TSTP Solution File: FLD025-3 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : FLD025-3 : 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 : n014.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 05:07:56 EDT 2024

% Result   : Unsatisfiable 0.22s 0.41s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   45 (   9 unt;   0 def)
%            Number of atoms       :   97 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  104 (  52   ~;  46   |;   0   &)
%                                         (   6 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    9 (   8 usr;   6 prp; 0-4 aty)
%            Number of functors    :    6 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :   41 (  41   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1031,plain,
    $false,
    inference(avatar_sat_refutation,[],[f232,f234,f237,f289,f970,f1030]) ).

fof(f1030,plain,
    ( ~ spl9_7
    | ~ spl9_8
    | spl9_15 ),
    inference(avatar_split_clause,[],[f1001,f967,f229,f225]) ).

fof(f225,plain,
    ( spl9_7
  <=> defined(c) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_7])]) ).

fof(f229,plain,
    ( spl9_8
  <=> defined(a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_8])]) ).

fof(f967,plain,
    ( spl9_15
  <=> product(c,a,multiply(a,c)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_15])]) ).

fof(f1001,plain,
    ( ~ defined(a)
    | ~ defined(c)
    | spl9_15 ),
    inference(resolution,[],[f975,f20]) ).

fof(f20,axiom,
    ! [X3,X0] :
      ( product(X0,X3,multiply(X0,X3))
      | ~ defined(X0)
      | ~ defined(X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality_of_multiplication) ).

fof(f975,plain,
    ( ~ product(a,c,multiply(a,c))
    | spl9_15 ),
    inference(resolution,[],[f969,f10]) ).

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

fof(f969,plain,
    ( ~ product(c,a,multiply(a,c))
    | spl9_15 ),
    inference(avatar_component_clause,[],[f967]) ).

fof(f970,plain,
    ( ~ spl9_5
    | ~ spl9_15
    | spl9_12 ),
    inference(avatar_split_clause,[],[f898,f286,f967,f214]) ).

fof(f214,plain,
    ( spl9_5
  <=> defined(multiply(a,c)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_5])]) ).

fof(f286,plain,
    ( spl9_12
  <=> product(a,d,multiply(a,c)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_12])]) ).

fof(f898,plain,
    ( ~ product(c,a,multiply(a,c))
    | ~ defined(multiply(a,c))
    | spl9_12 ),
    inference(resolution,[],[f754,f8]) ).

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

fof(f754,plain,
    ( ! [X0] :
        ( ~ product(multiplicative_identity,X0,multiply(a,c))
        | ~ product(c,a,X0) )
    | spl9_12 ),
    inference(resolution,[],[f145,f291]) ).

fof(f291,plain,
    ( ~ product(d,a,multiply(a,c))
    | spl9_12 ),
    inference(resolution,[],[f288,f10]) ).

fof(f288,plain,
    ( ~ product(a,d,multiply(a,c))
    | spl9_12 ),
    inference(avatar_component_clause,[],[f286]) ).

fof(f145,plain,
    ! [X2,X0,X1] :
      ( product(d,X0,X2)
      | ~ product(c,X0,X1)
      | ~ product(multiplicative_identity,X1,X2) ),
    inference(resolution,[],[f121,f36]) ).

fof(f36,plain,
    ! [X2,X0,X1,X4,X5] :
      ( sP1(X5,X4,X0,X1)
      | product(X4,X5,X2)
      | ~ product(X0,X1,X2) ),
    inference(cnf_transformation,[],[f36_D]) ).

fof(f36_D,plain,
    ! [X1,X0,X4,X5] :
      ( ! [X2] :
          ( product(X4,X5,X2)
          | ~ product(X0,X1,X2) )
    <=> ~ sP1(X5,X4,X0,X1) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP1])]) ).

fof(f121,plain,
    ! [X0,X1] :
      ( ~ sP1(X0,d,multiplicative_identity,X1)
      | ~ product(c,X0,X1) ),
    inference(resolution,[],[f37,f32]) ).

fof(f32,axiom,
    product(multiplicative_identity,c,d),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_6) ).

fof(f37,plain,
    ! [X3,X0,X1,X4,X5] :
      ( ~ product(X3,X5,X1)
      | ~ product(X0,X3,X4)
      | ~ sP1(X5,X4,X0,X1) ),
    inference(general_splitting,[],[f7,f36_D]) ).

fof(f7,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ product(X0,X1,X2)
      | ~ product(X3,X5,X1)
      | ~ product(X0,X3,X4)
      | product(X4,X5,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_multiplication_2) ).

