TSTP Solution File: REL046+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : REL046+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n007.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun May  5 08:53:11 EDT 2024

% Result   : Theorem 0.16s 0.38s
% Output   : Refutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   60
% Syntax   : Number of formulae    :  181 (  43 unt;   0 def)
%            Number of atoms       :  402 ( 148 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  395 ( 174   ~; 167   |;   6   &)
%                                         (  45 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :   47 (  45 usr;  46 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   6 con; 0-2 aty)
%            Number of variables   :  214 ( 208   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1113,plain,
    $false,
    inference(avatar_sat_refutation,[],[f44,f49,f53,f57,f61,f65,f69,f75,f80,f84,f96,f100,f112,f130,f134,f162,f188,f196,f201,f210,f228,f232,f236,f240,f244,f249,f253,f257,f261,f464,f468,f472,f476,f674,f679,f683,f737,f741,f745,f749,f860,f864,f868,f872,f876,f1112]) ).

fof(f1112,plain,
    ( spl3_2
    | ~ spl3_18
    | ~ spl3_43 ),
    inference(avatar_split_clause,[],[f1019,f866,f186,f41]) ).

fof(f41,plain,
    ( spl3_2
  <=> sK2 = join(sK0,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).

fof(f186,plain,
    ( spl3_18
  <=> ! [X0] : join(complement(join(complement(sK1),complement(sK2))),X0) = join(sK0,join(complement(join(complement(sK1),complement(sK2))),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_18])]) ).

fof(f866,plain,
    ( spl3_43
  <=> ! [X0,X1] : join(complement(join(complement(X1),complement(X0))),complement(join(complement(X0),X1))) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_43])]) ).

fof(f1019,plain,
    ( sK2 = join(sK0,sK2)
    | ~ spl3_18
    | ~ spl3_43 ),
    inference(superposition,[],[f187,f867]) ).

fof(f867,plain,
    ( ! [X0,X1] : join(complement(join(complement(X1),complement(X0))),complement(join(complement(X0),X1))) = X0
    | ~ spl3_43 ),
    inference(avatar_component_clause,[],[f866]) ).

fof(f187,plain,
    ( ! [X0] : join(complement(join(complement(sK1),complement(sK2))),X0) = join(sK0,join(complement(join(complement(sK1),complement(sK2))),X0))
    | ~ spl3_18 ),
    inference(avatar_component_clause,[],[f186]) ).

fof(f876,plain,
    ( spl3_45
    | ~ spl3_7
    | ~ spl3_17 ),
    inference(avatar_split_clause,[],[f173,f160,f63,f874]) ).

fof(f874,plain,
    ( spl3_45
  <=> ! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_45])]) ).

fof(f63,plain,
    ( spl3_7
  <=> ! [X0,X1] : join(X0,X1) = join(X1,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_7])]) ).

fof(f160,plain,
    ( spl3_17
  <=> ! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_17])]) ).

fof(f173,plain,
    ( ! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0
    | ~ spl3_7
    | ~ spl3_17 ),
    inference(superposition,[],[f161,f64]) ).

fof(f64,plain,
    ( ! [X0,X1] : join(X0,X1) = join(X1,X0)
    | ~ spl3_7 ),
    inference(avatar_component_clause,[],[f63]) ).

fof(f161,plain,
    ( ! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0
    | ~ spl3_17 ),
    inference(avatar_component_clause,[],[f160]) ).

fof(f872,plain,
    ( spl3_44
    | ~ spl3_7
    | ~ spl3_17 ),
    inference(avatar_split_clause,[],[f169,f160,f63,f870]) ).

fof(f870,plain,
    ( spl3_44
  <=> ! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(X1,complement(X0)))) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_44])]) ).

fof(f169,plain,
    ( ! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(X1,complement(X0)))) = X0
    | ~ spl3_7
    | ~ spl3_17 ),
    inference(superposition,[],[f161,f64]) ).

fof(f868,plain,
    ( spl3_43
    | ~ spl3_7
    | ~ spl3_17 ),
    inference(avatar_split_clause,[],[f166,f160,f63,f866]) ).

