TSTP Solution File: ALG069-10 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : ALG069-10 : TPTP v8.2.0. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n006.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 18:25:43 EDT 2024

% Result   : Unsatisfiable 0.14s 0.41s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   83
% Syntax   : Number of formulae    :  285 (  29 unt;   0 def)
%            Number of atoms       :  751 ( 213 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  873 ( 407   ~; 397   |;   0   &)
%                                         (  69 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :   71 (  69 usr;  70 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   2 con; 0-4 aty)
%            Number of variables   :  117 ( 117   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f841,plain,
    $false,
    inference(avatar_sat_refutation,[],[f18,f22,f26,f30,f35,f41,f45,f50,f57,f61,f65,f69,f75,f79,f83,f87,f98,f106,f110,f120,f124,f131,f141,f177,f183,f192,f198,f207,f212,f237,f248,f254,f267,f284,f289,f322,f365,f379,f395,f402,f406,f419,f442,f447,f455,f498,f510,f515,f524,f528,f537,f541,f553,f558,f568,f572,f577,f584,f600,f605,f610,f616,f631,f636,f667,f765,f770,f778,f797,f825]) ).

fof(f825,plain,
    ( ~ spl0_9
    | ~ spl0_12
    | ~ spl0_58
    | ~ spl0_67 ),
    inference(avatar_contradiction_clause,[],[f824]) ).

fof(f824,plain,
    ( $false
    | ~ spl0_9
    | ~ spl0_12
    | ~ spl0_58
    | ~ spl0_67 ),
    inference(trivial_inequality_removal,[],[f823]) ).

fof(f823,plain,
    ( tuple(sK1_ax4_U,true) != tuple(sK1_ax4_U,true)
    | ~ spl0_9
    | ~ spl0_12
    | ~ spl0_58
    | ~ spl0_67 ),
    inference(forward_demodulation,[],[f804,f773]) ).

fof(f773,plain,
    ( sK1_ax4_U = op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U))))
    | ~ spl0_9
    | ~ spl0_67 ),
    inference(superposition,[],[f769,f56]) ).

fof(f56,plain,
    ( ! [X2,X0,X1] : ifeq2(X0,X0,X1,X2) = X1
    | ~ spl0_9 ),
    inference(avatar_component_clause,[],[f55]) ).

fof(f55,plain,
    ( spl0_9
  <=> ! [X2,X0,X1] : ifeq2(X0,X0,X1,X2) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f769,plain,
    ( sK1_ax4_U = ifeq2(true,true,op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))),sK1_ax4_U)
    | ~ spl0_67 ),
    inference(avatar_component_clause,[],[f767]) ).

fof(f767,plain,
    ( spl0_67
  <=> sK1_ax4_U = ifeq2(true,true,op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))),sK1_ax4_U) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).

fof(f804,plain,
    ( tuple(sK1_ax4_U,true) != tuple(op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))),true)
    | ~ spl0_12
    | ~ spl0_58 ),
    inference(superposition,[],[f68,f583]) ).

fof(f583,plain,
    ( true = sorti2(h(sK2_ax3_V(j(sK1_ax4_U))))
    | ~ spl0_58 ),
    inference(avatar_component_clause,[],[f581]) ).

fof(f581,plain,
    ( spl0_58
  <=> true = sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).

fof(f68,plain,
    ( ! [X3] : tuple(op2(X3,X3),sorti2(X3)) != tuple(sK1_ax4_U,true)
    | ~ spl0_12 ),
    inference(avatar_component_clause,[],[f67]) ).

fof(f67,plain,
    ( spl0_12
  <=> ! [X3] : tuple(op2(X3,X3),sorti2(X3)) != tuple(sK1_ax4_U,true) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f797,plain,
    ( spl0_69
    | ~ spl0_14
    | ~ spl0_35 ),
    inference(avatar_split_clause,[],[f347,f286,f77,f794]) ).

fof(f794,plain,
    ( spl0_69
  <=> sK2_ax3_V(j(sK1_ax4_U)) = ifeq2(true,true,op1(sK2_ax3_V(sK2_ax3_V(j(sK1_ax4_U))),sK2_ax3_V(sK2_ax3_V(j(sK1_ax4_U)))),sK2_ax3_V(j(sK1_ax4_U))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).

fof(f77,plain,
    ( spl0_14
  <=> ! [X4] : ifeq2(sorti1(X4),true,op1(sK2_ax3_V(X4),sK2_ax3_V(X4)),X4) = X4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f286,plain,
    ( spl0_35
  <=> true = sorti1(sK2_ax3_V(j(sK1_ax4_U))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

fof(f347,plain,
    ( sK2_ax3_V(j(sK1_ax4_U)) = ifeq2(true,true,op1(sK2_ax3_V(sK2_ax3_V(j(sK1_ax4_U))),sK2_ax3_V(sK2_ax3_V(j(sK1_ax4_U)))),sK2_ax3_V(j(sK1_ax4_U)))
    | ~ spl0_14
    | ~ spl0_35 ),
    inference(superposition,[],[f78,f288]) ).

fof(f288,plain,
    ( true = sorti1(sK2_ax3_V(j(sK1_ax4_U)))
    | ~ spl0_35 ),
    inference(avatar_component_clause,[],[f286]) ).

fof(f78,plain,
    ( ! [X4] : ifeq2(sorti1(X4),true,op1(sK2_ax3_V(X4),sK2_ax3_V(X4)),X4) = X4
    | ~ spl0_14 ),
    inference(avatar_component_clause,[],[f77]) ).

fof(f778,plain,
    ( spl0_68
    | ~ spl0_15
    | ~ spl0_35 ),
    inference(avatar_split_clause,[],[f348,f286,f81,f776]) ).

fof(f776,plain,
    ( spl0_68
  <=> ! [X0] : true = ifeq(true,true,ifeq(sorti1(X0),true,sorti1(op1(X0,sK2_ax3_V(j(sK1_ax4_U)))),true),true) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).

fof(f81,plain,
    ( spl0_15
  <=> ! [X4,X3] : true = ifeq(sorti1(X3),true,ifeq(sorti1(X4),true,sorti1(op1(X4,X3)),true),true) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f348,plain,
    ( ! [X0] : true = ifeq(true,true,ifeq(sorti1(X0),true,sorti1(op1(X0,sK2_ax3_V(j(sK1_ax4_U)))),true),true)
    | ~ spl0_15
    | ~ spl0_35 ),
    inference(superposition,[],[f82,f288]) ).

fof(f82,plain,
    ( ! [X3,X4] : true = ifeq(sorti1(X3),true,ifeq(sorti1(X4),true,sorti1(op1(X4,X3)),true),true)
    | ~ spl0_15 ),
    inference(avatar_component_clause,[],[f81]) ).

fof(f770,plain,
    ( spl0_67
    | ~ spl0_6
    | ~ spl0_9
    | ~ spl0_18
    | ~ spl0_35
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f390,f376,f286,f103,f55,f39,f767]) ).

fof(f39,plain,
    ( spl0_6
  <=> ! [X6,X5] : h(op1(X6,X5)) = ifeq2(sorti1(X5),true,ifeq2(sorti1(X6),true,op2(h(X6),h(X5)),h(op1(X6,X5))),h(op1(X6,X5))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f103,plain,
    ( spl0_18
  <=> sK1_ax4_U = h(j(sK1_ax4_U)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f376,plain,
    ( spl0_38
  <=> j(sK1_ax4_U) = op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

fof(f390,plain,
    ( sK1_ax4_U = ifeq2(true,true,op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))),sK1_ax4_U)
    | ~ spl0_6
    | ~ spl0_9
    | ~ spl0_18
    | ~ spl0_35
    | ~ spl0_38 ),
    inference(forward_demodulation,[],[f389,f56]) ).

fof(f389,plain,
    ( sK1_ax4_U = ifeq2(true,true,ifeq2(true,true,op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))),sK1_ax4_U),sK1_ax4_U)
    | ~ spl0_6
    | ~ spl0_18
    | ~ spl0_35
    | ~ spl0_38 ),
    inference(forward_demodulation,[],[f388,f288]) ).

fof(f388,plain,
    ( sK1_ax4_U = ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))),true,ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))),true,op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))),sK1_ax4_U),sK1_ax4_U)
    | ~ spl0_6
    | ~ spl0_18
    | ~ spl0_38 ),
    inference(forward_demodulation,[],[f383,f105]) ).

fof(f105,plain,
    ( sK1_ax4_U = h(j(sK1_ax4_U))
    | ~ spl0_18 ),
    inference(avatar_component_clause,[],[f103]) ).

fof(f383,plain,
    ( h(j(sK1_ax4_U)) = ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))),true,ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))),true,op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))),h(j(sK1_ax4_U))),h(j(sK1_ax4_U)))
    | ~ spl0_6
    | ~ spl0_38 ),
    inference(superposition,[],[f40,f378]) ).

fof(f378,plain,
    ( j(sK1_ax4_U) = op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U)))
    | ~ spl0_38 ),
    inference(avatar_component_clause,[],[f376]) ).

