TSTP Solution File: FLD070-3 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : FLD070-3 : 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 : n027.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 05:08:10 EDT 2024

% Result   : Unsatisfiable 0.14s 0.41s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   26
% Syntax   : Number of formulae    :   74 (  11 unt;   0 def)
%            Number of atoms       :  175 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  196 (  95   ~;  89   |;   0   &)
%                                         (  12 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   16 (  15 usr;  12 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   47 (  47   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1618,plain,
    $false,
    inference(avatar_sat_refutation,[],[f241,f243,f514,f582,f620,f625,f1061,f1109,f1150,f1169,f1561,f1617]) ).

fof(f1617,plain,
    ( ~ spl9_11
    | ~ spl9_19
    | spl9_42 ),
    inference(avatar_split_clause,[],[f1612,f1558,f486,f232]) ).

fof(f232,plain,
    ( spl9_11
  <=> defined(b) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_11])]) ).

fof(f486,plain,
    ( spl9_19
  <=> less_or_equal(additive_identity,b) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_19])]) ).

fof(f1558,plain,
    ( spl9_42
  <=> sP0(additive_inverse(b),additive_identity,additive_identity) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_42])]) ).

fof(f1612,plain,
    ( ~ less_or_equal(additive_identity,b)
    | ~ defined(b)
    | spl9_42 ),
    inference(resolution,[],[f1585,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(f1585,plain,
    ( ! [X0] :
        ( ~ sum(additive_inverse(b),X0,additive_identity)
        | ~ less_or_equal(additive_identity,X0) )
    | spl9_42 ),
    inference(resolution,[],[f1578,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(f1578,plain,
    ( ! [X0] :
        ( ~ sum(X0,additive_inverse(b),additive_identity)
        | ~ less_or_equal(additive_identity,X0) )
    | spl9_42 ),
    inference(resolution,[],[f1560,f32]) ).

fof(f32,plain,
    ! [X3,X0,X1,X5] :
      ( sP0(X5,X0,X1)
      | ~ sum(X3,X5,X1)
      | ~ less_or_equal(X0,X3) ),
    inference(cnf_transformation,[],[f32_D]) ).

fof(f32_D,plain,
    ! [X1,X0,X5] :
      ( ! [X3] :
          ( ~ sum(X3,X5,X1)
          | ~ less_or_equal(X0,X3) )
    <=> ~ sP0(X5,X0,X1) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP0])]) ).

fof(f1560,plain,
    ( ~ sP0(additive_inverse(b),additive_identity,additive_identity)
    | spl9_42 ),
    inference(avatar_component_clause,[],[f1558]) ).

fof(f1561,plain,
    ( ~ spl9_28
    | ~ spl9_42
    | spl9_24
    | ~ spl9_30 ),
    inference(avatar_split_clause,[],[f1551,f1166,f617,f1558,f1139]) ).

fof(f1139,plain,
    ( spl9_28
  <=> defined(additive_inverse(b)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_28])]) ).

fof(f617,plain,
    ( spl9_24
  <=> less_or_equal(a,additive_identity) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_24])]) ).

fof(f1166,plain,
    ( spl9_30
  <=> less_or_equal(a,additive_inverse(b)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_30])]) ).

fof(f1551,plain,
    ( ~ sP0(additive_inverse(b),additive_identity,additive_identity)
    | ~ defined(additive_inverse(b))
    | spl9_24
    | ~ spl9_30 ),
    inference(resolution,[],[f1186,f3]) ).

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

fof(f1186,plain,
    ( ! [X0,X1] :
        ( ~ sum(X0,X1,additive_inverse(b))
        | ~ sP0(X1,X0,additive_identity) )
    | spl9_24
    | ~ spl9_30 ),
    inference(resolution,[],[f1171,f33]) ).

fof(f33,plain,
    ! [X0,X1,X4,X5] :
      ( less_or_equal(X4,X1)
      | ~ sum(X0,X5,X4)
      | ~ sP0(X5,X0,X1) ),
    inference(general_splitting,[],[f24,f32_D]) ).

fof(f24,axiom,
    ! [X3,X0,X1,X4,X5] :
      ( ~ less_or_equal(X0,X3)
      | less_or_equal(X4,X1)
      | ~ sum(X3,X5,X1)
      | ~ sum(X0,X5,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatibility_of_order_relation_and_addition) ).

fof(f1171,plain,
    ( ~ less_or_equal(additive_inverse(b),additive_identity)
    | spl9_24
    | ~ spl9_30 ),
    inference(resolution,[],[f1168,f629]) ).

fof(f629,plain,
    ( ! [X0] :
        ( ~ less_or_equal(a,X0)
        | ~ less_or_equal(X0,additive_identity) )
    | spl9_24 ),
    inference(resolution,[],[f619,f22]) ).

