TSTP Solution File: GEO093+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GEO093+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n008.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 11:14:02 EDT 2024

% Result   : Theorem 4.14s 0.94s
% Output   : Refutation 4.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   89 (  13 unt;   0 def)
%            Number of atoms       :  317 (  33 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  337 ( 109   ~; 140   |;  67   &)
%                                         (  10 <=>;  10  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-3 aty)
%            Number of variables   :  209 ( 187   !;  22   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f12073,plain,
    $false,
    inference(subsumption_resolution,[],[f11844,f104]) ).

fof(f104,plain,
    open(sK3),
    inference(cnf_transformation,[],[f61]) ).

fof(f61,plain,
    ( ~ open(sum(sK4,sK5))
    & meet(sK6,sK4,sK5)
    & part_of(sK5,sK3)
    & part_of(sK4,sK3)
    & open(sK3) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6])],[f35,f60]) ).

fof(f60,plain,
    ( ? [X0,X1,X2,X3] :
        ( ~ open(sum(X1,X2))
        & meet(X3,X1,X2)
        & part_of(X2,X0)
        & part_of(X1,X0)
        & open(X0) )
   => ( ~ open(sum(sK4,sK5))
      & meet(sK6,sK4,sK5)
      & part_of(sK5,sK3)
      & part_of(sK4,sK3)
      & open(sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f35,plain,
    ? [X0,X1,X2,X3] :
      ( ~ open(sum(X1,X2))
      & meet(X3,X1,X2)
      & part_of(X2,X0)
      & part_of(X1,X0)
      & open(X0) ),
    inference(flattening,[],[f34]) ).

fof(f34,plain,
    ? [X0,X1,X2,X3] :
      ( ~ open(sum(X1,X2))
      & meet(X3,X1,X2)
      & part_of(X2,X0)
      & part_of(X1,X0)
      & open(X0) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f19,plain,
    ~ ! [X0,X1,X2,X3] :
        ( ( meet(X3,X1,X2)
          & part_of(X2,X0)
          & part_of(X1,X0)
          & open(X0) )
       => open(sum(X1,X2)) ),
    inference(rectify,[],[f18]) ).

fof(f18,negated_conjecture,
    ~ ! [X0,X1,X3,X2] :
        ( ( meet(X2,X1,X3)
          & part_of(X3,X0)
          & part_of(X1,X0)
          & open(X0) )
       => open(sum(X1,X3)) ),
    inference(negated_conjecture,[],[f17]) ).

fof(f17,conjecture,
    ! [X0,X1,X3,X2] :
      ( ( meet(X2,X1,X3)
        & part_of(X3,X0)
        & part_of(X1,X0)
        & open(X0) )
     => open(sum(X1,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',proposition_2_14_2) ).

fof(f11844,plain,
    ~ open(sK3),
    inference(superposition,[],[f108,f11410]) ).

fof(f11410,plain,
    sK3 = sum(sK4,sK5),
    inference(resolution,[],[f11390,f1525]) ).

fof(f1525,plain,
    ! [X0] :
      ( ~ part_of(sum(sK4,sK5),X0)
      | sum(sK4,sK5) = X0 ),
    inference(subsumption_resolution,[],[f1521,f834]) ).

fof(f834,plain,
    ! [X0] :
      ( ~ incident_c(sK13(X0,sum(sK4,sK5)),X0)
      | sum(sK4,sK5) = X0 ),
    inference(duplicate_literal_removal,[],[f831]) ).

fof(f831,plain,
    ! [X0] :
      ( sum(sK4,sK5) = X0
      | sum(sK4,sK5) = X0
      | ~ incident_c(sK13(X0,sum(sK4,sK5)),X0) ),
    inference(resolution,[],[f734,f119]) ).

fof(f119,plain,
    ! [X0,X1] :
      ( ~ incident_c(sK13(X0,X1),X1)
      | X0 = X1
      | ~ incident_c(sK13(X0,X1),X0) ),
    inference(cnf_transformation,[],[f76]) ).

fof(f76,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ( ( ~ incident_c(sK13(X0,X1),X1)
          | ~ incident_c(sK13(X0,X1),X0) )
        & ( incident_c(sK13(X0,X1),X1)
          | incident_c(sK13(X0,X1),X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f74,f75]) ).