fof(f40,plain,
    ( ! [X6,X5] : h(op1(X6,X5)) = ifeq2(sorti1(X5),true,ifeq2(sorti1(X6),true,op2(h(X6),h(X5)),h(op1(X6,X5))),h(op1(X6,X5)))
    | ~ spl0_6 ),
    inference(avatar_component_clause,[],[f39]) ).

fof(f765,plain,
    ( spl0_66
    | ~ spl0_2
    | ~ spl0_35 ),
    inference(avatar_split_clause,[],[f343,f286,f20,f762]) ).

fof(f762,plain,
    ( spl0_66
  <=> sK2_ax3_V(j(sK1_ax4_U)) = ifeq2(true,true,j(h(sK2_ax3_V(j(sK1_ax4_U)))),sK2_ax3_V(j(sK1_ax4_U))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).

fof(f20,plain,
    ( spl0_2
  <=> ! [X7] : ifeq2(sorti1(X7),true,j(h(X7)),X7) = X7 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f343,plain,
    ( sK2_ax3_V(j(sK1_ax4_U)) = ifeq2(true,true,j(h(sK2_ax3_V(j(sK1_ax4_U)))),sK2_ax3_V(j(sK1_ax4_U)))
    | ~ spl0_2
    | ~ spl0_35 ),
    inference(superposition,[],[f21,f288]) ).

fof(f21,plain,
    ( ! [X7] : ifeq2(sorti1(X7),true,j(h(X7)),X7) = X7
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f20]) ).

fof(f667,plain,
    ( spl0_65
    | ~ spl0_10
    | ~ spl0_53 ),
    inference(avatar_split_clause,[],[f562,f550,f59,f664]) ).

fof(f664,plain,
    ( spl0_65
  <=> true = sorti1(sK2_ax3_V(sK2_ax3_V(j(sK1_ax4_U)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).

fof(f59,plain,
    ( spl0_10
  <=> ! [X2,X0,X1] : ifeq(X0,X0,X1,X2) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f550,plain,
    ( spl0_53
  <=> true = ifeq(true,true,sorti1(sK2_ax3_V(sK2_ax3_V(j(sK1_ax4_U)))),true) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).

fof(f562,plain,
    ( true = sorti1(sK2_ax3_V(sK2_ax3_V(j(sK1_ax4_U))))
    | ~ spl0_10
    | ~ spl0_53 ),
    inference(superposition,[],[f552,f60]) ).

fof(f60,plain,
    ( ! [X2,X0,X1] : ifeq(X0,X0,X1,X2) = X1
    | ~ spl0_10 ),
    inference(avatar_component_clause,[],[f59]) ).

fof(f552,plain,
    ( true = ifeq(true,true,sorti1(sK2_ax3_V(sK2_ax3_V(j(sK1_ax4_U)))),true)
    | ~ spl0_53 ),
    inference(avatar_component_clause,[],[f550]) ).

fof(f636,plain,
    ( spl0_64
    | ~ spl0_9
    | ~ spl0_44 ),
    inference(avatar_split_clause,[],[f450,f444,f55,f633]) ).

fof(f633,plain,
    ( spl0_64
  <=> j(op2(op2(sK1_ax4_U,sK1_ax4_U),sK1_ax4_U)) = op1(j(op2(sK1_ax4_U,sK1_ax4_U)),j(sK1_ax4_U)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).

fof(f444,plain,
    ( spl0_44
  <=> j(op2(op2(sK1_ax4_U,sK1_ax4_U),sK1_ax4_U)) = ifeq2(true,true,op1(j(op2(sK1_ax4_U,sK1_ax4_U)),j(sK1_ax4_U)),j(op2(op2(sK1_ax4_U,sK1_ax4_U),sK1_ax4_U))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

fof(f450,plain,
    ( j(op2(op2(sK1_ax4_U,sK1_ax4_U),sK1_ax4_U)) = op1(j(op2(sK1_ax4_U,sK1_ax4_U)),j(sK1_ax4_U))
    | ~ spl0_9
    | ~ spl0_44 ),
    inference(superposition,[],[f446,f56]) ).

fof(f446,plain,
    ( j(op2(op2(sK1_ax4_U,sK1_ax4_U),sK1_ax4_U)) = ifeq2(true,true,op1(j(op2(sK1_ax4_U,sK1_ax4_U)),j(sK1_ax4_U)),j(op2(op2(sK1_ax4_U,sK1_ax4_U),sK1_ax4_U)))
    | ~ spl0_44 ),
    inference(avatar_component_clause,[],[f444]) ).

fof(f631,plain,
    ( spl0_63
    | ~ spl0_9
    | ~ spl0_43 ),
    inference(avatar_split_clause,[],[f448,f439,f55,f628]) ).

fof(f628,plain,
    ( spl0_63
  <=> j(op2(sK1_ax4_U,op2(sK1_ax4_U,sK1_ax4_U))) = op1(j(sK1_ax4_U),j(op2(sK1_ax4_U,sK1_ax4_U))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).

fof(f439,plain,
    ( spl0_43
  <=> j(op2(sK1_ax4_U,op2(sK1_ax4_U,sK1_ax4_U))) = ifeq2(true,true,op1(j(sK1_ax4_U),j(op2(sK1_ax4_U,sK1_ax4_U))),j(op2(sK1_ax4_U,op2(sK1_ax4_U,sK1_ax4_U)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

fof(f448,plain,
    ( j(op2(sK1_ax4_U,op2(sK1_ax4_U,sK1_ax4_U))) = op1(j(sK1_ax4_U),j(op2(sK1_ax4_U,sK1_ax4_U)))
    | ~ spl0_9
    | ~ spl0_43 ),
    inference(superposition,[],[f441,f56]) ).

fof(f441,plain,
    ( j(op2(sK1_ax4_U,op2(sK1_ax4_U,sK1_ax4_U))) = ifeq2(true,true,op1(j(sK1_ax4_U),j(op2(sK1_ax4_U,sK1_ax4_U))),j(op2(sK1_ax4_U,op2(sK1_ax4_U,sK1_ax4_U))))
    | ~ spl0_43 ),
    inference(avatar_component_clause,[],[f439]) ).

fof(f616,plain,
    ( spl0_62
    | ~ spl0_9
    | ~ spl0_44
    | ~ spl0_61 ),
    inference(avatar_split_clause,[],[f611,f607,f444,f55,f613]) ).

fof(f613,plain,
    ( spl0_62
  <=> op2(op2(sK1_ax4_U,sK1_ax4_U),sK1_ax4_U) = h(j(op2(op2(sK1_ax4_U,sK1_ax4_U),sK1_ax4_U))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).

fof(f607,plain,
    ( spl0_61
  <=> op2(op2(sK1_ax4_U,sK1_ax4_U),sK1_ax4_U) = h(op1(j(op2(sK1_ax4_U,sK1_ax4_U)),j(sK1_ax4_U))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).

fof(f611,plain,
    ( op2(op2(sK1_ax4_U,sK1_ax4_U),sK1_ax4_U) = h(j(op2(op2(sK1_ax4_U,sK1_ax4_U),sK1_ax4_U)))
    | ~ spl0_9
    | ~ spl0_44
    | ~ spl0_61 ),
    inference(forward_demodulation,[],[f609,f450]) ).

fof(f609,plain,
    ( op2(op2(sK1_ax4_U,sK1_ax4_U),sK1_ax4_U) = h(op1(j(op2(sK1_ax4_U,sK1_ax4_U)),j(sK1_ax4_U)))
    | ~ spl0_61 ),
    inference(avatar_component_clause,[],[f607]) ).

fof(f610,plain,
    ( spl0_61
    | ~ spl0_9
    | ~ spl0_37
    | ~ spl0_40
    | ~ spl0_42 ),
    inference(avatar_split_clause,[],[f434,f417,f399,f362,f55,f607]) ).

fof(f362,plain,
    ( spl0_37
  <=> op2(sK1_ax4_U,sK1_ax4_U) = h(j(op2(sK1_ax4_U,sK1_ax4_U))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

fof(f399,plain,
    ( spl0_40
  <=> true = sorti1(j(op2(sK1_ax4_U,sK1_ax4_U))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

fof(f417,plain,
    ( spl0_42
  <=> ! [X0] : h(op1(X0,j(sK1_ax4_U))) = ifeq2(sorti1(X0),true,op2(h(X0),sK1_ax4_U),h(op1(X0,j(sK1_ax4_U)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

fof(f434,plain,
    ( op2(op2(sK1_ax4_U,sK1_ax4_U),sK1_ax4_U) = h(op1(j(op2(sK1_ax4_U,sK1_ax4_U)),j(sK1_ax4_U)))
    | ~ spl0_9
    | ~ spl0_37
    | ~ spl0_40
    | ~ spl0_42 ),
    inference(forward_demodulation,[],[f433,f56]) ).

fof(f433,plain,
    ( h(op1(j(op2(sK1_ax4_U,sK1_ax4_U)),j(sK1_ax4_U))) = ifeq2(true,true,op2(op2(sK1_ax4_U,sK1_ax4_U),sK1_ax4_U),h(op1(j(op2(sK1_ax4_U,sK1_ax4_U)),j(sK1_ax4_U))))
    | ~ spl0_37
    | ~ spl0_40
    | ~ spl0_42 ),
    inference(forward_demodulation,[],[f423,f401]) ).

