TSTP Solution File: SWV492+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SWV492+1 : 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 : 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 : Thu Aug 31 23:25:11 EDT 2023

% Result   : Theorem 1.47s 0.57s
% Output   : Refutation 1.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   25
% Syntax   : Number of formulae    :  132 (   5 unt;   0 def)
%            Number of atoms       :  534 (  96 equ)
%            Maximal formula atoms :   17 (   4 avg)
%            Number of connectives :  681 ( 279   ~; 268   |;  96   &)
%                                         (  16 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   18 (  16 usr;  15 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;  10 con; 0-2 aty)
%            Number of variables   :  145 (; 121   !;  24   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f407,plain,
    $false,
    inference(avatar_sat_refutation,[],[f82,f86,f90,f94,f101,f116,f187,f200,f225,f309,f374,f379,f385,f406]) ).

fof(f406,plain,
    ( ~ spl7_3
    | ~ spl7_4
    | ~ spl7_5
    | ~ spl7_13 ),
    inference(avatar_contradiction_clause,[],[f405]) ).

fof(f405,plain,
    ( $false
    | ~ spl7_3
    | ~ spl7_4
    | ~ spl7_5
    | ~ spl7_13 ),
    inference(subsumption_resolution,[],[f404,f102]) ).

fof(f102,plain,
    ( int_leq(sK3,n)
    | ~ spl7_3
    | ~ spl7_4 ),
    inference(backward_demodulation,[],[f89,f85]) ).

fof(f85,plain,
    ( sK3 = sK4
    | ~ spl7_3 ),
    inference(avatar_component_clause,[],[f84]) ).

fof(f84,plain,
    ( spl7_3
  <=> sK3 = sK4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_3])]) ).

fof(f89,plain,
    ( int_leq(sK4,n)
    | ~ spl7_4 ),
    inference(avatar_component_clause,[],[f88]) ).

fof(f88,plain,
    ( spl7_4
  <=> int_leq(sK4,n) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_4])]) ).

fof(f404,plain,
    ( ~ int_leq(sK3,n)
    | ~ spl7_5
    | ~ spl7_13 ),
    inference(subsumption_resolution,[],[f401,f93]) ).

fof(f93,plain,
    ( int_leq(int_one,sK3)
    | ~ spl7_5 ),
    inference(avatar_component_clause,[],[f92]) ).

fof(f92,plain,
    ( spl7_5
  <=> int_leq(int_one,sK3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_5])]) ).

fof(f401,plain,
    ( ~ int_leq(int_one,sK3)
    | ~ int_leq(sK3,n)
    | ~ spl7_13 ),
    inference(resolution,[],[f222,f73]) ).

fof(f73,plain,
    ! [X1] : int_leq(X1,X1),
    inference(equality_resolution,[],[f66]) ).

fof(f66,plain,
    ! [X0,X1] :
      ( int_leq(X0,X1)
      | X0 != X1 ),
    inference(cnf_transformation,[],[f41]) ).

fof(f41,plain,
    ! [X0,X1] :
      ( ( int_leq(X0,X1)
        | ( X0 != X1
          & ~ int_less(X0,X1) ) )
      & ( X0 = X1
        | int_less(X0,X1)
        | ~ int_leq(X0,X1) ) ),
    inference(flattening,[],[f40]) ).

fof(f40,plain,
    ! [X0,X1] :
      ( ( int_leq(X0,X1)
        | ( X0 != X1
          & ~ int_less(X0,X1) ) )
      & ( X0 = X1
        | int_less(X0,X1)
        | ~ int_leq(X0,X1) ) ),
    inference(nnf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1] :
      ( int_leq(X0,X1)
    <=> ( X0 = X1
        | int_less(X0,X1) ) ),
    file('/export/starexec/sandbox/tmp/tmp.QPKnhshnLL/Vampire---4.8_25743',int_leq) ).

fof(f222,plain,
    ( ! [X0] :
        ( ~ int_leq(sK3,X0)
        | ~ int_leq(int_one,X0)
        | ~ int_leq(X0,n) )
    | ~ spl7_13 ),
    inference(avatar_component_clause,[],[f221]) ).

fof(f221,plain,
    ( spl7_13
  <=> ! [X0] :
        ( ~ int_leq(int_one,X0)
        | ~ int_leq(sK3,X0)
        | ~ int_leq(X0,n) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_13])]) ).

fof(f385,plain,
    ( ~ spl7_1
    | spl7_11 ),
    inference(avatar_split_clause,[],[f44,f182,f77]) ).

fof(f77,plain,
    ( spl7_1
  <=> sP0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_1])]) ).

fof(f182,plain,
    ( spl7_11
  <=> int_leq(sK2,n) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_11])]) ).

