TSTP Solution File: GRP039-6 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GRP039-6 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n018.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 05:52:50 EDT 2024

% Result   : Unsatisfiable 0.16s 0.40s
% Output   : Refutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   58 (  10 unt;   0 def)
%            Number of atoms       :  131 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  128 (  55   ~;  69   |;   0   &)
%                                         (   4 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   7 usr;   5 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :   40 (  40   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f607,plain,
    $false,
    inference(avatar_sat_refutation,[],[f38,f130,f134,f253,f254,f606]) ).

fof(f606,plain,
    ( spl0_1
    | ~ spl0_2 ),
    inference(avatar_contradiction_clause,[],[f605]) ).

fof(f605,plain,
    ( $false
    | spl0_1
    | ~ spl0_2 ),
    inference(subsumption_resolution,[],[f604,f19]) ).

fof(f19,axiom,
    subgroup_member(b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_in_subgroup) ).

fof(f604,plain,
    ( ~ subgroup_member(b)
    | spl0_1
    | ~ spl0_2 ),
    inference(subsumption_resolution,[],[f603,f37]) ).

fof(f37,plain,
    ( subgroup_member(c)
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f35]) ).

fof(f35,plain,
    ( spl0_2
  <=> subgroup_member(c) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f603,plain,
    ( ~ subgroup_member(c)
    | ~ subgroup_member(b)
    | spl0_1 ),
    inference(subsumption_resolution,[],[f594,f33]) ).

fof(f33,plain,
    ( ~ subgroup_member(inverse(a))
    | spl0_1 ),
    inference(avatar_component_clause,[],[f31]) ).

fof(f31,plain,
    ( spl0_1
  <=> subgroup_member(inverse(a)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f594,plain,
    ( subgroup_member(inverse(a))
    | ~ subgroup_member(c)
    | ~ subgroup_member(b) ),
    inference(resolution,[],[f580,f24]) ).

fof(f24,plain,
    ! [X2,X0,X1] :
      ( ~ product(inverse(X2),X0,X1)
      | subgroup_member(X1)
      | ~ subgroup_member(X0)
      | ~ subgroup_member(X2) ),
    inference(resolution,[],[f6,f5]) ).

fof(f5,axiom,
    ! [X2] :
      ( subgroup_member(inverse(X2))
      | ~ subgroup_member(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_inverse) ).

fof(f6,axiom,
    ! [X0,X1,X6] :
      ( ~ subgroup_member(X0)
      | ~ subgroup_member(X1)
      | subgroup_member(X6)
      | ~ product(X0,X1,X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_product) ).

fof(f580,plain,
    product(inverse(b),c,inverse(a)),
    inference(resolution,[],[f230,f7]) ).

fof(f7,axiom,
    ! [X2] : product(identity,X2,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).

fof(f230,plain,
    ! [X0] :
      ( ~ product(identity,inverse(a),X0)
      | product(inverse(b),c,X0) ),
    inference(resolution,[],[f80,f9]) ).

fof(f9,axiom,
    ! [X2] : product(inverse(X2),X2,identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).

fof(f80,plain,
    ! [X2,X0,X1] :
      ( ~ product(X2,b,X0)
      | ~ product(X0,inverse(a),X1)
      | product(X2,c,X1) ),
    inference(resolution,[],[f11,f20]) ).

fof(f20,axiom,
    product(b,inverse(a),c),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).

fof(f11,axiom,
    ! [X2,X3,X8,X7,X4,X5] :
      ( ~ product(X3,X5,X8)
      | ~ product(X7,X5,X4)
      | ~ product(X2,X3,X7)
      | product(X2,X8,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity1) ).

fof(f254,plain,
    ( spl0_4
    | ~ spl0_1 ),
    inference(avatar_split_clause,[],[f199,f31,f136]) ).

fof(f136,plain,
    ( spl0_4
  <=> subgroup_member(a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f199,plain,
    ( subgroup_member(a)
    | ~ spl0_1 ),
    inference(resolution,[],[f192,f32]) ).

