TSTP Solution File: GEO117+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : GEO117+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -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 : Wed Aug 31 16:11:53 EDT 2022

% Result   : Theorem 0.20s 0.56s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   41 (  13 unt;   3 typ;   0 def)
%            Number of atoms       :  189 (  11 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :  229 (  78   ~;  73   |;  66   &)
%                                         (   8 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   7 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    4 (   0 usr;   3 ari)
%            Number of type conns  :    6 (   3   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :   13 (  11 usr;   1 prp; 0-4 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-4 aty)
%            Number of variables   :  137 ( 117   !;  20   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(pred_def_15,type,
    sQ25_eqProxy: ( $int * $int ) > $o ).

tff(pred_def_16,type,
    sQ26_eqProxy: ( $rat * $rat ) > $o ).

tff(pred_def_17,type,
    sQ27_eqProxy: ( $real * $real ) > $o ).

fof(f489,plain,
    $false,
    inference(subsumption_resolution,[],[f488,f315]) ).

fof(f315,plain,
    ! [X2,X3,X0] : ~ between_c(X2,X3,X0,X3),
    inference(literal_reordering,[],[f241]) ).

fof(f241,plain,
    ! [X2,X3,X0] : ~ between_c(X2,X3,X0,X3),
    inference(equality_resolution,[],[f201]) ).

fof(f201,plain,
    ! [X2,X3,X0,X1] :
      ( X1 != X3
      | ~ between_c(X2,X1,X0,X3) ),
    inference(cnf_transformation,[],[f127]) ).

fof(f127,plain,
    ! [X0,X1,X2,X3] :
      ( ( ( X1 != X3
          & end_point(X1,sK12(X0,X1,X2,X3))
          & part_of(sK12(X0,X1,X2,X3),X2)
          & end_point(X3,sK12(X0,X1,X2,X3))
          & inner_point(X0,sK12(X0,X1,X2,X3)) )
        | ~ between_c(X2,X1,X0,X3) )
      & ( between_c(X2,X1,X0,X3)
        | X1 = X3
        | ! [X5] :
            ( ~ end_point(X1,X5)
            | ~ part_of(X5,X2)
            | ~ end_point(X3,X5)
            | ~ inner_point(X0,X5) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f125,f126]) ).

fof(f126,plain,
    ! [X0,X1,X2,X3] :
      ( ? [X4] :
          ( end_point(X1,X4)
          & part_of(X4,X2)
          & end_point(X3,X4)
          & inner_point(X0,X4) )
     => ( end_point(X1,sK12(X0,X1,X2,X3))
        & part_of(sK12(X0,X1,X2,X3),X2)
        & end_point(X3,sK12(X0,X1,X2,X3))
        & inner_point(X0,sK12(X0,X1,X2,X3)) ) ),
    introduced(choice_axiom,[]) ).

fof(f125,plain,
    ! [X0,X1,X2,X3] :
      ( ( ( X1 != X3
          & ? [X4] :
              ( end_point(X1,X4)
              & part_of(X4,X2)
              & end_point(X3,X4)
              & inner_point(X0,X4) ) )
        | ~ between_c(X2,X1,X0,X3) )
      & ( between_c(X2,X1,X0,X3)
        | X1 = X3
        | ! [X5] :
            ( ~ end_point(X1,X5)
            | ~ part_of(X5,X2)
            | ~ end_point(X3,X5)
            | ~ inner_point(X0,X5) ) ) ),
    inference(rectify,[],[f124]) ).

fof(f124,plain,
    ! [X1,X3,X0,X2] :
      ( ( ( X2 != X3
          & ? [X4] :
              ( end_point(X3,X4)
              & part_of(X4,X0)
              & end_point(X2,X4)
              & inner_point(X1,X4) ) )
        | ~ between_c(X0,X3,X1,X2) )
      & ( between_c(X0,X3,X1,X2)
        | X2 = X3
        | ! [X4] :
            ( ~ end_point(X3,X4)
            | ~ part_of(X4,X0)
            | ~ end_point(X2,X4)
            | ~ inner_point(X1,X4) ) ) ),
    inference(flattening,[],[f123]) ).

fof(f123,plain,
    ! [X1,X3,X0,X2] :
      ( ( ( X2 != X3
          & ? [X4] :
              ( end_point(X3,X4)
              & part_of(X4,X0)
              & end_point(X2,X4)
              & inner_point(X1,X4) ) )
        | ~ between_c(X0,X3,X1,X2) )
      & ( between_c(X0,X3,X1,X2)
        | X2 = X3
        | ! [X4] :
            ( ~ end_point(X3,X4)
            | ~ part_of(X4,X0)
            | ~ end_point(X2,X4)
            | ~ inner_point(X1,X4) ) ) ),
    inference(nnf_transformation,[],[f45]) ).

fof(f45,plain,
    ! [X1,X3,X0,X2] :
      ( ( X2 != X3
        & ? [X4] :
            ( end_point(X3,X4)
            & part_of(X4,X0)
            & end_point(X2,X4)
            & inner_point(X1,X4) ) )
    <=> between_c(X0,X3,X1,X2) ),
    inference(rectify,[],[f17]) ).

