TSTP Solution File: NUM412+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : NUM412+1 : TPTP v8.1.0. Released v3.2.0.
% 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 : n029.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 17:59:22 EDT 2022

% Result   : Theorem 0.20s 0.50s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   51 (  13 unt;   0 def)
%            Number of atoms       :  169 (   6 equ)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives :  190 (  72   ~;  61   |;  34   &)
%                                         (   4 <=>;  19  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   78 (  70   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f355,plain,
    $false,
    inference(subsumption_resolution,[],[f350,f333]) ).

fof(f333,plain,
    transfinite_sequence_of(relation_dom_restriction(sK7,sK9),relation_rng(sK7)),
    inference(forward_demodulation,[],[f316,f322]) ).

fof(f322,plain,
    tseq_dom_restriction(sK7,sK9) = relation_dom_restriction(sK7,sK9),
    inference(unit_resulting_resolution,[],[f191,f250,f251,f253,f203]) ).

fof(f203,plain,
    ! [X0,X1] :
      ( ~ transfinite_sequence(X1)
      | tseq_dom_restriction(X1,X0) = relation_dom_restriction(X1,X0)
      | ~ ordinal(X0)
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f88]) ).

fof(f88,plain,
    ! [X0,X1] :
      ( ~ ordinal(X0)
      | ~ transfinite_sequence(X1)
      | ~ function(X1)
      | ~ relation(X1)
      | tseq_dom_restriction(X1,X0) = relation_dom_restriction(X1,X0) ),
    inference(flattening,[],[f87]) ).

fof(f87,plain,
    ! [X0,X1] :
      ( tseq_dom_restriction(X1,X0) = relation_dom_restriction(X1,X0)
      | ~ transfinite_sequence(X1)
      | ~ relation(X1)
      | ~ ordinal(X0)
      | ~ function(X1) ),
    inference(ennf_transformation,[],[f58]) ).

fof(f58,plain,
    ! [X0,X1] :
      ( ( transfinite_sequence(X1)
        & relation(X1)
        & ordinal(X0)
        & function(X1) )
     => tseq_dom_restriction(X1,X0) = relation_dom_restriction(X1,X0) ),
    inference(rectify,[],[f37]) ).

fof(f37,axiom,
    ! [X1,X0] :
      ( ( function(X0)
        & transfinite_sequence(X0)
        & ordinal(X1)
        & relation(X0) )
     => tseq_dom_restriction(X0,X1) = relation_dom_restriction(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_ordinal1) ).

fof(f253,plain,
    transfinite_sequence(sK7),
    inference(resolution,[],[f190,f155]) ).

fof(f155,plain,
    ! [X0,X1] :
      ( transfinite_sequence(X0)
      | ~ transfinite_sequence_of(X0,X1) ),
    inference(cnf_transformation,[],[f107]) ).

fof(f107,plain,
    ! [X0,X1] :
      ( ( transfinite_sequence(X0)
        & relation(X0)
        & function(X0) )
      | ~ transfinite_sequence_of(X0,X1) ),
    inference(rectify,[],[f81]) ).

fof(f81,plain,
    ! [X1,X0] :
      ( ( transfinite_sequence(X1)
        & relation(X1)
        & function(X1) )
      | ~ transfinite_sequence_of(X1,X0) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f11,axiom,
    ! [X1,X0] :
      ( transfinite_sequence_of(X1,X0)
     => ( transfinite_sequence(X1)
        & relation(X1)
        & function(X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_ordinal1) ).

fof(f190,plain,
    transfinite_sequence_of(sK7,sK8),
    inference(cnf_transformation,[],[f128]) ).

fof(f128,plain,
    ( ~ transfinite_sequence_of(tseq_dom_restriction(sK7,sK9),sK8)
    & ordinal(sK9)
    & transfinite_sequence_of(sK7,sK8) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f79,f127,f126]) ).

fof(f126,plain,
    ( ? [X0,X1] :
        ( ? [X2] :
            ( ~ transfinite_sequence_of(tseq_dom_restriction(X0,X2),X1)
            & ordinal(X2) )
        & transfinite_sequence_of(X0,X1) )
   => ( ? [X2] :
          ( ~ transfinite_sequence_of(tseq_dom_restriction(sK7,X2),sK8)
          & ordinal(X2) )
      & transfinite_sequence_of(sK7,sK8) ) ),
    introduced(choice_axiom,[]) ).

fof(f127,plain,
    ( ? [X2] :
        ( ~ transfinite_sequence_of(tseq_dom_restriction(sK7,X2),sK8)
        & ordinal(X2) )
   => ( ~ transfinite_sequence_of(tseq_dom_restriction(sK7,sK9),sK8)
      & ordinal(sK9) ) ),
    introduced(choice_axiom,[]) ).

