TSTP Solution File: KLE144+2 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : KLE144+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s

% Computer : n016.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 : Fri Sep  1 17:09:23 EDT 2023

% Result   : Theorem 1.69s 0.64s
% Output   : Refutation 1.69s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   32
% Syntax   : Number of formulae    :  130 (  46 unt;   0 def)
%            Number of atoms       :  224 (  81 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  169 (  75   ~;  69   |;   4   &)
%                                         (  18 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :   20 (  18 usr;  18 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :  118 (; 116   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f4782,plain,
    $false,
    inference(avatar_smt_refutation,[],[f76,f84,f91,f151,f158,f177,f182,f188,f189,f190,f191,f285,f290,f343,f623,f874,f915,f2671,f4781]) ).

fof(f4781,plain,
    spl1_7,
    inference(avatar_contradiction_clause,[],[f4779]) ).

fof(f4779,plain,
    ( $false
    | spl1_7 ),
    inference(resolution,[],[f4563,f176]) ).

fof(f176,plain,
    ( ~ leq(strong_iteration(one),strong_iteration(star(sK0)))
    | spl1_7 ),
    inference(avatar_component_clause,[],[f174]) ).

fof(f174,plain,
    ( spl1_7
  <=> leq(strong_iteration(one),strong_iteration(star(sK0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_7])]) ).

fof(f4563,plain,
    ! [X0,X1] : leq(X1,strong_iteration(star(X0))),
    inference(superposition,[],[f4558,f36]) ).

fof(f36,plain,
    ! [X0] : star(X0) = addition(one,multiplication(X0,star(X0))),
    inference(cnf_transformation,[],[f11]) ).

fof(f11,axiom,
    ! [X0] : star(X0) = addition(one,multiplication(X0,star(X0))),
    file('/export/starexec/sandbox2/tmp/tmp.e6woYXpmH4/Vampire---4.8_23364',star_unfold1) ).

fof(f4558,plain,
    ! [X0,X1] : leq(X1,strong_iteration(addition(one,X0))),
    inference(superposition,[],[f4449,f33]) ).

fof(f33,plain,
    ! [X0] : multiplication(X0,one) = X0,
    inference(cnf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0] : multiplication(X0,one) = X0,
    file('/export/starexec/sandbox2/tmp/tmp.e6woYXpmH4/Vampire---4.8_23364',multiplicative_right_identity) ).

fof(f4449,plain,
    ! [X16,X17,X15] : leq(X16,multiplication(strong_iteration(addition(one,X15)),X17)),
    inference(subsumption_resolution,[],[f4448,f372]) ).

fof(f372,plain,
    ! [X4,X5] : leq(X4,addition(X4,X5)),
    inference(trivial_inequality_removal,[],[f366]) ).

fof(f366,plain,
    ! [X4,X5] :
      ( addition(X4,X5) != addition(X4,X5)
      | leq(X4,addition(X4,X5)) ),
    inference(superposition,[],[f42,f218]) ).

fof(f218,plain,
    ! [X4,X5] : addition(X4,X5) = addition(X4,addition(X4,X5)),
    inference(superposition,[],[f43,f35]) ).

fof(f35,plain,
    ! [X0] : addition(X0,X0) = X0,
    inference(cnf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0] : addition(X0,X0) = X0,
    file('/export/starexec/sandbox2/tmp/tmp.e6woYXpmH4/Vampire---4.8_23364',idempotence) ).

fof(f43,plain,
    ! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,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/tmp/tmp.e6woYXpmH4/Vampire---4.8_23364',additive_associativity) ).

fof(f42,plain,
    ! [X0,X1] :
      ( addition(X0,X1) != X1
      | leq(X0,X1) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( ( leq(X0,X1)
        | addition(X0,X1) != X1 )
      & ( addition(X0,X1) = X1
        | ~ leq(X0,X1) ) ),
    inference(nnf_transformation,[],[f18]) ).

