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

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---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_sat --cores 0 -t %d %s

% Computer : n025.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 18:05:00 EDT 2022

% Result   : Theorem 0.20s 0.53s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   50 (  11 unt;   0 def)
%            Number of atoms       :  160 (   1 equ)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives :  186 (  76   ~;  66   |;  27   &)
%                                         (   3 <=>;  14  =>;   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;   4 con; 0-2 aty)
%            Number of variables   :   78 (  67   !;  11   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f429,plain,
    $false,
    inference(subsumption_resolution,[],[f428,f236]) ).

fof(f236,plain,
    ~ transfinite_sequence_of(sF19,sK12),
    inference(definition_folding,[],[f202,f235]) ).

fof(f235,plain,
    tseq_dom_restriction(sK11,sK13) = sF19,
    introduced(function_definition,[]) ).

fof(f202,plain,
    ~ transfinite_sequence_of(tseq_dom_restriction(sK11,sK13),sK12),
    inference(cnf_transformation,[],[f130]) ).

fof(f130,plain,
    ( ~ transfinite_sequence_of(tseq_dom_restriction(sK11,sK13),sK12)
    & ordinal(sK13)
    & transfinite_sequence_of(sK11,sK12) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13])],[f127,f129,f128]) ).

fof(f128,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(sK11,X2),sK12)
          & ordinal(X2) )
      & transfinite_sequence_of(sK11,sK12) ) ),
    introduced(choice_axiom,[]) ).

fof(f129,plain,
    ( ? [X2] :
        ( ~ transfinite_sequence_of(tseq_dom_restriction(sK11,X2),sK12)
        & ordinal(X2) )
   => ( ~ transfinite_sequence_of(tseq_dom_restriction(sK11,sK13),sK12)
      & ordinal(sK13) ) ),
    introduced(choice_axiom,[]) ).

fof(f127,plain,
    ? [X0,X1] :
      ( ? [X2] :
          ( ~ transfinite_sequence_of(tseq_dom_restriction(X0,X2),X1)
          & ordinal(X2) )
      & transfinite_sequence_of(X0,X1) ),
    inference(rectify,[],[f71]) ).

fof(f71,plain,
    ? [X1,X0] :
      ( ? [X2] :
          ( ~ transfinite_sequence_of(tseq_dom_restriction(X1,X2),X0)
          & ordinal(X2) )
      & transfinite_sequence_of(X1,X0) ),
    inference(ennf_transformation,[],[f44]) ).

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

fof(f43,conjecture,
    ! [X0,X1] :
      ( transfinite_sequence_of(X1,X0)
     => ! [X2] :
          ( ordinal(X2)
         => transfinite_sequence_of(tseq_dom_restriction(X1,X2),X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_ordinal1) ).

fof(f428,plain,
    transfinite_sequence_of(sF19,sK12),
    inference(resolution,[],[f423,f200]) ).

fof(f200,plain,
    transfinite_sequence_of(sK11,sK12),
    inference(cnf_transformation,[],[f130]) ).

fof(f423,plain,
    ! [X5] :
      ( ~ transfinite_sequence_of(sK11,X5)
      | transfinite_sequence_of(sF19,X5) ),
    inference(resolution,[],[f337,f377]) ).

fof(f377,plain,
    transfinite_sequence_of(sF19,relation_rng(sK11)),
    inference(subsumption_resolution,[],[f376,f288]) ).

fof(f288,plain,
    transfinite_sequence(sK11),
    inference(resolution,[],[f160,f200]) ).

fof(f160,plain,
    ! [X0,X1] :
      ( ~ transfinite_sequence_of(X1,X0)
      | transfinite_sequence(X1) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f102,plain,
    ! [X0,X1] :
      ( ~ transfinite_sequence_of(X1,X0)
      | ( function(X1)
        & transfinite_sequence(X1)
        & relation(X1) ) ),
    inference(rectify,[],[f70]) ).

fof(f70,plain,
    ! [X1,X0] :
      ( ~ transfinite_sequence_of(X0,X1)
      | ( function(X0)
        & transfinite_sequence(X0)
        & relation(X0) ) ),
    inference(ennf_transformation,[],[f54]) ).

