TSTP Solution File: SEU045+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEU045+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s

% Computer : n020.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 : Thu Aug 31 17:55:05 EDT 2023

% Result   : Theorem 0.21s 0.43s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   46 (  14 unt;   0 def)
%            Number of atoms       :  198 (  53 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :  240 (  88   ~;  78   |;  49   &)
%                                         (  11 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   7 con; 0-2 aty)
%            Number of variables   :   98 (;  85   !;  13   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f482,plain,
    $false,
    inference(subsumption_resolution,[],[f481,f173]) ).

fof(f173,plain,
    sF20 != sF21,
    inference(definition_folding,[],[f108,f172,f171,f170]) ).

fof(f170,plain,
    relation_rng_restriction(sK1,sK3) = sF19,
    introduced(function_definition,[]) ).

fof(f171,plain,
    apply(sF19,sK2) = sF20,
    introduced(function_definition,[]) ).

fof(f172,plain,
    apply(sK3,sK2) = sF21,
    introduced(function_definition,[]) ).

fof(f108,plain,
    apply(relation_rng_restriction(sK1,sK3),sK2) != apply(sK3,sK2),
    inference(cnf_transformation,[],[f72]) ).

fof(f72,plain,
    ( apply(relation_rng_restriction(sK1,sK3),sK2) != apply(sK3,sK2)
    & in(sK2,relation_dom(relation_rng_restriction(sK1,sK3)))
    & function(sK3)
    & relation(sK3) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f44,f71]) ).

fof(f71,plain,
    ( ? [X0,X1,X2] :
        ( apply(relation_rng_restriction(X0,X2),X1) != apply(X2,X1)
        & in(X1,relation_dom(relation_rng_restriction(X0,X2)))
        & function(X2)
        & relation(X2) )
   => ( apply(relation_rng_restriction(sK1,sK3),sK2) != apply(sK3,sK2)
      & in(sK2,relation_dom(relation_rng_restriction(sK1,sK3)))
      & function(sK3)
      & relation(sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f44,plain,
    ? [X0,X1,X2] :
      ( apply(relation_rng_restriction(X0,X2),X1) != apply(X2,X1)
      & in(X1,relation_dom(relation_rng_restriction(X0,X2)))
      & function(X2)
      & relation(X2) ),
    inference(flattening,[],[f43]) ).

fof(f43,plain,
    ? [X0,X1,X2] :
      ( apply(relation_rng_restriction(X0,X2),X1) != apply(X2,X1)
      & in(X1,relation_dom(relation_rng_restriction(X0,X2)))
      & function(X2)
      & relation(X2) ),
    inference(ennf_transformation,[],[f34]) ).

fof(f34,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( ( function(X2)
          & relation(X2) )
       => ( in(X1,relation_dom(relation_rng_restriction(X0,X2)))
         => apply(relation_rng_restriction(X0,X2),X1) = apply(X2,X1) ) ),
    inference(negated_conjecture,[],[f33]) ).

fof(f33,conjecture,
    ! [X0,X1,X2] :
      ( ( function(X2)
        & relation(X2) )
     => ( in(X1,relation_dom(relation_rng_restriction(X0,X2)))
       => apply(relation_rng_restriction(X0,X2),X1) = apply(X2,X1) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.NHbH9hKDI7/Vampire---4.8_4470',t87_funct_1) ).

fof(f481,plain,
    sF20 = sF21,
    inference(backward_demodulation,[],[f172,f480]) ).

fof(f480,plain,
    apply(sK3,sK2) = sF20,
    inference(forward_demodulation,[],[f476,f171]) ).

fof(f476,plain,
    apply(sK3,sK2) = apply(sF19,sK2),
    inference(resolution,[],[f473,f175]) ).

fof(f175,plain,
    in(sK2,sF22),
    inference(definition_folding,[],[f107,f174,f170]) ).

fof(f174,plain,
    relation_dom(sF19) = sF22,
    introduced(function_definition,[]) ).

fof(f107,plain,
    in(sK2,relation_dom(relation_rng_restriction(sK1,sK3))),
    inference(cnf_transformation,[],[f72]) ).

fof(f473,plain,
    ! [X0] :
      ( ~ in(X0,sF22)
      | apply(sK3,X0) = apply(sF19,X0) ),
    inference(forward_demodulation,[],[f472,f174]) ).

