TSTP Solution File: KLE074+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : KLE074+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 : n015.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 0.11s 0.38s
% Output   : Refutation 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   58
% Syntax   : Number of formulae    :  176 (  61 unt;   0 def)
%            Number of atoms       :  351 ( 134 equ)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :  316 ( 141   ~; 134   |;   0   &)
%                                         (  40 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :   42 (  40 usr;  41 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :  228 ( 222   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1039,plain,
    $false,
    inference(avatar_sat_refutation,[],[f50,f58,f63,f67,f71,f75,f79,f83,f87,f91,f96,f108,f112,f116,f140,f144,f148,f194,f198,f203,f277,f281,f300,f323,f327,f331,f381,f385,f390,f394,f398,f402,f406,f410,f830,f834,f989,f993,f997,f1001,f1023]) ).

fof(f1023,plain,
    ( spl3_2
    | ~ spl3_37 ),
    inference(avatar_contradiction_clause,[],[f1022]) ).

fof(f1022,plain,
    ( $false
    | spl3_2
    | ~ spl3_37 ),
    inference(trivial_inequality_removal,[],[f1011]) ).

fof(f1011,plain,
    ( domain(multiplication(sK0,multiplication(sK1,sK2))) != domain(multiplication(sK0,multiplication(sK1,sK2)))
    | spl3_2
    | ~ spl3_37 ),
    inference(superposition,[],[f57,f988]) ).

fof(f988,plain,
    ( ! [X2,X0,X1] : domain(multiplication(X2,multiplication(X0,domain(X1)))) = domain(multiplication(X2,multiplication(X0,X1)))
    | ~ spl3_37 ),
    inference(avatar_component_clause,[],[f987]) ).

fof(f987,plain,
    ( spl3_37
  <=> ! [X2,X0,X1] : domain(multiplication(X2,multiplication(X0,domain(X1)))) = domain(multiplication(X2,multiplication(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_37])]) ).

fof(f57,plain,
    ( domain(multiplication(sK0,multiplication(sK1,domain(sK2)))) != domain(multiplication(sK0,multiplication(sK1,sK2)))
    | spl3_2 ),
    inference(avatar_component_clause,[],[f55]) ).

fof(f55,plain,
    ( spl3_2
  <=> domain(multiplication(sK0,multiplication(sK1,domain(sK2)))) = domain(multiplication(sK0,multiplication(sK1,sK2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).

fof(f1001,plain,
    ( spl3_40
    | ~ spl3_12
    | ~ spl3_16 ),
    inference(avatar_split_clause,[],[f160,f142,f106,f999]) ).

fof(f999,plain,
    ( spl3_40
  <=> ! [X2,X0,X1] : addition(domain(X0),addition(domain(X1),X2)) = addition(domain(addition(X0,X1)),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_40])]) ).

fof(f106,plain,
    ( spl3_12
  <=> ! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_12])]) ).

fof(f142,plain,
    ( spl3_16
  <=> ! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_16])]) ).

fof(f160,plain,
    ( ! [X2,X0,X1] : addition(domain(X0),addition(domain(X1),X2)) = addition(domain(addition(X0,X1)),X2)
    | ~ spl3_12
    | ~ spl3_16 ),
    inference(superposition,[],[f143,f107]) ).

fof(f107,plain,
    ( ! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1))
    | ~ spl3_12 ),
    inference(avatar_component_clause,[],[f106]) ).

fof(f143,plain,
    ( ! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0)
    | ~ spl3_16 ),
    inference(avatar_component_clause,[],[f142]) ).

fof(f997,plain,
    ( spl3_39
    | ~ spl3_12
    | ~ spl3_13 ),
    inference(avatar_split_clause,[],[f136,f110,f106,f995]) ).

fof(f995,plain,
    ( spl3_39
  <=> ! [X2,X0,X1] : domain(addition(multiplication(X0,domain(X1)),X2)) = domain(addition(multiplication(X0,X1),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_39])]) ).

fof(f110,plain,
    ( spl3_13
  <=> ! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_13])]) ).

