TSTP Solution File: GEO087+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GEO087+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 : n010.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 05:15:25 EDT 2024

% Result   : Theorem 0.21s 0.38s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   50 (  10 unt;   0 def)
%            Number of atoms       :  206 (   0 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  245 (  89   ~;  71   |;  64   &)
%                                         (  10 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   6 usr;   1 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :  122 ( 101   !;  21   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f299,plain,
    $false,
    inference(resolution,[],[f298,f108]) ).

fof(f108,plain,
    ! [X0] : inner_point(sK8(X0),X0),
    inference(cnf_transformation,[],[f69]) ).

fof(f69,plain,
    ! [X0] : inner_point(sK8(X0),X0),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f22,f68]) ).

fof(f68,plain,
    ! [X0] :
      ( ? [X1] : inner_point(X1,X0)
     => inner_point(sK8(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f22,plain,
    ! [X0] :
    ? [X1] : inner_point(X1,X0),
    inference(rectify,[],[f10]) ).

fof(f10,axiom,
    ! [X0] :
    ? [X2] : inner_point(X2,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c3) ).

fof(f298,plain,
    ~ inner_point(sK8(sK3),sK3),
    inference(resolution,[],[f292,f117]) ).

fof(f117,plain,
    ! [X0,X1] :
      ( incident_c(X0,X1)
      | ~ inner_point(X0,X1) ),
    inference(cnf_transformation,[],[f81]) ).

fof(f81,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,[],[f80]) ).

fof(f80,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,[],[f26]) ).

fof(f26,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/sandbox2/benchmark/theBenchmark.p',inner_point_defn) ).

fof(f292,plain,
    ~ incident_c(sK8(sK3),sK3),
    inference(duplicate_literal_removal,[],[f289]) ).

fof(f289,plain,
    ( ~ incident_c(sK8(sK3),sK3)
    | ~ incident_c(sK8(sK3),sK3) ),
    inference(resolution,[],[f283,f104]) ).

fof(f104,plain,
    part_of(sK3,sK4),
    inference(cnf_transformation,[],[f63]) ).

fof(f63,plain,
    ( meet(sK5,sK3,sK4)
    & part_of(sK3,sK4) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f35,f62,f61]) ).

fof(f61,plain,
    ( ? [X0,X1] :
        ( ? [X2] : meet(X2,X0,X1)
        & part_of(X0,X1) )
   => ( ? [X2] : meet(X2,sK3,sK4)
      & part_of(sK3,sK4) ) ),
    introduced(choice_axiom,[]) ).

fof(f62,plain,
    ( ? [X2] : meet(X2,sK3,sK4)
   => meet(sK5,sK3,sK4) ),
    introduced(choice_axiom,[]) ).

fof(f35,plain,
    ? [X0,X1] :
      ( ? [X2] : meet(X2,X0,X1)
      & part_of(X0,X1) ),
    inference(ennf_transformation,[],[f19]) ).

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

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

fof(f17,conjecture,
    ! [X1,X3] :
      ( part_of(X1,X3)
     => ~ ? [X2] : meet(X2,X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_2_9) ).

fof(f283,plain,
    ! [X0] :
      ( ~ part_of(X0,sK4)
      | ~ incident_c(sK8(sK3),X0)
      | ~ incident_c(sK8(sK3),sK3) ),
    inference(resolution,[],[f280,f130]) ).

fof(f130,plain,
    ! [X3,X0,X1] :
      ( incident_c(X3,X0)
      | ~ incident_c(X3,X1)
      | ~ part_of(X1,X0) ),
    inference(cnf_transformation,[],[f91]) ).

fof(f91,plain,
    ! [X0,X1] :
      ( ( part_of(X1,X0)
        | ( ~ incident_c(sK16(X0,X1),X0)
          & incident_c(sK16(X0,X1),X1) ) )
      & ( ! [X3] :
            ( incident_c(X3,X0)
            | ~ incident_c(X3,X1) )
        | ~ part_of(X1,X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f89,f90]) ).

fof(f90,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ incident_c(X2,X0)
          & incident_c(X2,X1) )
     => ( ~ incident_c(sK16(X0,X1),X0)
        & incident_c(sK16(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,[],[f46]) ).