fof(f22,axiom,
    ! [X3,X0,X5] :
      ( less_or_equal(X0,X5)
      | ~ less_or_equal(X0,X3)
      | ~ less_or_equal(X3,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_order_relation) ).

fof(f619,plain,
    ( ~ less_or_equal(a,additive_identity)
    | spl9_24 ),
    inference(avatar_component_clause,[],[f617]) ).

fof(f1168,plain,
    ( less_or_equal(a,additive_inverse(b))
    | ~ spl9_30 ),
    inference(avatar_component_clause,[],[f1166]) ).

fof(f1169,plain,
    ( spl9_30
    | ~ spl9_28
    | ~ spl9_12
    | spl9_27 ),
    inference(avatar_split_clause,[],[f1111,f1106,f236,f1139,f1166]) ).

fof(f236,plain,
    ( spl9_12
  <=> defined(a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_12])]) ).

fof(f1106,plain,
    ( spl9_27
  <=> less_or_equal(additive_inverse(b),a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_27])]) ).

fof(f1111,plain,
    ( ~ defined(a)
    | ~ defined(additive_inverse(b))
    | less_or_equal(a,additive_inverse(b))
    | spl9_27 ),
    inference(resolution,[],[f1108,f23]) ).

fof(f23,axiom,
    ! [X3,X0] :
      ( less_or_equal(X3,X0)
      | ~ defined(X0)
      | ~ defined(X3)
      | less_or_equal(X0,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality_of_order_relation) ).

fof(f1108,plain,
    ( ~ less_or_equal(additive_inverse(b),a)
    | spl9_27 ),
    inference(avatar_component_clause,[],[f1106]) ).

fof(f1150,plain,
    spl9_28,
    inference(avatar_contradiction_clause,[],[f1149]) ).

fof(f1149,plain,
    ( $false
    | spl9_28 ),
    inference(resolution,[],[f1148,f28]) ).

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

fof(f1148,plain,
    ( ~ defined(b)
    | spl9_28 ),
    inference(resolution,[],[f1141,f15]) ).

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

fof(f1141,plain,
    ( ~ defined(additive_inverse(b))
    | spl9_28 ),
    inference(avatar_component_clause,[],[f1139]) ).

fof(f1109,plain,
    ( ~ spl9_11
    | ~ spl9_27
    | ~ spl9_26 ),
    inference(avatar_split_clause,[],[f1082,f1059,f1106,f232]) ).

fof(f1059,plain,
    ( spl9_26
  <=> ! [X0] :
        ( ~ sum(X0,b,additive_identity)
        | ~ less_or_equal(X0,a) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_26])]) ).

fof(f1082,plain,
    ( ~ less_or_equal(additive_inverse(b),a)
    | ~ defined(b)
    | ~ spl9_26 ),
    inference(resolution,[],[f1060,f4]) ).

fof(f1060,plain,
    ( ! [X0] :
        ( ~ sum(X0,b,additive_identity)
        | ~ less_or_equal(X0,a) )
    | ~ spl9_26 ),
    inference(avatar_component_clause,[],[f1059]) ).

fof(f1061,plain,
    ( ~ spl9_11
    | ~ spl9_12
    | spl9_26 ),
    inference(avatar_split_clause,[],[f388,f1059,f236,f232]) ).

fof(f388,plain,
    ! [X0] :
      ( ~ sum(X0,b,additive_identity)
      | ~ less_or_equal(X0,a)
      | ~ defined(a)
      | ~ defined(b) ),
    inference(resolution,[],[f190,f19]) ).

fof(f19,axiom,
    ! [X3,X0] :
      ( sum(X0,X3,add(X0,X3))
      | ~ defined(X0)
      | ~ defined(X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality_of_addition) ).

fof(f190,plain,
    ! [X2,X0,X1] :
      ( ~ sum(X0,X1,additive_identity)
      | ~ sum(X2,X1,add(a,b))
      | ~ less_or_equal(X0,X2) ),
    inference(resolution,[],[f103,f32]) ).

fof(f103,plain,
    ! [X0,X1] :
      ( ~ sP0(X1,X0,add(a,b))
      | ~ sum(X0,X1,additive_identity) ),
    inference(resolution,[],[f33,f31]) ).

fof(f31,axiom,
    ~ less_or_equal(additive_identity,add(a,b)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_less_or_equal_5) ).

fof(f625,plain,
    spl9_23,
    inference(avatar_contradiction_clause,[],[f621]) ).

fof(f621,plain,
    ( $false
    | spl9_23 ),
    inference(resolution,[],[f615,f29]) ).

fof(f29,axiom,
    less_or_equal(additive_identity,a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_3) ).

fof(f615,plain,
    ( ~ less_or_equal(additive_identity,a)
    | spl9_23 ),
    inference(avatar_component_clause,[],[f613]) ).

