TSTP Solution File: KLE070+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : KLE070+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 : n009.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Apr 30 13:11:51 EDT 2024

% Result   : Theorem 0.12s 0.41s
% Output   : Refutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   60
% Syntax   : Number of formulae    :  182 (  61 unt;   0 def)
%            Number of atoms       :  372 ( 138 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  344 ( 154   ~; 147   |;   0   &)
%                                         (  42 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :   44 (  42 usr;  43 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :  235 ( 231   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1260,plain,
    $false,
    inference(avatar_sat_refutation,[],[f50,f55,f59,f63,f67,f71,f75,f79,f83,f88,f100,f104,f118,f132,f136,f140,f186,f190,f224,f269,f273,f292,f315,f319,f323,f373,f377,f382,f386,f390,f394,f398,f402,f824,f828,f957,f961,f965,f969,f973,f1251,f1256,f1259]) ).

fof(f1259,plain,
    ( ~ spl2_6
    | spl2_36 ),
    inference(avatar_contradiction_clause,[],[f1258]) ).

fof(f1258,plain,
    ( $false
    | ~ spl2_6
    | spl2_36 ),
    inference(trivial_inequality_removal,[],[f1257]) ).

fof(f1257,plain,
    ( domain(sK0) != domain(sK0)
    | ~ spl2_6
    | spl2_36 ),
    inference(superposition,[],[f956,f70]) ).

fof(f70,plain,
    ( ! [X0] : multiplication(X0,one) = X0
    | ~ spl2_6 ),
    inference(avatar_component_clause,[],[f69]) ).

fof(f69,plain,
    ( spl2_6
  <=> ! [X0] : multiplication(X0,one) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_6])]) ).

fof(f956,plain,
    ( domain(sK0) != multiplication(domain(sK0),one)
    | spl2_36 ),
    inference(avatar_component_clause,[],[f954]) ).

fof(f954,plain,
    ( spl2_36
  <=> domain(sK0) = multiplication(domain(sK0),one) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_36])]) ).

fof(f1256,plain,
    ( spl2_42
    | ~ spl2_15
    | ~ spl2_17 ),
    inference(avatar_split_clause,[],[f205,f184,f134,f1254]) ).

fof(f1254,plain,
    ( spl2_42
  <=> ! [X0,X3,X2,X1] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(X1,X2)),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_42])]) ).

fof(f134,plain,
    ( spl2_15
  <=> ! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_15])]) ).

fof(f184,plain,
    ( spl2_17
  <=> ! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_17])]) ).

fof(f205,plain,
    ( ! [X2,X3,X0,X1] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(X1,X2)),X3)
    | ~ spl2_15
    | ~ spl2_17 ),
    inference(superposition,[],[f135,f185]) ).

fof(f185,plain,
    ( ! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2))
    | ~ spl2_17 ),
    inference(avatar_component_clause,[],[f184]) ).

fof(f135,plain,
    ( ! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0)
    | ~ spl2_15 ),
    inference(avatar_component_clause,[],[f134]) ).

fof(f1251,plain,
    ( spl2_41
    | ~ spl2_14
    | ~ spl2_15 ),
    inference(avatar_split_clause,[],[f150,f134,f130,f1249]) ).

fof(f1249,plain,
    ( spl2_41
  <=> ! [X0,X1] : addition(multiplication(domain(X0),X0),X1) = addition(X0,addition(multiplication(domain(X0),X0),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_41])]) ).

fof(f130,plain,
    ( spl2_14
  <=> ! [X0] : multiplication(domain(X0),X0) = addition(X0,multiplication(domain(X0),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_14])]) ).

fof(f150,plain,
    ( ! [X0,X1] : addition(multiplication(domain(X0),X0),X1) = addition(X0,addition(multiplication(domain(X0),X0),X1))
    | ~ spl2_14
    | ~ spl2_15 ),
    inference(superposition,[],[f135,f131]) ).

fof(f131,plain,
    ( ! [X0] : multiplication(domain(X0),X0) = addition(X0,multiplication(domain(X0),X0))
    | ~ spl2_14 ),
    inference(avatar_component_clause,[],[f130]) ).

fof(f973,plain,
    ( spl2_40
    | ~ spl2_11
    | ~ spl2_15 ),
    inference(avatar_split_clause,[],[f152,f134,f98,f971]) ).