fof(f32,plain,
    ( subgroup_member(inverse(a))
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f31]) ).

fof(f192,plain,
    ! [X0] :
      ( ~ subgroup_member(inverse(X0))
      | subgroup_member(X0) ),
    inference(resolution,[],[f186,f5]) ).

fof(f186,plain,
    ! [X0] :
      ( ~ subgroup_member(inverse(inverse(X0)))
      | subgroup_member(X0) ),
    inference(resolution,[],[f181,f1]) ).

fof(f1,axiom,
    ! [X0,X1] :
      ( ~ equalish(X0,X1)
      | subgroup_member(X1)
      | ~ subgroup_member(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subgroup_member_substitution) ).

fof(f181,plain,
    ! [X0] : equalish(inverse(inverse(X0)),X0),
    inference(resolution,[],[f57,f10]) ).

fof(f10,axiom,
    ! [X2] : product(X2,inverse(X2),identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).

fof(f57,plain,
    ! [X0,X1] :
      ( ~ product(inverse(X0),X1,identity)
      | equalish(X1,X0) ),
    inference(resolution,[],[f15,f9]) ).

fof(f15,axiom,
    ! [X0,X1,X6,X9] :
      ( ~ product(X0,X1,X6)
      | ~ product(X0,X9,X6)
      | equalish(X9,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).

fof(f253,plain,
    ( ~ spl0_2
    | ~ spl0_4 ),
    inference(avatar_contradiction_clause,[],[f252]) ).

fof(f252,plain,
    ( $false
    | ~ spl0_2
    | ~ spl0_4 ),
    inference(subsumption_resolution,[],[f251,f37]) ).

fof(f251,plain,
    ( ~ subgroup_member(c)
    | ~ spl0_4 ),
    inference(subsumption_resolution,[],[f246,f22]) ).

fof(f22,axiom,
    ~ subgroup_member(d),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_d_is_in_subgroup) ).

fof(f246,plain,
    ( subgroup_member(d)
    | ~ subgroup_member(c)
    | ~ spl0_4 ),
    inference(resolution,[],[f150,f21]) ).

fof(f21,axiom,
    product(a,c,d),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_c_is_d) ).

fof(f150,plain,
    ( ! [X0,X1] :
        ( ~ product(a,X0,X1)
        | subgroup_member(X1)
        | ~ subgroup_member(X0) )
    | ~ spl0_4 ),
    inference(resolution,[],[f138,f6]) ).

fof(f138,plain,
    ( subgroup_member(a)
    | ~ spl0_4 ),
    inference(avatar_component_clause,[],[f136]) ).

fof(f134,plain,
    ( spl0_1
    | spl0_3 ),
    inference(avatar_contradiction_clause,[],[f133]) ).

fof(f133,plain,
    ( $false
    | spl0_1
    | spl0_3 ),
    inference(subsumption_resolution,[],[f132,f41]) ).

fof(f41,plain,
    ( ~ subgroup_member(a)
    | spl0_1 ),
    inference(resolution,[],[f33,f5]) ).

fof(f132,plain,
    ( subgroup_member(a)
    | spl0_3 ),
    inference(subsumption_resolution,[],[f131,f22]) ).

fof(f131,plain,
    ( subgroup_member(d)
    | subgroup_member(a)
    | spl0_3 ),
    inference(resolution,[],[f129,f17]) ).

fof(f17,axiom,
    ! [X0,X1] :
      ( subgroup_member(element_in_O2(X0,X1))
      | subgroup_member(X1)
      | subgroup_member(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',an_element_in_O2) ).

fof(f129,plain,
    ( ~ subgroup_member(element_in_O2(a,d))
    | spl0_3 ),
    inference(avatar_component_clause,[],[f127]) ).

