TSTP Solution File: NUN080+2 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : NUN080+2 : 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 : n028.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 18:08:08 EDT 2022

% Result   : Theorem 0.19s 0.50s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   39 (   6 unt;   0 def)
%            Number of atoms       :  168 (  41 equ)
%            Maximal formula atoms :   10 (   4 avg)
%            Number of connectives :  176 (  47   ~;  29   |;  90   &)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   7 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   :  147 (  80   !;  67   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f139,plain,
    $false,
    inference(resolution,[],[f125,f80]) ).

fof(f80,plain,
    ! [X0,X1] : r2(X0,sK13(X0,X1)),
    inference(cnf_transformation,[],[f46]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( r4(X1,X0,sK11(X0,X1))
      & r3(sK11(X0,X1),X1,sK10(X0,X1))
      & sK10(X0,X1) = sK12(X0,X1)
      & r4(X1,sK13(X0,X1),sK12(X0,X1))
      & r2(X0,sK13(X0,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13])],[f22,f45,f44,f43,f42]) ).

fof(f42,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ? [X3] :
              ( r4(X1,X0,X3)
              & r3(X3,X1,X2) )
          & ? [X4] :
              ( X2 = X4
              & ? [X5] :
                  ( r4(X1,X5,X4)
                  & r2(X0,X5) ) ) )
     => ( ? [X3] :
            ( r4(X1,X0,X3)
            & r3(X3,X1,sK10(X0,X1)) )
        & ? [X4] :
            ( sK10(X0,X1) = X4
            & ? [X5] :
                ( r4(X1,X5,X4)
                & r2(X0,X5) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f43,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( r4(X1,X0,X3)
          & r3(X3,X1,sK10(X0,X1)) )
     => ( r4(X1,X0,sK11(X0,X1))
        & r3(sK11(X0,X1),X1,sK10(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( sK10(X0,X1) = X4
          & ? [X5] :
              ( r4(X1,X5,X4)
              & r2(X0,X5) ) )
     => ( sK10(X0,X1) = sK12(X0,X1)
        & ? [X5] :
            ( r4(X1,X5,sK12(X0,X1))
            & r2(X0,X5) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( r4(X1,X5,sK12(X0,X1))
          & r2(X0,X5) )
     => ( r4(X1,sK13(X0,X1),sK12(X0,X1))
        & r2(X0,sK13(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f22,plain,
    ! [X0,X1] :
    ? [X2] :
      ( ? [X3] :
          ( r4(X1,X0,X3)
          & r3(X3,X1,X2) )
      & ? [X4] :
          ( X2 = X4
          & ? [X5] :
              ( r4(X1,X5,X4)
              & r2(X0,X5) ) ) ),
    inference(rectify,[],[f6]) ).

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

fof(f125,plain,
    ! [X0] : ~ r2(sK9,X0),
    inference(resolution,[],[f121,f103]) ).

fof(f103,plain,
    ! [X0] : r2(X0,sK8(X0)),
    inference(equality_resolution,[],[f72]) ).

fof(f72,plain,
    ! [X2,X0] :
      ( sK8(X0) != X2
      | r2(X0,X2) ),
    inference(cnf_transformation,[],[f38]) ).

fof(f38,plain,
    ! [X0,X2] :
      ( ( ~ r2(X0,X2)
        & sK8(X0) != X2 )
      | ( r2(X0,X2)
        & sK8(X0) = X2 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f18,f37]) ).

fof(f37,plain,
    ! [X0] :
      ( ? [X1] :
        ! [X2] :
          ( ( ~ r2(X0,X2)
            & X1 != X2 )
          | ( r2(X0,X2)
            & X1 = X2 ) )
     => ! [X2] :
          ( ( ~ r2(X0,X2)
            & sK8(X0) != X2 )
          | ( r2(X0,X2)
            & sK8(X0) = X2 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f18,plain,
    ! [X0] :
    ? [X1] :
    ! [X2] :
      ( ( ~ r2(X0,X2)
        & X1 != X2 )
      | ( r2(X0,X2)
        & X1 = X2 ) ),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X2] :
    ? [X3] :
    ! [X4] :
      ( ( r2(X2,X4)
        & X3 = X4 )
      | ( X3 != X4
        & ~ r2(X2,X4) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).

