TSTP Solution File: SEU292+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEU292+1 : TPTP v8.1.2. Released v3.3.0.
% 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 : n015.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 17:57:39 EDT 2023

% Result   : Theorem 0.23s 0.45s
% Output   : Refutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   52 (  16 unt;   0 def)
%            Number of atoms       :  203 (  62 equ)
%            Maximal formula atoms :   16 (   3 avg)
%            Number of connectives :  232 (  81   ~;  65   |;  61   &)
%                                         (   7 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-3 aty)
%            Number of functors    :   12 (  12 usr;   6 con; 0-3 aty)
%            Number of variables   :   90 (;  73   !;  17   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f464,plain,
    $false,
    inference(subsumption_resolution,[],[f460,f304]) ).

fof(f304,plain,
    ~ relation(sK3),
    inference(subsumption_resolution,[],[f302,f149]) ).

fof(f149,plain,
    in(sK2,sK0),
    inference(cnf_transformation,[],[f107]) ).

fof(f107,plain,
    ( apply(relation_composition(sK3,sK4),sK2) != apply(sK4,apply(sK3,sK2))
    & empty_set != sK1
    & in(sK2,sK0)
    & function(sK4)
    & relation(sK4)
    & relation_of2_as_subset(sK3,sK0,sK1)
    & quasi_total(sK3,sK0,sK1)
    & function(sK3) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f67,f106,f105]) ).

fof(f105,plain,
    ( ? [X0,X1,X2,X3] :
        ( ? [X4] :
            ( apply(relation_composition(X3,X4),X2) != apply(X4,apply(X3,X2))
            & empty_set != X1
            & in(X2,X0)
            & function(X4)
            & relation(X4) )
        & relation_of2_as_subset(X3,X0,X1)
        & quasi_total(X3,X0,X1)
        & function(X3) )
   => ( ? [X4] :
          ( apply(relation_composition(sK3,X4),sK2) != apply(X4,apply(sK3,sK2))
          & empty_set != sK1
          & in(sK2,sK0)
          & function(X4)
          & relation(X4) )
      & relation_of2_as_subset(sK3,sK0,sK1)
      & quasi_total(sK3,sK0,sK1)
      & function(sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f106,plain,
    ( ? [X4] :
        ( apply(relation_composition(sK3,X4),sK2) != apply(X4,apply(sK3,sK2))
        & empty_set != sK1
        & in(sK2,sK0)
        & function(X4)
        & relation(X4) )
   => ( apply(relation_composition(sK3,sK4),sK2) != apply(sK4,apply(sK3,sK2))
      & empty_set != sK1
      & in(sK2,sK0)
      & function(sK4)
      & relation(sK4) ) ),
    introduced(choice_axiom,[]) ).

fof(f67,plain,
    ? [X0,X1,X2,X3] :
      ( ? [X4] :
          ( apply(relation_composition(X3,X4),X2) != apply(X4,apply(X3,X2))
          & empty_set != X1
          & in(X2,X0)
          & function(X4)
          & relation(X4) )
      & relation_of2_as_subset(X3,X0,X1)
      & quasi_total(X3,X0,X1)
      & function(X3) ),
    inference(flattening,[],[f66]) ).

fof(f66,plain,
    ? [X0,X1,X2,X3] :
      ( ? [X4] :
          ( apply(relation_composition(X3,X4),X2) != apply(X4,apply(X3,X2))
          & empty_set != X1
          & in(X2,X0)
          & function(X4)
          & relation(X4) )
      & relation_of2_as_subset(X3,X0,X1)
      & quasi_total(X3,X0,X1)
      & function(X3) ),
    inference(ennf_transformation,[],[f49]) ).

fof(f49,negated_conjecture,
    ~ ! [X0,X1,X2,X3] :
        ( ( relation_of2_as_subset(X3,X0,X1)
          & quasi_total(X3,X0,X1)
          & function(X3) )
       => ! [X4] :
            ( ( function(X4)
              & relation(X4) )
           => ( in(X2,X0)
             => ( apply(relation_composition(X3,X4),X2) = apply(X4,apply(X3,X2))
                | empty_set = X1 ) ) ) ),
    inference(negated_conjecture,[],[f48]) ).

fof(f48,conjecture,
    ! [X0,X1,X2,X3] :
      ( ( relation_of2_as_subset(X3,X0,X1)
        & quasi_total(X3,X0,X1)
        & function(X3) )
     => ! [X4] :
          ( ( function(X4)
            & relation(X4) )
         => ( in(X2,X0)
           => ( apply(relation_composition(X3,X4),X2) = apply(X4,apply(X3,X2))
              | empty_set = X1 ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.WFKJoTAzJl/Vampire---4.8_16679',t21_funct_2) ).

