TSTP Solution File: REL049+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : REL049+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n013.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 14:48:18 EDT 2024

% Result   : Theorem 0.15s 0.40s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   32
% Syntax   : Number of formulae    :   82 (  46 unt;   0 def)
%            Number of atoms       :  136 (  78 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :   84 (  30   ~;  22   |;  12   &)
%                                         (  17 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :   19 (  17 usr;  18 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   6 con; 0-2 aty)
%            Number of variables   :   96 (  87   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f193,plain,
    $false,
    inference(avatar_sat_refutation,[],[f41,f46,f51,f55,f59,f63,f67,f73,f79,f84,f88,f100,f104,f109,f137,f141,f169,f192]) ).

fof(f192,plain,
    ( ~ spl3_1
    | ~ spl3_2
    | spl3_3
    | ~ spl3_13 ),
    inference(avatar_split_clause,[],[f133,f102,f48,f43,f38]) ).

fof(f38,plain,
    ( spl3_1
  <=> sK1 = join(sK0,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

fof(f43,plain,
    ( spl3_2
  <=> sK1 = join(sK2,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).

fof(f48,plain,
    ( spl3_3
  <=> sK1 = join(join(sK0,sK2),sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).

fof(f102,plain,
    ( spl3_13
  <=> ! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_13])]) ).

fof(f133,plain,
    ( sK1 != join(sK0,sK1)
    | ~ spl3_2
    | spl3_3
    | ~ spl3_13 ),
    inference(forward_demodulation,[],[f130,f45]) ).

fof(f45,plain,
    ( sK1 = join(sK2,sK1)
    | ~ spl3_2 ),
    inference(avatar_component_clause,[],[f43]) ).

fof(f130,plain,
    ( sK1 != join(sK0,join(sK2,sK1))
    | spl3_3
    | ~ spl3_13 ),
    inference(superposition,[],[f50,f103]) ).

fof(f103,plain,
    ( ! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2)
    | ~ spl3_13 ),
    inference(avatar_component_clause,[],[f102]) ).

fof(f50,plain,
    ( sK1 != join(join(sK0,sK2),sK1)
    | spl3_3 ),
    inference(avatar_component_clause,[],[f48]) ).

fof(f169,plain,
    spl3_17,
    inference(avatar_split_clause,[],[f32,f167]) ).

fof(f167,plain,
    ( spl3_17
  <=> ! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_17])]) ).

fof(f32,plain,
    ! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux3_a_kind_of_de_Morgan) ).

fof(f141,plain,
    spl3_16,
    inference(avatar_split_clause,[],[f35,f139]) ).

fof(f139,plain,
    ( spl3_16
  <=> ! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_16])]) ).

fof(f35,plain,
    ! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
    inference(cnf_transformation,[],[f7]) ).

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

fof(f137,plain,
    spl3_15,
    inference(avatar_split_clause,[],[f31,f135]) ).

fof(f135,plain,
    ( spl3_15
  <=> ! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_15])]) ).

fof(f31,plain,
    ! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
    inference(cnf_transformation,[],[f11]) ).

fof(f11,axiom,
    ! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_cancellativity) ).

fof(f109,plain,
    ( ~ spl3_14
    | spl3_3
    | ~ spl3_7 ),
    inference(avatar_split_clause,[],[f68,f65,f48,f106]) ).

fof(f106,plain,
    ( spl3_14
  <=> sK1 = join(sK1,join(sK0,sK2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_14])]) ).

fof(f65,plain,
    ( spl3_7
  <=> ! [X0,X1] : join(X0,X1) = join(X1,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_7])]) ).

fof(f68,plain,
    ( sK1 != join(sK1,join(sK0,sK2))
    | spl3_3
    | ~ spl3_7 ),
    inference(superposition,[],[f50,f66]) ).

fof(f66,plain,
    ( ! [X0,X1] : join(X0,X1) = join(X1,X0)
    | ~ spl3_7 ),
    inference(avatar_component_clause,[],[f65]) ).

fof(f104,plain,
    spl3_13,
    inference(avatar_split_clause,[],[f34,f102]) ).

fof(f34,plain,
    ! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
    inference(cnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux2_join_associativity) ).

fof(f100,plain,
    spl3_12,
    inference(avatar_split_clause,[],[f33,f98]) ).

fof(f98,plain,
    ( spl3_12
  <=> ! [X2,X0,X1] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_12])]) ).

fof(f33,plain,
    ! [X2,X0,X1] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
    inference(cnf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_associativity) ).

fof(f88,plain,
    spl3_11,
    inference(avatar_split_clause,[],[f29,f86]) ).

fof(f86,plain,
    ( spl3_11
  <=> ! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_11])]) ).

fof(f29,plain,
    ! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
    inference(cnf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_additivity) ).

fof(f84,plain,
    spl3_10,
    inference(avatar_split_clause,[],[f28,f82]) ).

fof(f82,plain,
    ( spl3_10
  <=> ! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_10])]) ).

fof(f28,plain,
    ! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
    inference(cnf_transformation,[],[f10]) ).

fof(f10,axiom,
    ! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_multiplicativity) ).

fof(f79,plain,
    ( spl3_9
    | ~ spl3_6
    | ~ spl3_8 ),
    inference(avatar_split_clause,[],[f74,f71,f61,f76]) ).

fof(f76,plain,
    ( spl3_9
  <=> zero = complement(top) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_9])]) ).

fof(f61,plain,
    ( spl3_6
  <=> ! [X0] : top = join(X0,complement(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).

fof(f71,plain,
    ( spl3_8
  <=> ! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_8])]) ).

fof(f74,plain,
    ( zero = complement(top)
    | ~ spl3_6
    | ~ spl3_8 ),
    inference(forward_demodulation,[],[f72,f62]) ).

