TSTP Solution File: SEU204+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SEU204+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s

% Computer : n021.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 18:27:22 EDT 2022

% Result   : Theorem 0.15s 0.48s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   50 (  11 unt;   0 def)
%            Number of atoms       :  214 (  24 equ)
%            Maximal formula atoms :   15 (   4 avg)
%            Number of connectives :  256 (  92   ~;  90   |;  48   &)
%                                         (  11 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :    6 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;   2 con; 0-3 aty)
%            Number of variables   :  159 ( 126   !;  33   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f216,plain,
    $false,
    inference(subsumption_resolution,[],[f211,f145]) ).

fof(f145,plain,
    ~ subset(relation_image(sK7,sK8),relation_rng(sK7)),
    inference(cnf_transformation,[],[f99]) ).

fof(f99,plain,
    ( ~ subset(relation_image(sK7,sK8),relation_rng(sK7))
    & relation(sK7) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f62,f98]) ).

fof(f98,plain,
    ( ? [X0,X1] :
        ( ~ subset(relation_image(X0,X1),relation_rng(X0))
        & relation(X0) )
   => ( ~ subset(relation_image(sK7,sK8),relation_rng(sK7))
      & relation(sK7) ) ),
    introduced(choice_axiom,[]) ).

fof(f62,plain,
    ? [X0,X1] :
      ( ~ subset(relation_image(X0,X1),relation_rng(X0))
      & relation(X0) ),
    inference(ennf_transformation,[],[f48]) ).

fof(f48,plain,
    ~ ! [X0,X1] :
        ( relation(X0)
       => subset(relation_image(X0,X1),relation_rng(X0)) ),
    inference(rectify,[],[f33]) ).

fof(f33,negated_conjecture,
    ~ ! [X1,X0] :
        ( relation(X1)
       => subset(relation_image(X1,X0),relation_rng(X1)) ),
    inference(negated_conjecture,[],[f32]) ).

fof(f32,conjecture,
    ! [X1,X0] :
      ( relation(X1)
     => subset(relation_image(X1,X0),relation_rng(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t144_relat_1) ).

fof(f211,plain,
    subset(relation_image(sK7,sK8),relation_rng(sK7)),
    inference(resolution,[],[f209,f135]) ).

fof(f135,plain,
    ! [X0,X1] :
      ( ~ in(sK6(X0,X1),X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f93]) ).

fof(f93,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( in(sK6(X0,X1),X0)
          & ~ in(sK6(X0,X1),X1) ) )
      & ( ! [X3] :
            ( ~ in(X3,X0)
            | in(X3,X1) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f91,f92]) ).

fof(f92,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( in(X2,X0)
          & ~ in(X2,X1) )
     => ( in(sK6(X0,X1),X0)
        & ~ in(sK6(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f91,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( in(X2,X0)
            & ~ in(X2,X1) ) )
      & ( ! [X3] :
            ( ~ in(X3,X0)
            | in(X3,X1) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f90]) ).

fof(f90,plain,
    ! [X1,X0] :
      ( ( subset(X1,X0)
        | ? [X2] :
            ( in(X2,X1)
            & ~ in(X2,X0) ) )
      & ( ! [X2] :
            ( ~ in(X2,X1)
            | in(X2,X0) )
        | ~ subset(X1,X0) ) ),
    inference(nnf_transformation,[],[f55]) ).

fof(f55,plain,
    ! [X1,X0] :
      ( subset(X1,X0)
    <=> ! [X2] :
          ( ~ in(X2,X1)
          | in(X2,X0) ) ),
    inference(ennf_transformation,[],[f45]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( in(X2,X1)
         => in(X2,X0) )
    <=> subset(X1,X0) ),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X1,X0] :
      ( ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) )
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).

fof(f209,plain,
    in(sK6(relation_image(sK7,sK8),relation_rng(sK7)),relation_rng(sK7)),
    inference(subsumption_resolution,[],[f205,f144]) ).

fof(f144,plain,
    relation(sK7),
    inference(cnf_transformation,[],[f99]) ).

fof(f205,plain,
    ( ~ relation(sK7)
    | in(sK6(relation_image(sK7,sK8),relation_rng(sK7)),relation_rng(sK7)) ),
    inference(resolution,[],[f197,f178]) ).

