TSTP Solution File: FLD037-3 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : FLD037-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n024.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 05:08:00 EDT 2024

% Result   : Unsatisfiable 0.21s 0.41s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   35 (   8 unt;   0 def)
%            Number of atoms       :   72 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   74 (  37   ~;  32   |;   0   &)
%                                         (   5 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    9 (   8 usr;   5 prp; 0-4 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-1 aty)
%            Number of variables   :   34 (  34   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f991,plain,
    $false,
    inference(avatar_sat_refutation,[],[f64,f66,f889,f943,f990]) ).

fof(f990,plain,
    ~ spl9_17,
    inference(avatar_contradiction_clause,[],[f964]) ).

fof(f964,plain,
    ( $false
    | ~ spl9_17 ),
    inference(resolution,[],[f942,f29]) ).

fof(f29,axiom,
    ~ sum(additive_identity,a,additive_identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_3) ).

fof(f942,plain,
    ( sum(additive_identity,a,additive_identity)
    | ~ spl9_17 ),
    inference(avatar_component_clause,[],[f940]) ).

fof(f940,plain,
    ( spl9_17
  <=> sum(additive_identity,a,additive_identity) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_17])]) ).

fof(f943,plain,
    ( ~ spl9_1
    | spl9_17
    | spl9_16 ),
    inference(avatar_split_clause,[],[f910,f886,f940,f57]) ).

fof(f57,plain,
    ( spl9_1
  <=> defined(a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_1])]) ).

fof(f886,plain,
    ( spl9_16
  <=> product(multiplicative_inverse(a),a,multiplicative_identity) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_16])]) ).

fof(f910,plain,
    ( sum(additive_identity,a,additive_identity)
    | ~ defined(a)
    | spl9_16 ),
    inference(resolution,[],[f888,f9]) ).

fof(f9,axiom,
    ! [X0] :
      ( product(multiplicative_inverse(X0),X0,multiplicative_identity)
      | sum(additive_identity,X0,additive_identity)
      | ~ defined(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_inverse_multiplication) ).

fof(f888,plain,
    ( ~ product(multiplicative_inverse(a),a,multiplicative_identity)
    | spl9_16 ),
    inference(avatar_component_clause,[],[f886]) ).

fof(f889,plain,
    ( ~ spl9_2
    | ~ spl9_16 ),
    inference(avatar_split_clause,[],[f879,f886,f61]) ).

fof(f61,plain,
    ( spl9_2
  <=> defined(multiplicative_inverse(a)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_2])]) ).

fof(f879,plain,
    ( ~ product(multiplicative_inverse(a),a,multiplicative_identity)
    | ~ defined(multiplicative_inverse(a)) ),
    inference(resolution,[],[f857,f8]) ).

fof(f8,axiom,
    ! [X0] :
      ( product(multiplicative_identity,X0,X0)
      | ~ defined(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_identity_multiplication) ).

fof(f857,plain,
    ! [X0] :
      ( ~ product(multiplicative_identity,multiplicative_inverse(a),X0)
      | ~ product(X0,a,multiplicative_identity) ),
    inference(resolution,[],[f816,f10]) ).

fof(f10,axiom,
    ! [X3,X0,X5] :
      ( product(X3,X0,X5)
      | ~ product(X0,X3,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_multiplication) ).

fof(f816,plain,
    ! [X0] :
      ( ~ product(multiplicative_inverse(a),multiplicative_identity,X0)
      | ~ product(X0,a,multiplicative_identity) ),
    inference(resolution,[],[f139,f52]) ).

fof(f52,plain,
    ~ product(multiplicative_inverse(a),b,multiplicative_identity),
    inference(resolution,[],[f10,f31]) ).

fof(f31,axiom,
    ~ product(b,multiplicative_inverse(a),multiplicative_identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_product_5) ).

fof(f139,plain,
    ! [X2,X0,X1] :
      ( product(X0,b,X2)
      | ~ product(X0,multiplicative_identity,X1)
      | ~ product(X1,a,X2) ),
    inference(resolution,[],[f118,f34]) ).

