TSTP Solution File: GEO111+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GEO111+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 : n022.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 05:15:29 EDT 2024

% Result   : Theorem 0.18s 0.41s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   40
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   87 (   9 unt;   0 def)
%            Number of atoms       :  390 ( 118 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  457 ( 154   ~; 198   |;  83   &)
%                                         (  12 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   7 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-4 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-4 aty)
%            Number of variables   :  187 ( 168   !;  19   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f807,plain,
    $false,
    inference(resolution,[],[f806,f756]) ).

fof(f756,plain,
    between_c(sK4,sK5,sK5,sK7),
    inference(backward_demodulation,[],[f113,f754]) ).

fof(f754,plain,
    sK5 = sK6,
    inference(resolution,[],[f738,f170]) ).

fof(f170,plain,
    ! [X2,X3,X0] : ~ between_c(X0,X3,X2,X3),
    inference(equality_resolution,[],[f166]) ).

fof(f166,plain,
    ! [X2,X3,X0,X1] :
      ( X1 != X3
      | ~ between_c(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f66]) ).

fof(f66,plain,
    ! [X0,X1,X2,X3] :
      ( ( sP3(X2,X3,X1,X0)
        & X1 != X3 )
      | ~ between_c(X0,X1,X2,X3) ),
    inference(definition_folding,[],[f58,f65]) ).

fof(f65,plain,
    ! [X2,X3,X1,X0] :
      ( ? [X4] :
          ( inner_point(X2,X4)
          & end_point(X3,X4)
          & end_point(X1,X4)
          & part_of(X4,X0) )
      | ~ sP3(X2,X3,X1,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).

fof(f58,plain,
    ! [X0,X1,X2,X3] :
      ( ( ? [X4] :
            ( inner_point(X2,X4)
            & end_point(X3,X4)
            & end_point(X1,X4)
            & part_of(X4,X0) )
        & X1 != X3 )
      | ~ between_c(X0,X1,X2,X3) ),
    inference(ennf_transformation,[],[f35]) ).

fof(f35,plain,
    ! [X0,X1,X2,X3] :
      ( between_c(X0,X1,X2,X3)
     => ( ? [X4] :
            ( inner_point(X2,X4)
            & end_point(X3,X4)
            & end_point(X1,X4)
            & part_of(X4,X0) )
        & X1 != X3 ) ),
    inference(unused_predicate_definition_removal,[],[f34]) ).

fof(f34,plain,
    ! [X0,X1,X2,X3] :
      ( between_c(X0,X1,X2,X3)
    <=> ( ? [X4] :
            ( inner_point(X2,X4)
            & end_point(X3,X4)
            & end_point(X1,X4)
            & part_of(X4,X0) )
        & X1 != X3 ) ),
    inference(rectify,[],[f17]) ).

fof(f17,axiom,
    ! [X0,X2,X4,X6] :
      ( between_c(X0,X2,X4,X6)
    <=> ( ? [X7] :
            ( inner_point(X4,X7)
            & end_point(X6,X7)
            & end_point(X2,X7)
            & part_of(X7,X0) )
        & X2 != X6 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',between_c_defn) ).

fof(f738,plain,
    ( between_c(sK4,sK5,sK6,sK5)
    | sK5 = sK6 ),
    inference(superposition,[],[f113,f737]) ).

fof(f737,plain,
    ( sK5 = sK7
    | sK5 = sK6 ),
    inference(duplicate_literal_removal,[],[f736]) ).

fof(f736,plain,
    ( sK5 = sK7
    | sK5 = sK6
    | sK5 = sK7
    | sK5 = sK6 ),
    inference(resolution,[],[f735,f725]) ).

fof(f725,plain,
    ( between_c(sK4,sK5,sK6,sK6)
    | sK5 = sK7
    | sK5 = sK6 ),
    inference(superposition,[],[f113,f724]) ).

fof(f724,plain,
    ( sK6 = sK7
    | sK5 = sK7
    | sK5 = sK6 ),
    inference(resolution,[],[f723,f113]) ).

fof(f723,plain,
    ( ~ between_c(sK4,sK5,sK6,sK7)
    | sK6 = sK7
    | sK5 = sK7
    | sK5 = sK6 ),
    inference(resolution,[],[f716,f167]) ).