fof(f971,plain,
    ( spl2_40
  <=> ! [X2,X0,X1] : addition(domain(X0),addition(domain(X1),X2)) = addition(domain(addition(X0,X1)),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_40])]) ).

fof(f98,plain,
    ( spl2_11
  <=> ! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_11])]) ).

fof(f152,plain,
    ( ! [X2,X0,X1] : addition(domain(X0),addition(domain(X1),X2)) = addition(domain(addition(X0,X1)),X2)
    | ~ spl2_11
    | ~ spl2_15 ),
    inference(superposition,[],[f135,f99]) ).

fof(f99,plain,
    ( ! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1))
    | ~ spl2_11 ),
    inference(avatar_component_clause,[],[f98]) ).

fof(f969,plain,
    ( spl2_39
    | ~ spl2_11
    | ~ spl2_12 ),
    inference(avatar_split_clause,[],[f128,f102,f98,f967]) ).

fof(f967,plain,
    ( spl2_39
  <=> ! [X2,X0,X1] : domain(addition(multiplication(X0,domain(X1)),X2)) = domain(addition(multiplication(X0,X1),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_39])]) ).

fof(f102,plain,
    ( spl2_12
  <=> ! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_12])]) ).

fof(f128,plain,
    ( ! [X2,X0,X1] : domain(addition(multiplication(X0,domain(X1)),X2)) = domain(addition(multiplication(X0,X1),X2))
    | ~ spl2_11
    | ~ spl2_12 ),
    inference(forward_demodulation,[],[f123,f99]) ).

fof(f123,plain,
    ( ! [X2,X0,X1] : domain(addition(multiplication(X0,domain(X1)),X2)) = addition(domain(multiplication(X0,X1)),domain(X2))
    | ~ spl2_11
    | ~ spl2_12 ),
    inference(superposition,[],[f99,f103]) ).

fof(f103,plain,
    ( ! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1)))
    | ~ spl2_12 ),
    inference(avatar_component_clause,[],[f102]) ).

fof(f965,plain,
    ( spl2_38
    | ~ spl2_11
    | ~ spl2_12 ),
    inference(avatar_split_clause,[],[f127,f102,f98,f963]) ).

fof(f963,plain,
    ( spl2_38
  <=> ! [X2,X0,X1] : domain(addition(X2,multiplication(X0,domain(X1)))) = domain(addition(X2,multiplication(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_38])]) ).

fof(f127,plain,
    ( ! [X2,X0,X1] : domain(addition(X2,multiplication(X0,domain(X1)))) = domain(addition(X2,multiplication(X0,X1)))
    | ~ spl2_11
    | ~ spl2_12 ),
    inference(forward_demodulation,[],[f122,f99]) ).

fof(f122,plain,
    ( ! [X2,X0,X1] : domain(addition(X2,multiplication(X0,domain(X1)))) = addition(domain(X2),domain(multiplication(X0,X1)))
    | ~ spl2_11
    | ~ spl2_12 ),
    inference(superposition,[],[f99,f103]) ).

fof(f961,plain,
    ( spl2_37
    | ~ spl2_12 ),
    inference(avatar_split_clause,[],[f125,f102,f959]) ).

fof(f959,plain,
    ( spl2_37
  <=> ! [X2,X0,X1] : domain(multiplication(X2,multiplication(X0,domain(X1)))) = domain(multiplication(X2,multiplication(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_37])]) ).

fof(f125,plain,
    ( ! [X2,X0,X1] : domain(multiplication(X2,multiplication(X0,domain(X1)))) = domain(multiplication(X2,multiplication(X0,X1)))
    | ~ spl2_12 ),
    inference(forward_demodulation,[],[f119,f103]) ).

fof(f119,plain,
    ( ! [X2,X0,X1] : domain(multiplication(X2,multiplication(X0,domain(X1)))) = domain(multiplication(X2,domain(multiplication(X0,X1))))
    | ~ spl2_12 ),
    inference(superposition,[],[f103,f103]) ).

fof(f957,plain,
    ( ~ spl2_36
    | spl2_1
    | ~ spl2_20
    | ~ spl2_29 ),
    inference(avatar_split_clause,[],[f611,f384,f267,f47,f954]) ).

fof(f47,plain,
    ( spl2_1
  <=> domain(sK0) = addition(domain(sK0),multiplication(domain(sK0),domain(sK1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).