fof(f136,plain,
    ( ! [X2,X0,X1] : domain(addition(multiplication(X0,domain(X1)),X2)) = domain(addition(multiplication(X0,X1),X2))
    | ~ spl3_12
    | ~ spl3_13 ),
    inference(forward_demodulation,[],[f131,f107]) ).

fof(f131,plain,
    ( ! [X2,X0,X1] : domain(addition(multiplication(X0,domain(X1)),X2)) = addition(domain(multiplication(X0,X1)),domain(X2))
    | ~ spl3_12
    | ~ spl3_13 ),
    inference(superposition,[],[f107,f111]) ).

fof(f111,plain,
    ( ! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1)))
    | ~ spl3_13 ),
    inference(avatar_component_clause,[],[f110]) ).

fof(f993,plain,
    ( spl3_38
    | ~ spl3_12
    | ~ spl3_13 ),
    inference(avatar_split_clause,[],[f135,f110,f106,f991]) ).

fof(f991,plain,
    ( spl3_38
  <=> ! [X2,X0,X1] : domain(addition(X2,multiplication(X0,domain(X1)))) = domain(addition(X2,multiplication(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_38])]) ).

fof(f135,plain,
    ( ! [X2,X0,X1] : domain(addition(X2,multiplication(X0,domain(X1)))) = domain(addition(X2,multiplication(X0,X1)))
    | ~ spl3_12
    | ~ spl3_13 ),
    inference(forward_demodulation,[],[f130,f107]) ).

fof(f130,plain,
    ( ! [X2,X0,X1] : domain(addition(X2,multiplication(X0,domain(X1)))) = addition(domain(X2),domain(multiplication(X0,X1)))
    | ~ spl3_12
    | ~ spl3_13 ),
    inference(superposition,[],[f107,f111]) ).

fof(f989,plain,
    ( spl3_37
    | ~ spl3_13 ),
    inference(avatar_split_clause,[],[f133,f110,f987]) ).

fof(f133,plain,
    ( ! [X2,X0,X1] : domain(multiplication(X2,multiplication(X0,domain(X1)))) = domain(multiplication(X2,multiplication(X0,X1)))
    | ~ spl3_13 ),
    inference(forward_demodulation,[],[f127,f111]) ).

fof(f127,plain,
    ( ! [X2,X0,X1] : domain(multiplication(X2,multiplication(X0,domain(X1)))) = domain(multiplication(X2,domain(multiplication(X0,X1))))
    | ~ spl3_13 ),
    inference(superposition,[],[f111,f111]) ).

fof(f834,plain,
    ( spl3_36
    | ~ spl3_11
    | ~ spl3_19 ),
    inference(avatar_split_clause,[],[f245,f196,f94,f832]) ).

fof(f832,plain,
    ( spl3_36
  <=> ! [X2,X0,X1] : multiplication(addition(X0,X2),X1) = addition(multiplication(X2,X1),multiplication(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_36])]) ).

fof(f94,plain,
    ( spl3_11
  <=> ! [X0,X1] : addition(X0,X1) = addition(X1,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_11])]) ).

fof(f196,plain,
    ( spl3_19
  <=> ! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_19])]) ).

fof(f245,plain,
    ( ! [X2,X0,X1] : multiplication(addition(X0,X2),X1) = addition(multiplication(X2,X1),multiplication(X0,X1))
    | ~ spl3_11
    | ~ spl3_19 ),
    inference(superposition,[],[f197,f95]) ).

fof(f95,plain,
    ( ! [X0,X1] : addition(X0,X1) = addition(X1,X0)
    | ~ spl3_11 ),
    inference(avatar_component_clause,[],[f94]) ).

fof(f197,plain,
    ( ! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2))
    | ~ spl3_19 ),
    inference(avatar_component_clause,[],[f196]) ).

fof(f830,plain,
    ( spl3_35
    | ~ spl3_11
    | ~ spl3_18 ),
    inference(avatar_split_clause,[],[f215,f192,f94,f828]) ).

fof(f828,plain,
    ( spl3_35
  <=> ! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X2),multiplication(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_35])]) ).