fof(f79,plain,
    ? [X0,X1] :
      ( ? [X2] :
          ( ~ transfinite_sequence_of(tseq_dom_restriction(X0,X2),X1)
          & ordinal(X2) )
      & transfinite_sequence_of(X0,X1) ),
    inference(ennf_transformation,[],[f52]) ).

fof(f52,plain,
    ~ ! [X0,X1] :
        ( transfinite_sequence_of(X0,X1)
       => ! [X2] :
            ( ordinal(X2)
           => transfinite_sequence_of(tseq_dom_restriction(X0,X2),X1) ) ),
    inference(rectify,[],[f44]) ).

fof(f44,negated_conjecture,
    ~ ! [X1,X0] :
        ( transfinite_sequence_of(X1,X0)
       => ! [X2] :
            ( ordinal(X2)
           => transfinite_sequence_of(tseq_dom_restriction(X1,X2),X0) ) ),
    inference(negated_conjecture,[],[f43]) ).

fof(f43,conjecture,
    ! [X1,X0] :
      ( transfinite_sequence_of(X1,X0)
     => ! [X2] :
          ( ordinal(X2)
         => transfinite_sequence_of(tseq_dom_restriction(X1,X2),X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_ordinal1) ).

fof(f251,plain,
    function(sK7),
    inference(unit_resulting_resolution,[],[f190,f153]) ).

fof(f153,plain,
    ! [X0,X1] :
      ( ~ transfinite_sequence_of(X0,X1)
      | function(X0) ),
    inference(cnf_transformation,[],[f107]) ).

fof(f250,plain,
    relation(sK7),
    inference(unit_resulting_resolution,[],[f190,f154]) ).

fof(f154,plain,
    ! [X0,X1] :
      ( relation(X0)
      | ~ transfinite_sequence_of(X0,X1) ),
    inference(cnf_transformation,[],[f107]) ).

fof(f191,plain,
    ordinal(sK9),
    inference(cnf_transformation,[],[f128]) ).

fof(f316,plain,
    transfinite_sequence_of(tseq_dom_restriction(sK7,sK9),relation_rng(sK7)),
    inference(unit_resulting_resolution,[],[f191,f251,f250,f253,f165]) ).

fof(f165,plain,
    ! [X0,X1] :
      ( ~ ordinal(X0)
      | ~ function(X1)
      | ~ relation(X1)
      | transfinite_sequence_of(tseq_dom_restriction(X1,X0),relation_rng(X1))
      | ~ transfinite_sequence(X1) ),
    inference(cnf_transformation,[],[f95]) ).

fof(f95,plain,
    ! [X0,X1] :
      ( transfinite_sequence_of(tseq_dom_restriction(X1,X0),relation_rng(X1))
      | ~ function(X1)
      | ~ transfinite_sequence(X1)
      | ~ ordinal(X0)
      | ~ relation(X1) ),
    inference(flattening,[],[f94]) ).

fof(f94,plain,
    ! [X0,X1] :
      ( transfinite_sequence_of(tseq_dom_restriction(X1,X0),relation_rng(X1))
      | ~ ordinal(X0)
      | ~ relation(X1)
      | ~ transfinite_sequence(X1)
      | ~ function(X1) ),
    inference(ennf_transformation,[],[f59]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( ( ordinal(X0)
        & relation(X1)
        & transfinite_sequence(X1)
        & function(X1) )
     => transfinite_sequence_of(tseq_dom_restriction(X1,X0),relation_rng(X1)) ),
    inference(rectify,[],[f9]) ).

fof(f9,axiom,
    ! [X1,X0] :
      ( ( function(X0)
        & relation(X0)
        & ordinal(X1)
        & transfinite_sequence(X0) )
     => transfinite_sequence_of(tseq_dom_restriction(X0,X1),relation_rng(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_ordinal1) ).

fof(f350,plain,
    ~ transfinite_sequence_of(relation_dom_restriction(sK7,sK9),relation_rng(sK7)),
    inference(unit_resulting_resolution,[],[f332,f260,f239]) ).

fof(f239,plain,
    ! [X2,X0,X1] :
      ( ~ transfinite_sequence_of(X2,X0)
      | transfinite_sequence_of(X2,X1)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f148]) ).

fof(f148,plain,
    ! [X0,X1] :
      ( ~ subset(X0,X1)
      | ! [X2] :
          ( ~ transfinite_sequence_of(X2,X0)
          | transfinite_sequence_of(X2,X1) ) ),
    inference(rectify,[],[f99]) ).

fof(f99,plain,
    ! [X1,X0] :
      ( ~ subset(X1,X0)
      | ! [X2] :
          ( ~ transfinite_sequence_of(X2,X1)
          | transfinite_sequence_of(X2,X0) ) ),
    inference(ennf_transformation,[],[f61]) ).

fof(f61,plain,
    ! [X1,X0] :
      ( subset(X1,X0)
     => ! [X2] :
          ( transfinite_sequence_of(X2,X1)
         => transfinite_sequence_of(X2,X0) ) ),
    inference(rectify,[],[f42]) ).

