%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SYN730+1 : TPTP v8.1.2. Released v2.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n029.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 : Sun May  5 12:12:05 EDT 2024

% Result   : Theorem 0.21s 0.37s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    2
% Syntax   : Number of formulae    :    9 (   3 unt;   0 def)
%            Number of atoms       :   23 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   20 (   6   ~;   7   |;   4   &)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   1 con; 0-1 aty)
%            Number of variables   :   18 (  12   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f9,plain,
    $false,
    inference(resolution,[],[f8,f7]) ).

fof(f7,plain,
    ! [X2,X0] : ~ p(X0,sK0(X0),X2),
    inference(cnf_transformation,[],[f5]) ).

fof(f5,plain,
    ! [X0,X2] :
      ( ~ p(X0,sK0(X0),X2)
      & ( p(X0,sK0(X0),k(sK0(X0)))
        | p(a,sK0(X0),h(sK0(X0))) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f3,f4]) ).

fof(f4,plain,
    ! [X0] :
      ( ? [X1] :
        ! [X2] :
          ( ~ p(X0,X1,X2)
          & ( p(X0,X1,k(X1))
            | p(a,X1,h(X1)) ) )
     => ! [X2] :
          ( ~ p(X0,sK0(X0),X2)
          & ( p(X0,sK0(X0),k(sK0(X0)))
            | p(a,sK0(X0),h(sK0(X0))) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f3,plain,
    ! [X0] :
    ? [X1] :
    ! [X2] :
      ( ~ p(X0,X1,X2)
      & ( p(X0,X1,k(X1))
        | p(a,X1,h(X1)) ) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f2,negated_conjecture,
    ~ ? [X0] :
      ! [X1] :
      ? [X2] :
        ( ( p(X0,X1,k(X1))
          | p(a,X1,h(X1)) )
       => p(X0,X1,X2) ),
    inference(negated_conjecture,[],[f1]) ).

fof(f1,conjecture,
    ? [X0] :
    ! [X1] :
    ? [X2] :
      ( ( p(X0,X1,k(X1))
        | p(a,X1,h(X1)) )
     => p(X0,X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm75) ).

fof(f8,plain,
    p(a,sK0(a),k(sK0(a))),
    inference(resolution,[],[f6,f7]) ).

fof(f6,plain,
    ! [X0] :
      ( p(a,sK0(X0),h(sK0(X0)))
      | p(X0,sK0(X0),k(sK0(X0))) ),
    inference(cnf_transformation,[],[f5]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SYN730+1 : TPTP v8.1.2. Released v2.5.0.
% 0.13/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35  % Computer : n029.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Fri May  3 17:17:52 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.13/0.35  % (8925)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.36  % (8929)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)
% 0.21/0.36  % (8929)First to succeed.
% 0.21/0.37  % (8929)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-8925"
% 0.21/0.37  % (8929)Refutation found. Thanks to Tanya!
% 0.21/0.37  % SZS status Theorem for theBenchmark
% 0.21/0.37  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.37  % (8929)------------------------------
% 0.21/0.37  % (8929)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.37  % (8929)Termination reason: Refutation
% 0.21/0.37  
% 0.21/0.37  % (8929)Memory used [KB]: 732
% 0.21/0.37  % (8929)Time elapsed: 0.003 s
% 0.21/0.37  % (8929)Instructions burned: 2 (million)
% 0.21/0.37  % (8925)Success in time 0.013 s
%------------------------------------------------------------------------------