fof(f192,plain,
    ( spl3_18
  <=> ! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_18])]) ).

fof(f215,plain,
    ( ! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X2),multiplication(X0,X1))
    | ~ spl3_11
    | ~ spl3_18 ),
    inference(superposition,[],[f193,f95]) ).

fof(f193,plain,
    ( ! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2))
    | ~ spl3_18 ),
    inference(avatar_component_clause,[],[f192]) ).

fof(f410,plain,
    ( spl3_34
    | ~ spl3_8
    | ~ spl3_19 ),
    inference(avatar_split_clause,[],[f242,f196,f81,f408]) ).

fof(f408,plain,
    ( spl3_34
  <=> ! [X0,X1] : multiplication(addition(X1,one),X0) = addition(multiplication(X1,X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_34])]) ).

fof(f81,plain,
    ( spl3_8
  <=> ! [X0] : multiplication(one,X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_8])]) ).

fof(f242,plain,
    ( ! [X0,X1] : multiplication(addition(X1,one),X0) = addition(multiplication(X1,X0),X0)
    | ~ spl3_8
    | ~ spl3_19 ),
    inference(superposition,[],[f197,f82]) ).

fof(f82,plain,
    ( ! [X0] : multiplication(one,X0) = X0
    | ~ spl3_8 ),
    inference(avatar_component_clause,[],[f81]) ).

fof(f406,plain,
    ( spl3_33
    | ~ spl3_10
    | ~ spl3_11
    | ~ spl3_12
    | ~ spl3_20 ),
    inference(avatar_split_clause,[],[f268,f200,f106,f94,f89,f404]) ).

fof(f404,plain,
    ( spl3_33
  <=> ! [X0] : one = domain(addition(one,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_33])]) ).

fof(f89,plain,
    ( spl3_10
  <=> ! [X0] : one = addition(domain(X0),one) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_10])]) ).

fof(f200,plain,
    ( spl3_20
  <=> one = domain(one) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_20])]) ).

fof(f268,plain,
    ( ! [X0] : one = domain(addition(one,X0))
    | ~ spl3_10
    | ~ spl3_11
    | ~ spl3_12
    | ~ spl3_20 ),
    inference(forward_demodulation,[],[f264,f98]) ).

fof(f98,plain,
    ( ! [X0] : one = addition(one,domain(X0))
    | ~ spl3_10
    | ~ spl3_11 ),
    inference(superposition,[],[f95,f90]) ).

fof(f90,plain,
    ( ! [X0] : one = addition(domain(X0),one)
    | ~ spl3_10 ),
    inference(avatar_component_clause,[],[f89]) ).

fof(f264,plain,
    ( ! [X0] : addition(one,domain(X0)) = domain(addition(one,X0))
    | ~ spl3_12
    | ~ spl3_20 ),
    inference(superposition,[],[f107,f202]) ).

fof(f202,plain,
    ( one = domain(one)
    | ~ spl3_20 ),
    inference(avatar_component_clause,[],[f200]) ).

fof(f402,plain,
    ( spl3_32
    | ~ spl3_8
    | ~ spl3_19 ),
    inference(avatar_split_clause,[],[f237,f196,f81,f400]) ).

fof(f400,plain,
    ( spl3_32
  <=> ! [X0,X1] : multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_32])]) ).

fof(f237,plain,
    ( ! [X0,X1] : multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0))
    | ~ spl3_8
    | ~ spl3_19 ),
    inference(superposition,[],[f197,f82]) ).

fof(f398,plain,
    ( spl3_31
    | ~ spl3_7
    | ~ spl3_18 ),
    inference(avatar_split_clause,[],[f210,f192,f77,f396]) ).

fof(f396,plain,
    ( spl3_31
  <=> ! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_31])]) ).

fof(f77,plain,
    ( spl3_7
  <=> ! [X0] : multiplication(X0,one) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_7])]) ).

fof(f210,plain,
    ( ! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0)
    | ~ spl3_7
    | ~ spl3_18 ),
    inference(superposition,[],[f193,f78]) ).

