TSTP Solution File: GRP168-1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GRP168-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n025.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 11:51:59 EDT 2024

% Result   : Unsatisfiable 0.15s 0.37s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   35
% Syntax   : Number of formulae    :   65 (  35 unt;   0 def)
%            Number of atoms       :  108 (  44 equ)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :   69 (  26   ~;  25   |;   0   &)
%                                         (  18 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :   20 (  18 usr;  19 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   74 (  74   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f167,plain,
    $false,
    inference(avatar_sat_refutation,[],[f22,f27,f31,f35,f39,f43,f47,f51,f55,f59,f72,f76,f80,f85,f128,f132,f136,f140,f166]) ).

fof(f166,plain,
    ( spl0_1
    | ~ spl0_2
    | ~ spl0_15
    | ~ spl0_17 ),
    inference(avatar_contradiction_clause,[],[f165]) ).

fof(f165,plain,
    ( $false
    | spl0_1
    | ~ spl0_2
    | ~ spl0_15
    | ~ spl0_17 ),
    inference(trivial_inequality_removal,[],[f164]) ).

fof(f164,plain,
    ( multiply(inverse(c),multiply(b,c)) != multiply(inverse(c),multiply(b,c))
    | spl0_1
    | ~ spl0_2
    | ~ spl0_15
    | ~ spl0_17 ),
    inference(forward_demodulation,[],[f163,f26]) ).

fof(f26,plain,
    ( b = least_upper_bound(a,b)
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f24]) ).

fof(f24,plain,
    ( spl0_2
  <=> b = least_upper_bound(a,b) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f163,plain,
    ( multiply(inverse(c),multiply(b,c)) != multiply(inverse(c),multiply(least_upper_bound(a,b),c))
    | spl0_1
    | ~ spl0_15
    | ~ spl0_17 ),
    inference(forward_demodulation,[],[f150,f135]) ).

fof(f135,plain,
    ( ! [X2,X0,X1] : multiply(least_upper_bound(X1,X2),X0) = least_upper_bound(multiply(X1,X0),multiply(X2,X0))
    | ~ spl0_17 ),
    inference(avatar_component_clause,[],[f134]) ).

fof(f134,plain,
    ( spl0_17
  <=> ! [X2,X0,X1] : multiply(least_upper_bound(X1,X2),X0) = least_upper_bound(multiply(X1,X0),multiply(X2,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f150,plain,
    ( multiply(inverse(c),multiply(b,c)) != multiply(inverse(c),least_upper_bound(multiply(a,c),multiply(b,c)))
    | spl0_1
    | ~ spl0_15 ),
    inference(superposition,[],[f21,f127]) ).

fof(f127,plain,
    ( ! [X2,X0,X1] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,X1),multiply(X0,X2))
    | ~ spl0_15 ),
    inference(avatar_component_clause,[],[f126]) ).

fof(f126,plain,
    ( spl0_15
  <=> ! [X2,X0,X1] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,X1),multiply(X0,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f21,plain,
    ( multiply(inverse(c),multiply(b,c)) != least_upper_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c)))
    | spl0_1 ),
    inference(avatar_component_clause,[],[f19]) ).

fof(f19,plain,
    ( spl0_1
  <=> multiply(inverse(c),multiply(b,c)) = least_upper_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f140,plain,
    spl0_18,
    inference(avatar_split_clause,[],[f15,f138]) ).

fof(f138,plain,
    ( spl0_18
  <=> ! [X2,X0,X1] : multiply(greatest_lower_bound(X1,X2),X0) = greatest_lower_bound(multiply(X1,X0),multiply(X2,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f15,axiom,
    ! [X2,X0,X1] : multiply(greatest_lower_bound(X1,X2),X0) = greatest_lower_bound(multiply(X1,X0),multiply(X2,X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_glb2) ).

fof(f136,plain,
    spl0_17,
    inference(avatar_split_clause,[],[f14,f134]) ).

fof(f14,axiom,
    ! [X2,X0,X1] : multiply(least_upper_bound(X1,X2),X0) = least_upper_bound(multiply(X1,X0),multiply(X2,X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_lub2) ).

fof(f132,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f13,f130]) ).

fof(f130,plain,
    ( spl0_16
  <=> ! [X2,X0,X1] : multiply(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f13,axiom,
    ! [X2,X0,X1] : multiply(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_glb1) ).

