_35 ),
    inference(avatar_component_clause,[],[f231]) ).

fof(f231,plain,
    ( spl0_35
  <=> ! [X0] : theorem(or(not(X0),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

fof(f237,plain,
    ( spl0_36
    | ~ spl0_14
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f109,f102,f80,f235]) ).

fof(f235,plain,
    ( spl0_36
  <=> ! [X2,X0,X1] : theorem(or(not(or(X0,X1)),or(not(or(not(X1),X2)),or(X0,X2)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

fof(f80,plain,
    ( spl0_14
  <=> ! [X2,X0,X1] : theorem(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f102,plain,
    ( spl0_17
  <=> ! [X2,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(or(X1,or(X0,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f109,plain,
    ( ! [X2,X0,X1] : theorem(or(not(or(X0,X1)),or(not(or(not(X1),X2)),or(X0,X2))))
    | ~ spl0_14
    | ~ spl0_17 ),
    inference(resolution,[],[f103,f81]) ).

fof(f81,plain,
    ( ! [X2,X0,X1] : theorem(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1))))
    | ~ spl0_14 ),
    inference(avatar_component_clause,[],[f80]) ).

fof(f103,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(or(X1,or(X0,X2)))
        | theorem(or(X0,or(X1,X2))) )
    | ~ spl0_17 ),
    inference(avatar_component_clause,[],[f102]) ).

fof(f233,plain,
    ( spl0_35
    | ~ spl0_15
    | ~ spl0_23 ),
    inference(avatar_split_clause,[],[f154,f141,f85,f231]) ).

fof(f85,plain,
    ( spl0_15
  <=> ! [X0] :
        ( theorem(X0)
        | ~ theorem(or(X0,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f141,plain,
    ( spl0_23
  <=> ! [X0,X1] : theorem(or(X0,or(not(X1),X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f154,plain,
    ( ! [X0] : theorem(or(not(X0),X0))
    | ~ spl0_15
    | ~ spl0_23 ),
    inference(resolution,[],[f142,f86]) ).

fof(f86,plain,
    ( ! [X0] :
        ( ~ theorem(or(X0,X0))
        | theorem(X0) )
    | ~ spl0_15 ),
    inference(avatar_component_clause,[],[f85]) ).

fof(f142,plain,
    ( ! [X0,X1] : theorem(or(X0,or(not(X1),X1)))
    | ~ spl0_23 ),
    inference(avatar_component_clause,[],[f141]) ).

fof(f229,plain,
    ( spl0_34
    | ~ spl0_14
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f99,f92,f80,f227]) ).

fof(f227,plain,
    ( spl0_34
  <=> ! [X2,X0,X1] : theorem(or(or(not(or(X0,X1)),or(X0,X2)),not(or(not(X1),X2)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

fof(f92,plain,
    ( spl0_16
  <=> ! [X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(or(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f99,plain,
    ( ! [X2,X0,X1] : theorem(or(or(not(or(X0,X1)),or(X0,X2)),not(or(not(X1),X2))))
    | ~ spl0_14
    | ~ spl0_16 ),
    inference(resolution,[],[f93,f81]) ).

fof(f93,plain,
    ( ! [X0,X1] :
        ( ~ theorem(or(X1,X0))
        | theorem(or(X0,X1)) )
    | ~ spl0_16 ),
    inference(avatar_component_clause,[],[f92]) ).

fof(f220,plain,
    ( spl0_33
    | ~ spl0_16
    | ~ spl0_19 ),
    inference(avatar_split_clause,[],[f122,f117,f92,f218]) ).

fof(f218,plain,
    ( spl0_33
  <=> ! [X2,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(or(X2,X1),not(or(X2,X0)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

fof(f117,plain,
    ( spl0_19
  <=> ! [X2,X0,X1] :
        ( theorem(or(not(or(X0,X1)),or(X0,X2)))
        | ~ theorem(or(not(X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f122,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(or(X2,X1),not(or(X2,X0)))) )
    | ~ spl0_16
    | ~ spl0_19 ),
    inference(resolution,[],[f118,f93]) ).

fof(f118,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(not(or(X0,X1)),or(X0,X2)))
        | ~ theorem(or(not(X1),X2)) )
    | ~ spl0_19 ),
    inference(avatar_component_clause,[],[f117]) ).

fof(f216,plain,
    ( spl0_32
    | ~ spl0_17
    | ~ spl0_19 ),
    inference(avatar_split_clause,[],[f121,f117,f102,f214]) ).