fof(f78,plain,
    ( ! [X0] : multiplication(X0,one) = X0
    | ~ spl3_7 ),
    inference(avatar_component_clause,[],[f77]) ).

fof(f394,plain,
    ( spl3_30
    | ~ spl3_7
    | ~ spl3_18 ),
    inference(avatar_split_clause,[],[f205,f192,f77,f392]) ).

fof(f392,plain,
    ( spl3_30
  <=> ! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_30])]) ).

fof(f205,plain,
    ( ! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1))
    | ~ spl3_7
    | ~ spl3_18 ),
    inference(superposition,[],[f193,f78]) ).

fof(f390,plain,
    ( spl3_29
    | ~ spl3_11
    | ~ spl3_16 ),
    inference(avatar_split_clause,[],[f163,f142,f94,f388]) ).

fof(f388,plain,
    ( spl3_29
  <=> ! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_29])]) ).

fof(f163,plain,
    ( ! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1))
    | ~ spl3_11
    | ~ spl3_16 ),
    inference(superposition,[],[f143,f95]) ).

fof(f385,plain,
    ( spl3_28
    | ~ spl3_9
    | ~ spl3_16 ),
    inference(avatar_split_clause,[],[f162,f142,f85,f383]) ).

fof(f383,plain,
    ( spl3_28
  <=> ! [X0,X1] : addition(X0,X1) = addition(X0,addition(X1,addition(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_28])]) ).

fof(f85,plain,
    ( spl3_9
  <=> ! [X0] : addition(X0,X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_9])]) ).

fof(f162,plain,
    ( ! [X0,X1] : addition(X0,X1) = addition(X0,addition(X1,addition(X0,X1)))
    | ~ spl3_9
    | ~ spl3_16 ),
    inference(superposition,[],[f143,f86]) ).

fof(f86,plain,
    ( ! [X0] : addition(X0,X0) = X0
    | ~ spl3_9 ),
    inference(avatar_component_clause,[],[f85]) ).

fof(f381,plain,
    ( spl3_27
    | ~ spl3_11
    | ~ spl3_16 ),
    inference(avatar_split_clause,[],[f155,f142,f94,f379]) ).

fof(f379,plain,
    ( spl3_27
  <=> ! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_27])]) ).

fof(f155,plain,
    ( ! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2)
    | ~ spl3_11
    | ~ spl3_16 ),
    inference(superposition,[],[f143,f95]) ).

fof(f331,plain,
    ( spl3_26
    | ~ spl3_10
    | ~ spl3_16 ),
    inference(avatar_split_clause,[],[f159,f142,f89,f329]) ).

fof(f329,plain,
    ( spl3_26
  <=> ! [X0,X1] : addition(one,X1) = addition(domain(X0),addition(one,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_26])]) ).

fof(f159,plain,
    ( ! [X0,X1] : addition(one,X1) = addition(domain(X0),addition(one,X1))
    | ~ spl3_10
    | ~ spl3_16 ),
    inference(superposition,[],[f143,f90]) ).

fof(f327,plain,
    ( spl3_25
    | ~ spl3_11
    | ~ spl3_12 ),
    inference(avatar_split_clause,[],[f120,f106,f94,f325]) ).

fof(f325,plain,
    ( spl3_25
  <=> ! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X1),domain(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_25])]) ).

fof(f120,plain,
    ( ! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X1),domain(X0))
    | ~ spl3_11
    | ~ spl3_12 ),
    inference(superposition,[],[f107,f95]) ).

fof(f323,plain,
    ( spl3_24
    | ~ spl3_10
    | ~ spl3_12
    | ~ spl3_20 ),
    inference(avatar_split_clause,[],[f267,f200,f106,f89,f321]) ).

fof(f321,plain,
    ( spl3_24
  <=> ! [X0] : one = domain(addition(X0,one)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_24])]) ).

fof(f267,plain,
    ( ! [X0] : one = domain(addition(X0,one))
    | ~ spl3_10
    | ~ spl3_12
    | ~ spl3_20 ),
    inference(forward_demodulation,[],[f263,f90]) ).

