TSTP Solution File: SYN332+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SYN332+1 : TPTP v8.1.0. Released v2.0.0.
% 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 : n027.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 19:37:33 EDT 2022

% Result   : Theorem 0.18s 0.52s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   41 (   4 unt;   0 def)
%            Number of atoms       :  305 (   0 equ)
%            Maximal formula atoms :   60 (   7 avg)
%            Number of connectives :  394 ( 130   ~; 139   |;  90   &)
%                                         (  18 <=>;  11  =>;   0  <=;   6 <~>)
%            Maximal formula depth :   18 (   7 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    1 (   1 usr;   0 con; 2-2 aty)
%            Number of variables   :   82 (  72   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f154,plain,
    $false,
    inference(subsumption_resolution,[],[f99,f136]) ).

fof(f136,plain,
    ! [X0,X1] : big_f(X0,X1),
    inference(subsumption_resolution,[],[f135,f44]) ).

fof(f44,plain,
    ! [X2,X3] :
      ( big_f(X3,X2)
      | big_f(X2,sK0(X2,X3)) ),
    inference(resolution,[],[f37,f25]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( big_f(X1,sK0(X0,X1))
      | big_f(X1,X0) ),
    inference(literal_reordering,[],[f20]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( big_f(X1,sK0(X0,X1))
      | big_f(X1,X0) ),
    inference(cnf_transformation,[],[f9]) ).

fof(f9,plain,
    ! [X0,X1] :
      ( ( big_f(X1,sK0(X0,X1))
        | ~ big_f(X0,sK0(X0,X1)) )
      & ( big_f(X0,sK0(X0,X1))
        | ~ big_f(X1,sK0(X0,X1)) )
      & ( ~ big_f(X1,sK0(X0,X1))
        | ~ big_f(X1,X0)
        | ~ big_f(X0,X1) )
      & ( big_f(X1,sK0(X0,X1))
        | ( big_f(X1,X0)
          & big_f(X0,X1) ) )
      & ( big_f(X1,sK0(X0,X1))
        | ~ big_f(sK0(X0,X1),X1) )
      & ( big_f(sK0(X0,X1),X1)
        | ~ big_f(X1,sK0(X0,X1)) )
      & ( big_f(X1,X0)
        | ~ big_f(X0,X1)
        | ~ big_f(sK0(X0,X1),sK0(X0,X1)) )
      & ( big_f(sK0(X0,X1),sK0(X0,X1))
        | ( ~ big_f(X1,X0)
          & big_f(X0,X1) ) )
      & ( ~ big_f(sK0(X0,X1),X0)
        | ( ( ~ big_f(X0,X1)
            | ~ big_f(X1,X0) )
          & ( big_f(X0,X1)
            | big_f(X1,X0) ) ) )
      & ( big_f(sK0(X0,X1),X0)
        | ( ( big_f(X1,X0)
            | ~ big_f(X0,X1) )
          & ( big_f(X0,X1)
            | ~ big_f(X1,X0) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8]) ).

