TSTP Solution File: NUN060+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : NUN060+1 : TPTP v8.1.0. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -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 : Wed Aug 31 18:08:01 EDT 2022

% Result   : Theorem 0.21s 0.52s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   46 (  10 unt;   0 def)
%            Number of atoms       :  197 (   0 equ)
%            Maximal formula atoms :   10 (   4 avg)
%            Number of connectives :  204 (  53   ~;  38   |; 102   &)
%                                         (   0 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   7 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   1 con; 0-2 aty)
%            Number of variables   :  182 ( 100   !;  82   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f153,plain,
    $false,
    inference(resolution,[],[f151,f139]) ).

fof(f139,plain,
    r1(sK7(sK3)),
    inference(resolution,[],[f86,f110]) ).

fof(f110,plain,
    ! [X0] : id(sK7(X0),X0),
    inference(cnf_transformation,[],[f59]) ).

fof(f59,plain,
    ! [X0] :
      ( r1(sK8(X0))
      & r3(X0,sK8(X0),sK7(X0))
      & id(sK7(X0),X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f23,f58,f57]) ).

fof(f57,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( r1(X2)
              & r3(X0,X2,X1) )
          & id(X1,X0) )
     => ( ? [X2] :
            ( r1(X2)
            & r3(X0,X2,sK7(X0)) )
        & id(sK7(X0),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f58,plain,
    ! [X0] :
      ( ? [X2] :
          ( r1(X2)
          & r3(X0,X2,sK7(X0)) )
     => ( r1(sK8(X0))
        & r3(X0,sK8(X0),sK7(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f23,plain,
    ! [X0] :
    ? [X1] :
      ( ? [X2] :
          ( r1(X2)
          & r3(X0,X2,X1) )
      & id(X1,X0) ),
    inference(rectify,[],[f15]) ).

fof(f15,axiom,
    ! [X53] :
    ? [X54] :
      ( ? [X55] :
          ( r1(X55)
          & r3(X53,X55,X54) )
      & id(X54,X53) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4a) ).

fof(f86,plain,
    ! [X1] :
      ( ~ id(X1,sK3)
      | r1(X1) ),
    inference(cnf_transformation,[],[f45]) ).

fof(f45,plain,
    ! [X1] :
      ( ( ~ id(X1,sK3)
        & ~ r1(X1) )
      | ( r1(X1)
        & id(X1,sK3) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f1,f44]) ).

fof(f44,plain,
    ( ? [X0] :
      ! [X1] :
        ( ( ~ id(X1,X0)
          & ~ r1(X1) )
        | ( r1(X1)
          & id(X1,X0) ) )
   => ! [X1] :
        ( ( ~ id(X1,sK3)
          & ~ r1(X1) )
        | ( r1(X1)
          & id(X1,sK3) ) ) ),
    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(f151,plain,
    ! [X1] : ~ r1(X1),
    inference(resolution,[],[f148,f131]) ).

fof(f131,plain,
    ! [X0,X1] : r2(X0,sK18(X0,X1)),
    inference(cnf_transformation,[],[f76]) ).

fof(f76,plain,
    ! [X0,X1] :
      ( r4(X1,sK18(X0,X1),sK17(X0,X1))
      & r2(X0,sK18(X0,X1))
      & id(sK17(X0,X1),sK16(X0,X1))
      & r3(sK19(X0,X1),X1,sK16(X0,X1))
      & r4(X1,X0,sK19(X0,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK16,sK17,sK18,sK19])],[f71,f75,f74,f73,f72]) ).

