TSTP Solution File: NUN060+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUN060+1 : TPTP v8.2.0. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n012.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 May 21 02:17:49 EDT 2024

% Result   : Theorem 0.13s 0.40s
% Output   : Refutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   56 (  13 unt;   0 def)
%            Number of atoms       :  207 (   0 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  235 (  84   ~;  55   |;  82   &)
%                                         (   5 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   7 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   11 (  10 usr;   1 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   1 con; 0-2 aty)
%            Number of variables   :  183 ( 117   !;  66   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f259,plain,
    $false,
    inference(resolution,[],[f247,f198]) ).

fof(f198,plain,
    r1(sK19),
    inference(resolution,[],[f126,f69]) ).

fof(f69,plain,
    ! [X0] : id(X0,X0),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,plain,
    ! [X0] : id(X0,X0),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X13] : id(X13,X13),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).

fof(f126,plain,
    ! [X1] :
      ( ~ id(X1,sK19)
      | r1(X1) ),
    inference(cnf_transformation,[],[f67]) ).

fof(f67,plain,
    ! [X1] :
      ( ( ~ id(X1,sK19)
        & ~ r1(X1) )
      | ( r1(X1)
        & id(X1,sK19) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f1,f66]) ).

fof(f66,plain,
    ( ? [X0] :
      ! [X1] :
        ( ( ~ id(X1,X0)
          & ~ r1(X1) )
        | ( r1(X1)
          & id(X1,X0) ) )
   => ! [X1] :
        ( ( ~ id(X1,sK19)
          & ~ r1(X1) )
        | ( r1(X1)
          & id(X1,sK19) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f1,axiom,
    ? [X0] :
    ! [X1] :
      ( ( ~ id(X1,X0)
        & ~ r1(X1) )
      | ( r1(X1)
        & id(X1,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).

fof(f247,plain,
    ! [X0] : ~ r1(X0),
    inference(resolution,[],[f237,f202]) ).

fof(f202,plain,
    ! [X0,X1] :
      ( sP21(sK12(X1,X0))
      | ~ r1(X0) ),
    inference(resolution,[],[f129,f93]) ).

fof(f93,plain,
    ! [X0,X1] : r2(X1,sK12(X0,X1)),
    inference(cnf_transformation,[],[f56]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( r4(X0,X1,sK10(X0,X1))
      & r3(sK10(X0,X1),X0,sK9(X0,X1))
      & r4(X0,sK12(X0,X1),sK11(X0,X1))
      & r2(X1,sK12(X0,X1))
      & id(sK11(X0,X1),sK9(X0,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12])],[f31,f55,f54,f53,f52]) ).

fof(f52,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ? [X3] :
              ( r4(X0,X1,X3)
              & r3(X3,X0,X2) )
          & ? [X4] :
              ( ? [X5] :
                  ( r4(X0,X5,X4)
                  & r2(X1,X5) )
              & id(X4,X2) ) )
     => ( ? [X3] :
            ( r4(X0,X1,X3)
            & r3(X3,X0,sK9(X0,X1)) )
        & ? [X4] :
            ( ? [X5] :
                ( r4(X0,X5,X4)
                & r2(X1,X5) )
            & id(X4,sK9(X0,X1)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f53,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( r4(X0,X1,X3)
          & r3(X3,X0,sK9(X0,X1)) )
     => ( r4(X0,X1,sK10(X0,X1))
        & r3(sK10(X0,X1),X0,sK9(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f54,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( ? [X5] :
              ( r4(X0,X5,X4)
              & r2(X1,X5) )
          & id(X4,sK9(X0,X1)) )
     => ( ? [X5] :
            ( r4(X0,X5,sK11(X0,X1))
            & r2(X1,X5) )
        & id(sK11(X0,X1),sK9(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f55,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( r4(X0,X5,sK11(X0,X1))
          & r2(X1,X5) )
     => ( r4(X0,sK12(X0,X1),sK11(X0,X1))
        & r2(X1,sK12(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f31,plain,
    ! [X0,X1] :
    ? [X2] :
      ( ? [X3] :
          ( r4(X0,X1,X3)
          & r3(X3,X0,X2) )
      & ? [X4] :
          ( ? [X5] :
              ( r4(X0,X5,X4)
              & r2(X1,X5) )
          & id(X4,X2) ) ),
    inference(rectify,[],[f13]) ).