fof(f46,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/sandbox2/benchmark/theBenchmark.p',part_of_defn) ).

fof(f280,plain,
    ( ~ incident_c(sK8(sK3),sK4)
    | ~ incident_c(sK8(sK3),sK3) ),
    inference(resolution,[],[f277,f155]) ).

fof(f155,plain,
    ! [X0] : ~ end_point(sK8(X0),X0),
    inference(resolution,[],[f118,f108]) ).

fof(f118,plain,
    ! [X0,X1] :
      ( ~ inner_point(X0,X1)
      | ~ end_point(X0,X1) ),
    inference(cnf_transformation,[],[f81]) ).

fof(f277,plain,
    ! [X0] :
      ( end_point(X0,sK3)
      | ~ incident_c(X0,sK3)
      | ~ incident_c(X0,sK4) ),
    inference(resolution,[],[f240,f105]) ).

fof(f105,plain,
    meet(sK5,sK3,sK4),
    inference(cnf_transformation,[],[f63]) ).

fof(f240,plain,
    ! [X2,X3,X0,X1] :
      ( ~ meet(X3,X2,X1)
      | ~ incident_c(X0,X2)
      | end_point(X0,X2)
      | ~ incident_c(X0,X1) ),
    inference(resolution,[],[f135,f140]) ).

fof(f140,plain,
    ! [X2,X0,X1] :
      ( sP1(X2,X1,X0)
      | ~ meet(X0,X1,X2) ),
    inference(cnf_transformation,[],[f97]) ).

fof(f97,plain,
    ! [X0,X1,X2] :
      ( ( meet(X0,X1,X2)
        | ~ sP1(X2,X1,X0) )
      & ( sP1(X2,X1,X0)
        | ~ meet(X0,X1,X2) ) ),
    inference(nnf_transformation,[],[f58]) ).

fof(f58,plain,
    ! [X0,X1,X2] :
      ( meet(X0,X1,X2)
    <=> sP1(X2,X1,X0) ),
    inference(definition_folding,[],[f48,f57]) ).

fof(f57,plain,
    ! [X2,X1,X0] :
      ( sP1(X2,X1,X0)
    <=> ( ! [X3] :
            ( ( end_point(X3,X2)
              & end_point(X3,X1) )
            | ~ incident_c(X3,X2)
            | ~ incident_c(X3,X1) )
        & incident_c(X0,X2)
        & incident_c(X0,X1) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

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

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

fof(f28,plain,
    ! [X0,X1,X2] :
      ( meet(X0,X1,X2)
    <=> ( ! [X3] :
            ( ( incident_c(X3,X2)
              & incident_c(X3,X1) )
           => ( end_point(X3,X2)
              & end_point(X3,X1) ) )
        & incident_c(X0,X2)
        & incident_c(X0,X1) ) ),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X2,X0,X1] :
      ( meet(X2,X0,X1)
    <=> ( ! [X4] :
            ( ( incident_c(X4,X1)
              & incident_c(X4,X0) )
           => ( end_point(X4,X1)
              & end_point(X4,X0) ) )
        & incident_c(X2,X1)
        & incident_c(X2,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meet_defn) ).

fof(f135,plain,
    ! [X2,X0,X1,X4] :
      ( ~ sP1(X0,X1,X2)
      | ~ incident_c(X4,X0)
      | ~ incident_c(X4,X1)
      | end_point(X4,X1) ),
    inference(cnf_transformation,[],[f96]) ).

fof(f96,plain,
    ! [X0,X1,X2] :
      ( ( sP1(X0,X1,X2)
        | ( ( ~ end_point(sK17(X0,X1),X0)
            | ~ end_point(sK17(X0,X1),X1) )
          & incident_c(sK17(X0,X1),X0)
          & incident_c(sK17(X0,X1),X1) )
        | ~ incident_c(X2,X0)
        | ~ incident_c(X2,X1) )
      & ( ( ! [X4] :
              ( ( end_point(X4,X0)
                & end_point(X4,X1) )
              | ~ incident_c(X4,X0)
              | ~ incident_c(X4,X1) )
          & incident_c(X2,X0)
          & incident_c(X2,X1) )
        | ~ sP1(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f94,f95]) ).