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

fof(f488,plain,
    between_c(sK23(sK20,sK20,sK20,sK19),sK20,sK20,sK20),
    inference(resolution,[],[f299,f458]) ).

fof(f458,plain,
    between_o(sK19,sK20,sK20,sK20),
    inference(resolution,[],[f455,f270]) ).

fof(f270,plain,
    ordered_by(sK19,sK20,sK20),
    inference(literal_reordering,[],[f228]) ).

fof(f228,plain,
    ordered_by(sK19,sK20,sK20),
    inference(cnf_transformation,[],[f152]) ).

fof(f152,plain,
    ordered_by(sK19,sK20,sK20),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK19,sK20])],[f150,f151]) ).

fof(f151,plain,
    ( ? [X0,X1] : ordered_by(X0,X1,X1)
   => ordered_by(sK19,sK20,sK20) ),
    introduced(choice_axiom,[]) ).

fof(f150,plain,
    ? [X0,X1] : ordered_by(X0,X1,X1),
    inference(rectify,[],[f75]) ).

fof(f75,plain,
    ? [X1,X0] : ordered_by(X1,X0,X0),
    inference(ennf_transformation,[],[f43]) ).

fof(f43,plain,
    ~ ! [X0,X1] : ~ ordered_by(X1,X0,X0),
    inference(rectify,[],[f29]) ).

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

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

fof(f455,plain,
    ! [X0] :
      ( ~ ordered_by(sK19,X0,sK20)
      | between_o(sK19,X0,sK20,sK20) ),
    inference(resolution,[],[f291,f270]) ).

fof(f291,plain,
    ! [X2,X3,X0,X1] :
      ( ~ ordered_by(X1,X0,X2)
      | ~ ordered_by(X1,X3,X0)
      | between_o(X1,X3,X0,X2) ),
    inference(literal_reordering,[],[f202]) ).

fof(f202,plain,
    ! [X2,X3,X0,X1] :
      ( ~ ordered_by(X1,X3,X0)
      | ~ ordered_by(X1,X0,X2)
      | between_o(X1,X3,X0,X2) ),
    inference(cnf_transformation,[],[f129]) ).

fof(f129,plain,
    ! [X0,X1,X2,X3] :
      ( ( ( ordered_by(X1,X0,X3)
          & ordered_by(X1,X2,X0) )
        | ( ordered_by(X1,X3,X0)
          & ordered_by(X1,X0,X2) )
        | ~ between_o(X1,X3,X0,X2) )
      & ( between_o(X1,X3,X0,X2)
        | ( ( ~ ordered_by(X1,X0,X3)
            | ~ ordered_by(X1,X2,X0) )
          & ( ~ ordered_by(X1,X3,X0)
            | ~ ordered_by(X1,X0,X2) ) ) ) ),
    inference(flattening,[],[f128]) ).

fof(f128,plain,
    ! [X0,X1,X2,X3] :
      ( ( ( ordered_by(X1,X0,X3)
          & ordered_by(X1,X2,X0) )
        | ( ordered_by(X1,X3,X0)
          & ordered_by(X1,X0,X2) )
        | ~ between_o(X1,X3,X0,X2) )
      & ( between_o(X1,X3,X0,X2)
        | ( ( ~ ordered_by(X1,X0,X3)
            | ~ ordered_by(X1,X2,X0) )
          & ( ~ ordered_by(X1,X3,X0)
            | ~ ordered_by(X1,X0,X2) ) ) ) ),
    inference(nnf_transformation,[],[f47]) ).

fof(f47,plain,
    ! [X0,X1,X2,X3] :
      ( ( ( ordered_by(X1,X0,X3)
          & ordered_by(X1,X2,X0) )
        | ( ordered_by(X1,X3,X0)
          & ordered_by(X1,X0,X2) ) )
    <=> between_o(X1,X3,X0,X2) ),
    inference(rectify,[],[f18]) ).

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

fof(f299,plain,
    ! [X2,X3,X0,X1] :
      ( ~ between_o(X3,X0,X2,X1)
      | between_c(sK23(X0,X1,X2,X3),X0,X2,X1) ),
    inference(literal_reordering,[],[f237]) ).

fof(f237,plain,
    ! [X2,X3,X0,X1] :
      ( ~ between_o(X3,X0,X2,X1)
      | between_c(sK23(X0,X1,X2,X3),X0,X2,X1) ),
    inference(cnf_transformation,[],[f162]) ).