fof(f401,plain,
    ( true = sorti1(j(op2(sK1_ax4_U,sK1_ax4_U)))
    | ~ spl0_40 ),
    inference(avatar_component_clause,[],[f399]) ).

fof(f423,plain,
    ( h(op1(j(op2(sK1_ax4_U,sK1_ax4_U)),j(sK1_ax4_U))) = ifeq2(sorti1(j(op2(sK1_ax4_U,sK1_ax4_U))),true,op2(op2(sK1_ax4_U,sK1_ax4_U),sK1_ax4_U),h(op1(j(op2(sK1_ax4_U,sK1_ax4_U)),j(sK1_ax4_U))))
    | ~ spl0_37
    | ~ spl0_42 ),
    inference(superposition,[],[f418,f364]) ).

fof(f364,plain,
    ( op2(sK1_ax4_U,sK1_ax4_U) = h(j(op2(sK1_ax4_U,sK1_ax4_U)))
    | ~ spl0_37 ),
    inference(avatar_component_clause,[],[f362]) ).

fof(f418,plain,
    ( ! [X0] : h(op1(X0,j(sK1_ax4_U))) = ifeq2(sorti1(X0),true,op2(h(X0),sK1_ax4_U),h(op1(X0,j(sK1_ax4_U))))
    | ~ spl0_42 ),
    inference(avatar_component_clause,[],[f417]) ).

fof(f605,plain,
    ( spl0_60
    | ~ spl0_9
    | ~ spl0_35
    | ~ spl0_36 ),
    inference(avatar_split_clause,[],[f360,f320,f286,f55,f602]) ).

fof(f602,plain,
    ( spl0_60
  <=> h(op1(sK2_ax3_V(j(sK1_ax4_U)),j(sK1_ax4_U))) = op2(h(sK2_ax3_V(j(sK1_ax4_U))),sK1_ax4_U) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).

fof(f320,plain,
    ( spl0_36
  <=> ! [X0] : h(op1(X0,j(sK1_ax4_U))) = ifeq2(true,true,ifeq2(sorti1(X0),true,op2(h(X0),sK1_ax4_U),h(op1(X0,j(sK1_ax4_U)))),h(op1(X0,j(sK1_ax4_U)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

fof(f360,plain,
    ( h(op1(sK2_ax3_V(j(sK1_ax4_U)),j(sK1_ax4_U))) = op2(h(sK2_ax3_V(j(sK1_ax4_U))),sK1_ax4_U)
    | ~ spl0_9
    | ~ spl0_35
    | ~ spl0_36 ),
    inference(forward_demodulation,[],[f359,f56]) ).

fof(f359,plain,
    ( h(op1(sK2_ax3_V(j(sK1_ax4_U)),j(sK1_ax4_U))) = ifeq2(true,true,op2(h(sK2_ax3_V(j(sK1_ax4_U))),sK1_ax4_U),h(op1(sK2_ax3_V(j(sK1_ax4_U)),j(sK1_ax4_U))))
    | ~ spl0_9
    | ~ spl0_35
    | ~ spl0_36 ),
    inference(forward_demodulation,[],[f353,f56]) ).

fof(f353,plain,
    ( h(op1(sK2_ax3_V(j(sK1_ax4_U)),j(sK1_ax4_U))) = ifeq2(true,true,ifeq2(true,true,op2(h(sK2_ax3_V(j(sK1_ax4_U))),sK1_ax4_U),h(op1(sK2_ax3_V(j(sK1_ax4_U)),j(sK1_ax4_U)))),h(op1(sK2_ax3_V(j(sK1_ax4_U)),j(sK1_ax4_U))))
    | ~ spl0_35
    | ~ spl0_36 ),
    inference(superposition,[],[f321,f288]) ).

fof(f321,plain,
    ( ! [X0] : h(op1(X0,j(sK1_ax4_U))) = ifeq2(true,true,ifeq2(sorti1(X0),true,op2(h(X0),sK1_ax4_U),h(op1(X0,j(sK1_ax4_U)))),h(op1(X0,j(sK1_ax4_U))))
    | ~ spl0_36 ),
    inference(avatar_component_clause,[],[f320]) ).

fof(f600,plain,
    ( spl0_59
    | ~ spl0_9
    | ~ spl0_33
    | ~ spl0_35 ),
    inference(avatar_split_clause,[],[f358,f286,f265,f55,f597]) ).

fof(f597,plain,
    ( spl0_59
  <=> h(op1(j(sK1_ax4_U),sK2_ax3_V(j(sK1_ax4_U)))) = op2(sK1_ax4_U,h(sK2_ax3_V(j(sK1_ax4_U)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).

fof(f265,plain,
    ( spl0_33
  <=> ! [X0] : h(op1(j(sK1_ax4_U),X0)) = ifeq2(sorti1(X0),true,op2(sK1_ax4_U,h(X0)),h(op1(j(sK1_ax4_U),X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

fof(f358,plain,
    ( h(op1(j(sK1_ax4_U),sK2_ax3_V(j(sK1_ax4_U)))) = op2(sK1_ax4_U,h(sK2_ax3_V(j(sK1_ax4_U))))
    | ~ spl0_9
    | ~ spl0_33
    | ~ spl0_35 ),
    inference(forward_demodulation,[],[f352,f56]) ).

fof(f352,plain,
    ( h(op1(j(sK1_ax4_U),sK2_ax3_V(j(sK1_ax4_U)))) = ifeq2(true,true,op2(sK1_ax4_U,h(sK2_ax3_V(j(sK1_ax4_U)))),h(op1(j(sK1_ax4_U),sK2_ax3_V(j(sK1_ax4_U)))))
    | ~ spl0_33
    | ~ spl0_35 ),
    inference(superposition,[],[f266,f288]) ).

fof(f266,plain,
    ( ! [X0] : h(op1(j(sK1_ax4_U),X0)) = ifeq2(sorti1(X0),true,op2(sK1_ax4_U,h(X0)),h(op1(j(sK1_ax4_U),X0)))
    | ~ spl0_33 ),
    inference(avatar_component_clause,[],[f265]) ).

fof(f584,plain,
    ( spl0_58
    | ~ spl0_10
    | ~ spl0_51 ),
    inference(avatar_split_clause,[],[f560,f534,f59,f581]) ).

fof(f534,plain,
    ( spl0_51
  <=> true = ifeq(true,true,sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))),true) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).

fof(f560,plain,
    ( true = sorti2(h(sK2_ax3_V(j(sK1_ax4_U))))
    | ~ spl0_10
    | ~ spl0_51 ),
    inference(superposition,[],[f536,f60]) ).

fof(f536,plain,
    ( true = ifeq(true,true,sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))),true)
    | ~ spl0_51 ),
    inference(avatar_component_clause,[],[f534]) ).

fof(f577,plain,
    ( spl0_57
    | ~ spl0_10
    | ~ spl0_32
    | ~ spl0_35 ),
    inference(avatar_split_clause,[],[f357,f286,f252,f59,f574]) ).

fof(f574,plain,
    ( spl0_57
  <=> true = ifeq(true,true,sorti1(op1(sK2_ax3_V(j(sK1_ax4_U)),j(sK1_ax4_U))),true) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).

fof(f252,plain,
    ( spl0_32
  <=> ! [X0] : true = ifeq(true,true,ifeq(sorti1(X0),true,sorti1(op1(X0,j(sK1_ax4_U))),true),true) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f357,plain,
    ( true = ifeq(true,true,sorti1(op1(sK2_ax3_V(j(sK1_ax4_U)),j(sK1_ax4_U))),true)
    | ~ spl0_10
    | ~ spl0_32
    | ~ spl0_35 ),
    inference(forward_demodulation,[],[f351,f60]) ).

fof(f351,plain,
    ( true = ifeq(true,true,ifeq(true,true,sorti1(op1(sK2_ax3_V(j(sK1_ax4_U)),j(sK1_ax4_U))),true),true)
    | ~ spl0_32
    | ~ spl0_35 ),
    inference(superposition,[],[f253,f288]) ).

fof(f253,plain,
    ( ! [X0] : true = ifeq(true,true,ifeq(sorti1(X0),true,sorti1(op1(X0,j(sK1_ax4_U))),true),true)
    | ~ spl0_32 ),
    inference(avatar_component_clause,[],[f252]) ).

fof(f572,plain,
    ( spl0_56
    | ~ spl0_10
    | ~ spl0_15
    | ~ spl0_35 ),
    inference(avatar_split_clause,[],[f356,f286,f81,f59,f570]) ).

fof(f570,plain,
    ( spl0_56
  <=> ! [X0] : true = ifeq(sorti1(X0),true,sorti1(op1(sK2_ax3_V(j(sK1_ax4_U)),X0)),true) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).

fof(f356,plain,
    ( ! [X0] : true = ifeq(sorti1(X0),true,sorti1(op1(sK2_ax3_V(j(sK1_ax4_U)),X0)),true)
    | ~ spl0_10
    | ~ spl0_15
    | ~ spl0_35 ),
    inference(forward_demodulation,[],[f349,f60]) ).

