TSTP Solution File: SYN066+1 by Vampire-SAT---4.8

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SYN066+1 : TPTP v8.1.2. Bugfixed v3.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n012.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 18:02:02 EDT 2024

% Result   : Theorem 0.14s 0.38s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   42 (   9 unt;   0 def)
%            Number of atoms       :  100 (   0 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :   97 (  39   ~;  29   |;  14   &)
%                                         (   4 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    8 (   7 usr;   5 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   1 con; 0-2 aty)
%            Number of variables   :   85 (  57   !;  28   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f48,plain,
    $false,
    inference(avatar_sat_refutation,[],[f37,f41,f43,f47]) ).

fof(f47,plain,
    ~ spl6_3,
    inference(avatar_contradiction_clause,[],[f46]) ).

fof(f46,plain,
    ( $false
    | ~ spl6_3 ),
    inference(resolution,[],[f45,f40]) ).

fof(f40,plain,
    ( ! [X2,X1] : ~ big_q(X1,X2)
    | ~ spl6_3 ),
    inference(avatar_component_clause,[],[f39]) ).

fof(f39,plain,
    ( spl6_3
  <=> ! [X2,X1] : ~ big_q(X1,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_3])]) ).

fof(f45,plain,
    ( ! [X0] : big_q(sK3(X0),sK1(X0))
    | ~ spl6_3 ),
    inference(resolution,[],[f26,f44]) ).

fof(f44,plain,
    ( ! [X0,X1] : big_p(X0,X1)
    | ~ spl6_3 ),
    inference(resolution,[],[f27,f40]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( big_q(sK4(X1),X1)
      | big_p(X0,X1) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( big_q(sK4(X1),X1)
      | big_p(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f12,f20]) ).

fof(f20,plain,
    ! [X1] :
      ( ? [X2] : big_q(X2,X1)
     => big_q(sK4(X1),X1) ),
    introduced(choice_axiom,[]) ).

fof(f12,plain,
    ! [X0,X1] :
      ( ? [X2] : big_q(X2,X1)
      | big_p(X0,X1) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,plain,
    ! [X0,X1] :
      ( ~ big_p(X0,X1)
     => ? [X2] : big_q(X2,X1) ),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X2,X0] :
      ( ~ big_p(X2,X0)
     => ? [X3] : big_q(X3,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel37_2) ).

fof(f26,plain,
    ! [X2,X0] :
      ( ~ big_p(sK2(X0,X2),sK1(X0))
      | big_q(sK3(X0),sK1(X0)) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,plain,
    ! [X0,X2] :
      ( ( big_q(sK3(X0),sK1(X0))
        | ~ big_p(sK2(X0,X2),sK1(X0)) )
      & big_p(sK2(X0,X2),X0)
      & ( big_p(sK2(X0,X2),sK1(X0))
        | ~ big_p(X2,X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f11,f18,f17,f16]) ).

fof(f16,plain,
    ! [X0] :
      ( ? [X1] :
        ! [X2] :
        ? [X3] :
          ( ( ? [X4] : big_q(X4,X1)
            | ~ big_p(X3,X1) )
          & big_p(X3,X0)
          & ( big_p(X3,X1)
            | ~ big_p(X2,X0) ) )
     => ! [X2] :
        ? [X3] :
          ( ( ? [X4] : big_q(X4,sK1(X0))
            | ~ big_p(X3,sK1(X0)) )
          & big_p(X3,X0)
          & ( big_p(X3,sK1(X0))
            | ~ big_p(X2,X0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f17,plain,
    ! [X0,X2] :
      ( ? [X3] :
          ( ( ? [X4] : big_q(X4,sK1(X0))
            | ~ big_p(X3,sK1(X0)) )
          & big_p(X3,X0)
          & ( big_p(X3,sK1(X0))
            | ~ big_p(X2,X0) ) )
     => ( ( ? [X4] : big_q(X4,sK1(X0))
          | ~ big_p(sK2(X0,X2),sK1(X0)) )
        & big_p(sK2(X0,X2),X0)
        & ( big_p(sK2(X0,X2),sK1(X0))
          | ~ big_p(X2,X0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f18,plain,
    ! [X0] :
      ( ? [X4] : big_q(X4,sK1(X0))
     => big_q(sK3(X0),sK1(X0)) ),
    introduced(choice_axiom,[]) ).

fof(f11,plain,
    ! [X0] :
    ? [X1] :
    ! [X2] :
    ? [X3] :
      ( ( ? [X4] : big_q(X4,X1)
        | ~ big_p(X3,X1) )
      & big_p(X3,X0)
      & ( big_p(X3,X1)
        | ~ big_p(X2,X0) ) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0] :
    ? [X1] :
    ! [X2] :
    ? [X3] :
      ( ( big_p(X3,X1)
       => ? [X4] : big_q(X4,X1) )
      & big_p(X3,X0)
      & ( big_p(X2,X0)
       => big_p(X3,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel37_1) ).

fof(f43,plain,
    ~ spl6_2,
    inference(avatar_contradiction_clause,[],[f42]) ).

