TSTP Solution File: ALG039+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : ALG039+1 : TPTP v8.2.0. Released v2.7.0.
% 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 : Mon May 20 18:23:04 EDT 2024

% Result   : Theorem 0.21s 0.39s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   45
% Syntax   : Number of formulae    :  149 (  63 unt;   0 def)
%            Number of atoms       :  512 ( 368 equ)
%            Maximal formula atoms :   48 (   3 avg)
%            Number of connectives :  569 ( 206   ~; 133   |; 193   &)
%                                         (  37 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   49 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   42 (  40 usr;  41 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f375,plain,
    $false,
    inference(avatar_sat_refutation,[],[f189,f194,f199,f204,f209,f214,f219,f236,f253,f259,f264,f269,f274,f279,f284,f289,f294,f295,f300,f305,f310,f315,f320,f325,f330,f335,f340,f345,f350,f351,f354,f356,f361,f362,f366,f368,f369,f372,f374]) ).

fof(f374,plain,
    ( ~ spl3_1
    | spl3_14 ),
    inference(avatar_split_clause,[],[f30,f233,f174]) ).

fof(f174,plain,
    ( spl3_1
  <=> sP0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

fof(f233,plain,
    ( spl3_14
  <=> e0 = op(e3,e3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_14])]) ).

fof(f30,plain,
    ( e0 = op(e3,e3)
    | ~ sP0 ),
    inference(cnf_transformation,[],[f18]) ).

fof(f18,plain,
    ( ( e0 = op(e3,e3)
      & e0 = op(e2,e2)
      & e0 = op(e1,e1)
      & e0 = op(e0,e0) )
    | ~ sP0 ),
    inference(nnf_transformation,[],[f12]) ).

fof(f12,plain,
    ( ( e0 = op(e3,e3)
      & e0 = op(e2,e2)
      & e0 = op(e1,e1)
      & e0 = op(e0,e0) )
    | ~ sP0 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f372,plain,
    ( ~ spl3_1
    | spl3_13 ),
    inference(avatar_split_clause,[],[f29,f229,f174]) ).

fof(f229,plain,
    ( spl3_13
  <=> e0 = op(e2,e2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_13])]) ).

fof(f29,plain,
    ( e0 = op(e2,e2)
    | ~ sP0 ),
    inference(cnf_transformation,[],[f18]) ).

fof(f369,plain,
    ( ~ spl3_1
    | spl3_11 ),
    inference(avatar_split_clause,[],[f27,f221,f174]) ).

fof(f221,plain,
    ( spl3_11
  <=> e0 = op(e0,e0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_11])]) ).

fof(f27,plain,
    ( e0 = op(e0,e0)
    | ~ sP0 ),
    inference(cnf_transformation,[],[f18]) ).

fof(f368,plain,
    ( ~ spl3_1
    | spl3_7
    | ~ spl3_4 ),
    inference(avatar_split_clause,[],[f367,f186,f201,f174]) ).

fof(f201,plain,
    ( spl3_7
  <=> e0 = e3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_7])]) ).

fof(f186,plain,
    ( spl3_4
  <=> op(e0,e0) = e3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).

fof(f367,plain,
    ( e0 = e3
    | ~ sP0
    | ~ spl3_4 ),
    inference(forward_demodulation,[],[f27,f188]) ).

fof(f188,plain,
    ( op(e0,e0) = e3
    | ~ spl3_4 ),
    inference(avatar_component_clause,[],[f186]) ).

fof(f366,plain,
    ( spl3_1
    | spl3_2
    | spl3_3
    | spl3_7
    | ~ spl3_12 ),
    inference(avatar_split_clause,[],[f357,f225,f201,f182,f178,f174]) ).

fof(f178,plain,
    ( spl3_2
  <=> sP1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).

fof(f182,plain,
    ( spl3_3
  <=> sP2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).

fof(f225,plain,
    ( spl3_12
  <=> e0 = op(e1,e1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_12])]) ).