fof(f302,plain,
    ( ~ in(sK2,sK0)
    | ~ relation(sK3) ),
    inference(backward_demodulation,[],[f288,f301]) ).

fof(f301,plain,
    sK0 = relation_dom(sK3),
    inference(forward_demodulation,[],[f299,f279]) ).

fof(f279,plain,
    sK0 = relation_dom_as_subset(sK0,sK1,sK3),
    inference(subsumption_resolution,[],[f278,f146]) ).

fof(f146,plain,
    relation_of2_as_subset(sK3,sK0,sK1),
    inference(cnf_transformation,[],[f107]) ).

fof(f278,plain,
    ( sK0 = relation_dom_as_subset(sK0,sK1,sK3)
    | ~ relation_of2_as_subset(sK3,sK0,sK1) ),
    inference(subsumption_resolution,[],[f277,f150]) ).

fof(f150,plain,
    empty_set != sK1,
    inference(cnf_transformation,[],[f107]) ).

fof(f277,plain,
    ( sK0 = relation_dom_as_subset(sK0,sK1,sK3)
    | empty_set = sK1
    | ~ relation_of2_as_subset(sK3,sK0,sK1) ),
    inference(resolution,[],[f145,f197]) ).

fof(f197,plain,
    ! [X2,X0,X1] :
      ( relation_dom_as_subset(X0,X1,X2) = X0
      | ~ quasi_total(X2,X0,X1)
      | empty_set = X1
      | ~ relation_of2_as_subset(X2,X0,X1) ),
    inference(cnf_transformation,[],[f122]) ).

fof(f122,plain,
    ! [X0,X1,X2] :
      ( ( ( ( ( quasi_total(X2,X0,X1)
              | empty_set != X2 )
            & ( empty_set = X2
              | ~ quasi_total(X2,X0,X1) ) )
          | empty_set = X0
          | empty_set != X1 )
        & ( ( ( quasi_total(X2,X0,X1)
              | relation_dom_as_subset(X0,X1,X2) != X0 )
            & ( relation_dom_as_subset(X0,X1,X2) = X0
              | ~ quasi_total(X2,X0,X1) ) )
          | ( empty_set != X0
            & empty_set = X1 ) ) )
      | ~ relation_of2_as_subset(X2,X0,X1) ),
    inference(nnf_transformation,[],[f98]) ).

fof(f98,plain,
    ! [X0,X1,X2] :
      ( ( ( ( quasi_total(X2,X0,X1)
          <=> empty_set = X2 )
          | empty_set = X0
          | empty_set != X1 )
        & ( ( quasi_total(X2,X0,X1)
          <=> relation_dom_as_subset(X0,X1,X2) = X0 )
          | ( empty_set != X0
            & empty_set = X1 ) ) )
      | ~ relation_of2_as_subset(X2,X0,X1) ),
    inference(flattening,[],[f97]) ).

fof(f97,plain,
    ! [X0,X1,X2] :
      ( ( ( ( quasi_total(X2,X0,X1)
          <=> empty_set = X2 )
          | empty_set = X0
          | empty_set != X1 )
        & ( ( quasi_total(X2,X0,X1)
          <=> relation_dom_as_subset(X0,X1,X2) = X0 )
          | ( empty_set != X0
            & empty_set = X1 ) ) )
      | ~ relation_of2_as_subset(X2,X0,X1) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0,X1,X2] :
      ( relation_of2_as_subset(X2,X0,X1)
     => ( ( empty_set = X1
         => ( ( quasi_total(X2,X0,X1)
            <=> empty_set = X2 )
            | empty_set = X0 ) )
        & ( ( empty_set = X1
           => empty_set = X0 )
         => ( quasi_total(X2,X0,X1)
          <=> relation_dom_as_subset(X0,X1,X2) = X0 ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.WFKJoTAzJl/Vampire---4.8_16679',d1_funct_2) ).

fof(f145,plain,
    quasi_total(sK3,sK0,sK1),
    inference(cnf_transformation,[],[f107]) ).

fof(f299,plain,
    relation_dom(sK3) = relation_dom_as_subset(sK0,sK1,sK3),
    inference(resolution,[],[f280,f203]) ).

fof(f203,plain,
    ! [X2,X0,X1] :
      ( relation_dom_as_subset(X0,X1,X2) = relation_dom(X2)
      | ~ relation_of2(X2,X0,X1) ),
    inference(cnf_transformation,[],[f99]) ).