fof(f214,plain,
    ( spl0_32
  <=> ! [X2,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(X2,or(not(or(X2,X0)),X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f121,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(X2,or(not(or(X2,X0)),X1))) )
    | ~ spl0_17
    | ~ spl0_19 ),
    inference(resolution,[],[f118,f103]) ).

fof(f191,plain,
    ( spl0_31
    | ~ spl0_6
    | ~ spl0_19 ),
    inference(avatar_split_clause,[],[f120,f117,f41,f189]) ).

fof(f189,plain,
    ( spl0_31
  <=> ! [X2,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(X2,X1))
        | ~ theorem(or(X2,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f41,plain,
    ( spl0_6
  <=> ! [X4,X3] :
        ( ~ theorem(X4)
        | theorem(X3)
        | ~ theorem(or(not(X4),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f120,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(X2,X1))
        | ~ theorem(or(X2,X0)) )
    | ~ spl0_6
    | ~ spl0_19 ),
    inference(resolution,[],[f118,f42]) ).

fof(f42,plain,
    ( ! [X3,X4] :
        ( ~ theorem(or(not(X4),X3))
        | theorem(X3)
        | ~ theorem(X4) )
    | ~ spl0_6 ),
    inference(avatar_component_clause,[],[f41]) ).

fof(f187,plain,
    ( spl0_30
    | ~ spl0_10
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f108,f102,f60,f185]) ).

fof(f185,plain,
    ( spl0_30
  <=> ! [X0,X1] : theorem(or(X0,or(not(or(or(X0,X1),or(X0,X1))),X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

fof(f60,plain,
    ( spl0_10
  <=> ! [X0] : theorem(or(not(or(X0,X0)),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f108,plain,
    ( ! [X0,X1] : theorem(or(X0,or(not(or(or(X0,X1),or(X0,X1))),X1)))
    | ~ spl0_10
    | ~ spl0_17 ),
    inference(resolution,[],[f103,f61]) ).

fof(f61,plain,
    ( ! [X0] : theorem(or(not(or(X0,X0)),X0))
    | ~ spl0_10 ),
    inference(avatar_component_clause,[],[f60]) ).

fof(f183,plain,
    ( spl0_29
    | ~ spl0_12
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f107,f102,f71,f181]) ).

fof(f181,plain,
    ( spl0_29
  <=> ! [X2,X0,X1] : theorem(or(X0,or(not(or(X1,or(X0,X2))),or(X1,X2)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f71,plain,
    ( spl0_12
  <=> ! [X2,X0,X1] : theorem(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f107,plain,
    ( ! [X2,X0,X1] : theorem(or(X0,or(not(or(X1,or(X0,X2))),or(X1,X2))))
    | ~ spl0_12
    | ~ spl0_17 ),
    inference(resolution,[],[f103,f72]) ).

fof(f72,plain,
    ( ! [X2,X0,X1] : theorem(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2))))
    | ~ spl0_12 ),
    inference(avatar_component_clause,[],[f71]) ).

fof(f179,plain,
    ( spl0_28
    | ~ spl0_12
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f98,f92,f71,f177]) ).

fof(f177,plain,
    ( spl0_28
  <=> ! [X2,X0,X1] : theorem(or(or(X0,or(X1,X2)),not(or(X1,or(X0,X2))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

fof(f98,plain,
    ( ! [X2,X0,X1] : theorem(or(or(X0,or(X1,X2)),not(or(X1,or(X0,X2)))))
    | ~ spl0_12
    | ~ spl0_16 ),
    inference(resolution,[],[f93,f72]) ).

fof(f171,plain,
    ( spl0_27
    | ~ spl0_13
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f110,f102,f75,f169]) ).

fof(f169,plain,
    ( spl0_27
  <=> ! [X2,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(or(X0,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f75,plain,
    ( spl0_13
  <=> ! [X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f110,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(or(X0,X2)) )
    | ~ spl0_13
    | ~ spl0_17 ),
    inference(resolution,[],[f103,f76]) ).

fof(f76,plain,
    ( ! [X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(X1) )
    | ~ spl0_13 ),
    inference(avatar_component_clause,[],[f75]) ).

fof(f163,plain,
    ( spl0_26
    | ~ spl0_11
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f106,f102,f66,f161]) ).

fof(f161,plain,
    ( spl0_26
  <=> ! [X0,X1] : theorem(or(X0,or(not(or(X1,X0)),X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f66,plain,
    ( spl0_11
  <=> ! [X0,X1] : theorem(or(not(or(X0,X1)),or(X1,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f106,plain,
    ( ! [X0,X1] : theorem(or(X0,or(not(or(X1,X0)),X1)))
    | ~ spl0_11
    | ~ spl0_17 ),
    inference(resolution,[],[f103,f67]) ).

