TSTP Solution File: FLD065-1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : FLD065-1 : 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 : n007.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 : Tue Apr 30 11:06:34 EDT 2024

% Result   : Unsatisfiable 41.67s 6.34s
% Output   : Refutation 41.67s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   81 (   9 unt;   0 def)
%            Number of atoms       :  192 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  208 (  97   ~; 103   |;   0   &)
%                                         (   8 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   12 (  11 usr;   9 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   57 (  57   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f134145,plain,
    $false,
    inference(avatar_sat_refutation,[],[f75,f92,f117,f2049,f32070,f32090,f32113,f132423,f134142]) ).

fof(f134142,plain,
    ( ~ spl0_3
    | spl0_9 ),
    inference(avatar_contradiction_clause,[],[f134141]) ).

fof(f134141,plain,
    ( $false
    | ~ spl0_3
    | spl0_9 ),
    inference(subsumption_resolution,[],[f134104,f145]) ).

fof(f145,plain,
    less_or_equal(a,additive_identity),
    inference(subsumption_resolution,[],[f136,f30]) ).

fof(f30,axiom,
    ~ less_or_equal(additive_identity,a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_less_or_equal_3) ).

fof(f136,plain,
    ( less_or_equal(additive_identity,a)
    | less_or_equal(a,additive_identity) ),
    inference(resolution,[],[f99,f11]) ).

fof(f11,axiom,
    defined(additive_identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_identity) ).

fof(f99,plain,
    ! [X0] :
      ( ~ defined(X0)
      | less_or_equal(X0,a)
      | less_or_equal(a,X0) ),
    inference(resolution,[],[f18,f28]) ).

fof(f28,axiom,
    defined(a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).

fof(f18,axiom,
    ! [X0,X1] :
      ( ~ defined(X0)
      | ~ defined(X1)
      | less_or_equal(X1,X0)
      | less_or_equal(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality_of_order_relation) ).

fof(f134104,plain,
    ( ~ less_or_equal(a,additive_identity)
    | ~ spl0_3
    | spl0_9 ),
    inference(resolution,[],[f24669,f116]) ).

fof(f116,plain,
    ( ~ less_or_equal(additive_identity,add(additive_identity,additive_inverse(a)))
    | spl0_9 ),
    inference(avatar_component_clause,[],[f114]) ).

fof(f114,plain,
    ( spl0_9
  <=> less_or_equal(additive_identity,add(additive_identity,additive_inverse(a))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f24669,plain,
    ( ! [X0] :
        ( less_or_equal(additive_identity,add(X0,additive_inverse(a)))
        | ~ less_or_equal(a,X0) )
    | ~ spl0_3 ),
    inference(subsumption_resolution,[],[f24654,f28]) ).

fof(f24654,plain,
    ( ! [X0] :
        ( ~ less_or_equal(a,X0)
        | less_or_equal(additive_identity,add(X0,additive_inverse(a)))
        | ~ defined(a) )
    | ~ spl0_3 ),
    inference(resolution,[],[f373,f3]) ).

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

fof(f373,plain,
    ( ! [X2,X0,X1] :
        ( ~ equalish(add(X0,additive_inverse(a)),X2)
        | ~ less_or_equal(X0,X1)
        | less_or_equal(X2,add(X1,additive_inverse(a))) )
    | ~ spl0_3 ),
    inference(resolution,[],[f132,f69]) ).

fof(f69,plain,
    ( defined(additive_inverse(a))
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f68]) ).

fof(f68,plain,
    ( spl0_3
  <=> defined(additive_inverse(a)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f132,plain,
    ! [X2,X3,X0,X1] :
      ( ~ defined(X2)
      | ~ less_or_equal(X0,X1)
      | ~ equalish(add(X0,X2),X3)
      | less_or_equal(X3,add(X1,X2)) ),
    inference(resolution,[],[f19,f26]) ).

fof(f26,axiom,
    ! [X2,X0,X1] :
      ( ~ less_or_equal(X0,X2)
      | ~ equalish(X0,X1)
      | less_or_equal(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatibility_of_equality_and_order_relation) ).

fof(f19,axiom,
    ! [X2,X0,X1] :
      ( less_or_equal(add(X0,X2),add(X1,X2))
      | ~ less_or_equal(X0,X1)
      | ~ defined(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatibility_of_order_relation_and_addition) ).

fof(f132423,plain,
    ( spl0_90
    | ~ spl0_2964 ),
    inference(avatar_contradiction_clause,[],[f132422]) ).