fof(f44,plain,
    ( int_leq(sK2,n)
    | ~ sP0 ),
    inference(cnf_transformation,[],[f32]) ).

fof(f32,plain,
    ( ( real_zero != a(sK1,sK2)
      & int_leq(sK2,n)
      & int_less(sK1,sK2)
      & int_leq(int_one,sK1) )
    | ~ sP0 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f30,f31]) ).

fof(f31,plain,
    ( ? [X0,X1] :
        ( real_zero != a(X0,X1)
        & int_leq(X1,n)
        & int_less(X0,X1)
        & int_leq(int_one,X0) )
   => ( real_zero != a(sK1,sK2)
      & int_leq(sK2,n)
      & int_less(sK1,sK2)
      & int_leq(int_one,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f30,plain,
    ( ? [X0,X1] :
        ( real_zero != a(X0,X1)
        & int_leq(X1,n)
        & int_less(X0,X1)
        & int_leq(int_one,X0) )
    | ~ sP0 ),
    inference(rectify,[],[f29]) ).

fof(f29,plain,
    ( ? [X2,X3] :
        ( real_zero != a(X2,X3)
        & int_leq(X3,n)
        & int_less(X2,X3)
        & int_leq(int_one,X2) )
    | ~ sP0 ),
    inference(nnf_transformation,[],[f27]) ).

fof(f27,plain,
    ( ? [X2,X3] :
        ( real_zero != a(X2,X3)
        & int_leq(X3,n)
        & int_less(X2,X3)
        & int_leq(int_one,X2) )
    | ~ sP0 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f379,plain,
    ( ~ spl7_1
    | spl7_19 ),
    inference(avatar_contradiction_clause,[],[f378]) ).

fof(f378,plain,
    ( $false
    | ~ spl7_1
    | spl7_19 ),
    inference(subsumption_resolution,[],[f375,f78]) ).

fof(f78,plain,
    ( sP0
    | ~ spl7_1 ),
    inference(avatar_component_clause,[],[f77]) ).

fof(f375,plain,
    ( ~ sP0
    | spl7_19 ),
    inference(resolution,[],[f308,f42]) ).

fof(f42,plain,
    ( int_leq(int_one,sK1)
    | ~ sP0 ),
    inference(cnf_transformation,[],[f32]) ).

fof(f308,plain,
    ( ~ int_leq(int_one,sK1)
    | spl7_19 ),
    inference(avatar_component_clause,[],[f307]) ).

fof(f307,plain,
    ( spl7_19
  <=> int_leq(int_one,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_19])]) ).

fof(f374,plain,
    ( ~ spl7_1
    | spl7_18 ),
    inference(avatar_contradiction_clause,[],[f373]) ).

fof(f373,plain,
    ( $false
    | ~ spl7_1
    | spl7_18 ),
    inference(subsumption_resolution,[],[f370,f78]) ).

fof(f370,plain,
    ( ~ sP0
    | ~ spl7_1
    | spl7_18 ),
    inference(resolution,[],[f362,f42]) ).

fof(f362,plain,
    ( ~ int_leq(int_one,sK1)
    | ~ spl7_1
    | spl7_18 ),
    inference(resolution,[],[f336,f206]) ).

fof(f206,plain,
    ( int_less(sK1,sK2)
    | ~ spl7_1 ),
    inference(subsumption_resolution,[],[f43,f78]) ).

fof(f43,plain,
    ( int_less(sK1,sK2)
    | ~ sP0 ),
    inference(cnf_transformation,[],[f32]) ).

fof(f336,plain,
    ( ! [X0] :
        ( ~ int_less(X0,sK2)
        | ~ int_leq(int_one,X0) )
    | spl7_18 ),
    inference(resolution,[],[f313,f57]) ).

fof(f57,plain,
    ! [X0] :
      ( int_less(int_zero,X0)
      | ~ int_leq(int_one,X0) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f35,plain,
    ! [X0] :
      ( ( int_less(int_zero,X0)
        | ~ int_leq(int_one,X0) )
      & ( int_leq(int_one,X0)
        | ~ int_less(int_zero,X0) ) ),
    inference(nnf_transformation,[],[f10]) ).

fof(f10,axiom,
    ! [X0] :
      ( int_less(int_zero,X0)
    <=> int_leq(int_one,X0) ),
    file('/export/starexec/sandbox/tmp/tmp.QPKnhshnLL/Vampire---4.8_25743',one_successor_of_zero) ).

fof(f313,plain,
    ( ! [X0] :
        ( ~ int_less(int_zero,X0)
        | ~ int_less(X0,sK2) )
    | spl7_18 ),
    inference(resolution,[],[f310,f67]) ).