fof(f13,axiom,
    ! [X43,X44] :
    ? [X45] :
      ( ? [X48] :
          ( r4(X43,X44,X48)
          & r3(X48,X43,X45) )
      & ? [X46] :
          ( ? [X47] :
              ( r4(X43,X47,X46)
              & r2(X44,X47) )
          & id(X46,X45) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2a) ).

fof(f129,plain,
    ! [X6,X7] :
      ( ~ r2(X7,X6)
      | ~ r1(X7)
      | sP21(X6) ),
    inference(cnf_transformation,[],[f129_D]) ).

fof(f129_D,plain,
    ! [X6] :
      ( ! [X7] :
          ( ~ r2(X7,X6)
          | ~ r1(X7) )
    <=> ~ sP21(X6) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP21])]) ).

fof(f237,plain,
    ! [X0] : ~ sP21(X0),
    inference(resolution,[],[f228,f204]) ).

fof(f204,plain,
    ! [X0,X1] :
      ( sP22(sK12(X1,X0))
      | ~ sP21(X0) ),
    inference(resolution,[],[f131,f93]) ).

fof(f131,plain,
    ! [X6,X5] :
      ( ~ r2(X6,X5)
      | ~ sP21(X6)
      | sP22(X5) ),
    inference(cnf_transformation,[],[f131_D]) ).

fof(f131_D,plain,
    ! [X5] :
      ( ! [X6] :
          ( ~ r2(X6,X5)
          | ~ sP21(X6) )
    <=> ~ sP22(X5) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP22])]) ).

fof(f228,plain,
    ! [X0] : ~ sP22(X0),
    inference(resolution,[],[f222,f206]) ).

fof(f206,plain,
    ! [X0,X1] :
      ( sP23(sK12(X1,X0))
      | ~ sP22(X0) ),
    inference(resolution,[],[f133,f93]) ).

fof(f133,plain,
    ! [X4,X5] :
      ( ~ r2(X5,X4)
      | ~ sP22(X5)
      | sP23(X4) ),
    inference(cnf_transformation,[],[f133_D]) ).

fof(f133_D,plain,
    ! [X4] :
      ( ! [X5] :
          ( ~ r2(X5,X4)
          | ~ sP22(X5) )
    <=> ~ sP23(X4) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP23])]) ).

fof(f222,plain,
    ! [X0] : ~ sP23(X0),
    inference(resolution,[],[f219,f208]) ).

fof(f208,plain,
    ! [X0,X1] :
      ( sP24(sK12(X1,X0))
      | ~ sP23(X0) ),
    inference(resolution,[],[f135,f93]) ).

fof(f135,plain,
    ! [X3,X4] :
      ( ~ r2(X4,X3)
      | ~ sP23(X4)
      | sP24(X3) ),
    inference(cnf_transformation,[],[f135_D]) ).

fof(f135_D,plain,
    ! [X3] :
      ( ! [X4] :
          ( ~ r2(X4,X3)
          | ~ sP23(X4) )
    <=> ~ sP24(X3) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP24])]) ).

fof(f219,plain,
    ! [X0] : ~ sP24(X0),
    inference(resolution,[],[f216,f193]) ).

fof(f193,plain,
    ! [X0] : sP20(X0),
    inference(resolution,[],[f127,f69]) ).

fof(f127,plain,
    ! [X2,X0] :
      ( ~ id(X2,X0)
      | sP20(X2) ),
    inference(cnf_transformation,[],[f127_D]) ).

fof(f127_D,plain,
    ! [X2] :
      ( ! [X0] : ~ id(X2,X0)
    <=> ~ sP20(X2) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP20])]) ).

fof(f216,plain,
    ! [X0,X1] :
      ( ~ sP20(sK14(X0,X1))
      | ~ sP24(X1) ),
    inference(resolution,[],[f136,f101]) ).

fof(f101,plain,
    ! [X0,X1] : r3(X0,X1,sK14(X0,X1)),
    inference(cnf_transformation,[],[f61]) ).