fof(f167,plain,
    ! [X2,X3,X0,X1] :
      ( sP3(X2,X3,X1,X0)
      | ~ between_c(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f66]) ).

fof(f716,plain,
    ( ~ sP3(sK6,sK7,sK5,sK4)
    | sK5 = sK6
    | sK6 = sK7
    | sK5 = sK7 ),
    inference(resolution,[],[f714,f163]) ).

fof(f163,plain,
    ! [X2,X3,X0,X1] :
      ( end_point(X2,sK21(X0,X1,X2,X3))
      | ~ sP3(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f112]) ).

fof(f112,plain,
    ! [X0,X1,X2,X3] :
      ( ( inner_point(X0,sK21(X0,X1,X2,X3))
        & end_point(X1,sK21(X0,X1,X2,X3))
        & end_point(X2,sK21(X0,X1,X2,X3))
        & part_of(sK21(X0,X1,X2,X3),X3) )
      | ~ sP3(X0,X1,X2,X3) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f110,f111]) ).

fof(f111,plain,
    ! [X0,X1,X2,X3] :
      ( ? [X4] :
          ( inner_point(X0,X4)
          & end_point(X1,X4)
          & end_point(X2,X4)
          & part_of(X4,X3) )
     => ( inner_point(X0,sK21(X0,X1,X2,X3))
        & end_point(X1,sK21(X0,X1,X2,X3))
        & end_point(X2,sK21(X0,X1,X2,X3))
        & part_of(sK21(X0,X1,X2,X3),X3) ) ),
    introduced(choice_axiom,[]) ).

fof(f110,plain,
    ! [X0,X1,X2,X3] :
      ( ? [X4] :
          ( inner_point(X0,X4)
          & end_point(X1,X4)
          & end_point(X2,X4)
          & part_of(X4,X3) )
      | ~ sP3(X0,X1,X2,X3) ),
    inference(rectify,[],[f109]) ).

fof(f109,plain,
    ! [X2,X3,X1,X0] :
      ( ? [X4] :
          ( inner_point(X2,X4)
          & end_point(X3,X4)
          & end_point(X1,X4)
          & part_of(X4,X0) )
      | ~ sP3(X2,X3,X1,X0) ),
    inference(nnf_transformation,[],[f65]) ).

fof(f714,plain,
    ( ~ end_point(sK5,sK21(sK6,sK7,sK5,sK4))
    | sK5 = sK7
    | sK5 = sK6
    | sK6 = sK7 ),
    inference(resolution,[],[f712,f136]) ).

fof(f136,plain,
    ! [X0,X1] :
      ( incident_c(X0,X1)
      | ~ end_point(X0,X1) ),
    inference(cnf_transformation,[],[f92]) ).

fof(f92,plain,
    ! [X0,X1] :
      ( ( end_point(X0,X1)
        | ~ sP0(X0,X1)
        | ~ incident_c(X0,X1) )
      & ( ( sP0(X0,X1)
          & incident_c(X0,X1) )
        | ~ end_point(X0,X1) ) ),
    inference(flattening,[],[f91]) ).

fof(f91,plain,
    ! [X0,X1] :
      ( ( end_point(X0,X1)
        | ~ sP0(X0,X1)
        | ~ incident_c(X0,X1) )
      & ( ( sP0(X0,X1)
          & incident_c(X0,X1) )
        | ~ end_point(X0,X1) ) ),
    inference(nnf_transformation,[],[f60]) ).

fof(f60,plain,
    ! [X0,X1] :
      ( end_point(X0,X1)
    <=> ( sP0(X0,X1)
        & incident_c(X0,X1) ) ),
    inference(definition_folding,[],[f48,f59]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
    <=> ! [X2,X3] :
          ( part_of(X3,X2)
          | part_of(X2,X3)
          | ~ incident_c(X0,X3)
          | ~ incident_c(X0,X2)
          | ~ part_of(X3,X1)
          | ~ part_of(X2,X1) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( end_point(X0,X1)
    <=> ( ! [X2,X3] :
            ( part_of(X3,X2)
            | part_of(X2,X3)
            | ~ incident_c(X0,X3)
            | ~ incident_c(X0,X2)
            | ~ part_of(X3,X1)
            | ~ part_of(X2,X1) )
        & incident_c(X0,X1) ) ),
    inference(flattening,[],[f47]) ).

