TSTP Solution File: GRP038-3 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GRP038-3 : 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 : n009.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 11:50:35 EDT 2024

% Result   : Unsatisfiable 0.14s 0.36s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   30
% Syntax   : Number of formulae    :   50 (  26 unt;   0 def)
%            Number of atoms       :  102 (   2 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   91 (  39   ~;  37   |;   0   &)
%                                         (  15 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   19 (  17 usr;  16 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   55 (  55   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f106,plain,
    $false,
    inference(avatar_sat_refutation,[],[f20,f25,f30,f35,f39,f43,f48,f52,f56,f60,f64,f68,f72,f88,f92,f105]) ).

fof(f105,plain,
    ( ~ spl0_3
    | spl0_1
    | ~ spl0_2
    | ~ spl0_7
    | ~ spl0_13 ),
    inference(avatar_split_clause,[],[f83,f70,f45,f22,f17,f27]) ).

fof(f27,plain,
    ( spl0_3
  <=> subgroup_member(b) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f17,plain,
    ( spl0_1
  <=> subgroup_member(c) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f22,plain,
    ( spl0_2
  <=> subgroup_member(a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f45,plain,
    ( spl0_7
  <=> product(a,inverse(b),c) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f70,plain,
    ( spl0_13
  <=> ! [X6,X7,X8] :
        ( ~ subgroup_member(X7)
        | ~ subgroup_member(X6)
        | subgroup_member(X8)
        | ~ product(X6,inverse(X7),X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f83,plain,
    ( ~ subgroup_member(a)
    | subgroup_member(c)
    | ~ subgroup_member(b)
    | ~ spl0_7
    | ~ spl0_13 ),
    inference(resolution,[],[f71,f47]) ).

fof(f47,plain,
    ( product(a,inverse(b),c)
    | ~ spl0_7 ),
    inference(avatar_component_clause,[],[f45]) ).

fof(f71,plain,
    ( ! [X8,X6,X7] :
        ( ~ product(X6,inverse(X7),X8)
        | ~ subgroup_member(X6)
        | subgroup_member(X8)
        | ~ subgroup_member(X7) )
    | ~ spl0_13 ),
    inference(avatar_component_clause,[],[f70]) ).

fof(f92,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f8,f90]) ).

fof(f90,plain,
    ( spl0_15
  <=> ! [X5,X4,X2,X0,X3,X1] :
        ( ~ product(X0,X1,X4)
        | ~ product(X0,X5,X3)
        | ~ product(X1,X2,X5)
        | product(X4,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f8,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ product(X0,X1,X4)
      | ~ product(X0,X5,X3)
      | ~ product(X1,X2,X5)
      | product(X4,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity2) ).

fof(f88,plain,
    spl0_14,
    inference(avatar_split_clause,[],[f7,f86]) ).

fof(f86,plain,
    ( spl0_14
  <=> ! [X2,X4,X0,X3,X5,X1] :
        ( ~ product(X0,X1,X4)
        | ~ product(X4,X2,X3)
        | ~ product(X1,X2,X5)
        | product(X0,X5,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f7,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ product(X0,X1,X4)
      | ~ product(X4,X2,X3)
      | ~ product(X1,X2,X5)
      | product(X0,X5,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity1) ).

fof(f72,plain,
    spl0_13,
    inference(avatar_split_clause,[],[f9,f70]) ).

fof(f9,axiom,
    ! [X8,X6,X7] :
      ( ~ subgroup_member(X7)
      | ~ subgroup_member(X6)
      | subgroup_member(X8)
      | ~ product(X6,inverse(X7),X8) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_product_and_inverse) ).

fof(f68,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f6,f66]) ).

fof(f66,plain,
    ( spl0_12
  <=> ! [X0,X3,X2,X1] :
        ( X2 = X3
        | ~ product(X0,X1,X3)
        | ~ product(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f6,axiom,
    ! [X2,X3,X0,X1] :
      ( X2 = X3
      | ~ product(X0,X1,X3)
      | ~ product(X0,X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function2) ).

fof(f64,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f5,f62]) ).

fof(f62,plain,
    ( spl0_11
  <=> ! [X0,X1] : product(X0,X1,multiply(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f5,axiom,
    ! [X0,X1] : product(X0,X1,multiply(X0,X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function1) ).

fof(f60,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f10,f58]) ).

fof(f58,plain,
    ( spl0_10
  <=> ! [X6] :
        ( ~ subgroup_member(X6)
        | subgroup_member(inverse(X6)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f10,axiom,
    ! [X6] :
      ( ~ subgroup_member(X6)
      | subgroup_member(inverse(X6)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_inverse) ).

fof(f56,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f4,f54]) ).

fof(f54,plain,
    ( spl0_9
  <=> ! [X0] : product(X0,inverse(X0),identity) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f4,axiom,
    ! [X0] : product(X0,inverse(X0),identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).

fof(f52,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f3,f50]) ).

fof(f50,plain,
    ( spl0_8
  <=> ! [X0] : product(inverse(X0),X0,identity) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f3,axiom,
    ! [X0] : product(inverse(X0),X0,identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).

fof(f48,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f14,f45]) ).

fof(f14,axiom,
    product(a,inverse(b),c),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_inverse_b_is_c) ).

fof(f43,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f2,f41]) ).

fof(f41,plain,
    ( spl0_6
  <=> ! [X0] : product(X0,identity,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f2,axiom,
    ! [X0] : product(X0,identity,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).

fof(f39,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f1,f37]) ).

fof(f37,plain,
    ( spl0_5
  <=> ! [X0] : product(identity,X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f1,axiom,
    ! [X0] : product(identity,X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).

fof(f35,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f11,f32]) ).

fof(f32,plain,
    ( spl0_4
  <=> subgroup_member(identity) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f11,axiom,
    subgroup_member(identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_is_in_subgroup) ).

fof(f30,plain,
    spl0_3,
    inference(avatar_split_clause,[],[f13,f27]) ).

fof(f13,axiom,
    subgroup_member(b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_in_subgroup) ).

fof(f25,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f12,f22]) ).

fof(f12,axiom,
    subgroup_member(a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_in_subgroup) ).

fof(f20,plain,
    ~ spl0_1,
    inference(avatar_split_clause,[],[f15,f17]) ).

fof(f15,axiom,
    ~ subgroup_member(c),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_is_in_subgroup) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : GRP038-3 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34  % Computer : n009.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Tue Apr 30 04:28:26 EDT 2024
% 0.14/0.34  % CPUTime    : 
% 0.14/0.35  % (13562)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.36  % (13567)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.36  % (13565)WARNING: value z3 for option sas not known
% 0.14/0.36  % (13567)First to succeed.
% 0.14/0.36  % (13563)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.36  % (13564)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.36  % (13565)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.36  % (13566)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.36  % (13568)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.36  % (13567)Refutation found. Thanks to Tanya!
% 0.14/0.36  % SZS status Unsatisfiable for theBenchmark
% 0.14/0.36  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.36  % (13567)------------------------------
% 0.14/0.36  % (13567)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.36  % (13567)Termination reason: Refutation
% 0.14/0.36  
% 0.14/0.36  % (13567)Memory used [KB]: 821
% 0.14/0.36  % (13567)Time elapsed: 0.005 s
% 0.14/0.36  % (13567)Instructions burned: 5 (million)
% 0.14/0.36  % (13567)------------------------------
% 0.14/0.36  % (13567)------------------------------
% 0.14/0.36  % (13562)Success in time 0.017 s
%------------------------------------------------------------------------------