TSTP Solution File: NUN059+2 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : NUN059+2 : TPTP v8.1.0. Bugfixed v7.4.0.
% 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 : n018.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 0.20s 0.49s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   50 (  18 unt;   0 def)
%            Number of atoms       :  166 (  40 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  152 (  36   ~;  23   |;  83   &)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :   10 (  10 usr;   1 con; 0-2 aty)
%            Number of variables   :  152 (  84   !;  68   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f129,plain,
    $false,
    inference(resolution,[],[f128,f124]) ).

fof(f124,plain,
    ! [X0] : ~ r4(X0,X0,sK3),
    inference(resolution,[],[f123,f70]) ).

fof(f70,plain,
    ! [X0,X1] : r4(X0,X1,sK7(X0,X1)),
    inference(cnf_transformation,[],[f38]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( sK4(X0,X1) = sK5(X0,X1)
      & r4(X0,sK6(X0,X1),sK5(X0,X1))
      & r2(X1,sK6(X0,X1))
      & r3(sK7(X0,X1),X0,sK4(X0,X1))
      & r4(X0,X1,sK7(X0,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f33,f37,f36,f35,f34]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ? [X3] :
              ( X2 = X3
              & ? [X4] :
                  ( r4(X0,X4,X3)
                  & r2(X1,X4) ) )
          & ? [X5] :
              ( r3(X5,X0,X2)
              & r4(X0,X1,X5) ) )
     => ( ? [X3] :
            ( sK4(X0,X1) = X3
            & ? [X4] :
                ( r4(X0,X4,X3)
                & r2(X1,X4) ) )
        & ? [X5] :
            ( r3(X5,X0,sK4(X0,X1))
            & r4(X0,X1,X5) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( sK4(X0,X1) = X3
          & ? [X4] :
              ( r4(X0,X4,X3)
              & r2(X1,X4) ) )
     => ( sK4(X0,X1) = sK5(X0,X1)
        & ? [X4] :
            ( r4(X0,X4,sK5(X0,X1))
            & r2(X1,X4) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( r4(X0,X4,sK5(X0,X1))
          & r2(X1,X4) )
     => ( r4(X0,sK6(X0,X1),sK5(X0,X1))
        & r2(X1,sK6(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( r3(X5,X0,sK4(X0,X1))
          & r4(X0,X1,X5) )
     => ( r3(sK7(X0,X1),X0,sK4(X0,X1))
        & r4(X0,X1,sK7(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f33,plain,
    ! [X0,X1] :
    ? [X2] :
      ( ? [X3] :
          ( X2 = X3
          & ? [X4] :
              ( r4(X0,X4,X3)
              & r2(X1,X4) ) )
      & ? [X5] :
          ( r3(X5,X0,X2)
          & r4(X0,X1,X5) ) ),
    inference(rectify,[],[f24]) ).

fof(f24,plain,
    ! [X1,X0] :
    ? [X2] :
      ( ? [X4] :
          ( X2 = X4
          & ? [X5] :
              ( r4(X1,X5,X4)
              & r2(X0,X5) ) )
      & ? [X3] :
          ( r3(X3,X1,X2)
          & r4(X1,X0,X3) ) ),
    inference(rectify,[],[f6]) ).

fof(f6,axiom,
    ! [X20,X19] :
    ? [X21] :
      ( ? [X24] :
          ( r3(X24,X19,X21)
          & r4(X19,X20,X24) )
      & ? [X22] :
          ( ? [X23] :
              ( r2(X20,X23)
              & r4(X19,X23,X22) )
          & X21 = X22 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2a) ).

fof(f123,plain,
    ! [X2,X0,X1] :
      ( ~ r4(X0,X0,sK7(X1,X1))
      | ~ r4(X2,X2,sK3) ),
    inference(resolution,[],[f70,f122]) ).

fof(f122,plain,
    ! [X2,X3,X0,X1] :
      ( ~ r4(X1,X1,X2)
      | ~ r4(X3,X3,X2)
      | ~ r4(X0,X0,sK3) ),
    inference(resolution,[],[f121,f106]) ).

fof(f106,plain,
    ! [X2,X3,X1,X6,X4,X5] :
      ( ~ r3(X5,X4,X6)
      | ~ r4(X1,X1,X4)
      | ~ r4(X2,X2,X6)
      | ~ r4(X3,X3,X5) ),
    inference(equality_resolution,[],[f75]) ).

fof(f75,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ r4(X1,X1,X4)
      | ~ r3(X5,X4,X0)
      | ~ r4(X3,X3,X5)
      | ~ r4(X2,X2,X6)
      | X0 != X6 ),
    inference(cnf_transformation,[],[f39]) ).

