TSTP Solution File: SYN063+1 by Vampire-SAT---4.8

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SYN063+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 : n032.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 12:08:43 EDT 2024

% Result   : Theorem 0.11s 0.35s
% Output   : Refutation 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   59 (   7 unt;   0 def)
%            Number of atoms       :  242 (   0 equ)
%            Maximal formula atoms :   10 (   4 avg)
%            Number of connectives :  280 (  97   ~; 120   |;  48   &)
%                                         (   6 <=>;   6  =>;   0  <=;   3 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   4 prp; 0-1 aty)
%            Number of functors    :    5 (   5 usr;   5 con; 0-0 aty)
%            Number of variables   :   43 (  37   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f127,plain,
    $false,
    inference(subsumption_resolution,[],[f125,f89]) ).

fof(f89,plain,
    ~ sP2,
    inference(resolution,[],[f86,f41]) ).

fof(f41,plain,
    ( ~ sP3
    | ~ sP2 ),
    inference(cnf_transformation,[],[f23]) ).

fof(f23,plain,
    ( ( ~ sP3
      | ~ sP2 )
    & ( sP3
      | sP2 ) ),
    inference(nnf_transformation,[],[f9]) ).

fof(f9,plain,
    ( sP2
  <~> sP3 ),
    inference(definition_folding,[],[f4,f8,f7,f6,f5]) ).

fof(f5,plain,
    ! [X1] :
      ( sP0(X1)
    <=> ( big_p(c)
        | big_p(X1)
        | ~ big_p(a) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f6,plain,
    ( sP1
  <=> ( big_p(c)
      | ~ big_p(b)
      | ~ big_p(a) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f7,plain,
    ( sP2
  <=> ! [X0] :
        ( big_p(c)
        | ( ~ big_p(b)
          & big_p(X0) )
        | ~ big_p(a) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

fof(f8,plain,
    ( sP3
  <=> ! [X1] :
        ( sP1
        & sP0(X1) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).

fof(f4,plain,
    ( ! [X0] :
        ( big_p(c)
        | ( ~ big_p(b)
          & big_p(X0) )
        | ~ big_p(a) )
  <~> ! [X1] :
        ( ( big_p(c)
          | ~ big_p(b)
          | ~ big_p(a) )
        & ( big_p(c)
          | big_p(X1)
          | ~ big_p(a) ) ) ),
    inference(flattening,[],[f3]) ).

fof(f3,plain,
    ( ! [X0] :
        ( big_p(c)
        | ( ~ big_p(b)
          & big_p(X0) )
        | ~ big_p(a) )
  <~> ! [X1] :
        ( ( big_p(c)
          | ~ big_p(b)
          | ~ big_p(a) )
        & ( big_p(c)
          | big_p(X1)
          | ~ big_p(a) ) ) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f2,negated_conjecture,
    ~ ( ! [X0] :
          ( ( ( big_p(X0)
             => big_p(b) )
            & big_p(a) )
         => big_p(c) )
    <=> ! [X1] :
          ( ( big_p(c)
            | ~ big_p(b)
            | ~ big_p(a) )
          & ( big_p(c)
            | big_p(X1)
            | ~ big_p(a) ) ) ),
    inference(negated_conjecture,[],[f1]) ).

fof(f1,conjecture,
    ( ! [X0] :
        ( ( ( big_p(X0)
           => big_p(b) )
          & big_p(a) )
       => big_p(c) )
  <=> ! [X1] :
        ( ( big_p(c)
          | ~ big_p(b)
          | ~ big_p(a) )
        & ( big_p(c)
          | big_p(X1)
          | ~ big_p(a) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel33) ).

fof(f86,plain,
    sP3,
    inference(subsumption_resolution,[],[f85,f65]) ).

fof(f65,plain,
    sP1,
    inference(duplicate_literal_removal,[],[f62]) ).

fof(f62,plain,
    ( sP1
    | sP1 ),
    inference(resolution,[],[f58,f35]) ).

fof(f35,plain,
    ( ~ big_p(c)
    | sP1 ),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,plain,
    ( ( sP1
      | ( ~ big_p(c)
        & big_p(b)
        & big_p(a) ) )
    & ( big_p(c)
      | ~ big_p(b)
      | ~ big_p(a)
      | ~ sP1 ) ),
    inference(flattening,[],[f18]) ).

fof(f18,plain,
    ( ( sP1
      | ( ~ big_p(c)
        & big_p(b)
        & big_p(a) ) )
    & ( big_p(c)
      | ~ big_p(b)
      | ~ big_p(a)
      | ~ sP1 ) ),
    inference(nnf_transformation,[],[f6]) ).

