TSTP Solution File: NUN062+2 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUN062+2 : TPTP v8.1.2. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -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 : Sun May  5 08:45:01 EDT 2024

% Result   : Theorem 0.21s 0.38s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   29 (   7 unt;   0 def)
%            Number of atoms       :   99 (  31 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  104 (  34   ~;  24   |;  40   &)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   1 con; 0-2 aty)
%            Number of variables   :   98 (  63   !;  35   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f137,plain,
    $false,
    inference(resolution,[],[f133,f81]) ).

fof(f81,plain,
    ! [X0,X1] : r2(X1,sK18(X0,X1)),
    inference(cnf_transformation,[],[f50]) ).

fof(f50,plain,
    ! [X0,X1] :
      ( r3(X0,X1,sK16(X0,X1))
      & r2(sK16(X0,X1),sK15(X0,X1))
      & sK15(X0,X1) = sK17(X0,X1)
      & r3(X0,sK18(X0,X1),sK17(X0,X1))
      & r2(X1,sK18(X0,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16,sK17,sK18])],[f22,f49,f48,f47,f46]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ? [X3] :
              ( r3(X0,X1,X3)
              & r2(X3,X2) )
          & ? [X4] :
              ( X2 = X4
              & ? [X5] :
                  ( r3(X0,X5,X4)
                  & r2(X1,X5) ) ) )
     => ( ? [X3] :
            ( r3(X0,X1,X3)
            & r2(X3,sK15(X0,X1)) )
        & ? [X4] :
            ( sK15(X0,X1) = X4
            & ? [X5] :
                ( r3(X0,X5,X4)
                & r2(X1,X5) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f47,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( r3(X0,X1,X3)
          & r2(X3,sK15(X0,X1)) )
     => ( r3(X0,X1,sK16(X0,X1))
        & r2(sK16(X0,X1),sK15(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( sK15(X0,X1) = X4
          & ? [X5] :
              ( r3(X0,X5,X4)
              & r2(X1,X5) ) )
     => ( sK15(X0,X1) = sK17(X0,X1)
        & ? [X5] :
            ( r3(X0,X5,sK17(X0,X1))
            & r2(X1,X5) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f49,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( r3(X0,X5,sK17(X0,X1))
          & r2(X1,X5) )
     => ( r3(X0,sK18(X0,X1),sK17(X0,X1))
        & r2(X1,sK18(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f22,plain,
    ! [X0,X1] :
    ? [X2] :
      ( ? [X3] :
          ( r3(X0,X1,X3)
          & r2(X3,X2) )
      & ? [X4] :
          ( X2 = X4
          & ? [X5] :
              ( r3(X0,X5,X4)
              & r2(X1,X5) ) ) ),
    inference(rectify,[],[f5]) ).

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

fof(f133,plain,
    ! [X0,X1] : ~ r2(X0,X1),
    inference(resolution,[],[f132,f102]) ).

fof(f102,plain,
    ! [X2,X0] :
      ( ~ r1(X2)
      | ~ r2(X0,X2) ),
    inference(equality_resolution,[],[f74]) ).

fof(f74,plain,
    ! [X2,X0,X1] :
      ( ~ r2(X0,X1)
      | X1 != X2
      | ~ r1(X2) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( ~ r2(X0,X1)
      | ! [X2] :
          ( X1 != X2
          | ~ r1(X2) ) ),
    inference(rectify,[],[f11]) ).

fof(f11,axiom,
    ! [X40,X41] :
      ( ~ r2(X40,X41)
      | ! [X42] :
          ( X41 != X42
          | ~ r1(X42) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7a) ).

fof(f132,plain,
    ! [X0] : r1(X0),
    inference(forward_demodulation,[],[f130,f129]) ).

fof(f129,plain,
    ! [X0] : sK1(X0) = X0,
    inference(resolution,[],[f85,f98]) ).

fof(f98,plain,
    ! [X2,X3] :
      ( ~ r3(sK0,X2,X3)
      | sK1(X2) = X2 ),
    inference(equality_resolution,[],[f58]) ).

fof(f58,plain,
    ! [X2,X3,X1] :
      ( X1 != X3
      | ~ r3(sK0,X2,X3)
      | sK1(X2) = X2 ),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,plain,
    ! [X1,X2] :
      ( ! [X3] :
          ( X1 != X3
          | ~ r3(sK0,X2,X3) )
      | ( sK1(X2) = X2
        & r1(sK1(X2)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f25,f27,f26]) ).