fof(f72,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ? [X3] :
              ( ? [X4] :
                  ( r4(X1,X4,X3)
                  & r2(X0,X4) )
              & id(X3,X2) )
          & ? [X5] :
              ( r3(X5,X1,X2)
              & r4(X1,X0,X5) ) )
     => ( ? [X3] :
            ( ? [X4] :
                ( r4(X1,X4,X3)
                & r2(X0,X4) )
            & id(X3,sK16(X0,X1)) )
        & ? [X5] :
            ( r3(X5,X1,sK16(X0,X1))
            & r4(X1,X0,X5) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f73,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( ? [X4] :
              ( r4(X1,X4,X3)
              & r2(X0,X4) )
          & id(X3,sK16(X0,X1)) )
     => ( ? [X4] :
            ( r4(X1,X4,sK17(X0,X1))
            & r2(X0,X4) )
        & id(sK17(X0,X1),sK16(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f74,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( r4(X1,X4,sK17(X0,X1))
          & r2(X0,X4) )
     => ( r4(X1,sK18(X0,X1),sK17(X0,X1))
        & r2(X0,sK18(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f75,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( r3(X5,X1,sK16(X0,X1))
          & r4(X1,X0,X5) )
     => ( r3(sK19(X0,X1),X1,sK16(X0,X1))
        & r4(X1,X0,sK19(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f71,plain,
    ! [X0,X1] :
    ? [X2] :
      ( ? [X3] :
          ( ? [X4] :
              ( r4(X1,X4,X3)
              & r2(X0,X4) )
          & id(X3,X2) )
      & ? [X5] :
          ( r3(X5,X1,X2)
          & r4(X1,X0,X5) ) ),
    inference(rectify,[],[f21]) ).

fof(f21,plain,
    ! [X1,X0] :
    ? [X2] :
      ( ? [X3] :
          ( ? [X4] :
              ( r4(X0,X4,X3)
              & r2(X1,X4) )
          & id(X3,X2) )
      & ? [X5] :
          ( r3(X5,X0,X2)
          & r4(X0,X1,X5) ) ),
    inference(rectify,[],[f13]) ).

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

fof(f148,plain,
    ! [X2,X0,X1] :
      ( ~ r2(sK12(X1,X0),X2)
      | ~ r1(X0) ),
    inference(resolution,[],[f146,f114]) ).

fof(f114,plain,
    ! [X0,X1] : r2(X1,sK12(X0,X1)),
    inference(cnf_transformation,[],[f65]) ).

fof(f65,plain,
    ! [X0,X1] :
      ( r2(sK10(X0,X1),sK9(X0,X1))
      & r3(X0,X1,sK10(X0,X1))
      & r3(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])],[f60,f64,f63,f62,f61]) ).

fof(f61,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ? [X3] :
              ( r2(X3,X2)
              & r3(X0,X1,X3) )
          & ? [X4] :
              ( ? [X5] :
                  ( r3(X0,X5,X4)
                  & r2(X1,X5) )
              & id(X4,X2) ) )
     => ( ? [X3] :
            ( r2(X3,sK9(X0,X1))
            & r3(X0,X1,X3) )
        & ? [X4] :
            ( ? [X5] :
                ( r3(X0,X5,X4)
                & r2(X1,X5) )
            & id(X4,sK9(X0,X1)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( r2(X3,sK9(X0,X1))
          & r3(X0,X1,X3) )
     => ( r2(sK10(X0,X1),sK9(X0,X1))
        & r3(X0,X1,sK10(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( ? [X5] :
              ( r3(X0,X5,X4)
              & r2(X1,X5) )
          & id(X4,sK9(X0,X1)) )
     => ( ? [X5] :
            ( r3(X0,X5,sK11(X0,X1))
            & r2(X1,X5) )
        & id(sK11(X0,X1),sK9(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f64,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( r3(X0,X5,sK11(X0,X1))
          & r2(X1,X5) )
     => ( r3(X0,sK12(X0,X1),sK11(X0,X1))
        & r2(X1,sK12(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f60,plain,
    ! [X0,X1] :
    ? [X2] :
      ( ? [X3] :
          ( r2(X3,X2)
          & r3(X0,X1,X3) )
      & ? [X4] :
          ( ? [X5] :
              ( r3(X0,X5,X4)
              & r2(X1,X5) )
          & id(X4,X2) ) ),
    inference(rectify,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1] :
    ? [X2] :
      ( ? [X5] :
          ( r2(X5,X2)
          & r3(X0,X1,X5) )
      & ? [X3] :
          ( ? [X4] :
              ( r3(X0,X4,X3)
              & r2(X1,X4) )
          & id(X3,X2) ) ),
    inference(rectify,[],[f12]) ).

