TSTP Solution File: SYN082+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SYN082+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 : n028.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 18:02:08 EDT 2024

% Result   : Theorem 0.15s 0.38s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   29 (   5 unt;   0 def)
%            Number of atoms       :  100 (   0 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  111 (  40   ~;  40   |;  21   &)
%                                         (   3 <=>;   5  =>;   0  <=;   2 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   1 con; 0-2 aty)
%            Number of variables   :   42 (  28   !;  14   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f33,plain,
    $false,
    inference(subsumption_resolution,[],[f32,f28]) ).

fof(f28,plain,
    sP0(sK3),
    inference(resolution,[],[f27,f18]) ).

fof(f18,plain,
    ( big_f(sK3,f(sK3))
    | sP0(sK3) ),
    inference(cnf_transformation,[],[f13]) ).

fof(f13,plain,
    ( ( ~ sP0(sK3)
      | ~ big_f(sK3,f(sK3)) )
    & ( sP0(sK3)
      | big_f(sK3,f(sK3)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f11,f12]) ).

fof(f12,plain,
    ( ? [X0] :
        ( ( ~ sP0(X0)
          | ~ big_f(X0,f(X0)) )
        & ( sP0(X0)
          | big_f(X0,f(X0)) ) )
   => ( ( ~ sP0(sK3)
        | ~ big_f(sK3,f(sK3)) )
      & ( sP0(sK3)
        | big_f(sK3,f(sK3)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f11,plain,
    ? [X0] :
      ( ( ~ sP0(X0)
        | ~ big_f(X0,f(X0)) )
      & ( sP0(X0)
        | big_f(X0,f(X0)) ) ),
    inference(nnf_transformation,[],[f5]) ).

fof(f5,plain,
    ? [X0] :
      ( big_f(X0,f(X0))
    <~> sP0(X0) ),
    inference(definition_folding,[],[f3,f4]) ).

fof(f4,plain,
    ! [X0] :
      ( sP0(X0)
    <=> ? [X1] :
          ( big_f(X0,X1)
          & ! [X2] :
              ( big_f(X2,f(X0))
              | ~ big_f(X2,X1) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

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

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

fof(f1,conjecture,
    ! [X0] :
      ( big_f(X0,f(X0))
    <=> ? [X1] :
          ( big_f(X0,X1)
          & ! [X2] :
              ( big_f(X2,X1)
             => big_f(X2,f(X0)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel60) ).

fof(f27,plain,
    ~ big_f(sK3,f(sK3)),
    inference(subsumption_resolution,[],[f26,f19]) ).

fof(f19,plain,
    ( ~ big_f(sK3,f(sK3))
    | ~ sP0(sK3) ),
    inference(cnf_transformation,[],[f13]) ).

fof(f26,plain,
    ( ~ big_f(sK3,f(sK3))
    | sP0(sK3) ),
    inference(duplicate_literal_removal,[],[f25]) ).

fof(f25,plain,
    ( ~ big_f(sK3,f(sK3))
    | sP0(sK3)
    | sP0(sK3) ),
    inference(resolution,[],[f17,f22]) ).

fof(f22,plain,
    ( big_f(sK1(sK3,f(sK3)),f(sK3))
    | sP0(sK3) ),
    inference(duplicate_literal_removal,[],[f21]) ).

fof(f21,plain,
    ( sP0(sK3)
    | big_f(sK1(sK3,f(sK3)),f(sK3))
    | sP0(sK3) ),
    inference(resolution,[],[f16,f18]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( ~ big_f(X0,X1)
      | sP0(X0)
      | big_f(sK1(X0,X1),X1) ),
    inference(cnf_transformation,[],[f10]) ).

fof(f10,plain,
    ! [X0] :
      ( ( sP0(X0)
        | ! [X1] :
            ( ~ big_f(X0,X1)
            | ( ~ big_f(sK1(X0,X1),f(X0))
              & big_f(sK1(X0,X1),X1) ) ) )
      & ( ( big_f(X0,sK2(X0))
          & ! [X4] :
              ( big_f(X4,f(X0))
              | ~ big_f(X4,sK2(X0)) ) )
        | ~ sP0(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f7,f9,f8]) ).