fof(f47,plain,
    ! [X0,X1] :
      ( end_point(X0,X1)
    <=> ( ! [X2,X3] :
            ( part_of(X3,X2)
            | part_of(X2,X3)
            | ~ incident_c(X0,X3)
            | ~ incident_c(X0,X2)
            | ~ part_of(X3,X1)
            | ~ part_of(X2,X1) )
        & incident_c(X0,X1) ) ),
    inference(ennf_transformation,[],[f28]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( end_point(X0,X1)
    <=> ( ! [X2,X3] :
            ( ( incident_c(X0,X3)
              & incident_c(X0,X2)
              & part_of(X3,X1)
              & part_of(X2,X1) )
           => ( part_of(X3,X2)
              | part_of(X2,X3) ) )
        & incident_c(X0,X1) ) ),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ! [X2,X0] :
      ( end_point(X2,X0)
    <=> ( ! [X1,X3] :
            ( ( incident_c(X2,X3)
              & incident_c(X2,X1)
              & part_of(X3,X0)
              & part_of(X1,X0) )
           => ( part_of(X3,X1)
              | part_of(X1,X3) ) )
        & incident_c(X2,X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',end_point_defn) ).

fof(f712,plain,
    ( ~ incident_c(sK5,sK21(sK6,sK7,sK5,sK4))
    | sK6 = sK7
    | sK5 = sK7
    | sK5 = sK6 ),
    inference(resolution,[],[f610,f113]) ).

fof(f610,plain,
    ! [X2,X0,X1] :
      ( ~ between_c(sK4,X2,X0,X1)
      | ~ incident_c(sK5,sK21(X0,X1,X2,sK4))
      | sK6 = sK7
      | sK5 = sK7
      | sK5 = sK6 ),
    inference(resolution,[],[f568,f167]) ).

fof(f568,plain,
    ! [X2,X0,X1] :
      ( ~ sP3(X0,X1,X2,sK4)
      | sK5 = sK6
      | ~ incident_c(sK5,sK21(X0,X1,X2,sK4))
      | sK6 = sK7
      | sK5 = sK7 ),
    inference(resolution,[],[f557,f162]) ).

fof(f162,plain,
    ! [X2,X3,X0,X1] :
      ( part_of(sK21(X0,X1,X2,X3),X3)
      | ~ sP3(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f112]) ).

fof(f557,plain,
    ! [X0] :
      ( ~ part_of(X0,sK4)
      | sK5 = sK7
      | sK5 = sK6
      | ~ incident_c(sK5,X0)
      | sK6 = sK7 ),
    inference(resolution,[],[f556,f139]) ).

fof(f139,plain,
    ! [X3,X0,X1] :
      ( incident_c(X3,X0)
      | ~ incident_c(X3,X1)
      | ~ part_of(X1,X0) ),
    inference(cnf_transformation,[],[f96]) ).

fof(f96,plain,
    ! [X0,X1] :
      ( ( part_of(X1,X0)
        | ( ~ incident_c(sK18(X0,X1),X0)
          & incident_c(sK18(X0,X1),X1) ) )
      & ( ! [X3] :
            ( incident_c(X3,X0)
            | ~ incident_c(X3,X1) )
        | ~ part_of(X1,X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f94,f95]) ).

fof(f95,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ incident_c(X2,X0)
          & incident_c(X2,X1) )
     => ( ~ incident_c(sK18(X0,X1),X0)
        & incident_c(sK18(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f94,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,[],[f93]) ).

fof(f93,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,[],[f49]) ).

fof(f49,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(f556,plain,
    ( ~ incident_c(sK5,sK4)
    | sK6 = sK7
    | sK5 = sK7
    | sK5 = sK6 ),
    inference(resolution,[],[f555,f113]) ).

fof(f555,plain,
    ( ~ between_c(sK4,sK5,sK6,sK7)
    | sK5 = sK6
    | sK6 = sK7
    | sK5 = sK7
    | ~ incident_c(sK5,sK4) ),
    inference(resolution,[],[f553,f167]) ).

fof(f553,plain,
    ( ~ sP3(sK6,sK7,sK5,sK4)
    | ~ incident_c(sK5,sK4)
    | sK5 = sK6
    | sK6 = sK7
    | sK5 = sK7 ),
    inference(resolution,[],[f552,f165]) ).