fof(f267,plain,
    ( spl2_20
  <=> ! [X0] : one = addition(one,domain(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_20])]) ).

fof(f384,plain,
    ( spl2_29
  <=> ! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_29])]) ).

fof(f611,plain,
    ( domain(sK0) != multiplication(domain(sK0),one)
    | spl2_1
    | ~ spl2_20
    | ~ spl2_29 ),
    inference(forward_demodulation,[],[f592,f268]) ).

fof(f268,plain,
    ( ! [X0] : one = addition(one,domain(X0))
    | ~ spl2_20 ),
    inference(avatar_component_clause,[],[f267]) ).

fof(f592,plain,
    ( domain(sK0) != multiplication(domain(sK0),addition(one,domain(sK1)))
    | spl2_1
    | ~ spl2_29 ),
    inference(superposition,[],[f49,f385]) ).

fof(f385,plain,
    ( ! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1))
    | ~ spl2_29 ),
    inference(avatar_component_clause,[],[f384]) ).

fof(f49,plain,
    ( domain(sK0) != addition(domain(sK0),multiplication(domain(sK0),domain(sK1)))
    | spl2_1 ),
    inference(avatar_component_clause,[],[f47]) ).

fof(f828,plain,
    ( spl2_35
    | ~ spl2_10
    | ~ spl2_18 ),
    inference(avatar_split_clause,[],[f237,f188,f86,f826]) ).

fof(f826,plain,
    ( spl2_35
  <=> ! [X2,X0,X1] : multiplication(addition(X0,X2),X1) = addition(multiplication(X2,X1),multiplication(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_35])]) ).

fof(f86,plain,
    ( spl2_10
  <=> ! [X0,X1] : addition(X0,X1) = addition(X1,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_10])]) ).

fof(f188,plain,
    ( spl2_18
  <=> ! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_18])]) ).

fof(f237,plain,
    ( ! [X2,X0,X1] : multiplication(addition(X0,X2),X1) = addition(multiplication(X2,X1),multiplication(X0,X1))
    | ~ spl2_10
    | ~ spl2_18 ),
    inference(superposition,[],[f189,f87]) ).

fof(f87,plain,
    ( ! [X0,X1] : addition(X0,X1) = addition(X1,X0)
    | ~ spl2_10 ),
    inference(avatar_component_clause,[],[f86]) ).

fof(f189,plain,
    ( ! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2))
    | ~ spl2_18 ),
    inference(avatar_component_clause,[],[f188]) ).

fof(f824,plain,
    ( spl2_34
    | ~ spl2_10
    | ~ spl2_17 ),
    inference(avatar_split_clause,[],[f202,f184,f86,f822]) ).

fof(f822,plain,
    ( spl2_34
  <=> ! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X2),multiplication(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_34])]) ).

fof(f202,plain,
    ( ! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X2),multiplication(X0,X1))
    | ~ spl2_10
    | ~ spl2_17 ),
    inference(superposition,[],[f185,f87]) ).

fof(f402,plain,
    ( spl2_33
    | ~ spl2_9
    | ~ spl2_10
    | ~ spl2_11
    | ~ spl2_19 ),
    inference(avatar_split_clause,[],[f260,f221,f98,f86,f81,f400]) ).

fof(f400,plain,
    ( spl2_33
  <=> ! [X0] : one = domain(addition(one,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_33])]) ).

fof(f81,plain,
    ( spl2_9
  <=> ! [X0] : one = addition(domain(X0),one) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_9])]) ).

fof(f221,plain,
    ( spl2_19
  <=> one = domain(one) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_19])]) ).

fof(f260,plain,
    ( ! [X0] : one = domain(addition(one,X0))
    | ~ spl2_9
    | ~ spl2_10
    | ~ spl2_11
    | ~ spl2_19 ),
    inference(forward_demodulation,[],[f256,f90]) ).

fof(f90,plain,
    ( ! [X0] : one = addition(one,domain(X0))
    | ~ spl2_9
    | ~ spl2_10 ),
    inference(superposition,[],[f87,f82]) ).

fof(f82,plain,
    ( ! [X0] : one = addition(domain(X0),one)
    | ~ spl2_9 ),
    inference(avatar_component_clause,[],[f81]) ).

fof(f256,plain,
    ( ! [X0] : addition(one,domain(X0)) = domain(addition(one,X0))
    | ~ spl2_11
    | ~ spl2_19 ),
    inference(superposition,[],[f99,f223]) ).