fof(f127,plain,
    ( spl0_3
  <=> subgroup_member(element_in_O2(a,d)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f130,plain,
    ( ~ spl0_3
    | spl0_2
    | spl0_1 ),
    inference(avatar_split_clause,[],[f125,f31,f35,f127]) ).

fof(f125,plain,
    ( subgroup_member(c)
    | ~ subgroup_member(element_in_O2(a,d))
    | spl0_1 ),
    inference(resolution,[],[f85,f1]) ).

fof(f85,plain,
    ( equalish(element_in_O2(a,d),c)
    | spl0_1 ),
    inference(subsumption_resolution,[],[f84,f41]) ).

fof(f84,plain,
    ( equalish(element_in_O2(a,d),c)
    | subgroup_member(a) ),
    inference(subsumption_resolution,[],[f83,f22]) ).

fof(f83,plain,
    ( equalish(element_in_O2(a,d),c)
    | subgroup_member(d)
    | subgroup_member(a) ),
    inference(resolution,[],[f60,f18]) ).

fof(f18,axiom,
    ! [X0,X1] :
      ( product(X0,element_in_O2(X0,X1),X1)
      | subgroup_member(X1)
      | subgroup_member(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_O2) ).

fof(f60,plain,
    ! [X0] :
      ( ~ product(a,X0,d)
      | equalish(X0,c) ),
    inference(resolution,[],[f15,f21]) ).

fof(f38,plain,
    ( ~ spl0_1
    | spl0_2 ),
    inference(avatar_split_clause,[],[f27,f35,f31]) ).

fof(f27,plain,
    ( subgroup_member(c)
    | ~ subgroup_member(inverse(a)) ),
    inference(resolution,[],[f26,f20]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ~ product(b,X0,X1)
      | subgroup_member(X1)
      | ~ subgroup_member(X0) ),
    inference(resolution,[],[f6,f19]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13  % Problem    : GRP039-6 : TPTP v8.1.2. Released v1.0.0.
% 0.13/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.36  % Computer : n018.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit   : 300
% 0.16/0.36  % WCLimit    : 300
% 0.16/0.36  % DateTime   : Fri May  3 20:51:08 EDT 2024
% 0.16/0.36  % CPUTime    : 
% 0.16/0.36  % (11048)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.38  % (11050)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.16/0.38  % (11052)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.16/0.38  % (11051)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)
% 0.16/0.38  % (11049)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.16/0.38  % (11055)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)
% 0.16/0.38  % (11053)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.16/0.38  % (11054)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.16/0.38  TRYING [1]
% 0.16/0.38  TRYING [1]
% 0.16/0.38  TRYING [1]
% 0.16/0.38  TRYING [1]
% 0.16/0.38  TRYING [2]
% 0.16/0.38  TRYING [2]
% 0.16/0.38  TRYING [2]
% 0.16/0.38  TRYING [2]
% 0.16/0.38  TRYING [3]
% 0.16/0.38  TRYING [3]
% 0.16/0.38  TRYING [3]
% 0.16/0.38  TRYING [3]
% 0.16/0.39  TRYING [4]
% 0.16/0.39  TRYING [4]
% 0.16/0.39  TRYING [4]
% 0.16/0.39  TRYING [4]
% 0.16/0.39  % (11054)First to succeed.
% 0.16/0.40  % (11054)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-11048"
% 0.16/0.40  % (11054)Refutation found. Thanks to Tanya!
% 0.16/0.40  % SZS status Unsatisfiable for theBenchmark
% 0.16/0.40  % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.40  % (11054)------------------------------
% 0.16/0.40  % (11054)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.16/0.40  % (11054)Termination reason: Refutation
% 0.16/0.40  
% 0.16/0.40  % (11054)Memory used [KB]: 900
% 0.16/0.40  % (11054)Time elapsed: 0.019 s
% 0.16/0.40  % (11054)Instructions burned: 27 (million)
% 0.16/0.40  % (11048)Success in time 0.036 s
%------------------------------------------------------------------------------