TSTP Solution File: FLD016-5 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : FLD016-5 : TPTP v8.2.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n021.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 : Mon May 20 19:56:20 EDT 2024

% Result   : Unsatisfiable 102.06s 14.95s
% Output   : Refutation 102.06s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   55 (  10 unt;   0 def)
%            Number of atoms       :  120 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  131 (  66   ~;  58   |;   0   &)
%                                         (   7 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   10 (   9 usr;   6 prp; 0-4 aty)
%            Number of functors    :    7 (   7 usr;   6 con; 0-1 aty)
%            Number of variables   :   72 (  72   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f262306,plain,
    $false,
    inference(avatar_sat_refutation,[],[f659,f1699,f54246,f110422,f260434,f262305]) ).

fof(f262305,plain,
    spl9_292,
    inference(avatar_contradiction_clause,[],[f262304]) ).

fof(f262304,plain,
    ( $false
    | spl9_292 ),
    inference(resolution,[],[f262258,f29]) ).

fof(f29,axiom,
    defined(v),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_is_defined) ).

fof(f262258,plain,
    ( ~ defined(v)
    | spl9_292 ),
    inference(resolution,[],[f260433,f3]) ).

fof(f3,axiom,
    ! [X0] :
      ( sum(additive_identity,X0,X0)
      | ~ defined(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_identity_addition) ).

fof(f260433,plain,
    ( ~ sum(additive_identity,v,v)
    | spl9_292 ),
    inference(avatar_component_clause,[],[f260431]) ).

fof(f260431,plain,
    ( spl9_292
  <=> sum(additive_identity,v,v) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_292])]) ).

fof(f260434,plain,
    ( ~ spl9_16
    | ~ spl9_292
    | spl9_218 ),
    inference(avatar_split_clause,[],[f260396,f110419,f260431,f646]) ).

fof(f646,plain,
    ( spl9_16
  <=> defined(a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_16])]) ).

fof(f110419,plain,
    ( spl9_218
  <=> sum(r,additive_inverse(a),v) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_218])]) ).

fof(f260396,plain,
    ( ~ sum(additive_identity,v,v)
    | ~ defined(a)
    | spl9_218 ),
    inference(resolution,[],[f110705,f4]) ).

fof(f4,axiom,
    ! [X0] :
      ( sum(additive_inverse(X0),X0,additive_identity)
      | ~ defined(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_inverse_addition) ).

fof(f110705,plain,
    ( ! [X0] :
        ( ~ sum(additive_inverse(a),a,X0)
        | ~ sum(X0,v,v) )
    | spl9_218 ),
    inference(resolution,[],[f110429,f213]) ).

fof(f213,plain,
    ! [X2,X0,X1] :
      ( sum(X0,r,X2)
      | ~ sum(X0,a,X1)
      | ~ sum(X1,v,X2) ),
    inference(resolution,[],[f161,f42]) ).

fof(f42,plain,
    ! [X2,X0,X1,X4,X5] :
      ( sP3(X4,X0,X5,X1)
      | sum(X0,X1,X2)
      | ~ sum(X4,X5,X2) ),
    inference(cnf_transformation,[],[f42_D]) ).

fof(f42_D,plain,
    ! [X1,X5,X0,X4] :
      ( ! [X2] :
          ( sum(X0,X1,X2)
          | ~ sum(X4,X5,X2) )
    <=> ~ sP3(X4,X0,X5,X1) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP3])]) ).

fof(f161,plain,
    ! [X0,X1] :
      ( ~ sP3(X1,X0,v,r)
      | ~ sum(X0,a,X1) ),
    inference(resolution,[],[f43,f33]) ).

fof(f33,axiom,
    sum(a,v,r),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_7) ).

fof(f43,plain,
    ! [X3,X0,X1,X4,X5] :
      ( ~ sum(X3,X5,X1)
      | ~ sum(X0,X3,X4)
      | ~ sP3(X4,X0,X5,X1) ),
    inference(general_splitting,[],[f1,f42_D]) ).

fof(f1,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ sum(X4,X5,X2)
      | ~ sum(X3,X5,X1)
      | ~ sum(X0,X3,X4)
      | sum(X0,X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_addition_1) ).

fof(f110429,plain,
    ( ~ sum(additive_inverse(a),r,v)
    | spl9_218 ),
    inference(resolution,[],[f110421,f5]) ).