fof(f8,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( big_f(X1,X2)
            | ~ big_f(X0,X2) )
          & ( big_f(X0,X2)
            | ~ big_f(X1,X2) )
          & ( ~ big_f(X1,X2)
            | ~ big_f(X1,X0)
            | ~ big_f(X0,X1) )
          & ( big_f(X1,X2)
            | ( big_f(X1,X0)
              & big_f(X0,X1) ) )
          & ( big_f(X1,X2)
            | ~ big_f(X2,X1) )
          & ( big_f(X2,X1)
            | ~ big_f(X1,X2) )
          & ( big_f(X1,X0)
            | ~ big_f(X0,X1)
            | ~ big_f(X2,X2) )
          & ( big_f(X2,X2)
            | ( ~ big_f(X1,X0)
              & big_f(X0,X1) ) )
          & ( ~ big_f(X2,X0)
            | ( ( ~ big_f(X0,X1)
                | ~ big_f(X1,X0) )
              & ( big_f(X0,X1)
                | big_f(X1,X0) ) ) )
          & ( big_f(X2,X0)
            | ( ( big_f(X1,X0)
                | ~ big_f(X0,X1) )
              & ( big_f(X0,X1)
                | ~ big_f(X1,X0) ) ) ) )
     => ( ( big_f(X1,sK0(X0,X1))
          | ~ big_f(X0,sK0(X0,X1)) )
        & ( big_f(X0,sK0(X0,X1))
          | ~ big_f(X1,sK0(X0,X1)) )
        & ( ~ big_f(X1,sK0(X0,X1))
          | ~ big_f(X1,X0)
          | ~ big_f(X0,X1) )
        & ( big_f(X1,sK0(X0,X1))
          | ( big_f(X1,X0)
            & big_f(X0,X1) ) )
        & ( big_f(X1,sK0(X0,X1))
          | ~ big_f(sK0(X0,X1),X1) )
        & ( big_f(sK0(X0,X1),X1)
          | ~ big_f(X1,sK0(X0,X1)) )
        & ( big_f(X1,X0)
          | ~ big_f(X0,X1)
          | ~ big_f(sK0(X0,X1),sK0(X0,X1)) )
        & ( big_f(sK0(X0,X1),sK0(X0,X1))
          | ( ~ big_f(X1,X0)
            & big_f(X0,X1) ) )
        & ( ~ big_f(sK0(X0,X1),X0)
          | ( ( ~ big_f(X0,X1)
              | ~ big_f(X1,X0) )
            & ( big_f(X0,X1)
              | big_f(X1,X0) ) ) )
        & ( big_f(sK0(X0,X1),X0)
          | ( ( big_f(X1,X0)
              | ~ big_f(X0,X1) )
            & ( big_f(X0,X1)
              | ~ big_f(X1,X0) ) ) ) ) ),
    introduced(choice_axiom,[]) ).

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

fof(f6,plain,
    ! [X1,X0] :
    ? [X2] :
      ( ( big_f(X0,X2)
        | ~ big_f(X1,X2) )
      & ( big_f(X1,X2)
        | ~ big_f(X0,X2) )
      & ( ~ big_f(X0,X2)
        | ~ big_f(X0,X1)
        | ~ big_f(X1,X0) )
      & ( big_f(X0,X2)
        | ( big_f(X0,X1)
          & big_f(X1,X0) ) )
      & ( big_f(X0,X2)
        | ~ big_f(X2,X0) )
      & ( big_f(X2,X0)
        | ~ big_f(X0,X2) )
      & ( big_f(X0,X1)
        | ~ big_f(X1,X0)
        | ~ big_f(X2,X2) )
      & ( big_f(X2,X2)
        | ( ~ big_f(X0,X1)
          & big_f(X1,X0) ) )
      & ( ~ big_f(X2,X1)
        | ( ( ~ big_f(X1,X0)
            | ~ big_f(X0,X1) )
          & ( big_f(X1,X0)
            | big_f(X0,X1) ) ) )
      & ( big_f(X2,X1)
        | ( ( big_f(X0,X1)
            | ~ big_f(X1,X0) )
          & ( big_f(X1,X0)
            | ~ big_f(X0,X1) ) ) ) ),
    inference(flattening,[],[f5]) ).

fof(f5,plain,
    ! [X1,X0] :
    ? [X2] :
      ( ( big_f(X0,X2)
        | ~ big_f(X1,X2) )
      & ( big_f(X1,X2)
        | ~ big_f(X0,X2) )
      & ( ~ big_f(X0,X2)
        | ~ big_f(X0,X1)
        | ~ big_f(X1,X0) )
      & ( big_f(X0,X2)
        | ( big_f(X0,X1)
          & big_f(X1,X0) ) )
      & ( big_f(X0,X2)
        | ~ big_f(X2,X0) )
      & ( big_f(X2,X0)
        | ~ big_f(X0,X2) )
      & ( big_f(X0,X1)
        | ~ big_f(X1,X0)
        | ~ big_f(X2,X2) )
      & ( big_f(X2,X2)
        | ( ~ big_f(X0,X1)
          & big_f(X1,X0) ) )
      & ( ~ big_f(X2,X1)
        | ( ( ~ big_f(X1,X0)
            | ~ big_f(X0,X1) )
          & ( big_f(X1,X0)
            | big_f(X0,X1) ) ) )
      & ( big_f(X2,X1)
        | ( ( big_f(X0,X1)
            | ~ big_f(X1,X0) )
          & ( big_f(X1,X0)
            | ~ big_f(X0,X1) ) ) ) ),
    inference(nnf_transformation,[],[f4]) ).