fof(f223,plain,
    ( one = domain(one)
    | ~ spl2_19 ),
    inference(avatar_component_clause,[],[f221]) ).

fof(f398,plain,
    ( spl2_32
    | ~ spl2_7
    | ~ spl2_18 ),
    inference(avatar_split_clause,[],[f234,f188,f73,f396]) ).

fof(f396,plain,
    ( spl2_32
  <=> ! [X0,X1] : multiplication(addition(X1,one),X0) = addition(multiplication(X1,X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_32])]) ).

fof(f73,plain,
    ( spl2_7
  <=> ! [X0] : multiplication(one,X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_7])]) ).

fof(f234,plain,
    ( ! [X0,X1] : multiplication(addition(X1,one),X0) = addition(multiplication(X1,X0),X0)
    | ~ spl2_7
    | ~ spl2_18 ),
    inference(superposition,[],[f189,f74]) ).

fof(f74,plain,
    ( ! [X0] : multiplication(one,X0) = X0
    | ~ spl2_7 ),
    inference(avatar_component_clause,[],[f73]) ).

fof(f394,plain,
    ( spl2_31
    | ~ spl2_7
    | ~ spl2_18 ),
    inference(avatar_split_clause,[],[f229,f188,f73,f392]) ).

fof(f392,plain,
    ( spl2_31
  <=> ! [X0,X1] : multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_31])]) ).

fof(f229,plain,
    ( ! [X0,X1] : multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0))
    | ~ spl2_7
    | ~ spl2_18 ),
    inference(superposition,[],[f189,f74]) ).

fof(f390,plain,
    ( spl2_30
    | ~ spl2_6
    | ~ spl2_17 ),
    inference(avatar_split_clause,[],[f197,f184,f69,f388]) ).

fof(f388,plain,
    ( spl2_30
  <=> ! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_30])]) ).

fof(f197,plain,
    ( ! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0)
    | ~ spl2_6
    | ~ spl2_17 ),
    inference(superposition,[],[f185,f70]) ).

fof(f386,plain,
    ( spl2_29
    | ~ spl2_6
    | ~ spl2_17 ),
    inference(avatar_split_clause,[],[f192,f184,f69,f384]) ).

fof(f192,plain,
    ( ! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1))
    | ~ spl2_6
    | ~ spl2_17 ),
    inference(superposition,[],[f185,f70]) ).

fof(f382,plain,
    ( spl2_28
    | ~ spl2_10
    | ~ spl2_15 ),
    inference(avatar_split_clause,[],[f155,f134,f86,f380]) ).

fof(f380,plain,
    ( spl2_28
  <=> ! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_28])]) ).

fof(f155,plain,
    ( ! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1))
    | ~ spl2_10
    | ~ spl2_15 ),
    inference(superposition,[],[f135,f87]) ).

fof(f377,plain,
    ( spl2_27
    | ~ spl2_8
    | ~ spl2_15 ),
    inference(avatar_split_clause,[],[f154,f134,f77,f375]) ).

fof(f375,plain,
    ( spl2_27
  <=> ! [X0,X1] : addition(X0,X1) = addition(X0,addition(X1,addition(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_27])]) ).

fof(f77,plain,
    ( spl2_8
  <=> ! [X0] : addition(X0,X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_8])]) ).

fof(f154,plain,
    ( ! [X0,X1] : addition(X0,X1) = addition(X0,addition(X1,addition(X0,X1)))
    | ~ spl2_8
    | ~ spl2_15 ),
    inference(superposition,[],[f135,f78]) ).

fof(f78,plain,
    ( ! [X0] : addition(X0,X0) = X0
    | ~ spl2_8 ),
    inference(avatar_component_clause,[],[f77]) ).

fof(f373,plain,
    ( spl2_26
    | ~ spl2_10
    | ~ spl2_15 ),
    inference(avatar_split_clause,[],[f147,f134,f86,f371]) ).

fof(f371,plain,
    ( spl2_26
  <=> ! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_26])]) ).

fof(f147,plain,
    ( ! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2)
    | ~ spl2_10
    | ~ spl2_15 ),
    inference(superposition,[],[f135,f87]) ).

fof(f323,plain,
    ( spl2_25
    | ~ spl2_9
    | ~ spl2_15 ),
    inference(avatar_split_clause,[],[f151,f134,f81,f321]) ).