fof(f67,plain,
    ! [X2,X0,X1] :
      ( int_less(X0,X2)
      | ~ int_less(X1,X2)
      | ~ int_less(X0,X1) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1,X2] :
      ( int_less(X0,X2)
      | ~ int_less(X1,X2)
      | ~ int_less(X0,X1) ),
    inference(flattening,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1,X2] :
      ( int_less(X0,X2)
      | ~ int_less(X1,X2)
      | ~ int_less(X0,X1) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1,X2] :
      ( ( int_less(X1,X2)
        & int_less(X0,X1) )
     => int_less(X0,X2) ),
    file('/export/starexec/sandbox/tmp/tmp.QPKnhshnLL/Vampire---4.8_25743',int_less_transitive) ).

fof(f310,plain,
    ( ~ int_less(int_zero,sK2)
    | spl7_18 ),
    inference(resolution,[],[f305,f56]) ).

fof(f56,plain,
    ! [X0] :
      ( int_leq(int_one,X0)
      | ~ int_less(int_zero,X0) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f305,plain,
    ( ~ int_leq(int_one,sK2)
    | spl7_18 ),
    inference(avatar_component_clause,[],[f304]) ).

fof(f304,plain,
    ( spl7_18
  <=> int_leq(int_one,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_18])]) ).

fof(f309,plain,
    ( ~ spl7_8
    | ~ spl7_18
    | ~ spl7_19
    | ~ spl7_1 ),
    inference(avatar_split_clause,[],[f302,f77,f307,f304,f112]) ).

fof(f112,plain,
    ( spl7_8
  <=> int_leq(sK1,n) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_8])]) ).

fof(f302,plain,
    ( ~ int_leq(int_one,sK1)
    | ~ int_leq(int_one,sK2)
    | ~ int_leq(sK1,n)
    | ~ spl7_1 ),
    inference(subsumption_resolution,[],[f301,f206]) ).

fof(f301,plain,
    ( ~ int_leq(int_one,sK1)
    | ~ int_leq(int_one,sK2)
    | ~ int_leq(sK1,n)
    | ~ int_less(sK1,sK2)
    | ~ spl7_1 ),
    inference(subsumption_resolution,[],[f298,f205]) ).

fof(f205,plain,
    ( int_leq(sK2,n)
    | ~ spl7_1 ),
    inference(subsumption_resolution,[],[f44,f78]) ).

fof(f298,plain,
    ( ~ int_leq(int_one,sK1)
    | ~ int_leq(sK2,n)
    | ~ int_leq(int_one,sK2)
    | ~ int_leq(sK1,n)
    | ~ int_less(sK1,sK2)
    | ~ spl7_1 ),
    inference(trivial_inequality_removal,[],[f297]) ).

fof(f297,plain,
    ( real_zero != real_zero
    | ~ int_leq(int_one,sK1)
    | ~ int_leq(sK2,n)
    | ~ int_leq(int_one,sK2)
    | ~ int_leq(sK1,n)
    | ~ int_less(sK1,sK2)
    | ~ spl7_1 ),
    inference(superposition,[],[f204,f261]) ).

fof(f261,plain,
    ! [X0,X1] :
      ( real_zero = a(X0,X1)
      | ~ int_leq(int_one,X0)
      | ~ int_leq(X1,n)
      | ~ int_leq(int_one,X1)
      | ~ int_leq(X0,n)
      | ~ int_less(X0,X1) ),
    inference(subsumption_resolution,[],[f260,f73]) ).

fof(f260,plain,
    ! [X0,X1] :
      ( ~ int_leq(X1,n)
      | ~ int_leq(X0,X0)
      | ~ int_leq(int_one,X0)
      | real_zero = a(X0,X1)
      | ~ int_leq(int_one,X1)
      | ~ int_leq(X0,n)
      | ~ int_less(X0,X1) ),
    inference(duplicate_literal_removal,[],[f257]) ).

fof(f257,plain,
    ! [X0,X1] :
      ( ~ int_leq(X1,n)
      | ~ int_leq(X0,X0)
      | ~ int_leq(int_one,X0)
      | real_zero = a(X0,X1)
      | ~ int_leq(int_one,X1)
      | ~ int_leq(X0,n)
      | ~ int_leq(int_one,X0)
      | ~ int_less(X0,X1)
      | ~ int_less(X0,X1) ),
    inference(superposition,[],[f203,f61]) ).