fof(f99,plain,
    ! [X0,X1,X2] :
      ( relation_dom_as_subset(X0,X1,X2) = relation_dom(X2)
      | ~ relation_of2(X2,X0,X1) ),
    inference(ennf_transformation,[],[f44]) ).

fof(f44,axiom,
    ! [X0,X1,X2] :
      ( relation_of2(X2,X0,X1)
     => relation_dom_as_subset(X0,X1,X2) = relation_dom(X2) ),
    file('/export/starexec/sandbox/tmp/tmp.WFKJoTAzJl/Vampire---4.8_16679',redefinition_k4_relset_1) ).

fof(f280,plain,
    relation_of2(sK3,sK0,sK1),
    inference(resolution,[],[f146,f207]) ).

fof(f207,plain,
    ! [X2,X0,X1] :
      ( relation_of2(X2,X0,X1)
      | ~ relation_of2_as_subset(X2,X0,X1) ),
    inference(cnf_transformation,[],[f123]) ).

fof(f123,plain,
    ! [X0,X1,X2] :
      ( ( relation_of2_as_subset(X2,X0,X1)
        | ~ relation_of2(X2,X0,X1) )
      & ( relation_of2(X2,X0,X1)
        | ~ relation_of2_as_subset(X2,X0,X1) ) ),
    inference(nnf_transformation,[],[f45]) ).

fof(f45,axiom,
    ! [X0,X1,X2] :
      ( relation_of2_as_subset(X2,X0,X1)
    <=> relation_of2(X2,X0,X1) ),
    file('/export/starexec/sandbox/tmp/tmp.WFKJoTAzJl/Vampire---4.8_16679',redefinition_m2_relset_1) ).

fof(f288,plain,
    ( ~ in(sK2,relation_dom(sK3))
    | ~ relation(sK3) ),
    inference(subsumption_resolution,[],[f287,f144]) ).

fof(f144,plain,
    function(sK3),
    inference(cnf_transformation,[],[f107]) ).

fof(f287,plain,
    ( ~ in(sK2,relation_dom(sK3))
    | ~ function(sK3)
    | ~ relation(sK3) ),
    inference(subsumption_resolution,[],[f286,f147]) ).

fof(f147,plain,
    relation(sK4),
    inference(cnf_transformation,[],[f107]) ).

fof(f286,plain,
    ( ~ in(sK2,relation_dom(sK3))
    | ~ relation(sK4)
    | ~ function(sK3)
    | ~ relation(sK3) ),
    inference(subsumption_resolution,[],[f285,f148]) ).

fof(f148,plain,
    function(sK4),
    inference(cnf_transformation,[],[f107]) ).

fof(f285,plain,
    ( ~ in(sK2,relation_dom(sK3))
    | ~ function(sK4)
    | ~ relation(sK4)
    | ~ function(sK3)
    | ~ relation(sK3) ),
    inference(trivial_inequality_removal,[],[f284]) ).

fof(f284,plain,
    ( apply(sK4,apply(sK3,sK2)) != apply(sK4,apply(sK3,sK2))
    | ~ in(sK2,relation_dom(sK3))
    | ~ function(sK4)
    | ~ relation(sK4)
    | ~ function(sK3)
    | ~ relation(sK3) ),
    inference(superposition,[],[f151,f182]) ).

fof(f182,plain,
    ! [X2,X0,X1] :
      ( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
      | ~ in(X0,relation_dom(X1))
      | ~ function(X2)
      | ~ relation(X2)
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f90]) ).

fof(f90,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
          | ~ in(X0,relation_dom(X1))
          | ~ function(X2)
          | ~ relation(X2) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(flattening,[],[f89]) ).

fof(f89,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
          | ~ in(X0,relation_dom(X1))
          | ~ function(X2)
          | ~ relation(X2) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(ennf_transformation,[],[f50]) ).

fof(f50,axiom,
    ! [X0,X1] :
      ( ( function(X1)
        & relation(X1) )
     => ! [X2] :
          ( ( function(X2)
            & relation(X2) )
         => ( in(X0,relation_dom(X1))
           => apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.WFKJoTAzJl/Vampire---4.8_16679',t23_funct_1) ).

fof(f151,plain,
    apply(relation_composition(sK3,sK4),sK2) != apply(sK4,apply(sK3,sK2)),
    inference(cnf_transformation,[],[f107]) ).

fof(f460,plain,
    relation(sK3),
    inference(resolution,[],[f283,f205]) ).

fof(f205,plain,
    ! [X2,X0,X1] :
      ( relation(X2)
      | ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
    inference(cnf_transformation,[],[f101]) ).