fof(f5,axiom,
    ! [X3,X0,X5] :
      ( sum(X3,X0,X5)
      | ~ sum(X0,X3,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_addition) ).

fof(f110421,plain,
    ( ~ sum(r,additive_inverse(a),v)
    | spl9_218 ),
    inference(avatar_component_clause,[],[f110419]) ).

fof(f110422,plain,
    ( ~ spl9_140
    | ~ spl9_218
    | spl9_29 ),
    inference(avatar_split_clause,[],[f110092,f1696,f110419,f54234]) ).

fof(f54234,plain,
    ( spl9_140
  <=> defined(additive_inverse(a)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_140])]) ).

fof(f1696,plain,
    ( spl9_29
  <=> sum(q,additive_inverse(a),v) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_29])]) ).

fof(f110092,plain,
    ( ~ sum(r,additive_inverse(a),v)
    | ~ defined(additive_inverse(a))
    | spl9_29 ),
    inference(resolution,[],[f60720,f3]) ).

fof(f60720,plain,
    ( ! [X0] :
        ( ~ sum(additive_identity,X0,additive_inverse(a))
        | ~ sum(r,X0,v) )
    | spl9_29 ),
    inference(resolution,[],[f561,f1698]) ).

fof(f1698,plain,
    ( ~ sum(q,additive_inverse(a),v)
    | spl9_29 ),
    inference(avatar_component_clause,[],[f1696]) ).

fof(f561,plain,
    ! [X2,X0,X1] :
      ( sum(q,X1,X2)
      | ~ sum(additive_identity,X0,X1)
      | ~ sum(r,X0,X2) ),
    inference(resolution,[],[f474,f42]) ).

fof(f474,plain,
    ! [X0,X1] :
      ( ~ sP3(r,q,X0,X1)
      | ~ sum(additive_identity,X0,X1) ),
    inference(resolution,[],[f162,f34]) ).

fof(f34,axiom,
    sum(additive_identity,q,r),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_8) ).

fof(f162,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ sum(X0,X1,X2)
      | ~ sP3(X3,X4,X1,X2)
      | ~ sum(X0,X4,X3) ),
    inference(resolution,[],[f43,f5]) ).

fof(f54246,plain,
    spl9_140,
    inference(avatar_contradiction_clause,[],[f54245]) ).

fof(f54245,plain,
    ( $false
    | spl9_140 ),
    inference(resolution,[],[f54243,f27]) ).

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

fof(f54243,plain,
    ( ~ defined(a)
    | spl9_140 ),
    inference(resolution,[],[f54236,f15]) ).

fof(f15,axiom,
    ! [X0] :
      ( defined(additive_inverse(X0))
      | ~ defined(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_inverse) ).

fof(f54236,plain,
    ( ~ defined(additive_inverse(a))
    | spl9_140 ),
    inference(avatar_component_clause,[],[f54234]) ).

fof(f1699,plain,
    ( ~ spl9_16
    | ~ spl9_29 ),
    inference(avatar_split_clause,[],[f1682,f1696,f646]) ).

fof(f1682,plain,
    ( ~ sum(q,additive_inverse(a),v)
    | ~ defined(a) ),
    inference(resolution,[],[f1635,f4]) ).

fof(f1635,plain,
    ! [X0] :
      ( ~ sum(X0,a,additive_identity)
      | ~ sum(q,X0,v) ),
    inference(resolution,[],[f1625,f5]) ).

fof(f1625,plain,
    ! [X0] :
      ( ~ sum(X0,q,v)
      | ~ sum(X0,a,additive_identity) ),
    inference(resolution,[],[f223,f35]) ).

fof(f35,axiom,
    ~ sum(additive_identity,u,v),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_9) ).

fof(f223,plain,
    ! [X2,X0,X1] :
      ( sum(X1,u,X2)
      | ~ sum(X0,a,X1)
      | ~ sum(X0,q,X2) ),
    inference(resolution,[],[f185,f44]) ).

fof(f44,plain,
    ! [X2,X0,X1,X4,X5] :
      ( sP4(X5,X4,X0,X1)
      | sum(X4,X5,X2)
      | ~ sum(X0,X1,X2) ),
    inference(cnf_transformation,[],[f44_D]) ).

fof(f44_D,plain,
    ! [X1,X0,X4,X5] :
      ( ! [X2] :
          ( sum(X4,X5,X2)
          | ~ sum(X0,X1,X2) )
    <=> ~ sP4(X5,X4,X0,X1) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP4])]) ).