fof(f357,plain,
    ( e0 = e3
    | sP2
    | sP1
    | sP0
    | ~ spl3_12 ),
    inference(forward_demodulation,[],[f32,f226]) ).

fof(f226,plain,
    ( e0 = op(e1,e1)
    | ~ spl3_12 ),
    inference(avatar_component_clause,[],[f225]) ).

fof(f32,plain,
    ( e3 = op(e1,e1)
    | sP2
    | sP1
    | sP0 ),
    inference(cnf_transformation,[],[f15]) ).

fof(f15,plain,
    ( ( e3 != op(e3,e3)
      | e3 != op(e2,e2)
      | e3 != op(e1,e1)
      | op(e0,e0) != e3 )
    & ( e2 != op(e3,e3)
      | e2 != op(e2,e2)
      | e2 != op(e1,e1)
      | op(e0,e0) != e2 )
    & ( e1 != op(e3,e3)
      | e1 != op(e2,e2)
      | e1 != op(e1,e1)
      | op(e0,e0) != e1 )
    & ( e0 != op(e3,e3)
      | e0 != op(e2,e2)
      | e0 != op(e1,e1)
      | e0 != op(e0,e0) )
    & ( ( e3 = op(e3,e3)
        & e3 = op(e2,e2)
        & e3 = op(e1,e1)
        & op(e0,e0) = e3 )
      | sP2
      | sP1
      | sP0 ) ),
    inference(definition_folding,[],[f11,f14,f13,f12]) ).

fof(f13,plain,
    ( ( e1 = op(e3,e3)
      & e1 = op(e2,e2)
      & e1 = op(e1,e1)
      & op(e0,e0) = e1 )
    | ~ sP1 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f14,plain,
    ( ( e2 = op(e3,e3)
      & e2 = op(e2,e2)
      & e2 = op(e1,e1)
      & op(e0,e0) = e2 )
    | ~ sP2 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

fof(f11,plain,
    ( ( e3 != op(e3,e3)
      | e3 != op(e2,e2)
      | e3 != op(e1,e1)
      | op(e0,e0) != e3 )
    & ( e2 != op(e3,e3)
      | e2 != op(e2,e2)
      | e2 != op(e1,e1)
      | op(e0,e0) != e2 )
    & ( e1 != op(e3,e3)
      | e1 != op(e2,e2)
      | e1 != op(e1,e1)
      | op(e0,e0) != e1 )
    & ( e0 != op(e3,e3)
      | e0 != op(e2,e2)
      | e0 != op(e1,e1)
      | e0 != op(e0,e0) )
    & ( ( e3 = op(e3,e3)
        & e3 = op(e2,e2)
        & e3 = op(e1,e1)
        & op(e0,e0) = e3 )
      | ( e2 = op(e3,e3)
        & e2 = op(e2,e2)
        & e2 = op(e1,e1)
        & op(e0,e0) = e2 )
      | ( e1 = op(e3,e3)
        & e1 = op(e2,e2)
        & e1 = op(e1,e1)
        & op(e0,e0) = e1 )
      | ( e0 = op(e3,e3)
        & e0 = op(e2,e2)
        & e0 = op(e1,e1)
        & e0 = op(e0,e0) ) ) ),
    inference(flattening,[],[f10]) ).