fof(f62,plain,
    ( ! [X0] : top = join(X0,complement(X0))
    | ~ spl3_6 ),
    inference(avatar_component_clause,[],[f61]) ).

fof(f72,plain,
    ( ! [X0] : zero = complement(join(complement(X0),complement(complement(X0))))
    | ~ spl3_8 ),
    inference(avatar_component_clause,[],[f71]) ).

fof(f73,plain,
    spl3_8,
    inference(avatar_split_clause,[],[f36,f71]) ).

fof(f36,plain,
    ! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
    inference(definition_unfolding,[],[f25,f30]) ).

fof(f30,plain,
    ! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
    inference(cnf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux4_definiton_of_meet) ).

fof(f25,plain,
    ! [X0] : zero = meet(X0,complement(X0)),
    inference(cnf_transformation,[],[f13]) ).

fof(f13,axiom,
    ! [X0] : zero = meet(X0,complement(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_zero) ).

fof(f67,plain,
    spl3_7,
    inference(avatar_split_clause,[],[f27,f65]) ).

fof(f27,plain,
    ! [X0,X1] : join(X0,X1) = join(X1,X0),
    inference(cnf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1] : join(X0,X1) = join(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux1_join_commutativity) ).

fof(f63,plain,
    spl3_6,
    inference(avatar_split_clause,[],[f26,f61]) ).

fof(f26,plain,
    ! [X0] : top = join(X0,complement(X0)),
    inference(cnf_transformation,[],[f12]) ).

fof(f12,axiom,
    ! [X0] : top = join(X0,complement(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_top) ).

fof(f59,plain,
    spl3_5,
    inference(avatar_split_clause,[],[f24,f57]) ).

fof(f57,plain,
    ( spl3_5
  <=> ! [X0] : composition(X0,one) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).

fof(f24,plain,
    ! [X0] : composition(X0,one) = X0,
    inference(cnf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0] : composition(X0,one) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_identity) ).

fof(f55,plain,
    spl3_4,
    inference(avatar_split_clause,[],[f23,f53]) ).

fof(f53,plain,
    ( spl3_4
  <=> ! [X0] : converse(converse(X0)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).

fof(f23,plain,
    ! [X0] : converse(converse(X0)) = X0,
    inference(cnf_transformation,[],[f8]) ).

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

fof(f51,plain,
    ~ spl3_3,
    inference(avatar_split_clause,[],[f22,f48]) ).

fof(f22,plain,
    sK1 != join(join(sK0,sK2),sK1),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,plain,
    ( sK1 != join(join(sK0,sK2),sK1)
    & sK1 = join(sK2,sK1)
    & sK1 = join(sK0,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f17,f18]) ).

fof(f18,plain,
    ( ? [X0,X1,X2] :
        ( join(join(X0,X2),X1) != X1
        & join(X2,X1) = X1
        & join(X0,X1) = X1 )
   => ( sK1 != join(join(sK0,sK2),sK1)
      & sK1 = join(sK2,sK1)
      & sK1 = join(sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f17,plain,
    ? [X0,X1,X2] :
      ( join(join(X0,X2),X1) != X1
      & join(X2,X1) = X1
      & join(X0,X1) = X1 ),
    inference(flattening,[],[f16]) ).

fof(f16,plain,
    ? [X0,X1,X2] :
      ( join(join(X0,X2),X1) != X1
      & join(X2,X1) = X1
      & join(X0,X1) = X1 ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( ( join(X2,X1) = X1
          & join(X0,X1) = X1 )
       => join(join(X0,X2),X1) = X1 ),
    inference(negated_conjecture,[],[f14]) ).

fof(f14,conjecture,
    ! [X0,X1,X2] :
      ( ( join(X2,X1) = X1
        & join(X0,X1) = X1 )
     => join(join(X0,X2),X1) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).

fof(f46,plain,
    spl3_2,
    inference(avatar_split_clause,[],[f21,f43]) ).

fof(f21,plain,
    sK1 = join(sK2,sK1),
    inference(cnf_transformation,[],[f19]) ).

fof(f41,plain,
    spl3_1,
    inference(avatar_split_clause,[],[f20,f38]) ).

fof(f20,plain,
    sK1 = join(sK0,sK1),
    inference(cnf_transformation,[],[f19]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem    : REL049+1 : TPTP v8.1.2. Released v4.0.0.
% 0.15/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36  % Computer : n013.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Tue Apr 30 00:17:49 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.37  % (14386)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.39  % (14391)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)
% 0.15/0.39  % (14392)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)
% 0.15/0.39  % (14389)WARNING: value z3 for option sas not known
% 0.15/0.39  % (14390)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.39  % (14389)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)
% 0.15/0.39  TRYING [1]
% 0.15/0.39  TRYING [2]
% 0.15/0.39  % (14388)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.39  % (14393)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)
% 0.15/0.39  % (14387)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.39  % (14391)First to succeed.
% 0.15/0.39  TRYING [3]
% 0.15/0.39  % (14392)Also succeeded, but the first one will report.
% 0.15/0.40  % (14391)Refutation found. Thanks to Tanya!
% 0.15/0.40  % SZS status Theorem for theBenchmark
% 0.15/0.40  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.40  % (14391)------------------------------
% 0.15/0.40  % (14391)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.40  % (14391)Termination reason: Refutation
% 0.15/0.40  
% 0.15/0.40  % (14391)Memory used [KB]: 874
% 0.15/0.40  % (14391)Time elapsed: 0.010 s
% 0.15/0.40  % (14391)Instructions burned: 12 (million)
% 0.15/0.40  % (14391)------------------------------
% 0.15/0.40  % (14391)------------------------------
% 0.15/0.40  % (14386)Success in time 0.027 s
%------------------------------------------------------------------------------