TSTP Solution File: SYN352+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SYN352+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n022.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 : Tue Apr 30 18:03:00 EDT 2024

% Result   : Theorem 0.14s 0.40s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   25 (   5 unt;   0 def)
%            Number of atoms       :  159 (   0 equ)
%            Maximal formula atoms :   24 (   6 avg)
%            Number of connectives :  177 (  43   ~;  66   |;  44   &)
%                                         (   4 <=>;  14  =>;   0  <=;   6 <~>)
%            Maximal formula depth :   13 (   7 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :   64 (  43   !;  21   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f39,plain,
    $false,
    inference(resolution,[],[f35,f30]) ).

fof(f30,plain,
    ~ big_f(sK1,sK3(sK1,sK2)),
    inference(subsumption_resolution,[],[f29,f15]) ).

fof(f15,plain,
    big_f(sK1,sK2),
    inference(cnf_transformation,[],[f12]) ).

fof(f12,plain,
    ! [X2,X3] :
      ( ( ( ( ~ big_f(X3,sK3(X2,X3))
            | ~ big_f(X2,sK3(X2,X3)) )
          & ( big_f(X3,sK3(X2,X3))
            | big_f(X2,sK3(X2,X3)) ) )
        | ~ big_f(X2,X3) )
      & ( big_f(sK3(X2,X3),sK3(X2,X3))
        | ( sP0(sK3(X2,X3),X2,sK2)
          & big_f(X2,X3) ) )
      & ( big_f(X3,sK3(X2,X3))
        | big_f(sK2,sK3(X2,X3))
        | ~ big_f(X2,X3) )
      & big_f(sK1,sK2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f9,f11,f10]) ).

fof(f10,plain,
    ( ? [X0,X1] :
      ! [X2,X3] :
      ? [X4] :
        ( ( ( ( ~ big_f(X3,X4)
              | ~ big_f(X2,X4) )
            & ( big_f(X3,X4)
              | big_f(X2,X4) ) )
          | ~ big_f(X2,X3) )
        & ( big_f(X4,X4)
          | ( sP0(X4,X2,X1)
            & big_f(X2,X3) ) )
        & ( big_f(X3,X4)
          | big_f(X1,X4)
          | ~ big_f(X2,X3) )
        & big_f(X0,X1) )
   => ! [X3,X2] :
      ? [X4] :
        ( ( ( ( ~ big_f(X3,X4)
              | ~ big_f(X2,X4) )
            & ( big_f(X3,X4)
              | big_f(X2,X4) ) )
          | ~ big_f(X2,X3) )
        & ( big_f(X4,X4)
          | ( sP0(X4,X2,sK2)
            & big_f(X2,X3) ) )
        & ( big_f(X3,X4)
          | big_f(sK2,X4)
          | ~ big_f(X2,X3) )
        & big_f(sK1,sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f11,plain,
    ! [X2,X3] :
      ( ? [X4] :
          ( ( ( ( ~ big_f(X3,X4)
                | ~ big_f(X2,X4) )
              & ( big_f(X3,X4)
                | big_f(X2,X4) ) )
            | ~ big_f(X2,X3) )
          & ( big_f(X4,X4)
            | ( sP0(X4,X2,sK2)
              & big_f(X2,X3) ) )
          & ( big_f(X3,X4)
            | big_f(sK2,X4)
            | ~ big_f(X2,X3) )
          & big_f(sK1,sK2) )
     => ( ( ( ( ~ big_f(X3,sK3(X2,X3))
              | ~ big_f(X2,sK3(X2,X3)) )
            & ( big_f(X3,sK3(X2,X3))
              | big_f(X2,sK3(X2,X3)) ) )
          | ~ big_f(X2,X3) )
        & ( big_f(sK3(X2,X3),sK3(X2,X3))
          | ( sP0(sK3(X2,X3),X2,sK2)
            & big_f(X2,X3) ) )
        & ( big_f(X3,sK3(X2,X3))
          | big_f(sK2,sK3(X2,X3))
          | ~ big_f(X2,X3) )
        & big_f(sK1,sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f9,plain,
    ? [X0,X1] :
    ! [X2,X3] :
    ? [X4] :
      ( ( ( ( ~ big_f(X3,X4)
            | ~ big_f(X2,X4) )
          & ( big_f(X3,X4)
            | big_f(X2,X4) ) )
        | ~ big_f(X2,X3) )
      & ( big_f(X4,X4)
        | ( sP0(X4,X2,X1)
          & big_f(X2,X3) ) )
      & ( big_f(X3,X4)
        | big_f(X1,X4)
        | ~ big_f(X2,X3) )
      & big_f(X0,X1) ),
    inference(nnf_transformation,[],[f6]) ).