fof(f67,plain,
    ( ! [X0,X1] : theorem(or(not(or(X0,X1)),or(X1,X0)))
    | ~ spl0_11 ),
    inference(avatar_component_clause,[],[f66]) ).

fof(f159,plain,
    ( spl0_25
    | ~ spl0_11
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f97,f92,f66,f157]) ).

fof(f157,plain,
    ( spl0_25
  <=> ! [X0,X1] : theorem(or(or(X0,X1),not(or(X1,X0)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f97,plain,
    ( ! [X0,X1] : theorem(or(or(X0,X1),not(or(X1,X0))))
    | ~ spl0_11
    | ~ spl0_16 ),
    inference(resolution,[],[f93,f67]) ).

fof(f151,plain,
    ( ~ spl0_24
    | spl0_1
    | ~ spl0_20 ),
    inference(avatar_split_clause,[],[f127,f124,f18,f148]) ).

fof(f148,plain,
    ( spl0_24
  <=> theorem(not(p)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f124,plain,
    ( spl0_20
  <=> ! [X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f127,plain,
    ( ~ theorem(not(p))
    | spl0_1
    | ~ spl0_20 ),
    inference(resolution,[],[f125,f20]) ).

fof(f125,plain,
    ( ! [X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(X0) )
    | ~ spl0_20 ),
    inference(avatar_component_clause,[],[f124]) ).

fof(f143,plain,
    ( spl0_23
    | ~ spl0_7
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f105,f102,f46,f141]) ).

fof(f46,plain,
    ( spl0_7
  <=> ! [X0,X1] : theorem(or(not(X0),or(X1,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f105,plain,
    ( ! [X0,X1] : theorem(or(X0,or(not(X1),X1)))
    | ~ spl0_7
    | ~ spl0_17 ),
    inference(resolution,[],[f103,f47]) ).

fof(f47,plain,
    ( ! [X0,X1] : theorem(or(not(X0),or(X1,X0)))
    | ~ spl0_7 ),
    inference(avatar_component_clause,[],[f46]) ).

fof(f139,plain,
    ( spl0_22
    | ~ spl0_10
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f96,f92,f60,f137]) ).

fof(f137,plain,
    ( spl0_22
  <=> ! [X0] : theorem(or(X0,not(or(X0,X0)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f96,plain,
    ( ! [X0] : theorem(or(X0,not(or(X0,X0))))
    | ~ spl0_10
    | ~ spl0_16 ),
    inference(resolution,[],[f93,f61]) ).

fof(f135,plain,
    ( spl0_21
    | ~ spl0_7
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f95,f92,f46,f133]) ).

fof(f133,plain,
    ( spl0_21
  <=> ! [X0,X1] : theorem(or(or(X0,X1),not(X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f95,plain,
    ( ! [X0,X1] : theorem(or(or(X0,X1),not(X1)))
    | ~ spl0_7
    | ~ spl0_16 ),
    inference(resolution,[],[f93,f47]) ).

fof(f126,plain,
    ( spl0_20
    | ~ spl0_13
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f100,f92,f75,f124]) ).

fof(f100,plain,
    ( ! [X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(X0) )
    | ~ spl0_13
    | ~ spl0_16 ),
    inference(resolution,[],[f93,f76]) ).

fof(f119,plain,
    ( spl0_19
    | ~ spl0_6
    | ~ spl0_14 ),
    inference(avatar_split_clause,[],[f83,f80,f41,f117]) ).

fof(f83,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(not(or(X0,X1)),or(X0,X2)))
        | ~ theorem(or(not(X1),X2)) )
    | ~ spl0_6
    | ~ spl0_14 ),
    inference(resolution,[],[f81,f42]) ).

fof(f115,plain,
    ( ~ spl0_18
    | spl0_1
    | ~ spl0_13 ),
    inference(avatar_split_clause,[],[f88,f75,f18,f112]) ).

fof(f112,plain,
    ( spl0_18
  <=> theorem(p) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f88,plain,
    ( ~ theorem(p)
    | spl0_1
    | ~ spl0_13 ),
    inference(resolution,[],[f76,f20]) ).

fof(f104,plain,
    ( spl0_17
    | ~ spl0_6
    | ~ spl0_12 ),
    inference(avatar_split_clause,[],[f78,f71,f41,f102]) ).

fof(f78,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(or(X1,or(X0,X2))) )
    | ~ spl0_6
    | ~ spl0_12 ),
    inference(resolution,[],[f72,f42]) ).