fof(f54,plain,
    ! [X1,X0] :
      ( transfinite_sequence_of(X0,X1)
     => ( function(X0)
        & transfinite_sequence(X0)
        & relation(X0) ) ),
    inference(rectify,[],[f11]) ).

fof(f11,axiom,
    ! [X1,X0] :
      ( transfinite_sequence_of(X1,X0)
     => ( function(X1)
        & relation(X1)
        & transfinite_sequence(X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_ordinal1) ).

fof(f376,plain,
    ( ~ transfinite_sequence(sK11)
    | transfinite_sequence_of(sF19,relation_rng(sK11)) ),
    inference(subsumption_resolution,[],[f375,f201]) ).

fof(f201,plain,
    ordinal(sK13),
    inference(cnf_transformation,[],[f130]) ).

fof(f375,plain,
    ( ~ ordinal(sK13)
    | ~ transfinite_sequence(sK11)
    | transfinite_sequence_of(sF19,relation_rng(sK11)) ),
    inference(subsumption_resolution,[],[f374,f290]) ).

fof(f290,plain,
    function(sK11),
    inference(resolution,[],[f161,f200]) ).

fof(f161,plain,
    ! [X0,X1] :
      ( ~ transfinite_sequence_of(X1,X0)
      | function(X1) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f374,plain,
    ( ~ function(sK11)
    | transfinite_sequence_of(sF19,relation_rng(sK11))
    | ~ transfinite_sequence(sK11)
    | ~ ordinal(sK13) ),
    inference(subsumption_resolution,[],[f372,f286]) ).

fof(f286,plain,
    relation(sK11),
    inference(resolution,[],[f159,f200]) ).

fof(f159,plain,
    ! [X0,X1] :
      ( ~ transfinite_sequence_of(X1,X0)
      | relation(X1) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f372,plain,
    ( transfinite_sequence_of(sF19,relation_rng(sK11))
    | ~ relation(sK11)
    | ~ ordinal(sK13)
    | ~ transfinite_sequence(sK11)
    | ~ function(sK11) ),
    inference(superposition,[],[f171,f235]) ).

fof(f171,plain,
    ! [X0,X1] :
      ( transfinite_sequence_of(tseq_dom_restriction(X1,X0),relation_rng(X1))
      | ~ function(X1)
      | ~ ordinal(X0)
      | ~ relation(X1)
      | ~ transfinite_sequence(X1) ),
    inference(cnf_transformation,[],[f111]) ).

fof(f111,plain,
    ! [X0,X1] :
      ( ~ transfinite_sequence(X1)
      | ~ relation(X1)
      | ~ ordinal(X0)
      | transfinite_sequence_of(tseq_dom_restriction(X1,X0),relation_rng(X1))
      | ~ function(X1) ),
    inference(rectify,[],[f98]) ).

fof(f98,plain,
    ! [X1,X0] :
      ( ~ transfinite_sequence(X0)
      | ~ relation(X0)
      | ~ ordinal(X1)
      | transfinite_sequence_of(tseq_dom_restriction(X0,X1),relation_rng(X0))
      | ~ function(X0) ),
    inference(flattening,[],[f97]) ).

fof(f97,plain,
    ! [X1,X0] :
      ( transfinite_sequence_of(tseq_dom_restriction(X0,X1),relation_rng(X0))
      | ~ ordinal(X1)
      | ~ relation(X0)
      | ~ transfinite_sequence(X0)
      | ~ function(X0) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X1,X0] :
      ( ( ordinal(X1)
        & relation(X0)
        & transfinite_sequence(X0)
        & function(X0) )
     => transfinite_sequence_of(tseq_dom_restriction(X0,X1),relation_rng(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_ordinal1) ).

fof(f337,plain,
    ! [X2,X3,X4] :
      ( ~ transfinite_sequence_of(X2,relation_rng(X4))
      | ~ transfinite_sequence_of(X4,X3)
      | transfinite_sequence_of(X2,X3) ),
    inference(resolution,[],[f175,f239]) ).

fof(f239,plain,
    ! [X0,X1] :
      ( subset(relation_rng(X0),X1)
      | ~ transfinite_sequence_of(X0,X1) ),
    inference(subsumption_resolution,[],[f238,f161]) ).