fof(f263,plain,
    ( ! [X0] : addition(domain(X0),one) = domain(addition(X0,one))
    | ~ spl3_12
    | ~ spl3_20 ),
    inference(superposition,[],[f107,f202]) ).

fof(f300,plain,
    ( spl3_23
    | ~ spl3_9
    | ~ spl3_16 ),
    inference(avatar_split_clause,[],[f154,f142,f85,f298]) ).

fof(f298,plain,
    ( spl3_23
  <=> ! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_23])]) ).

fof(f154,plain,
    ( ! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1))
    | ~ spl3_9
    | ~ spl3_16 ),
    inference(superposition,[],[f143,f86]) ).

fof(f281,plain,
    ( spl3_22
    | ~ spl3_8
    | ~ spl3_13 ),
    inference(avatar_split_clause,[],[f134,f110,f81,f279]) ).

fof(f279,plain,
    ( spl3_22
  <=> ! [X0] : domain(X0) = domain(domain(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_22])]) ).

fof(f134,plain,
    ( ! [X0] : domain(X0) = domain(domain(X0))
    | ~ spl3_8
    | ~ spl3_13 ),
    inference(forward_demodulation,[],[f129,f82]) ).

fof(f129,plain,
    ( ! [X0] : domain(multiplication(one,X0)) = domain(domain(X0))
    | ~ spl3_8
    | ~ spl3_13 ),
    inference(superposition,[],[f111,f82]) ).

fof(f277,plain,
    ( spl3_21
    | ~ spl3_10
    | ~ spl3_11 ),
    inference(avatar_split_clause,[],[f98,f94,f89,f275]) ).

fof(f275,plain,
    ( spl3_21
  <=> ! [X0] : one = addition(one,domain(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_21])]) ).

fof(f203,plain,
    ( spl3_20
    | ~ spl3_7
    | ~ spl3_10
    | ~ spl3_11
    | ~ spl3_15 ),
    inference(avatar_split_clause,[],[f153,f138,f94,f89,f77,f200]) ).

fof(f138,plain,
    ( spl3_15
  <=> ! [X0] : multiplication(domain(X0),X0) = addition(X0,multiplication(domain(X0),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_15])]) ).

fof(f153,plain,
    ( one = domain(one)
    | ~ spl3_7
    | ~ spl3_10
    | ~ spl3_11
    | ~ spl3_15 ),
    inference(forward_demodulation,[],[f152,f98]) ).

fof(f152,plain,
    ( domain(one) = addition(one,domain(one))
    | ~ spl3_7
    | ~ spl3_15 ),
    inference(superposition,[],[f139,f78]) ).

fof(f139,plain,
    ( ! [X0] : multiplication(domain(X0),X0) = addition(X0,multiplication(domain(X0),X0))
    | ~ spl3_15 ),
    inference(avatar_component_clause,[],[f138]) ).

fof(f198,plain,
    spl3_19,
    inference(avatar_split_clause,[],[f45,f196]) ).

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/sandbox2/benchmark/theBenchmark.p',left_distributivity) ).

fof(f194,plain,
    spl3_18,
    inference(avatar_split_clause,[],[f44,f192]) ).

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/sandbox2/benchmark/theBenchmark.p',right_distributivity) ).

fof(f148,plain,
    spl3_17,
    inference(avatar_split_clause,[],[f43,f146]) ).

fof(f146,plain,
    ( spl3_17
  <=> ! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_17])]) ).

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/sandbox2/benchmark/theBenchmark.p',multiplicative_associativity) ).

fof(f144,plain,
    spl3_16,
    inference(avatar_split_clause,[],[f42,f142]) ).

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/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).

fof(f140,plain,
    spl3_15,
    inference(avatar_split_clause,[],[f38,f138]) ).