fof(f10,plain,
    ( ( e3 != op(e3,e3)
      | e3 != op(e2,e2)
      | e3 != op(e1,e1)
      | op(e0,e0) != e3 )
    & ( e2 != op(e3,e3)
      | e2 != op(e2,e2)
      | e2 != op(e1,e1)
      | op(e0,e0) != e2 )
    & ( e1 != op(e3,e3)
      | e1 != op(e2,e2)
      | e1 != op(e1,e1)
      | op(e0,e0) != e1 )
    & ( e0 != op(e3,e3)
      | e0 != op(e2,e2)
      | e0 != op(e1,e1)
      | e0 != op(e0,e0) )
    & ( ( e3 = op(e3,e3)
        & e3 = op(e2,e2)
        & e3 = op(e1,e1)
        & op(e0,e0) = e3 )
      | ( e2 = op(e3,e3)
        & e2 = op(e2,e2)
        & e2 = op(e1,e1)
        & op(e0,e0) = e2 )
      | ( e1 = op(e3,e3)
        & e1 = op(e2,e2)
        & e1 = op(e1,e1)
        & op(e0,e0) = e1 )
      | ( e0 = op(e3,e3)
        & e0 = op(e2,e2)
        & e0 = op(e1,e1)
        & e0 = op(e0,e0) ) ) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,plain,
    ( ~ ( ( e3 = op(e3,e3)
          & e3 = op(e2,e2)
          & e3 = op(e1,e1)
          & op(e0,e0) = e3 )
        | ( e2 = op(e3,e3)
          & e2 = op(e2,e2)
          & e2 = op(e1,e1)
          & op(e0,e0) = e2 )
        | ( e1 = op(e3,e3)
          & e1 = op(e2,e2)
          & e1 = op(e1,e1)
          & op(e0,e0) = e1 )
        | ( e0 = op(e3,e3)
          & e0 = op(e2,e2)
          & e0 = op(e1,e1)
          & e0 = op(e0,e0) ) )
    & ( ( e3 = op(e3,e3)
        & e3 = op(e2,e2)
        & e3 = op(e1,e1)
        & op(e0,e0) = e3 )
      | ( e2 = op(e3,e3)
        & e2 = op(e2,e2)
        & e2 = op(e1,e1)
        & op(e0,e0) = e2 )
      | ( e1 = op(e3,e3)
        & e1 = op(e2,e2)
        & e1 = op(e1,e1)
        & op(e0,e0) = e1 )
      | ( e0 = op(e3,e3)
        & e0 = op(e2,e2)
        & e0 = op(e1,e1)
        & e0 = op(e0,e0) ) ) ),
    inference(flattening,[],[f8]) ).

fof(f8,negated_conjecture,
    ~ ~ ( ~ ( ( e3 = op(e3,e3)
              & e3 = op(e2,e2)
              & e3 = op(e1,e1)
              & op(e0,e0) = e3 )
            | ( e2 = op(e3,e3)
              & e2 = op(e2,e2)
              & e2 = op(e1,e1)
              & op(e0,e0) = e2 )
            | ( e1 = op(e3,e3)
              & e1 = op(e2,e2)
              & e1 = op(e1,e1)
              & op(e0,e0) = e1 )
            | ( e0 = op(e3,e3)
              & e0 = op(e2,e2)
              & e0 = op(e1,e1)
              & e0 = op(e0,e0) ) )
        & ( ( e3 = op(e3,e3)
            & e3 = op(e2,e2)
            & e3 = op(e1,e1)
            & op(e0,e0) = e3 )
          | ( e2 = op(e3,e3)
            & e2 = op(e2,e2)
            & e2 = op(e1,e1)
            & op(e0,e0) = e2 )
          | ( e1 = op(e3,e3)
            & e1 = op(e2,e2)
            & e1 = op(e1,e1)
            & op(e0,e0) = e1 )
          | ( e0 = op(e3,e3)
            & e0 = op(e2,e2)
            & e0 = op(e1,e1)
            & e0 = op(e0,e0) ) ) ),
    inference(negated_conjecture,[],[f7]) ).