fof(f18,axiom,
    ! [X0,X1] :
      ( leq(X0,X1)
    <=> addition(X0,X1) = X1 ),
    file('/export/starexec/sandbox2/tmp/tmp.e6woYXpmH4/Vampire---4.8_23364',order) ).

fof(f4448,plain,
    ! [X16,X17,X15] :
      ( ~ leq(X16,addition(X16,addition(multiplication(X15,X16),X17)))
      | leq(X16,multiplication(strong_iteration(addition(one,X15)),X17)) ),
    inference(forward_demodulation,[],[f4349,f43]) ).

fof(f4349,plain,
    ! [X16,X17,X15] :
      ( ~ leq(X16,addition(addition(X16,multiplication(X15,X16)),X17))
      | leq(X16,multiplication(strong_iteration(addition(one,X15)),X17)) ),
    inference(superposition,[],[f47,f494]) ).

fof(f494,plain,
    ! [X8,X9] : multiplication(addition(one,X9),X8) = addition(X8,multiplication(X9,X8)),
    inference(superposition,[],[f46,f34]) ).

fof(f34,plain,
    ! [X0] : multiplication(one,X0) = X0,
    inference(cnf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0] : multiplication(one,X0) = X0,
    file('/export/starexec/sandbox2/tmp/tmp.e6woYXpmH4/Vampire---4.8_23364',multiplicative_left_identity) ).

fof(f46,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/tmp/tmp.e6woYXpmH4/Vampire---4.8_23364',distributivity2) ).

fof(f47,plain,
    ! [X2,X0,X1] :
      ( ~ leq(X2,addition(multiplication(X0,X2),X1))
      | leq(X2,multiplication(strong_iteration(X0),X1)) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1,X2] :
      ( leq(X2,multiplication(strong_iteration(X0),X1))
      | ~ leq(X2,addition(multiplication(X0,X2),X1)) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f16,axiom,
    ! [X0,X1,X2] :
      ( leq(X2,addition(multiplication(X0,X2),X1))
     => leq(X2,multiplication(strong_iteration(X0),X1)) ),
    file('/export/starexec/sandbox2/tmp/tmp.e6woYXpmH4/Vampire---4.8_23364',infty_coinduction) ).

fof(f2671,plain,
    ( spl1_17
    | ~ spl1_2 ),
    inference(avatar_split_clause,[],[f2641,f81,f2668]) ).

fof(f2668,plain,
    ( spl1_17
  <=> star(one) = addition(star(one),one) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_17])]) ).

fof(f81,plain,
    ( spl1_2
  <=> star(one) = addition(one,star(one)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_2])]) ).

fof(f2641,plain,
    ( star(one) = addition(star(one),one)
    | ~ spl1_2 ),
    inference(forward_demodulation,[],[f2556,f50]) ).

fof(f50,plain,
    ! [X0] : addition(zero,X0) = X0,
    inference(superposition,[],[f40,f32]) ).

fof(f32,plain,
    ! [X0] : addition(X0,zero) = X0,
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0] : addition(X0,zero) = X0,
    file('/export/starexec/sandbox2/tmp/tmp.e6woYXpmH4/Vampire---4.8_23364',additive_identity) ).

fof(f40,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/tmp/tmp.e6woYXpmH4/Vampire---4.8_23364',additive_commutativity) ).

fof(f2556,plain,
    ( addition(star(one),one) = addition(zero,star(one))
    | ~ spl1_2 ),
    inference(superposition,[],[f1972,f83]) ).

fof(f83,plain,
    ( star(one) = addition(one,star(one))
    | ~ spl1_2 ),
    inference(avatar_component_clause,[],[f81]) ).

fof(f1972,plain,
    ! [X48,X47] : addition(X48,X47) = addition(zero,addition(X47,X48)),
    inference(superposition,[],[f235,f50]) ).

fof(f235,plain,
    ! [X10,X11,X9] : addition(X9,addition(X10,X11)) = addition(X11,addition(X9,X10)),
    inference(superposition,[],[f43,f40]) ).

