TSTP Solution File: LCL455+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : LCL455+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n008.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 07:46:03 EDT 2024

% Result   : Theorem 0.22s 0.39s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   49
% Syntax   : Number of formulae    :  112 (  66 unt;   0 def)
%            Number of atoms       :  159 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   67 (  20   ~;  15   |;   0   &)
%                                         (  28 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :   47 (  46 usr;  46 prp; 0-1 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   32 (  28   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f270,plain,
    $false,
    inference(avatar_sat_refutation,[],[f154,f159,f164,f169,f174,f179,f184,f189,f194,f199,f204,f209,f214,f219,f224,f229,f234,f239,f244,f249,f254,f259,f263,f267,f269]) ).

fof(f269,plain,
    ( spl2_22
    | ~ spl2_24 ),
    inference(avatar_contradiction_clause,[],[f268]) ).

fof(f268,plain,
    ( $false
    | spl2_22
    | ~ spl2_24 ),
    inference(resolution,[],[f266,f258]) ).

fof(f258,plain,
    ( ~ is_a_theorem(implies(sK1,or(sK0,sK1)))
    | spl2_22 ),
    inference(avatar_component_clause,[],[f256]) ).

fof(f256,plain,
    ( spl2_22
  <=> is_a_theorem(implies(sK1,or(sK0,sK1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_22])]) ).

fof(f266,plain,
    ( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
    | ~ spl2_24 ),
    inference(avatar_component_clause,[],[f265]) ).

fof(f265,plain,
    ( spl2_24
  <=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_24])]) ).

fof(f267,plain,
    ( ~ spl2_10
    | spl2_24 ),
    inference(avatar_split_clause,[],[f136,f265,f196]) ).

fof(f196,plain,
    ( spl2_10
  <=> or_2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_10])]) ).

fof(f136,plain,
    ! [X0,X1] :
      ( is_a_theorem(implies(X1,or(X0,X1)))
      | ~ or_2 ),
    inference(cnf_transformation,[],[f90]) ).

fof(f90,plain,
    ( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
    | ~ or_2 ),
    inference(ennf_transformation,[],[f72]) ).

fof(f72,plain,
    ( or_2
   => ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
    inference(unused_predicate_definition_removal,[],[f11]) ).

fof(f11,axiom,
    ( or_2
  <=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_2) ).

fof(f263,plain,
    ( ~ spl2_11
    | spl2_23 ),
    inference(avatar_split_clause,[],[f135,f261,f201]) ).

fof(f201,plain,
    ( spl2_11
  <=> or_1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_11])]) ).

fof(f261,plain,
    ( spl2_23
  <=> ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_23])]) ).

fof(f135,plain,
    ! [X0,X1] :
      ( is_a_theorem(implies(X0,or(X0,X1)))
      | ~ or_1 ),
    inference(cnf_transformation,[],[f89]) ).

fof(f89,plain,
    ( ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1)))
    | ~ or_1 ),
    inference(ennf_transformation,[],[f73]) ).

fof(f73,plain,
    ( or_1
   => ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
    inference(unused_predicate_definition_removal,[],[f10]) ).

fof(f10,axiom,
    ( or_1
  <=> ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_1) ).

fof(f259,plain,
    ( ~ spl2_22
    | spl2_1 ),
    inference(avatar_split_clause,[],[f134,f151,f256]) ).

fof(f151,plain,
    ( spl2_1
  <=> r2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).

fof(f134,plain,
    ( r2
    | ~ is_a_theorem(implies(sK1,or(sK0,sK1))) ),
    inference(cnf_transformation,[],[f106]) ).

fof(f106,plain,
    ( r2
    | ~ is_a_theorem(implies(sK1,or(sK0,sK1))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f88,f105]) ).

fof(f105,plain,
    ( ? [X0,X1] : ~ is_a_theorem(implies(X1,or(X0,X1)))
   => ~ is_a_theorem(implies(sK1,or(sK0,sK1))) ),
    introduced(choice_axiom,[]) ).

fof(f88,plain,
    ( r2
    | ? [X0,X1] : ~ is_a_theorem(implies(X1,or(X0,X1))) ),
    inference(ennf_transformation,[],[f67]) ).

fof(f67,plain,
    ( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
   => r2 ),
    inference(unused_predicate_definition_removal,[],[f66]) ).

fof(f66,plain,
    ( r2
  <=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
    inference(rectify,[],[f23]) ).

fof(f23,axiom,
    ( r2
  <=> ! [X3,X4] : is_a_theorem(implies(X4,or(X3,X4))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2) ).

fof(f254,plain,
    spl2_21,
    inference(avatar_split_clause,[],[f127,f251]) ).

