TSTP Solution File: SYN349+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SYN349+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_uns --cores 0 -t %d %s

% Computer : n026.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 19:26:20 EDT 2022

% Result   : Theorem 0.19s 0.55s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   28 (   5 unt;   0 def)
%            Number of atoms       :  249 (   0 equ)
%            Maximal formula atoms :   52 (   8 avg)
%            Number of connectives :  334 ( 113   ~; 141   |;  64   &)
%                                         (  11 <=>;   4  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   15 (   7 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   0 con; 1-2 aty)
%            Number of variables   :   56 (  42   !;  14   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f49,plain,
    $false,
    inference(subsumption_resolution,[],[f48,f37]) ).

fof(f37,plain,
    ! [X3] : big_f(sK0(X3),sK1(X3,sK0(X3))),
    inference(subsumption_resolution,[],[f36,f27]) ).

fof(f27,plain,
    ! [X0] :
      ( big_f(sK1(X0,sK0(X0)),sK0(X0))
      | big_f(sK0(X0),sK1(X0,sK0(X0))) ),
    inference(subsumption_resolution,[],[f24,f17]) ).

fof(f17,plain,
    ! [X2,X0] :
      ( big_f(sK0(X0),sK1(X0,X2))
      | ~ big_f(X0,sK1(X0,X2)) ),
    inference(cnf_transformation,[],[f8]) ).

fof(f8,plain,
    ! [X0,X2] :
      ( ( big_f(X0,sK1(X0,X2))
        | ~ big_f(sK0(X0),sK1(X0,X2)) )
      & ( big_f(sK0(X0),sK1(X0,X2))
        | ~ big_f(X0,sK1(X0,X2)) )
      & ( ~ big_f(sK1(X0,X2),sK0(X0))
        | ( ( ( ( ~ big_f(sK1(X0,X2),X2)
                | ~ big_f(X0,sK1(X0,X2)) )
              & ( big_f(sK1(X0,X2),X2)
                | big_f(X0,sK1(X0,X2)) ) )
            | ~ big_f(X2,sK1(X0,X2)) )
          & ( ( ( big_f(X0,sK1(X0,X2))
                | ~ big_f(sK1(X0,X2),X2) )
              & ( big_f(sK1(X0,X2),X2)
                | ~ big_f(X0,sK1(X0,X2)) ) )
            | big_f(X2,sK1(X0,X2)) ) ) )
      & ( big_f(sK1(X0,X2),sK0(X0))
        | ( ( big_f(X2,sK1(X0,X2))
            | ( ( ~ big_f(sK1(X0,X2),X2)
                | ~ big_f(X0,sK1(X0,X2)) )
              & ( big_f(sK1(X0,X2),X2)
                | big_f(X0,sK1(X0,X2)) ) ) )
          & ( ( ( big_f(X0,sK1(X0,X2))
                | ~ big_f(sK1(X0,X2),X2) )
              & ( big_f(sK1(X0,X2),X2)
                | ~ big_f(X0,sK1(X0,X2)) ) )
            | ~ big_f(X2,sK1(X0,X2)) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f5,f7,f6]) ).