fof(f61,plain,
    ! [X0,X1] :
      ( r3(X0,X1,sK14(X0,X1))
      & r2(sK14(X0,X1),sK13(X0,X1))
      & r3(X0,sK16(X0,X1),sK15(X0,X1))
      & r2(X1,sK16(X0,X1))
      & id(sK15(X0,X1),sK13(X0,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16])],[f32,f60,f59,f58,f57]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ? [X3] :
              ( r3(X0,X1,X3)
              & r2(X3,X2) )
          & ? [X4] :
              ( ? [X5] :
                  ( r3(X0,X5,X4)
                  & r2(X1,X5) )
              & id(X4,X2) ) )
     => ( ? [X3] :
            ( r3(X0,X1,X3)
            & r2(X3,sK13(X0,X1)) )
        & ? [X4] :
            ( ? [X5] :
                ( r3(X0,X5,X4)
                & r2(X1,X5) )
            & id(X4,sK13(X0,X1)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f58,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( r3(X0,X1,X3)
          & r2(X3,sK13(X0,X1)) )
     => ( r3(X0,X1,sK14(X0,X1))
        & r2(sK14(X0,X1),sK13(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( ? [X5] :
              ( r3(X0,X5,X4)
              & r2(X1,X5) )
          & id(X4,sK13(X0,X1)) )
     => ( ? [X5] :
            ( r3(X0,X5,sK15(X0,X1))
            & r2(X1,X5) )
        & id(sK15(X0,X1),sK13(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f60,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( r3(X0,X5,sK15(X0,X1))
          & r2(X1,X5) )
     => ( r3(X0,sK16(X0,X1),sK15(X0,X1))
        & r2(X1,sK16(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f32,plain,
    ! [X0,X1] :
    ? [X2] :
      ( ? [X3] :
          ( r3(X0,X1,X3)
          & r2(X3,X2) )
      & ? [X4] :
          ( ? [X5] :
              ( r3(X0,X5,X4)
              & r2(X1,X5) )
          & id(X4,X2) ) ),
    inference(rectify,[],[f12]) ).

fof(f12,axiom,
    ! [X37,X38] :
    ? [X39] :
      ( ? [X42] :
          ( r3(X37,X38,X42)
          & r2(X42,X39) )
      & ? [X40] :
          ( ? [X41] :
              ( r3(X37,X41,X40)
              & r2(X38,X41) )
          & id(X40,X39) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1a) ).

fof(f136,plain,
    ! [X2,X3,X1] :
      ( ~ r3(X1,X3,X2)
      | ~ sP20(X2)
      | ~ sP24(X3) ),
    inference(general_splitting,[],[f134,f135_D]) ).

fof(f134,plain,
    ! [X2,X3,X1,X4] :
      ( ~ r2(X4,X3)
      | ~ r3(X1,X3,X2)
      | ~ sP20(X2)
      | ~ sP23(X4) ),
    inference(general_splitting,[],[f132,f133_D]) ).

fof(f132,plain,
    ! [X2,X3,X1,X4,X5] :
      ( ~ r2(X5,X4)
      | ~ r2(X4,X3)
      | ~ r3(X1,X3,X2)
      | ~ sP20(X2)
      | ~ sP22(X5) ),
    inference(general_splitting,[],[f130,f131_D]) ).

fof(f130,plain,
    ! [X2,X3,X1,X6,X4,X5] :
      ( ~ r2(X6,X5)
      | ~ r2(X5,X4)
      | ~ r2(X4,X3)
      | ~ r3(X1,X3,X2)
      | ~ sP20(X2)
      | ~ sP21(X6) ),
    inference(general_splitting,[],[f128,f129_D]) ).

fof(f128,plain,
    ! [X2,X3,X1,X6,X7,X4,X5] :
      ( ~ r2(X7,X6)
      | ~ r1(X7)
      | ~ r2(X6,X5)
      | ~ r2(X5,X4)
      | ~ r2(X4,X3)
      | ~ r3(X1,X3,X2)
      | ~ sP20(X2) ),
    inference(general_splitting,[],[f68,f127_D]) ).