fof(f58,plain,
    ! [X0] :
      ( big_p(X0)
      | sP1 ),
    inference(subsumption_resolution,[],[f57,f43]) ).

fof(f43,plain,
    ( sP2
    | sP1 ),
    inference(resolution,[],[f25,f40]) ).

fof(f40,plain,
    ( sP3
    | sP2 ),
    inference(cnf_transformation,[],[f23]) ).

fof(f25,plain,
    ( ~ sP3
    | sP1 ),
    inference(cnf_transformation,[],[f13]) ).

fof(f13,plain,
    ( ( sP3
      | ~ sP1
      | ~ sP0(sK4) )
    & ( ! [X1] :
          ( sP1
          & sP0(X1) )
      | ~ sP3 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f11,f12]) ).

fof(f12,plain,
    ( ? [X0] :
        ( ~ sP1
        | ~ sP0(X0) )
   => ( ~ sP1
      | ~ sP0(sK4) ) ),
    introduced(choice_axiom,[]) ).

fof(f11,plain,
    ( ( sP3
      | ? [X0] :
          ( ~ sP1
          | ~ sP0(X0) ) )
    & ( ! [X1] :
          ( sP1
          & sP0(X1) )
      | ~ sP3 ) ),
    inference(rectify,[],[f10]) ).

fof(f10,plain,
    ( ( sP3
      | ? [X1] :
          ( ~ sP1
          | ~ sP0(X1) ) )
    & ( ! [X1] :
          ( sP1
          & sP0(X1) )
      | ~ sP3 ) ),
    inference(nnf_transformation,[],[f8]) ).

fof(f57,plain,
    ! [X0] :
      ( big_p(X0)
      | ~ sP2
      | sP1 ),
    inference(subsumption_resolution,[],[f54,f35]) ).

fof(f54,plain,
    ! [X0] :
      ( big_p(X0)
      | big_p(c)
      | ~ sP2
      | sP1 ),
    inference(resolution,[],[f27,f33]) ).

fof(f33,plain,
    ( big_p(a)
    | sP1 ),
    inference(cnf_transformation,[],[f19]) ).

fof(f27,plain,
    ! [X1] :
      ( ~ big_p(a)
      | big_p(X1)
      | big_p(c)
      | ~ sP2 ),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,plain,
    ( ( sP2
      | ( ~ big_p(c)
        & ( big_p(b)
          | ~ big_p(sK5) )
        & big_p(a) ) )
    & ( ! [X1] :
          ( big_p(c)
          | ( ~ big_p(b)
            & big_p(X1) )
          | ~ big_p(a) )
      | ~ sP2 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f15,f16]) ).

fof(f16,plain,
    ( ? [X0] :
        ( ~ big_p(c)
        & ( big_p(b)
          | ~ big_p(X0) )
        & big_p(a) )
   => ( ~ big_p(c)
      & ( big_p(b)
        | ~ big_p(sK5) )
      & big_p(a) ) ),
    introduced(choice_axiom,[]) ).

fof(f15,plain,
    ( ( sP2
      | ? [X0] :
          ( ~ big_p(c)
          & ( big_p(b)
            | ~ big_p(X0) )
          & big_p(a) ) )
    & ( ! [X1] :
          ( big_p(c)
          | ( ~ big_p(b)
            & big_p(X1) )
          | ~ big_p(a) )
      | ~ sP2 ) ),
    inference(rectify,[],[f14]) ).

fof(f14,plain,
    ( ( sP2
      | ? [X0] :
          ( ~ big_p(c)
          & ( big_p(b)
            | ~ big_p(X0) )
          & big_p(a) ) )
    & ( ! [X0] :
          ( big_p(c)
          | ( ~ big_p(b)
            & big_p(X0) )
          | ~ big_p(a) )
      | ~ sP2 ) ),
    inference(nnf_transformation,[],[f7]) ).

fof(f85,plain,
    ( ~ sP1
    | sP3 ),
    inference(resolution,[],[f80,f26]) ).

fof(f26,plain,
    ( ~ sP0(sK4)
    | ~ sP1
    | sP3 ),
    inference(cnf_transformation,[],[f13]) ).

fof(f80,plain,
    ! [X0] : sP0(X0),
    inference(subsumption_resolution,[],[f79,f24]) ).

fof(f24,plain,
    ! [X1] :
      ( ~ sP3
      | sP0(X1) ),
    inference(cnf_transformation,[],[f13]) ).

fof(f79,plain,
    ! [X0] :
      ( sP3
      | sP0(X0) ),
    inference(subsumption_resolution,[],[f67,f39]) ).