fof(f178,plain,
    ! [X2,X3,X0] :
      ( ~ in(unordered_pair(unordered_pair(X3,X2),singleton(X3)),X0)
      | in(X2,relation_rng(X0))
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f171]) ).

fof(f171,plain,
    ! [X2,X3,X0,X1] :
      ( in(X2,X1)
      | ~ in(unordered_pair(unordered_pair(X3,X2),singleton(X3)),X0)
      | relation_rng(X0) != X1
      | ~ relation(X0) ),
    inference(definition_unfolding,[],[f158,f116]) ).

fof(f116,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    inference(cnf_transformation,[],[f73]) ).

fof(f73,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    inference(rectify,[],[f50]) ).

fof(f50,plain,
    ! [X1,X0] : unordered_pair(unordered_pair(X1,X0),singleton(X1)) = ordered_pair(X1,X0),
    inference(rectify,[],[f7]) ).

fof(f7,axiom,
    ! [X1,X0] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).

fof(f158,plain,
    ! [X2,X3,X0,X1] :
      ( in(X2,X1)
      | ~ in(ordered_pair(X3,X2),X0)
      | relation_rng(X0) != X1
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f107]) ).

fof(f107,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ! [X2] :
                ( ( in(X2,X1)
                  | ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
                & ( in(ordered_pair(sK10(X0,X2),X2),X0)
                  | ~ in(X2,X1) ) )
            | relation_rng(X0) != X1 )
          & ( relation_rng(X0) = X1
            | ( ( ! [X6] : ~ in(ordered_pair(X6,sK11(X0,X1)),X0)
                | ~ in(sK11(X0,X1),X1) )
              & ( in(ordered_pair(sK12(X0,X1),sK11(X0,X1)),X0)
                | in(sK11(X0,X1),X1) ) ) ) )
      | ~ relation(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f103,f106,f105,f104]) ).

fof(f104,plain,
    ! [X0,X2] :
      ( ? [X4] : in(ordered_pair(X4,X2),X0)
     => in(ordered_pair(sK10(X0,X2),X2),X0) ),
    introduced(choice_axiom,[]) ).

fof(f105,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
            | ~ in(X5,X1) )
          & ( ? [X7] : in(ordered_pair(X7,X5),X0)
            | in(X5,X1) ) )
     => ( ( ! [X6] : ~ in(ordered_pair(X6,sK11(X0,X1)),X0)
          | ~ in(sK11(X0,X1),X1) )
        & ( ? [X7] : in(ordered_pair(X7,sK11(X0,X1)),X0)
          | in(sK11(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f106,plain,
    ! [X0,X1] :
      ( ? [X7] : in(ordered_pair(X7,sK11(X0,X1)),X0)
     => in(ordered_pair(sK12(X0,X1),sK11(X0,X1)),X0) ),
    introduced(choice_axiom,[]) ).

fof(f103,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ! [X2] :
                ( ( in(X2,X1)
                  | ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
                & ( ? [X4] : in(ordered_pair(X4,X2),X0)
                  | ~ in(X2,X1) ) )
            | relation_rng(X0) != X1 )
          & ( relation_rng(X0) = X1
            | ? [X5] :
                ( ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
                  | ~ in(X5,X1) )
                & ( ? [X7] : in(ordered_pair(X7,X5),X0)
                  | in(X5,X1) ) ) ) )
      | ~ relation(X0) ),
    inference(rectify,[],[f102]) ).

fof(f102,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ! [X2] :
                ( ( in(X2,X1)
                  | ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
                & ( ? [X3] : in(ordered_pair(X3,X2),X0)
                  | ~ in(X2,X1) ) )
            | relation_rng(X0) != X1 )
          & ( relation_rng(X0) = X1
            | ? [X2] :
                ( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
                  | ~ in(X2,X1) )
                & ( ? [X3] : in(ordered_pair(X3,X2),X0)
                  | in(X2,X1) ) ) ) )
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f56]) ).

fof(f56,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] : in(ordered_pair(X3,X2),X0) )
        <=> relation_rng(X0) = X1 )
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0] :
      ( relation(X0)
     => ! [X1] :
          ( ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] : in(ordered_pair(X3,X2),X0) )
        <=> relation_rng(X0) = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).

fof(f197,plain,
    in(unordered_pair(unordered_pair(sK2(sK7,sK8,sK6(relation_image(sK7,sK8),relation_rng(sK7))),sK6(relation_image(sK7,sK8),relation_rng(sK7))),singleton(sK2(sK7,sK8,sK6(relation_image(sK7,sK8),relation_rng(sK7))))),sK7),
    inference(subsumption_resolution,[],[f192,f144]) ).