fof(f251,plain,
    ( spl2_21
  <=> op_equiv ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_21])]) ).

fof(f127,plain,
    op_equiv,
    inference(cnf_transformation,[],[f34]) ).

fof(f34,axiom,
    op_equiv,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_equiv) ).

fof(f249,plain,
    spl2_20,
    inference(avatar_split_clause,[],[f126,f246]) ).

fof(f246,plain,
    ( spl2_20
  <=> op_implies_and ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_20])]) ).

fof(f126,plain,
    op_implies_and,
    inference(cnf_transformation,[],[f33]) ).

fof(f33,axiom,
    op_implies_and,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_implies_and) ).

fof(f244,plain,
    spl2_19,
    inference(avatar_split_clause,[],[f125,f241]) ).

fof(f241,plain,
    ( spl2_19
  <=> op_or ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_19])]) ).

fof(f125,plain,
    op_or,
    inference(cnf_transformation,[],[f32]) ).

fof(f32,axiom,
    op_or,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_or) ).

fof(f239,plain,
    spl2_18,
    inference(avatar_split_clause,[],[f124,f236]) ).

fof(f236,plain,
    ( spl2_18
  <=> op_and ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_18])]) ).

fof(f124,plain,
    op_and,
    inference(cnf_transformation,[],[f51]) ).

fof(f51,axiom,
    op_and,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_and) ).

fof(f234,plain,
    spl2_17,
    inference(avatar_split_clause,[],[f123,f231]) ).

fof(f231,plain,
    ( spl2_17
  <=> op_implies_or ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_17])]) ).

fof(f123,plain,
    op_implies_or,
    inference(cnf_transformation,[],[f50]) ).

fof(f50,axiom,
    op_implies_or,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_implies_or) ).

fof(f229,plain,
    spl2_16,
    inference(avatar_split_clause,[],[f122,f226]) ).

fof(f226,plain,
    ( spl2_16
  <=> implies_2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_16])]) ).

fof(f122,plain,
    implies_2,
    inference(cnf_transformation,[],[f38]) ).

fof(f38,axiom,
    implies_2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_2) ).

fof(f224,plain,
    spl2_15,
    inference(avatar_split_clause,[],[f121,f221]) ).

fof(f221,plain,
    ( spl2_15
  <=> implies_3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_15])]) ).

fof(f121,plain,
    implies_3,
    inference(cnf_transformation,[],[f39]) ).

fof(f39,axiom,
    implies_3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_3) ).

fof(f219,plain,
    spl2_14,
    inference(avatar_split_clause,[],[f120,f216]) ).

fof(f216,plain,
    ( spl2_14
  <=> and_1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_14])]) ).

fof(f120,plain,
    and_1,
    inference(cnf_transformation,[],[f40]) ).

fof(f40,axiom,
    and_1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_1) ).

fof(f214,plain,
    spl2_13,
    inference(avatar_split_clause,[],[f119,f211]) ).

fof(f211,plain,
    ( spl2_13
  <=> and_2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_13])]) ).

fof(f119,plain,
    and_2,
    inference(cnf_transformation,[],[f41]) ).

fof(f41,axiom,
    and_2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_2) ).

fof(f209,plain,
    spl2_12,
    inference(avatar_split_clause,[],[f118,f206]) ).

fof(f206,plain,
    ( spl2_12
  <=> and_3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_12])]) ).

fof(f118,plain,
    and_3,
    inference(cnf_transformation,[],[f42]) ).

fof(f42,axiom,
    and_3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_3) ).

fof(f204,plain,
    spl2_11,
    inference(avatar_split_clause,[],[f117,f201]) ).

fof(f117,plain,
    or_1,
    inference(cnf_transformation,[],[f43]) ).

fof(f43,axiom,
    or_1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_1) ).

fof(f199,plain,
    spl2_10,
    inference(avatar_split_clause,[],[f116,f196]) ).

fof(f116,plain,
    or_2,
    inference(cnf_transformation,[],[f44]) ).

fof(f44,axiom,
    or_2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_2) ).

fof(f194,plain,
    spl2_9,
    inference(avatar_split_clause,[],[f115,f191]) ).

fof(f191,plain,
    ( spl2_9
  <=> or_3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_9])]) ).

fof(f115,plain,
    or_3,
    inference(cnf_transformation,[],[f45]) ).

fof(f45,axiom,
    or_3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_3) ).

fof(f189,plain,
    spl2_8,
    inference(avatar_split_clause,[],[f114,f186]) ).

fof(f186,plain,
    ( spl2_8
  <=> equivalence_1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_8])]) ).