fof(f166,plain,
    ( ! [X0,X1] : join(complement(join(complement(X1),complement(X0))),complement(join(complement(X0),X1))) = X0
    | ~ spl3_7
    | ~ spl3_17 ),
    inference(superposition,[],[f161,f64]) ).

fof(f864,plain,
    ( spl3_42
    | ~ spl3_11
    | ~ spl3_13 ),
    inference(avatar_split_clause,[],[f118,f98,f82,f862]) ).

fof(f862,plain,
    ( spl3_42
  <=> ! [X2,X0,X1] : join(converse(X0),join(converse(X1),X2)) = join(converse(join(X0,X1)),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_42])]) ).

fof(f82,plain,
    ( spl3_11
  <=> ! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_11])]) ).

fof(f98,plain,
    ( spl3_13
  <=> ! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_13])]) ).

fof(f118,plain,
    ( ! [X2,X0,X1] : join(converse(X0),join(converse(X1),X2)) = join(converse(join(X0,X1)),X2)
    | ~ spl3_11
    | ~ spl3_13 ),
    inference(superposition,[],[f99,f83]) ).

fof(f83,plain,
    ( ! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1))
    | ~ spl3_11 ),
    inference(avatar_component_clause,[],[f82]) ).

fof(f99,plain,
    ( ! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2)
    | ~ spl3_13 ),
    inference(avatar_component_clause,[],[f98]) ).

fof(f860,plain,
    ( spl3_41
    | ~ spl3_10
    | ~ spl3_12 ),
    inference(avatar_split_clause,[],[f102,f94,f78,f858]) ).

fof(f858,plain,
    ( spl3_41
  <=> ! [X2,X0,X1] : composition(converse(X0),composition(converse(X1),X2)) = composition(converse(composition(X1,X0)),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_41])]) ).

fof(f78,plain,
    ( spl3_10
  <=> ! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_10])]) ).

fof(f94,plain,
    ( spl3_12
  <=> ! [X2,X0,X1] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_12])]) ).

fof(f102,plain,
    ( ! [X2,X0,X1] : composition(converse(X0),composition(converse(X1),X2)) = composition(converse(composition(X1,X0)),X2)
    | ~ spl3_10
    | ~ spl3_12 ),
    inference(superposition,[],[f95,f79]) ).

fof(f79,plain,
    ( ! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0))
    | ~ spl3_10 ),
    inference(avatar_component_clause,[],[f78]) ).

fof(f95,plain,
    ( ! [X2,X0,X1] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2)
    | ~ spl3_12 ),
    inference(avatar_component_clause,[],[f94]) ).

fof(f749,plain,
    ( spl3_40
    | ~ spl3_7
    | ~ spl3_9
    | ~ spl3_17 ),
    inference(avatar_split_clause,[],[f179,f160,f72,f63,f747]) ).

fof(f747,plain,
    ( spl3_40
  <=> ! [X0] : join(complement(join(zero,complement(X0))),complement(join(top,complement(X0)))) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_40])]) ).

fof(f72,plain,
    ( spl3_9
  <=> zero = complement(top) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_9])]) ).

fof(f179,plain,
    ( ! [X0] : join(complement(join(zero,complement(X0))),complement(join(top,complement(X0)))) = X0
    | ~ spl3_7
    | ~ spl3_9
    | ~ spl3_17 ),
    inference(forward_demodulation,[],[f178,f64]) ).

fof(f178,plain,
    ( ! [X0] : join(complement(join(complement(X0),zero)),complement(join(top,complement(X0)))) = X0
    | ~ spl3_7
    | ~ spl3_9
    | ~ spl3_17 ),
    inference(forward_demodulation,[],[f163,f64]) ).

fof(f163,plain,
    ( ! [X0] : join(complement(join(complement(X0),zero)),complement(join(complement(X0),top))) = X0
    | ~ spl3_9
    | ~ spl3_17 ),
    inference(superposition,[],[f161,f74]) ).