fof(f472,plain,
    ! [X0] :
      ( ~ in(X0,relation_dom(sF19))
      | apply(sK3,X0) = apply(sF19,X0) ),
    inference(superposition,[],[f451,f170]) ).

fof(f451,plain,
    ! [X10,X9] :
      ( ~ in(X9,relation_dom(relation_rng_restriction(X10,sK3)))
      | apply(sK3,X9) = apply(relation_rng_restriction(X10,sK3),X9) ),
    inference(subsumption_resolution,[],[f444,f105]) ).

fof(f105,plain,
    relation(sK3),
    inference(cnf_transformation,[],[f72]) ).

fof(f444,plain,
    ! [X10,X9] :
      ( ~ in(X9,relation_dom(relation_rng_restriction(X10,sK3)))
      | apply(sK3,X9) = apply(relation_rng_restriction(X10,sK3),X9)
      | ~ relation(sK3) ),
    inference(resolution,[],[f177,f106]) ).

fof(f106,plain,
    function(sK3),
    inference(cnf_transformation,[],[f72]) ).

fof(f177,plain,
    ! [X2,X0,X4] :
      ( ~ function(X2)
      | ~ in(X4,relation_dom(relation_rng_restriction(X0,X2)))
      | apply(X2,X4) = apply(relation_rng_restriction(X0,X2),X4)
      | ~ relation(X2) ),
    inference(subsumption_resolution,[],[f176,f129]) ).

fof(f129,plain,
    ! [X0,X1] :
      ( relation(relation_rng_restriction(X0,X1))
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f54]) ).

fof(f54,plain,
    ! [X0,X1] :
      ( relation(relation_rng_restriction(X0,X1))
      | ~ relation(X1) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f19,axiom,
    ! [X0,X1] :
      ( relation(X1)
     => relation(relation_rng_restriction(X0,X1)) ),
    file('/export/starexec/sandbox2/tmp/tmp.NHbH9hKDI7/Vampire---4.8_4470',dt_k8_relat_1) ).

fof(f176,plain,
    ! [X2,X0,X4] :
      ( apply(X2,X4) = apply(relation_rng_restriction(X0,X2),X4)
      | ~ in(X4,relation_dom(relation_rng_restriction(X0,X2)))
      | ~ function(X2)
      | ~ relation(X2)
      | ~ relation(relation_rng_restriction(X0,X2)) ),
    inference(subsumption_resolution,[],[f164,f134]) ).

fof(f134,plain,
    ! [X0,X1] :
      ( function(relation_rng_restriction(X0,X1))
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f60]) ).

fof(f60,plain,
    ! [X0,X1] :
      ( ( function(relation_rng_restriction(X0,X1))
        & relation(relation_rng_restriction(X0,X1)) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(flattening,[],[f59]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( ( function(relation_rng_restriction(X0,X1))
        & relation(relation_rng_restriction(X0,X1)) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f20,axiom,
    ! [X0,X1] :
      ( ( function(X1)
        & relation(X1) )
     => ( function(relation_rng_restriction(X0,X1))
        & relation(relation_rng_restriction(X0,X1)) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.NHbH9hKDI7/Vampire---4.8_4470',fc5_funct_1) ).

fof(f164,plain,
    ! [X2,X0,X4] :
      ( apply(X2,X4) = apply(relation_rng_restriction(X0,X2),X4)
      | ~ in(X4,relation_dom(relation_rng_restriction(X0,X2)))
      | ~ function(X2)
      | ~ relation(X2)
      | ~ function(relation_rng_restriction(X0,X2))
      | ~ relation(relation_rng_restriction(X0,X2)) ),
    inference(equality_resolution,[],[f142]) ).

fof(f142,plain,
    ! [X2,X0,X1,X4] :
      ( apply(X2,X4) = apply(X1,X4)
      | ~ in(X4,relation_dom(X1))
      | relation_rng_restriction(X0,X2) != X1
      | ~ function(X2)
      | ~ relation(X2)
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f88]) ).

