TSTP Solution File: FLD015-3 by Vampire-SAT---4.8

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : FLD015-3 : 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 : n003.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 05:07:53 EDT 2024

% Result   : Unsatisfiable 0.15s 0.44s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   47 (  10 unt;   0 def)
%            Number of atoms       :  106 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  119 (  60   ~;  52   |;   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    :    4 (   4 usr;   3 con; 0-1 aty)
%            Number of variables   :   65 (  65   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f4587,plain,
    $false,
    inference(avatar_sat_refutation,[],[f98,f100,f1529,f1546,f4566,f4586]) ).

fof(f4586,plain,
    spl9_55,
    inference(avatar_contradiction_clause,[],[f4585]) ).

fof(f4585,plain,
    ( $false
    | spl9_55 ),
    inference(resolution,[],[f4568,f14]) ).

fof(f14,axiom,
    defined(additive_identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_additive_identity) ).

fof(f4568,plain,
    ( ~ defined(additive_identity)
    | spl9_55 ),
    inference(resolution,[],[f4565,f3]) ).

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

fof(f4565,plain,
    ( ~ sum(additive_identity,additive_identity,additive_identity)
    | spl9_55 ),
    inference(avatar_component_clause,[],[f4563]) ).

fof(f4563,plain,
    ( spl9_55
  <=> sum(additive_identity,additive_identity,additive_identity) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_55])]) ).

fof(f4566,plain,
    ( ~ spl9_6
    | ~ spl9_55
    | spl9_31 ),
    inference(avatar_split_clause,[],[f4550,f1543,f4563,f89]) ).

fof(f89,plain,
    ( spl9_6
  <=> defined(a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_6])]) ).

fof(f1543,plain,
    ( spl9_31
  <=> sum(a,additive_inverse(b),additive_identity) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_31])]) ).

fof(f4550,plain,
    ( ~ sum(additive_identity,additive_identity,additive_identity)
    | ~ defined(a)
    | spl9_31 ),
    inference(resolution,[],[f1780,f4]) ).

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

fof(f1780,plain,
    ( ! [X0] :
        ( ~ sum(additive_inverse(a),a,X0)
        | ~ sum(additive_identity,X0,additive_identity) )
    | spl9_31 ),
    inference(resolution,[],[f306,f1551]) ).

fof(f1551,plain,
    ( ~ sum(additive_inverse(b),a,additive_identity)
    | spl9_31 ),
    inference(resolution,[],[f1545,f5]) ).

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

fof(f1545,plain,
    ( ~ sum(a,additive_inverse(b),additive_identity)
    | spl9_31 ),
    inference(avatar_component_clause,[],[f1543]) ).

fof(f306,plain,
    ! [X2,X0,X1] :
      ( sum(additive_inverse(b),X0,X2)
      | ~ sum(additive_inverse(a),X0,X1)
      | ~ sum(additive_identity,X1,X2) ),
    inference(resolution,[],[f176,f39]) ).

fof(f39,plain,
    ! [X2,X0,X1,X4,X5] :
      ( sP4(X5,X4,X0,X1)
      | sum(X4,X5,X2)
      | ~ sum(X0,X1,X2) ),
    inference(cnf_transformation,[],[f39_D]) ).

fof(f39_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(f176,plain,
    ! [X0,X1] :
      ( ~ sP4(X0,additive_inverse(b),additive_identity,X1)
      | ~ sum(additive_inverse(a),X0,X1) ),
    inference(resolution,[],[f40,f29]) ).

fof(f29,axiom,
    sum(additive_identity,additive_inverse(a),additive_inverse(b)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_3) ).

fof(f40,plain,
    ! [X3,X0,X1,X4,X5] :
      ( ~ sum(X3,X5,X1)
      | ~ sum(X0,X3,X4)
      | ~ sP4(X5,X4,X0,X1) ),
    inference(general_splitting,[],[f2,f39_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/sandbox/benchmark/theBenchmark.p',associativity_addition_2) ).

fof(f1546,plain,
    ( ~ spl9_5
    | ~ spl9_31
    | ~ spl9_30 ),
    inference(avatar_split_clause,[],[f1536,f1527,f1543,f85]) ).

fof(f85,plain,
    ( spl9_5
  <=> defined(b) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_5])]) ).

fof(f1527,plain,
    ( spl9_30
  <=> ! [X0] :
        ( ~ sum(a,X0,additive_identity)
        | ~ sum(X0,b,additive_identity) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_30])]) ).

fof(f1536,plain,
    ( ~ sum(a,additive_inverse(b),additive_identity)
    | ~ defined(b)
    | ~ spl9_30 ),
    inference(resolution,[],[f1528,f4]) ).

fof(f1528,plain,
    ( ! [X0] :
        ( ~ sum(a,X0,additive_identity)
        | ~ sum(X0,b,additive_identity) )
    | ~ spl9_30 ),
    inference(avatar_component_clause,[],[f1527]) ).