fof(f321,plain,
    ( spl2_25
  <=> ! [X0,X1] : addition(one,X1) = addition(domain(X0),addition(one,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_25])]) ).

fof(f151,plain,
    ( ! [X0,X1] : addition(one,X1) = addition(domain(X0),addition(one,X1))
    | ~ spl2_9
    | ~ spl2_15 ),
    inference(superposition,[],[f135,f82]) ).

fof(f319,plain,
    ( spl2_24
    | ~ spl2_9
    | ~ spl2_11
    | ~ spl2_19 ),
    inference(avatar_split_clause,[],[f259,f221,f98,f81,f317]) ).

fof(f317,plain,
    ( spl2_24
  <=> ! [X0] : one = domain(addition(X0,one)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_24])]) ).

fof(f259,plain,
    ( ! [X0] : one = domain(addition(X0,one))
    | ~ spl2_9
    | ~ spl2_11
    | ~ spl2_19 ),
    inference(forward_demodulation,[],[f255,f82]) ).

fof(f255,plain,
    ( ! [X0] : addition(domain(X0),one) = domain(addition(X0,one))
    | ~ spl2_11
    | ~ spl2_19 ),
    inference(superposition,[],[f99,f223]) ).

fof(f315,plain,
    ( spl2_23
    | ~ spl2_10
    | ~ spl2_11 ),
    inference(avatar_split_clause,[],[f108,f98,f86,f313]) ).

fof(f313,plain,
    ( spl2_23
  <=> ! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X1),domain(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_23])]) ).

fof(f108,plain,
    ( ! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X1),domain(X0))
    | ~ spl2_10
    | ~ spl2_11 ),
    inference(superposition,[],[f99,f87]) ).

fof(f292,plain,
    ( spl2_22
    | ~ spl2_8
    | ~ spl2_15 ),
    inference(avatar_split_clause,[],[f146,f134,f77,f290]) ).

fof(f290,plain,
    ( spl2_22
  <=> ! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_22])]) ).

fof(f146,plain,
    ( ! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1))
    | ~ spl2_8
    | ~ spl2_15 ),
    inference(superposition,[],[f135,f78]) ).

fof(f273,plain,
    ( spl2_21
    | ~ spl2_7
    | ~ spl2_12 ),
    inference(avatar_split_clause,[],[f126,f102,f73,f271]) ).

fof(f271,plain,
    ( spl2_21
  <=> ! [X0] : domain(X0) = domain(domain(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_21])]) ).

fof(f126,plain,
    ( ! [X0] : domain(X0) = domain(domain(X0))
    | ~ spl2_7
    | ~ spl2_12 ),
    inference(forward_demodulation,[],[f121,f74]) ).

fof(f121,plain,
    ( ! [X0] : domain(multiplication(one,X0)) = domain(domain(X0))
    | ~ spl2_7
    | ~ spl2_12 ),
    inference(superposition,[],[f103,f74]) ).

fof(f269,plain,
    ( spl2_20
    | ~ spl2_9
    | ~ spl2_10 ),
    inference(avatar_split_clause,[],[f90,f86,f81,f267]) ).

fof(f224,plain,
    ( spl2_19
    | ~ spl2_6
    | ~ spl2_9
    | ~ spl2_10
    | ~ spl2_14 ),
    inference(avatar_split_clause,[],[f145,f130,f86,f81,f69,f221]) ).

fof(f145,plain,
    ( one = domain(one)
    | ~ spl2_6
    | ~ spl2_9
    | ~ spl2_10
    | ~ spl2_14 ),
    inference(forward_demodulation,[],[f144,f90]) ).

fof(f144,plain,
    ( domain(one) = addition(one,domain(one))
    | ~ spl2_6
    | ~ spl2_14 ),
    inference(superposition,[],[f131,f70]) ).

fof(f190,plain,
    spl2_18,
    inference(avatar_split_clause,[],[f45,f188]) ).

fof(f45,plain,
    ! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
    inference(cnf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_distributivity) ).

fof(f186,plain,
    spl2_17,
    inference(avatar_split_clause,[],[f44,f184]) ).

fof(f44,plain,
    ! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
    inference(cnf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_distributivity) ).

fof(f140,plain,
    spl2_16,
    inference(avatar_split_clause,[],[f43,f138]) ).

fof(f138,plain,
    ( spl2_16
  <=> ! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_16])]) ).

fof(f43,plain,
    ! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
    inference(cnf_transformation,[],[f5]) ).