fof(f74,plain,
    ( zero = complement(top)
    | ~ spl3_9 ),
    inference(avatar_component_clause,[],[f72]) ).

fof(f745,plain,
    ( spl3_39
    | ~ spl3_7
    | ~ spl3_16 ),
    inference(avatar_split_clause,[],[f152,f132,f63,f743]) ).

fof(f743,plain,
    ( spl3_39
  <=> ! [X2,X0,X1] : composition(join(X0,X2),X1) = join(composition(X2,X1),composition(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_39])]) ).

fof(f132,plain,
    ( spl3_16
  <=> ! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_16])]) ).

fof(f152,plain,
    ( ! [X2,X0,X1] : composition(join(X0,X2),X1) = join(composition(X2,X1),composition(X0,X1))
    | ~ spl3_7
    | ~ spl3_16 ),
    inference(superposition,[],[f133,f64]) ).

fof(f133,plain,
    ( ! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2))
    | ~ spl3_16 ),
    inference(avatar_component_clause,[],[f132]) ).

fof(f741,plain,
    ( spl3_38
    | ~ spl3_7
    | ~ spl3_15 ),
    inference(avatar_split_clause,[],[f140,f128,f63,f739]) ).

fof(f739,plain,
    ( spl3_38
  <=> ! [X0,X1] : complement(X1) = join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_38])]) ).

fof(f128,plain,
    ( spl3_15
  <=> ! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_15])]) ).

fof(f140,plain,
    ( ! [X0,X1] : complement(X1) = join(complement(X1),composition(converse(X0),complement(composition(X0,X1))))
    | ~ spl3_7
    | ~ spl3_15 ),
    inference(superposition,[],[f129,f64]) ).

fof(f129,plain,
    ( ! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1))
    | ~ spl3_15 ),
    inference(avatar_component_clause,[],[f128]) ).

fof(f737,plain,
    ( spl3_37
    | ~ spl3_4
    | ~ spl3_15 ),
    inference(avatar_split_clause,[],[f135,f128,f51,f735]) ).

fof(f735,plain,
    ( spl3_37
  <=> ! [X0,X1] : complement(X1) = join(composition(X0,complement(composition(converse(X0),X1))),complement(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_37])]) ).

fof(f51,plain,
    ( spl3_4
  <=> ! [X0] : converse(converse(X0)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).

fof(f135,plain,
    ( ! [X0,X1] : complement(X1) = join(composition(X0,complement(composition(converse(X0),X1))),complement(X1))
    | ~ spl3_4
    | ~ spl3_15 ),
    inference(superposition,[],[f129,f52]) ).

fof(f52,plain,
    ( ! [X0] : converse(converse(X0)) = X0
    | ~ spl3_4 ),
    inference(avatar_component_clause,[],[f51]) ).

fof(f683,plain,
    ( spl3_36
    | ~ spl3_6
    | ~ spl3_9
    | ~ spl3_17 ),
    inference(avatar_split_clause,[],[f184,f160,f72,f59,f681]) ).

fof(f681,plain,
    ( spl3_36
  <=> ! [X0] : join(complement(join(complement(X0),complement(complement(complement(X0))))),zero) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_36])]) ).

fof(f59,plain,
    ( spl3_6
  <=> ! [X0] : top = join(X0,complement(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).

fof(f184,plain,
    ( ! [X0] : join(complement(join(complement(X0),complement(complement(complement(X0))))),zero) = X0
    | ~ spl3_6
    | ~ spl3_9
    | ~ spl3_17 ),
    inference(forward_demodulation,[],[f172,f74]) ).

fof(f172,plain,
    ( ! [X0] : join(complement(join(complement(X0),complement(complement(complement(X0))))),complement(top)) = X0
    | ~ spl3_6
    | ~ spl3_17 ),
    inference(superposition,[],[f161,f60]) ).

fof(f60,plain,
    ( ! [X0] : top = join(X0,complement(X0))
    | ~ spl3_6 ),
    inference(avatar_component_clause,[],[f59]) ).