fof(f61,plain,
    ! [X0,X1] :
      ( plus(X0,sK5(X0,X1)) = X1
      | ~ int_less(X0,X1) ),
    inference(cnf_transformation,[],[f39]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( ( int_less(X0,X1)
        | ! [X2] :
            ( ~ int_less(int_zero,X2)
            | plus(X0,X2) != X1 ) )
      & ( ( int_less(int_zero,sK5(X0,X1))
          & plus(X0,sK5(X0,X1)) = X1 )
        | ~ int_less(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f37,f38]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( int_less(int_zero,X3)
          & plus(X0,X3) = X1 )
     => ( int_less(int_zero,sK5(X0,X1))
        & plus(X0,sK5(X0,X1)) = X1 ) ),
    introduced(choice_axiom,[]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( ( int_less(X0,X1)
        | ! [X2] :
            ( ~ int_less(int_zero,X2)
            | plus(X0,X2) != X1 ) )
      & ( ? [X3] :
            ( int_less(int_zero,X3)
            & plus(X0,X3) = X1 )
        | ~ int_less(X0,X1) ) ),
    inference(rectify,[],[f36]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( ( int_less(X0,X1)
        | ! [X2] :
            ( ~ int_less(int_zero,X2)
            | plus(X0,X2) != X1 ) )
      & ( ? [X2] :
            ( int_less(int_zero,X2)
            & plus(X0,X2) = X1 )
        | ~ int_less(X0,X1) ) ),
    inference(nnf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0,X1] :
      ( int_less(X0,X1)
    <=> ? [X2] :
          ( int_less(int_zero,X2)
          & plus(X0,X2) = X1 ) ),
    file('/export/starexec/sandbox/tmp/tmp.QPKnhshnLL/Vampire---4.8_25743',plus_and_inverse) ).

fof(f203,plain,
    ! [X10,X8,X9] :
      ( ~ int_leq(plus(X10,sK5(X8,X9)),n)
      | ~ int_leq(X8,X10)
      | ~ int_leq(int_one,X8)
      | real_zero = a(X8,X9)
      | ~ int_leq(int_one,plus(X10,sK5(X8,X9)))
      | ~ int_leq(X10,n)
      | ~ int_leq(int_one,X10)
      | ~ int_less(X8,X9) ),
    inference(subsumption_resolution,[],[f123,f62]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( int_less(int_zero,sK5(X0,X1))
      | ~ int_less(X0,X1) ),
    inference(cnf_transformation,[],[f39]) ).

fof(f123,plain,
    ! [X10,X8,X9] :
      ( real_zero = a(X8,X9)
      | ~ int_leq(X8,X10)
      | ~ int_leq(int_one,X8)
      | ~ int_less(int_zero,sK5(X8,X9))
      | ~ int_leq(plus(X10,sK5(X8,X9)),n)
      | ~ int_leq(int_one,plus(X10,sK5(X8,X9)))
      | ~ int_leq(X10,n)
      | ~ int_leq(int_one,X10)
      | ~ int_less(X8,X9) ),
    inference(superposition,[],[f69,f61]) ).

fof(f69,plain,
    ! [X2,X3,X0] :
      ( real_zero = a(X3,plus(X3,X2))
      | ~ int_leq(X3,X0)
      | ~ int_leq(int_one,X3)
      | ~ int_less(int_zero,X2)
      | ~ int_leq(plus(X0,X2),n)
      | ~ int_leq(int_one,plus(X0,X2))
      | ~ int_leq(X0,n)
      | ~ int_leq(int_one,X0) ),
    inference(equality_resolution,[],[f52]) ).