fof(f7,conjecture,
    ~ ( ~ ( ( e3 = op(e3,e3)
            & e3 = op(e2,e2)
            & e3 = op(e1,e1)
            & op(e0,e0) = e3 )
          | ( e2 = op(e3,e3)
            & e2 = op(e2,e2)
            & e2 = op(e1,e1)
            & op(e0,e0) = e2 )
          | ( e1 = op(e3,e3)
            & e1 = op(e2,e2)
            & e1 = op(e1,e1)
            & op(e0,e0) = e1 )
          | ( e0 = op(e3,e3)
            & e0 = op(e2,e2)
            & e0 = op(e1,e1)
            & e0 = op(e0,e0) ) )
      & ( ( e3 = op(e3,e3)
          & e3 = op(e2,e2)
          & e3 = op(e1,e1)
          & op(e0,e0) = e3 )
        | ( e2 = op(e3,e3)
          & e2 = op(e2,e2)
          & e2 = op(e1,e1)
          & op(e0,e0) = e2 )
        | ( e1 = op(e3,e3)
          & e1 = op(e2,e2)
          & e1 = op(e1,e1)
          & op(e0,e0) = e1 )
        | ( e0 = op(e3,e3)
          & e0 = op(e2,e2)
          & e0 = op(e1,e1)
          & e0 = op(e0,e0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(f362,plain,
    ( ~ spl3_3
    | spl3_6
    | ~ spl3_12 ),
    inference(avatar_split_clause,[],[f359,f225,f196,f182]) ).

fof(f196,plain,
    ( spl3_6
  <=> e0 = e2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).

fof(f359,plain,
    ( e0 = e2
    | ~ sP2
    | ~ spl3_12 ),
    inference(forward_demodulation,[],[f20,f226]) ).

fof(f20,plain,
    ( e2 = op(e1,e1)
    | ~ sP2 ),
    inference(cnf_transformation,[],[f16]) ).

fof(f16,plain,
    ( ( e2 = op(e3,e3)
      & e2 = op(e2,e2)
      & e2 = op(e1,e1)
      & op(e0,e0) = e2 )
    | ~ sP2 ),
    inference(nnf_transformation,[],[f14]) ).

fof(f361,plain,
    ( ~ spl3_3
    | spl3_8
    | ~ spl3_15 ),
    inference(avatar_split_clause,[],[f358,f238,f206,f182]) ).

fof(f206,plain,
    ( spl3_8
  <=> e1 = e2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_8])]) ).

fof(f238,plain,
    ( spl3_15
  <=> op(e0,e0) = e1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_15])]) ).

fof(f358,plain,
    ( e1 = e2
    | ~ sP2
    | ~ spl3_15 ),
    inference(forward_demodulation,[],[f19,f239]) ).

fof(f239,plain,
    ( op(e0,e0) = e1
    | ~ spl3_15 ),
    inference(avatar_component_clause,[],[f238]) ).

fof(f19,plain,
    ( op(e0,e0) = e2
    | ~ sP2 ),
    inference(cnf_transformation,[],[f16]) ).

fof(f356,plain,
    ( spl3_5
    | ~ spl3_12
    | ~ spl3_16 ),
    inference(avatar_split_clause,[],[f355,f242,f225,f191]) ).

fof(f191,plain,
    ( spl3_5
  <=> e0 = e1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).

fof(f242,plain,
    ( spl3_16
  <=> e1 = op(e1,e1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_16])]) ).

fof(f355,plain,
    ( e0 = e1
    | ~ spl3_12
    | ~ spl3_16 ),
    inference(forward_demodulation,[],[f243,f226]) ).

fof(f243,plain,
    ( e1 = op(e1,e1)
    | ~ spl3_16 ),
    inference(avatar_component_clause,[],[f242]) ).

fof(f354,plain,
    ( ~ spl3_2
    | spl3_16 ),
    inference(avatar_split_clause,[],[f24,f242,f178]) ).

fof(f24,plain,
    ( e1 = op(e1,e1)
    | ~ sP1 ),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,plain,
    ( ( e1 = op(e3,e3)
      & e1 = op(e2,e2)
      & e1 = op(e1,e1)
      & op(e0,e0) = e1 )
    | ~ sP1 ),
    inference(nnf_transformation,[],[f13]) ).

fof(f351,plain,
    ( ~ spl3_2
    | spl3_15 ),
    inference(avatar_split_clause,[],[f23,f238,f178]) ).