fof(f679,plain,
    ( spl3_35
    | ~ spl3_7
    | ~ spl3_26 ),
    inference(avatar_split_clause,[],[f450,f246,f63,f676]) ).

fof(f676,plain,
    ( spl3_35
  <=> top = join(top,sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_35])]) ).

fof(f246,plain,
    ( spl3_26
  <=> top = join(sK0,top) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_26])]) ).

fof(f450,plain,
    ( top = join(top,sK0)
    | ~ spl3_7
    | ~ spl3_26 ),
    inference(superposition,[],[f248,f64]) ).

fof(f248,plain,
    ( top = join(sK0,top)
    | ~ spl3_26 ),
    inference(avatar_component_clause,[],[f246]) ).

fof(f674,plain,
    ( spl3_34
    | ~ spl3_9
    | ~ spl3_17 ),
    inference(avatar_split_clause,[],[f168,f160,f72,f672]) ).

fof(f672,plain,
    ( spl3_34
  <=> ! [X0] : top = join(complement(join(zero,complement(X0))),complement(join(zero,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_34])]) ).

fof(f168,plain,
    ( ! [X0] : top = join(complement(join(zero,complement(X0))),complement(join(zero,X0)))
    | ~ spl3_9
    | ~ spl3_17 ),
    inference(superposition,[],[f161,f74]) ).

fof(f476,plain,
    ( spl3_33
    | ~ spl3_9
    | ~ spl3_15 ),
    inference(avatar_split_clause,[],[f139,f128,f72,f474]) ).

fof(f474,plain,
    ( spl3_33
  <=> ! [X0] : zero = join(composition(converse(X0),complement(composition(X0,top))),zero) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_33])]) ).

fof(f139,plain,
    ( ! [X0] : zero = join(composition(converse(X0),complement(composition(X0,top))),zero)
    | ~ spl3_9
    | ~ spl3_15 ),
    inference(superposition,[],[f129,f74]) ).

fof(f472,plain,
    ( spl3_32
    | ~ spl3_5
    | ~ spl3_15 ),
    inference(avatar_split_clause,[],[f136,f128,f55,f470]) ).

fof(f470,plain,
    ( spl3_32
  <=> ! [X0] : complement(one) = join(composition(converse(X0),complement(X0)),complement(one)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_32])]) ).

fof(f55,plain,
    ( spl3_5
  <=> ! [X0] : composition(X0,one) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).

fof(f136,plain,
    ( ! [X0] : complement(one) = join(composition(converse(X0),complement(X0)),complement(one))
    | ~ spl3_5
    | ~ spl3_15 ),
    inference(superposition,[],[f129,f56]) ).

fof(f56,plain,
    ( ! [X0] : composition(X0,one) = X0
    | ~ spl3_5 ),
    inference(avatar_component_clause,[],[f55]) ).

fof(f468,plain,
    ( spl3_31
    | ~ spl3_7
    | ~ spl3_13 ),
    inference(avatar_split_clause,[],[f119,f98,f63,f466]) ).

fof(f466,plain,
    ( spl3_31
  <=> ! [X2,X0,X1] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_31])]) ).

fof(f119,plain,
    ( ! [X2,X0,X1] : join(X0,join(X1,X2)) = join(X2,join(X0,X1))
    | ~ spl3_7
    | ~ spl3_13 ),
    inference(superposition,[],[f99,f64]) ).

fof(f464,plain,
    ( spl3_30
    | ~ spl3_7
    | ~ spl3_13 ),
    inference(avatar_split_clause,[],[f113,f98,f63,f462]) ).

fof(f462,plain,
    ( spl3_30
  <=> ! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X1,X0),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_30])]) ).

fof(f113,plain,
    ( ! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X1,X0),X2)
    | ~ spl3_7
    | ~ spl3_13 ),
    inference(superposition,[],[f99,f64]) ).