fof(f121,plain,
    ! [X0,X1] :
      ( ~ r2(X0,X1)
      | ~ r2(sK9,X0) ),
    inference(resolution,[],[f120,f106]) ).

fof(f106,plain,
    r1(sK9),
    inference(equality_resolution,[],[f79]) ).

fof(f79,plain,
    ! [X1] :
      ( r1(X1)
      | sK9 != X1 ),
    inference(cnf_transformation,[],[f41]) ).

fof(f41,plain,
    ! [X1] :
      ( ( r1(X1)
        & sK9 = X1 )
      | ( sK9 != X1
        & ~ r1(X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f1,f40]) ).

fof(f40,plain,
    ( ? [X0] :
      ! [X1] :
        ( ( r1(X1)
          & X0 = X1 )
        | ( X0 != X1
          & ~ r1(X1) ) )
   => ! [X1] :
        ( ( r1(X1)
          & sK9 = X1 )
        | ( sK9 != X1
          & ~ r1(X1) ) ) ),
    introduced(choice_axiom,[]) ).

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

fof(f120,plain,
    ! [X2,X0,X1] :
      ( ~ r1(X0)
      | ~ r2(X1,X2)
      | ~ r2(X0,X1) ),
    inference(resolution,[],[f67,f105]) ).

fof(f105,plain,
    ! [X2,X3,X1,X4,X5] :
      ( ~ r3(X2,X3,X1)
      | ~ r2(X5,X4)
      | ~ r1(X5)
      | ~ r2(X4,X3) ),
    inference(equality_resolution,[],[f75]) ).

fof(f75,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ r2(X5,X4)
      | ~ r1(X5)
      | ~ r2(X4,X3)
      | ~ r3(X2,X3,X0)
      | X0 != X1 ),
    inference(cnf_transformation,[],[f39]) ).

fof(f39,plain,
    ! [X0,X1,X2] :
      ( ! [X3] :
          ( ! [X4] :
              ( ! [X5] :
                  ( ~ r2(X5,X4)
                  | ~ r1(X5) )
              | ~ r2(X4,X3) )
          | ~ r3(X2,X3,X0) )
      | X0 != X1 ),
    inference(rectify,[],[f25]) ).

fof(f25,plain,
    ! [X1,X0,X2] :
      ( ! [X3] :
          ( ! [X4] :
              ( ! [X5] :
                  ( ~ r2(X5,X4)
                  | ~ r1(X5) )
              | ~ r2(X4,X3) )
          | ~ r3(X2,X3,X1) )
      | X0 != X1 ),
    inference(ennf_transformation,[],[f20]) ).

fof(f20,plain,
    ~ ? [X2,X0,X1] :
        ( ? [X3] :
            ( ? [X4] :
                ( r2(X4,X3)
                & ? [X5] :
                    ( r2(X5,X4)
                    & r1(X5) ) )
            & r3(X2,X3,X1) )
        & X0 = X1 ),
    inference(rectify,[],[f13]) ).

fof(f13,negated_conjecture,
    ~ ? [X21,X22,X38] :
        ( ? [X15] :
            ( r3(X38,X15,X22)
            & ? [X16] :
                ( r2(X16,X15)
                & ? [X24] :
                    ( r1(X24)
                    & r2(X24,X16) ) ) )
        & X21 = X22 ),
    inference(negated_conjecture,[],[f12]) ).

fof(f12,conjecture,
    ? [X21,X22,X38] :
      ( ? [X15] :
          ( r3(X38,X15,X22)
          & ? [X16] :
              ( r2(X16,X15)
              & ? [X24] :
                  ( r1(X24)
                  & r2(X24,X16) ) ) )
      & X21 = X22 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',xplustwoeqy) ).

