TSTP Solution File: GEO117+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GEO117+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 : n004.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 05:15:30 EDT 2024

% Result   : Theorem 0.14s 0.39s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   44 (  12 unt;   0 def)
%            Number of atoms       :  218 (  11 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :  264 (  90   ~;  82   |;  75   &)
%                                         (  13 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   8 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   12 (  10 usr;   1 prp; 0-4 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-4 aty)
%            Number of variables   :  175 ( 156   !;  19   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f447,plain,
    $false,
    inference(resolution,[],[f446,f166]) ).

fof(f166,plain,
    ordered_by(sK5,sK6,sK6),
    inference(cnf_transformation,[],[f93]) ).

fof(f93,plain,
    ordered_by(sK5,sK6,sK6),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f57,f92]) ).

fof(f92,plain,
    ( ? [X0,X1] : ordered_by(X0,X1,X1)
   => ordered_by(sK5,sK6,sK6) ),
    introduced(choice_axiom,[]) ).

fof(f57,plain,
    ? [X0,X1] : ordered_by(X0,X1,X1),
    inference(ennf_transformation,[],[f30]) ).

fof(f30,plain,
    ~ ! [X0,X1] : ~ ordered_by(X0,X1,X1),
    inference(rectify,[],[f29]) ).

fof(f29,negated_conjecture,
    ~ ! [X8,X2] : ~ ordered_by(X8,X2,X2),
    inference(negated_conjecture,[],[f28]) ).

fof(f28,conjecture,
    ! [X8,X2] : ~ ordered_by(X8,X2,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',theorem_4_4) ).

fof(f446,plain,
    ! [X0,X1] : ~ ordered_by(X0,X1,X1),
    inference(factoring,[],[f439]) ).

fof(f439,plain,
    ! [X2,X0,X1] :
      ( ~ ordered_by(X0,X1,X2)
      | ~ ordered_by(X0,X2,X1) ),
    inference(resolution,[],[f438,f243]) ).

fof(f243,plain,
    ! [X2,X3,X0,X1] :
      ( sP3(X0,X1,X2,X3)
      | ~ ordered_by(X2,X1,X0)
      | ~ ordered_by(X2,X3,X1) ),
    inference(cnf_transformation,[],[f158]) ).

fof(f158,plain,
    ! [X0,X1,X2,X3] :
      ( ( sP3(X0,X1,X2,X3)
        | ( ( ~ ordered_by(X2,X1,X0)
            | ~ ordered_by(X2,X3,X1) )
          & ( ~ ordered_by(X2,X1,X3)
            | ~ ordered_by(X2,X0,X1) ) ) )
      & ( ( ordered_by(X2,X1,X0)
          & ordered_by(X2,X3,X1) )
        | ( ordered_by(X2,X1,X3)
          & ordered_by(X2,X0,X1) )
        | ~ sP3(X0,X1,X2,X3) ) ),
    inference(rectify,[],[f157]) ).

fof(f157,plain,
    ! [X1,X2,X0,X3] :
      ( ( sP3(X1,X2,X0,X3)
        | ( ( ~ ordered_by(X0,X2,X1)
            | ~ ordered_by(X0,X3,X2) )
          & ( ~ ordered_by(X0,X2,X3)
            | ~ ordered_by(X0,X1,X2) ) ) )
      & ( ( ordered_by(X0,X2,X1)
          & ordered_by(X0,X3,X2) )
        | ( ordered_by(X0,X2,X3)
          & ordered_by(X0,X1,X2) )
        | ~ sP3(X1,X2,X0,X3) ) ),
    inference(flattening,[],[f156]) ).