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

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

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

fof(f1,conjecture,
    ? [X0,X1] :
    ! [X2] :
      ( ( ( big_f(X0,X1)
          & big_f(X1,X0) )
      <~> big_f(X0,X2) )
     => ( ( big_f(X0,X2)
        <=> big_f(X2,X0) )
       => ( ( big_f(X0,X2)
          <=> big_f(X1,X2) )
         => ( ( big_f(X2,X2)
            <=> ( big_f(X1,X0)
               => big_f(X0,X1) ) )
           => ( big_f(X2,X1)
            <=> ( big_f(X0,X1)
              <=> big_f(X1,X0) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',church_46_14_4) ).

fof(f37,plain,
    ! [X0,X1] :
      ( ~ big_f(X1,sK0(X0,X1))
      | big_f(X0,sK0(X0,X1)) ),
    inference(literal_reordering,[],[f22]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ~ big_f(X1,sK0(X0,X1))
      | big_f(X0,sK0(X0,X1)) ),
    inference(cnf_transformation,[],[f9]) ).

fof(f135,plain,
    ! [X0,X1] :
      ( ~ big_f(X1,sK0(X1,X0))
      | big_f(X0,X1) ),
    inference(subsumption_resolution,[],[f132,f69]) ).

fof(f69,plain,
    ! [X0,X1] :
      ( ~ big_f(X0,X1)
      | big_f(X1,X0) ),
    inference(subsumption_resolution,[],[f28,f62]) ).

fof(f62,plain,
    ! [X0] : big_f(X0,X0),
    inference(subsumption_resolution,[],[f61,f32]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( big_f(X0,X1)
      | big_f(X1,sK0(X0,X1)) ),
    inference(literal_reordering,[],[f19]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( big_f(X0,X1)
      | big_f(X1,sK0(X0,X1)) ),
    inference(cnf_transformation,[],[f9]) ).

fof(f61,plain,
    ! [X0] :
      ( ~ big_f(X0,sK0(X0,X0))
      | big_f(X0,X0) ),
    inference(duplicate_literal_removal,[],[f55]) ).

fof(f55,plain,
    ! [X0] :
      ( ~ big_f(X0,sK0(X0,X0))
      | big_f(X0,X0)
      | big_f(X0,X0) ),
    inference(resolution,[],[f31,f36]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( big_f(sK0(X0,X1),X1)
      | ~ big_f(X1,sK0(X0,X1)) ),
    inference(literal_reordering,[],[f17]) ).

fof(f17,plain,
    ! [X0,X1] :
      ( ~ big_f(X1,sK0(X0,X1))
      | big_f(sK0(X0,X1),X1) ),
    inference(cnf_transformation,[],[f9]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( ~ big_f(sK0(X0,X1),X0)
      | big_f(X0,X1)
      | big_f(X1,X0) ),
    inference(literal_reordering,[],[f12]) ).

fof(f12,plain,
    ! [X0,X1] :
      ( big_f(X0,X1)
      | ~ big_f(sK0(X0,X1),X0)
      | big_f(X1,X0) ),
    inference(cnf_transformation,[],[f9]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( ~ big_f(sK0(X0,X1),sK0(X0,X1))
      | big_f(X1,X0)
      | ~ big_f(X0,X1) ),
    inference(literal_reordering,[],[f16]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( ~ big_f(sK0(X0,X1),sK0(X0,X1))
      | ~ big_f(X0,X1)
      | big_f(X1,X0) ),
    inference(cnf_transformation,[],[f9]) ).

fof(f132,plain,
    ! [X0,X1] :
      ( ~ big_f(sK0(X1,X0),X1)
      | big_f(X0,X1)
      | ~ big_f(X1,sK0(X1,X0)) ),
    inference(resolution,[],[f123,f33]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ~ big_f(X1,sK0(X0,X1))
      | ~ big_f(X0,X1)
      | ~ big_f(X1,X0) ),
    inference(literal_reordering,[],[f21]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ~ big_f(X1,X0)
      | ~ big_f(X1,sK0(X0,X1))
      | ~ big_f(X0,X1) ),
    inference(cnf_transformation,[],[f9]) ).