fof(f132422,plain,
    ( $false
    | spl0_90
    | ~ spl0_2964 ),
    inference(subsumption_resolution,[],[f132390,f926]) ).

fof(f926,plain,
    ( ~ equalish(additive_identity,a)
    | spl0_90 ),
    inference(avatar_component_clause,[],[f924]) ).

fof(f924,plain,
    ( spl0_90
  <=> equalish(additive_identity,a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).

fof(f132390,plain,
    ( equalish(additive_identity,a)
    | ~ spl0_2964 ),
    inference(resolution,[],[f32089,f896]) ).

fof(f896,plain,
    ! [X0] :
      ( ~ equalish(add(a,additive_inverse(a)),X0)
      | equalish(additive_identity,X0) ),
    inference(resolution,[],[f58,f28]) ).

fof(f58,plain,
    ! [X0,X1] :
      ( ~ defined(X0)
      | equalish(additive_identity,X1)
      | ~ equalish(add(X0,additive_inverse(X0)),X1) ),
    inference(resolution,[],[f23,f35]) ).

fof(f35,plain,
    ! [X0] :
      ( equalish(additive_identity,add(X0,additive_inverse(X0)))
      | ~ defined(X0) ),
    inference(resolution,[],[f3,f22]) ).

fof(f22,axiom,
    ! [X0,X1] :
      ( ~ equalish(X1,X0)
      | equalish(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_equality) ).

fof(f23,axiom,
    ! [X2,X0,X1] :
      ( ~ equalish(X0,X1)
      | ~ equalish(X1,X2)
      | equalish(X0,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_equality) ).

fof(f32089,plain,
    ( equalish(add(a,additive_inverse(a)),a)
    | ~ spl0_2964 ),
    inference(avatar_component_clause,[],[f32087]) ).

fof(f32087,plain,
    ( spl0_2964
  <=> equalish(add(a,additive_inverse(a)),a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2964])]) ).

fof(f32113,plain,
    ( spl0_1
    | ~ spl0_3
    | ~ spl0_8 ),
    inference(avatar_split_clause,[],[f6874,f110,f68,f44]) ).

fof(f44,plain,
    ( spl0_1
  <=> equalish(additive_inverse(a),additive_identity) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f110,plain,
    ( spl0_8
  <=> equalish(add(additive_identity,additive_inverse(a)),additive_identity) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f6874,plain,
    ( equalish(additive_inverse(a),additive_identity)
    | ~ spl0_3
    | ~ spl0_8 ),
    inference(resolution,[],[f575,f112]) ).

fof(f112,plain,
    ( equalish(add(additive_identity,additive_inverse(a)),additive_identity)
    | ~ spl0_8 ),
    inference(avatar_component_clause,[],[f110]) ).

fof(f575,plain,
    ( ! [X0] :
        ( ~ equalish(add(additive_identity,additive_inverse(a)),X0)
        | equalish(additive_inverse(a),X0) )
    | ~ spl0_3 ),
    inference(resolution,[],[f57,f69]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( ~ defined(X0)
      | equalish(X0,X1)
      | ~ equalish(add(additive_identity,X0),X1) ),
    inference(resolution,[],[f23,f32]) ).

fof(f32,plain,
    ! [X0] :
      ( equalish(X0,add(additive_identity,X0))
      | ~ defined(X0) ),
    inference(resolution,[],[f2,f22]) ).

fof(f2,axiom,
    ! [X0] :
      ( equalish(add(additive_identity,X0),X0)
      | ~ defined(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_identity_addition) ).

fof(f32090,plain,
    ( ~ spl0_1
    | spl0_2964
    | ~ spl0_3 ),
    inference(avatar_split_clause,[],[f20385,f68,f32087,f44]) ).

fof(f20385,plain,
    ( equalish(add(a,additive_inverse(a)),a)
    | ~ equalish(additive_inverse(a),additive_identity)
    | ~ spl0_3 ),
    inference(subsumption_resolution,[],[f20362,f28]) ).

fof(f20362,plain,
    ( ~ defined(a)
    | equalish(add(a,additive_inverse(a)),a)
    | ~ equalish(additive_inverse(a),additive_identity)
    | ~ spl0_3 ),
    inference(resolution,[],[f337,f1239]) ).

fof(f1239,plain,
    ! [X0] :
      ( equalish(add(X0,a),a)
      | ~ equalish(X0,additive_identity) ),
    inference(subsumption_resolution,[],[f1224,f28]) ).