fof(f915,plain,
    ( ~ spl1_15
    | spl1_16 ),
    inference(avatar_split_clause,[],[f905,f913,f909]) ).

fof(f909,plain,
    ( spl1_15
  <=> leq(one,zero) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_15])]) ).

fof(f913,plain,
    ( spl1_16
  <=> ! [X4] : leq(star(X4),zero) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_16])]) ).

fof(f905,plain,
    ! [X4] :
      ( leq(star(X4),zero)
      | ~ leq(one,zero) ),
    inference(superposition,[],[f704,f34]) ).

fof(f704,plain,
    ! [X2,X3] :
      ( leq(multiplication(X3,star(X2)),zero)
      | ~ leq(X3,zero) ),
    inference(forward_demodulation,[],[f687,f50]) ).

fof(f687,plain,
    ! [X2,X3] :
      ( ~ leq(addition(zero,X3),zero)
      | leq(multiplication(X3,star(X2)),zero) ),
    inference(superposition,[],[f48,f31]) ).

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

fof(f10,axiom,
    ! [X0] : zero = multiplication(zero,X0),
    file('/export/starexec/sandbox2/tmp/tmp.e6woYXpmH4/Vampire---4.8_23364',left_annihilation) ).

fof(f48,plain,
    ! [X2,X0,X1] :
      ( ~ leq(addition(multiplication(X2,X0),X1),X2)
      | leq(multiplication(X1,star(X0)),X2) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1,X2] :
      ( leq(multiplication(X1,star(X0)),X2)
      | ~ leq(addition(multiplication(X2,X0),X1),X2) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f14,axiom,
    ! [X0,X1,X2] :
      ( leq(addition(multiplication(X2,X0),X1),X2)
     => leq(multiplication(X1,star(X0)),X2) ),
    file('/export/starexec/sandbox2/tmp/tmp.e6woYXpmH4/Vampire---4.8_23364',star_induction2) ).

fof(f874,plain,
    ( ~ spl1_14
    | spl1_7 ),
    inference(avatar_split_clause,[],[f867,f174,f871]) ).

fof(f871,plain,
    ( spl1_14
  <=> strong_iteration(one) = strong_iteration(star(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_14])]) ).

fof(f867,plain,
    ( strong_iteration(one) != strong_iteration(star(sK0))
    | spl1_7 ),
    inference(resolution,[],[f638,f176]) ).

fof(f638,plain,
    ! [X6] :
      ( leq(strong_iteration(one),X6)
      | strong_iteration(one) != X6 ),
    inference(superposition,[],[f60,f621]) ).

fof(f621,plain,
    ! [X0] : strong_iteration(one) = addition(X0,strong_iteration(one)),
    inference(resolution,[],[f620,f41]) ).

fof(f41,plain,
    ! [X0,X1] :
      ( ~ leq(X0,X1)
      | addition(X0,X1) = X1 ),
    inference(cnf_transformation,[],[f29]) ).

fof(f620,plain,
    ! [X0] : leq(X0,strong_iteration(one)),
    inference(superposition,[],[f616,f33]) ).

fof(f616,plain,
    ! [X8,X9] : leq(X8,multiplication(strong_iteration(one),X9)),
    inference(subsumption_resolution,[],[f601,f372]) ).

fof(f601,plain,
    ! [X8,X9] :
      ( ~ leq(X8,addition(X8,X9))
      | leq(X8,multiplication(strong_iteration(one),X9)) ),
    inference(superposition,[],[f47,f34]) ).

fof(f60,plain,
    ! [X2,X3] :
      ( addition(X3,X2) != X3
      | leq(X2,X3) ),
    inference(superposition,[],[f42,f40]) ).

fof(f623,plain,
    spl1_6,
    inference(avatar_contradiction_clause,[],[f622]) ).

fof(f622,plain,
    ( $false
    | spl1_6 ),
    inference(resolution,[],[f620,f172]) ).

fof(f172,plain,
    ( ~ leq(strong_iteration(star(sK0)),strong_iteration(one))
    | spl1_6 ),
    inference(avatar_component_clause,[],[f170]) ).