fof(f349,plain,
    ( ! [X0] : true = ifeq(sorti1(X0),true,ifeq(true,true,sorti1(op1(sK2_ax3_V(j(sK1_ax4_U)),X0)),true),true)
    | ~ spl0_15
    | ~ spl0_35 ),
    inference(superposition,[],[f82,f288]) ).

fof(f568,plain,
    ( spl0_55
    | ~ spl0_30
    | ~ spl0_35 ),
    inference(avatar_split_clause,[],[f350,f286,f235,f565]) ).

fof(f565,plain,
    ( spl0_55
  <=> true = ifeq(true,true,sorti1(op1(j(sK1_ax4_U),sK2_ax3_V(j(sK1_ax4_U)))),true) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).

fof(f235,plain,
    ( spl0_30
  <=> ! [X0] : true = ifeq(sorti1(X0),true,sorti1(op1(j(sK1_ax4_U),X0)),true) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

fof(f350,plain,
    ( true = ifeq(true,true,sorti1(op1(j(sK1_ax4_U),sK2_ax3_V(j(sK1_ax4_U)))),true)
    | ~ spl0_30
    | ~ spl0_35 ),
    inference(superposition,[],[f236,f288]) ).

fof(f236,plain,
    ( ! [X0] : true = ifeq(sorti1(X0),true,sorti1(op1(j(sK1_ax4_U),X0)),true)
    | ~ spl0_30 ),
    inference(avatar_component_clause,[],[f235]) ).

fof(f558,plain,
    ( spl0_54
    | ~ spl0_1
    | ~ spl0_34
    | ~ spl0_37 ),
    inference(avatar_split_clause,[],[f374,f362,f281,f16,f555]) ).

fof(f555,plain,
    ( spl0_54
  <=> true = ifeq(sorti1(j(op2(sK1_ax4_U,sK1_ax4_U))),true,true,true) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).

fof(f16,plain,
    ( spl0_1
  <=> ! [X4] : true = ifeq(sorti1(X4),true,sorti2(h(X4)),true) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f281,plain,
    ( spl0_34
  <=> true = sorti2(op2(sK1_ax4_U,sK1_ax4_U)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

fof(f374,plain,
    ( true = ifeq(sorti1(j(op2(sK1_ax4_U,sK1_ax4_U))),true,true,true)
    | ~ spl0_1
    | ~ spl0_34
    | ~ spl0_37 ),
    inference(forward_demodulation,[],[f372,f283]) ).

fof(f283,plain,
    ( true = sorti2(op2(sK1_ax4_U,sK1_ax4_U))
    | ~ spl0_34 ),
    inference(avatar_component_clause,[],[f281]) ).

fof(f372,plain,
    ( true = ifeq(sorti1(j(op2(sK1_ax4_U,sK1_ax4_U))),true,sorti2(op2(sK1_ax4_U,sK1_ax4_U)),true)
    | ~ spl0_1
    | ~ spl0_37 ),
    inference(superposition,[],[f17,f364]) ).

fof(f17,plain,
    ( ! [X4] : true = ifeq(sorti1(X4),true,sorti2(h(X4)),true)
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f16]) ).

fof(f553,plain,
    ( spl0_53
    | ~ spl0_11
    | ~ spl0_35 ),
    inference(avatar_split_clause,[],[f346,f286,f63,f550]) ).

fof(f63,plain,
    ( spl0_11
  <=> ! [X4] : true = ifeq(sorti1(X4),true,sorti1(sK2_ax3_V(X4)),true) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f346,plain,
    ( true = ifeq(true,true,sorti1(sK2_ax3_V(sK2_ax3_V(j(sK1_ax4_U)))),true)
    | ~ spl0_11
    | ~ spl0_35 ),
    inference(superposition,[],[f64,f288]) ).

fof(f64,plain,
    ( ! [X4] : true = ifeq(sorti1(X4),true,sorti1(sK2_ax3_V(X4)),true)
    | ~ spl0_11 ),
    inference(avatar_component_clause,[],[f63]) ).

fof(f541,plain,
    ( spl0_52
    | ~ spl0_16
    | ~ spl0_34 ),
    inference(avatar_split_clause,[],[f300,f281,f85,f539]) ).

fof(f539,plain,
    ( spl0_52
  <=> ! [X0] : true = ifeq(true,true,ifeq(sorti2(X0),true,sorti2(op2(X0,op2(sK1_ax4_U,sK1_ax4_U))),true),true) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).

fof(f85,plain,
    ( spl0_16
  <=> ! [X4,X3] : true = ifeq(sorti2(X3),true,ifeq(sorti2(X4),true,sorti2(op2(X4,X3)),true),true) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f300,plain,
    ( ! [X0] : true = ifeq(true,true,ifeq(sorti2(X0),true,sorti2(op2(X0,op2(sK1_ax4_U,sK1_ax4_U))),true),true)
    | ~ spl0_16
    | ~ spl0_34 ),
    inference(superposition,[],[f86,f283]) ).

fof(f86,plain,
    ( ! [X3,X4] : true = ifeq(sorti2(X3),true,ifeq(sorti2(X4),true,sorti2(op2(X4,X3)),true),true)
    | ~ spl0_16 ),
    inference(avatar_component_clause,[],[f85]) ).

fof(f537,plain,
    ( spl0_51
    | ~ spl0_1
    | ~ spl0_35 ),
    inference(avatar_split_clause,[],[f342,f286,f16,f534]) ).

fof(f342,plain,
    ( true = ifeq(true,true,sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))),true)
    | ~ spl0_1
    | ~ spl0_35 ),
    inference(superposition,[],[f17,f288]) ).

fof(f528,plain,
    ( spl0_50
    | ~ spl0_10
    | ~ spl0_16
    | ~ spl0_34 ),
    inference(avatar_split_clause,[],[f316,f281,f85,f59,f526]) ).

fof(f526,plain,
    ( spl0_50
  <=> ! [X0] : true = ifeq(sorti2(X0),true,sorti2(op2(op2(sK1_ax4_U,sK1_ax4_U),X0)),true) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).

fof(f316,plain,
    ( ! [X0] : true = ifeq(sorti2(X0),true,sorti2(op2(op2(sK1_ax4_U,sK1_ax4_U),X0)),true)
    | ~ spl0_10
    | ~ spl0_16
    | ~ spl0_34 ),
    inference(forward_demodulation,[],[f301,f60]) ).

fof(f301,plain,
    ( ! [X0] : true = ifeq(sorti2(X0),true,ifeq(true,true,sorti2(op2(op2(sK1_ax4_U,sK1_ax4_U),X0)),true),true)
    | ~ spl0_16
    | ~ spl0_34 ),
    inference(superposition,[],[f86,f283]) ).

fof(f524,plain,
    ( ~ spl0_49
    | ~ spl0_12
    | ~ spl0_34 ),
    inference(avatar_split_clause,[],[f299,f281,f67,f521]) ).

fof(f521,plain,
    ( spl0_49
  <=> tuple(sK1_ax4_U,true) = tuple(op2(op2(sK1_ax4_U,sK1_ax4_U),op2(sK1_ax4_U,sK1_ax4_U)),true) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).

fof(f299,plain,
    ( tuple(sK1_ax4_U,true) != tuple(op2(op2(sK1_ax4_U,sK1_ax4_U),op2(sK1_ax4_U,sK1_ax4_U)),true)
    | ~ spl0_12
    | ~ spl0_34 ),
    inference(superposition,[],[f68,f283]) ).

fof(f515,plain,
    ( spl0_48
    | ~ spl0_10
    | ~ spl0_22
    | ~ spl0_34 ),
    inference(avatar_split_clause,[],[f318,f281,f129,f59,f512]) ).

fof(f512,plain,
    ( spl0_48
  <=> true = ifeq(true,true,sorti2(op2(op2(sK1_ax4_U,sK1_ax4_U),sK1_ax4_U)),true) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).

fof(f129,plain,
    ( spl0_22
  <=> ! [X0] : true = ifeq(true,true,ifeq(sorti2(X0),true,sorti2(op2(X0,sK1_ax4_U)),true),true) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f318,plain,
    ( true = ifeq(true,true,sorti2(op2(op2(sK1_ax4_U,sK1_ax4_U),sK1_ax4_U)),true)
    | ~ spl0_10
    | ~ spl0_22
    | ~ spl0_34 ),
    inference(forward_demodulation,[],[f305,f60]) ).

fof(f305,plain,
    ( true = ifeq(true,true,ifeq(true,true,sorti2(op2(op2(sK1_ax4_U,sK1_ax4_U),sK1_ax4_U)),true),true)
    | ~ spl0_22
    | ~ spl0_34 ),
    inference(superposition,[],[f130,f283]) ).

fof(f130,plain,
    ( ! [X0] : true = ifeq(true,true,ifeq(sorti2(X0),true,sorti2(op2(X0,sK1_ax4_U)),true),true)
    | ~ spl0_22 ),
    inference(avatar_component_clause,[],[f129]) ).