fof(f23,plain,
    ( op(e0,e0) = e1
    | ~ sP1 ),
    inference(cnf_transformation,[],[f17]) ).

fof(f350,plain,
    ~ spl3_37,
    inference(avatar_split_clause,[],[f163,f347]) ).

fof(f347,plain,
    ( spl3_37
  <=> e0 = op(e0,e1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_37])]) ).

fof(f163,plain,
    e0 != op(e0,e1),
    inference(forward_demodulation,[],[f62,f54]) ).

fof(f54,plain,
    e0 = op(e1,e1),
    inference(cnf_transformation,[],[f6]) ).

fof(f6,axiom,
    ( e2 = op(e3,e1)
    & e0 = op(e1,e1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6) ).

fof(f62,plain,
    op(e0,e1) != op(e1,e1),
    inference(cnf_transformation,[],[f4]) ).

fof(f4,axiom,
    ( op(e3,e2) != op(e3,e3)
    & op(e3,e1) != op(e3,e3)
    & op(e3,e1) != op(e3,e2)
    & op(e3,e0) != op(e3,e3)
    & op(e3,e0) != op(e3,e2)
    & op(e3,e0) != op(e3,e1)
    & op(e2,e2) != op(e2,e3)
    & op(e2,e1) != op(e2,e3)
    & op(e2,e1) != op(e2,e2)
    & op(e2,e0) != op(e2,e3)
    & op(e2,e0) != op(e2,e2)
    & op(e2,e0) != op(e2,e1)
    & op(e1,e2) != op(e1,e3)
    & op(e1,e1) != op(e1,e3)
    & op(e1,e1) != op(e1,e2)
    & op(e1,e0) != op(e1,e3)
    & op(e1,e0) != op(e1,e2)
    & op(e1,e0) != op(e1,e1)
    & op(e0,e2) != op(e0,e3)
    & op(e0,e1) != op(e0,e3)
    & op(e0,e1) != op(e0,e2)
    & op(e0,e0) != op(e0,e3)
    & op(e0,e0) != op(e0,e2)
    & op(e0,e0) != op(e0,e1)
    & op(e2,e3) != op(e3,e3)
    & op(e1,e3) != op(e3,e3)
    & op(e1,e3) != op(e2,e3)
    & op(e0,e3) != op(e3,e3)
    & op(e0,e3) != op(e2,e3)
    & op(e0,e3) != op(e1,e3)
    & op(e2,e2) != op(e3,e2)
    & op(e1,e2) != op(e3,e2)
    & op(e1,e2) != op(e2,e2)
    & op(e0,e2) != op(e3,e2)
    & op(e0,e2) != op(e2,e2)
    & op(e0,e2) != op(e1,e2)
    & op(e2,e1) != op(e3,e1)
    & op(e1,e1) != op(e3,e1)
    & op(e1,e1) != op(e2,e1)
    & op(e0,e1) != op(e3,e1)
    & op(e0,e1) != op(e2,e1)
    & op(e0,e1) != op(e1,e1)
    & op(e2,e0) != op(e3,e0)
    & op(e1,e0) != op(e3,e0)
    & op(e1,e0) != op(e2,e0)
    & op(e0,e0) != op(e3,e0)
    & op(e0,e0) != op(e2,e0)
    & op(e0,e0) != op(e1,e0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).

fof(f345,plain,
    ~ spl3_36,
    inference(avatar_split_clause,[],[f162,f342]) ).

fof(f342,plain,
    ( spl3_36
  <=> e2 = op(e0,e1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_36])]) ).

fof(f162,plain,
    e2 != op(e0,e1),
    inference(forward_demodulation,[],[f64,f55]) ).

fof(f55,plain,
    e2 = op(e3,e1),
    inference(cnf_transformation,[],[f6]) ).

fof(f64,plain,
    op(e0,e1) != op(e3,e1),
    inference(cnf_transformation,[],[f4]) ).