fof(f75,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ incident_c(X2,X1)
            | ~ incident_c(X2,X0) )
          & ( incident_c(X2,X1)
            | incident_c(X2,X0) ) )
     => ( ( ~ incident_c(sK13(X0,X1),X1)
          | ~ incident_c(sK13(X0,X1),X0) )
        & ( incident_c(sK13(X0,X1),X1)
          | incident_c(sK13(X0,X1),X0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f74,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ? [X2] :
          ( ( ~ incident_c(X2,X1)
            | ~ incident_c(X2,X0) )
          & ( incident_c(X2,X1)
            | incident_c(X2,X0) ) ) ),
    inference(nnf_transformation,[],[f41]) ).

fof(f41,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ? [X2] :
          ( incident_c(X2,X0)
        <~> incident_c(X2,X1) ) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f16,axiom,
    ! [X0,X1] :
      ( ! [X2] :
          ( incident_c(X2,X0)
        <=> incident_c(X2,X1) )
     => X0 = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c9) ).

fof(f734,plain,
    ! [X0,X1] :
      ( incident_c(sK13(X0,X1),sum(sK4,sK5))
      | X0 = X1 ),
    inference(subsumption_resolution,[],[f701,f678]) ).

fof(f678,plain,
    ! [X0,X1] :
      ( ~ incident_c(X1,X0)
      | incident_c(X1,sum(sK4,sK5)) ),
    inference(superposition,[],[f238,f377]) ).

fof(f377,plain,
    ! [X0] : sum(sK4,sK5) = sum(sum(sK4,sK5),X0),
    inference(resolution,[],[f353,f108]) ).

fof(f353,plain,
    ! [X0,X1] :
      ( open(X0)
      | sum(X0,X1) = X0 ),
    inference(resolution,[],[f350,f117]) ).

fof(f117,plain,
    ! [X0,X1] :
      ( ~ part_of(X1,X0)
      | X0 = X1
      | open(X1) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f40,plain,
    ! [X0,X1] :
      ( open(X1)
      | X0 = X1
      | ~ part_of(X1,X0) ),
    inference(flattening,[],[f39]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( open(X1)
      | X0 = X1
      | ~ part_of(X1,X0) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0,X1] :
      ( ( X0 != X1
        & part_of(X1,X0) )
     => open(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c1) ).

fof(f350,plain,
    ! [X0,X1] : part_of(X0,sum(X0,X1)),
    inference(duplicate_literal_removal,[],[f344]) ).

fof(f344,plain,
    ! [X0,X1] :
      ( part_of(X0,sum(X0,X1))
      | part_of(X0,sum(X0,X1)) ),
    inference(resolution,[],[f236,f135]) ).

fof(f135,plain,
    ! [X0,X1] :
      ( incident_c(sK17(X0,X1),X1)
      | part_of(X1,X0) ),
    inference(cnf_transformation,[],[f91]) ).

fof(f91,plain,
    ! [X0,X1] :
      ( ( part_of(X1,X0)
        | ( ~ incident_c(sK17(X0,X1),X0)
          & incident_c(sK17(X0,X1),X1) ) )
      & ( ! [X3] :
            ( incident_c(X3,X0)
            | ~ incident_c(X3,X1) )
        | ~ part_of(X1,X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f89,f90]) ).

fof(f90,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ incident_c(X2,X0)
          & incident_c(X2,X1) )
     => ( ~ incident_c(sK17(X0,X1),X0)
        & incident_c(sK17(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f89,plain,
    ! [X0,X1] :
      ( ( part_of(X1,X0)
        | ? [X2] :
            ( ~ incident_c(X2,X0)
            & incident_c(X2,X1) ) )
      & ( ! [X3] :
            ( incident_c(X3,X0)
            | ~ incident_c(X3,X1) )
        | ~ part_of(X1,X0) ) ),
    inference(rectify,[],[f88]) ).