fof(f510,plain,
    ( spl0_47
    | ~ spl0_21
    | ~ spl0_34 ),
    inference(avatar_split_clause,[],[f304,f281,f122,f507]) ).

fof(f507,plain,
    ( spl0_47
  <=> true = ifeq(true,true,sorti2(op2(sK1_ax4_U,op2(sK1_ax4_U,sK1_ax4_U))),true) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).

fof(f122,plain,
    ( spl0_21
  <=> ! [X0] : true = ifeq(sorti2(X0),true,sorti2(op2(sK1_ax4_U,X0)),true) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f304,plain,
    ( true = ifeq(true,true,sorti2(op2(sK1_ax4_U,op2(sK1_ax4_U,sK1_ax4_U))),true)
    | ~ spl0_21
    | ~ spl0_34 ),
    inference(superposition,[],[f123,f283]) ).

fof(f123,plain,
    ( ! [X0] : true = ifeq(sorti2(X0),true,sorti2(op2(sK1_ax4_U,X0)),true)
    | ~ spl0_21 ),
    inference(avatar_component_clause,[],[f122]) ).

fof(f498,plain,
    ( spl0_46
    | ~ spl0_7
    | ~ spl0_34 ),
    inference(avatar_split_clause,[],[f297,f281,f43,f496]) ).

fof(f496,plain,
    ( spl0_46
  <=> ! [X0] : j(op2(X0,op2(sK1_ax4_U,sK1_ax4_U))) = ifeq2(true,true,ifeq2(sorti2(X0),true,op1(j(X0),j(op2(sK1_ax4_U,sK1_ax4_U))),j(op2(X0,op2(sK1_ax4_U,sK1_ax4_U)))),j(op2(X0,op2(sK1_ax4_U,sK1_ax4_U)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).

fof(f43,plain,
    ( spl0_7
  <=> ! [X9,X8] : j(op2(X9,X8)) = ifeq2(sorti2(X8),true,ifeq2(sorti2(X9),true,op1(j(X9),j(X8)),j(op2(X9,X8))),j(op2(X9,X8))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f297,plain,
    ( ! [X0] : j(op2(X0,op2(sK1_ax4_U,sK1_ax4_U))) = ifeq2(true,true,ifeq2(sorti2(X0),true,op1(j(X0),j(op2(sK1_ax4_U,sK1_ax4_U))),j(op2(X0,op2(sK1_ax4_U,sK1_ax4_U)))),j(op2(X0,op2(sK1_ax4_U,sK1_ax4_U))))
    | ~ spl0_7
    | ~ spl0_34 ),
    inference(superposition,[],[f44,f283]) ).

fof(f44,plain,
    ( ! [X8,X9] : j(op2(X9,X8)) = ifeq2(sorti2(X8),true,ifeq2(sorti2(X9),true,op1(j(X9),j(X8)),j(op2(X9,X8))),j(op2(X9,X8)))
    | ~ spl0_7 ),
    inference(avatar_component_clause,[],[f43]) ).

fof(f455,plain,
    ( spl0_45
    | ~ spl0_7
    | ~ spl0_9
    | ~ spl0_34 ),
    inference(avatar_split_clause,[],[f315,f281,f55,f43,f453]) ).

fof(f453,plain,
    ( spl0_45
  <=> ! [X0] : j(op2(op2(sK1_ax4_U,sK1_ax4_U),X0)) = ifeq2(sorti2(X0),true,op1(j(op2(sK1_ax4_U,sK1_ax4_U)),j(X0)),j(op2(op2(sK1_ax4_U,sK1_ax4_U),X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

fof(f315,plain,
    ( ! [X0] : j(op2(op2(sK1_ax4_U,sK1_ax4_U),X0)) = ifeq2(sorti2(X0),true,op1(j(op2(sK1_ax4_U,sK1_ax4_U)),j(X0)),j(op2(op2(sK1_ax4_U,sK1_ax4_U),X0)))
    | ~ spl0_7
    | ~ spl0_9
    | ~ spl0_34 ),
    inference(forward_demodulation,[],[f298,f56]) ).

fof(f298,plain,
    ( ! [X0] : j(op2(op2(sK1_ax4_U,sK1_ax4_U),X0)) = ifeq2(sorti2(X0),true,ifeq2(true,true,op1(j(op2(sK1_ax4_U,sK1_ax4_U)),j(X0)),j(op2(op2(sK1_ax4_U,sK1_ax4_U),X0))),j(op2(op2(sK1_ax4_U,sK1_ax4_U),X0)))
    | ~ spl0_7
    | ~ spl0_34 ),
    inference(superposition,[],[f44,f283]) ).

fof(f447,plain,
    ( spl0_44
    | ~ spl0_9
    | ~ spl0_19
    | ~ spl0_34 ),
    inference(avatar_split_clause,[],[f317,f281,f108,f55,f444]) ).

fof(f108,plain,
    ( spl0_19
  <=> ! [X0] : j(op2(X0,sK1_ax4_U)) = ifeq2(true,true,ifeq2(sorti2(X0),true,op1(j(X0),j(sK1_ax4_U)),j(op2(X0,sK1_ax4_U))),j(op2(X0,sK1_ax4_U))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f317,plain,
    ( j(op2(op2(sK1_ax4_U,sK1_ax4_U),sK1_ax4_U)) = ifeq2(true,true,op1(j(op2(sK1_ax4_U,sK1_ax4_U)),j(sK1_ax4_U)),j(op2(op2(sK1_ax4_U,sK1_ax4_U),sK1_ax4_U)))
    | ~ spl0_9
    | ~ spl0_19
    | ~ spl0_34 ),
    inference(forward_demodulation,[],[f303,f56]) ).

fof(f303,plain,
    ( j(op2(op2(sK1_ax4_U,sK1_ax4_U),sK1_ax4_U)) = ifeq2(true,true,ifeq2(true,true,op1(j(op2(sK1_ax4_U,sK1_ax4_U)),j(sK1_ax4_U)),j(op2(op2(sK1_ax4_U,sK1_ax4_U),sK1_ax4_U))),j(op2(op2(sK1_ax4_U,sK1_ax4_U),sK1_ax4_U)))
    | ~ spl0_19
    | ~ spl0_34 ),
    inference(superposition,[],[f109,f283]) ).

fof(f109,plain,
    ( ! [X0] : j(op2(X0,sK1_ax4_U)) = ifeq2(true,true,ifeq2(sorti2(X0),true,op1(j(X0),j(sK1_ax4_U)),j(op2(X0,sK1_ax4_U))),j(op2(X0,sK1_ax4_U)))
    | ~ spl0_19 ),
    inference(avatar_component_clause,[],[f108]) ).

fof(f442,plain,
    ( spl0_43
    | ~ spl0_17
    | ~ spl0_34 ),
    inference(avatar_split_clause,[],[f302,f281,f96,f439]) ).

fof(f96,plain,
    ( spl0_17
  <=> ! [X0] : j(op2(sK1_ax4_U,X0)) = ifeq2(sorti2(X0),true,op1(j(sK1_ax4_U),j(X0)),j(op2(sK1_ax4_U,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f302,plain,
    ( j(op2(sK1_ax4_U,op2(sK1_ax4_U,sK1_ax4_U))) = ifeq2(true,true,op1(j(sK1_ax4_U),j(op2(sK1_ax4_U,sK1_ax4_U))),j(op2(sK1_ax4_U,op2(sK1_ax4_U,sK1_ax4_U))))
    | ~ spl0_17
    | ~ spl0_34 ),
    inference(superposition,[],[f97,f283]) ).

fof(f97,plain,
    ( ! [X0] : j(op2(sK1_ax4_U,X0)) = ifeq2(sorti2(X0),true,op1(j(sK1_ax4_U),j(X0)),j(op2(sK1_ax4_U,X0)))
    | ~ spl0_17 ),
    inference(avatar_component_clause,[],[f96]) ).

fof(f419,plain,
    ( spl0_42
    | ~ spl0_9
    | ~ spl0_36 ),
    inference(avatar_split_clause,[],[f326,f320,f55,f417]) ).

fof(f326,plain,
    ( ! [X0] : h(op1(X0,j(sK1_ax4_U))) = ifeq2(sorti1(X0),true,op2(h(X0),sK1_ax4_U),h(op1(X0,j(sK1_ax4_U))))
    | ~ spl0_9
    | ~ spl0_36 ),
    inference(superposition,[],[f321,f56]) ).

fof(f406,plain,
    ( spl0_41
    | ~ spl0_10
    | ~ spl0_32 ),
    inference(avatar_split_clause,[],[f258,f252,f59,f404]) ).

fof(f404,plain,
    ( spl0_41
  <=> ! [X0] : true = ifeq(sorti1(X0),true,sorti1(op1(X0,j(sK1_ax4_U))),true) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

fof(f258,plain,
    ( ! [X0] : true = ifeq(sorti1(X0),true,sorti1(op1(X0,j(sK1_ax4_U))),true)
    | ~ spl0_10
    | ~ spl0_32 ),
    inference(superposition,[],[f253,f60]) ).

fof(f402,plain,
    ( spl0_40
    | ~ spl0_10
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f396,f392,f59,f399]) ).