fof(f67,plain,
    ! [X0,X1] : r3(X0,X1,sK7(X0,X1)),
    inference(cnf_transformation,[],[f36]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( sK5(X0,X1) = sK4(X0,X1)
      & r3(X0,sK6(X0,X1),sK5(X0,X1))
      & r2(X1,sK6(X0,X1))
      & r3(X0,X1,sK7(X0,X1))
      & r2(sK7(X0,X1),sK4(X0,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f31,f35,f34,f33,f32]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ? [X3] :
              ( X2 = X3
              & ? [X4] :
                  ( r3(X0,X4,X3)
                  & r2(X1,X4) ) )
          & ? [X5] :
              ( r3(X0,X1,X5)
              & r2(X5,X2) ) )
     => ( ? [X3] :
            ( sK4(X0,X1) = X3
            & ? [X4] :
                ( r3(X0,X4,X3)
                & r2(X1,X4) ) )
        & ? [X5] :
            ( r3(X0,X1,X5)
            & r2(X5,sK4(X0,X1)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( sK4(X0,X1) = X3
          & ? [X4] :
              ( r3(X0,X4,X3)
              & r2(X1,X4) ) )
     => ( sK5(X0,X1) = sK4(X0,X1)
        & ? [X4] :
            ( r3(X0,X4,sK5(X0,X1))
            & r2(X1,X4) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( r3(X0,X4,sK5(X0,X1))
          & r2(X1,X4) )
     => ( r3(X0,sK6(X0,X1),sK5(X0,X1))
        & r2(X1,sK6(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( r3(X0,X1,X5)
          & r2(X5,sK4(X0,X1)) )
     => ( r3(X0,X1,sK7(X0,X1))
        & r2(sK7(X0,X1),sK4(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f31,plain,
    ! [X0,X1] :
    ? [X2] :
      ( ? [X3] :
          ( X2 = X3
          & ? [X4] :
              ( r3(X0,X4,X3)
              & r2(X1,X4) ) )
      & ? [X5] :
          ( r3(X0,X1,X5)
          & r2(X5,X2) ) ),
    inference(rectify,[],[f16]) ).

fof(f16,plain,
    ! [X0,X1] :
    ? [X2] :
      ( ? [X4] :
          ( X2 = X4
          & ? [X5] :
              ( r3(X0,X5,X4)
              & r2(X1,X5) ) )
      & ? [X3] :
          ( r3(X0,X1,X3)
          & r2(X3,X2) ) ),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X13,X14] :
    ? [X15] :
      ( ? [X18] :
          ( r3(X13,X14,X18)
          & r2(X18,X15) )
      & ? [X16] :
          ( ? [X17] :
              ( r2(X14,X17)
              & r3(X13,X17,X16) )
          & X15 = X16 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1a) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : NUN080+2 : 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
% 0.13/0.33  % Computer : n028.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Tue Aug 30 09:56:48 EDT 2022
% 0.13/0.33  % CPUTime    : 
% 0.19/0.49  % (15340)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)
% 0.19/0.50  % (15332)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)
% 0.19/0.50  % (15340)First to succeed.
% 0.19/0.50  % (15322)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.50  % (15324)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.50  % (15326)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.50  % (15340)Refutation found. Thanks to Tanya!
% 0.19/0.50  % SZS status Theorem for theBenchmark
% 0.19/0.50  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.50  % (15340)------------------------------
% 0.19/0.50  % (15340)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50  % (15340)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.50  % (15340)Termination reason: Refutation
% 0.19/0.50  
% 0.19/0.50  % (15340)Memory used [KB]: 1023
% 0.19/0.50  % (15340)Time elapsed: 0.060 s
% 0.19/0.50  % (15340)Instructions burned: 3 (million)
% 0.19/0.50  % (15340)------------------------------
% 0.19/0.50  % (15340)------------------------------
% 0.19/0.50  % (15317)Success in time 0.164 s
%------------------------------------------------------------------------------