fof(f340,plain,
    ~ spl3_35,
    inference(avatar_split_clause,[],[f161,f337]) ).

fof(f337,plain,
    ( spl3_35
  <=> e0 = op(e2,e1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_35])]) ).

fof(f161,plain,
    e0 != op(e2,e1),
    inference(forward_demodulation,[],[f65,f54]) ).

fof(f65,plain,
    op(e1,e1) != op(e2,e1),
    inference(cnf_transformation,[],[f4]) ).

fof(f335,plain,
    ~ spl3_34,
    inference(avatar_split_clause,[],[f158,f332]) ).

fof(f332,plain,
    ( spl3_34
  <=> e2 = op(e2,e1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_34])]) ).

fof(f158,plain,
    e2 != op(e2,e1),
    inference(forward_demodulation,[],[f67,f55]) ).

fof(f67,plain,
    op(e2,e1) != op(e3,e1),
    inference(cnf_transformation,[],[f4]) ).

fof(f330,plain,
    ~ spl3_33,
    inference(avatar_split_clause,[],[f157,f327]) ).

fof(f327,plain,
    ( spl3_33
  <=> e0 = op(e1,e0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_33])]) ).

fof(f157,plain,
    e0 != op(e1,e0),
    inference(forward_demodulation,[],[f86,f54]) ).

fof(f86,plain,
    op(e1,e0) != op(e1,e1),
    inference(cnf_transformation,[],[f4]) ).

fof(f325,plain,
    ~ spl3_32,
    inference(avatar_split_clause,[],[f156,f322]) ).

fof(f322,plain,
    ( spl3_32
  <=> e0 = op(e1,e2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_32])]) ).

fof(f156,plain,
    e0 != op(e1,e2),
    inference(forward_demodulation,[],[f89,f54]) ).

fof(f89,plain,
    op(e1,e1) != op(e1,e2),
    inference(cnf_transformation,[],[f4]) ).

fof(f320,plain,
    ~ spl3_31,
    inference(avatar_split_clause,[],[f155,f317]) ).

fof(f317,plain,
    ( spl3_31
  <=> e0 = op(e1,e3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_31])]) ).

fof(f155,plain,
    e0 != op(e1,e3),
    inference(forward_demodulation,[],[f90,f54]) ).

fof(f90,plain,
    op(e1,e1) != op(e1,e3),
    inference(cnf_transformation,[],[f4]) ).

fof(f315,plain,
    ~ spl3_30,
    inference(avatar_split_clause,[],[f154,f312]) ).

fof(f312,plain,
    ( spl3_30
  <=> e2 = op(e3,e0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_30])]) ).

fof(f154,plain,
    e2 != op(e3,e0),
    inference(forward_demodulation,[],[f98,f55]) ).

fof(f98,plain,
    op(e3,e0) != op(e3,e1),
    inference(cnf_transformation,[],[f4]) ).

fof(f310,plain,
    ~ spl3_29,
    inference(avatar_split_clause,[],[f153,f307]) ).

fof(f307,plain,
    ( spl3_29
  <=> e2 = op(e3,e2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_29])]) ).

fof(f153,plain,
    e2 != op(e3,e2),
    inference(forward_demodulation,[],[f101,f55]) ).

fof(f101,plain,
    op(e3,e1) != op(e3,e2),
    inference(cnf_transformation,[],[f4]) ).

fof(f305,plain,
    ~ spl3_28,
    inference(avatar_split_clause,[],[f152,f302]) ).

fof(f302,plain,
    ( spl3_28
  <=> e2 = op(e3,e3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_28])]) ).

fof(f152,plain,
    e2 != op(e3,e3),
    inference(forward_demodulation,[],[f102,f55]) ).

fof(f102,plain,
    op(e3,e1) != op(e3,e3),
    inference(cnf_transformation,[],[f4]) ).

fof(f300,plain,
    spl3_27,
    inference(avatar_split_clause,[],[f55,f297]) ).