fof(f88,plain,
    ! [X0,X1] :
      ( ( part_of(X1,X0)
        | ? [X2] :
            ( ~ incident_c(X2,X0)
            & incident_c(X2,X1) ) )
      & ( ! [X2] :
            ( incident_c(X2,X0)
            | ~ incident_c(X2,X1) )
        | ~ part_of(X1,X0) ) ),
    inference(nnf_transformation,[],[f45]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( part_of(X1,X0)
    <=> ! [X2] :
          ( incident_c(X2,X0)
          | ~ incident_c(X2,X1) ) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1] :
      ( part_of(X1,X0)
    <=> ! [X2] :
          ( incident_c(X2,X1)
         => incident_c(X2,X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',part_of_defn) ).

fof(f236,plain,
    ! [X2,X0,X1] :
      ( ~ incident_c(sK17(sum(X0,X1),X2),X0)
      | part_of(X2,sum(X0,X1)) ),
    inference(resolution,[],[f235,f136]) ).

fof(f136,plain,
    ! [X0,X1] :
      ( ~ incident_c(sK17(X0,X1),X0)
      | part_of(X1,X0) ),
    inference(cnf_transformation,[],[f91]) ).

fof(f235,plain,
    ! [X2,X0,X1] :
      ( incident_c(X0,sum(X1,X2))
      | ~ incident_c(X0,X1) ),
    inference(resolution,[],[f147,f157]) ).

fof(f157,plain,
    ! [X2,X1] : sP2(X2,X1,sum(X1,X2)),
    inference(equality_resolution,[],[f152]) ).

fof(f152,plain,
    ! [X2,X0,X1] :
      ( sP2(X2,X1,X0)
      | sum(X1,X2) != X0 ),
    inference(cnf_transformation,[],[f103]) ).

fof(f103,plain,
    ! [X0,X1,X2] :
      ( ( sum(X1,X2) = X0
        | ~ sP2(X2,X1,X0) )
      & ( sP2(X2,X1,X0)
        | sum(X1,X2) != X0 ) ),
    inference(nnf_transformation,[],[f59]) ).

fof(f59,plain,
    ! [X0,X1,X2] :
      ( sum(X1,X2) = X0
    <=> sP2(X2,X1,X0) ),
    inference(definition_folding,[],[f29,f58]) ).

fof(f58,plain,
    ! [X2,X1,X0] :
      ( sP2(X2,X1,X0)
    <=> ! [X3] :
          ( incident_c(X3,X0)
        <=> ( incident_c(X3,X2)
            | incident_c(X3,X1) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

fof(f29,plain,
    ! [X0,X1,X2] :
      ( sum(X1,X2) = X0
    <=> ! [X3] :
          ( incident_c(X3,X0)
        <=> ( incident_c(X3,X2)
            | incident_c(X3,X1) ) ) ),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1,X3] :
      ( sum(X1,X3) = X0
    <=> ! [X4] :
          ( incident_c(X4,X0)
        <=> ( incident_c(X4,X3)
            | incident_c(X4,X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_defn) ).

fof(f147,plain,
    ! [X2,X0,X1,X4] :
      ( ~ sP2(X0,X1,X2)
      | ~ incident_c(X4,X1)
      | incident_c(X4,X2) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f102,plain,
    ! [X0,X1,X2] :
      ( ( sP2(X0,X1,X2)
        | ( ( ( ~ incident_c(sK19(X0,X1,X2),X0)
              & ~ incident_c(sK19(X0,X1,X2),X1) )
            | ~ incident_c(sK19(X0,X1,X2),X2) )
          & ( incident_c(sK19(X0,X1,X2),X0)
            | incident_c(sK19(X0,X1,X2),X1)
            | incident_c(sK19(X0,X1,X2),X2) ) ) )
      & ( ! [X4] :
            ( ( incident_c(X4,X2)
              | ( ~ incident_c(X4,X0)
                & ~ incident_c(X4,X1) ) )
            & ( incident_c(X4,X0)
              | incident_c(X4,X1)
              | ~ incident_c(X4,X2) ) )
        | ~ sP2(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f100,f101]) ).