fof(f52,plain,
    ! [X2,X3,X0,X1] :
      ( real_zero = a(X3,plus(X3,X2))
      | ~ int_leq(X3,X0)
      | ~ int_leq(int_one,X3)
      | plus(X0,X2) != X1
      | ~ int_less(int_zero,X2)
      | ~ int_leq(X1,n)
      | ~ int_leq(int_one,X1)
      | ~ int_leq(X0,n)
      | ~ int_leq(int_one,X0) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ! [X3] :
                ( real_zero = a(X3,plus(X3,X2))
                | ~ int_leq(X3,X0)
                | ~ int_leq(int_one,X3) )
            | plus(X0,X2) != X1
            | ~ int_less(int_zero,X2) )
        & ! [X4] :
            ( real_one = a(X4,X4)
            | ~ int_leq(X4,X1)
            | ~ int_leq(int_one,X4) )
        & ! [X5] :
            ( ! [X6] :
                ( a(plus(X6,X5),X6) = qr(plus(X6,X5),X6)
                | ~ int_leq(X6,X1)
                | ~ int_leq(int_one,X6) )
            | plus(X1,X5) != X0
            | ~ int_less(int_zero,X5) ) )
      | ~ int_leq(X1,n)
      | ~ int_leq(int_one,X1)
      | ~ int_leq(X0,n)
      | ~ int_leq(int_one,X0) ),
    inference(flattening,[],[f20]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ! [X3] :
                ( real_zero = a(X3,plus(X3,X2))
                | ~ int_leq(X3,X0)
                | ~ int_leq(int_one,X3) )
            | plus(X0,X2) != X1
            | ~ int_less(int_zero,X2) )
        & ! [X4] :
            ( real_one = a(X4,X4)
            | ~ int_leq(X4,X1)
            | ~ int_leq(int_one,X4) )
        & ! [X5] :
            ( ! [X6] :
                ( a(plus(X6,X5),X6) = qr(plus(X6,X5),X6)
                | ~ int_leq(X6,X1)
                | ~ int_leq(int_one,X6) )
            | plus(X1,X5) != X0
            | ~ int_less(int_zero,X5) ) )
      | ~ int_leq(X1,n)
      | ~ int_leq(int_one,X1)
      | ~ int_leq(X0,n)
      | ~ int_leq(int_one,X0) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( ( int_leq(X1,n)
        & int_leq(int_one,X1)
        & int_leq(X0,n)
        & int_leq(int_one,X0) )
     => ( ! [X2] :
            ( ( plus(X0,X2) = X1
              & int_less(int_zero,X2) )
           => ! [X3] :
                ( ( int_leq(X3,X0)
                  & int_leq(int_one,X3) )
               => real_zero = a(X3,plus(X3,X2)) ) )
        & ! [X4] :
            ( ( int_leq(X4,X1)
              & int_leq(int_one,X4) )
           => real_one = a(X4,X4) )
        & ! [X5] :
            ( ( plus(X1,X5) = X0
              & int_less(int_zero,X5) )
           => ! [X6] :
                ( ( int_leq(X6,X1)
                  & int_leq(int_one,X6) )
               => a(plus(X6,X5),X6) = qr(plus(X6,X5),X6) ) ) ) ),
    inference(rectify,[],[f12]) ).

fof(f12,axiom,
    ! [X0,X1] :
      ( ( int_leq(X1,n)
        & int_leq(int_one,X1)
        & int_leq(X0,n)
        & int_leq(int_one,X0) )
     => ( ! [X7] :
            ( ( plus(X0,X7) = X1
              & int_less(int_zero,X7) )
           => ! [X2] :
                ( ( int_leq(X2,X0)
                  & int_leq(int_one,X2) )
               => real_zero = a(X2,plus(X2,X7)) ) )
        & ! [X2] :
            ( ( int_leq(X2,X1)
              & int_leq(int_one,X2) )
           => real_one = a(X2,X2) )
        & ! [X7] :
            ( ( plus(X1,X7) = X0
              & int_less(int_zero,X7) )
           => ! [X2] :
                ( ( int_leq(X2,X1)
                  & int_leq(int_one,X2) )
               => a(plus(X2,X7),X2) = qr(plus(X2,X7),X2) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.QPKnhshnLL/Vampire---4.8_25743',qih) ).

fof(f204,plain,
    ( real_zero != a(sK1,sK2)
    | ~ spl7_1 ),
    inference(subsumption_resolution,[],[f45,f78]) ).

fof(f45,plain,
    ( real_zero != a(sK1,sK2)
    | ~ sP0 ),
    inference(cnf_transformation,[],[f32]) ).

fof(f225,plain,
    ( ~ spl7_5
    | spl7_13
    | ~ spl7_2
    | ~ spl7_3
    | ~ spl7_7 ),
    inference(avatar_split_clause,[],[f224,f99,f84,f80,f221,f92]) ).

fof(f80,plain,
    ( spl7_2
  <=> real_zero = sF6 ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_2])]) ).

fof(f99,plain,
    ( spl7_7
  <=> ! [X4,X1] :
        ( real_one = a(X4,X4)
        | ~ int_leq(int_one,X1)
        | ~ int_leq(X1,n)
        | ~ int_leq(int_one,X4)
        | ~ int_leq(X4,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_7])]) ).

fof(f224,plain,
    ( ! [X0] :
        ( ~ int_leq(int_one,X0)
        | ~ int_leq(X0,n)
        | ~ int_leq(int_one,sK3)
        | ~ int_leq(sK3,X0) )
    | ~ spl7_2
    | ~ spl7_3
    | ~ spl7_7 ),
    inference(subsumption_resolution,[],[f217,f53]) ).

fof(f53,plain,
    real_zero != real_one,
    inference(cnf_transformation,[],[f11]) ).

fof(f11,axiom,
    real_zero != real_one,
    file('/export/starexec/sandbox/tmp/tmp.QPKnhshnLL/Vampire---4.8_25743',real_constants) ).

fof(f217,plain,
    ( ! [X0] :
        ( real_zero = real_one
        | ~ int_leq(int_one,X0)
        | ~ int_leq(X0,n)
        | ~ int_leq(int_one,sK3)
        | ~ int_leq(sK3,X0) )
    | ~ spl7_2
    | ~ spl7_3
    | ~ spl7_7 ),
    inference(superposition,[],[f104,f100]) ).