fof(f392,plain,
    ( spl0_39
  <=> true = ifeq(true,true,sorti1(j(op2(sK1_ax4_U,sK1_ax4_U))),true) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

fof(f396,plain,
    ( true = sorti1(j(op2(sK1_ax4_U,sK1_ax4_U)))
    | ~ spl0_10
    | ~ spl0_39 ),
    inference(superposition,[],[f394,f60]) ).

fof(f394,plain,
    ( true = ifeq(true,true,sorti1(j(op2(sK1_ax4_U,sK1_ax4_U))),true)
    | ~ spl0_39 ),
    inference(avatar_component_clause,[],[f392]) ).

fof(f395,plain,
    ( spl0_39
    | ~ spl0_10
    | ~ spl0_15
    | ~ spl0_23
    | ~ spl0_29 ),
    inference(avatar_split_clause,[],[f229,f209,f138,f81,f59,f392]) ).

fof(f138,plain,
    ( spl0_23
  <=> true = sorti1(j(sK1_ax4_U)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f209,plain,
    ( spl0_29
  <=> j(op2(sK1_ax4_U,sK1_ax4_U)) = op1(j(sK1_ax4_U),j(sK1_ax4_U)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f229,plain,
    ( true = ifeq(true,true,sorti1(j(op2(sK1_ax4_U,sK1_ax4_U))),true)
    | ~ spl0_10
    | ~ spl0_15
    | ~ spl0_23
    | ~ spl0_29 ),
    inference(forward_demodulation,[],[f228,f60]) ).

fof(f228,plain,
    ( true = ifeq(true,true,ifeq(true,true,sorti1(j(op2(sK1_ax4_U,sK1_ax4_U))),true),true)
    | ~ spl0_15
    | ~ spl0_23
    | ~ spl0_29 ),
    inference(forward_demodulation,[],[f220,f140]) ).

fof(f140,plain,
    ( true = sorti1(j(sK1_ax4_U))
    | ~ spl0_23 ),
    inference(avatar_component_clause,[],[f138]) ).

fof(f220,plain,
    ( true = ifeq(sorti1(j(sK1_ax4_U)),true,ifeq(sorti1(j(sK1_ax4_U)),true,sorti1(j(op2(sK1_ax4_U,sK1_ax4_U))),true),true)
    | ~ spl0_15
    | ~ spl0_29 ),
    inference(superposition,[],[f82,f211]) ).

fof(f211,plain,
    ( j(op2(sK1_ax4_U,sK1_ax4_U)) = op1(j(sK1_ax4_U),j(sK1_ax4_U))
    | ~ spl0_29 ),
    inference(avatar_component_clause,[],[f209]) ).

fof(f379,plain,
    ( spl0_38
    | ~ spl0_9
    | ~ spl0_31 ),
    inference(avatar_split_clause,[],[f249,f245,f55,f376]) ).

fof(f245,plain,
    ( spl0_31
  <=> j(sK1_ax4_U) = ifeq2(true,true,op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))),j(sK1_ax4_U)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f249,plain,
    ( j(sK1_ax4_U) = op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U)))
    | ~ spl0_9
    | ~ spl0_31 ),
    inference(superposition,[],[f247,f56]) ).

fof(f247,plain,
    ( j(sK1_ax4_U) = ifeq2(true,true,op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))),j(sK1_ax4_U))
    | ~ spl0_31 ),
    inference(avatar_component_clause,[],[f245]) ).

fof(f365,plain,
    ( spl0_37
    | ~ spl0_6
    | ~ spl0_9
    | ~ spl0_18
    | ~ spl0_23
    | ~ spl0_29 ),
    inference(avatar_split_clause,[],[f233,f209,f138,f103,f55,f39,f362]) ).

fof(f233,plain,
    ( op2(sK1_ax4_U,sK1_ax4_U) = h(j(op2(sK1_ax4_U,sK1_ax4_U)))
    | ~ spl0_6
    | ~ spl0_9
    | ~ spl0_18
    | ~ spl0_23
    | ~ spl0_29 ),
    inference(forward_demodulation,[],[f232,f56]) ).

fof(f232,plain,
    ( h(j(op2(sK1_ax4_U,sK1_ax4_U))) = ifeq2(true,true,op2(sK1_ax4_U,sK1_ax4_U),h(j(op2(sK1_ax4_U,sK1_ax4_U))))
    | ~ spl0_6
    | ~ spl0_9
    | ~ spl0_18
    | ~ spl0_23
    | ~ spl0_29 ),
    inference(forward_demodulation,[],[f231,f56]) ).

fof(f231,plain,
    ( h(j(op2(sK1_ax4_U,sK1_ax4_U))) = ifeq2(true,true,ifeq2(true,true,op2(sK1_ax4_U,sK1_ax4_U),h(j(op2(sK1_ax4_U,sK1_ax4_U)))),h(j(op2(sK1_ax4_U,sK1_ax4_U))))
    | ~ spl0_6
    | ~ spl0_18
    | ~ spl0_23
    | ~ spl0_29 ),
    inference(forward_demodulation,[],[f230,f140]) ).

fof(f230,plain,
    ( h(j(op2(sK1_ax4_U,sK1_ax4_U))) = ifeq2(sorti1(j(sK1_ax4_U)),true,ifeq2(sorti1(j(sK1_ax4_U)),true,op2(sK1_ax4_U,sK1_ax4_U),h(j(op2(sK1_ax4_U,sK1_ax4_U)))),h(j(op2(sK1_ax4_U,sK1_ax4_U))))
    | ~ spl0_6
    | ~ spl0_18
    | ~ spl0_29 ),
    inference(forward_demodulation,[],[f221,f105]) ).

fof(f221,plain,
    ( h(j(op2(sK1_ax4_U,sK1_ax4_U))) = ifeq2(sorti1(j(sK1_ax4_U)),true,ifeq2(sorti1(j(sK1_ax4_U)),true,op2(h(j(sK1_ax4_U)),h(j(sK1_ax4_U))),h(j(op2(sK1_ax4_U,sK1_ax4_U)))),h(j(op2(sK1_ax4_U,sK1_ax4_U))))
    | ~ spl0_6
    | ~ spl0_29 ),
    inference(superposition,[],[f40,f211]) ).

fof(f322,plain,
    ( spl0_36
    | ~ spl0_6
    | ~ spl0_18
    | ~ spl0_23 ),
    inference(avatar_split_clause,[],[f149,f138,f103,f39,f320]) ).

fof(f149,plain,
    ( ! [X0] : h(op1(X0,j(sK1_ax4_U))) = ifeq2(true,true,ifeq2(sorti1(X0),true,op2(h(X0),sK1_ax4_U),h(op1(X0,j(sK1_ax4_U)))),h(op1(X0,j(sK1_ax4_U))))
    | ~ spl0_6
    | ~ spl0_18
    | ~ spl0_23 ),
    inference(forward_demodulation,[],[f144,f140]) ).

fof(f144,plain,
    ( ! [X0] : h(op1(X0,j(sK1_ax4_U))) = ifeq2(sorti1(j(sK1_ax4_U)),true,ifeq2(sorti1(X0),true,op2(h(X0),sK1_ax4_U),h(op1(X0,j(sK1_ax4_U)))),h(op1(X0,j(sK1_ax4_U))))
    | ~ spl0_6
    | ~ spl0_18 ),
    inference(superposition,[],[f40,f105]) ).

fof(f289,plain,
    ( spl0_35
    | ~ spl0_10
    | ~ spl0_28 ),
    inference(avatar_split_clause,[],[f213,f204,f59,f286]) ).

fof(f204,plain,
    ( spl0_28
  <=> true = ifeq(true,true,sorti1(sK2_ax3_V(j(sK1_ax4_U))),true) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

fof(f213,plain,
    ( true = sorti1(sK2_ax3_V(j(sK1_ax4_U)))
    | ~ spl0_10
    | ~ spl0_28 ),
    inference(superposition,[],[f206,f60]) ).

fof(f206,plain,
    ( true = ifeq(true,true,sorti1(sK2_ax3_V(j(sK1_ax4_U))),true)
    | ~ spl0_28 ),
    inference(avatar_component_clause,[],[f204]) ).

fof(f284,plain,
    ( spl0_34
    | ~ spl0_10
    | ~ spl0_26 ),
    inference(avatar_split_clause,[],[f193,f189,f59,f281]) ).

fof(f189,plain,
    ( spl0_26
  <=> true = ifeq(true,true,sorti2(op2(sK1_ax4_U,sK1_ax4_U)),true) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f193,plain,
    ( true = sorti2(op2(sK1_ax4_U,sK1_ax4_U))
    | ~ spl0_10
    | ~ spl0_26 ),
    inference(superposition,[],[f191,f60]) ).

fof(f191,plain,
    ( true = ifeq(true,true,sorti2(op2(sK1_ax4_U,sK1_ax4_U)),true)
    | ~ spl0_26 ),
    inference(avatar_component_clause,[],[f189]) ).