fof(f6,plain,
    ! [X0] :
      ( ? [X1] :
        ! [X2] :
        ? [X3] :
          ( ( big_f(X0,X3)
            | ~ big_f(X1,X3) )
          & ( big_f(X1,X3)
            | ~ big_f(X0,X3) )
          & ( ~ big_f(X3,X1)
            | ( ( ( ( ~ big_f(X3,X2)
                    | ~ big_f(X0,X3) )
                  & ( big_f(X3,X2)
                    | big_f(X0,X3) ) )
                | ~ big_f(X2,X3) )
              & ( ( ( big_f(X0,X3)
                    | ~ big_f(X3,X2) )
                  & ( big_f(X3,X2)
                    | ~ big_f(X0,X3) ) )
                | big_f(X2,X3) ) ) )
          & ( big_f(X3,X1)
            | ( ( big_f(X2,X3)
                | ( ( ~ big_f(X3,X2)
                    | ~ big_f(X0,X3) )
                  & ( big_f(X3,X2)
                    | big_f(X0,X3) ) ) )
              & ( ( ( big_f(X0,X3)
                    | ~ big_f(X3,X2) )
                  & ( big_f(X3,X2)
                    | ~ big_f(X0,X3) ) )
                | ~ big_f(X2,X3) ) ) ) )
     => ! [X2] :
        ? [X3] :
          ( ( big_f(X0,X3)
            | ~ big_f(sK0(X0),X3) )
          & ( big_f(sK0(X0),X3)
            | ~ big_f(X0,X3) )
          & ( ~ big_f(X3,sK0(X0))
            | ( ( ( ( ~ big_f(X3,X2)
                    | ~ big_f(X0,X3) )
                  & ( big_f(X3,X2)
                    | big_f(X0,X3) ) )
                | ~ big_f(X2,X3) )
              & ( ( ( big_f(X0,X3)
                    | ~ big_f(X3,X2) )
                  & ( big_f(X3,X2)
                    | ~ big_f(X0,X3) ) )
                | big_f(X2,X3) ) ) )
          & ( big_f(X3,sK0(X0))
            | ( ( big_f(X2,X3)
                | ( ( ~ big_f(X3,X2)
                    | ~ big_f(X0,X3) )
                  & ( big_f(X3,X2)
                    | big_f(X0,X3) ) ) )
              & ( ( ( big_f(X0,X3)
                    | ~ big_f(X3,X2) )
                  & ( big_f(X3,X2)
                    | ~ big_f(X0,X3) ) )
                | ~ big_f(X2,X3) ) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f7,plain,
    ! [X0,X2] :
      ( ? [X3] :
          ( ( big_f(X0,X3)
            | ~ big_f(sK0(X0),X3) )
          & ( big_f(sK0(X0),X3)
            | ~ big_f(X0,X3) )
          & ( ~ big_f(X3,sK0(X0))
            | ( ( ( ( ~ big_f(X3,X2)
                    | ~ big_f(X0,X3) )
                  & ( big_f(X3,X2)
                    | big_f(X0,X3) ) )
                | ~ big_f(X2,X3) )
              & ( ( ( big_f(X0,X3)
                    | ~ big_f(X3,X2) )
                  & ( big_f(X3,X2)
                    | ~ big_f(X0,X3) ) )
                | big_f(X2,X3) ) ) )
          & ( big_f(X3,sK0(X0))
            | ( ( big_f(X2,X3)
                | ( ( ~ big_f(X3,X2)
                    | ~ big_f(X0,X3) )
                  & ( big_f(X3,X2)
                    | big_f(X0,X3) ) ) )
              & ( ( ( big_f(X0,X3)
                    | ~ big_f(X3,X2) )
                  & ( big_f(X3,X2)
                    | ~ big_f(X0,X3) ) )
                | ~ big_f(X2,X3) ) ) ) )
     => ( ( big_f(X0,sK1(X0,X2))
          | ~ big_f(sK0(X0),sK1(X0,X2)) )
        & ( big_f(sK0(X0),sK1(X0,X2))
          | ~ big_f(X0,sK1(X0,X2)) )
        & ( ~ big_f(sK1(X0,X2),sK0(X0))
          | ( ( ( ( ~ big_f(sK1(X0,X2),X2)
                  | ~ big_f(X0,sK1(X0,X2)) )
                & ( big_f(sK1(X0,X2),X2)
                  | big_f(X0,sK1(X0,X2)) ) )
              | ~ big_f(X2,sK1(X0,X2)) )
            & ( ( ( big_f(X0,sK1(X0,X2))
                  | ~ big_f(sK1(X0,X2),X2) )
                & ( big_f(sK1(X0,X2),X2)
                  | ~ big_f(X0,sK1(X0,X2)) ) )
              | big_f(X2,sK1(X0,X2)) ) ) )
        & ( big_f(sK1(X0,X2),sK0(X0))
          | ( ( big_f(X2,sK1(X0,X2))
              | ( ( ~ big_f(sK1(X0,X2),X2)
                  | ~ big_f(X0,sK1(X0,X2)) )
                & ( big_f(sK1(X0,X2),X2)
                  | big_f(X0,sK1(X0,X2)) ) ) )
            & ( ( ( big_f(X0,sK1(X0,X2))
                  | ~ big_f(sK1(X0,X2),X2) )
                & ( big_f(sK1(X0,X2),X2)
                  | ~ big_f(X0,sK1(X0,X2)) ) )
              | ~ big_f(X2,sK1(X0,X2)) ) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f5,plain,
    ! [X0] :
    ? [X1] :
    ! [X2] :
    ? [X3] :
      ( ( big_f(X0,X3)
        | ~ big_f(X1,X3) )
      & ( big_f(X1,X3)
        | ~ big_f(X0,X3) )
      & ( ~ big_f(X3,X1)
        | ( ( ( ( ~ big_f(X3,X2)
                | ~ big_f(X0,X3) )
              & ( big_f(X3,X2)
                | big_f(X0,X3) ) )
            | ~ big_f(X2,X3) )
          & ( ( ( big_f(X0,X3)
                | ~ big_f(X3,X2) )
              & ( big_f(X3,X2)
                | ~ big_f(X0,X3) ) )
            | big_f(X2,X3) ) ) )
      & ( big_f(X3,X1)
        | ( ( big_f(X2,X3)
            | ( ( ~ big_f(X3,X2)
                | ~ big_f(X0,X3) )
              & ( big_f(X3,X2)
                | big_f(X0,X3) ) ) )
          & ( ( ( big_f(X0,X3)
                | ~ big_f(X3,X2) )
              & ( big_f(X3,X2)
                | ~ big_f(X0,X3) ) )
            | ~ big_f(X2,X3) ) ) ) ),
    inference(flattening,[],[f4]) ).