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/sandbox2/benchmark/theBenchmark.p',domain1) ).

fof(f116,plain,
    ( spl3_14
    | ~ spl3_6
    | ~ spl3_11 ),
    inference(avatar_split_clause,[],[f97,f94,f73,f114]) ).

fof(f114,plain,
    ( spl3_14
  <=> ! [X0] : addition(zero,X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_14])]) ).

fof(f73,plain,
    ( spl3_6
  <=> ! [X0] : addition(X0,zero) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).

fof(f97,plain,
    ( ! [X0] : addition(zero,X0) = X0
    | ~ spl3_6
    | ~ spl3_11 ),
    inference(superposition,[],[f95,f74]) ).

fof(f74,plain,
    ( ! [X0] : addition(X0,zero) = X0
    | ~ spl3_6 ),
    inference(avatar_component_clause,[],[f73]) ).

fof(f112,plain,
    spl3_13,
    inference(avatar_split_clause,[],[f41,f110]) ).

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/sandbox2/benchmark/theBenchmark.p',domain2) ).

fof(f108,plain,
    spl3_12,
    inference(avatar_split_clause,[],[f40,f106]) ).

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/sandbox2/benchmark/theBenchmark.p',domain5) ).

fof(f96,plain,
    spl3_11,
    inference(avatar_split_clause,[],[f39,f94]) ).

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/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).

fof(f91,plain,
    spl3_10,
    inference(avatar_split_clause,[],[f37,f89]) ).

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/sandbox2/benchmark/theBenchmark.p',domain3) ).

fof(f87,plain,
    spl3_9,
    inference(avatar_split_clause,[],[f36,f85]) ).

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

fof(f4,axiom,
    ! [X0] : addition(X0,X0) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).

fof(f83,plain,
    spl3_8,
    inference(avatar_split_clause,[],[f35,f81]) ).

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

fof(f7,axiom,
    ! [X0] : multiplication(one,X0) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).

fof(f79,plain,
    spl3_7,
    inference(avatar_split_clause,[],[f34,f77]) ).

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

fof(f6,axiom,
    ! [X0] : multiplication(X0,one) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).

fof(f75,plain,
    spl3_6,
    inference(avatar_split_clause,[],[f33,f73]) ).

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

fof(f3,axiom,
    ! [X0] : addition(X0,zero) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).

fof(f71,plain,
    spl3_5,
    inference(avatar_split_clause,[],[f32,f69]) ).

fof(f69,plain,
    ( spl3_5
  <=> ! [X0] : zero = multiplication(zero,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).

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

fof(f11,axiom,
    ! [X0] : zero = multiplication(zero,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).

fof(f67,plain,
    spl3_4,
    inference(avatar_split_clause,[],[f31,f65]) ).

fof(f65,plain,
    ( spl3_4
  <=> ! [X0] : zero = multiplication(X0,zero) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).

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

fof(f10,axiom,
    ! [X0] : zero = multiplication(X0,zero),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_annihilation) ).

fof(f63,plain,
    spl3_3,
    inference(avatar_split_clause,[],[f30,f60]) ).

fof(f60,plain,
    ( spl3_3
  <=> zero = domain(zero) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).

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

fof(f16,axiom,
    zero = domain(zero),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain4) ).

fof(f58,plain,
    ( ~ spl3_2
    | spl3_1 ),
    inference(avatar_split_clause,[],[f53,f47,f55]) ).

fof(f47,plain,
    ( spl3_1
  <=> domain(multiplication(multiplication(sK0,sK1),domain(sK2))) = domain(multiplication(sK0,domain(multiplication(sK1,domain(sK2))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

fof(f53,plain,
    ( domain(multiplication(sK0,multiplication(sK1,domain(sK2)))) != domain(multiplication(sK0,multiplication(sK1,sK2)))
    | spl3_1 ),
    inference(forward_demodulation,[],[f52,f43]) ).

fof(f52,plain,
    ( domain(multiplication(sK0,multiplication(sK1,domain(sK2)))) != domain(multiplication(multiplication(sK0,sK1),sK2))
    | spl3_1 ),
    inference(forward_demodulation,[],[f51,f41]) ).

fof(f51,plain,
    ( domain(multiplication(multiplication(sK0,sK1),domain(sK2))) != domain(multiplication(sK0,multiplication(sK1,domain(sK2))))
    | spl3_1 ),
    inference(forward_demodulation,[],[f49,f41]) ).