fof(f101,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ( ~ incident_c(X3,X0)
              & ~ incident_c(X3,X1) )
            | ~ incident_c(X3,X2) )
          & ( incident_c(X3,X0)
            | incident_c(X3,X1)
            | incident_c(X3,X2) ) )
     => ( ( ( ~ incident_c(sK19(X0,X1,X2),X0)
            & ~ incident_c(sK19(X0,X1,X2),X1) )
          | ~ incident_c(sK19(X0,X1,X2),X2) )
        & ( incident_c(sK19(X0,X1,X2),X0)
          | incident_c(sK19(X0,X1,X2),X1)
          | incident_c(sK19(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f100,plain,
    ! [X0,X1,X2] :
      ( ( sP2(X0,X1,X2)
        | ? [X3] :
            ( ( ( ~ incident_c(X3,X0)
                & ~ incident_c(X3,X1) )
              | ~ incident_c(X3,X2) )
            & ( incident_c(X3,X0)
              | incident_c(X3,X1)
              | incident_c(X3,X2) ) ) )
      & ( ! [X4] :
            ( ( incident_c(X4,X2)
              | ( ~ incident_c(X4,X0)
                & ~ incident_c(X4,X1) ) )
            & ( incident_c(X4,X0)
              | incident_c(X4,X1)
              | ~ incident_c(X4,X2) ) )
        | ~ sP2(X0,X1,X2) ) ),
    inference(rectify,[],[f99]) ).

fof(f99,plain,
    ! [X2,X1,X0] :
      ( ( sP2(X2,X1,X0)
        | ? [X3] :
            ( ( ( ~ incident_c(X3,X2)
                & ~ incident_c(X3,X1) )
              | ~ incident_c(X3,X0) )
            & ( incident_c(X3,X2)
              | incident_c(X3,X1)
              | incident_c(X3,X0) ) ) )
      & ( ! [X3] :
            ( ( incident_c(X3,X0)
              | ( ~ incident_c(X3,X2)
                & ~ incident_c(X3,X1) ) )
            & ( incident_c(X3,X2)
              | incident_c(X3,X1)
              | ~ incident_c(X3,X0) ) )
        | ~ sP2(X2,X1,X0) ) ),
    inference(flattening,[],[f98]) ).

fof(f98,plain,
    ! [X2,X1,X0] :
      ( ( sP2(X2,X1,X0)
        | ? [X3] :
            ( ( ( ~ incident_c(X3,X2)
                & ~ incident_c(X3,X1) )
              | ~ incident_c(X3,X0) )
            & ( incident_c(X3,X2)
              | incident_c(X3,X1)
              | incident_c(X3,X0) ) ) )
      & ( ! [X3] :
            ( ( incident_c(X3,X0)
              | ( ~ incident_c(X3,X2)
                & ~ incident_c(X3,X1) ) )
            & ( incident_c(X3,X2)
              | incident_c(X3,X1)
              | ~ incident_c(X3,X0) ) )
        | ~ sP2(X2,X1,X0) ) ),
    inference(nnf_transformation,[],[f58]) ).

fof(f238,plain,
    ! [X2,X0,X1] :
      ( incident_c(X0,sum(X2,X1))
      | ~ incident_c(X0,X1) ),
    inference(resolution,[],[f148,f157]) ).

fof(f148,plain,
    ! [X2,X0,X1,X4] :
      ( ~ sP2(X0,X1,X2)
      | ~ incident_c(X4,X0)
      | incident_c(X4,X2) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f701,plain,
    ! [X0,X1] :
      ( incident_c(sK13(X0,X1),sum(sK4,sK5))
      | incident_c(sK13(X0,X1),X1)
      | X0 = X1 ),
    inference(resolution,[],[f678,f118]) ).

fof(f118,plain,
    ! [X0,X1] :
      ( incident_c(sK13(X0,X1),X1)
      | incident_c(sK13(X0,X1),X0)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f76]) ).

fof(f1521,plain,
    ! [X0] :
      ( sum(sK4,sK5) = X0
      | incident_c(sK13(X0,sum(sK4,sK5)),X0)
      | ~ part_of(sum(sK4,sK5),X0) ),
    inference(duplicate_literal_removal,[],[f1515]) ).

fof(f1515,plain,
    ! [X0] :
      ( sum(sK4,sK5) = X0
      | incident_c(sK13(X0,sum(sK4,sK5)),X0)
      | sum(sK4,sK5) = X0
      | ~ part_of(sum(sK4,sK5),X0) ),
    inference(resolution,[],[f834,f316]) ).

fof(f316,plain,
    ! [X2,X0,X1] :
      ( incident_c(sK13(X0,X1),X2)
      | incident_c(sK13(X0,X1),X0)
      | X0 = X1
      | ~ part_of(X1,X2) ),
    inference(resolution,[],[f118,f134]) ).