fof(f170,plain,
    ( spl1_6
  <=> leq(strong_iteration(star(sK0)),strong_iteration(one)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_6])]) ).

fof(f343,plain,
    ( ~ spl1_12
    | spl1_13
    | ~ spl1_2 ),
    inference(avatar_split_clause,[],[f333,f81,f340,f336]) ).

fof(f336,plain,
    ( spl1_12
  <=> zero = star(one) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_12])]) ).

fof(f340,plain,
    ( spl1_13
  <=> zero = one ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_13])]) ).

fof(f333,plain,
    ( zero = one
    | zero != star(one)
    | ~ spl1_2 ),
    inference(inner_rewriting,[],[f313]) ).

fof(f313,plain,
    ( one = star(one)
    | zero != star(one)
    | ~ spl1_2 ),
    inference(superposition,[],[f251,f83]) ).

fof(f251,plain,
    ! [X6,X5] :
      ( addition(X6,X5) = X6
      | zero != X5 ),
    inference(superposition,[],[f244,f40]) ).

fof(f244,plain,
    ! [X0,X1] :
      ( addition(X0,X1) = X1
      | zero != X0 ),
    inference(forward_demodulation,[],[f216,f50]) ).

fof(f216,plain,
    ! [X0,X1] :
      ( addition(zero,X1) = addition(X0,addition(zero,X1))
      | zero != X0 ),
    inference(superposition,[],[f43,f79]) ).

fof(f79,plain,
    ! [X0] :
      ( zero = addition(X0,zero)
      | zero != X0 ),
    inference(resolution,[],[f58,f41]) ).

fof(f58,plain,
    ! [X0] :
      ( leq(X0,zero)
      | zero != X0 ),
    inference(superposition,[],[f42,f32]) ).

fof(f290,plain,
    ( ~ spl1_11
    | spl1_6 ),
    inference(avatar_split_clause,[],[f279,f170,f287]) ).

fof(f287,plain,
    ( spl1_11
  <=> zero = strong_iteration(star(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_11])]) ).

fof(f279,plain,
    ( zero != strong_iteration(star(sK0))
    | spl1_6 ),
    inference(resolution,[],[f275,f172]) ).

fof(f275,plain,
    ! [X8,X9] :
      ( leq(X8,X9)
      | zero != X8 ),
    inference(trivial_inequality_removal,[],[f264]) ).

fof(f264,plain,
    ! [X8,X9] :
      ( X9 != X9
      | leq(X8,X9)
      | zero != X8 ),
    inference(superposition,[],[f42,f244]) ).

fof(f285,plain,
    ( ~ spl1_10
    | spl1_7 ),
    inference(avatar_split_clause,[],[f280,f174,f282]) ).

fof(f282,plain,
    ( spl1_10
  <=> zero = strong_iteration(one) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_10])]) ).

fof(f280,plain,
    ( zero != strong_iteration(one)
    | spl1_7 ),
    inference(resolution,[],[f275,f176]) ).

fof(f191,plain,
    ( spl1_9
    | ~ spl1_5 ),
    inference(avatar_split_clause,[],[f166,f155,f185]) ).

fof(f185,plain,
    ( spl1_9
  <=> strong_iteration(one) = addition(one,strong_iteration(one)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_9])]) ).

fof(f155,plain,
    ( spl1_5
  <=> strong_iteration(one) = addition(strong_iteration(one),one) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_5])]) ).

fof(f166,plain,
    ( strong_iteration(one) = addition(one,strong_iteration(one))
    | ~ spl1_5 ),
    inference(superposition,[],[f40,f157]) ).

fof(f157,plain,
    ( strong_iteration(one) = addition(strong_iteration(one),one)
    | ~ spl1_5 ),
    inference(avatar_component_clause,[],[f155]) ).

fof(f190,plain,
    ( spl1_9
    | ~ spl1_5 ),
    inference(avatar_split_clause,[],[f165,f155,f185]) ).