fof(f1224,plain,
    ! [X0] :
      ( ~ equalish(X0,additive_identity)
      | equalish(add(X0,a),a)
      | ~ defined(a) ),
    inference(resolution,[],[f397,f2]) ).

fof(f397,plain,
    ! [X2,X0,X1] :
      ( ~ equalish(add(X1,a),X2)
      | ~ equalish(X0,X1)
      | equalish(add(X0,a),X2) ),
    inference(resolution,[],[f182,f28]) ).

fof(f182,plain,
    ! [X2,X3,X0,X1] :
      ( ~ defined(X2)
      | ~ equalish(X0,X1)
      | ~ equalish(add(X1,X2),X3)
      | equalish(add(X0,X2),X3) ),
    inference(resolution,[],[f24,f23]) ).

fof(f24,axiom,
    ! [X2,X0,X1] :
      ( equalish(add(X0,X2),add(X1,X2))
      | ~ equalish(X0,X1)
      | ~ defined(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatibility_of_equality_and_addition) ).

fof(f337,plain,
    ( ! [X0,X1] :
        ( ~ equalish(add(additive_inverse(a),X0),X1)
        | ~ defined(X0)
        | equalish(add(X0,additive_inverse(a)),X1) )
    | ~ spl0_3 ),
    inference(resolution,[],[f101,f69]) ).

fof(f101,plain,
    ! [X2,X0,X1] :
      ( ~ defined(X1)
      | ~ defined(X0)
      | ~ equalish(add(X1,X0),X2)
      | equalish(add(X0,X1),X2) ),
    inference(resolution,[],[f4,f23]) ).

fof(f4,axiom,
    ! [X0,X1] :
      ( equalish(add(X0,X1),add(X1,X0))
      | ~ defined(X0)
      | ~ defined(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_addition) ).

fof(f32070,plain,
    ( ~ spl0_90
    | spl0_183 ),
    inference(avatar_contradiction_clause,[],[f32069]) ).

fof(f32069,plain,
    ( $false
    | ~ spl0_90
    | spl0_183 ),
    inference(subsumption_resolution,[],[f32053,f1999]) ).

fof(f1999,plain,
    ( ~ equalish(a,additive_identity)
    | spl0_183 ),
    inference(avatar_component_clause,[],[f1998]) ).

fof(f1998,plain,
    ( spl0_183
  <=> equalish(a,additive_identity) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).

fof(f32053,plain,
    ( equalish(a,additive_identity)
    | ~ spl0_90 ),
    inference(resolution,[],[f925,f22]) ).

fof(f925,plain,
    ( equalish(additive_identity,a)
    | ~ spl0_90 ),
    inference(avatar_component_clause,[],[f924]) ).

fof(f2049,plain,
    ~ spl0_183,
    inference(avatar_contradiction_clause,[],[f2048]) ).

fof(f2048,plain,
    ( $false
    | ~ spl0_183 ),
    inference(subsumption_resolution,[],[f2044,f30]) ).

fof(f2044,plain,
    ( less_or_equal(additive_identity,a)
    | ~ spl0_183 ),
    inference(resolution,[],[f2000,f195]) ).

fof(f195,plain,
    ! [X0] :
      ( ~ equalish(a,X0)
      | less_or_equal(X0,a) ),
    inference(resolution,[],[f144,f26]) ).

fof(f144,plain,
    less_or_equal(a,a),
    inference(duplicate_literal_removal,[],[f143]) ).

fof(f143,plain,
    ( less_or_equal(a,a)
    | less_or_equal(a,a) ),
    inference(resolution,[],[f99,f28]) ).

fof(f2000,plain,
    ( equalish(a,additive_identity)
    | ~ spl0_183 ),
    inference(avatar_component_clause,[],[f1998]) ).

fof(f117,plain,
    ( spl0_8
    | ~ spl0_9
    | ~ spl0_4 ),
    inference(avatar_split_clause,[],[f108,f72,f114,f110]) ).

fof(f72,plain,
    ( spl0_4
  <=> less_or_equal(add(additive_identity,additive_inverse(a)),additive_identity) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f108,plain,
    ( ~ less_or_equal(additive_identity,add(additive_identity,additive_inverse(a)))
    | equalish(add(additive_identity,additive_inverse(a)),additive_identity)
    | ~ spl0_4 ),
    inference(resolution,[],[f74,f16]) ).