fof(f42,axiom,
    ! [X1,X0] :
      ( subset(X0,X1)
     => ! [X2] :
          ( transfinite_sequence_of(X2,X0)
         => transfinite_sequence_of(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_ordinal1) ).

fof(f260,plain,
    subset(relation_rng(sK7),sK8),
    inference(subsumption_resolution,[],[f259,f253]) ).

fof(f259,plain,
    ( subset(relation_rng(sK7),sK8)
    | ~ transfinite_sequence(sK7) ),
    inference(subsumption_resolution,[],[f258,f251]) ).

fof(f258,plain,
    ( ~ function(sK7)
    | subset(relation_rng(sK7),sK8)
    | ~ transfinite_sequence(sK7) ),
    inference(subsumption_resolution,[],[f257,f250]) ).

fof(f257,plain,
    ( ~ relation(sK7)
    | subset(relation_rng(sK7),sK8)
    | ~ transfinite_sequence(sK7)
    | ~ function(sK7) ),
    inference(resolution,[],[f190,f156]) ).

fof(f156,plain,
    ! [X0,X1] :
      ( ~ transfinite_sequence(X1)
      | ~ function(X1)
      | ~ relation(X1)
      | subset(relation_rng(X1),X0)
      | ~ transfinite_sequence_of(X1,X0) ),
    inference(cnf_transformation,[],[f109]) ).

fof(f109,plain,
    ! [X0,X1] :
      ( ( ( transfinite_sequence_of(X1,X0)
          | ~ subset(relation_rng(X1),X0) )
        & ( subset(relation_rng(X1),X0)
          | ~ transfinite_sequence_of(X1,X0) ) )
      | ~ relation(X1)
      | ~ function(X1)
      | ~ transfinite_sequence(X1) ),
    inference(rectify,[],[f108]) ).

fof(f108,plain,
    ! [X1,X0] :
      ( ( ( transfinite_sequence_of(X0,X1)
          | ~ subset(relation_rng(X0),X1) )
        & ( subset(relation_rng(X0),X1)
          | ~ transfinite_sequence_of(X0,X1) ) )
      | ~ relation(X0)
      | ~ function(X0)
      | ~ transfinite_sequence(X0) ),
    inference(nnf_transformation,[],[f92]) ).

fof(f92,plain,
    ! [X1,X0] :
      ( ( transfinite_sequence_of(X0,X1)
      <=> subset(relation_rng(X0),X1) )
      | ~ relation(X0)
      | ~ function(X0)
      | ~ transfinite_sequence(X0) ),
    inference(flattening,[],[f91]) ).

fof(f91,plain,
    ! [X1,X0] :
      ( ( transfinite_sequence_of(X0,X1)
      <=> subset(relation_rng(X0),X1) )
      | ~ function(X0)
      | ~ relation(X0)
      | ~ transfinite_sequence(X0) ),
    inference(ennf_transformation,[],[f54]) ).

fof(f54,plain,
    ! [X1,X0] :
      ( ( function(X0)
        & relation(X0)
        & transfinite_sequence(X0) )
     => ( transfinite_sequence_of(X0,X1)
      <=> subset(relation_rng(X0),X1) ) ),
    inference(rectify,[],[f8]) ).

fof(f8,axiom,
    ! [X1,X0] :
      ( ( function(X1)
        & relation(X1)
        & transfinite_sequence(X1) )
     => ( transfinite_sequence_of(X1,X0)
      <=> subset(relation_rng(X1),X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_ordinal1) ).

fof(f332,plain,
    ~ transfinite_sequence_of(relation_dom_restriction(sK7,sK9),sK8),
    inference(backward_demodulation,[],[f192,f322]) ).

fof(f192,plain,
    ~ transfinite_sequence_of(tseq_dom_restriction(sK7,sK9),sK8),
    inference(cnf_transformation,[],[f128]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : NUM412+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34  % Computer : n029.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   : Tue Aug 30 06:39:11 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.20/0.49  % (31889)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.20/0.49  % (31905)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.20/0.49  % (31882)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.20/0.50  % (31890)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.20/0.50  % (31889)First to succeed.
% 0.20/0.50  % (31889)Refutation found. Thanks to Tanya!
% 0.20/0.50  % SZS status Theorem for theBenchmark
% 0.20/0.50  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.50  % (31889)------------------------------
% 0.20/0.50  % (31889)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.50  % (31889)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.50  % (31889)Termination reason: Refutation
% 0.20/0.50  
% 0.20/0.50  % (31889)Memory used [KB]: 6140
% 0.20/0.50  % (31889)Time elapsed: 0.097 s
% 0.20/0.50  % (31889)Instructions burned: 5 (million)
% 0.20/0.50  % (31889)------------------------------
% 0.20/0.50  % (31889)------------------------------
% 0.20/0.50  % (31881)Success in time 0.156 s
%------------------------------------------------------------------------------