fof(f261,plain,
    ( spl3_29
    | ~ spl3_6
    | ~ spl3_9
    | ~ spl3_17 ),
    inference(avatar_split_clause,[],[f182,f160,f72,f59,f259]) ).

fof(f259,plain,
    ( spl3_29
  <=> ! [X0] : join(zero,complement(join(complement(X0),complement(X0)))) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_29])]) ).

fof(f182,plain,
    ( ! [X0] : join(zero,complement(join(complement(X0),complement(X0)))) = X0
    | ~ spl3_6
    | ~ spl3_9
    | ~ spl3_17 ),
    inference(forward_demodulation,[],[f165,f74]) ).

fof(f165,plain,
    ( ! [X0] : join(complement(top),complement(join(complement(X0),complement(X0)))) = X0
    | ~ spl3_6
    | ~ spl3_17 ),
    inference(superposition,[],[f161,f60]) ).

fof(f257,plain,
    ( spl3_28
    | ~ spl3_6
    | ~ spl3_13 ),
    inference(avatar_split_clause,[],[f121,f98,f59,f255]) ).

fof(f255,plain,
    ( spl3_28
  <=> ! [X0,X1] : top = join(X0,join(X1,complement(join(X0,X1)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_28])]) ).

fof(f121,plain,
    ( ! [X0,X1] : top = join(X0,join(X1,complement(join(X0,X1))))
    | ~ spl3_6
    | ~ spl3_13 ),
    inference(superposition,[],[f99,f60]) ).

fof(f253,plain,
    ( spl3_27
    | ~ spl3_6
    | ~ spl3_13 ),
    inference(avatar_split_clause,[],[f117,f98,f59,f251]) ).

fof(f251,plain,
    ( spl3_27
  <=> ! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_27])]) ).

fof(f117,plain,
    ( ! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,X1)
    | ~ spl3_6
    | ~ spl3_13 ),
    inference(superposition,[],[f99,f60]) ).

fof(f249,plain,
    ( spl3_26
    | ~ spl3_6
    | ~ spl3_18 ),
    inference(avatar_split_clause,[],[f192,f186,f59,f246]) ).

fof(f192,plain,
    ( top = join(sK0,top)
    | ~ spl3_6
    | ~ spl3_18 ),
    inference(superposition,[],[f187,f60]) ).

fof(f244,plain,
    ( spl3_25
    | ~ spl3_7
    | ~ spl3_11 ),
    inference(avatar_split_clause,[],[f89,f82,f63,f242]) ).

fof(f242,plain,
    ( spl3_25
  <=> ! [X0,X1] : converse(join(X0,X1)) = join(converse(X1),converse(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_25])]) ).

fof(f89,plain,
    ( ! [X0,X1] : converse(join(X0,X1)) = join(converse(X1),converse(X0))
    | ~ spl3_7
    | ~ spl3_11 ),
    inference(superposition,[],[f83,f64]) ).

fof(f240,plain,
    ( spl3_24
    | ~ spl3_4
    | ~ spl3_11 ),
    inference(avatar_split_clause,[],[f88,f82,f51,f238]) ).

fof(f238,plain,
    ( spl3_24
  <=> ! [X0,X1] : converse(join(X1,converse(X0))) = join(converse(X1),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_24])]) ).

fof(f88,plain,
    ( ! [X0,X1] : converse(join(X1,converse(X0))) = join(converse(X1),X0)
    | ~ spl3_4
    | ~ spl3_11 ),
    inference(superposition,[],[f83,f52]) ).

fof(f236,plain,
    ( spl3_23
    | ~ spl3_4
    | ~ spl3_11 ),
    inference(avatar_split_clause,[],[f87,f82,f51,f234]) ).

fof(f234,plain,
    ( spl3_23
  <=> ! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_23])]) ).

fof(f87,plain,
    ( ! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1))
    | ~ spl3_4
    | ~ spl3_11 ),
    inference(superposition,[],[f83,f52]) ).

fof(f232,plain,
    ( spl3_22
    | ~ spl3_4
    | ~ spl3_10 ),
    inference(avatar_split_clause,[],[f86,f78,f51,f230]) ).