fof(f68,plain,
    ! [X2,X3,X0,X1,X6,X7,X4,X5] :
      ( ~ r2(X7,X6)
      | ~ r1(X7)
      | ~ r2(X6,X5)
      | ~ r2(X5,X4)
      | ~ r2(X4,X3)
      | ~ r3(X1,X3,X2)
      | ~ id(X2,X0) ),
    inference(cnf_transformation,[],[f39]) ).

fof(f39,plain,
    ! [X0,X1,X2] :
      ( ! [X3] :
          ( ! [X4] :
              ( ! [X5] :
                  ( ! [X6] :
                      ( ! [X7] :
                          ( ~ r2(X7,X6)
                          | ~ r1(X7) )
                      | ~ r2(X6,X5) )
                  | ~ r2(X5,X4) )
              | ~ r2(X4,X3) )
          | ~ r3(X1,X3,X2) )
      | ~ id(X2,X0) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,plain,
    ~ ? [X0,X1,X2] :
        ( ? [X3] :
            ( ? [X4] :
                ( ? [X5] :
                    ( ? [X6] :
                        ( ? [X7] :
                            ( r2(X7,X6)
                            & r1(X7) )
                        & r2(X6,X5) )
                    & r2(X5,X4) )
                & r2(X4,X3) )
            & r3(X1,X3,X2) )
        & id(X2,X0) ),
    inference(rectify,[],[f20]) ).

fof(f20,negated_conjecture,
    ~ ? [X62,X45,X46] :
        ( ? [X39] :
            ( ? [X40] :
                ( ? [X48] :
                    ( ? [X42] :
                        ( ? [X57] :
                            ( r2(X57,X42)
                            & r1(X57) )
                        & r2(X42,X48) )
                    & r2(X48,X40) )
                & r2(X40,X39) )
            & r3(X45,X39,X46) )
        & id(X46,X62) ),
    inference(negated_conjecture,[],[f19]) ).

fof(f19,conjecture,
    ? [X62,X45,X46] :
      ( ? [X39] :
          ( ? [X40] :
              ( ? [X48] :
                  ( ? [X42] :
                      ( ? [X57] :
                          ( r2(X57,X42)
                          & r1(X57) )
                      & r2(X42,X48) )
                  & r2(X48,X40) )
              & r2(X40,X39) )
          & r3(X45,X39,X46) )
      & id(X46,X62) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',greq4id) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14  % Problem    : NUN060+1 : TPTP v8.2.0. Released v7.3.0.
% 0.13/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.37  % Computer : n012.cluster.edu
% 0.13/0.37  % Model    : x86_64 x86_64
% 0.13/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37  % Memory   : 8042.1875MB
% 0.13/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.37  % CPULimit   : 300
% 0.13/0.37  % WCLimit    : 300
% 0.13/0.37  % DateTime   : Sat May 18 15:09:38 EDT 2024
% 0.13/0.37  % CPUTime    : 
% 0.13/0.37  % (23786)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.39  % (23787)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.13/0.39  % (23789)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)
% 0.13/0.39  % (23792)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.13/0.39  % (23791)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.13/0.39  % (23793)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)
% 0.13/0.39  % (23790)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.13/0.40  TRYING [1]
% 0.13/0.40  TRYING [1]
% 0.13/0.40  TRYING [2]
% 0.13/0.40  TRYING [2]
% 0.13/0.40  % (23788)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.13/0.40  TRYING [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
% 0.13/0.40  % (23789)First to succeed.
% 0.13/0.40  TRYING [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
% 0.13/0.40  % (23789)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-23786"
% 0.13/0.40  TRYING [3]
% 0.13/0.40  % (23789)Refutation found. Thanks to Tanya!
% 0.13/0.40  % SZS status Theorem for theBenchmark
% 0.13/0.40  % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.40  % (23789)------------------------------
% 0.13/0.40  % (23789)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.40  % (23789)Termination reason: Refutation
% 0.13/0.40  
% 0.13/0.40  % (23789)Memory used [KB]: 943
% 0.13/0.40  % (23789)Time elapsed: 0.008 s
% 0.13/0.40  % (23789)Instructions burned: 10 (million)
% 0.13/0.40  % (23786)Success in time 0.025 s
%------------------------------------------------------------------------------