fof(f88,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( ( relation_rng_restriction(X0,X2) = X1
              | ( apply(X2,sK8(X1,X2)) != apply(X1,sK8(X1,X2))
                & in(sK8(X1,X2),relation_dom(X1)) )
              | ~ sP0(X0,X2,X1) )
            & ( ( ! [X4] :
                    ( apply(X2,X4) = apply(X1,X4)
                    | ~ in(X4,relation_dom(X1)) )
                & sP0(X0,X2,X1) )
              | relation_rng_restriction(X0,X2) != X1 ) )
          | ~ function(X2)
          | ~ relation(X2) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f86,f87]) ).

fof(f87,plain,
    ! [X1,X2] :
      ( ? [X3] :
          ( apply(X2,X3) != apply(X1,X3)
          & in(X3,relation_dom(X1)) )
     => ( apply(X2,sK8(X1,X2)) != apply(X1,sK8(X1,X2))
        & in(sK8(X1,X2),relation_dom(X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f86,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( ( relation_rng_restriction(X0,X2) = X1
              | ? [X3] :
                  ( apply(X2,X3) != apply(X1,X3)
                  & in(X3,relation_dom(X1)) )
              | ~ sP0(X0,X2,X1) )
            & ( ( ! [X4] :
                    ( apply(X2,X4) = apply(X1,X4)
                    | ~ in(X4,relation_dom(X1)) )
                & sP0(X0,X2,X1) )
              | relation_rng_restriction(X0,X2) != X1 ) )
          | ~ function(X2)
          | ~ relation(X2) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(rectify,[],[f85]) ).

fof(f85,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( ( relation_rng_restriction(X0,X2) = X1
              | ? [X3] :
                  ( apply(X2,X3) != apply(X1,X3)
                  & in(X3,relation_dom(X1)) )
              | ~ sP0(X0,X2,X1) )
            & ( ( ! [X3] :
                    ( apply(X2,X3) = apply(X1,X3)
                    | ~ in(X3,relation_dom(X1)) )
                & sP0(X0,X2,X1) )
              | relation_rng_restriction(X0,X2) != X1 ) )
          | ~ function(X2)
          | ~ relation(X2) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(flattening,[],[f84]) ).

fof(f84,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( ( relation_rng_restriction(X0,X2) = X1
              | ? [X3] :
                  ( apply(X2,X3) != apply(X1,X3)
                  & in(X3,relation_dom(X1)) )
              | ~ sP0(X0,X2,X1) )
            & ( ( ! [X3] :
                    ( apply(X2,X3) = apply(X1,X3)
                    | ~ in(X3,relation_dom(X1)) )
                & sP0(X0,X2,X1) )
              | relation_rng_restriction(X0,X2) != X1 ) )
          | ~ function(X2)
          | ~ relation(X2) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(nnf_transformation,[],[f70]) ).

fof(f70,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( relation_rng_restriction(X0,X2) = X1
          <=> ( ! [X3] :
                  ( apply(X2,X3) = apply(X1,X3)
                  | ~ in(X3,relation_dom(X1)) )
              & sP0(X0,X2,X1) ) )
          | ~ function(X2)
          | ~ relation(X2) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(definition_folding,[],[f62,f69]) ).

fof(f69,plain,
    ! [X0,X2,X1] :
      ( sP0(X0,X2,X1)
    <=> ! [X4] :
          ( in(X4,relation_dom(X1))
        <=> ( in(apply(X2,X4),X0)
            & in(X4,relation_dom(X2)) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( relation_rng_restriction(X0,X2) = X1
          <=> ( ! [X3] :
                  ( apply(X2,X3) = apply(X1,X3)
                  | ~ in(X3,relation_dom(X1)) )
              & ! [X4] :
                  ( in(X4,relation_dom(X1))
                <=> ( in(apply(X2,X4),X0)
                    & in(X4,relation_dom(X2)) ) ) ) )
          | ~ function(X2)
          | ~ relation(X2) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(flattening,[],[f61]) ).

fof(f61,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( relation_rng_restriction(X0,X2) = X1
          <=> ( ! [X3] :
                  ( apply(X2,X3) = apply(X1,X3)
                  | ~ in(X3,relation_dom(X1)) )
              & ! [X4] :
                  ( in(X4,relation_dom(X1))
                <=> ( in(apply(X2,X4),X0)
                    & in(X4,relation_dom(X2)) ) ) ) )
          | ~ function(X2)
          | ~ relation(X2) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(ennf_transformation,[],[f37]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( ( function(X1)
        & relation(X1) )
     => ! [X2] :
          ( ( function(X2)
            & relation(X2) )
         => ( relation_rng_restriction(X0,X2) = X1
          <=> ( ! [X3] :
                  ( in(X3,relation_dom(X1))
                 => apply(X2,X3) = apply(X1,X3) )
              & ! [X4] :
                  ( in(X4,relation_dom(X1))
                <=> ( in(apply(X2,X4),X0)
                    & in(X4,relation_dom(X2)) ) ) ) ) ) ),
    inference(rectify,[],[f35]) ).