fof(f230,plain,
    ( spl3_22
  <=> ! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_22])]) ).

fof(f86,plain,
    ( ! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0)
    | ~ spl3_4
    | ~ spl3_10 ),
    inference(superposition,[],[f79,f52]) ).

fof(f228,plain,
    ( spl3_21
    | ~ spl3_4
    | ~ spl3_10 ),
    inference(avatar_split_clause,[],[f85,f78,f51,f226]) ).

fof(f226,plain,
    ( spl3_21
  <=> ! [X0,X1] : converse(composition(X1,converse(X0))) = composition(X0,converse(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_21])]) ).

fof(f85,plain,
    ( ! [X0,X1] : converse(composition(X1,converse(X0))) = composition(X0,converse(X1))
    | ~ spl3_4
    | ~ spl3_10 ),
    inference(superposition,[],[f79,f52]) ).

fof(f210,plain,
    ( spl3_20
    | ~ spl3_5
    | ~ spl3_12 ),
    inference(avatar_split_clause,[],[f101,f94,f55,f208]) ).

fof(f208,plain,
    ( spl3_20
  <=> ! [X0,X1] : composition(X0,X1) = composition(X0,composition(one,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_20])]) ).

fof(f101,plain,
    ( ! [X0,X1] : composition(X0,X1) = composition(X0,composition(one,X1))
    | ~ spl3_5
    | ~ spl3_12 ),
    inference(superposition,[],[f95,f56]) ).

fof(f201,plain,
    ( spl3_19
    | ~ spl3_1
    | ~ spl3_13 ),
    inference(avatar_split_clause,[],[f197,f98,f37,f199]) ).

fof(f199,plain,
    ( spl3_19
  <=> ! [X0] : join(sK1,X0) = join(sK0,join(sK1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_19])]) ).

fof(f37,plain,
    ( spl3_1
  <=> sK1 = join(sK0,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

fof(f197,plain,
    ( ! [X0] : join(sK1,X0) = join(sK0,join(sK1,X0))
    | ~ spl3_1
    | ~ spl3_13 ),
    inference(superposition,[],[f99,f38]) ).

fof(f38,plain,
    ( sK1 = join(sK0,sK1)
    | ~ spl3_1 ),
    inference(avatar_component_clause,[],[f37]) ).

fof(f196,plain,
    ( spl3_1
    | ~ spl3_17
    | ~ spl3_18 ),
    inference(avatar_split_clause,[],[f191,f186,f160,f37]) ).

fof(f191,plain,
    ( sK1 = join(sK0,sK1)
    | ~ spl3_17
    | ~ spl3_18 ),
    inference(superposition,[],[f187,f161]) ).

fof(f188,plain,
    ( spl3_18
    | ~ spl3_3
    | ~ spl3_13 ),
    inference(avatar_split_clause,[],[f116,f98,f46,f186]) ).

fof(f46,plain,
    ( spl3_3
  <=> complement(join(complement(sK1),complement(sK2))) = join(sK0,complement(join(complement(sK1),complement(sK2)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).

fof(f116,plain,
    ( ! [X0] : join(complement(join(complement(sK1),complement(sK2))),X0) = join(sK0,join(complement(join(complement(sK1),complement(sK2))),X0))
    | ~ spl3_3
    | ~ spl3_13 ),
    inference(superposition,[],[f99,f48]) ).

fof(f48,plain,
    ( complement(join(complement(sK1),complement(sK2))) = join(sK0,complement(join(complement(sK1),complement(sK2))))
    | ~ spl3_3 ),
    inference(avatar_component_clause,[],[f46]) ).

fof(f162,plain,
    spl3_17,
    inference(avatar_split_clause,[],[f30,f160]) ).

fof(f30,plain,
    ! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux3_a_kind_of_de_Morgan) ).

fof(f134,plain,
    spl3_16,
    inference(avatar_split_clause,[],[f33,f132]) ).