fof(f95,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( ( ~ end_point(X3,X0)
            | ~ end_point(X3,X1) )
          & incident_c(X3,X0)
          & incident_c(X3,X1) )
     => ( ( ~ end_point(sK17(X0,X1),X0)
          | ~ end_point(sK17(X0,X1),X1) )
        & incident_c(sK17(X0,X1),X0)
        & incident_c(sK17(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f94,plain,
    ! [X0,X1,X2] :
      ( ( sP1(X0,X1,X2)
        | ? [X3] :
            ( ( ~ end_point(X3,X0)
              | ~ end_point(X3,X1) )
            & incident_c(X3,X0)
            & incident_c(X3,X1) )
        | ~ incident_c(X2,X0)
        | ~ incident_c(X2,X1) )
      & ( ( ! [X4] :
              ( ( end_point(X4,X0)
                & end_point(X4,X1) )
              | ~ incident_c(X4,X0)
              | ~ incident_c(X4,X1) )
          & incident_c(X2,X0)
          & incident_c(X2,X1) )
        | ~ sP1(X0,X1,X2) ) ),
    inference(rectify,[],[f93]) ).

fof(f93,plain,
    ! [X2,X1,X0] :
      ( ( sP1(X2,X1,X0)
        | ? [X3] :
            ( ( ~ end_point(X3,X2)
              | ~ end_point(X3,X1) )
            & incident_c(X3,X2)
            & incident_c(X3,X1) )
        | ~ incident_c(X0,X2)
        | ~ incident_c(X0,X1) )
      & ( ( ! [X3] :
              ( ( end_point(X3,X2)
                & end_point(X3,X1) )
              | ~ incident_c(X3,X2)
              | ~ incident_c(X3,X1) )
          & incident_c(X0,X2)
          & incident_c(X0,X1) )
        | ~ sP1(X2,X1,X0) ) ),
    inference(flattening,[],[f92]) ).

fof(f92,plain,
    ! [X2,X1,X0] :
      ( ( sP1(X2,X1,X0)
        | ? [X3] :
            ( ( ~ end_point(X3,X2)
              | ~ end_point(X3,X1) )
            & incident_c(X3,X2)
            & incident_c(X3,X1) )
        | ~ incident_c(X0,X2)
        | ~ incident_c(X0,X1) )
      & ( ( ! [X3] :
              ( ( end_point(X3,X2)
                & end_point(X3,X1) )
              | ~ incident_c(X3,X2)
              | ~ incident_c(X3,X1) )
          & incident_c(X0,X2)
          & incident_c(X0,X1) )
        | ~ sP1(X2,X1,X0) ) ),
    inference(nnf_transformation,[],[f57]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : GEO087+1 : TPTP v8.1.2. Released v2.4.0.
% 0.13/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35  % Computer : n010.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Fri May  3 21:54:08 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.13/0.35  % (26295)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.37  % (26298)WARNING: value z3 for option sas not known
% 0.21/0.37  % (26297)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.37  % (26296)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.37  % (26302)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)
% 0.21/0.37  % (26299)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.37  % (26301)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)
% 0.21/0.37  % (26300)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)
% 0.21/0.37  % (26298)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)
% 0.21/0.38  TRYING [1]
% 0.21/0.38  TRYING [2]
% 0.21/0.38  TRYING [3]
% 0.21/0.38  % (26301)First to succeed.
% 0.21/0.38  % (26301)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-26295"
% 0.21/0.38  TRYING [1]
% 0.21/0.38  TRYING [2]
% 0.21/0.38  % (26301)Refutation found. Thanks to Tanya!
% 0.21/0.38  % SZS status Theorem for theBenchmark
% 0.21/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.39  % (26301)------------------------------
% 0.21/0.39  % (26301)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.39  % (26301)Termination reason: Refutation
% 0.21/0.39  
% 0.21/0.39  % (26301)Memory used [KB]: 959
% 0.21/0.39  % (26301)Time elapsed: 0.012 s
% 0.21/0.39  % (26301)Instructions burned: 16 (million)
% 0.21/0.39  % (26295)Success in time 0.019 s
%------------------------------------------------------------------------------