fof(f192,plain,
    ( in(unordered_pair(unordered_pair(sK2(sK7,sK8,sK6(relation_image(sK7,sK8),relation_rng(sK7))),sK6(relation_image(sK7,sK8),relation_rng(sK7))),singleton(sK2(sK7,sK8,sK6(relation_image(sK7,sK8),relation_rng(sK7))))),sK7)
    | ~ relation(sK7) ),
    inference(resolution,[],[f191,f175]) ).

fof(f175,plain,
    ! [X0,X1,X6] :
      ( ~ in(X6,relation_image(X0,X1))
      | in(unordered_pair(unordered_pair(sK2(X0,X1,X6),X6),singleton(sK2(X0,X1,X6))),X0)
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f168]) ).

fof(f168,plain,
    ! [X2,X0,X1,X6] :
      ( ~ relation(X0)
      | in(unordered_pair(unordered_pair(sK2(X0,X1,X6),X6),singleton(sK2(X0,X1,X6))),X0)
      | ~ in(X6,X2)
      | relation_image(X0,X1) != X2 ),
    inference(definition_unfolding,[],[f122,f116]) ).

fof(f122,plain,
    ! [X2,X0,X1,X6] :
      ( ~ relation(X0)
      | in(ordered_pair(sK2(X0,X1,X6),X6),X0)
      | ~ in(X6,X2)
      | relation_image(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f81]) ).

fof(f81,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ! [X1,X2] :
          ( ( relation_image(X0,X1) = X2
            | ( ( ~ in(sK0(X0,X1,X2),X2)
                | ! [X4] :
                    ( ~ in(ordered_pair(X4,sK0(X0,X1,X2)),X0)
                    | ~ in(X4,X1) ) )
              & ( in(sK0(X0,X1,X2),X2)
                | ( in(ordered_pair(sK1(X0,X1,X2),sK0(X0,X1,X2)),X0)
                  & in(sK1(X0,X1,X2),X1) ) ) ) )
          & ( ! [X6] :
                ( ( ( in(ordered_pair(sK2(X0,X1,X6),X6),X0)
                    & in(sK2(X0,X1,X6),X1) )
                  | ~ in(X6,X2) )
                & ( in(X6,X2)
                  | ! [X8] :
                      ( ~ in(ordered_pair(X8,X6),X0)
                      | ~ in(X8,X1) ) ) )
            | relation_image(X0,X1) != X2 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f77,f80,f79,f78]) ).

fof(f78,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ~ in(X3,X2)
            | ! [X4] :
                ( ~ in(ordered_pair(X4,X3),X0)
                | ~ in(X4,X1) ) )
          & ( in(X3,X2)
            | ? [X5] :
                ( in(ordered_pair(X5,X3),X0)
                & in(X5,X1) ) ) )
     => ( ( ~ in(sK0(X0,X1,X2),X2)
          | ! [X4] :
              ( ~ in(ordered_pair(X4,sK0(X0,X1,X2)),X0)
              | ~ in(X4,X1) ) )
        & ( in(sK0(X0,X1,X2),X2)
          | ? [X5] :
              ( in(ordered_pair(X5,sK0(X0,X1,X2)),X0)
              & in(X5,X1) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f79,plain,
    ! [X0,X1,X2] :
      ( ? [X5] :
          ( in(ordered_pair(X5,sK0(X0,X1,X2)),X0)
          & in(X5,X1) )
     => ( in(ordered_pair(sK1(X0,X1,X2),sK0(X0,X1,X2)),X0)
        & in(sK1(X0,X1,X2),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f80,plain,
    ! [X0,X1,X6] :
      ( ? [X7] :
          ( in(ordered_pair(X7,X6),X0)
          & in(X7,X1) )
     => ( in(ordered_pair(sK2(X0,X1,X6),X6),X0)
        & in(sK2(X0,X1,X6),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f77,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ! [X1,X2] :
          ( ( relation_image(X0,X1) = X2
            | ? [X3] :
                ( ( ~ in(X3,X2)
                  | ! [X4] :
                      ( ~ in(ordered_pair(X4,X3),X0)
                      | ~ in(X4,X1) ) )
                & ( in(X3,X2)
                  | ? [X5] :
                      ( in(ordered_pair(X5,X3),X0)
                      & in(X5,X1) ) ) ) )
          & ( ! [X6] :
                ( ( ? [X7] :
                      ( in(ordered_pair(X7,X6),X0)
                      & in(X7,X1) )
                  | ~ in(X6,X2) )
                & ( in(X6,X2)
                  | ! [X8] :
                      ( ~ in(ordered_pair(X8,X6),X0)
                      | ~ in(X8,X1) ) ) )
            | relation_image(X0,X1) != X2 ) ) ),
    inference(rectify,[],[f76]) ).