fof(f100,plain,
    ( ! [X1,X4] :
        ( real_one = a(X4,X4)
        | ~ int_leq(int_one,X1)
        | ~ int_leq(X1,n)
        | ~ int_leq(int_one,X4)
        | ~ int_leq(X4,X1) )
    | ~ spl7_7 ),
    inference(avatar_component_clause,[],[f99]) ).

fof(f104,plain,
    ( real_zero = a(sK3,sK3)
    | ~ spl7_2
    | ~ spl7_3 ),
    inference(backward_demodulation,[],[f103,f81]) ).

fof(f81,plain,
    ( real_zero = sF6
    | ~ spl7_2 ),
    inference(avatar_component_clause,[],[f80]) ).

fof(f103,plain,
    ( sF6 = a(sK3,sK3)
    | ~ spl7_3 ),
    inference(backward_demodulation,[],[f74,f85]) ).

fof(f74,plain,
    a(sK3,sK4) = sF6,
    introduced(function_definition,[]) ).

fof(f200,plain,
    ( ~ spl7_1
    | spl7_8
    | ~ spl7_12 ),
    inference(avatar_contradiction_clause,[],[f199]) ).

fof(f199,plain,
    ( $false
    | ~ spl7_1
    | spl7_8
    | ~ spl7_12 ),
    inference(subsumption_resolution,[],[f198,f78]) ).

fof(f198,plain,
    ( ~ sP0
    | spl7_8
    | ~ spl7_12 ),
    inference(subsumption_resolution,[],[f192,f119]) ).

fof(f119,plain,
    ( ~ int_less(sK1,n)
    | spl7_8 ),
    inference(resolution,[],[f113,f65]) ).

fof(f65,plain,
    ! [X0,X1] :
      ( int_leq(X0,X1)
      | ~ int_less(X0,X1) ),
    inference(cnf_transformation,[],[f41]) ).

fof(f113,plain,
    ( ~ int_leq(sK1,n)
    | spl7_8 ),
    inference(avatar_component_clause,[],[f112]) ).

fof(f192,plain,
    ( int_less(sK1,n)
    | ~ sP0
    | ~ spl7_12 ),
    inference(backward_demodulation,[],[f43,f186]) ).

fof(f186,plain,
    ( n = sK2
    | ~ spl7_12 ),
    inference(avatar_component_clause,[],[f185]) ).

fof(f185,plain,
    ( spl7_12
  <=> n = sK2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_12])]) ).

fof(f187,plain,
    ( ~ spl7_11
    | spl7_12
    | ~ spl7_1
    | spl7_8 ),
    inference(avatar_split_clause,[],[f179,f112,f77,f185,f182]) ).

fof(f179,plain,
    ( n = sK2
    | ~ int_leq(sK2,n)
    | ~ spl7_1
    | spl7_8 ),
    inference(resolution,[],[f176,f64]) ).

fof(f64,plain,
    ! [X0,X1] :
      ( int_less(X0,X1)
      | X0 = X1
      | ~ int_leq(X0,X1) ),
    inference(cnf_transformation,[],[f41]) ).

fof(f176,plain,
    ( ~ int_less(sK2,n)
    | ~ spl7_1
    | spl7_8 ),
    inference(subsumption_resolution,[],[f171,f78]) ).

fof(f171,plain,
    ( ~ int_less(sK2,n)
    | ~ sP0
    | spl7_8 ),
    inference(resolution,[],[f138,f43]) ).

fof(f138,plain,
    ( ! [X0] :
        ( ~ int_less(sK1,X0)
        | ~ int_less(X0,n) )
    | spl7_8 ),
    inference(resolution,[],[f119,f67]) ).

fof(f116,plain,
    ( ~ spl7_3
    | ~ spl7_4
    | ~ spl7_5
    | ~ spl7_6 ),
    inference(avatar_contradiction_clause,[],[f115]) ).

fof(f115,plain,
    ( $false
    | ~ spl7_3
    | ~ spl7_4
    | ~ spl7_5
    | ~ spl7_6 ),
    inference(subsumption_resolution,[],[f107,f102]) ).

fof(f107,plain,
    ( ~ int_leq(sK3,n)
    | ~ spl7_5
    | ~ spl7_6 ),
    inference(resolution,[],[f97,f93]) ).

fof(f97,plain,
    ( ! [X0] :
        ( ~ int_leq(int_one,X0)
        | ~ int_leq(X0,n) )
    | ~ spl7_6 ),
    inference(avatar_component_clause,[],[f96]) ).

fof(f96,plain,
    ( spl7_6
  <=> ! [X0] :
        ( ~ int_leq(X0,n)
        | ~ int_leq(int_one,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_6])]) ).