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

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

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

fof(f1,conjecture,
    ? [X0] :
    ! [X1] :
    ? [X2] :
    ! [X3] :
      ( ( big_f(X0,X3)
      <=> big_f(X1,X3) )
     => ( ( big_f(X2,X3)
        <=> ( big_f(X0,X3)
          <=> big_f(X3,X2) ) )
      <=> big_f(X3,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',church_46_17_5) ).

fof(f24,plain,
    ! [X0] :
      ( big_f(X0,sK1(X0,sK0(X0)))
      | big_f(sK1(X0,sK0(X0)),sK0(X0))
      | big_f(sK0(X0),sK1(X0,sK0(X0))) ),
    inference(factoring,[],[f11]) ).

fof(f11,plain,
    ! [X2,X0] :
      ( big_f(sK1(X0,X2),sK0(X0))
      | big_f(sK1(X0,X2),X2)
      | big_f(X0,sK1(X0,X2))
      | big_f(X2,sK1(X0,X2)) ),
    inference(cnf_transformation,[],[f8]) ).

fof(f36,plain,
    ! [X3] :
      ( ~ big_f(sK1(X3,sK0(X3)),sK0(X3))
      | big_f(sK0(X3),sK1(X3,sK0(X3))) ),
    inference(subsumption_resolution,[],[f35,f17]) ).

fof(f35,plain,
    ! [X3] :
      ( big_f(X3,sK1(X3,sK0(X3)))
      | big_f(sK0(X3),sK1(X3,sK0(X3)))
      | ~ big_f(sK1(X3,sK0(X3)),sK0(X3)) ),
    inference(duplicate_literal_removal,[],[f32]) ).

fof(f32,plain,
    ! [X3] :
      ( big_f(sK0(X3),sK1(X3,sK0(X3)))
      | big_f(X3,sK1(X3,sK0(X3)))
      | ~ big_f(sK1(X3,sK0(X3)),sK0(X3))
      | big_f(sK0(X3),sK1(X3,sK0(X3))) ),
    inference(resolution,[],[f14,f27]) ).

fof(f14,plain,
    ! [X2,X0] :
      ( ~ big_f(sK1(X0,X2),sK0(X0))
      | big_f(X0,sK1(X0,X2))
      | ~ big_f(sK1(X0,X2),X2)
      | big_f(X2,sK1(X0,X2)) ),
    inference(cnf_transformation,[],[f8]) ).