fof(f101,plain,
    ! [X0,X1,X2] :
      ( relation(X2)
      | ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X1,X2] :
      ( element(X2,powerset(cartesian_product2(X0,X1)))
     => relation(X2) ),
    file('/export/starexec/sandbox/tmp/tmp.WFKJoTAzJl/Vampire---4.8_16679',cc1_relset_1) ).

fof(f283,plain,
    element(sK3,powerset(cartesian_product2(sK0,sK1))),
    inference(resolution,[],[f146,f196]) ).

fof(f196,plain,
    ! [X2,X0,X1] :
      ( element(X2,powerset(cartesian_product2(X0,X1)))
      | ~ relation_of2_as_subset(X2,X0,X1) ),
    inference(cnf_transformation,[],[f96]) ).

fof(f96,plain,
    ! [X0,X1,X2] :
      ( element(X2,powerset(cartesian_product2(X0,X1)))
      | ~ relation_of2_as_subset(X2,X0,X1) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f16,axiom,
    ! [X0,X1,X2] :
      ( relation_of2_as_subset(X2,X0,X1)
     => element(X2,powerset(cartesian_product2(X0,X1))) ),
    file('/export/starexec/sandbox/tmp/tmp.WFKJoTAzJl/Vampire---4.8_16679',dt_m2_relset_1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SEU292+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.15  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.38  % Computer : n015.cluster.edu
% 0.15/0.38  % Model    : x86_64 x86_64
% 0.15/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.38  % Memory   : 8042.1875MB
% 0.15/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.38  % CPULimit   : 300
% 0.15/0.38  % WCLimit    : 300
% 0.15/0.38  % DateTime   : Wed Aug 23 20:16:05 EDT 2023
% 0.15/0.38  % CPUTime    : 
% 0.15/0.38  This is a FOF_THM_RFO_SEQ problem
% 0.15/0.38  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.WFKJoTAzJl/Vampire---4.8_16679
% 0.23/0.38  % (16803)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.44  % (16815)lrs+2_5:4_anc=none:br=off:fde=unused:gsp=on:nm=32:nwc=1.3:sims=off:sos=all:urr=on:stl=62_558 on Vampire---4 for (558ds/0Mi)
% 0.23/0.44  % (16805)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_1192 on Vampire---4 for (1192ds/0Mi)
% 0.23/0.44  % (16818)lrs-1010_20_afr=on:anc=all_dependent:bs=on:bsr=on:cond=on:er=known:fde=none:nm=4:nwc=1.3:sims=off:sp=frequency:urr=on:stl=62_533 on Vampire---4 for (533ds/0Mi)
% 0.23/0.44  % (16809)ott+3_2:7_add=large:amm=off:anc=all:bce=on:drc=off:fsd=off:fde=unused:gs=on:irw=on:lcm=predicate:lma=on:msp=off:nwc=10.0:sac=on_598 on Vampire---4 for (598ds/0Mi)
% 0.23/0.44  % (16822)lrs-1010_2_av=off:bce=on:cond=on:er=filter:fde=unused:lcm=predicate:nm=2:nwc=3.0:sims=off:sp=frequency:urr=on:stl=188_520 on Vampire---4 for (520ds/0Mi)
% 0.23/0.44  % (16811)lrs+11_10:1_bs=unit_only:drc=off:fsd=off:fde=none:gs=on:msp=off:nm=16:nwc=2.0:nicw=on:sos=all:sac=on:sp=reverse_frequency:stl=62_575 on Vampire---4 for (575ds/0Mi)
% 0.23/0.44  % (16823)ott+1010_1_aac=none:bce=on:ep=RS:fsd=off:nm=4:nwc=2.0:nicw=on:sas=z3:sims=off_453 on Vampire---4 for (453ds/0Mi)
% 0.23/0.45  % (16811)First to succeed.
% 0.23/0.45  % (16811)Refutation found. Thanks to Tanya!
% 0.23/0.45  % SZS status Theorem for Vampire---4
% 0.23/0.45  % SZS output start Proof for Vampire---4
% See solution above
% 0.23/0.45  % (16811)------------------------------
% 0.23/0.45  % (16811)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.23/0.45  % (16811)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.23/0.45  % (16811)Termination reason: Refutation
% 0.23/0.45  
% 0.23/0.45  % (16811)Memory used [KB]: 10362
% 0.23/0.45  % (16811)Time elapsed: 0.013 s
% 0.23/0.45  % (16811)------------------------------
% 0.23/0.45  % (16811)------------------------------
% 0.23/0.45  % (16803)Success in time 0.072 s
% 0.23/0.46  % Vampire---4.8 exiting
%------------------------------------------------------------------------------