fof(f134,plain,
    ! [X3,X0,X1] :
      ( ~ incident_c(X3,X1)
      | incident_c(X3,X0)
      | ~ part_of(X1,X0) ),
    inference(cnf_transformation,[],[f91]) ).

fof(f11390,plain,
    ! [X0] : part_of(X0,sK3),
    inference(subsumption_resolution,[],[f11389,f10291]) ).

fof(f10291,plain,
    ! [X0] :
      ( ~ incident_c(sK17(sK3,X0),sK4)
      | part_of(X0,sK3) ),
    inference(forward_demodulation,[],[f10206,f10114]) ).

fof(f10114,plain,
    sK3 = sum(sK3,sK4),
    inference(resolution,[],[f6543,f105]) ).

fof(f105,plain,
    part_of(sK4,sK3),
    inference(cnf_transformation,[],[f61]) ).

fof(f6543,plain,
    ! [X0,X1] :
      ( ~ part_of(X0,X1)
      | sum(X1,X0) = X1 ),
    inference(resolution,[],[f5691,f153]) ).

fof(f153,plain,
    ! [X2,X0,X1] :
      ( ~ sP2(X2,X1,X0)
      | sum(X1,X2) = X0 ),
    inference(cnf_transformation,[],[f103]) ).

fof(f5691,plain,
    ! [X0,X1] :
      ( sP2(X0,X1,X1)
      | ~ part_of(X0,X1) ),
    inference(subsumption_resolution,[],[f5690,f878]) ).

fof(f878,plain,
    ! [X0,X1] :
      ( incident_c(sK19(X0,X1,X1),X0)
      | sP2(X0,X1,X1) ),
    inference(subsumption_resolution,[],[f863,f150]) ).

fof(f150,plain,
    ! [X2,X0,X1] :
      ( ~ incident_c(sK19(X0,X1,X2),X2)
      | ~ incident_c(sK19(X0,X1,X2),X1)
      | sP2(X0,X1,X2) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f863,plain,
    ! [X0,X1] :
      ( incident_c(sK19(X0,X1,X1),X1)
      | incident_c(sK19(X0,X1,X1),X0)
      | sP2(X0,X1,X1) ),
    inference(factoring,[],[f149]) ).

fof(f149,plain,
    ! [X2,X0,X1] :
      ( incident_c(sK19(X0,X1,X2),X2)
      | incident_c(sK19(X0,X1,X2),X1)
      | incident_c(sK19(X0,X1,X2),X0)
      | sP2(X0,X1,X2) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f5690,plain,
    ! [X0,X1] :
      ( sP2(X0,X1,X1)
      | ~ part_of(X0,X1)
      | ~ incident_c(sK19(X0,X1,X1),X0) ),
    inference(duplicate_literal_removal,[],[f5671]) ).

fof(f5671,plain,
    ! [X0,X1] :
      ( sP2(X0,X1,X1)
      | ~ part_of(X0,X1)
      | ~ incident_c(sK19(X0,X1,X1),X0)
      | sP2(X0,X1,X1) ),
    inference(resolution,[],[f954,f151]) ).

fof(f151,plain,
    ! [X2,X0,X1] :
      ( ~ incident_c(sK19(X0,X1,X2),X2)
      | ~ incident_c(sK19(X0,X1,X2),X0)
      | sP2(X0,X1,X2) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f954,plain,
    ! [X2,X0,X1] :
      ( incident_c(sK19(X0,X1,X1),X2)
      | sP2(X0,X1,X1)
      | ~ part_of(X0,X2) ),
    inference(resolution,[],[f878,f134]) ).

fof(f10206,plain,
    ! [X0] :
      ( ~ incident_c(sK17(sK3,X0),sK4)
      | part_of(X0,sum(sK3,sK4)) ),
    inference(superposition,[],[f239,f10114]) ).

fof(f239,plain,
    ! [X2,X0,X1] :
      ( ~ incident_c(sK17(sum(X0,X1),X2),X1)
      | part_of(X2,sum(X0,X1)) ),
    inference(resolution,[],[f238,f136]) ).

