TSTP Solution File: NUM854+2 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUM854+2 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n013.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 : Sun May  5 08:42:37 EDT 2024

% Result   : Theorem 0.20s 0.39s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   55
% Syntax   : Number of formulae    :  164 (  59 unt;   0 def)
%            Number of atoms       :  304 (  94 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  246 ( 106   ~;  84   |;   8   &)
%                                         (  33 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   33 (  31 usr;  30 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   5 con; 0-2 aty)
%            Number of variables   :  283 ( 267   !;  16   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f387,plain,
    $false,
    inference(avatar_sat_refutation,[],[f117,f122,f127,f131,f135,f139,f143,f147,f151,f155,f159,f163,f167,f176,f180,f192,f199,f203,f208,f212,f216,f220,f224,f228,f232,f236,f262,f330,f360,f386]) ).

fof(f386,plain,
    ( ~ spl4_2
    | spl4_1
    | ~ spl4_23 ),
    inference(avatar_split_clause,[],[f281,f222,f114,f119]) ).

fof(f119,plain,
    ( spl4_2
  <=> greater(vd508,vd509) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).

fof(f114,plain,
    ( spl4_1
  <=> greater(vmul(vd508,vd511),vmul(vd509,vd511)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).

fof(f222,plain,
    ( spl4_23
  <=> ! [X2,X0,X1] :
        ( greater(vmul(X1,X0),vmul(X2,X0))
        | ~ greater(X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_23])]) ).

fof(f281,plain,
    ( ~ greater(vd508,vd509)
    | spl4_1
    | ~ spl4_23 ),
    inference(resolution,[],[f223,f116]) ).

fof(f116,plain,
    ( ~ greater(vmul(vd508,vd511),vmul(vd509,vd511))
    | spl4_1 ),
    inference(avatar_component_clause,[],[f114]) ).

fof(f223,plain,
    ( ! [X2,X0,X1] :
        ( greater(vmul(X1,X0),vmul(X2,X0))
        | ~ greater(X1,X2) )
    | ~ spl4_23 ),
    inference(avatar_component_clause,[],[f222]) ).

fof(f360,plain,
    spl4_29,
    inference(avatar_split_clause,[],[f98,f358]) ).

fof(f358,plain,
    ( spl4_29
  <=> ! [X2,X0,X1] : vmul(X0,vplus(X1,X2)) = vplus(vmul(X0,X1),vmul(X0,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_29])]) ).

fof(f98,plain,
    ! [X2,X0,X1] : vmul(X0,vplus(X1,X2)) = vplus(vmul(X0,X1),vmul(X0,X2)),
    inference(cnf_transformation,[],[f47]) ).

fof(f47,plain,
    ! [X0,X1,X2] : vmul(X0,vplus(X1,X2)) = vplus(vmul(X0,X1),vmul(X0,X2)),
    inference(rectify,[],[f12]) ).

fof(f12,axiom,
    ! [X19,X20,X21] : vmul(X19,vplus(X20,X21)) = vplus(vmul(X19,X20),vmul(X19,X21)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(281, 0), 0)') ).

fof(f330,plain,
    spl4_28,
    inference(avatar_split_clause,[],[f97,f328]) ).

fof(f328,plain,
    ( spl4_28
  <=> ! [X2,X0,X1] : vmul(vmul(X0,X1),X2) = vmul(X0,vmul(X1,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_28])]) ).

fof(f97,plain,
    ! [X2,X0,X1] : vmul(vmul(X0,X1),X2) = vmul(X0,vmul(X1,X2)),
    inference(cnf_transformation,[],[f46]) ).

fof(f46,plain,
    ! [X0,X1,X2] : vmul(vmul(X0,X1),X2) = vmul(X0,vmul(X1,X2)),
    inference(rectify,[],[f11]) ).

fof(f11,axiom,
    ! [X16,X17,X18] : vmul(vmul(X16,X17),X18) = vmul(X16,vmul(X17,X18)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(290, 0), 0)') ).

fof(f262,plain,
    ( spl4_27
    | ~ spl4_3
    | ~ spl4_13 ),
    inference(avatar_split_clause,[],[f171,f165,f124,f259]) ).