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

fof(f136,plain,
    spl2_15,
    inference(avatar_split_clause,[],[f42,f134]) ).

fof(f42,plain,
    ! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
    inference(cnf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
    inference(rectify,[],[f2]) ).

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

fof(f132,plain,
    spl2_14,
    inference(avatar_split_clause,[],[f38,f130]) ).

fof(f38,plain,
    ! [X0] : multiplication(domain(X0),X0) = addition(X0,multiplication(domain(X0),X0)),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,plain,
    ! [X0] : multiplication(domain(X0),X0) = addition(X0,multiplication(domain(X0),X0)),
    inference(rectify,[],[f13]) ).

fof(f13,axiom,
    ! [X3] : multiplication(domain(X3),X3) = addition(X3,multiplication(domain(X3),X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).

fof(f118,plain,
    ( spl2_13
    | ~ spl2_5
    | ~ spl2_10 ),
    inference(avatar_split_clause,[],[f89,f86,f65,f116]) ).

fof(f116,plain,
    ( spl2_13
  <=> ! [X0] : addition(zero,X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_13])]) ).

fof(f65,plain,
    ( spl2_5
  <=> ! [X0] : addition(X0,zero) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_5])]) ).

fof(f89,plain,
    ( ! [X0] : addition(zero,X0) = X0
    | ~ spl2_5
    | ~ spl2_10 ),
    inference(superposition,[],[f87,f66]) ).

fof(f66,plain,
    ( ! [X0] : addition(X0,zero) = X0
    | ~ spl2_5 ),
    inference(avatar_component_clause,[],[f65]) ).

fof(f104,plain,
    spl2_12,
    inference(avatar_split_clause,[],[f41,f102]) ).

fof(f41,plain,
    ! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
    inference(rectify,[],[f14]) ).

fof(f14,axiom,
    ! [X3,X4] : domain(multiplication(X3,X4)) = domain(multiplication(X3,domain(X4))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain2) ).

fof(f100,plain,
    spl2_11,
    inference(avatar_split_clause,[],[f40,f98]) ).

fof(f40,plain,
    ! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
    inference(cnf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
    inference(rectify,[],[f17]) ).

fof(f17,axiom,
    ! [X3,X4] : domain(addition(X3,X4)) = addition(domain(X3),domain(X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain5) ).

fof(f88,plain,
    spl2_10,
    inference(avatar_split_clause,[],[f39,f86]) ).

fof(f39,plain,
    ! [X0,X1] : addition(X0,X1) = addition(X1,X0),
    inference(cnf_transformation,[],[f1]) ).

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

fof(f83,plain,
    spl2_9,
    inference(avatar_split_clause,[],[f37,f81]) ).

fof(f37,plain,
    ! [X0] : one = addition(domain(X0),one),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,plain,
    ! [X0] : one = addition(domain(X0),one),
    inference(rectify,[],[f15]) ).

fof(f15,axiom,
    ! [X3] : one = addition(domain(X3),one),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain3) ).

fof(f79,plain,
    spl2_8,
    inference(avatar_split_clause,[],[f36,f77]) ).

fof(f36,plain,
    ! [X0] : addition(X0,X0) = X0,
    inference(cnf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0] : addition(X0,X0) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).

fof(f75,plain,
    spl2_7,
    inference(avatar_split_clause,[],[f35,f73]) ).

fof(f35,plain,
    ! [X0] : multiplication(one,X0) = X0,
    inference(cnf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0] : multiplication(one,X0) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).

fof(f71,plain,
    spl2_6,
    inference(avatar_split_clause,[],[f34,f69]) ).

fof(f34,plain,
    ! [X0] : multiplication(X0,one) = X0,
    inference(cnf_transformation,[],[f6]) ).