fof(f238,plain,
    ! [X0,X1] :
      ( ~ function(X0)
      | ~ transfinite_sequence_of(X0,X1)
      | subset(relation_rng(X0),X1) ),
    inference(subsumption_resolution,[],[f237,f159]) ).

fof(f237,plain,
    ! [X0,X1] :
      ( ~ function(X0)
      | ~ transfinite_sequence_of(X0,X1)
      | ~ relation(X0)
      | subset(relation_rng(X0),X1) ),
    inference(subsumption_resolution,[],[f173,f160]) ).

fof(f173,plain,
    ! [X0,X1] :
      ( ~ transfinite_sequence(X0)
      | ~ function(X0)
      | ~ relation(X0)
      | subset(relation_rng(X0),X1)
      | ~ transfinite_sequence_of(X0,X1) ),
    inference(cnf_transformation,[],[f115]) ).

fof(f115,plain,
    ! [X0,X1] :
      ( ( ( 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(rectify,[],[f114]) ).

fof(f114,plain,
    ! [X1,X0] :
      ( ( ( 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(nnf_transformation,[],[f84]) ).

fof(f84,plain,
    ! [X1,X0] :
      ( ( transfinite_sequence_of(X1,X0)
      <=> subset(relation_rng(X1),X0) )
      | ~ relation(X1)
      | ~ function(X1)
      | ~ transfinite_sequence(X1) ),
    inference(flattening,[],[f83]) ).

fof(f83,plain,
    ! [X0,X1] :
      ( ( transfinite_sequence_of(X1,X0)
      <=> subset(relation_rng(X1),X0) )
      | ~ relation(X1)
      | ~ transfinite_sequence(X1)
      | ~ function(X1) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0,X1] :
      ( ( relation(X1)
        & transfinite_sequence(X1)
        & function(X1) )
     => ( transfinite_sequence_of(X1,X0)
      <=> subset(relation_rng(X1),X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_ordinal1) ).

fof(f175,plain,
    ! [X2,X0,X1] :
      ( ~ subset(X0,X1)
      | transfinite_sequence_of(X2,X1)
      | ~ transfinite_sequence_of(X2,X0) ),
    inference(cnf_transformation,[],[f116]) ).

fof(f116,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ~ transfinite_sequence_of(X2,X0)
          | transfinite_sequence_of(X2,X1) )
      | ~ subset(X0,X1) ),
    inference(rectify,[],[f88]) ).

fof(f88,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( ~ transfinite_sequence_of(X2,X1)
          | transfinite_sequence_of(X2,X0) )
      | ~ subset(X1,X0) ),
    inference(ennf_transformation,[],[f55]) ).

fof(f55,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/sandbox2/benchmark/theBenchmark.p',t47_ordinal1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : NUM412+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13  % 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 : n025.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 06:38:14 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.20/0.52  % (26253)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.52  % (26261)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.52  % (26249)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  % (26261)First to succeed.
% 0.20/0.53  % (26244)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.53  % (26248)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)
% 0.20/0.53  TRYING [1]
% 0.20/0.53  TRYING [2]
% 0.20/0.53  % (26244)Refutation not found, incomplete strategy% (26244)------------------------------
% 0.20/0.53  % (26244)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53  % (26244)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53  % (26244)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.53  
% 0.20/0.53  % (26244)Memory used [KB]: 5500
% 0.20/0.53  % (26244)Time elapsed: 0.131 s
% 0.20/0.53  % (26244)Instructions burned: 4 (million)
% 0.20/0.53  % (26244)------------------------------
% 0.20/0.53  % (26244)------------------------------
% 0.20/0.53  % (26261)Refutation found. Thanks to Tanya!
% 0.20/0.53  % SZS status Theorem for theBenchmark
% 0.20/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.53  % (26261)------------------------------
% 0.20/0.53  % (26261)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53  % (26261)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53  % (26261)Termination reason: Refutation
% 0.20/0.53  
% 0.20/0.53  % (26261)Memory used [KB]: 5628
% 0.20/0.53  % (26261)Time elapsed: 0.125 s
% 0.20/0.53  % (26261)Instructions burned: 9 (million)
% 0.20/0.53  % (26261)------------------------------
% 0.20/0.53  % (26261)------------------------------
% 0.20/0.53  % (26242)Success in time 0.18 s
%------------------------------------------------------------------------------