fof(f259,plain,
    ( spl4_27
  <=> less(vd512,vd511) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_27])]) ).

fof(f124,plain,
    ( spl4_3
  <=> greater(vd511,vd512) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_3])]) ).

fof(f165,plain,
    ( spl4_13
  <=> ! [X0,X1] :
        ( less(X1,X0)
        | ~ greater(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_13])]) ).

fof(f171,plain,
    ( less(vd512,vd511)
    | ~ spl4_3
    | ~ spl4_13 ),
    inference(resolution,[],[f166,f126]) ).

fof(f126,plain,
    ( greater(vd511,vd512)
    | ~ spl4_3 ),
    inference(avatar_component_clause,[],[f124]) ).

fof(f166,plain,
    ( ! [X0,X1] :
        ( ~ greater(X0,X1)
        | less(X1,X0) )
    | ~ spl4_13 ),
    inference(avatar_component_clause,[],[f165]) ).

fof(f236,plain,
    spl4_26,
    inference(avatar_split_clause,[],[f104,f234]) ).

fof(f234,plain,
    ( spl4_26
  <=> ! [X2,X0,X1] :
        ( greater(X0,X2)
        | ~ greater(vmul(X0,X1),vmul(X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_26])]) ).

fof(f104,plain,
    ! [X2,X0,X1] :
      ( greater(X0,X2)
      | ~ greater(vmul(X0,X1),vmul(X2,X1)) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f63,plain,
    ! [X0,X1,X2] :
      ( greater(X0,X2)
      | ~ greater(vmul(X0,X1),vmul(X2,X1)) ),
    inference(ennf_transformation,[],[f52]) ).

fof(f52,plain,
    ! [X0,X1,X2] :
      ( greater(vmul(X0,X1),vmul(X2,X1))
     => greater(X0,X2) ),
    inference(rectify,[],[f7]) ).

fof(f7,axiom,
    ! [X6,X7,X8] :
      ( greater(vmul(X6,X7),vmul(X8,X7))
     => greater(X6,X8) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conjunct1(307), 0), 0)') ).

fof(f232,plain,
    spl4_25,
    inference(avatar_split_clause,[],[f103,f230]) ).

fof(f230,plain,
    ( spl4_25
  <=> ! [X2,X0,X1] :
        ( less(X0,X2)
        | ~ less(vmul(X0,X1),vmul(X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_25])]) ).

fof(f103,plain,
    ! [X2,X0,X1] :
      ( less(X0,X2)
      | ~ less(vmul(X0,X1),vmul(X2,X1)) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f62,plain,
    ! [X0,X1,X2] :
      ( less(X0,X2)
      | ~ less(vmul(X0,X1),vmul(X2,X1)) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X1,X2] :
      ( less(vmul(X0,X1),vmul(X2,X1))
     => less(X0,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conjunct2(conjunct2(307)), 0), 0)') ).

fof(f228,plain,
    spl4_24,
    inference(avatar_split_clause,[],[f102,f226]) ).

fof(f226,plain,
    ( spl4_24
  <=> ! [X2,X0,X1] :
        ( X0 = X2
        | vmul(X0,X1) != vmul(X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_24])]) ).

fof(f102,plain,
    ! [X2,X0,X1] :
      ( X0 = X2
      | vmul(X0,X1) != vmul(X2,X1) ),
    inference(cnf_transformation,[],[f61]) ).

fof(f61,plain,
    ! [X0,X1,X2] :
      ( X0 = X2
      | vmul(X0,X1) != vmul(X2,X1) ),
    inference(ennf_transformation,[],[f51]) ).

fof(f51,plain,
    ! [X0,X1,X2] :
      ( vmul(X0,X1) = vmul(X2,X1)
     => X0 = X2 ),
    inference(rectify,[],[f6]) ).

fof(f6,axiom,
    ! [X3,X4,X5] :
      ( vmul(X3,X4) = vmul(X5,X4)
     => X3 = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conjunct1(conjunct2(307)), 0), 0)') ).

fof(f224,plain,
    spl4_23,
    inference(avatar_split_clause,[],[f101,f222]) ).