fof(f165,plain,
    ( strong_iteration(one) = addition(one,strong_iteration(one))
    | ~ spl1_5 ),
    inference(superposition,[],[f40,f157]) ).

fof(f189,plain,
    ( spl1_9
    | ~ spl1_5 ),
    inference(avatar_split_clause,[],[f162,f155,f185]) ).

fof(f162,plain,
    ( strong_iteration(one) = addition(one,strong_iteration(one))
    | ~ spl1_5 ),
    inference(superposition,[],[f157,f40]) ).

fof(f188,plain,
    ( spl1_9
    | ~ spl1_5 ),
    inference(avatar_split_clause,[],[f161,f155,f185]) ).

fof(f161,plain,
    ( strong_iteration(one) = addition(one,strong_iteration(one))
    | ~ spl1_5 ),
    inference(superposition,[],[f157,f40]) ).

fof(f182,plain,
    ( spl1_8
    | ~ spl1_5 ),
    inference(avatar_split_clause,[],[f167,f155,f179]) ).

fof(f179,plain,
    ( spl1_8
  <=> leq(one,strong_iteration(one)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_8])]) ).

fof(f167,plain,
    ( leq(one,strong_iteration(one))
    | ~ spl1_5 ),
    inference(trivial_inequality_removal,[],[f163]) ).

fof(f163,plain,
    ( strong_iteration(one) != strong_iteration(one)
    | leq(one,strong_iteration(one))
    | ~ spl1_5 ),
    inference(superposition,[],[f60,f157]) ).

fof(f177,plain,
    ( ~ spl1_6
    | ~ spl1_7 ),
    inference(avatar_split_clause,[],[f30,f174,f170]) ).

fof(f30,plain,
    ( ~ leq(strong_iteration(one),strong_iteration(star(sK0)))
    | ~ leq(strong_iteration(star(sK0)),strong_iteration(one)) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,plain,
    ( ~ leq(strong_iteration(one),strong_iteration(star(sK0)))
    | ~ leq(strong_iteration(star(sK0)),strong_iteration(one)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f23,f27]) ).

fof(f27,plain,
    ( ? [X0] :
        ( ~ leq(strong_iteration(one),strong_iteration(star(X0)))
        | ~ leq(strong_iteration(star(X0)),strong_iteration(one)) )
   => ( ~ leq(strong_iteration(one),strong_iteration(star(sK0)))
      | ~ leq(strong_iteration(star(sK0)),strong_iteration(one)) ) ),
    introduced(choice_axiom,[]) ).

fof(f23,plain,
    ? [X0] :
      ( ~ leq(strong_iteration(one),strong_iteration(star(X0)))
      | ~ leq(strong_iteration(star(X0)),strong_iteration(one)) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,plain,
    ~ ! [X0] :
        ( leq(strong_iteration(one),strong_iteration(star(X0)))
        & leq(strong_iteration(star(X0)),strong_iteration(one)) ),
    inference(rectify,[],[f20]) ).

fof(f20,negated_conjecture,
    ~ ! [X3] :
        ( leq(strong_iteration(one),strong_iteration(star(X3)))
        & leq(strong_iteration(star(X3)),strong_iteration(one)) ),
    inference(negated_conjecture,[],[f19]) ).

fof(f19,conjecture,
    ! [X3] :
      ( leq(strong_iteration(one),strong_iteration(star(X3)))
      & leq(strong_iteration(star(X3)),strong_iteration(one)) ),
    file('/export/starexec/sandbox2/tmp/tmp.e6woYXpmH4/Vampire---4.8_23364',goals) ).

fof(f158,plain,
    spl1_5,
    inference(avatar_split_clause,[],[f136,f155]) ).

fof(f136,plain,
    strong_iteration(one) = addition(strong_iteration(one),one),
    inference(superposition,[],[f38,f34]) ).

fof(f38,plain,
    ! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
    inference(cnf_transformation,[],[f15]) ).

fof(f15,axiom,
    ! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
    file('/export/starexec/sandbox2/tmp/tmp.e6woYXpmH4/Vampire---4.8_23364',infty_unfold1) ).