fof(f267,plain,
    ( spl0_33
    | ~ spl0_6
    | ~ spl0_9
    | ~ spl0_18
    | ~ spl0_23 ),
    inference(avatar_split_clause,[],[f151,f138,f103,f55,f39,f265]) ).

fof(f151,plain,
    ( ! [X0] : h(op1(j(sK1_ax4_U),X0)) = ifeq2(sorti1(X0),true,op2(sK1_ax4_U,h(X0)),h(op1(j(sK1_ax4_U),X0)))
    | ~ spl0_6
    | ~ spl0_9
    | ~ spl0_18
    | ~ spl0_23 ),
    inference(forward_demodulation,[],[f150,f56]) ).

fof(f150,plain,
    ( ! [X0] : h(op1(j(sK1_ax4_U),X0)) = ifeq2(sorti1(X0),true,ifeq2(true,true,op2(sK1_ax4_U,h(X0)),h(op1(j(sK1_ax4_U),X0))),h(op1(j(sK1_ax4_U),X0)))
    | ~ spl0_6
    | ~ spl0_18
    | ~ spl0_23 ),
    inference(forward_demodulation,[],[f145,f140]) ).

fof(f145,plain,
    ( ! [X0] : h(op1(j(sK1_ax4_U),X0)) = ifeq2(sorti1(X0),true,ifeq2(sorti1(j(sK1_ax4_U)),true,op2(sK1_ax4_U,h(X0)),h(op1(j(sK1_ax4_U),X0))),h(op1(j(sK1_ax4_U),X0)))
    | ~ spl0_6
    | ~ spl0_18 ),
    inference(superposition,[],[f40,f105]) ).

fof(f254,plain,
    ( spl0_32
    | ~ spl0_15
    | ~ spl0_23 ),
    inference(avatar_split_clause,[],[f163,f138,f81,f252]) ).

fof(f163,plain,
    ( ! [X0] : true = ifeq(true,true,ifeq(sorti1(X0),true,sorti1(op1(X0,j(sK1_ax4_U))),true),true)
    | ~ spl0_15
    | ~ spl0_23 ),
    inference(superposition,[],[f82,f140]) ).

fof(f248,plain,
    ( spl0_31
    | ~ spl0_14
    | ~ spl0_23 ),
    inference(avatar_split_clause,[],[f162,f138,f77,f245]) ).

fof(f162,plain,
    ( j(sK1_ax4_U) = ifeq2(true,true,op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))),j(sK1_ax4_U))
    | ~ spl0_14
    | ~ spl0_23 ),
    inference(superposition,[],[f78,f140]) ).

fof(f237,plain,
    ( spl0_30
    | ~ spl0_10
    | ~ spl0_15
    | ~ spl0_23 ),
    inference(avatar_split_clause,[],[f172,f138,f81,f59,f235]) ).

fof(f172,plain,
    ( ! [X0] : true = ifeq(sorti1(X0),true,sorti1(op1(j(sK1_ax4_U),X0)),true)
    | ~ spl0_10
    | ~ spl0_15
    | ~ spl0_23 ),
    inference(forward_demodulation,[],[f164,f60]) ).

fof(f164,plain,
    ( ! [X0] : true = ifeq(sorti1(X0),true,ifeq(true,true,sorti1(op1(j(sK1_ax4_U),X0)),true),true)
    | ~ spl0_15
    | ~ spl0_23 ),
    inference(superposition,[],[f82,f140]) ).

fof(f212,plain,
    ( spl0_29
    | ~ spl0_9
    | ~ spl0_24 ),
    inference(avatar_split_clause,[],[f178,f174,f55,f209]) ).

fof(f174,plain,
    ( spl0_24
  <=> j(op2(sK1_ax4_U,sK1_ax4_U)) = ifeq2(true,true,op1(j(sK1_ax4_U),j(sK1_ax4_U)),j(op2(sK1_ax4_U,sK1_ax4_U))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f178,plain,
    ( j(op2(sK1_ax4_U,sK1_ax4_U)) = op1(j(sK1_ax4_U),j(sK1_ax4_U))
    | ~ spl0_9
    | ~ spl0_24 ),
    inference(superposition,[],[f176,f56]) ).

fof(f176,plain,
    ( j(op2(sK1_ax4_U,sK1_ax4_U)) = ifeq2(true,true,op1(j(sK1_ax4_U),j(sK1_ax4_U)),j(op2(sK1_ax4_U,sK1_ax4_U)))
    | ~ spl0_24 ),
    inference(avatar_component_clause,[],[f174]) ).

fof(f207,plain,
    ( spl0_28
    | ~ spl0_11
    | ~ spl0_23 ),
    inference(avatar_split_clause,[],[f161,f138,f63,f204]) ).

fof(f161,plain,
    ( true = ifeq(true,true,sorti1(sK2_ax3_V(j(sK1_ax4_U))),true)
    | ~ spl0_11
    | ~ spl0_23 ),
    inference(superposition,[],[f64,f140]) ).

fof(f198,plain,
    ( spl0_27
    | ~ spl0_10
    | ~ spl0_22 ),
    inference(avatar_split_clause,[],[f134,f129,f59,f196]) ).

fof(f196,plain,
    ( spl0_27
  <=> ! [X0] : true = ifeq(sorti2(X0),true,sorti2(op2(X0,sK1_ax4_U)),true) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f134,plain,
    ( ! [X0] : true = ifeq(sorti2(X0),true,sorti2(op2(X0,sK1_ax4_U)),true)
    | ~ spl0_10
    | ~ spl0_22 ),
    inference(superposition,[],[f130,f60]) ).

fof(f192,plain,
    ( spl0_26
    | ~ spl0_5
    | ~ spl0_21 ),
    inference(avatar_split_clause,[],[f125,f122,f32,f189]) ).

fof(f32,plain,
    ( spl0_5
  <=> true = sorti2(sK1_ax4_U) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f125,plain,
    ( true = ifeq(true,true,sorti2(op2(sK1_ax4_U,sK1_ax4_U)),true)
    | ~ spl0_5
    | ~ spl0_21 ),
    inference(superposition,[],[f123,f34]) ).

fof(f34,plain,
    ( true = sorti2(sK1_ax4_U)
    | ~ spl0_5 ),
    inference(avatar_component_clause,[],[f32]) ).

fof(f183,plain,
    ( spl0_25
    | ~ spl0_9
    | ~ spl0_19 ),
    inference(avatar_split_clause,[],[f113,f108,f55,f181]) ).

fof(f181,plain,
    ( spl0_25
  <=> ! [X0] : j(op2(X0,sK1_ax4_U)) = ifeq2(sorti2(X0),true,op1(j(X0),j(sK1_ax4_U)),j(op2(X0,sK1_ax4_U))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f113,plain,
    ( ! [X0] : j(op2(X0,sK1_ax4_U)) = ifeq2(sorti2(X0),true,op1(j(X0),j(sK1_ax4_U)),j(op2(X0,sK1_ax4_U)))
    | ~ spl0_9
    | ~ spl0_19 ),
    inference(superposition,[],[f109,f56]) ).

fof(f177,plain,
    ( spl0_24
    | ~ spl0_5
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f99,f96,f32,f174]) ).

fof(f99,plain,
    ( j(op2(sK1_ax4_U,sK1_ax4_U)) = ifeq2(true,true,op1(j(sK1_ax4_U),j(sK1_ax4_U)),j(op2(sK1_ax4_U,sK1_ax4_U)))
    | ~ spl0_5
    | ~ spl0_17 ),
    inference(superposition,[],[f97,f34]) ).

fof(f141,plain,
    ( spl0_23
    | ~ spl0_10
    | ~ spl0_13 ),
    inference(avatar_split_clause,[],[f93,f72,f59,f138]) ).

fof(f72,plain,
    ( spl0_13
  <=> true = ifeq(true,true,sorti1(j(sK1_ax4_U)),true) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f93,plain,
    ( true = sorti1(j(sK1_ax4_U))
    | ~ spl0_10
    | ~ spl0_13 ),
    inference(superposition,[],[f74,f60]) ).

fof(f74,plain,
    ( true = ifeq(true,true,sorti1(j(sK1_ax4_U)),true)
    | ~ spl0_13 ),
    inference(avatar_component_clause,[],[f72]) ).

fof(f131,plain,
    ( spl0_22
    | ~ spl0_5
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f88,f85,f32,f129]) ).

fof(f88,plain,
    ( ! [X0] : true = ifeq(true,true,ifeq(sorti2(X0),true,sorti2(op2(X0,sK1_ax4_U)),true),true)
    | ~ spl0_5
    | ~ spl0_16 ),
    inference(superposition,[],[f86,f34]) ).

fof(f124,plain,
    ( spl0_21
    | ~ spl0_5
    | ~ spl0_10
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f90,f85,f59,f32,f122]) ).

fof(f90,plain,
    ( ! [X0] : true = ifeq(sorti2(X0),true,sorti2(op2(sK1_ax4_U,X0)),true)
    | ~ spl0_5
    | ~ spl0_10
    | ~ spl0_16 ),
    inference(forward_demodulation,[],[f89,f60]) ).