fof(f185,plain,
    ! [X0,X1] :
      ( ~ sP4(u,X1,X0,q)
      | ~ sum(X0,a,X1) ),
    inference(resolution,[],[f45,f32]) ).

fof(f32,axiom,
    sum(a,u,q),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_6) ).

fof(f45,plain,
    ! [X3,X0,X1,X4,X5] :
      ( ~ sum(X3,X5,X1)
      | ~ sum(X0,X3,X4)
      | ~ sP4(X5,X4,X0,X1) ),
    inference(general_splitting,[],[f2,f44_D]) ).

fof(f2,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ sum(X0,X1,X2)
      | ~ sum(X3,X5,X1)
      | ~ sum(X0,X3,X4)
      | sum(X4,X5,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_addition_2) ).

fof(f659,plain,
    spl9_16,
    inference(avatar_contradiction_clause,[],[f658]) ).

fof(f658,plain,
    ( $false
    | spl9_16 ),
    inference(resolution,[],[f648,f27]) ).

fof(f648,plain,
    ( ~ defined(a)
    | spl9_16 ),
    inference(avatar_component_clause,[],[f646]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : FLD016-5 : TPTP v8.2.0. Bugfixed v2.1.0.
% 0.11/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35  % Computer : n021.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   : Sat May 18 21:28:08 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.13/0.35  % (23162)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.37  % (23169)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)
% 0.13/0.37  % (23167)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.13/0.37  % (23163)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.13/0.37  TRYING [1]
% 0.13/0.37  % (23168)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.13/0.37  TRYING [2]
% 0.13/0.37  TRYING [1]
% 0.13/0.37  TRYING [2]
% 0.13/0.37  TRYING [3]
% 0.13/0.37  % (23165)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)
% 0.13/0.38  TRYING [3]
% 0.13/0.38  % (23164)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.13/0.38  TRYING [1]
% 0.13/0.38  % (23166)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.13/0.38  TRYING [2]
% 0.13/0.38  TRYING [1]
% 0.13/0.38  TRYING [2]
% 0.13/0.38  TRYING [3]
% 0.13/0.38  TRYING [3]
% 0.13/0.39  TRYING [4]
% 0.13/0.39  TRYING [4]
% 0.13/0.40  TRYING [4]
% 0.13/0.40  TRYING [4]
% 0.21/0.42  TRYING [5]
% 0.21/0.42  TRYING [5]
% 0.21/0.44  TRYING [5]
% 0.21/0.44  TRYING [5]
% 0.21/0.48  TRYING [6]
% 0.21/0.49  TRYING [6]
% 0.21/0.50  TRYING [6]
% 0.21/0.54  TRYING [6]
% 1.82/0.62  TRYING [7]
% 2.07/0.66  TRYING [7]
% 2.07/0.68  TRYING [7]
% 2.63/0.73  TRYING [7]
% 4.72/1.07  TRYING [8]
% 5.98/1.21  TRYING [8]
% 6.26/1.25  TRYING [8]
% 7.17/1.37  TRYING [8]
% 15.15/2.52  TRYING [9]
% 15.15/2.57  TRYING [9]
% 19.30/3.09  TRYING [9]
% 20.06/3.24  TRYING [9]
% 44.64/6.71  TRYING [10]
% 51.22/7.65  TRYING [10]
% 51.79/7.72  TRYING [10]
% 58.52/8.77  TRYING [10]
% 102.06/14.93  % (23165)First to succeed.
% 102.06/14.93  % (23165)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-23162"
% 102.06/14.95  % (23165)Refutation found. Thanks to Tanya!
% 102.06/14.95  % SZS status Unsatisfiable for theBenchmark
% 102.06/14.95  % SZS output start Proof for theBenchmark
% See solution above
% 102.06/14.95  % (23165)------------------------------
% 102.06/14.95  % (23165)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 102.06/14.95  % (23165)Termination reason: Refutation
% 102.06/14.95  
% 102.06/14.95  % (23165)Memory used [KB]: 104727
% 102.06/14.95  % (23165)Time elapsed: 14.560 s
% 102.06/14.95  % (23165)Instructions burned: 64563 (million)
% 102.06/14.95  % (23162)Success in time 14.528 s
%------------------------------------------------------------------------------