fof(f42,plain,
    ( $false
    | ~ spl6_2 ),
    inference(resolution,[],[f36,f22]) ).

fof(f22,plain,
    ! [X1] : ~ big_r(sK0,X1),
    inference(cnf_transformation,[],[f14]) ).

fof(f14,plain,
    ! [X1] : ~ big_r(sK0,X1),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f9,f13]) ).

fof(f13,plain,
    ( ? [X0] :
      ! [X1] : ~ big_r(X0,X1)
   => ! [X1] : ~ big_r(sK0,X1) ),
    introduced(choice_axiom,[]) ).

fof(f9,plain,
    ? [X0] :
    ! [X1] : ~ big_r(X0,X1),
    inference(ennf_transformation,[],[f6]) ).

fof(f6,plain,
    ~ ! [X0] :
      ? [X1] : big_r(X0,X1),
    inference(rectify,[],[f5]) ).

fof(f5,negated_conjecture,
    ~ ! [X2] :
      ? [X3] : big_r(X2,X3),
    inference(negated_conjecture,[],[f4]) ).

fof(f4,conjecture,
    ! [X2] :
    ? [X3] : big_r(X2,X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel37) ).

fof(f36,plain,
    ( ! [X0] : big_r(X0,X0)
    | ~ spl6_2 ),
    inference(avatar_component_clause,[],[f35]) ).

fof(f35,plain,
    ( spl6_2
  <=> ! [X0] : big_r(X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_2])]) ).

fof(f41,plain,
    ( ~ spl6_1
    | spl6_3 ),
    inference(avatar_split_clause,[],[f29,f39,f31]) ).

fof(f31,plain,
    ( spl6_1
  <=> sP5 ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_1])]) ).

fof(f29,plain,
    ! [X2,X1] :
      ( ~ big_q(X1,X2)
      | ~ sP5 ),
    inference(general_splitting,[],[f23,f28_D]) ).

fof(f28,plain,
    ! [X0] :
      ( big_r(X0,X0)
      | sP5 ),
    inference(cnf_transformation,[],[f28_D]) ).

fof(f28_D,plain,
    ( ! [X0] : big_r(X0,X0)
  <=> ~ sP5 ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP5])]) ).

fof(f23,plain,
    ! [X2,X0,X1] :
      ( big_r(X0,X0)
      | ~ big_q(X1,X2) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f15,plain,
    ( ! [X0] : big_r(X0,X0)
    | ! [X1,X2] : ~ big_q(X1,X2) ),
    inference(rectify,[],[f10]) ).

fof(f10,plain,
    ( ! [X2] : big_r(X2,X2)
    | ! [X0,X1] : ~ big_q(X0,X1) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,plain,
    ( ? [X0,X1] : big_q(X0,X1)
   => ! [X2] : big_r(X2,X2) ),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ( ? [X2,X3] : big_q(X2,X3)
   => ! [X0] : big_r(X0,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel37_3) ).

fof(f37,plain,
    ( spl6_1
    | spl6_2 ),
    inference(avatar_split_clause,[],[f28,f35,f31]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SYN066+1 : TPTP v8.1.2. Bugfixed v3.0.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n012.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Tue Apr 30 01:51:00 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.36  % (15780)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37  % (15783)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)
% 0.14/0.37  % (15781)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.37  % (15782)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.37  % (15784)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.14/0.37  % (15785)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.14/0.37  % (15786)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.14/0.37  % (15787)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)
% 0.14/0.37  % (15783)First to succeed.
% 0.14/0.37  TRYING [1]
% 0.14/0.37  TRYING [1,1,1,1]
% 0.14/0.37  TRYING [2]
% 0.14/0.37  % (15785)Also succeeded, but the first one will report.
% 0.14/0.37  TRYING [1,1,1,1]
% 0.14/0.37  TRYING [1]
% 0.14/0.37  TRYING [2,2,1,1]
% 0.14/0.37  TRYING [2,2,1,1]
% 0.14/0.37  TRYING [2]
% 0.14/0.38  TRYING [3]
% 0.14/0.38  TRYING [2,1,2,1]
% 0.14/0.38  TRYING [2,1,2,1]
% 0.14/0.38  TRYING [2,1,1,2]
% 0.14/0.38  TRYING [3]
% 0.14/0.38  TRYING [2,1,1,2]
% 0.14/0.38  % (15786)Also succeeded, but the first one will report.
% 0.14/0.38  % (15783)Refutation found. Thanks to Tanya!
% 0.14/0.38  % SZS status Theorem for theBenchmark
% 0.14/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.38  % (15783)------------------------------
% 0.14/0.38  % (15783)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.38  % (15783)Termination reason: Refutation
% 0.14/0.38  
% 0.14/0.38  % (15783)Memory used [KB]: 748
% 0.14/0.38  % (15783)Time elapsed: 0.004 s
% 0.14/0.38  % (15783)Instructions burned: 3 (million)
% 0.14/0.38  % (15783)------------------------------
% 0.14/0.38  % (15783)------------------------------
% 0.14/0.38  % (15780)Success in time 0.017 s
%------------------------------------------------------------------------------