fof(f89,plain,
    ( ! [X0] : true = ifeq(sorti2(X0),true,ifeq(true,true,sorti2(op2(sK1_ax4_U,X0)),true),true)
    | ~ spl0_5
    | ~ spl0_16 ),
    inference(superposition,[],[f86,f34]) ).

fof(f120,plain,
    ( ~ spl0_20
    | ~ spl0_5
    | ~ spl0_12 ),
    inference(avatar_split_clause,[],[f70,f67,f32,f117]) ).

fof(f117,plain,
    ( spl0_20
  <=> tuple(sK1_ax4_U,true) = tuple(op2(sK1_ax4_U,sK1_ax4_U),true) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f70,plain,
    ( tuple(sK1_ax4_U,true) != tuple(op2(sK1_ax4_U,sK1_ax4_U),true)
    | ~ spl0_5
    | ~ spl0_12 ),
    inference(superposition,[],[f68,f34]) ).

fof(f110,plain,
    ( spl0_19
    | ~ spl0_5
    | ~ spl0_7 ),
    inference(avatar_split_clause,[],[f51,f43,f32,f108]) ).

fof(f51,plain,
    ( ! [X0] : j(op2(X0,sK1_ax4_U)) = ifeq2(true,true,ifeq2(sorti2(X0),true,op1(j(X0),j(sK1_ax4_U)),j(op2(X0,sK1_ax4_U))),j(op2(X0,sK1_ax4_U)))
    | ~ spl0_5
    | ~ spl0_7 ),
    inference(superposition,[],[f44,f34]) ).

fof(f106,plain,
    ( spl0_18
    | ~ spl0_8
    | ~ spl0_9 ),
    inference(avatar_split_clause,[],[f91,f55,f47,f103]) ).

fof(f47,plain,
    ( spl0_8
  <=> sK1_ax4_U = ifeq2(true,true,h(j(sK1_ax4_U)),sK1_ax4_U) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f91,plain,
    ( sK1_ax4_U = h(j(sK1_ax4_U))
    | ~ spl0_8
    | ~ spl0_9 ),
    inference(superposition,[],[f49,f56]) ).

fof(f49,plain,
    ( sK1_ax4_U = ifeq2(true,true,h(j(sK1_ax4_U)),sK1_ax4_U)
    | ~ spl0_8 ),
    inference(avatar_component_clause,[],[f47]) ).

fof(f98,plain,
    ( spl0_17
    | ~ spl0_5
    | ~ spl0_7 ),
    inference(avatar_split_clause,[],[f53,f43,f32,f96]) ).

fof(f53,plain,
    ( ! [X0] : j(op2(sK1_ax4_U,X0)) = ifeq2(sorti2(X0),true,op1(j(sK1_ax4_U),j(X0)),j(op2(sK1_ax4_U,X0)))
    | ~ spl0_5
    | ~ spl0_7 ),
    inference(forward_demodulation,[],[f52,f1]) ).

fof(f1,axiom,
    ! [X2,X0,X1] : ifeq2(X0,X0,X1,X2) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).

fof(f52,plain,
    ( ! [X0] : j(op2(sK1_ax4_U,X0)) = ifeq2(sorti2(X0),true,ifeq2(true,true,op1(j(sK1_ax4_U),j(X0)),j(op2(sK1_ax4_U,X0))),j(op2(sK1_ax4_U,X0)))
    | ~ spl0_5
    | ~ spl0_7 ),
    inference(superposition,[],[f44,f34]) ).

fof(f87,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f4,f85]) ).

fof(f4,axiom,
    ! [X3,X4] : true = ifeq(sorti2(X3),true,ifeq(sorti2(X4),true,sorti2(op2(X4,X3)),true),true),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).

fof(f83,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f3,f81]) ).

fof(f3,axiom,
    ! [X3,X4] : true = ifeq(sorti1(X3),true,ifeq(sorti1(X4),true,sorti1(op1(X4,X3)),true),true),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).

fof(f79,plain,
    spl0_14,
    inference(avatar_split_clause,[],[f6,f77]) ).

fof(f6,axiom,
    ! [X4] : ifeq2(sorti1(X4),true,op1(sK2_ax3_V(X4),sK2_ax3_V(X4)),X4) = X4,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).

fof(f75,plain,
    ( spl0_13
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(avatar_split_clause,[],[f37,f32,f24,f72]) ).

fof(f24,plain,
    ( spl0_3
  <=> ! [X3] : true = ifeq(sorti2(X3),true,sorti1(j(X3)),true) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f37,plain,
    ( true = ifeq(true,true,sorti1(j(sK1_ax4_U)),true)
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(superposition,[],[f25,f34]) ).

fof(f25,plain,
    ( ! [X3] : true = ifeq(sorti2(X3),true,sorti1(j(X3)),true)
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f24]) ).

fof(f69,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f7,f67]) ).

fof(f7,axiom,
    ! [X3] : tuple(op2(X3,X3),sorti2(X3)) != tuple(sK1_ax4_U,true),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4_1) ).

fof(f65,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f5,f63]) ).

fof(f5,axiom,
    ! [X4] : true = ifeq(sorti1(X4),true,sorti1(sK2_ax3_V(X4)),true),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3_1) ).

fof(f61,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f2,f59]) ).

fof(f2,axiom,
    ! [X2,X0,X1] : ifeq(X0,X0,X1,X2) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).

fof(f57,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f1,f55]) ).

fof(f50,plain,
    ( spl0_8
    | ~ spl0_4
    | ~ spl0_5 ),
    inference(avatar_split_clause,[],[f36,f32,f28,f47]) ).

fof(f28,plain,
    ( spl0_4
  <=> ! [X10] : ifeq2(sorti2(X10),true,h(j(X10)),X10) = X10 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f36,plain,
    ( sK1_ax4_U = ifeq2(true,true,h(j(sK1_ax4_U)),sK1_ax4_U)
    | ~ spl0_4
    | ~ spl0_5 ),
    inference(superposition,[],[f29,f34]) ).

fof(f29,plain,
    ( ! [X10] : ifeq2(sorti2(X10),true,h(j(X10)),X10) = X10
    | ~ spl0_4 ),
    inference(avatar_component_clause,[],[f28]) ).

fof(f45,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f13,f43]) ).

fof(f13,axiom,
    ! [X8,X9] : j(op2(X9,X8)) = ifeq2(sorti2(X8),true,ifeq2(sorti2(X9),true,op1(j(X9),j(X8)),j(op2(X9,X8))),j(op2(X9,X8))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_4) ).

fof(f41,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f10,f39]) ).

fof(f10,axiom,
    ! [X6,X5] : h(op1(X6,X5)) = ifeq2(sorti1(X5),true,ifeq2(sorti1(X6),true,op2(h(X6),h(X5)),h(op1(X6,X5))),h(op1(X6,X5))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).

fof(f35,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f8,f32]) ).

fof(f8,axiom,
    true = sorti2(sK1_ax4_U),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).

fof(f30,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f14,f28]) ).

fof(f14,axiom,
    ! [X10] : ifeq2(sorti2(X10),true,h(j(X10)),X10) = X10,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).

fof(f26,plain,
    spl0_3,
    inference(avatar_split_clause,[],[f12,f24]) ).

fof(f12,axiom,
    ! [X3] : true = ifeq(sorti2(X3),true,sorti1(j(X3)),true),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).

fof(f22,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f11,f20]) ).

fof(f11,axiom,
    ! [X7] : ifeq2(sorti1(X7),true,j(h(X7)),X7) = X7,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_2) ).

fof(f18,plain,
    spl0_1,
    inference(avatar_split_clause,[],[f9,f16]) ).

fof(f9,axiom,
    ! [X4] : true = ifeq(sorti1(X4),true,sorti2(h(X4)),true),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem    : ALG069-10 : TPTP v8.2.0. Released v7.3.0.
% 0.14/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36  % Computer : n006.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Sat May 18 22:58:38 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.37  % (23768)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38  % (23771)WARNING: value z3 for option sas not known
% 0.14/0.38  % (23769)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38  % (23773)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)
% 0.14/0.38  % (23772)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38  % (23770)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38  % (23774)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)
% 0.14/0.38  % (23771)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)
% 0.14/0.38  % (23775)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)
% 0.14/0.39  TRYING [1]
% 0.14/0.39  TRYING [2]
% 0.14/0.39  TRYING [3]
% 0.14/0.39  TRYING [1]
% 0.14/0.39  TRYING [2]
% 0.14/0.40  % (23773)First to succeed.
% 0.14/0.41  % (23773)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-23768"
% 0.14/0.41  % (23773)Refutation found. Thanks to Tanya!
% 0.14/0.41  % SZS status Unsatisfiable for theBenchmark
% 0.14/0.41  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.41  % (23773)------------------------------
% 0.14/0.41  % (23773)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.41  % (23773)Termination reason: Refutation
% 0.14/0.41  
% 0.14/0.41  % (23773)Memory used [KB]: 1217
% 0.14/0.41  % (23773)Time elapsed: 0.027 s
% 0.14/0.41  % (23773)Instructions burned: 43 (million)
% 0.14/0.41  % (23768)Success in time 0.043 s
%------------------------------------------------------------------------------