fof(f156,plain,
    ! [X1,X2,X0,X3] :
      ( ( sP3(X1,X2,X0,X3)
        | ( ( ~ ordered_by(X0,X2,X1)
            | ~ ordered_by(X0,X3,X2) )
          & ( ~ ordered_by(X0,X2,X3)
            | ~ ordered_by(X0,X1,X2) ) ) )
      & ( ( ordered_by(X0,X2,X1)
          & ordered_by(X0,X3,X2) )
        | ( ordered_by(X0,X2,X3)
          & ordered_by(X0,X1,X2) )
        | ~ sP3(X1,X2,X0,X3) ) ),
    inference(nnf_transformation,[],[f88]) ).

fof(f88,plain,
    ! [X1,X2,X0,X3] :
      ( sP3(X1,X2,X0,X3)
    <=> ( ( ordered_by(X0,X2,X1)
          & ordered_by(X0,X3,X2) )
        | ( ordered_by(X0,X2,X3)
          & ordered_by(X0,X1,X2) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).

fof(f438,plain,
    ! [X2,X0,X1] : ~ sP3(X0,X1,X2,X0),
    inference(resolution,[],[f433,f245]) ).

fof(f245,plain,
    ! [X2,X3,X0,X1] :
      ( between_o(X0,X1,X2,X3)
      | ~ sP3(X1,X2,X0,X3) ),
    inference(cnf_transformation,[],[f159]) ).

fof(f159,plain,
    ! [X0,X1,X2,X3] :
      ( ( between_o(X0,X1,X2,X3)
        | ~ sP3(X1,X2,X0,X3) )
      & ( sP3(X1,X2,X0,X3)
        | ~ between_o(X0,X1,X2,X3) ) ),
    inference(nnf_transformation,[],[f89]) ).

fof(f89,plain,
    ! [X0,X1,X2,X3] :
      ( between_o(X0,X1,X2,X3)
    <=> sP3(X1,X2,X0,X3) ),
    inference(definition_folding,[],[f53,f88]) ).

fof(f53,plain,
    ! [X0,X1,X2,X3] :
      ( between_o(X0,X1,X2,X3)
    <=> ( ( ordered_by(X0,X2,X1)
          & ordered_by(X0,X3,X2) )
        | ( ordered_by(X0,X2,X3)
          & ordered_by(X0,X1,X2) ) ) ),
    inference(rectify,[],[f18]) ).

fof(f18,axiom,
    ! [X8,X2,X4,X6] :
      ( between_o(X8,X2,X4,X6)
    <=> ( ( ordered_by(X8,X4,X2)
          & ordered_by(X8,X6,X4) )
        | ( ordered_by(X8,X4,X6)
          & ordered_by(X8,X2,X4) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',between_o_defn) ).

fof(f433,plain,
    ! [X2,X0,X1] : ~ between_o(X0,X1,X2,X1),
    inference(resolution,[],[f431,f251]) ).

fof(f251,plain,
    ! [X2,X3,X0,X1] :
      ( sP4(X2,X1,X0,X3)
      | ~ between_o(X3,X0,X1,X2) ),
    inference(cnf_transformation,[],[f165]) ).

fof(f165,plain,
    ! [X0,X1,X2,X3] :
      ( ( between_o(X3,X0,X1,X2)
        | ~ sP4(X2,X1,X0,X3) )
      & ( sP4(X2,X1,X0,X3)
        | ~ between_o(X3,X0,X1,X2) ) ),
    inference(nnf_transformation,[],[f91]) ).

fof(f91,plain,
    ! [X0,X1,X2,X3] :
      ( between_o(X3,X0,X1,X2)
    <=> sP4(X2,X1,X0,X3) ),
    inference(definition_folding,[],[f54,f90]) ).

fof(f90,plain,
    ! [X2,X1,X0,X3] :
      ( sP4(X2,X1,X0,X3)
    <=> ? [X4] :
          ( between_c(X4,X0,X1,X2)
          & ! [X5] :
              ( incident_o(X5,X3)
            <=> incident_c(X5,X4) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).