fof(f165,plain,
    ! [X2,X3,X0,X1] :
      ( inner_point(X0,sK21(X0,X1,X2,X3))
      | ~ sP3(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f112]) ).

fof(f552,plain,
    ( ~ inner_point(sK6,sK21(sK6,sK7,sK5,sK4))
    | sK5 = sK7
    | ~ incident_c(sK5,sK4)
    | sK5 = sK6
    | sK6 = sK7 ),
    inference(resolution,[],[f538,f126]) ).

fof(f126,plain,
    ! [X0,X1] :
      ( incident_c(X0,X1)
      | ~ inner_point(X0,X1) ),
    inference(cnf_transformation,[],[f86]) ).

fof(f86,plain,
    ! [X0,X1] :
      ( ( inner_point(X0,X1)
        | end_point(X0,X1)
        | ~ incident_c(X0,X1) )
      & ( ( ~ end_point(X0,X1)
          & incident_c(X0,X1) )
        | ~ inner_point(X0,X1) ) ),
    inference(flattening,[],[f85]) ).

fof(f85,plain,
    ! [X0,X1] :
      ( ( inner_point(X0,X1)
        | end_point(X0,X1)
        | ~ incident_c(X0,X1) )
      & ( ( ~ end_point(X0,X1)
          & incident_c(X0,X1) )
        | ~ inner_point(X0,X1) ) ),
    inference(nnf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( inner_point(X0,X1)
    <=> ( ~ end_point(X0,X1)
        & incident_c(X0,X1) ) ),
    inference(rectify,[],[f4]) ).

fof(f4,axiom,
    ! [X2,X0] :
      ( inner_point(X2,X0)
    <=> ( ~ end_point(X2,X0)
        & incident_c(X2,X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',inner_point_defn) ).

fof(f538,plain,
    ( ~ incident_c(sK6,sK21(sK6,sK7,sK5,sK4))
    | sK6 = sK7
    | sK5 = sK7
    | ~ incident_c(sK5,sK4)
    | sK5 = sK6 ),
    inference(resolution,[],[f501,f113]) ).

fof(f501,plain,
    ! [X2,X0,X1] :
      ( ~ between_c(sK4,X2,X0,X1)
      | sK6 = sK7
      | ~ incident_c(sK6,sK21(X0,X1,X2,sK4))
      | sK5 = sK7
      | ~ incident_c(sK5,sK4)
      | sK5 = sK6 ),
    inference(resolution,[],[f459,f167]) ).

fof(f459,plain,
    ! [X2,X0,X1] :
      ( ~ sP3(X0,X1,X2,sK4)
      | sK5 = sK6
      | sK6 = sK7
      | ~ incident_c(sK6,sK21(X0,X1,X2,sK4))
      | sK5 = sK7
      | ~ incident_c(sK5,sK4) ),
    inference(resolution,[],[f450,f162]) ).

fof(f450,plain,
    ! [X0] :
      ( ~ part_of(X0,sK4)
      | ~ incident_c(sK5,sK4)
      | sK5 = sK6
      | sK6 = sK7
      | ~ incident_c(sK6,X0)
      | sK5 = sK7 ),
    inference(resolution,[],[f449,f139]) ).

fof(f449,plain,
    ( ~ incident_c(sK6,sK4)
    | sK5 = sK7
    | ~ incident_c(sK5,sK4)
    | sK5 = sK6
    | sK6 = sK7 ),
    inference(resolution,[],[f448,f113]) ).

fof(f448,plain,
    ( ~ between_c(sK4,sK5,sK6,sK7)
    | sK5 = sK6
    | sK5 = sK7
    | ~ incident_c(sK5,sK4)
    | ~ incident_c(sK6,sK4)
    | sK6 = sK7 ),
    inference(resolution,[],[f445,f167]) ).

fof(f445,plain,
    ( ~ sP3(sK6,sK7,sK5,sK4)
    | sK6 = sK7
    | sK5 = sK6
    | sK5 = sK7
    | ~ incident_c(sK5,sK4)
    | ~ incident_c(sK6,sK4) ),
    inference(resolution,[],[f443,f164]) ).