fof(f151,plain,
    spl1_4,
    inference(avatar_split_clause,[],[f143,f148]) ).

fof(f148,plain,
    ( spl1_4
  <=> one = strong_iteration(zero) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_4])]) ).

fof(f143,plain,
    one = strong_iteration(zero),
    inference(forward_demodulation,[],[f135,f50]) ).

fof(f135,plain,
    strong_iteration(zero) = addition(zero,one),
    inference(superposition,[],[f38,f31]) ).

fof(f91,plain,
    ( spl1_3
    | ~ spl1_2 ),
    inference(avatar_split_clause,[],[f86,f81,f88]) ).

fof(f88,plain,
    ( spl1_3
  <=> leq(one,star(one)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_3])]) ).

fof(f86,plain,
    ( leq(one,star(one))
    | ~ spl1_2 ),
    inference(trivial_inequality_removal,[],[f85]) ).

fof(f85,plain,
    ( star(one) != star(one)
    | leq(one,star(one))
    | ~ spl1_2 ),
    inference(superposition,[],[f42,f83]) ).

fof(f84,plain,
    spl1_2,
    inference(avatar_split_clause,[],[f67,f81]) ).

fof(f67,plain,
    star(one) = addition(one,star(one)),
    inference(superposition,[],[f36,f34]) ).

fof(f76,plain,
    spl1_1,
    inference(avatar_split_clause,[],[f69,f73]) ).

fof(f73,plain,
    ( spl1_1
  <=> one = star(zero) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_1])]) ).

fof(f69,plain,
    one = star(zero),
    inference(forward_demodulation,[],[f66,f32]) ).

fof(f66,plain,
    star(zero) = addition(one,zero),
    inference(superposition,[],[f36,f31]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : KLE144+2 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.14  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.14/0.35  % Computer : n016.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Wed Aug 30 18:16:48 EDT 2023
% 0.14/0.36  % CPUTime    : 
% 0.14/0.42  % (23546)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.42  % (23551)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 Vampire---4 for (531ds/0Mi)
% 0.20/0.42  % (23553)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 Vampire---4 for (497ds/0Mi)
% 0.20/0.42  % (23548)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.20/0.42  % (23550)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.20/0.42  % (23549)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 Vampire---4 for (569ds/0Mi)
% 0.20/0.42  % (23547)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.20/0.42  % (23552)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 Vampire---4 for (522ds/0Mi)
% 0.20/0.43  TRYING [1]
% 0.20/0.43  TRYING [2]
% 0.20/0.43  TRYING [3]
% 0.20/0.44  TRYING [1]
% 0.20/0.44  TRYING [2]
% 0.20/0.45  TRYING [4]
% 0.20/0.46  TRYING [3]
% 0.20/0.50  TRYING [4]
% 0.20/0.50  TRYING [5]
% 1.37/0.62  TRYING [5]
% 1.37/0.62  TRYING [6]
% 1.37/0.62  TRYING [1]
% 1.37/0.62  TRYING [2]
% 1.37/0.62  TRYING [3]
% 1.69/0.64  % (23549)First to succeed.
% 1.69/0.64  % (23549)Refutation found. Thanks to Tanya!
% 1.69/0.64  % SZS status Theorem for Vampire---4
% 1.69/0.64  % SZS output start Proof for Vampire---4
% See solution above
% 1.69/0.64  % (23549)------------------------------
% 1.69/0.64  % (23549)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 1.69/0.64  % (23549)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 1.69/0.64  % (23549)Termination reason: Refutation
% 1.69/0.64  
% 1.69/0.64  % (23549)Memory used [KB]: 8571
% 1.69/0.64  % (23549)Time elapsed: 0.217 s
% 1.69/0.64  % (23549)------------------------------
% 1.69/0.64  % (23549)------------------------------
% 1.69/0.64  % (23546)Success in time 0.282 s
% 1.69/0.64  % Vampire---4.8 exiting
%------------------------------------------------------------------------------