fof(f94,plain,
    ( spl0_16
    | ~ spl0_6
    | ~ spl0_11 ),
    inference(avatar_split_clause,[],[f69,f66,f41,f92]) ).

fof(f69,plain,
    ( ! [X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(or(X1,X0)) )
    | ~ spl0_6
    | ~ spl0_11 ),
    inference(resolution,[],[f67,f42]) ).

fof(f87,plain,
    ( spl0_15
    | ~ spl0_6
    | ~ spl0_10 ),
    inference(avatar_split_clause,[],[f64,f60,f41,f85]) ).

fof(f64,plain,
    ( ! [X0] :
        ( theorem(X0)
        | ~ theorem(or(X0,X0)) )
    | ~ spl0_6
    | ~ spl0_10 ),
    inference(resolution,[],[f61,f42]) ).

fof(f82,plain,
    ( spl0_14
    | ~ spl0_2
    | ~ spl0_9 ),
    inference(avatar_split_clause,[],[f58,f55,f23,f80]) ).

fof(f23,plain,
    ( spl0_2
  <=> ! [X3] :
        ( ~ axiom(X3)
        | theorem(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f55,plain,
    ( spl0_9
  <=> ! [X2,X0,X1] : axiom(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f58,plain,
    ( ! [X2,X0,X1] : theorem(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1))))
    | ~ spl0_2
    | ~ spl0_9 ),
    inference(resolution,[],[f56,f24]) ).

fof(f24,plain,
    ( ! [X3] :
        ( ~ axiom(X3)
        | theorem(X3) )
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f23]) ).

fof(f56,plain,
    ( ! [X2,X0,X1] : axiom(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1))))
    | ~ spl0_9 ),
    inference(avatar_component_clause,[],[f55]) ).

fof(f77,plain,
    ( spl0_13
    | ~ spl0_6
    | ~ spl0_7 ),
    inference(avatar_split_clause,[],[f63,f46,f41,f75]) ).

fof(f63,plain,
    ( ! [X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(X1) )
    | ~ spl0_6
    | ~ spl0_7 ),
    inference(resolution,[],[f47,f42]) ).

fof(f73,plain,
    ( spl0_12
    | ~ spl0_2
    | ~ spl0_8 ),
    inference(avatar_split_clause,[],[f53,f50,f23,f71]) ).

fof(f50,plain,
    ( spl0_8
  <=> ! [X2,X0,X1] : axiom(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f53,plain,
    ( ! [X2,X0,X1] : theorem(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2))))
    | ~ spl0_2
    | ~ spl0_8 ),
    inference(resolution,[],[f51,f24]) ).

fof(f51,plain,
    ( ! [X2,X0,X1] : axiom(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2))))
    | ~ spl0_8 ),
    inference(avatar_component_clause,[],[f50]) ).

fof(f68,plain,
    ( spl0_11
    | ~ spl0_2
    | ~ spl0_5 ),
    inference(avatar_split_clause,[],[f44,f37,f23,f66]) ).

fof(f37,plain,
    ( spl0_5
  <=> ! [X0,X1] : axiom(or(not(or(X0,X1)),or(X1,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f44,plain,
    ( ! [X0,X1] : theorem(or(not(or(X0,X1)),or(X1,X0)))
    | ~ spl0_2
    | ~ spl0_5 ),
    inference(resolution,[],[f38,f24]) ).

fof(f38,plain,
    ( ! [X0,X1] : axiom(or(not(or(X0,X1)),or(X1,X0)))
    | ~ spl0_5 ),
    inference(avatar_component_clause,[],[f37]) ).

fof(f62,plain,
    ( spl0_10
    | ~ spl0_2
    | ~ spl0_4 ),
    inference(avatar_split_clause,[],[f35,f31,f23,f60]) ).

fof(f31,plain,
    ( spl0_4
  <=> ! [X0] : axiom(or(not(or(X0,X0)),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f35,plain,
    ( ! [X0] : theorem(or(not(or(X0,X0)),X0))
    | ~ spl0_2
    | ~ spl0_4 ),
    inference(resolution,[],[f32,f24]) ).

fof(f32,plain,
    ( ! [X0] : axiom(or(not(or(X0,X0)),X0))
    | ~ spl0_4 ),
    inference(avatar_component_clause,[],[f31]) ).

fof(f57,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f14,f55]) ).

fof(f14,plain,
    ! [X2,X0,X1] : axiom(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1)))),
    inference(definition_unfolding,[],[f5,f6,f6,f6]) ).

fof(f6,axiom,
    ! [X3,X4] : implies(X3,X4) = or(not(X3),X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_definition) ).