fof(f11389,plain,
    ! [X0] :
      ( part_of(X0,sK3)
      | incident_c(sK17(sK3,X0),sK4) ),
    inference(duplicate_literal_removal,[],[f11378]) ).

fof(f11378,plain,
    ! [X0] :
      ( part_of(X0,sK3)
      | incident_c(sK17(sK3,X0),sK4)
      | part_of(X0,sK3) ),
    inference(resolution,[],[f10488,f1140]) ).

fof(f1140,plain,
    ! [X0,X1] :
      ( incident_c(sK17(X0,X1),sK5)
      | incident_c(sK17(X0,X1),sK4)
      | part_of(X1,X0) ),
    inference(resolution,[],[f457,f710]) ).

fof(f710,plain,
    ! [X0,X1] :
      ( incident_c(sK17(X0,X1),sum(sK4,sK5))
      | part_of(X1,X0) ),
    inference(resolution,[],[f678,f135]) ).

fof(f457,plain,
    ! [X2,X0,X1] :
      ( ~ incident_c(X0,sum(X1,X2))
      | incident_c(X0,X1)
      | incident_c(X0,X2) ),
    inference(resolution,[],[f146,f157]) ).

fof(f146,plain,
    ! [X2,X0,X1,X4] :
      ( ~ sP2(X0,X1,X2)
      | incident_c(X4,X1)
      | ~ incident_c(X4,X2)
      | incident_c(X4,X0) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f10488,plain,
    ! [X0] :
      ( ~ incident_c(sK17(sK3,X0),sK5)
      | part_of(X0,sK3) ),
    inference(forward_demodulation,[],[f10403,f10115]) ).

fof(f10115,plain,
    sK3 = sum(sK3,sK5),
    inference(resolution,[],[f6543,f106]) ).

fof(f106,plain,
    part_of(sK5,sK3),
    inference(cnf_transformation,[],[f61]) ).

fof(f10403,plain,
    ! [X0] :
      ( ~ incident_c(sK17(sK3,X0),sK5)
      | part_of(X0,sum(sK3,sK5)) ),
    inference(superposition,[],[f239,f10115]) ).

fof(f108,plain,
    ~ open(sum(sK4,sK5)),
    inference(cnf_transformation,[],[f61]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem    : GEO093+1 : TPTP v8.1.2. Released v2.4.0.
% 0.06/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34  % Computer : n008.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Tue Apr 30 05:45:57 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.13/0.35  % (10012)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.36  % (10016)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.36  TRYING [1]
% 0.13/0.36  TRYING [2]
% 0.13/0.36  % (10015)WARNING: value z3 for option sas not known
% 0.13/0.36  % (10013)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.36  % (10014)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.36  % (10015)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)
% 0.13/0.36  TRYING [3]
% 0.13/0.36  % (10017)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)
% 0.13/0.36  % (10019)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)
% 0.13/0.37  % (10018)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)
% 0.13/0.37  TRYING [4]
% 0.13/0.38  TRYING [1]
% 0.13/0.38  TRYING [2]
% 0.20/0.39  TRYING [5]
% 0.20/0.42  TRYING [3]
% 0.20/0.43  TRYING [6]
% 0.20/0.48  TRYING [4]
% 1.38/0.54  TRYING [7]
% 1.38/0.59  TRYING [5]
% 2.51/0.70  TRYING [8]
% 3.50/0.91  TRYING [6]
% 4.14/0.94  % (10015)First to succeed.
% 4.14/0.94  % (10015)Refutation found. Thanks to Tanya!
% 4.14/0.94  % SZS status Theorem for theBenchmark
% 4.14/0.94  % SZS output start Proof for theBenchmark
% See solution above
% 4.14/0.94  % (10015)------------------------------
% 4.14/0.94  % (10015)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 4.14/0.94  % (10015)Termination reason: Refutation
% 4.14/0.94  
% 4.14/0.94  % (10015)Memory used [KB]: 12965
% 4.14/0.94  % (10015)Time elapsed: 0.574 s
% 4.14/0.94  % (10015)Instructions burned: 1438 (million)
% 4.14/0.94  % (10015)------------------------------
% 4.14/0.94  % (10015)------------------------------
% 4.14/0.94  % (10012)Success in time 0.582 s
%------------------------------------------------------------------------------