fof(f49,plain,
    ( domain(multiplication(multiplication(sK0,sK1),domain(sK2))) != domain(multiplication(sK0,domain(multiplication(sK1,domain(sK2)))))
    | spl3_1 ),
    inference(avatar_component_clause,[],[f47]) ).

fof(f50,plain,
    ~ spl3_1,
    inference(avatar_split_clause,[],[f29,f47]) ).

fof(f29,plain,
    domain(multiplication(multiplication(sK0,sK1),domain(sK2))) != domain(multiplication(sK0,domain(multiplication(sK1,domain(sK2))))),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,plain,
    domain(multiplication(multiplication(sK0,sK1),domain(sK2))) != domain(multiplication(sK0,domain(multiplication(sK1,domain(sK2))))),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f26,f27]) ).

fof(f27,plain,
    ( ? [X0,X1,X2] : domain(multiplication(multiplication(X0,X1),domain(X2))) != domain(multiplication(X0,domain(multiplication(X1,domain(X2)))))
   => domain(multiplication(multiplication(sK0,sK1),domain(sK2))) != domain(multiplication(sK0,domain(multiplication(sK1,domain(sK2))))) ),
    introduced(choice_axiom,[]) ).

fof(f26,plain,
    ? [X0,X1,X2] : domain(multiplication(multiplication(X0,X1),domain(X2))) != domain(multiplication(X0,domain(multiplication(X1,domain(X2))))),
    inference(ennf_transformation,[],[f20]) ).

fof(f20,plain,
    ~ ! [X0,X1,X2] : domain(multiplication(multiplication(X0,X1),domain(X2))) = domain(multiplication(X0,domain(multiplication(X1,domain(X2))))),
    inference(rectify,[],[f19]) ).

fof(f19,negated_conjecture,
    ~ ! [X3,X4,X5] : domain(multiplication(multiplication(X3,X4),domain(X5))) = domain(multiplication(X3,domain(multiplication(X4,domain(X5))))),
    inference(negated_conjecture,[],[f18]) ).

fof(f18,conjecture,
    ! [X3,X4,X5] : domain(multiplication(multiplication(X3,X4),domain(X5))) = domain(multiplication(X3,domain(multiplication(X4,domain(X5))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10  % Problem    : KLE074+1 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.12  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.32  % Computer : n015.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Tue Apr 30 05:22:48 EDT 2024
% 0.11/0.32  % CPUTime    : 
% 0.11/0.33  % (31004)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.34  % (31007)WARNING: value z3 for option sas not known
% 0.11/0.34  % (31010)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)
% 0.11/0.34  % (31008)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.11/0.34  % (31011)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)
% 0.11/0.34  % (31005)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.11/0.34  % (31006)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.11/0.34  % (31007)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)
% 0.11/0.34  % (31009)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)
% 0.11/0.34  TRYING [1]
% 0.11/0.34  TRYING [2]
% 0.11/0.35  TRYING [3]
% 0.11/0.35  TRYING [1]
% 0.11/0.35  TRYING [2]
% 0.11/0.35  TRYING [4]
% 0.11/0.36  TRYING [3]
% 0.11/0.37  % (31009)First to succeed.
% 0.11/0.38  % (31009)Refutation found. Thanks to Tanya!
% 0.11/0.38  % SZS status Theorem for theBenchmark
% 0.11/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.38  % (31009)------------------------------
% 0.11/0.38  % (31009)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.11/0.38  % (31009)Termination reason: Refutation
% 0.11/0.38  
% 0.11/0.38  % (31009)Memory used [KB]: 1398
% 0.11/0.38  % (31009)Time elapsed: 0.037 s
% 0.11/0.38  % (31009)Instructions burned: 69 (million)
% 0.11/0.38  % (31009)------------------------------
% 0.11/0.38  % (31009)------------------------------
% 0.11/0.38  % (31004)Success in time 0.052 s
%------------------------------------------------------------------------------