fof(f101,plain,
    ! [X2,X0,X1] :
      ( greater(vmul(X1,X0),vmul(X2,X0))
      | ~ greater(X1,X2) ),
    inference(cnf_transformation,[],[f60]) ).

fof(f60,plain,
    ! [X0,X1,X2] :
      ( greater(vmul(X1,X0),vmul(X2,X0))
      | ~ greater(X1,X2) ),
    inference(ennf_transformation,[],[f50]) ).

fof(f50,plain,
    ! [X0,X1,X2] :
      ( greater(X1,X2)
     => greater(vmul(X1,X0),vmul(X2,X0)) ),
    inference(rectify,[],[f10]) ).

fof(f10,axiom,
    ! [X9,X14,X15] :
      ( greater(X14,X15)
     => greater(vmul(X14,X9),vmul(X15,X9)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(299, 0), 2)') ).

fof(f220,plain,
    spl4_22,
    inference(avatar_split_clause,[],[f100,f218]) ).

fof(f218,plain,
    ( spl4_22
  <=> ! [X2,X0,X1] :
        ( less(vmul(X1,X0),vmul(X2,X0))
        | ~ less(X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_22])]) ).

fof(f100,plain,
    ! [X2,X0,X1] :
      ( less(vmul(X1,X0),vmul(X2,X0))
      | ~ less(X1,X2) ),
    inference(cnf_transformation,[],[f59]) ).

fof(f59,plain,
    ! [X0,X1,X2] :
      ( less(vmul(X1,X0),vmul(X2,X0))
      | ~ less(X1,X2) ),
    inference(ennf_transformation,[],[f49]) ).

fof(f49,plain,
    ! [X0,X1,X2] :
      ( less(X1,X2)
     => less(vmul(X1,X0),vmul(X2,X0)) ),
    inference(rectify,[],[f8]) ).

fof(f8,axiom,
    ! [X9,X10,X11] :
      ( less(X10,X11)
     => less(vmul(X10,X9),vmul(X11,X9)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(299, 0), 0)') ).

fof(f216,plain,
    spl4_21,
    inference(avatar_split_clause,[],[f95,f214]) ).

fof(f214,plain,
    ( spl4_21
  <=> ! [X0,X1] :
        ( vplus(X0,sK3(X0,X1)) = X1
        | ~ greater(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_21])]) ).

fof(f95,plain,
    ! [X0,X1] :
      ( vplus(X0,sK3(X0,X1)) = X1
      | ~ greater(X1,X0) ),
    inference(cnf_transformation,[],[f74]) ).

fof(f74,plain,
    ! [X0,X1] :
      ( ( greater(X1,X0)
        | ! [X2] : vplus(X0,X2) != X1 )
      & ( vplus(X0,sK3(X0,X1)) = X1
        | ~ greater(X1,X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f72,f73]) ).

fof(f73,plain,
    ! [X0,X1] :
      ( ? [X3] : vplus(X0,X3) = X1
     => vplus(X0,sK3(X0,X1)) = X1 ),
    introduced(choice_axiom,[]) ).

fof(f72,plain,
    ! [X0,X1] :
      ( ( greater(X1,X0)
        | ! [X2] : vplus(X0,X2) != X1 )
      & ( ? [X3] : vplus(X0,X3) = X1
        | ~ greater(X1,X0) ) ),
    inference(rectify,[],[f71]) ).

fof(f71,plain,
    ! [X0,X1] :
      ( ( greater(X1,X0)
        | ! [X2] : vplus(X0,X2) != X1 )
      & ( ? [X2] : vplus(X0,X2) = X1
        | ~ greater(X1,X0) ) ),
    inference(nnf_transformation,[],[f45]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( greater(X1,X0)
    <=> ? [X2] : vplus(X0,X2) = X1 ),
    inference(rectify,[],[f24]) ).

fof(f24,axiom,
    ! [X38,X39] :
      ( greater(X39,X38)
    <=> ? [X40] : vplus(X38,X40) = X39 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).

fof(f212,plain,
    spl4_20,
    inference(avatar_split_clause,[],[f93,f210]) ).

fof(f210,plain,
    ( spl4_20
  <=> ! [X0,X1] :
        ( vplus(X1,sK2(X0,X1)) = X0
        | ~ less(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_20])]) ).