fof(f1529,plain,
    ( ~ spl9_5
    | spl9_30 ),
    inference(avatar_split_clause,[],[f1264,f1527,f85]) ).

fof(f1264,plain,
    ! [X0] :
      ( ~ sum(a,X0,additive_identity)
      | ~ sum(X0,b,additive_identity)
      | ~ defined(b) ),
    inference(resolution,[],[f827,f3]) ).

fof(f827,plain,
    ! [X2,X0,X1] :
      ( ~ sum(a,X0,X1)
      | ~ sum(X0,X2,additive_identity)
      | ~ sum(X1,X2,b) ),
    inference(resolution,[],[f162,f49]) ).

fof(f49,plain,
    ~ sum(a,additive_identity,b),
    inference(resolution,[],[f5,f30]) ).

fof(f30,axiom,
    ~ sum(additive_identity,a,b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_4) ).

fof(f162,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( sum(X3,X2,X5)
      | ~ sum(X3,X0,X4)
      | ~ sum(X0,X1,X2)
      | ~ sum(X4,X1,X5) ),
    inference(resolution,[],[f38,f37]) ).

fof(f37,plain,
    ! [X2,X0,X1,X4,X5] :
      ( sP3(X4,X0,X5,X1)
      | sum(X0,X1,X2)
      | ~ sum(X4,X5,X2) ),
    inference(cnf_transformation,[],[f37_D]) ).

fof(f37_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(f38,plain,
    ! [X3,X0,X1,X4,X5] :
      ( ~ sum(X3,X5,X1)
      | ~ sum(X0,X3,X4)
      | ~ sP3(X4,X0,X5,X1) ),
    inference(general_splitting,[],[f1,f37_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/sandbox/benchmark/theBenchmark.p',associativity_addition_1) ).

fof(f100,plain,
    spl9_6,
    inference(avatar_contradiction_clause,[],[f99]) ).

fof(f99,plain,
    ( $false
    | spl9_6 ),
    inference(resolution,[],[f91,f27]) ).

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

fof(f91,plain,
    ( ~ defined(a)
    | spl9_6 ),
    inference(avatar_component_clause,[],[f89]) ).

fof(f98,plain,
    spl9_5,
    inference(avatar_contradiction_clause,[],[f97]) ).

fof(f97,plain,
    ( $false
    | spl9_5 ),
    inference(resolution,[],[f87,f28]) ).

fof(f28,axiom,
    defined(b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).

fof(f87,plain,
    ( ~ defined(b)
    | spl9_5 ),
    inference(avatar_component_clause,[],[f85]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem    : FLD015-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.11  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.31  % Computer : n003.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit   : 300
% 0.10/0.31  % WCLimit    : 300
% 0.10/0.31  % DateTime   : Fri May  3 19:45:23 EDT 2024
% 0.10/0.31  % CPUTime    : 
% 0.10/0.31  % (3041)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.33  % (3048)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.15/0.33  % (3046)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.15/0.33  % (3049)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)
% 0.15/0.33  % (3043)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.15/0.33  % (3044)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.33  % (3045)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)
% 0.15/0.33  % (3047)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.15/0.33  TRYING [1]
% 0.15/0.33  TRYING [1]
% 0.15/0.33  TRYING [2]
% 0.15/0.33  TRYING [2]
% 0.15/0.33  TRYING [1]
% 0.15/0.33  TRYING [1]
% 0.15/0.33  TRYING [2]
% 0.15/0.33  TRYING [2]
% 0.15/0.33  TRYING [3]
% 0.15/0.33  TRYING [3]
% 0.15/0.33  TRYING [3]
% 0.15/0.33  TRYING [3]
% 0.15/0.34  TRYING [4]
% 0.15/0.34  TRYING [4]
% 0.15/0.34  TRYING [4]
% 0.15/0.34  TRYING [4]
% 0.15/0.37  TRYING [5]
% 0.15/0.37  TRYING [5]
% 0.15/0.37  TRYING [5]
% 0.15/0.37  TRYING [5]
% 0.15/0.44  % (3045)First to succeed.
% 0.15/0.44  TRYING [6]
% 0.15/0.44  % (3045)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3041"
% 0.15/0.44  % (3045)Refutation found. Thanks to Tanya!
% 0.15/0.44  % SZS status Unsatisfiable for theBenchmark
% 0.15/0.44  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.44  % (3045)------------------------------
% 0.15/0.44  % (3045)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.44  % (3045)Termination reason: Refutation
% 0.15/0.44  
% 0.15/0.44  % (3045)Memory used [KB]: 2560
% 0.15/0.44  % (3045)Time elapsed: 0.115 s
% 0.15/0.44  % (3045)Instructions burned: 236 (million)
% 0.15/0.44  % (3041)Success in time 0.126 s
%------------------------------------------------------------------------------