fof(f162,plain,
    ! [X0,X1,X2,X3] :
      ( ( between_o(X3,X0,X2,X1)
        | ! [X4] :
            ( ~ between_c(X4,X0,X2,X1)
            | ( ( ~ incident_o(sK22(X3,X4),X3)
                | ~ incident_c(sK22(X3,X4),X4) )
              & ( incident_o(sK22(X3,X4),X3)
                | incident_c(sK22(X3,X4),X4) ) ) ) )
      & ( ( between_c(sK23(X0,X1,X2,X3),X0,X2,X1)
          & ! [X7] :
              ( ( incident_c(X7,sK23(X0,X1,X2,X3))
                | ~ incident_o(X7,X3) )
              & ( incident_o(X7,X3)
                | ~ incident_c(X7,sK23(X0,X1,X2,X3)) ) ) )
        | ~ between_o(X3,X0,X2,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK22,sK23])],[f159,f161,f160]) ).

fof(f160,plain,
    ! [X3,X4] :
      ( ? [X5] :
          ( ( ~ incident_o(X5,X3)
            | ~ incident_c(X5,X4) )
          & ( incident_o(X5,X3)
            | incident_c(X5,X4) ) )
     => ( ( ~ incident_o(sK22(X3,X4),X3)
          | ~ incident_c(sK22(X3,X4),X4) )
        & ( incident_o(sK22(X3,X4),X3)
          | incident_c(sK22(X3,X4),X4) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f161,plain,
    ! [X0,X1,X2,X3] :
      ( ? [X6] :
          ( between_c(X6,X0,X2,X1)
          & ! [X7] :
              ( ( incident_c(X7,X6)
                | ~ incident_o(X7,X3) )
              & ( incident_o(X7,X3)
                | ~ incident_c(X7,X6) ) ) )
     => ( between_c(sK23(X0,X1,X2,X3),X0,X2,X1)
        & ! [X7] :
            ( ( incident_c(X7,sK23(X0,X1,X2,X3))
              | ~ incident_o(X7,X3) )
            & ( incident_o(X7,X3)
              | ~ incident_c(X7,sK23(X0,X1,X2,X3)) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f159,plain,
    ! [X0,X1,X2,X3] :
      ( ( between_o(X3,X0,X2,X1)
        | ! [X4] :
            ( ~ between_c(X4,X0,X2,X1)
            | ? [X5] :
                ( ( ~ incident_o(X5,X3)
                  | ~ incident_c(X5,X4) )
                & ( incident_o(X5,X3)
                  | incident_c(X5,X4) ) ) ) )
      & ( ? [X6] :
            ( between_c(X6,X0,X2,X1)
            & ! [X7] :
                ( ( incident_c(X7,X6)
                  | ~ incident_o(X7,X3) )
                & ( incident_o(X7,X3)
                  | ~ incident_c(X7,X6) ) ) )
        | ~ between_o(X3,X0,X2,X1) ) ),
    inference(rectify,[],[f158]) ).

fof(f158,plain,
    ! [X3,X1,X2,X0] :
      ( ( between_o(X0,X3,X2,X1)
        | ! [X4] :
            ( ~ between_c(X4,X3,X2,X1)
            | ? [X5] :
                ( ( ~ incident_o(X5,X0)
                  | ~ incident_c(X5,X4) )
                & ( incident_o(X5,X0)
                  | incident_c(X5,X4) ) ) ) )
      & ( ? [X4] :
            ( between_c(X4,X3,X2,X1)
            & ! [X5] :
                ( ( incident_c(X5,X4)
                  | ~ incident_o(X5,X0) )
                & ( incident_o(X5,X0)
                  | ~ incident_c(X5,X4) ) ) )
        | ~ between_o(X0,X3,X2,X1) ) ),
    inference(nnf_transformation,[],[f36]) ).

fof(f36,plain,
    ! [X3,X1,X2,X0] :
      ( between_o(X0,X3,X2,X1)
    <=> ? [X4] :
          ( between_c(X4,X3,X2,X1)
          & ! [X5] :
              ( incident_c(X5,X4)
            <=> incident_o(X5,X0) ) ) ),
    inference(rectify,[],[f23]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : GEO117+1 : TPTP v8.1.0. Released v2.4.0.
% 0.12/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34  % Computer : n022.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   : Mon Aug 29 21:16:56 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.20/0.53  % (12340)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.53  % (12348)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.20/0.55  TRYING [1]
% 0.20/0.55  TRYING [2]
% 0.20/0.55  % (12348)First to succeed.
% 0.20/0.56  % (12339)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.20/0.56  % (12356)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.20/0.56  % (12352)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.56  % (12348)Refutation found. Thanks to Tanya!
% 0.20/0.56  % SZS status Theorem for theBenchmark
% 0.20/0.56  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.56  % (12348)------------------------------
% 0.20/0.56  % (12348)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.56  % (12348)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.56  % (12348)Termination reason: Refutation
% 0.20/0.56  
% 0.20/0.56  % (12348)Memory used [KB]: 6012
% 0.20/0.56  % (12348)Time elapsed: 0.014 s
% 0.20/0.56  % (12348)Instructions burned: 12 (million)
% 0.20/0.56  % (12348)------------------------------
% 0.20/0.56  % (12348)------------------------------
% 0.20/0.56  % (12333)Success in time 0.211 s
%------------------------------------------------------------------------------