fof(f101,plain,
    ( spl7_6
    | spl7_7 ),
    inference(avatar_split_clause,[],[f51,f99,f96]) ).

fof(f51,plain,
    ! [X0,X1,X4] :
      ( real_one = a(X4,X4)
      | ~ int_leq(X4,X1)
      | ~ int_leq(int_one,X4)
      | ~ int_leq(X1,n)
      | ~ int_leq(int_one,X1)
      | ~ int_leq(X0,n)
      | ~ int_leq(int_one,X0) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f94,plain,
    ( spl7_1
    | spl7_5 ),
    inference(avatar_split_clause,[],[f46,f92,f77]) ).

fof(f46,plain,
    ( int_leq(int_one,sK3)
    | sP0 ),
    inference(cnf_transformation,[],[f34]) ).

fof(f34,plain,
    ( ( real_zero = a(sK3,sK4)
      & sK3 = sK4
      & int_leq(sK4,n)
      & int_leq(int_one,sK3) )
    | sP0 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f28,f33]) ).

fof(f33,plain,
    ( ? [X0,X1] :
        ( real_zero = a(X0,X1)
        & X0 = X1
        & int_leq(X1,n)
        & int_leq(int_one,X0) )
   => ( real_zero = a(sK3,sK4)
      & sK3 = sK4
      & int_leq(sK4,n)
      & int_leq(int_one,sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f28,plain,
    ( ? [X0,X1] :
        ( real_zero = a(X0,X1)
        & X0 = X1
        & int_leq(X1,n)
        & int_leq(int_one,X0) )
    | sP0 ),
    inference(definition_folding,[],[f19,f27]) ).

fof(f19,plain,
    ( ? [X0,X1] :
        ( real_zero = a(X0,X1)
        & X0 = X1
        & int_leq(X1,n)
        & int_leq(int_one,X0) )
    | ? [X2,X3] :
        ( real_zero != a(X2,X3)
        & int_leq(X3,n)
        & int_less(X2,X3)
        & int_leq(int_one,X2) ) ),
    inference(flattening,[],[f18]) ).

fof(f18,plain,
    ( ? [X0,X1] :
        ( real_zero = a(X0,X1)
        & X0 = X1
        & int_leq(X1,n)
        & int_leq(int_one,X0) )
    | ? [X2,X3] :
        ( real_zero != a(X2,X3)
        & int_leq(X3,n)
        & int_less(X2,X3)
        & int_leq(int_one,X2) ) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,plain,
    ~ ( ! [X0,X1] :
          ( ( X0 = X1
            & int_leq(X1,n)
            & int_leq(int_one,X0) )
         => real_zero != a(X0,X1) )
      & ! [X2,X3] :
          ( ( int_leq(X3,n)
            & int_less(X2,X3)
            & int_leq(int_one,X2) )
         => real_zero = a(X2,X3) ) ),
    inference(rectify,[],[f14]) ).

fof(f14,negated_conjecture,
    ~ ( ! [X0,X1] :
          ( ( X0 = X1
            & int_leq(X1,n)
            & int_leq(int_one,X0) )
         => real_zero != a(X0,X1) )
      & ! [X0,X1] :
          ( ( int_leq(X1,n)
            & int_less(X0,X1)
            & int_leq(int_one,X0) )
         => real_zero = a(X0,X1) ) ),
    inference(negated_conjecture,[],[f13]) ).

fof(f13,conjecture,
    ( ! [X0,X1] :
        ( ( X0 = X1
          & int_leq(X1,n)
          & int_leq(int_one,X0) )
       => real_zero != a(X0,X1) )
    & ! [X0,X1] :
        ( ( int_leq(X1,n)
          & int_less(X0,X1)
          & int_leq(int_one,X0) )
       => real_zero = a(X0,X1) ) ),
    file('/export/starexec/sandbox/tmp/tmp.QPKnhshnLL/Vampire---4.8_25743',lti) ).

fof(f90,plain,
    ( spl7_1
    | spl7_4 ),
    inference(avatar_split_clause,[],[f47,f88,f77]) ).

fof(f47,plain,
    ( int_leq(sK4,n)
    | sP0 ),
    inference(cnf_transformation,[],[f34]) ).

fof(f86,plain,
    ( spl7_1
    | spl7_3 ),
    inference(avatar_split_clause,[],[f48,f84,f77]) ).

fof(f48,plain,
    ( sK3 = sK4
    | sP0 ),
    inference(cnf_transformation,[],[f34]) ).

fof(f82,plain,
    ( spl7_1
    | spl7_2 ),
    inference(avatar_split_clause,[],[f75,f80,f77]) ).

fof(f75,plain,
    ( real_zero = sF6
    | sP0 ),
    inference(definition_folding,[],[f49,f74]) ).