fof(f26,plain,
    ( ? [X0] :
      ! [X1,X2] :
        ( ! [X3] :
            ( X1 != X3
            | ~ r3(X0,X2,X3) )
        | ? [X4] :
            ( X2 = X4
            & r1(X4) ) )
   => ! [X2,X1] :
        ( ! [X3] :
            ( X1 != X3
            | ~ r3(sK0,X2,X3) )
        | ? [X4] :
            ( X2 = X4
            & r1(X4) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f27,plain,
    ! [X2] :
      ( ? [X4] :
          ( X2 = X4
          & r1(X4) )
     => ( sK1(X2) = X2
        & r1(sK1(X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f25,plain,
    ? [X0] :
    ! [X1,X2] :
      ( ! [X3] :
          ( X1 != X3
          | ~ r3(X0,X2,X3) )
      | ? [X4] :
          ( X2 = X4
          & r1(X4) ) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f14,plain,
    ~ ! [X0] :
      ? [X1,X2] :
        ( ? [X3] :
            ( X1 = X3
            & r3(X0,X2,X3) )
        & ! [X4] :
            ( X2 != X4
            | ~ r1(X4) ) ),
    inference(rectify,[],[f13]) ).

fof(f13,negated_conjecture,
    ~ ! [X13] :
      ? [X21,X38] :
        ( ? [X22] :
            ( X21 = X22
            & r3(X13,X38,X22) )
        & ! [X15] :
            ( X15 != X38
            | ~ r1(X15) ) ),
    inference(negated_conjecture,[],[f12]) ).

fof(f12,conjecture,
    ! [X13] :
    ? [X21,X38] :
      ( ? [X22] :
          ( X21 = X22
          & r3(X13,X38,X22) )
      & ! [X15] :
          ( X15 != X38
          | ~ r1(X15) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',infiniteNumbers) ).

fof(f85,plain,
    ! [X0,X1] : r3(X0,X1,sK16(X0,X1)),
    inference(cnf_transformation,[],[f50]) ).

fof(f130,plain,
    ! [X0] : r1(sK1(X0)),
    inference(resolution,[],[f85,f99]) ).

fof(f99,plain,
    ! [X2,X3] :
      ( ~ r3(sK0,X2,X3)
      | r1(sK1(X2)) ),
    inference(equality_resolution,[],[f57]) ).

fof(f57,plain,
    ! [X2,X3,X1] :
      ( X1 != X3
      | ~ r3(sK0,X2,X3)
      | r1(sK1(X2)) ),
    inference(cnf_transformation,[],[f28]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : NUN062+2 : TPTP v8.1.2. Released v7.3.0.
% 0.13/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36  % Computer : n018.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Fri May  3 18:51:38 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.21/0.36  % (15003)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.38  % (15006)WARNING: value z3 for option sas not known
% 0.21/0.38  % (15007)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.38  % (15005)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.38  % (15006)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)
% 0.21/0.38  % (15008)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)
% 0.21/0.38  % (15009)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)
% 0.21/0.38  % (15010)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)
% 0.21/0.38  % (15004)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.38  TRYING [1]
% 0.21/0.38  TRYING [2]
% 0.21/0.38  % (15009)First to succeed.
% 0.21/0.38  TRYING [3]
% 0.21/0.38  % (15009)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-15003"
% 0.21/0.38  % (15010)Also succeeded, but the first one will report.
% 0.21/0.38  % (15006)Also succeeded, but the first one will report.
% 0.21/0.38  TRYING [1]
% 0.21/0.38  % (15009)Refutation found. Thanks to Tanya!
% 0.21/0.38  % SZS status Theorem for theBenchmark
% 0.21/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.38  % (15009)------------------------------
% 0.21/0.38  % (15009)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.38  % (15009)Termination reason: Refutation
% 0.21/0.38  
% 0.21/0.38  % (15009)Memory used [KB]: 852
% 0.21/0.38  % (15009)Time elapsed: 0.006 s
% 0.21/0.38  % (15009)Instructions burned: 6 (million)
% 0.21/0.38  % (15003)Success in time 0.022 s
%------------------------------------------------------------------------------