fof(f39,plain,
    ! [X0,X1,X2,X3] :
      ( ! [X4] :
          ( ~ r4(X1,X1,X4)
          | ! [X5] :
              ( ~ r3(X5,X4,X0)
              | ~ r4(X3,X3,X5) ) )
      | ! [X6] :
          ( ~ r4(X2,X2,X6)
          | X0 != X6 ) ),
    inference(rectify,[],[f25]) ).

fof(f25,plain,
    ! [X2,X3,X0,X1] :
      ( ! [X5] :
          ( ~ r4(X3,X3,X5)
          | ! [X6] :
              ( ~ r3(X6,X5,X2)
              | ~ r4(X1,X1,X6) ) )
      | ! [X4] :
          ( ~ r4(X0,X0,X4)
          | X2 != X4 ) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f23,plain,
    ~ ? [X1,X0,X2,X3] :
        ( ? [X4] :
            ( X2 = X4
            & r4(X0,X0,X4) )
        & ? [X5] :
            ( r4(X3,X3,X5)
            & ? [X6] :
                ( r3(X6,X5,X2)
                & r4(X1,X1,X6) ) ) ),
    inference(rectify,[],[f13]) ).

fof(f13,negated_conjecture,
    ~ ? [X21,X38,X15,X22] :
        ( ? [X16] :
            ( X15 = X16
            & r4(X21,X21,X16) )
        & ? [X24] :
            ( ? [X18] :
                ( r3(X18,X24,X15)
                & r4(X38,X38,X18) )
            & r4(X22,X22,X24) ) ),
    inference(negated_conjecture,[],[f12]) ).

fof(f12,conjecture,
    ? [X21,X38,X15,X22] :
      ( ? [X16] :
          ( X15 = X16
          & r4(X21,X21,X16) )
      & ? [X24] :
          ( ? [X18] :
              ( r3(X18,X24,X15)
              & r4(X38,X38,X18) )
          & r4(X22,X22,X24) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fermattothepoweroftwo) ).

fof(f121,plain,
    ! [X0] : r3(X0,sK3,X0),
    inference(forward_demodulation,[],[f120,f112]) ).

fof(f112,plain,
    ! [X0] : sK3 = sK1(X0),
    inference(resolution,[],[f67,f59]) ).

fof(f59,plain,
    ! [X0] : r1(sK1(X0)),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,plain,
    ! [X0] :
      ( r3(X0,sK1(X0),sK0(X0))
      & r1(sK1(X0))
      & sK0(X0) = X0 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f16,f27,f26]) ).

fof(f26,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( r3(X0,X2,X1)
              & r1(X2) )
          & X0 = X1 )
     => ( ? [X2] :
            ( r3(X0,X2,sK0(X0))
            & r1(X2) )
        & sK0(X0) = X0 ) ),
    introduced(choice_axiom,[]) ).

fof(f27,plain,
    ! [X0] :
      ( ? [X2] :
          ( r3(X0,X2,sK0(X0))
          & r1(X2) )
     => ( r3(X0,sK1(X0),sK0(X0))
        & r1(sK1(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f16,plain,
    ! [X0] :
    ? [X1] :
      ( ? [X2] :
          ( r3(X0,X2,X1)
          & r1(X2) )
      & X0 = X1 ),
    inference(rectify,[],[f8]) ).

fof(f8,axiom,
    ! [X29] :
    ? [X30] :
      ( ? [X31] :
          ( r3(X29,X31,X30)
          & r1(X31) )
      & X29 = X30 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4a) ).

fof(f67,plain,
    ! [X1] :
      ( ~ r1(X1)
      | sK3 = X1 ),
    inference(cnf_transformation,[],[f32]) ).

fof(f32,plain,
    ! [X1] :
      ( ( r1(X1)
        & sK3 = X1 )
      | ( ~ r1(X1)
        & sK3 != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f1,f31]) ).

fof(f31,plain,
    ( ? [X0] :
      ! [X1] :
        ( ( r1(X1)
          & X0 = X1 )
        | ( ~ r1(X1)
          & X0 != X1 ) )
   => ! [X1] :
        ( ( r1(X1)
          & sK3 = X1 )
        | ( ~ r1(X1)
          & sK3 != X1 ) ) ),
    introduced(choice_axiom,[]) ).