fof(f93,plain,
    ! [X0,X1] :
      ( vplus(X1,sK2(X0,X1)) = X0
      | ~ less(X1,X0) ),
    inference(cnf_transformation,[],[f70]) ).

fof(f70,plain,
    ! [X0,X1] :
      ( ( less(X1,X0)
        | ! [X2] : vplus(X1,X2) != X0 )
      & ( vplus(X1,sK2(X0,X1)) = X0
        | ~ less(X1,X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f68,f69]) ).

fof(f69,plain,
    ! [X0,X1] :
      ( ? [X3] : vplus(X1,X3) = X0
     => vplus(X1,sK2(X0,X1)) = X0 ),
    introduced(choice_axiom,[]) ).

fof(f68,plain,
    ! [X0,X1] :
      ( ( less(X1,X0)
        | ! [X2] : vplus(X1,X2) != X0 )
      & ( ? [X3] : vplus(X1,X3) = X0
        | ~ less(X1,X0) ) ),
    inference(rectify,[],[f67]) ).

fof(f67,plain,
    ! [X0,X1] :
      ( ( less(X1,X0)
        | ! [X2] : vplus(X1,X2) != X0 )
      & ( ? [X2] : vplus(X1,X2) = X0
        | ~ less(X1,X0) ) ),
    inference(nnf_transformation,[],[f44]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( less(X1,X0)
    <=> ? [X2] : vplus(X1,X2) = X0 ),
    inference(rectify,[],[f23]) ).

fof(f23,axiom,
    ! [X35,X36] :
      ( less(X36,X35)
    <=> ? [X37] : vplus(X36,X37) = X35 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)') ).

fof(f208,plain,
    ( spl4_19
    | ~ spl4_2
    | ~ spl4_13 ),
    inference(avatar_split_clause,[],[f170,f165,f119,f205]) ).

fof(f205,plain,
    ( spl4_19
  <=> less(vd509,vd508) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_19])]) ).

fof(f170,plain,
    ( less(vd509,vd508)
    | ~ spl4_2
    | ~ spl4_13 ),
    inference(resolution,[],[f166,f121]) ).

fof(f121,plain,
    ( greater(vd508,vd509)
    | ~ spl4_2 ),
    inference(avatar_component_clause,[],[f119]) ).

fof(f203,plain,
    spl4_18,
    inference(avatar_split_clause,[],[f81,f201]) ).

fof(f201,plain,
    ( spl4_18
  <=> ! [X0,X1] : vmul(X0,vsucc(X1)) = vplus(vmul(X0,X1),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_18])]) ).

fof(f81,plain,
    ! [X0,X1] : vmul(X0,vsucc(X1)) = vplus(vmul(X0,X1),X0),
    inference(cnf_transformation,[],[f33]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( vmul(X0,v1) = X0
      & vmul(X0,vsucc(X1)) = vplus(vmul(X0,X1),X0) ),
    inference(rectify,[],[f16]) ).

fof(f16,axiom,
    ! [X27,X28] :
      ( vmul(X27,v1) = X27
      & vmul(X27,vsucc(X28)) = vplus(vmul(X27,X28),X27) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))') ).

fof(f199,plain,
    spl4_17,
    inference(avatar_split_clause,[],[f80,f197]) ).

fof(f197,plain,
    ( spl4_17
  <=> ! [X0,X1] : vmul(vsucc(X0),X1) = vplus(vmul(X0,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_17])]) ).

fof(f80,plain,
    ! [X0,X1] : vmul(vsucc(X0),X1) = vplus(vmul(X0,X1),X1),
    inference(cnf_transformation,[],[f32]) ).

fof(f32,plain,
    ! [X0,X1] : vmul(vsucc(X0),X1) = vplus(vmul(X0,X1),X1),
    inference(rectify,[],[f14]) ).

fof(f14,axiom,
    ! [X24,X25] : vmul(vsucc(X24),X25) = vplus(vmul(X24,X25),X25),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(261, 0), 0)') ).

fof(f192,plain,
    spl4_16,
    inference(avatar_split_clause,[],[f88,f190]) ).