fof(f6,plain,
    ? [X0,X1] :
    ! [X2,X3] :
    ? [X4] :
      ( ( ( big_f(X2,X4)
        <~> big_f(X3,X4) )
        | ~ big_f(X2,X3) )
      & ( big_f(X4,X4)
        | ( sP0(X4,X2,X1)
          & big_f(X2,X3) ) )
      & ( big_f(X3,X4)
        | big_f(X1,X4)
        | ~ big_f(X2,X3) )
      & big_f(X0,X1) ),
    inference(definition_folding,[],[f4,f5]) ).

fof(f5,plain,
    ! [X4,X2,X1] :
      ( ( big_f(X1,X4)
      <~> big_f(X2,X4) )
      | ~ sP0(X4,X2,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f4,plain,
    ? [X0,X1] :
    ! [X2,X3] :
    ? [X4] :
      ( ( ( big_f(X2,X4)
        <~> big_f(X3,X4) )
        | ~ big_f(X2,X3) )
      & ( big_f(X4,X4)
        | ( ( big_f(X1,X4)
          <~> big_f(X2,X4) )
          & big_f(X2,X3) ) )
      & ( big_f(X3,X4)
        | big_f(X1,X4)
        | ~ big_f(X2,X3) )
      & big_f(X0,X1) ),
    inference(flattening,[],[f3]) ).

fof(f3,plain,
    ? [X0,X1] :
    ! [X2,X3] :
    ? [X4] :
      ( ( ( big_f(X2,X4)
        <~> big_f(X3,X4) )
        | ~ big_f(X2,X3) )
      & ( big_f(X4,X4)
        | ( ( big_f(X1,X4)
          <~> big_f(X2,X4) )
          & big_f(X2,X3) ) )
      & ( big_f(X3,X4)
        | big_f(X1,X4)
        | ~ big_f(X2,X3) )
      & big_f(X0,X1) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f2,negated_conjecture,
    ~ ! [X0,X1] :
      ? [X2,X3] :
      ! [X4] :
        ( big_f(X0,X1)
       => ( ( big_f(X2,X3)
           => ( big_f(X3,X4)
              | big_f(X1,X4) ) )
         => ( ( ( big_f(X2,X3)
               => ( big_f(X1,X4)
                <=> big_f(X2,X4) ) )
             => big_f(X4,X4) )
           => ( ( big_f(X2,X4)
              <=> big_f(X3,X4) )
              & big_f(X2,X3) ) ) ) ),
    inference(negated_conjecture,[],[f1]) ).

fof(f1,conjecture,
    ! [X0,X1] :
    ? [X2,X3] :
    ! [X4] :
      ( big_f(X0,X1)
     => ( ( big_f(X2,X3)
         => ( big_f(X3,X4)
            | big_f(X1,X4) ) )
       => ( ( ( big_f(X2,X3)
             => ( big_f(X1,X4)
              <=> big_f(X2,X4) ) )
           => big_f(X4,X4) )
         => ( ( big_f(X2,X4)
            <=> big_f(X3,X4) )
            & big_f(X2,X3) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',church_46_18_4) ).

fof(f29,plain,
    ( ~ big_f(sK1,sK3(sK1,sK2))
    | ~ big_f(sK1,sK2) ),
    inference(resolution,[],[f20,f23]) ).

fof(f23,plain,
    big_f(sK2,sK3(sK1,sK2)),
    inference(duplicate_literal_removal,[],[f21]) ).

fof(f21,plain,
    ( big_f(sK2,sK3(sK1,sK2))
    | big_f(sK2,sK3(sK1,sK2)) ),
    inference(resolution,[],[f16,f15]) ).