fof(f39,plain,
    ! [X0] :
      ( ~ big_p(c)
      | sP0(X0) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,plain,
    ! [X0] :
      ( ( sP0(X0)
        | ( ~ big_p(c)
          & ~ big_p(X0)
          & big_p(a) ) )
      & ( big_p(c)
        | big_p(X0)
        | ~ big_p(a)
        | ~ sP0(X0) ) ),
    inference(rectify,[],[f21]) ).

fof(f21,plain,
    ! [X1] :
      ( ( sP0(X1)
        | ( ~ big_p(c)
          & ~ big_p(X1)
          & big_p(a) ) )
      & ( big_p(c)
        | big_p(X1)
        | ~ big_p(a)
        | ~ sP0(X1) ) ),
    inference(flattening,[],[f20]) ).

fof(f20,plain,
    ! [X1] :
      ( ( sP0(X1)
        | ( ~ big_p(c)
          & ~ big_p(X1)
          & big_p(a) ) )
      & ( big_p(c)
        | big_p(X1)
        | ~ big_p(a)
        | ~ sP0(X1) ) ),
    inference(nnf_transformation,[],[f5]) ).

fof(f67,plain,
    ! [X0] :
      ( big_p(c)
      | sP3
      | sP0(X0) ),
    inference(resolution,[],[f56,f38]) ).

fof(f38,plain,
    ! [X0] :
      ( ~ big_p(X0)
      | sP0(X0) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f56,plain,
    ! [X0] :
      ( big_p(X0)
      | big_p(c)
      | sP3 ),
    inference(subsumption_resolution,[],[f53,f40]) ).

fof(f53,plain,
    ! [X0] :
      ( big_p(X0)
      | big_p(c)
      | ~ sP2
      | sP3 ),
    inference(resolution,[],[f27,f47]) ).

fof(f47,plain,
    ( big_p(a)
    | sP3 ),
    inference(subsumption_resolution,[],[f46,f33]) ).

fof(f46,plain,
    ( big_p(a)
    | ~ sP1
    | sP3 ),
    inference(resolution,[],[f37,f26]) ).

fof(f37,plain,
    ! [X0] :
      ( sP0(X0)
      | big_p(a) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f125,plain,
    sP2,
    inference(resolution,[],[f116,f31]) ).

fof(f31,plain,
    ( ~ big_p(c)
    | sP2 ),
    inference(cnf_transformation,[],[f17]) ).

fof(f116,plain,
    big_p(c),
    inference(factoring,[],[f103]) ).

fof(f103,plain,
    ! [X0] :
      ( big_p(X0)
      | big_p(c) ),
    inference(subsumption_resolution,[],[f99,f89]) ).

fof(f99,plain,
    ! [X0] :
      ( big_p(X0)
      | big_p(c)
      | sP2 ),
    inference(resolution,[],[f96,f29]) ).

fof(f29,plain,
    ( big_p(a)
    | sP2 ),
    inference(cnf_transformation,[],[f17]) ).

fof(f96,plain,
    ! [X0] :
      ( ~ big_p(a)
      | big_p(X0)
      | big_p(c) ),
    inference(subsumption_resolution,[],[f36,f80]) ).

fof(f36,plain,
    ! [X0] :
      ( big_p(c)
      | big_p(X0)
      | ~ big_p(a)
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f22]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem    : SYN063+1 : TPTP v8.1.2. Released v2.0.0.
% 0.08/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.34  % Computer : n032.cluster.edu
% 0.11/0.34  % Model    : x86_64 x86_64
% 0.11/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34  % Memory   : 8042.1875MB
% 0.11/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34  % CPULimit   : 300
% 0.11/0.34  % WCLimit    : 300
% 0.11/0.34  % DateTime   : Fri May  3 17:38:38 EDT 2024
% 0.11/0.34  % CPUTime    : 
% 0.11/0.34  % (9372)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.35  % (9377)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.11/0.35  % (9377)First to succeed.
% 0.11/0.35  % (9377)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-9372"
% 0.11/0.35  % (9377)Refutation found. Thanks to Tanya!
% 0.11/0.35  % SZS status Theorem for theBenchmark
% 0.11/0.35  % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.35  % (9377)------------------------------
% 0.11/0.35  % (9377)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.11/0.35  % (9377)Termination reason: Refutation
% 0.11/0.35  
% 0.11/0.35  % (9377)Memory used [KB]: 753
% 0.11/0.35  % (9377)Time elapsed: 0.003 s
% 0.11/0.35  % (9377)Instructions burned: 4 (million)
% 0.11/0.35  % (9372)Success in time 0.001 s
%------------------------------------------------------------------------------