fof(f33,plain,
    ! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
    inference(cnf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_distributivity) ).

fof(f130,plain,
    spl3_15,
    inference(avatar_split_clause,[],[f29,f128]) ).

fof(f29,plain,
    ! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
    inference(cnf_transformation,[],[f11]) ).

fof(f11,axiom,
    ! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_cancellativity) ).

fof(f112,plain,
    ( spl3_14
    | ~ spl3_6
    | ~ spl3_9 ),
    inference(avatar_split_clause,[],[f76,f72,f59,f109]) ).

fof(f109,plain,
    ( spl3_14
  <=> top = join(top,zero) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_14])]) ).

fof(f76,plain,
    ( top = join(top,zero)
    | ~ spl3_6
    | ~ spl3_9 ),
    inference(superposition,[],[f60,f74]) ).

fof(f100,plain,
    spl3_13,
    inference(avatar_split_clause,[],[f32,f98]) ).

fof(f32,plain,
    ! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
    inference(cnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux2_join_associativity) ).

fof(f96,plain,
    spl3_12,
    inference(avatar_split_clause,[],[f31,f94]) ).

fof(f31,plain,
    ! [X2,X0,X1] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
    inference(cnf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_associativity) ).

fof(f84,plain,
    spl3_11,
    inference(avatar_split_clause,[],[f27,f82]) ).

fof(f27,plain,
    ! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
    inference(cnf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_additivity) ).

fof(f80,plain,
    spl3_10,
    inference(avatar_split_clause,[],[f26,f78]) ).

fof(f26,plain,
    ! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
    inference(cnf_transformation,[],[f10]) ).

fof(f10,axiom,
    ! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_multiplicativity) ).

fof(f75,plain,
    ( spl3_9
    | ~ spl3_6
    | ~ spl3_8 ),
    inference(avatar_split_clause,[],[f70,f67,f59,f72]) ).

fof(f67,plain,
    ( spl3_8
  <=> ! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_8])]) ).

fof(f70,plain,
    ( zero = complement(top)
    | ~ spl3_6
    | ~ spl3_8 ),
    inference(forward_demodulation,[],[f68,f60]) ).

fof(f68,plain,
    ( ! [X0] : zero = complement(join(complement(X0),complement(complement(X0))))
    | ~ spl3_8 ),
    inference(avatar_component_clause,[],[f67]) ).

fof(f69,plain,
    spl3_8,
    inference(avatar_split_clause,[],[f35,f67]) ).

fof(f35,plain,
    ! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
    inference(definition_unfolding,[],[f23,f28]) ).

fof(f28,plain,
    ! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
    inference(cnf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux4_definiton_of_meet) ).

fof(f23,plain,
    ! [X0] : zero = meet(X0,complement(X0)),
    inference(cnf_transformation,[],[f13]) ).

fof(f13,axiom,
    ! [X0] : zero = meet(X0,complement(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_zero) ).

fof(f65,plain,
    spl3_7,
    inference(avatar_split_clause,[],[f25,f63]) ).

fof(f25,plain,
    ! [X0,X1] : join(X0,X1) = join(X1,X0),
    inference(cnf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1] : join(X0,X1) = join(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity) ).

fof(f61,plain,
    spl3_6,
    inference(avatar_split_clause,[],[f24,f59]) ).

fof(f24,plain,
    ! [X0] : top = join(X0,complement(X0)),
    inference(cnf_transformation,[],[f12]) ).

fof(f12,axiom,
    ! [X0] : top = join(X0,complement(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top) ).

fof(f57,plain,
    spl3_5,
    inference(avatar_split_clause,[],[f22,f55]) ).

fof(f22,plain,
    ! [X0] : composition(X0,one) = X0,
    inference(cnf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0] : composition(X0,one) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity) ).

fof(f53,plain,
    spl3_4,
    inference(avatar_split_clause,[],[f21,f51]) ).

fof(f21,plain,
    ! [X0] : converse(converse(X0)) = X0,
    inference(cnf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0] : converse(converse(X0)) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence) ).