fof(f54,plain,
    ! [X0,X1,X2,X3] :
      ( between_o(X3,X0,X1,X2)
    <=> ? [X4] :
          ( between_c(X4,X0,X1,X2)
          & ! [X5] :
              ( incident_o(X5,X3)
            <=> incident_c(X5,X4) ) ) ),
    inference(rectify,[],[f23]) ).

fof(f23,axiom,
    ! [X2,X4,X6,X8] :
      ( between_o(X8,X2,X4,X6)
    <=> ? [X0] :
          ( between_c(X0,X2,X4,X6)
          & ! [X2] :
              ( incident_o(X2,X8)
            <=> incident_c(X2,X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',o3) ).

fof(f431,plain,
    ! [X2,X0,X1] : ~ sP4(X0,X1,X0,X2),
    inference(resolution,[],[f248,f257]) ).

fof(f257,plain,
    ! [X2,X3,X0] : ~ between_c(X0,X3,X2,X3),
    inference(equality_resolution,[],[f232]) ).

fof(f232,plain,
    ! [X2,X3,X0,X1] :
      ( X1 != X3
      | ~ between_c(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f155]) ).

fof(f155,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 )
      & ( ( inner_point(X2,sK26(X0,X1,X2,X3))
          & end_point(X3,sK26(X0,X1,X2,X3))
          & end_point(X1,sK26(X0,X1,X2,X3))
          & part_of(sK26(X0,X1,X2,X3),X0)
          & X1 != X3 )
        | ~ between_c(X0,X1,X2,X3) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f153,f154]) ).

fof(f154,plain,
    ! [X0,X1,X2,X3] :
      ( ? [X5] :
          ( inner_point(X2,X5)
          & end_point(X3,X5)
          & end_point(X1,X5)
          & part_of(X5,X0) )
     => ( inner_point(X2,sK26(X0,X1,X2,X3))
        & end_point(X3,sK26(X0,X1,X2,X3))
        & end_point(X1,sK26(X0,X1,X2,X3))
        & part_of(sK26(X0,X1,X2,X3),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f153,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 )
      & ( ( ? [X5] :
              ( inner_point(X2,X5)
              & end_point(X3,X5)
              & end_point(X1,X5)
              & part_of(X5,X0) )
          & X1 != X3 )
        | ~ between_c(X0,X1,X2,X3) ) ),
    inference(rectify,[],[f152]) ).

fof(f152,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 )
      & ( ( ? [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(flattening,[],[f151]) ).

fof(f151,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 )
      & ( ( ? [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(nnf_transformation,[],[f52]) ).

fof(f52,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(f248,plain,
    ! [X2,X3,X0,X1] :
      ( between_c(sK28(X0,X1,X2,X3),X2,X1,X0)
      | ~ sP4(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f164]) ).

fof(f164,plain,
    ! [X0,X1,X2,X3] :
      ( ( sP4(X0,X1,X2,X3)
        | ! [X4] :
            ( ~ between_c(X4,X2,X1,X0)
            | ( ( ~ incident_c(sK27(X3,X4),X4)
                | ~ incident_o(sK27(X3,X4),X3) )
              & ( incident_c(sK27(X3,X4),X4)
                | incident_o(sK27(X3,X4),X3) ) ) ) )
      & ( ( between_c(sK28(X0,X1,X2,X3),X2,X1,X0)
          & ! [X7] :
              ( ( incident_o(X7,X3)
                | ~ incident_c(X7,sK28(X0,X1,X2,X3)) )
              & ( incident_c(X7,sK28(X0,X1,X2,X3))
                | ~ incident_o(X7,X3) ) ) )
        | ~ sP4(X0,X1,X2,X3) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK27,sK28])],[f161,f163,f162]) ).