fof(f34,plain,
    ! [X2,X0,X1,X4,X5] :
      ( sP1(X4,X0,X5,X1)
      | product(X0,X1,X2)
      | ~ product(X4,X5,X2) ),
    inference(cnf_transformation,[],[f34_D]) ).

fof(f34_D,plain,
    ! [X1,X5,X0,X4] :
      ( ! [X2] :
          ( product(X0,X1,X2)
          | ~ product(X4,X5,X2) )
    <=> ~ sP1(X4,X0,X5,X1) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP1])]) ).

fof(f118,plain,
    ! [X0,X1] :
      ( ~ sP1(X1,X0,a,b)
      | ~ product(X0,multiplicative_identity,X1) ),
    inference(resolution,[],[f35,f30]) ).

fof(f30,axiom,
    product(multiplicative_identity,a,b),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_4) ).

fof(f35,plain,
    ! [X3,X0,X1,X4,X5] :
      ( ~ product(X3,X5,X1)
      | ~ product(X0,X3,X4)
      | ~ sP1(X4,X0,X5,X1) ),
    inference(general_splitting,[],[f6,f34_D]) ).

fof(f6,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ product(X4,X5,X2)
      | ~ product(X3,X5,X1)
      | ~ product(X0,X3,X4)
      | product(X0,X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_multiplication_1) ).

fof(f66,plain,
    spl9_1,
    inference(avatar_contradiction_clause,[],[f65]) ).

fof(f65,plain,
    ( $false
    | spl9_1 ),
    inference(resolution,[],[f59,f27]) ).

fof(f27,axiom,
    defined(a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).

fof(f59,plain,
    ( ~ defined(a)
    | spl9_1 ),
    inference(avatar_component_clause,[],[f57]) ).

fof(f64,plain,
    ( ~ spl9_1
    | spl9_2 ),
    inference(avatar_split_clause,[],[f55,f61,f57]) ).

fof(f55,plain,
    ( defined(multiplicative_inverse(a))
    | ~ defined(a) ),
    inference(resolution,[],[f18,f29]) ).

fof(f18,axiom,
    ! [X0] :
      ( sum(additive_identity,X0,additive_identity)
      | defined(multiplicative_inverse(X0))
      | ~ defined(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_multiplicative_inverse) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : FLD037-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36  % Computer : n024.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Fri May  3 19:44:38 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.37  % (14774)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38  % (14780)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.14/0.38  % (14777)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)
% 0.14/0.38  % (14776)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.39  TRYING [1]
% 0.14/0.39  % (14775)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.39  TRYING [2]
% 0.14/0.39  % (14778)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.14/0.39  % (14781)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)
% 0.14/0.39  TRYING [1]
% 0.14/0.39  TRYING [3]
% 0.14/0.39  % (14779)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.14/0.39  TRYING [2]
% 0.14/0.39  TRYING [1]
% 0.14/0.39  TRYING [1]
% 0.14/0.39  TRYING [3]
% 0.14/0.39  TRYING [2]
% 0.14/0.39  TRYING [2]
% 0.14/0.39  TRYING [3]
% 0.14/0.39  TRYING [3]
% 0.14/0.40  TRYING [4]
% 0.14/0.40  TRYING [4]
% 0.14/0.40  TRYING [4]
% 0.14/0.41  TRYING [4]
% 0.21/0.41  % (14777)First to succeed.
% 0.21/0.41  % (14777)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-14774"
% 0.21/0.41  % (14780)Also succeeded, but the first one will report.
% 0.21/0.41  % (14777)Refutation found. Thanks to Tanya!
% 0.21/0.41  % SZS status Unsatisfiable for theBenchmark
% 0.21/0.41  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.41  % (14777)------------------------------
% 0.21/0.41  % (14777)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.41  % (14777)Termination reason: Refutation
% 0.21/0.41  
% 0.21/0.41  % (14777)Memory used [KB]: 1204
% 0.21/0.41  % (14777)Time elapsed: 0.028 s
% 0.21/0.41  % (14777)Instructions burned: 41 (million)
% 0.21/0.41  % (14774)Success in time 0.046 s
%------------------------------------------------------------------------------