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

fof(f67,plain,
    spl2_5,
    inference(avatar_split_clause,[],[f33,f65]) ).

fof(f33,plain,
    ! [X0] : addition(X0,zero) = X0,
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0] : addition(X0,zero) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).

fof(f63,plain,
    spl2_4,
    inference(avatar_split_clause,[],[f32,f61]) ).

fof(f61,plain,
    ( spl2_4
  <=> ! [X0] : zero = multiplication(zero,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).

fof(f32,plain,
    ! [X0] : zero = multiplication(zero,X0),
    inference(cnf_transformation,[],[f11]) ).

fof(f11,axiom,
    ! [X0] : zero = multiplication(zero,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).

fof(f59,plain,
    spl2_3,
    inference(avatar_split_clause,[],[f31,f57]) ).

fof(f57,plain,
    ( spl2_3
  <=> ! [X0] : zero = multiplication(X0,zero) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).

fof(f31,plain,
    ! [X0] : zero = multiplication(X0,zero),
    inference(cnf_transformation,[],[f10]) ).

fof(f10,axiom,
    ! [X0] : zero = multiplication(X0,zero),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_annihilation) ).

fof(f55,plain,
    spl2_2,
    inference(avatar_split_clause,[],[f30,f52]) ).

fof(f52,plain,
    ( spl2_2
  <=> zero = domain(zero) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).

fof(f30,plain,
    zero = domain(zero),
    inference(cnf_transformation,[],[f16]) ).

fof(f16,axiom,
    zero = domain(zero),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain4) ).

fof(f50,plain,
    ~ spl2_1,
    inference(avatar_split_clause,[],[f29,f47]) ).

fof(f29,plain,
    domain(sK0) != addition(domain(sK0),multiplication(domain(sK0),domain(sK1))),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,plain,
    domain(sK0) != addition(domain(sK0),multiplication(domain(sK0),domain(sK1))),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f26,f27]) ).

fof(f27,plain,
    ( ? [X0,X1] : domain(X0) != addition(domain(X0),multiplication(domain(X0),domain(X1)))
   => domain(sK0) != addition(domain(sK0),multiplication(domain(sK0),domain(sK1))) ),
    introduced(choice_axiom,[]) ).

fof(f26,plain,
    ? [X0,X1] : domain(X0) != addition(domain(X0),multiplication(domain(X0),domain(X1))),
    inference(ennf_transformation,[],[f20]) ).

fof(f20,plain,
    ~ ! [X0,X1] : domain(X0) = addition(domain(X0),multiplication(domain(X0),domain(X1))),
    inference(rectify,[],[f19]) ).

fof(f19,negated_conjecture,
    ~ ! [X3,X4] : domain(X3) = addition(domain(X3),multiplication(domain(X3),domain(X4))),
    inference(negated_conjecture,[],[f18]) ).

fof(f18,conjecture,
    ! [X3,X4] : domain(X3) = addition(domain(X3),multiplication(domain(X3),domain(X4))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : KLE070+1 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.34  % Computer : n009.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Tue Apr 30 04:57:41 EDT 2024
% 0.12/0.35  % CPUTime    : 
% 0.12/0.35  % (29089)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.36  % (29092)WARNING: value z3 for option sas not known
% 0.12/0.36  % (29094)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)
% 0.12/0.36  % (29096)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)
% 0.12/0.36  % (29093)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.36  % (29095)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)
% 0.12/0.36  % (29092)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)
% 0.12/0.37  TRYING [1]
% 0.12/0.37  TRYING [2]
% 0.12/0.37  % (29091)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.12/0.37  % (29090)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.12/0.37  TRYING [3]
% 0.12/0.37  TRYING [1]
% 0.12/0.37  TRYING [2]
% 0.12/0.38  TRYING [4]
% 0.12/0.39  TRYING [3]
% 0.12/0.40  TRYING [1]
% 0.12/0.40  TRYING [2]
% 0.12/0.40  TRYING [3]
% 0.12/0.40  % (29094)First to succeed.
% 0.12/0.41  TRYING [5]
% 0.12/0.41  % (29094)Refutation found. Thanks to Tanya!
% 0.12/0.41  % SZS status Theorem for theBenchmark
% 0.12/0.41  % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.41  % (29094)------------------------------
% 0.12/0.41  % (29094)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.12/0.41  % (29094)Termination reason: Refutation
% 0.12/0.41  
% 0.12/0.41  % (29094)Memory used [KB]: 1524
% 0.12/0.41  % (29094)Time elapsed: 0.043 s
% 0.12/0.41  % (29094)Instructions burned: 86 (million)
% 0.12/0.41  % (29094)------------------------------
% 0.12/0.41  % (29094)------------------------------
% 0.12/0.41  % (29089)Success in time 0.058 s
%------------------------------------------------------------------------------