fof(f16,plain,
    ! [X2,X3] :
      ( ~ big_f(X2,X3)
      | big_f(sK2,sK3(X2,X3))
      | big_f(X3,sK3(X2,X3)) ),
    inference(cnf_transformation,[],[f12]) ).

fof(f20,plain,
    ! [X2,X3] :
      ( ~ big_f(X3,sK3(X2,X3))
      | ~ big_f(X2,sK3(X2,X3))
      | ~ big_f(X2,X3) ),
    inference(cnf_transformation,[],[f12]) ).

fof(f35,plain,
    ! [X0,X1] : big_f(X0,X1),
    inference(subsumption_resolution,[],[f34,f17]) ).

fof(f17,plain,
    ! [X2,X3] :
      ( big_f(sK3(X2,X3),sK3(X2,X3))
      | big_f(X2,X3) ),
    inference(cnf_transformation,[],[f12]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( big_f(X0,X1)
      | ~ big_f(sK3(X0,X1),sK3(X0,X1)) ),
    inference(subsumption_resolution,[],[f31,f28]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( big_f(sK3(X0,X1),sK3(sK3(X0,X1),sK3(X0,X1)))
      | big_f(X0,X1) ),
    inference(duplicate_literal_removal,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( big_f(sK3(X0,X1),sK3(sK3(X0,X1),sK3(X0,X1)))
      | big_f(sK3(X0,X1),sK3(sK3(X0,X1),sK3(X0,X1)))
      | big_f(X0,X1) ),
    inference(resolution,[],[f19,f17]) ).

fof(f19,plain,
    ! [X2,X3] :
      ( ~ big_f(X2,X3)
      | big_f(X2,sK3(X2,X3))
      | big_f(X3,sK3(X2,X3)) ),
    inference(cnf_transformation,[],[f12]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( big_f(X0,X1)
      | ~ big_f(sK3(X0,X1),sK3(sK3(X0,X1),sK3(X0,X1)))
      | ~ big_f(sK3(X0,X1),sK3(X0,X1)) ),
    inference(resolution,[],[f28,f20]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem    : SYN352+1 : TPTP v8.1.2. Released v2.0.0.
% 0.14/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36  % Computer : n022.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Tue Apr 30 01:44:28 EDT 2024
% 0.14/0.37  % CPUTime    : 
% 0.14/0.37  % (16672)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.39  % (16673)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.39  TRYING [1]
% 0.14/0.39  TRYING [2]
% 0.14/0.39  TRYING [3]
% 0.14/0.39  TRYING [4]
% 0.14/0.39  % (16679)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.39  % (16674)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.39  % (16675)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.14/0.39  % (16677)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.14/0.39  % (16678)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.14/0.39  % (16676)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.14/0.39  TRYING [5]
% 0.14/0.39  TRYING [1]
% 0.14/0.39  TRYING [2]
% 0.14/0.39  TRYING [1]
% 0.14/0.39  % (16677)First to succeed.
% 0.14/0.39  TRYING [2]
% 0.14/0.39  TRYING [3]
% 0.14/0.39  TRYING [1]
% 0.14/0.39  TRYING [3]
% 0.14/0.40  TRYING [2]
% 0.14/0.40  % (16678)Also succeeded, but the first one will report.
% 0.14/0.40  TRYING [4]
% 0.14/0.40  TRYING [3]
% 0.14/0.40  % (16675)Also succeeded, but the first one will report.
% 0.14/0.40  % (16677)Refutation found. Thanks to Tanya!
% 0.14/0.40  % SZS status Theorem for theBenchmark
% 0.14/0.40  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.40  % (16677)------------------------------
% 0.14/0.40  % (16677)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.40  % (16677)Termination reason: Refutation
% 0.14/0.40  
% 0.14/0.40  % (16677)Memory used [KB]: 748
% 0.14/0.40  % (16677)Time elapsed: 0.005 s
% 0.14/0.40  % (16677)Instructions burned: 4 (million)
% 0.14/0.40  % (16677)------------------------------
% 0.14/0.40  % (16677)------------------------------
% 0.14/0.40  % (16672)Success in time 0.026 s
%------------------------------------------------------------------------------