fof(f49,plain,
    spl3_3,
    inference(avatar_split_clause,[],[f34,f46]) ).

fof(f34,plain,
    complement(join(complement(sK1),complement(sK2))) = join(sK0,complement(join(complement(sK1),complement(sK2)))),
    inference(definition_unfolding,[],[f19,f28,f28]) ).

fof(f19,plain,
    meet(sK1,sK2) = join(sK0,meet(sK1,sK2)),
    inference(cnf_transformation,[],[f18]) ).

fof(f18,plain,
    ( ( sK2 != join(sK0,sK2)
      | sK1 != join(sK0,sK1) )
    & meet(sK1,sK2) = join(sK0,meet(sK1,sK2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f16,f17]) ).

fof(f17,plain,
    ( ? [X0,X1,X2] :
        ( ( join(X0,X2) != X2
          | join(X0,X1) != X1 )
        & meet(X1,X2) = join(X0,meet(X1,X2)) )
   => ( ( sK2 != join(sK0,sK2)
        | sK1 != join(sK0,sK1) )
      & meet(sK1,sK2) = join(sK0,meet(sK1,sK2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f16,plain,
    ? [X0,X1,X2] :
      ( ( join(X0,X2) != X2
        | join(X0,X1) != X1 )
      & meet(X1,X2) = join(X0,meet(X1,X2)) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( meet(X1,X2) = join(X0,meet(X1,X2))
       => ( join(X0,X2) = X2
          & join(X0,X1) = X1 ) ),
    inference(negated_conjecture,[],[f14]) ).

fof(f14,conjecture,
    ! [X0,X1,X2] :
      ( meet(X1,X2) = join(X0,meet(X1,X2))
     => ( join(X0,X2) = X2
        & join(X0,X1) = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

fof(f44,plain,
    ( ~ spl3_1
    | ~ spl3_2 ),
    inference(avatar_split_clause,[],[f20,f41,f37]) ).

fof(f20,plain,
    ( sK2 != join(sK0,sK2)
    | sK1 != join(sK0,sK1) ),
    inference(cnf_transformation,[],[f18]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10  % Problem    : REL046+1 : TPTP v8.1.2. Released v4.0.0.
% 0.02/0.11  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.31  % Computer : n007.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit   : 300
% 0.10/0.31  % WCLimit    : 300
% 0.10/0.31  % DateTime   : Fri May  3 15:36:22 EDT 2024
% 0.10/0.31  % CPUTime    : 
% 0.10/0.31  % (6471)Running in auto input_syntax mode. Trying TPTP
% 0.10/0.33  % (6474)WARNING: value z3 for option sas not known
% 0.10/0.33  % (6472)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.10/0.33  % (6473)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.10/0.33  % (6475)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.10/0.33  % (6476)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)
% 0.10/0.33  % (6474)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)
% 0.10/0.33  % (6477)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)
% 0.10/0.33  % (6478)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)
% 0.10/0.33  TRYING [1]
% 0.10/0.33  TRYING [2]
% 0.10/0.34  TRYING [3]
% 0.10/0.34  TRYING [1]
% 0.10/0.34  TRYING [2]
% 0.16/0.35  TRYING [3]
% 0.16/0.35  TRYING [4]
% 0.16/0.37  % (6476)First to succeed.
% 0.16/0.38  % (6476)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-6471"
% 0.16/0.38  % (6476)Refutation found. Thanks to Tanya!
% 0.16/0.38  % SZS status Theorem for theBenchmark
% 0.16/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.38  % (6476)------------------------------
% 0.16/0.38  % (6476)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.16/0.38  % (6476)Termination reason: Refutation
% 0.16/0.38  
% 0.16/0.38  % (6476)Memory used [KB]: 1606
% 0.16/0.38  % (6476)Time elapsed: 0.046 s
% 0.16/0.38  % (6476)Instructions burned: 87 (million)
% 0.16/0.38  % (6471)Success in time 0.061 s
%------------------------------------------------------------------------------