fof(f289,plain,
    ( ~ spl9_5
    | ~ spl9_12 ),
    inference(avatar_split_clause,[],[f279,f286,f214]) ).

fof(f279,plain,
    ( ~ product(a,d,multiply(a,c))
    | ~ defined(multiply(a,c)) ),
    inference(resolution,[],[f272,f8]) ).

fof(f272,plain,
    ! [X0] :
      ( ~ product(multiplicative_identity,X0,multiply(a,c))
      | ~ product(a,d,X0) ),
    inference(resolution,[],[f130,f53]) ).

fof(f53,plain,
    ~ product(b,d,multiply(a,c)),
    inference(resolution,[],[f10,f33]) ).

fof(f33,axiom,
    ~ product(d,b,multiply(a,c)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_product_7) ).

fof(f130,plain,
    ! [X2,X0,X1] :
      ( product(b,X0,X2)
      | ~ product(a,X0,X1)
      | ~ product(multiplicative_identity,X1,X2) ),
    inference(resolution,[],[f120,f36]) ).

fof(f120,plain,
    ! [X0,X1] :
      ( ~ sP1(X0,b,multiplicative_identity,X1)
      | ~ product(a,X0,X1) ),
    inference(resolution,[],[f37,f31]) ).

fof(f31,axiom,
    product(multiplicative_identity,a,b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_5) ).

fof(f237,plain,
    spl9_8,
    inference(avatar_contradiction_clause,[],[f236]) ).

fof(f236,plain,
    ( $false
    | spl9_8 ),
    inference(resolution,[],[f231,f27]) ).

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

fof(f231,plain,
    ( ~ defined(a)
    | spl9_8 ),
    inference(avatar_component_clause,[],[f229]) ).

fof(f234,plain,
    spl9_7,
    inference(avatar_contradiction_clause,[],[f233]) ).

fof(f233,plain,
    ( $false
    | spl9_7 ),
    inference(resolution,[],[f227,f29]) ).

fof(f29,axiom,
    defined(c),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_is_defined) ).

fof(f227,plain,
    ( ~ defined(c)
    | spl9_7 ),
    inference(avatar_component_clause,[],[f225]) ).

fof(f232,plain,
    ( ~ spl9_7
    | ~ spl9_8
    | spl9_5 ),
    inference(avatar_split_clause,[],[f222,f214,f229,f225]) ).

fof(f222,plain,
    ( ~ defined(a)
    | ~ defined(c)
    | spl9_5 ),
    inference(resolution,[],[f216,f16]) ).

fof(f16,axiom,
    ! [X3,X0] :
      ( defined(multiply(X0,X3))
      | ~ defined(X0)
      | ~ defined(X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_multiplication) ).

fof(f216,plain,
    ( ~ defined(multiply(a,c))
    | spl9_5 ),
    inference(avatar_component_clause,[],[f214]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : FLD025-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.14/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36  % Computer : n014.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Fri May  3 19:48:53 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  % (30569)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.38  % (30570)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.22/0.38  % (30571)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.22/0.38  % (30572)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)
% 0.22/0.38  % (30574)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.22/0.38  % (30573)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.22/0.38  % (30575)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.22/0.38  % (30576)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)
% 0.22/0.38  TRYING [1]
% 0.22/0.38  TRYING [2]
% 0.22/0.38  TRYING [1]
% 0.22/0.38  TRYING [1]
% 0.22/0.38  TRYING [2]
% 0.22/0.38  TRYING [2]
% 0.22/0.38  TRYING [1]
% 0.22/0.39  TRYING [2]
% 0.22/0.39  TRYING [3]
% 0.22/0.39  TRYING [3]
% 0.22/0.39  TRYING [3]
% 0.22/0.39  TRYING [3]
% 0.22/0.40  TRYING [4]
% 0.22/0.40  TRYING [4]
% 0.22/0.40  TRYING [4]
% 0.22/0.40  TRYING [4]
% 0.22/0.41  % (30572)First to succeed.
% 0.22/0.41  % (30572)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-30569"
% 0.22/0.41  % (30572)Refutation found. Thanks to Tanya!
% 0.22/0.41  % SZS status Unsatisfiable for theBenchmark
% 0.22/0.41  % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.41  % (30572)------------------------------
% 0.22/0.41  % (30572)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.41  % (30572)Termination reason: Refutation
% 0.22/0.41  
% 0.22/0.41  % (30572)Memory used [KB]: 1240
% 0.22/0.41  % (30572)Time elapsed: 0.029 s
% 0.22/0.41  % (30572)Instructions burned: 48 (million)
% 0.22/0.41  % (30569)Success in time 0.046 s
%------------------------------------------------------------------------------