fof(f162,plain,
    ! [X3,X4] :
      ( ? [X5] :
          ( ( ~ incident_c(X5,X4)
            | ~ incident_o(X5,X3) )
          & ( incident_c(X5,X4)
            | incident_o(X5,X3) ) )
     => ( ( ~ incident_c(sK27(X3,X4),X4)
          | ~ incident_o(sK27(X3,X4),X3) )
        & ( incident_c(sK27(X3,X4),X4)
          | incident_o(sK27(X3,X4),X3) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f163,plain,
    ! [X0,X1,X2,X3] :
      ( ? [X6] :
          ( between_c(X6,X2,X1,X0)
          & ! [X7] :
              ( ( incident_o(X7,X3)
                | ~ incident_c(X7,X6) )
              & ( incident_c(X7,X6)
                | ~ incident_o(X7,X3) ) ) )
     => ( between_c(sK28(X0,X1,X2,X3),X2,X1,X0)
        & ! [X7] :
            ( ( incident_o(X7,X3)
              | ~ incident_c(X7,sK28(X0,X1,X2,X3)) )
            & ( incident_c(X7,sK28(X0,X1,X2,X3))
              | ~ incident_o(X7,X3) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f161,plain,
    ! [X0,X1,X2,X3] :
      ( ( sP4(X0,X1,X2,X3)
        | ! [X4] :
            ( ~ between_c(X4,X2,X1,X0)
            | ? [X5] :
                ( ( ~ incident_c(X5,X4)
                  | ~ incident_o(X5,X3) )
                & ( incident_c(X5,X4)
                  | incident_o(X5,X3) ) ) ) )
      & ( ? [X6] :
            ( between_c(X6,X2,X1,X0)
            & ! [X7] :
                ( ( incident_o(X7,X3)
                  | ~ incident_c(X7,X6) )
                & ( incident_c(X7,X6)
                  | ~ incident_o(X7,X3) ) ) )
        | ~ sP4(X0,X1,X2,X3) ) ),
    inference(rectify,[],[f160]) ).

fof(f160,plain,
    ! [X2,X1,X0,X3] :
      ( ( sP4(X2,X1,X0,X3)
        | ! [X4] :
            ( ~ between_c(X4,X0,X1,X2)
            | ? [X5] :
                ( ( ~ incident_c(X5,X4)
                  | ~ incident_o(X5,X3) )
                & ( incident_c(X5,X4)
                  | incident_o(X5,X3) ) ) ) )
      & ( ? [X4] :
            ( between_c(X4,X0,X1,X2)
            & ! [X5] :
                ( ( incident_o(X5,X3)
                  | ~ incident_c(X5,X4) )
                & ( incident_c(X5,X4)
                  | ~ incident_o(X5,X3) ) ) )
        | ~ sP4(X2,X1,X0,X3) ) ),
    inference(nnf_transformation,[],[f90]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : GEO117+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n004.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 22:05:23 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.36  % (3544)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37  % (3548)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37  TRYING [1]
% 0.14/0.37  TRYING [2]
% 0.14/0.37  % (3547)WARNING: value z3 for option sas not known
% 0.14/0.37  % (3545)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37  % (3546)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37  % (3547)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)
% 0.14/0.37  % (3549)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)
% 0.14/0.37  % (3550)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)
% 0.14/0.37  % (3551)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)
% 0.14/0.38  TRYING [3]
% 0.14/0.39  % (3550)First to succeed.
% 0.14/0.39  % (3550)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3544"
% 0.14/0.39  % (3550)Refutation found. Thanks to Tanya!
% 0.14/0.39  % SZS status Theorem for theBenchmark
% 0.14/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.39  % (3550)------------------------------
% 0.14/0.39  % (3550)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.39  % (3550)Termination reason: Refutation
% 0.14/0.39  
% 0.14/0.39  % (3550)Memory used [KB]: 1176
% 0.14/0.39  % (3550)Time elapsed: 0.016 s
% 0.14/0.39  % (3550)Instructions burned: 22 (million)
% 0.14/0.39  % (3544)Success in time 0.033 s
%------------------------------------------------------------------------------