fof(f35,axiom,
    ! [X0,X1] :
      ( ( function(X1)
        & relation(X1) )
     => ! [X2] :
          ( ( function(X2)
            & relation(X2) )
         => ( relation_rng_restriction(X0,X2) = X1
          <=> ( ! [X3] :
                  ( in(X3,relation_dom(X1))
                 => apply(X2,X3) = apply(X1,X3) )
              & ! [X3] :
                  ( in(X3,relation_dom(X1))
                <=> ( in(apply(X2,X3),X0)
                    & in(X3,relation_dom(X2)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.NHbH9hKDI7/Vampire---4.8_4470',t85_funct_1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU045+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.35  % Computer : n020.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Wed Aug 23 18:31:16 EDT 2023
% 0.15/0.35  % CPUTime    : 
% 0.15/0.35  This is a FOF_THM_RFO_SEQ problem
% 0.15/0.36  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.NHbH9hKDI7/Vampire---4.8_4470
% 0.15/0.36  % (4623)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.42  % (4630)ott+11_14_av=off:bs=on:bsr=on:cond=on:flr=on:fsd=off:fde=unused:gsp=on:nm=4:nwc=1.5:tgt=full_386 on Vampire---4 for (386ds/0Mi)
% 0.21/0.42  % (4628)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_424 on Vampire---4 for (424ds/0Mi)
% 0.21/0.42  % (4627)lrs-3_8_anc=none:bce=on:cond=on:drc=off:flr=on:fsd=off:fsr=off:fde=unused:gsp=on:gs=on:gsaa=full_model:lcm=predicate:lma=on:nm=16:sos=all:sp=weighted_frequency:tgt=ground:urr=ec_only:stl=188_482 on Vampire---4 for (482ds/0Mi)
% 0.21/0.42  % (4626)dis-11_4:1_aac=none:add=off:afr=on:anc=none:bd=preordered:bs=on:bsr=on:drc=off:fsr=off:fde=none:gsp=on:irw=on:lcm=reverse:lma=on:nm=0:nwc=1.7:nicw=on:sas=z3:sims=off:sos=all:sac=on:sp=weighted_frequency:tgt=full_602 on Vampire---4 for (602ds/0Mi)
% 0.21/0.42  % (4629)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_413 on Vampire---4 for (413ds/0Mi)
% 0.21/0.42  % (4625)dis+1010_4:1_anc=none:bd=off:drc=off:flr=on:fsr=off:nm=4:nwc=1.1:nicw=on:sas=z3_680 on Vampire---4 for (680ds/0Mi)
% 0.21/0.42  % (4624)lrs+10_11_cond=on:drc=off:flr=on:fsr=off:gsp=on:gs=on:gsem=off:lma=on:msp=off:nm=4:nwc=1.5:nicw=on:sas=z3:sims=off:sp=scramble:stl=188_730 on Vampire---4 for (730ds/0Mi)
% 0.21/0.43  % (4630)First to succeed.
% 0.21/0.43  % (4630)Refutation found. Thanks to Tanya!
% 0.21/0.43  % SZS status Theorem for Vampire---4
% 0.21/0.43  % SZS output start Proof for Vampire---4
% See solution above
% 0.21/0.43  % (4630)------------------------------
% 0.21/0.43  % (4630)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.43  % (4630)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.43  % (4630)Termination reason: Refutation
% 0.21/0.43  
% 0.21/0.43  % (4630)Memory used [KB]: 1407
% 0.21/0.43  % (4630)Time elapsed: 0.012 s
% 0.21/0.43  % (4630)------------------------------
% 0.21/0.43  % (4630)------------------------------
% 0.21/0.43  % (4623)Success in time 0.07 s
% 0.21/0.43  % Vampire---4.8 exiting
%------------------------------------------------------------------------------