fof(f123,plain,
    ! [X6,X5] :
      ( big_f(X6,X5)
      | big_f(X5,sK0(sK0(X5,X6),X5)) ),
    inference(subsumption_resolution,[],[f58,f118]) ).

fof(f118,plain,
    ! [X3,X4] :
      ( big_f(X4,sK0(sK0(X4,X3),X4))
      | ~ big_f(X4,X3) ),
    inference(subsumption_resolution,[],[f49,f69]) ).

fof(f49,plain,
    ! [X3,X4] :
      ( big_f(X4,sK0(sK0(X4,X3),X4))
      | ~ big_f(X3,X4)
      | ~ big_f(X4,X3) ),
    inference(resolution,[],[f29,f32]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( ~ big_f(sK0(X0,X1),X0)
      | ~ big_f(X1,X0)
      | ~ big_f(X0,X1) ),
    inference(literal_reordering,[],[f13]) ).

fof(f13,plain,
    ! [X0,X1] :
      ( ~ big_f(X1,X0)
      | ~ big_f(X0,X1)
      | ~ big_f(sK0(X0,X1),X0) ),
    inference(cnf_transformation,[],[f9]) ).

fof(f58,plain,
    ! [X6,X5] :
      ( big_f(X5,X6)
      | big_f(X5,sK0(sK0(X5,X6),X5))
      | big_f(X6,X5) ),
    inference(resolution,[],[f31,f32]) ).

fof(f99,plain,
    ! [X0] : ~ big_f(X0,sK0(X0,X0)),
    inference(subsumption_resolution,[],[f50,f62]) ).

fof(f50,plain,
    ! [X0] :
      ( ~ big_f(X0,sK0(X0,X0))
      | ~ big_f(X0,X0) ),
    inference(duplicate_literal_removal,[],[f47]) ).

fof(f47,plain,
    ! [X0] :
      ( ~ big_f(X0,sK0(X0,X0))
      | ~ big_f(X0,X0)
      | ~ big_f(X0,X0) ),
    inference(resolution,[],[f29,f36]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SYN332+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.33  % Computer : n027.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Tue Aug 30 21:59:46 EDT 2022
% 0.13/0.33  % CPUTime    : 
% 0.18/0.49  % (30684)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/51Mi)
% 0.18/0.50  % (30681)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/51Mi)
% 0.18/0.50  TRYING [1]
% 0.18/0.50  % (30700)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/498Mi)
% 0.18/0.50  TRYING [2]
% 0.18/0.50  TRYING [3]
% 0.18/0.50  % (30687)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/51Mi)
% 0.18/0.50  % (30692)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/68Mi)
% 0.18/0.50  % (30695)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/59Mi)
% 0.18/0.50  TRYING [4]
% 0.18/0.50  TRYING [1]
% 0.18/0.50  TRYING [2]
% 0.18/0.50  TRYING [3]
% 0.18/0.50  TRYING [5]
% 0.18/0.50  TRYING [4]
% 0.18/0.51  % (30692)First to succeed.
% 0.18/0.51  % (30679)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/50Mi)
% 0.18/0.51  % (30680)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/37Mi)
% 0.18/0.51  TRYING [5]
% 0.18/0.52  % (30698)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/176Mi)
% 0.18/0.52  % (30692)Refutation found. Thanks to Tanya!
% 0.18/0.52  % SZS status Theorem for theBenchmark
% 0.18/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.52  % (30692)------------------------------
% 0.18/0.52  % (30692)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.52  % (30692)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.52  % (30692)Termination reason: Refutation
% 0.18/0.52  
% 0.18/0.52  % (30692)Memory used [KB]: 5756
% 0.18/0.52  % (30692)Time elapsed: 0.010 s
% 0.18/0.52  % (30692)Instructions burned: 7 (million)
% 0.18/0.52  % (30692)------------------------------
% 0.18/0.52  % (30692)------------------------------
% 0.18/0.52  % (30677)Success in time 0.177 s
%------------------------------------------------------------------------------