fof(f114,plain,
    equivalence_1,
    inference(cnf_transformation,[],[f46]) ).

fof(f46,axiom,
    equivalence_1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_equivalence_1) ).

fof(f184,plain,
    spl2_7,
    inference(avatar_split_clause,[],[f113,f181]) ).

fof(f181,plain,
    ( spl2_7
  <=> equivalence_2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_7])]) ).

fof(f113,plain,
    equivalence_2,
    inference(cnf_transformation,[],[f47]) ).

fof(f47,axiom,
    equivalence_2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_equivalence_2) ).

fof(f179,plain,
    spl2_6,
    inference(avatar_split_clause,[],[f112,f176]) ).

fof(f176,plain,
    ( spl2_6
  <=> equivalence_3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_6])]) ).

fof(f112,plain,
    equivalence_3,
    inference(cnf_transformation,[],[f48]) ).

fof(f48,axiom,
    equivalence_3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_equivalence_3) ).

fof(f174,plain,
    spl2_5,
    inference(avatar_split_clause,[],[f111,f171]) ).

fof(f171,plain,
    ( spl2_5
  <=> substitution_of_equivalents ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_5])]) ).

fof(f111,plain,
    substitution_of_equivalents,
    inference(cnf_transformation,[],[f49]) ).

fof(f49,axiom,
    substitution_of_equivalents,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substitution_of_equivalents) ).

fof(f169,plain,
    spl2_4,
    inference(avatar_split_clause,[],[f110,f166]) ).

fof(f166,plain,
    ( spl2_4
  <=> implies_1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).

fof(f110,plain,
    implies_1,
    inference(cnf_transformation,[],[f37]) ).

fof(f37,axiom,
    implies_1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_1) ).

fof(f164,plain,
    spl2_3,
    inference(avatar_split_clause,[],[f109,f161]) ).

fof(f161,plain,
    ( spl2_3
  <=> modus_tollens ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).

fof(f109,plain,
    modus_tollens,
    inference(cnf_transformation,[],[f36]) ).

fof(f36,axiom,
    modus_tollens,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_modus_tollens) ).

fof(f159,plain,
    spl2_2,
    inference(avatar_split_clause,[],[f108,f156]) ).

fof(f156,plain,
    ( spl2_2
  <=> modus_ponens ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).

fof(f108,plain,
    modus_ponens,
    inference(cnf_transformation,[],[f35]) ).

fof(f35,axiom,
    modus_ponens,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_modus_ponens) ).

fof(f154,plain,
    ~ spl2_1,
    inference(avatar_split_clause,[],[f107,f151]) ).

fof(f107,plain,
    ~ r2,
    inference(cnf_transformation,[],[f55]) ).

fof(f55,plain,
    ~ r2,
    inference(flattening,[],[f54]) ).

fof(f54,negated_conjecture,
    ~ r2,
    inference(negated_conjecture,[],[f53]) ).

fof(f53,conjecture,
    r2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r2) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : LCL455+1 : TPTP v8.1.2. Released v3.3.0.
% 0.15/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.36  % Computer : n008.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 13:23:57 EDT 2024
% 0.22/0.36  % CPUTime    : 
% 0.22/0.36  % (22926)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.38  % (22939)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.39  % (22941)WARNING: value z3 for option sas not known
% 0.22/0.39  % (22943)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)
% 0.22/0.39  % (22940)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.39  % (22942)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.39  % (22941)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)
% 0.22/0.39  % (22944)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)
% 0.22/0.39  % (22945)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)
% 0.22/0.39  TRYING [1]
% 0.22/0.39  % (22943)First to succeed.
% 0.22/0.39  % (22944)Also succeeded, but the first one will report.
% 0.22/0.39  % (22945)Also succeeded, but the first one will report.
% 0.22/0.39  % (22943)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-22926"
% 0.22/0.39  TRYING [2]
% 0.22/0.39  TRYING [1]
% 0.22/0.39  % (22941)Also succeeded, but the first one will report.
% 0.22/0.39  % (22943)Refutation found. Thanks to Tanya!
% 0.22/0.39  % SZS status Theorem for theBenchmark
% 0.22/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.39  % (22943)------------------------------
% 0.22/0.39  % (22943)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.39  % (22943)Termination reason: Refutation
% 0.22/0.39  
% 0.22/0.39  % (22943)Memory used [KB]: 916
% 0.22/0.39  % (22943)Time elapsed: 0.005 s
% 0.22/0.39  % (22943)Instructions burned: 5 (million)
% 0.22/0.39  % (22926)Success in time 0.029 s
%------------------------------------------------------------------------------