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

fof(f120,plain,
    ! [X0] : r3(X0,sK1(X0),X0),
    inference(forward_demodulation,[],[f60,f58]) ).

fof(f58,plain,
    ! [X0] : sK0(X0) = X0,
    inference(cnf_transformation,[],[f28]) ).

fof(f60,plain,
    ! [X0] : r3(X0,sK1(X0),sK0(X0)),
    inference(cnf_transformation,[],[f28]) ).

fof(f128,plain,
    ! [X0] : r4(X0,sK3,sK3),
    inference(forward_demodulation,[],[f127,f114]) ).

fof(f114,plain,
    ! [X1] : sK3 = sK10(X1),
    inference(resolution,[],[f67,f83]) ).

fof(f83,plain,
    ! [X0] : r1(sK10(X0)),
    inference(cnf_transformation,[],[f45]) ).

fof(f45,plain,
    ! [X0] :
      ( r1(sK10(X0))
      & r4(X0,sK10(X0),sK9(X0))
      & r1(sK11(X0))
      & sK9(X0) = sK11(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f21,f44,f43,f42]) ).

fof(f42,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( r1(X2)
              & r4(X0,X2,X1) )
          & ? [X3] :
              ( r1(X3)
              & X1 = X3 ) )
     => ( ? [X2] :
            ( r1(X2)
            & r4(X0,X2,sK9(X0)) )
        & ? [X3] :
            ( r1(X3)
            & sK9(X0) = X3 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f43,plain,
    ! [X0] :
      ( ? [X2] :
          ( r1(X2)
          & r4(X0,X2,sK9(X0)) )
     => ( r1(sK10(X0))
        & r4(X0,sK10(X0),sK9(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f44,plain,
    ! [X0] :
      ( ? [X3] :
          ( r1(X3)
          & sK9(X0) = X3 )
     => ( r1(sK11(X0))
        & sK9(X0) = sK11(X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f21,plain,
    ! [X0] :
    ? [X1] :
      ( ? [X2] :
          ( r1(X2)
          & r4(X0,X2,X1) )
      & ? [X3] :
          ( r1(X3)
          & X1 = X3 ) ),
    inference(rectify,[],[f9]) ).

fof(f9,axiom,
    ! [X32] :
    ? [X33] :
      ( ? [X34] :
          ( r4(X32,X34,X33)
          & r1(X34) )
      & ? [X35] :
          ( X33 = X35
          & r1(X35) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5a) ).

fof(f127,plain,
    ! [X0] : r4(X0,sK10(X0),sK3),
    inference(forward_demodulation,[],[f99,f115]) ).

fof(f115,plain,
    ! [X2] : sK3 = sK11(X2),
    inference(resolution,[],[f67,f81]) ).

fof(f81,plain,
    ! [X0] : r1(sK11(X0)),
    inference(cnf_transformation,[],[f45]) ).

fof(f99,plain,
    ! [X0] : r4(X0,sK10(X0),sK11(X0)),
    inference(definition_unfolding,[],[f82,f80]) ).

fof(f80,plain,
    ! [X0] : sK9(X0) = sK11(X0),
    inference(cnf_transformation,[],[f45]) ).

fof(f82,plain,
    ! [X0] : r4(X0,sK10(X0),sK9(X0)),
    inference(cnf_transformation,[],[f45]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : NUN059+2 : TPTP v8.1.0. Bugfixed v7.4.0.
% 0.07/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.15/0.34  % Computer : n018.cluster.edu
% 0.15/0.34  % Model    : x86_64 x86_64
% 0.15/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34  % Memory   : 8042.1875MB
% 0.15/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34  % CPULimit   : 300
% 0.15/0.34  % WCLimit    : 300
% 0.15/0.34  % DateTime   : Tue Aug 30 09:47:10 EDT 2022
% 0.15/0.35  % CPUTime    : 
% 0.20/0.48  % (20460)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)
% 0.20/0.48  % (20469)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.20/0.48  % (20469)First to succeed.
% 0.20/0.49  % (20469)Refutation found. Thanks to Tanya!
% 0.20/0.49  % SZS status Theorem for theBenchmark
% 0.20/0.49  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.49  % (20469)------------------------------
% 0.20/0.49  % (20469)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.49  % (20469)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.49  % (20469)Termination reason: Refutation
% 0.20/0.49  
% 0.20/0.49  % (20469)Memory used [KB]: 1023
% 0.20/0.49  % (20469)Time elapsed: 0.073 s
% 0.20/0.49  % (20469)Instructions burned: 3 (million)
% 0.20/0.49  % (20469)------------------------------
% 0.20/0.49  % (20469)------------------------------
% 0.20/0.49  % (20442)Success in time 0.136 s
%------------------------------------------------------------------------------