fof(f297,plain,
    ( spl3_27
  <=> e2 = op(e3,e1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_27])]) ).

fof(f295,plain,
    spl3_12,
    inference(avatar_split_clause,[],[f54,f225]) ).

fof(f294,plain,
    spl3_26,
    inference(avatar_split_clause,[],[f52,f291]) ).

fof(f291,plain,
    ( spl3_26
  <=> e3 = op(e3,unit) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_26])]) ).

fof(f52,plain,
    e3 = op(e3,unit),
    inference(cnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ( ( e3 = unit
      | e2 = unit
      | e1 = unit
      | e0 = unit )
    & e3 = op(e3,unit)
    & e3 = op(unit,e3)
    & e2 = op(e2,unit)
    & e2 = op(unit,e2)
    & e1 = op(e1,unit)
    & e1 = op(unit,e1)
    & e0 = op(e0,unit)
    & e0 = op(unit,e0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).

fof(f289,plain,
    spl3_25,
    inference(avatar_split_clause,[],[f51,f286]) ).

fof(f286,plain,
    ( spl3_25
  <=> e3 = op(unit,e3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_25])]) ).

fof(f51,plain,
    e3 = op(unit,e3),
    inference(cnf_transformation,[],[f2]) ).

fof(f284,plain,
    spl3_24,
    inference(avatar_split_clause,[],[f50,f281]) ).

fof(f281,plain,
    ( spl3_24
  <=> e2 = op(e2,unit) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_24])]) ).

fof(f50,plain,
    e2 = op(e2,unit),
    inference(cnf_transformation,[],[f2]) ).

fof(f279,plain,
    spl3_23,
    inference(avatar_split_clause,[],[f49,f276]) ).

fof(f276,plain,
    ( spl3_23
  <=> e2 = op(unit,e2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_23])]) ).

fof(f49,plain,
    e2 = op(unit,e2),
    inference(cnf_transformation,[],[f2]) ).

fof(f274,plain,
    spl3_22,
    inference(avatar_split_clause,[],[f48,f271]) ).

fof(f271,plain,
    ( spl3_22
  <=> e1 = op(e1,unit) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_22])]) ).

fof(f48,plain,
    e1 = op(e1,unit),
    inference(cnf_transformation,[],[f2]) ).

fof(f269,plain,
    spl3_21,
    inference(avatar_split_clause,[],[f47,f266]) ).

fof(f266,plain,
    ( spl3_21
  <=> e1 = op(unit,e1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_21])]) ).

fof(f47,plain,
    e1 = op(unit,e1),
    inference(cnf_transformation,[],[f2]) ).

fof(f264,plain,
    spl3_20,
    inference(avatar_split_clause,[],[f46,f261]) ).

fof(f261,plain,
    ( spl3_20
  <=> e0 = op(e0,unit) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_20])]) ).

fof(f46,plain,
    e0 = op(e0,unit),
    inference(cnf_transformation,[],[f2]) ).

fof(f259,plain,
    spl3_19,
    inference(avatar_split_clause,[],[f45,f256]) ).

fof(f256,plain,
    ( spl3_19
  <=> e0 = op(unit,e0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_19])]) ).

fof(f45,plain,
    e0 = op(unit,e0),
    inference(cnf_transformation,[],[f2]) ).

fof(f253,plain,
    ( ~ spl3_15
    | ~ spl3_16
    | ~ spl3_17
    | ~ spl3_18 ),
    inference(avatar_split_clause,[],[f36,f250,f246,f242,f238]) ).

fof(f246,plain,
    ( spl3_17
  <=> e1 = op(e2,e2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_17])]) ).

fof(f250,plain,
    ( spl3_18
  <=> e1 = op(e3,e3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_18])]) ).

fof(f36,plain,
    ( e1 != op(e3,e3)
    | e1 != op(e2,e2)
    | e1 != op(e1,e1)
    | op(e0,e0) != e1 ),
    inference(cnf_transformation,[],[f15]) ).