fof(f8,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ big_f(X2,f(X0))
          & big_f(X2,X1) )
     => ( ~ big_f(sK1(X0,X1),f(X0))
        & big_f(sK1(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f9,plain,
    ! [X0] :
      ( ? [X3] :
          ( big_f(X0,X3)
          & ! [X4] :
              ( big_f(X4,f(X0))
              | ~ big_f(X4,X3) ) )
     => ( big_f(X0,sK2(X0))
        & ! [X4] :
            ( big_f(X4,f(X0))
            | ~ big_f(X4,sK2(X0)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f7,plain,
    ! [X0] :
      ( ( sP0(X0)
        | ! [X1] :
            ( ~ big_f(X0,X1)
            | ? [X2] :
                ( ~ big_f(X2,f(X0))
                & big_f(X2,X1) ) ) )
      & ( ? [X3] :
            ( big_f(X0,X3)
            & ! [X4] :
                ( big_f(X4,f(X0))
                | ~ big_f(X4,X3) ) )
        | ~ sP0(X0) ) ),
    inference(rectify,[],[f6]) ).

fof(f6,plain,
    ! [X0] :
      ( ( sP0(X0)
        | ! [X1] :
            ( ~ big_f(X0,X1)
            | ? [X2] :
                ( ~ big_f(X2,f(X0))
                & big_f(X2,X1) ) ) )
      & ( ? [X1] :
            ( big_f(X0,X1)
            & ! [X2] :
                ( big_f(X2,f(X0))
                | ~ big_f(X2,X1) ) )
        | ~ sP0(X0) ) ),
    inference(nnf_transformation,[],[f4]) ).

fof(f17,plain,
    ! [X0,X1] :
      ( ~ big_f(sK1(X0,X1),f(X0))
      | ~ big_f(X0,X1)
      | sP0(X0) ),
    inference(cnf_transformation,[],[f10]) ).

fof(f32,plain,
    ~ sP0(sK3),
    inference(subsumption_resolution,[],[f30,f27]) ).

fof(f30,plain,
    ( big_f(sK3,f(sK3))
    | ~ sP0(sK3) ),
    inference(resolution,[],[f29,f14]) ).

fof(f14,plain,
    ! [X0,X4] :
      ( ~ big_f(X4,sK2(X0))
      | big_f(X4,f(X0))
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f10]) ).

fof(f29,plain,
    big_f(sK3,sK2(sK3)),
    inference(resolution,[],[f28,f15]) ).

fof(f15,plain,
    ! [X0] :
      ( ~ sP0(X0)
      | big_f(X0,sK2(X0)) ),
    inference(cnf_transformation,[],[f10]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SYN082+1 : TPTP v8.1.2. Released v2.0.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35  % Computer : n028.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   : Tue Apr 30 02:09:44 EDT 2024
% 0.15/0.35  % CPUTime    : 
% 0.15/0.36  % (28513)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37  % (28515)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.37  % (28516)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)
% 0.15/0.37  % (28519)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.15/0.37  % (28517)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.15/0.37  % (28514)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.15/0.37  % (28518)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.15/0.37  % (28520)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)
% 0.15/0.37  TRYING [1]
% 0.15/0.37  TRYING [1]
% 0.15/0.37  % (28518)First to succeed.
% 0.15/0.37  TRYING [1,1]
% 0.15/0.37  TRYING [1,1]
% 0.15/0.37  TRYING [2]
% 0.15/0.37  TRYING [2]
% 0.15/0.37  TRYING [2,1]
% 0.15/0.37  TRYING [2,1]
% 0.15/0.37  TRYING [3]
% 0.15/0.37  TRYING [2,2]
% 0.15/0.37  TRYING [2,2]
% 0.15/0.37  TRYING [3]
% 0.15/0.37  % (28519)Also succeeded, but the first one will report.
% 0.15/0.37  TRYING [3,3]
% 0.15/0.37  TRYING [3,3]
% 0.15/0.38  % (28518)Refutation found. Thanks to Tanya!
% 0.15/0.38  % SZS status Theorem for theBenchmark
% 0.15/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.38  % (28518)------------------------------
% 0.15/0.38  % (28518)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.38  % (28518)Termination reason: Refutation
% 0.15/0.38  
% 0.15/0.38  % (28518)Memory used [KB]: 747
% 0.15/0.38  % (28518)Time elapsed: 0.003 s
% 0.15/0.38  % (28518)Instructions burned: 3 (million)
% 0.15/0.38  % (28518)------------------------------
% 0.15/0.38  % (28518)------------------------------
% 0.15/0.38  % (28513)Success in time 0.008 s
%------------------------------------------------------------------------------