fof(f16,axiom,
    ! [X0,X1] :
      ( ~ less_or_equal(X0,X1)
      | ~ less_or_equal(X1,X0)
      | equalish(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_of_order_relation) ).

fof(f74,plain,
    ( less_or_equal(add(additive_identity,additive_inverse(a)),additive_identity)
    | ~ spl0_4 ),
    inference(avatar_component_clause,[],[f72]) ).

fof(f92,plain,
    spl0_3,
    inference(avatar_contradiction_clause,[],[f91]) ).

fof(f91,plain,
    ( $false
    | spl0_3 ),
    inference(subsumption_resolution,[],[f90,f28]) ).

fof(f90,plain,
    ( ~ defined(a)
    | spl0_3 ),
    inference(resolution,[],[f70,f12]) ).

fof(f12,axiom,
    ! [X0] :
      ( defined(additive_inverse(X0))
      | ~ defined(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_inverse) ).

fof(f70,plain,
    ( ~ defined(additive_inverse(a))
    | spl0_3 ),
    inference(avatar_component_clause,[],[f68]) ).

fof(f75,plain,
    ( ~ spl0_3
    | spl0_4 ),
    inference(avatar_split_clause,[],[f64,f72,f68]) ).

fof(f64,plain,
    ( less_or_equal(add(additive_identity,additive_inverse(a)),additive_identity)
    | ~ defined(additive_inverse(a)) ),
    inference(resolution,[],[f62,f32]) ).

fof(f62,plain,
    ! [X0] :
      ( ~ equalish(additive_inverse(a),X0)
      | less_or_equal(X0,additive_identity) ),
    inference(resolution,[],[f26,f29]) ).

fof(f29,axiom,
    less_or_equal(additive_inverse(a),additive_identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal_2) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13  % Problem    : FLD065-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.10/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36  % Computer : n007.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   : Tue Apr 30 03:16:17 EDT 2024
% 0.14/0.37  % CPUTime    : 
% 0.14/0.37  % (1110)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.38  % (1115)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.22/0.38  % (1117)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  % (1114)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  % (1111)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.22/0.38  % (1113)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  % (1116)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.22/0.38  % (1112)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.22/0.39  TRYING [1]
% 0.22/0.39  TRYING [1]
% 0.22/0.39  TRYING [2]
% 0.22/0.39  TRYING [2]
% 0.22/0.39  TRYING [1]
% 0.22/0.39  TRYING [1]
% 0.22/0.39  TRYING [2]
% 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]
% 0.22/0.43  TRYING [5]
% 0.22/0.43  TRYING [5]
% 0.22/0.43  TRYING [5]
% 0.22/0.45  TRYING [5]
% 0.22/0.50  TRYING [6]
% 0.22/0.52  TRYING [6]
% 0.22/0.53  TRYING [6]
% 0.22/0.57  TRYING [6]
% 0.22/0.75  TRYING [7]
% 0.22/0.75  TRYING [7]
% 0.22/0.79  TRYING [7]
% 3.96/0.96  TRYING [7]
% 6.50/1.37  TRYING [8]
% 7.35/1.44  TRYING [8]
% 7.61/1.45  TRYING [8]
% 11.30/1.99  TRYING [8]
% 13.89/2.42  TRYING [9]
% 15.46/2.57  TRYING [9]
% 15.46/2.58  TRYING [9]
% 25.01/3.97  TRYING [9]
% 26.98/4.23  TRYING [10]
% 27.76/4.35  TRYING [10]
% 29.35/4.59  TRYING [10]
% 41.47/6.30  % (1116)First to succeed.
% 41.67/6.34  % (1116)Refutation found. Thanks to Tanya!
% 41.67/6.34  % SZS status Unsatisfiable for theBenchmark
% 41.67/6.34  % SZS output start Proof for theBenchmark
% See solution above
% 41.67/6.34  % (1116)------------------------------
% 41.67/6.34  % (1116)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 41.67/6.34  % (1116)Termination reason: Refutation
% 41.67/6.34  
% 41.67/6.34  % (1116)Memory used [KB]: 48551
% 41.67/6.34  % (1116)Time elapsed: 5.932 s
% 41.67/6.34  % (1116)Instructions burned: 11396 (million)
% 41.67/6.34  % (1116)------------------------------
% 41.67/6.34  % (1116)------------------------------
% 41.67/6.34  % (1110)Success in time 5.922 s
%------------------------------------------------------------------------------