fof(f128,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f12,f126]) ).

fof(f12,axiom,
    ! [X2,X0,X1] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,X1),multiply(X0,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_lub1) ).

fof(f85,plain,
    ( spl0_14
    | ~ spl0_2
    | ~ spl0_10 ),
    inference(avatar_split_clause,[],[f63,f57,f24,f82]) ).

fof(f82,plain,
    ( spl0_14
  <=> a = greatest_lower_bound(a,b) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f57,plain,
    ( spl0_10
  <=> ! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f63,plain,
    ( a = greatest_lower_bound(a,b)
    | ~ spl0_2
    | ~ spl0_10 ),
    inference(superposition,[],[f58,f26]) ).

fof(f58,plain,
    ( ! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0
    | ~ spl0_10 ),
    inference(avatar_component_clause,[],[f57]) ).

fof(f80,plain,
    spl0_13,
    inference(avatar_split_clause,[],[f7,f78]) ).

fof(f78,plain,
    ( spl0_13
  <=> ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(least_upper_bound(X0,X1),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f7,axiom,
    ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(least_upper_bound(X0,X1),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_lub) ).

fof(f76,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f6,f74]) ).

fof(f74,plain,
    ( spl0_12
  <=> ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(greatest_lower_bound(X0,X1),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f6,axiom,
    ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(greatest_lower_bound(X0,X1),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_glb) ).

fof(f72,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f3,f70]) ).

fof(f70,plain,
    ( spl0_11
  <=> ! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f3,axiom,
    ! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).

fof(f59,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f11,f57]) ).

fof(f11,axiom,
    ! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',glb_absorbtion) ).

fof(f55,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f10,f53]) ).

fof(f53,plain,
    ( spl0_9
  <=> ! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f10,axiom,
    ! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lub_absorbtion) ).

fof(f51,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f5,f49]) ).

fof(f49,plain,
    ( spl0_8
  <=> ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f5,axiom,
    ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_lub) ).

fof(f47,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f4,f45]) ).

fof(f45,plain,
    ( spl0_7
  <=> ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f4,axiom,
    ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_glb) ).

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

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

fof(f2,axiom,
    ! [X0] : identity = multiply(inverse(X0),X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).

fof(f39,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f9,f37]) ).

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

fof(f9,axiom,
    ! [X0] : greatest_lower_bound(X0,X0) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_gld) ).

fof(f35,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f8,f33]) ).

fof(f33,plain,
    ( spl0_4
  <=> ! [X0] : least_upper_bound(X0,X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f8,axiom,
    ! [X0] : least_upper_bound(X0,X0) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_lub) ).

fof(f31,plain,
    spl0_3,
    inference(avatar_split_clause,[],[f1,f29]) ).

fof(f29,plain,
    ( spl0_3
  <=> ! [X0] : multiply(identity,X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f1,axiom,
    ! [X0] : multiply(identity,X0) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).

fof(f27,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f16,f24]) ).

fof(f16,axiom,
    b = least_upper_bound(a,b),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p01a_1) ).

fof(f22,plain,
    ~ spl0_1,
    inference(avatar_split_clause,[],[f17,f19]) ).

fof(f17,axiom,
    multiply(inverse(c),multiply(b,c)) != least_upper_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p01a) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : GRP168-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.12/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35  % Computer : n025.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Tue Apr 30 04:45:41 EDT 2024
% 0.15/0.35  % CPUTime    : 
% 0.15/0.35  % (28398)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.36  % (28404)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)
% 0.15/0.36  % (28403)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)
% 0.15/0.36  % (28405)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.37  % (28403)First to succeed.
% 0.15/0.37  % (28403)Refutation found. Thanks to Tanya!
% 0.15/0.37  % SZS status Unsatisfiable for theBenchmark
% 0.15/0.37  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.37  % (28403)------------------------------
% 0.15/0.37  % (28403)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.37  % (28403)Termination reason: Refutation
% 0.15/0.37  
% 0.15/0.37  % (28403)Memory used [KB]: 886
% 0.15/0.37  % (28403)Time elapsed: 0.004 s
% 0.15/0.37  % (28403)Instructions burned: 10 (million)
% 0.15/0.37  % (28403)------------------------------
% 0.15/0.37  % (28403)------------------------------
% 0.15/0.37  % (28398)Success in time 0.013 s
%------------------------------------------------------------------------------