fof(f164,plain,
    ! [X2,X3,X0,X1] :
      ( end_point(X1,sK21(X0,X1,X2,X3))
      | ~ sP3(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f112]) ).

fof(f443,plain,
    ( ~ end_point(sK7,sK21(sK6,sK7,sK5,sK4))
    | ~ incident_c(sK6,sK4)
    | sK6 = sK7
    | sK5 = sK6
    | sK5 = sK7
    | ~ incident_c(sK5,sK4) ),
    inference(resolution,[],[f414,f136]) ).

fof(f414,plain,
    ( ~ incident_c(sK7,sK21(sK6,sK7,sK5,sK4))
    | ~ incident_c(sK5,sK4)
    | ~ incident_c(sK6,sK4)
    | sK6 = sK7
    | sK5 = sK6
    | sK5 = sK7 ),
    inference(resolution,[],[f413,f113]) ).

fof(f413,plain,
    ! [X2,X0,X1] :
      ( ~ between_c(sK4,X2,X0,X1)
      | ~ incident_c(sK6,sK4)
      | ~ incident_c(sK5,sK4)
      | ~ incident_c(sK7,sK21(X0,X1,X2,sK4))
      | sK6 = sK7
      | sK5 = sK6
      | sK5 = sK7 ),
    inference(resolution,[],[f257,f167]) ).

fof(f257,plain,
    ! [X2,X0,X1] :
      ( ~ sP3(X0,X1,X2,sK4)
      | sK5 = sK7
      | ~ incident_c(sK6,sK4)
      | ~ incident_c(sK5,sK4)
      | ~ incident_c(sK7,sK21(X0,X1,X2,sK4))
      | sK6 = sK7
      | sK5 = sK6 ),
    inference(resolution,[],[f184,f162]) ).

fof(f184,plain,
    ! [X0] :
      ( ~ part_of(X0,sK4)
      | sK5 = sK6
      | sK5 = sK7
      | ~ incident_c(sK6,sK4)
      | ~ incident_c(sK5,sK4)
      | ~ incident_c(sK7,X0)
      | sK6 = sK7 ),
    inference(resolution,[],[f114,f139]) ).

fof(f114,plain,
    ( ~ incident_c(sK7,sK4)
    | sK6 = sK7
    | sK5 = sK6
    | sK5 = sK7
    | ~ incident_c(sK6,sK4)
    | ~ incident_c(sK5,sK4) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f68,plain,
    ( ( sK5 = sK7
      | sK6 = sK7
      | sK5 = sK6
      | ~ incident_c(sK7,sK4)
      | ~ incident_c(sK6,sK4)
      | ~ incident_c(sK5,sK4) )
    & between_c(sK4,sK5,sK6,sK7) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f38,f67]) ).

fof(f67,plain,
    ( ? [X0,X1,X2,X3] :
        ( ( X1 = X3
          | X2 = X3
          | X1 = X2
          | ~ incident_c(X3,X0)
          | ~ incident_c(X2,X0)
          | ~ incident_c(X1,X0) )
        & between_c(X0,X1,X2,X3) )
   => ( ( sK5 = sK7
        | sK6 = sK7
        | sK5 = sK6
        | ~ incident_c(sK7,sK4)
        | ~ incident_c(sK6,sK4)
        | ~ incident_c(sK5,sK4) )
      & between_c(sK4,sK5,sK6,sK7) ) ),
    introduced(choice_axiom,[]) ).

fof(f38,plain,
    ? [X0,X1,X2,X3] :
      ( ( X1 = X3
        | X2 = X3
        | X1 = X2
        | ~ incident_c(X3,X0)
        | ~ incident_c(X2,X0)
        | ~ incident_c(X1,X0) )
      & between_c(X0,X1,X2,X3) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f20,plain,
    ~ ! [X0,X1,X2,X3] :
        ( between_c(X0,X1,X2,X3)
       => ( X1 != X3
          & X2 != X3
          & X1 != X2
          & incident_c(X3,X0)
          & incident_c(X2,X0)
          & incident_c(X1,X0) ) ),
    inference(rectify,[],[f19]) ).

fof(f19,negated_conjecture,
    ~ ! [X0,X2,X4,X6] :
        ( between_c(X0,X2,X4,X6)
       => ( X2 != X6
          & X4 != X6
          & X2 != X4
          & incident_c(X6,X0)
          & incident_c(X4,X0)
          & incident_c(X2,X0) ) ),
    inference(negated_conjecture,[],[f18]) ).