fof(f190,plain,
    ( spl4_16
  <=> ! [X0,X1] :
        ( less(X0,X1)
        | greater(X0,X1)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_16])]) ).

fof(f88,plain,
    ! [X0,X1] :
      ( less(X0,X1)
      | greater(X0,X1)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f39]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( less(X0,X1)
      | greater(X0,X1)
      | X0 = X1 ),
    inference(rectify,[],[f19]) ).

fof(f19,axiom,
    ! [X33,X34] :
      ( less(X33,X34)
      | greater(X33,X34)
      | X33 = X34 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 0)') ).

fof(f180,plain,
    spl4_15,
    inference(avatar_split_clause,[],[f109,f178]) ).

fof(f178,plain,
    ( spl4_15
  <=> ! [X2,X0,X3] : vplus(vplus(X0,X2),X3) != X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_15])]) ).

fof(f109,plain,
    ! [X2,X3,X0] : vplus(vplus(X0,X2),X3) != X0,
    inference(equality_resolution,[],[f90]) ).

fof(f90,plain,
    ! [X2,X3,X0,X1] :
      ( vplus(X0,X2) != X1
      | vplus(X1,X3) != X0 ),
    inference(cnf_transformation,[],[f55]) ).

fof(f55,plain,
    ! [X0,X1] :
      ( ! [X2] : vplus(X0,X2) != X1
      | ! [X3] : vplus(X1,X3) != X0 ),
    inference(ennf_transformation,[],[f41]) ).

fof(f41,plain,
    ! [X0,X1] :
      ( ~ ? [X2] : vplus(X0,X2) = X1
      | ~ ? [X3] : vplus(X1,X3) = X0 ),
    inference(rectify,[],[f27]) ).

fof(f27,axiom,
    ! [X41,X42] :
      ( ~ ? [X44] : vplus(X41,X44) = X42
      | ~ ? [X43] : vplus(X42,X43) = X41 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 2)') ).

fof(f176,plain,
    spl4_14,
    inference(avatar_split_clause,[],[f79,f174]) ).

fof(f174,plain,
    ( spl4_14
  <=> ! [X0,X1] : vmul(X0,X1) = vmul(X1,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_14])]) ).

fof(f79,plain,
    ! [X0,X1] : vmul(X0,X1) = vmul(X1,X0),
    inference(cnf_transformation,[],[f31]) ).

fof(f31,plain,
    ! [X0,X1] : vmul(X0,X1) = vmul(X1,X0),
    inference(rectify,[],[f13]) ).

fof(f13,axiom,
    ! [X22,X23] : vmul(X22,X23) = vmul(X23,X22),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).

fof(f167,plain,
    spl4_13,
    inference(avatar_split_clause,[],[f92,f165]) ).

fof(f92,plain,
    ! [X0,X1] :
      ( less(X1,X0)
      | ~ greater(X0,X1) ),
    inference(cnf_transformation,[],[f57]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( less(X1,X0)
      | ~ greater(X0,X1) ),
    inference(ennf_transformation,[],[f43]) ).

fof(f43,plain,
    ! [X0,X1] :
      ( greater(X0,X1)
     => less(X1,X0) ),
    inference(rectify,[],[f18]) ).

fof(f18,axiom,
    ! [X31,X32] :
      ( greater(X31,X32)
     => less(X32,X31) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).

fof(f163,plain,
    spl4_12,
    inference(avatar_split_clause,[],[f91,f161]) ).

fof(f161,plain,
    ( spl4_12
  <=> ! [X0,X1] :
        ( greater(X1,X0)
        | ~ less(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_12])]) ).

fof(f91,plain,
    ! [X0,X1] :
      ( greater(X1,X0)
      | ~ less(X0,X1) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( greater(X1,X0)
      | ~ less(X0,X1) ),
    inference(ennf_transformation,[],[f42]) ).

fof(f42,plain,
    ! [X0,X1] :
      ( less(X0,X1)
     => greater(X1,X0) ),
    inference(rectify,[],[f17]) ).

fof(f17,axiom,
    ! [X29,X30] :
      ( less(X29,X30)
     => greater(X30,X29) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(147, 0), 0)') ).

fof(f159,plain,
    spl4_11,
    inference(avatar_split_clause,[],[f87,f157]) ).