fof(f613,plain,
    ( spl9_23
  <=> less_or_equal(additive_identity,a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_23])]) ).

fof(f620,plain,
    ( ~ spl9_23
    | ~ spl9_24
    | spl9_21 ),
    inference(avatar_split_clause,[],[f585,f579,f617,f613]) ).

fof(f579,plain,
    ( spl9_21
  <=> sum(additive_identity,a,additive_identity) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_21])]) ).

fof(f585,plain,
    ( ~ less_or_equal(a,additive_identity)
    | ~ less_or_equal(additive_identity,a)
    | spl9_21 ),
    inference(resolution,[],[f581,f21]) ).

fof(f21,axiom,
    ! [X3,X0] :
      ( sum(additive_identity,X0,X3)
      | ~ less_or_equal(X0,X3)
      | ~ less_or_equal(X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_of_order_relation) ).

fof(f581,plain,
    ( ~ sum(additive_identity,a,additive_identity)
    | spl9_21 ),
    inference(avatar_component_clause,[],[f579]) ).

fof(f582,plain,
    ( ~ spl9_11
    | ~ spl9_12
    | ~ spl9_21 ),
    inference(avatar_split_clause,[],[f575,f579,f236,f232]) ).

fof(f575,plain,
    ( ~ sum(additive_identity,a,additive_identity)
    | ~ defined(a)
    | ~ defined(b) ),
    inference(resolution,[],[f560,f19]) ).

fof(f560,plain,
    ! [X0] :
      ( ~ sum(X0,b,add(a,b))
      | ~ sum(additive_identity,X0,additive_identity) ),
    inference(resolution,[],[f394,f5]) ).

fof(f394,plain,
    ! [X0] :
      ( ~ sum(b,X0,add(a,b))
      | ~ sum(additive_identity,X0,additive_identity) ),
    inference(resolution,[],[f190,f30]) ).

fof(f30,axiom,
    less_or_equal(additive_identity,b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_4) ).

fof(f514,plain,
    spl9_19,
    inference(avatar_contradiction_clause,[],[f510]) ).

fof(f510,plain,
    ( $false
    | spl9_19 ),
    inference(resolution,[],[f488,f30]) ).

fof(f488,plain,
    ( ~ less_or_equal(additive_identity,b)
    | spl9_19 ),
    inference(avatar_component_clause,[],[f486]) ).

fof(f243,plain,
    spl9_12,
    inference(avatar_contradiction_clause,[],[f242]) ).

fof(f242,plain,
    ( $false
    | spl9_12 ),
    inference(resolution,[],[f238,f27]) ).

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

fof(f238,plain,
    ( ~ defined(a)
    | spl9_12 ),
    inference(avatar_component_clause,[],[f236]) ).

fof(f241,plain,
    spl9_11,
    inference(avatar_contradiction_clause,[],[f240]) ).

fof(f240,plain,
    ( $false
    | spl9_11 ),
    inference(resolution,[],[f234,f28]) ).

fof(f234,plain,
    ( ~ defined(b)
    | spl9_11 ),
    inference(avatar_component_clause,[],[f232]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem    : FLD070-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.13/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36  % Computer : n027.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 19:47:53 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.37  % (15938)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38  % (15940)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.38  % (15945)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)
% 0.14/0.38  % (15941)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  % (15943)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.14/0.38  % (15944)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.14/0.38  TRYING [1]
% 0.14/0.38  TRYING [1]
% 0.14/0.38  % (15942)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.14/0.38  TRYING [2]
% 0.14/0.38  TRYING [2]
% 0.14/0.39  TRYING [3]
% 0.14/0.39  TRYING [3]
% 0.14/0.39  TRYING [1]
% 0.14/0.39  TRYING [2]
% 0.14/0.39  TRYING [3]
% 0.14/0.39  % (15939)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.39  TRYING [1]
% 0.14/0.39  TRYING [4]
% 0.14/0.40  TRYING [2]
% 0.14/0.40  TRYING [4]
% 0.14/0.40  TRYING [3]
% 0.14/0.40  TRYING [4]
% 0.14/0.41  % (15941)First to succeed.
% 0.14/0.41  % (15941)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-15938"
% 0.14/0.41  % (15941)Refutation found. Thanks to Tanya!
% 0.14/0.41  % SZS status Unsatisfiable for theBenchmark
% 0.14/0.41  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.41  % (15941)------------------------------
% 0.14/0.41  % (15941)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.41  % (15941)Termination reason: Refutation
% 0.14/0.41  
% 0.14/0.41  % (15941)Memory used [KB]: 1377
% 0.14/0.41  % (15941)Time elapsed: 0.030 s
% 0.14/0.41  % (15941)Instructions burned: 60 (million)
% 0.14/0.41  % (15938)Success in time 0.043 s
%------------------------------------------------------------------------------