fof(f18,conjecture,
    ! [X0,X2,X4,X6] :
      ( between_c(X0,X2,X4,X6)
     => ( X2 != X6
        & X4 != X6
        & X2 != X4
        & incident_c(X6,X0)
        & incident_c(X4,X0)
        & incident_c(X2,X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',theorem_3_8_1) ).

fof(f735,plain,
    ( ~ between_c(sK4,sK5,sK6,sK6)
    | sK5 = sK7
    | sK5 = sK6 ),
    inference(resolution,[],[f732,f167]) ).

fof(f732,plain,
    ( ~ sP3(sK6,sK6,sK5,sK4)
    | sK5 = sK6
    | sK5 = sK7 ),
    inference(resolution,[],[f726,f164]) ).

fof(f726,plain,
    ( ~ end_point(sK6,sK21(sK6,sK6,sK5,sK4))
    | sK5 = sK7
    | sK5 = sK6 ),
    inference(superposition,[],[f231,f724]) ).

fof(f231,plain,
    ~ end_point(sK6,sK21(sK6,sK7,sK5,sK4)),
    inference(resolution,[],[f230,f113]) ).

fof(f230,plain,
    ! [X2,X3,X0,X1] :
      ( ~ between_c(X3,X2,X0,X1)
      | ~ end_point(X0,sK21(X0,X1,X2,X3)) ),
    inference(resolution,[],[f229,f167]) ).

fof(f229,plain,
    ! [X2,X3,X0,X1] :
      ( ~ sP3(X0,X1,X2,X3)
      | ~ end_point(X0,sK21(X0,X1,X2,X3)) ),
    inference(resolution,[],[f165,f127]) ).

fof(f127,plain,
    ! [X0,X1] :
      ( ~ inner_point(X0,X1)
      | ~ end_point(X0,X1) ),
    inference(cnf_transformation,[],[f86]) ).

fof(f113,plain,
    between_c(sK4,sK5,sK6,sK7),
    inference(cnf_transformation,[],[f68]) ).

fof(f806,plain,
    ~ between_c(sK4,sK5,sK5,sK7),
    inference(resolution,[],[f803,f167]) ).

fof(f803,plain,
    ~ sP3(sK5,sK7,sK5,sK4),
    inference(resolution,[],[f757,f163]) ).

fof(f757,plain,
    ~ end_point(sK5,sK21(sK5,sK7,sK5,sK4)),
    inference(backward_demodulation,[],[f231,f754]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem    : GEO111+1 : TPTP v8.1.2. Released v2.4.0.
% 0.04/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34  % Computer : n022.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Fri May  3 22:07:37 EDT 2024
% 0.14/0.34  % CPUTime    : 
% 0.14/0.34  % (30082)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.35  % (30086)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.35  TRYING [1]
% 0.14/0.36  TRYING [2]
% 0.14/0.36  TRYING [3]
% 0.14/0.36  % (30085)WARNING: value z3 for option sas not known
% 0.14/0.36  % (30083)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.36  % (30084)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.36  % (30085)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)
% 0.14/0.36  % (30087)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)
% 0.14/0.36  % (30088)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)
% 0.14/0.36  % (30089)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)
% 0.18/0.37  TRYING [4]
% 0.18/0.38  TRYING [1]
% 0.18/0.38  TRYING [2]
% 0.18/0.39  TRYING [5]
% 0.18/0.41  % (30088)First to succeed.
% 0.18/0.41  % (30088)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-30082"
% 0.18/0.41  % (30088)Refutation found. Thanks to Tanya!
% 0.18/0.41  % SZS status Theorem for theBenchmark
% 0.18/0.41  % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.41  % (30088)------------------------------
% 0.18/0.41  % (30088)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.18/0.41  % (30088)Termination reason: Refutation
% 0.18/0.41  
% 0.18/0.41  % (30088)Memory used [KB]: 1481
% 0.18/0.41  % (30088)Time elapsed: 0.052 s
% 0.18/0.41  % (30088)Instructions burned: 87 (million)
% 0.18/0.41  % (30082)Success in time 0.067 s
%------------------------------------------------------------------------------