fof(f157,plain,
    ( spl4_11
  <=> ! [X0,X1] :
        ( ~ less(X0,X1)
        | ~ greater(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_11])]) ).

fof(f87,plain,
    ! [X0,X1] :
      ( ~ less(X0,X1)
      | ~ greater(X0,X1) ),
    inference(cnf_transformation,[],[f38]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( ~ less(X0,X1)
      | ~ greater(X0,X1) ),
    inference(rectify,[],[f21]) ).

fof(f21,axiom,
    ! [X33,X34] :
      ( ~ less(X33,X34)
      | ~ greater(X33,X34) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 2)') ).

fof(f155,plain,
    spl4_10,
    inference(avatar_split_clause,[],[f111,f153]) ).

fof(f153,plain,
    ( spl4_10
  <=> ! [X2,X0] : greater(vplus(X0,X2),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_10])]) ).

fof(f111,plain,
    ! [X2,X0] : greater(vplus(X0,X2),X0),
    inference(equality_resolution,[],[f96]) ).

fof(f96,plain,
    ! [X2,X0,X1] :
      ( greater(X1,X0)
      | vplus(X0,X2) != X1 ),
    inference(cnf_transformation,[],[f74]) ).

fof(f151,plain,
    spl4_9,
    inference(avatar_split_clause,[],[f110,f149]) ).

fof(f149,plain,
    ( spl4_9
  <=> ! [X2,X1] : less(X1,vplus(X1,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_9])]) ).

fof(f110,plain,
    ! [X2,X1] : less(X1,vplus(X1,X2)),
    inference(equality_resolution,[],[f94]) ).

fof(f94,plain,
    ! [X2,X0,X1] :
      ( less(X1,X0)
      | vplus(X1,X2) != X0 ),
    inference(cnf_transformation,[],[f70]) ).

fof(f147,plain,
    spl4_8,
    inference(avatar_split_clause,[],[f107,f145]) ).

fof(f145,plain,
    ( spl4_8
  <=> ! [X2,X1] : vplus(X1,X2) != X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_8])]) ).

fof(f107,plain,
    ! [X2,X1] : vplus(X1,X2) != X1,
    inference(equality_resolution,[],[f85]) ).

fof(f85,plain,
    ! [X2,X0,X1] :
      ( vplus(X1,X2) != X0
      | X0 != X1 ),
    inference(cnf_transformation,[],[f53]) ).

fof(f53,plain,
    ! [X0,X1] :
      ( ! [X2] : vplus(X1,X2) != X0
      | X0 != X1 ),
    inference(ennf_transformation,[],[f36]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( ~ ? [X2] : vplus(X1,X2) = X0
      | X0 != X1 ),
    inference(rectify,[],[f28]) ).

fof(f28,axiom,
    ! [X41,X42] :
      ( ~ ? [X43] : vplus(X42,X43) = X41
      | X41 != X42 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 3)') ).

fof(f143,plain,
    spl4_7,
    inference(avatar_split_clause,[],[f82,f141]) ).

fof(f141,plain,
    ( spl4_7
  <=> ! [X0] : vmul(X0,v1) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_7])]) ).

fof(f82,plain,
    ! [X0] : vmul(X0,v1) = X0,
    inference(cnf_transformation,[],[f33]) ).

fof(f139,plain,
    spl4_6,
    inference(avatar_split_clause,[],[f78,f137]) ).

fof(f137,plain,
    ( spl4_6
  <=> ! [X0] : vmul(v1,X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_6])]) ).

fof(f78,plain,
    ! [X0] : vmul(v1,X0) = X0,
    inference(cnf_transformation,[],[f30]) ).

fof(f30,plain,
    ! [X0] : vmul(v1,X0) = X0,
    inference(rectify,[],[f15]) ).

fof(f15,axiom,
    ! [X26] : vmul(v1,X26) = X26,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(253, 0), 0)') ).

fof(f135,plain,
    spl4_5,
    inference(avatar_split_clause,[],[f106,f133]) ).

fof(f133,plain,
    ( spl4_5
  <=> ! [X1] : ~ greater(X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_5])]) ).