fof(f49,plain,
    ( real_zero = a(sK3,sK4)
    | sP0 ),
    inference(cnf_transformation,[],[f34]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SWV492+1 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.14  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.14/0.35  % Computer : n009.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   : Tue Aug 29 10:10:05 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  This is a FOF_THM_RFO_SEQ problem
% 0.14/0.35  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.QPKnhshnLL/Vampire---4.8_25743
% 0.14/0.36  % (25850)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.40  % (25854)lrs-3_8_anc=none:bce=on:cond=on:drc=off:flr=on:fsd=off:fsr=off:fde=unused:gsp=on:gs=on:gsaa=full_model:lcm=predicate:lma=on:nm=16:sos=all:sp=weighted_frequency:tgt=ground:urr=ec_only:stl=188_482 on Vampire---4 for (482ds/0Mi)
% 0.21/0.42  % (25851)lrs+10_11_cond=on:drc=off:flr=on:fsr=off:gsp=on:gs=on:gsem=off:lma=on:msp=off:nm=4:nwc=1.5:nicw=on:sas=z3:sims=off:sp=scramble:stl=188_730 on Vampire---4 for (730ds/0Mi)
% 0.21/0.42  % (25855)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_424 on Vampire---4 for (424ds/0Mi)
% 0.21/0.42  % (25852)dis+1010_4:1_anc=none:bd=off:drc=off:flr=on:fsr=off:nm=4:nwc=1.1:nicw=on:sas=z3_680 on Vampire---4 for (680ds/0Mi)
% 0.21/0.42  % (25856)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_413 on Vampire---4 for (413ds/0Mi)
% 0.21/0.42  % (25857)ott+11_14_av=off:bs=on:bsr=on:cond=on:flr=on:fsd=off:fde=unused:gsp=on:nm=4:nwc=1.5:tgt=full_386 on Vampire---4 for (386ds/0Mi)
% 0.21/0.42  % (25853)dis-11_4:1_aac=none:add=off:afr=on:anc=none:bd=preordered:bs=on:bsr=on:drc=off:fsr=off:fde=none:gsp=on:irw=on:lcm=reverse:lma=on:nm=0:nwc=1.7:nicw=on:sas=z3:sims=off:sos=all:sac=on:sp=weighted_frequency:tgt=full_602 on Vampire---4 for (602ds/0Mi)
% 0.21/0.49  % (25853)Refutation not found, incomplete strategy% (25853)------------------------------
% 0.21/0.49  % (25853)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.49  % (25853)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.49  % (25853)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.49  
% 0.21/0.49  % (25853)Memory used [KB]: 1151
% 0.21/0.49  % (25853)Time elapsed: 0.076 s
% 0.21/0.49  % (25853)------------------------------
% 0.21/0.49  % (25853)------------------------------
% 0.21/0.53  % (25858)ott+10_5_av=off:bsr=on:br=off:drc=off:fsd=off:fsr=off:fde=unused:gsp=on:lcm=predicate:lma=on:nwc=2.5:sos=all:sp=occurrence:tgt=full:urr=on_375 on Vampire---4 for (375ds/0Mi)
% 0.21/0.53  % (25858)Refutation not found, incomplete strategy% (25858)------------------------------
% 0.21/0.53  % (25858)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.53  % (25858)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.53  % (25858)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.53  
% 0.21/0.53  % (25858)Memory used [KB]: 1023
% 0.21/0.53  % (25858)Time elapsed: 0.003 s
% 0.21/0.53  % (25858)------------------------------
% 0.21/0.53  % (25858)------------------------------
% 1.47/0.56  % (25859)lrs-1010_3_aac=none:anc=none:er=known:fsd=off:fde=unused:gs=on:lcm=predicate:sos=on:sp=weighted_frequency:tgt=ground:stl=62_365 on Vampire---4 for (365ds/0Mi)
% 1.47/0.57  % (25859)First to succeed.
% 1.47/0.57  % (25859)Refutation found. Thanks to Tanya!
% 1.47/0.57  % SZS status Theorem for Vampire---4
% 1.47/0.57  % SZS output start Proof for Vampire---4
% See solution above
% 1.47/0.57  % (25859)------------------------------
% 1.47/0.57  % (25859)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 1.47/0.57  % (25859)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 1.47/0.57  % (25859)Termination reason: Refutation
% 1.47/0.57  
% 1.47/0.57  % (25859)Memory used [KB]: 10234
% 1.47/0.57  % (25859)Time elapsed: 0.011 s
% 1.47/0.57  % (25859)------------------------------
% 1.47/0.57  % (25859)------------------------------
% 1.47/0.57  % (25850)Success in time 0.212 s
% 1.47/0.57  % Vampire---4.8 exiting
%------------------------------------------------------------------------------