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

fof(f146,plain,
    ! [X2,X0,X1] :
      ( ~ r2(X2,X0)
      | ~ r1(X2)
      | ~ r2(X0,X1) ),
    inference(resolution,[],[f144,f114]) ).

fof(f144,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ r2(sK12(X0,X1),X2)
      | ~ r2(X3,X1)
      | ~ r2(X4,X3)
      | ~ r1(X4) ),
    inference(resolution,[],[f142,f114]) ).

fof(f142,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ r2(X4,X2)
      | ~ r2(X2,X3)
      | ~ r2(X1,X4)
      | ~ r1(X0)
      | ~ r2(X0,X1) ),
    inference(resolution,[],[f141,f99]) ).

fof(f99,plain,
    ! [X0] : id(X0,X0),
    inference(cnf_transformation,[],[f35]) ).

fof(f35,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(f141,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ id(sK10(X0,X1),X2)
      | ~ r1(X5)
      | ~ r2(X5,X3)
      | ~ r2(X6,X1)
      | ~ r2(X4,X6)
      | ~ r2(X3,X4) ),
    inference(resolution,[],[f116,f101]) ).

fof(f101,plain,
    ! [X2,X3,X0,X1,X6,X7,X4,X5] :
      ( ~ r3(X0,X3,X1)
      | ~ id(X1,X2)
      | ~ r2(X6,X5)
      | ~ r2(X7,X6)
      | ~ r1(X7)
      | ~ r2(X5,X4)
      | ~ r2(X4,X3) ),
    inference(cnf_transformation,[],[f52]) ).

fof(f52,plain,
    ! [X0,X1,X2] :
      ( ! [X3] :
          ( ! [X4] :
              ( ! [X5] :
                  ( ~ r2(X5,X4)
                  | ! [X6] :
                      ( ~ r2(X6,X5)
                      | ! [X7] :
                          ( ~ r1(X7)
                          | ~ r2(X7,X6) ) ) )
              | ~ r2(X4,X3) )
          | ~ r3(X0,X3,X1) )
      | ~ id(X1,X2) ),
    inference(rectify,[],[f39]) ).

fof(f39,plain,
    ! [X0,X2,X1] :
      ( ! [X3] :
          ( ! [X4] :
              ( ! [X5] :
                  ( ~ r2(X5,X4)
                  | ! [X6] :
                      ( ~ r2(X6,X5)
                      | ! [X7] :
                          ( ~ r1(X7)
                          | ~ r2(X7,X6) ) ) )
              | ~ r2(X4,X3) )
          | ~ r3(X0,X3,X2) )
      | ~ id(X2,X1) ),
    inference(ennf_transformation,[],[f27]) ).

fof(f27,plain,
    ~ ? [X1,X2,X0] :
        ( id(X2,X1)
        & ? [X3] :
            ( ? [X4] :
                ( ? [X5] :
                    ( ? [X6] :
                        ( ? [X7] :
                            ( r1(X7)
                            & r2(X7,X6) )
                        & r2(X6,X5) )
                    & r2(X5,X4) )
                & r2(X4,X3) )
            & r3(X0,X3,X2) ) ),
    inference(rectify,[],[f20]) ).

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

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

fof(f116,plain,
    ! [X0,X1] : r3(X0,X1,sK10(X0,X1)),
    inference(cnf_transformation,[],[f65]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : NUN060+1 : TPTP v8.1.0. Released v7.3.0.
% 0.11/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34  % Computer : n008.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Tue Aug 30 09:46:40 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.21/0.48  % (31291)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.21/0.48  % (31274)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.21/0.50  % (31283)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 0.21/0.51  % (31283)First to succeed.
% 0.21/0.51  % (31263)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.21/0.51  % (31265)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.21/0.52  % (31277)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.21/0.52  % (31283)Refutation found. Thanks to Tanya!
% 0.21/0.52  % SZS status Theorem for theBenchmark
% 0.21/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.52  % (31283)------------------------------
% 0.21/0.52  % (31283)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.52  % (31283)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.52  % (31283)Termination reason: Refutation
% 0.21/0.52  
% 0.21/0.52  % (31283)Memory used [KB]: 5500
% 0.21/0.52  % (31283)Time elapsed: 0.117 s
% 0.21/0.52  % (31283)Instructions burned: 5 (million)
% 0.21/0.52  % (31283)------------------------------
% 0.21/0.52  % (31283)------------------------------
% 0.21/0.52  % (31262)Success in time 0.165 s
%------------------------------------------------------------------------------