fof(f236,plain,
    ( ~ spl3_11
    | ~ spl3_12
    | ~ spl3_13
    | ~ spl3_14 ),
    inference(avatar_split_clause,[],[f35,f233,f229,f225,f221]) ).

fof(f35,plain,
    ( e0 != op(e3,e3)
    | e0 != op(e2,e2)
    | e0 != op(e1,e1)
    | e0 != op(e0,e0) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f219,plain,
    ~ spl3_10,
    inference(avatar_split_clause,[],[f44,f216]) ).

fof(f216,plain,
    ( spl3_10
  <=> e2 = e3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_10])]) ).

fof(f44,plain,
    e2 != e3,
    inference(cnf_transformation,[],[f5]) ).

fof(f5,axiom,
    ( e2 != e3
    & e1 != e3
    & e1 != e2
    & e0 != e3
    & e0 != e2
    & e0 != e1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).

fof(f214,plain,
    ~ spl3_9,
    inference(avatar_split_clause,[],[f43,f211]) ).

fof(f211,plain,
    ( spl3_9
  <=> e1 = e3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_9])]) ).

fof(f43,plain,
    e1 != e3,
    inference(cnf_transformation,[],[f5]) ).

fof(f209,plain,
    ~ spl3_8,
    inference(avatar_split_clause,[],[f42,f206]) ).

fof(f42,plain,
    e1 != e2,
    inference(cnf_transformation,[],[f5]) ).

fof(f204,plain,
    ~ spl3_7,
    inference(avatar_split_clause,[],[f41,f201]) ).

fof(f41,plain,
    e0 != e3,
    inference(cnf_transformation,[],[f5]) ).

fof(f199,plain,
    ~ spl3_6,
    inference(avatar_split_clause,[],[f40,f196]) ).

fof(f40,plain,
    e0 != e2,
    inference(cnf_transformation,[],[f5]) ).

fof(f194,plain,
    ~ spl3_5,
    inference(avatar_split_clause,[],[f39,f191]) ).

fof(f39,plain,
    e0 != e1,
    inference(cnf_transformation,[],[f5]) ).

fof(f189,plain,
    ( spl3_1
    | spl3_2
    | spl3_3
    | spl3_4 ),
    inference(avatar_split_clause,[],[f31,f186,f182,f178,f174]) ).

fof(f31,plain,
    ( op(e0,e0) = e3
    | sP2
    | sP1
    | sP0 ),
    inference(cnf_transformation,[],[f15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : ALG039+1 : TPTP v8.2.0. Released v2.7.0.
% 0.03/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n025.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Sat May 18 23:27:08 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  % (20566)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.38  % (20577)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.38  % (20576)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.38  % (20579)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.38  % (20581)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)
% 0.21/0.38  % (20580)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)
% 0.21/0.38  % (20582)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)
% 0.21/0.38  % (20578)WARNING: value z3 for option sas not known
% 0.21/0.39  % (20578)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)
% 0.21/0.39  % (20580)First to succeed.
% 0.21/0.39  % (20578)Also succeeded, but the first one will report.
% 0.21/0.39  % (20580)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-20566"
% 0.21/0.39  Detected minimum model sizes of [4]
% 0.21/0.39  Detected maximum model sizes of [max]
% 0.21/0.39  % (20580)Refutation found. Thanks to Tanya!
% 0.21/0.39  % SZS status Theorem for theBenchmark
% 0.21/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.39  % (20580)------------------------------
% 0.21/0.39  % (20580)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.39  % (20580)Termination reason: Refutation
% 0.21/0.39  
% 0.21/0.39  % (20580)Memory used [KB]: 937
% 0.21/0.39  % (20580)Time elapsed: 0.013 s
% 0.21/0.39  % (20580)Instructions burned: 21 (million)
% 0.21/0.39  % (20566)Success in time 0.033 s
%------------------------------------------------------------------------------