fof(f106,plain,
    ! [X1] : ~ greater(X1,X1),
    inference(equality_resolution,[],[f84]) ).

fof(f84,plain,
    ! [X0,X1] :
      ( ~ greater(X0,X1)
      | X0 != X1 ),
    inference(cnf_transformation,[],[f35]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( ~ greater(X0,X1)
      | X0 != X1 ),
    inference(rectify,[],[f22]) ).

fof(f22,axiom,
    ! [X33,X34] :
      ( ~ greater(X33,X34)
      | X33 != X34 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 3)') ).

fof(f131,plain,
    spl4_4,
    inference(avatar_split_clause,[],[f105,f129]) ).

fof(f129,plain,
    ( spl4_4
  <=> ! [X1] : ~ less(X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_4])]) ).

fof(f105,plain,
    ! [X1] : ~ less(X1,X1),
    inference(equality_resolution,[],[f83]) ).

fof(f83,plain,
    ! [X0,X1] :
      ( ~ less(X0,X1)
      | X0 != X1 ),
    inference(cnf_transformation,[],[f34]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( ~ less(X0,X1)
      | X0 != X1 ),
    inference(rectify,[],[f20]) ).

fof(f20,axiom,
    ! [X33,X34] :
      ( ~ less(X33,X34)
      | X33 != X34 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 1)') ).

fof(f127,plain,
    spl4_3,
    inference(avatar_split_clause,[],[f77,f124]) ).

fof(f77,plain,
    greater(vd511,vd512),
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    greater(vd511,vd512),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct2(314), 513, 0)') ).

fof(f122,plain,
    spl4_2,
    inference(avatar_split_clause,[],[f76,f119]) ).

fof(f76,plain,
    greater(vd508,vd509),
    inference(cnf_transformation,[],[f4]) ).

fof(f4,axiom,
    greater(vd508,vd509),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct1(314), 510, 0)') ).

fof(f117,plain,
    ~ spl4_1,
    inference(avatar_split_clause,[],[f75,f114]) ).

fof(f75,plain,
    ~ greater(vmul(vd508,vd511),vmul(vd509,vd511)),
    inference(cnf_transformation,[],[f29]) ).

fof(f29,plain,
    ~ greater(vmul(vd508,vd511),vmul(vd509,vd511)),
    inference(flattening,[],[f2]) ).

fof(f2,negated_conjecture,
    ~ greater(vmul(vd508,vd511),vmul(vd509,vd511)),
    inference(negated_conjecture,[],[f1]) ).

fof(f1,conjecture,
    greater(vmul(vd508,vd511),vmul(vd509,vd511)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct1(315), 514, 0)') ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : NUM854+2 : TPTP v8.1.2. Released v4.1.0.
% 0.03/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n013.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   : Fri May  3 14:57:53 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.36  % (25975)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.37  % (25978)WARNING: value z3 for option sas not known
% 0.20/0.37  % (25976)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.37  % (25978)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)
% 0.20/0.37  % (25979)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.37  % (25980)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)
% 0.20/0.37  % (25977)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.37  % (25981)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)
% 0.20/0.38  TRYING [1]
% 0.20/0.38  TRYING [2]
% 0.20/0.38  TRYING [3]
% 0.20/0.38  TRYING [1]
% 0.20/0.38  % (25980)First to succeed.
% 0.20/0.38  % (25981)Also succeeded, but the first one will report.
% 0.20/0.38  % (25978)Also succeeded, but the first one will report.
% 0.20/0.38  TRYING [2]
% 0.20/0.39  % (25980)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-25975"
% 0.20/0.39  % (25982)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)
% 0.20/0.39  % (25980)Refutation found. Thanks to Tanya!
% 0.20/0.39  % SZS status Theorem for theBenchmark
% 0.20/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.39  % (25980)------------------------------
% 0.20/0.39  % (25980)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.39  % (25980)Termination reason: Refutation
% 0.20/0.39  
% 0.20/0.39  % (25980)Memory used [KB]: 919
% 0.20/0.39  % (25980)Time elapsed: 0.013 s
% 0.20/0.39  % (25980)Instructions burned: 17 (million)
% 0.20/0.39  % (25975)Success in time 0.028 s
%------------------------------------------------------------------------------