fof(f5,axiom,
    ! [X2,X0,X1] : axiom(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_6) ).

fof(f52,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f15,f50]) ).

fof(f15,plain,
    ! [X2,X0,X1] : axiom(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))),
    inference(definition_unfolding,[],[f4,f6]) ).

fof(f4,axiom,
    ! [X2,X0,X1] : axiom(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_5) ).

fof(f48,plain,
    ( spl0_7
    | ~ spl0_2
    | ~ spl0_3 ),
    inference(avatar_split_clause,[],[f34,f27,f23,f46]) ).

fof(f27,plain,
    ( spl0_3
  <=> ! [X0,X1] : axiom(or(not(X0),or(X1,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f34,plain,
    ( ! [X0,X1] : theorem(or(not(X0),or(X1,X0)))
    | ~ spl0_2
    | ~ spl0_3 ),
    inference(resolution,[],[f28,f24]) ).

fof(f28,plain,
    ( ! [X0,X1] : axiom(or(not(X0),or(X1,X0)))
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f27]) ).

fof(f43,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f16,f41]) ).

fof(f16,plain,
    ! [X3,X4] :
      ( ~ theorem(X4)
      | theorem(X3)
      | ~ theorem(or(not(X4),X3)) ),
    inference(definition_unfolding,[],[f8,f6]) ).

fof(f8,axiom,
    ! [X3,X4] :
      ( ~ theorem(X4)
      | theorem(X3)
      | ~ theorem(implies(X4,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_2) ).

fof(f39,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f13,f37]) ).

fof(f13,plain,
    ! [X0,X1] : axiom(or(not(or(X0,X1)),or(X1,X0))),
    inference(definition_unfolding,[],[f3,f6]) ).

fof(f3,axiom,
    ! [X0,X1] : axiom(implies(or(X0,X1),or(X1,X0))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_4) ).

fof(f33,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f12,f31]) ).

fof(f12,plain,
    ! [X0] : axiom(or(not(or(X0,X0)),X0)),
    inference(definition_unfolding,[],[f1,f6]) ).

fof(f1,axiom,
    ! [X0] : axiom(implies(or(X0,X0),X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_2) ).

fof(f29,plain,
    spl0_3,
    inference(avatar_split_clause,[],[f11,f27]) ).

fof(f11,plain,
    ! [X0,X1] : axiom(or(not(X0),or(X1,X0))),
    inference(definition_unfolding,[],[f2,f6]) ).

fof(f2,axiom,
    ! [X0,X1] : axiom(implies(X0,or(X1,X0))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_3) ).

fof(f25,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f7,f23]) ).

fof(f7,axiom,
    ! [X3] :
      ( ~ axiom(X3)
      | theorem(X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_1) ).

fof(f21,plain,
    ~ spl0_1,
    inference(avatar_split_clause,[],[f10,f18]) ).

fof(f10,plain,
    ~ theorem(or(not(p),p)),
    inference(definition_unfolding,[],[f9,f6]) ).

fof(f9,axiom,
    ~ theorem(implies(p,p)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : LCL176-3 : TPTP v8.1.2. Released v2.3.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36  % Computer : n025.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Mon Apr 29 23:12:11 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  % (15567)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38  % (15572)WARNING: value z3 for option sas not known
% 0.15/0.38  % (15573)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38  % (15571)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38  % (15572)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.38  % (15570)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38  % (15574)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.38  % (15575)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.38  % (15576)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.38  TRYING [1]
% 0.15/0.38  TRYING [1]
% 0.15/0.38  TRYING [2]
% 0.15/0.38  TRYING [2]
% 0.15/0.38  TRYING [3]
% 0.15/0.39  TRYING [3]
% 0.15/0.39  % (15574)First to succeed.
% 0.15/0.39  TRYING [1]
% 0.15/0.39  % (15575)Also succeeded, but the first one will report.
% 0.15/0.39  TRYING [2]
% 0.15/0.39  % (15574)Refutation found. Thanks to Tanya!
% 0.15/0.39  % SZS status Unsatisfiable for theBenchmark
% 0.15/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.39  % (15574)------------------------------
% 0.15/0.39  % (15574)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.39  % (15574)Termination reason: Refutation
% 0.15/0.39  
% 0.15/0.39  % (15574)Memory used [KB]: 901
% 0.15/0.39  % (15574)Time elapsed: 0.009 s
% 0.15/0.39  % (15574)Instructions burned: 11 (million)
% 0.15/0.39  % (15574)------------------------------
% 0.15/0.39  % (15574)------------------------------
% 0.15/0.39  % (15567)Success in time 0.026 s
%------------------------------------------------------------------------------