fof(f48,plain,
    ! [X1] : ~ big_f(sK0(X1),sK1(X1,sK0(X1))),
    inference(subsumption_resolution,[],[f47,f43]) ).

fof(f43,plain,
    ! [X2] : big_f(sK1(X2,sK0(X2)),sK0(X2)),
    inference(subsumption_resolution,[],[f42,f37]) ).

fof(f42,plain,
    ! [X2] :
      ( ~ big_f(sK0(X2),sK1(X2,sK0(X2)))
      | big_f(sK1(X2,sK0(X2)),sK0(X2)) ),
    inference(duplicate_literal_removal,[],[f41]) ).

fof(f41,plain,
    ! [X2] :
      ( big_f(sK1(X2,sK0(X2)),sK0(X2))
      | ~ big_f(sK0(X2),sK1(X2,sK0(X2)))
      | big_f(sK1(X2,sK0(X2)),sK0(X2)) ),
    inference(resolution,[],[f38,f9]) ).

fof(f9,plain,
    ! [X2,X0] :
      ( ~ big_f(X0,sK1(X0,X2))
      | ~ big_f(X2,sK1(X0,X2))
      | big_f(sK1(X0,X2),X2)
      | big_f(sK1(X0,X2),sK0(X0)) ),
    inference(cnf_transformation,[],[f8]) ).

fof(f38,plain,
    ! [X0] : big_f(X0,sK1(X0,sK0(X0))),
    inference(resolution,[],[f37,f18]) ).

fof(f18,plain,
    ! [X2,X0] :
      ( ~ big_f(sK0(X0),sK1(X0,X2))
      | big_f(X0,sK1(X0,X2)) ),
    inference(cnf_transformation,[],[f8]) ).

fof(f47,plain,
    ! [X1] :
      ( ~ big_f(sK1(X1,sK0(X1)),sK0(X1))
      | ~ big_f(sK0(X1),sK1(X1,sK0(X1))) ),
    inference(subsumption_resolution,[],[f45,f38]) ).

fof(f45,plain,
    ! [X1] :
      ( ~ big_f(X1,sK1(X1,sK0(X1)))
      | ~ big_f(sK1(X1,sK0(X1)),sK0(X1))
      | ~ big_f(sK0(X1),sK1(X1,sK0(X1))) ),
    inference(resolution,[],[f43,f16]) ).

fof(f16,plain,
    ! [X2,X0] :
      ( ~ big_f(sK1(X0,X2),sK0(X0))
      | ~ big_f(X0,sK1(X0,X2))
      | ~ big_f(X2,sK1(X0,X2))
      | ~ big_f(sK1(X0,X2),X2) ),
    inference(cnf_transformation,[],[f8]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SYN349+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.13  % 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 : n026.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 22:00:51 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.54  % (9655)lrs+11_1:1_plsq=on:plsqc=1:plsqr=32,1:ss=included:i=95:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/95Mi)
% 0.19/0.54  % (9640)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 0.19/0.54  % (9653)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)
% 0.19/0.54  % (9655)First to succeed.
% 0.19/0.54  % (9645)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.54  % (9640)Also succeeded, but the first one will report.
% 0.19/0.55  % (9630)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.19/0.55  % (9655)Refutation found. Thanks to Tanya!
% 0.19/0.55  % SZS status Theorem for theBenchmark
% 0.19/0.55  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.55  % (9655)------------------------------
% 0.19/0.55  % (9655)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.55  % (9655)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.55  % (9655)Termination reason: Refutation
% 0.19/0.55  
% 0.19/0.55  % (9655)Memory used [KB]: 5884
% 0.19/0.55  % (9655)Time elapsed: 0.108 s
% 0.19/0.55  % (9655)Instructions burned: 3 (million)
% 0.19/0.55  % (9655)------------------------------
% 0.19/0.55  % (9655)------------------------------
% 0.19/0.55  % (9629)Success in time 0.198 s
%------------------------------------------------------------------------------