fof(f76,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ! [X1,X2] :
          ( ( relation_image(X0,X1) = X2
            | ? [X3] :
                ( ( ~ in(X3,X2)
                  | ! [X4] :
                      ( ~ in(ordered_pair(X4,X3),X0)
                      | ~ in(X4,X1) ) )
                & ( in(X3,X2)
                  | ? [X4] :
                      ( in(ordered_pair(X4,X3),X0)
                      & in(X4,X1) ) ) ) )
          & ( ! [X3] :
                ( ( ? [X4] :
                      ( in(ordered_pair(X4,X3),X0)
                      & in(X4,X1) )
                  | ~ in(X3,X2) )
                & ( in(X3,X2)
                  | ! [X4] :
                      ( ~ in(ordered_pair(X4,X3),X0)
                      | ~ in(X4,X1) ) ) )
            | relation_image(X0,X1) != X2 ) ) ),
    inference(nnf_transformation,[],[f54]) ).

fof(f54,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ! [X1,X2] :
          ( relation_image(X0,X1) = X2
        <=> ! [X3] :
              ( ? [X4] :
                  ( in(ordered_pair(X4,X3),X0)
                  & in(X4,X1) )
            <=> in(X3,X2) ) ) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0] :
      ( relation(X0)
     => ! [X1,X2] :
          ( relation_image(X0,X1) = X2
        <=> ! [X3] :
              ( ? [X4] :
                  ( in(ordered_pair(X4,X3),X0)
                  & in(X4,X1) )
            <=> in(X3,X2) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_relat_1) ).

fof(f191,plain,
    in(sK6(relation_image(sK7,sK8),relation_rng(sK7)),relation_image(sK7,sK8)),
    inference(resolution,[],[f145,f136]) ).

fof(f136,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | in(sK6(X0,X1),X0) ),
    inference(cnf_transformation,[],[f93]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem    : SEU204+1 : TPTP v8.1.0. Released v3.3.0.
% 0.00/0.10  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.10/0.30  % Computer : n021.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit   : 300
% 0.10/0.30  % WCLimit    : 300
% 0.10/0.30  % DateTime   : Tue Aug 30 14:46:41 EDT 2022
% 0.10/0.30  % CPUTime    : 
% 0.15/0.46  % (24266)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.15/0.46  % (24276)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.15/0.46  % (24260)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.15/0.47  % (24282)dis+2_3:1_aac=none:abs=on:ep=R:lcm=reverse:nwc=10.0:sos=on:sp=const_frequency:spb=units:urr=ec_only:i=8:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/8Mi)
% 0.15/0.47  % (24268)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.15/0.47  % (24268)Instruction limit reached!
% 0.15/0.47  % (24268)------------------------------
% 0.15/0.47  % (24268)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.15/0.47  % (24266)First to succeed.
% 0.15/0.47  % (24274)dis+1010_1:1_bs=on:ep=RS:erd=off:newcnf=on:nwc=10.0:s2a=on:sgt=32:ss=axioms:i=30:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/30Mi)
% 0.15/0.48  % (24266)Refutation found. Thanks to Tanya!
% 0.15/0.48  % SZS status Theorem for theBenchmark
% 0.15/0.48  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.48  % (24266)------------------------------
% 0.15/0.48  % (24266)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.15/0.48  % (24266)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.15/0.48  % (24266)Termination reason: Refutation
% 0.15/0.48  
% 0.15/0.48  % (24266)Memory used [KB]: 1535
% 0.15/0.48  % (24266)Time elapsed: 0.116 s
% 0.15/0.48  % (24266)Instructions burned: 4 (million)
% 0.15/0.48  % (24266)------------------------------
% 0.15/0.48  % (24266)------------------------------
% 0.15/0.48  % (24253)Success in time 0.174 s
%------------------------------------------------------------------------------