TSTP Solution File: KRS087+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : KRS087+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n025.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 07:19:29 EDT 2024

% Result   : Unsatisfiable 0.21s 0.38s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   38 (   9 unt;   0 def)
%            Number of atoms       :  153 (   0 equ)
%            Maximal formula atoms :   10 (   4 avg)
%            Number of connectives :  174 (  59   ~;  50   |;  51   &)
%                                         (   7 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   1 con; 0-1 aty)
%            Number of variables   :   78 (  60   !;  18   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f160,plain,
    $false,
    inference(unit_resulting_resolution,[],[f135,f150,f133,f111]) ).

fof(f111,plain,
    ! [X2,X0,X1] :
      ( ~ rr(X1,X2)
      | rr(X0,X2)
      | ~ rr(X0,X1) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f62,plain,
    ! [X0,X1,X2] :
      ( rr(X0,X2)
      | ~ rr(X1,X2)
      | ~ rr(X0,X1) ),
    inference(flattening,[],[f61]) ).

fof(f61,plain,
    ! [X0,X1,X2] :
      ( rr(X0,X2)
      | ~ rr(X1,X2)
      | ~ rr(X0,X1) ),
    inference(ennf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1,X2] :
      ( ( rr(X1,X2)
        & rr(X0,X1) )
     => rr(X0,X2) ),
    inference(rectify,[],[f21]) ).

fof(f21,axiom,
    ! [X3,X4,X5] :
      ( ( rr(X4,X5)
        & rr(X3,X4) )
     => rr(X3,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).

fof(f133,plain,
    rr(sK3(i2003_11_14_17_19_46763),sK2(sK3(i2003_11_14_17_19_46763))),
    inference(unit_resulting_resolution,[],[f129,f83]) ).

fof(f83,plain,
    ! [X0] :
      ( ~ sP0(X0)
      | rr(X0,sK2(X0)) ),
    inference(cnf_transformation,[],[f70]) ).

fof(f70,plain,
    ! [X0] :
      ( ( sP0(X0)
        | ! [X1] :
            ( ~ cp1(X1)
            | ( cp1(sK1(X1))
              & rinvR(X1,sK1(X1)) )
            | ~ rr(X0,X1) ) )
      & ( ( cp1(sK2(X0))
          & ! [X4] :
              ( ~ cp1(X4)
              | ~ rinvR(sK2(X0),X4) )
          & rr(X0,sK2(X0)) )
        | ~ sP0(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f67,f69,f68]) ).

fof(f68,plain,
    ! [X1] :
      ( ? [X2] :
          ( cp1(X2)
          & rinvR(X1,X2) )
     => ( cp1(sK1(X1))
        & rinvR(X1,sK1(X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f69,plain,
    ! [X0] :
      ( ? [X3] :
          ( cp1(X3)
          & ! [X4] :
              ( ~ cp1(X4)
              | ~ rinvR(X3,X4) )
          & rr(X0,X3) )
     => ( cp1(sK2(X0))
        & ! [X4] :
            ( ~ cp1(X4)
            | ~ rinvR(sK2(X0),X4) )
        & rr(X0,sK2(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f67,plain,
    ! [X0] :
      ( ( sP0(X0)
        | ! [X1] :
            ( ~ cp1(X1)
            | ? [X2] :
                ( cp1(X2)
                & rinvR(X1,X2) )
            | ~ rr(X0,X1) ) )
      & ( ? [X3] :
            ( cp1(X3)
            & ! [X4] :
                ( ~ cp1(X4)
                | ~ rinvR(X3,X4) )
            & rr(X0,X3) )
        | ~ sP0(X0) ) ),
    inference(rectify,[],[f66]) ).

fof(f66,plain,
    ! [X1] :
      ( ( sP0(X1)
        | ! [X2] :
            ( ~ cp1(X2)
            | ? [X3] :
                ( cp1(X3)
                & rinvR(X2,X3) )
            | ~ rr(X1,X2) ) )
      & ( ? [X2] :
            ( cp1(X2)
            & ! [X3] :
                ( ~ cp1(X3)
                | ~ rinvR(X2,X3) )
            & rr(X1,X2) )
        | ~ sP0(X1) ) ),
    inference(nnf_transformation,[],[f63]) ).

fof(f63,plain,
    ! [X1] :
      ( sP0(X1)
    <=> ? [X2] :
          ( cp1(X2)
          & ! [X3] :
              ( ~ cp1(X3)
              | ~ rinvR(X2,X3) )
          & rr(X1,X2) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f129,plain,
    sP0(sK3(i2003_11_14_17_19_46763)),
    inference(unit_resulting_resolution,[],[f78,f90]) ).

fof(f90,plain,
    ! [X0] :
      ( ~ cUnsatisfiable(X0)
      | sP0(sK3(X0)) ),
    inference(cnf_transformation,[],[f75]) ).

fof(f75,plain,
    ! [X0] :
      ( ( cUnsatisfiable(X0)
        | ! [X1] :
            ( ~ sP0(X1)
            | ~ rr(X0,X1) )
        | ~ cp1(X0) )
      & ( ( sP0(sK3(X0))
          & rr(X0,sK3(X0))
          & cp1(X0) )
        | ~ cUnsatisfiable(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f73,f74]) ).

fof(f74,plain,
    ! [X0] :
      ( ? [X2] :
          ( sP0(X2)
          & rr(X0,X2) )
     => ( sP0(sK3(X0))
        & rr(X0,sK3(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f73,plain,
    ! [X0] :
      ( ( cUnsatisfiable(X0)
        | ! [X1] :
            ( ~ sP0(X1)
            | ~ rr(X0,X1) )
        | ~ cp1(X0) )
      & ( ( ? [X2] :
              ( sP0(X2)
              & rr(X0,X2) )
          & cp1(X0) )
        | ~ cUnsatisfiable(X0) ) ),
    inference(rectify,[],[f72]) ).

fof(f72,plain,
    ! [X0] :
      ( ( cUnsatisfiable(X0)
        | ! [X1] :
            ( ~ sP0(X1)
            | ~ rr(X0,X1) )
        | ~ cp1(X0) )
      & ( ( ? [X1] :
              ( sP0(X1)
              & rr(X0,X1) )
          & cp1(X0) )
        | ~ cUnsatisfiable(X0) ) ),
    inference(flattening,[],[f71]) ).

fof(f71,plain,
    ! [X0] :
      ( ( cUnsatisfiable(X0)
        | ! [X1] :
            ( ~ sP0(X1)
            | ~ rr(X0,X1) )
        | ~ cp1(X0) )
      & ( ( ? [X1] :
              ( sP0(X1)
              & rr(X0,X1) )
          & cp1(X0) )
        | ~ cUnsatisfiable(X0) ) ),
    inference(nnf_transformation,[],[f64]) ).

fof(f64,plain,
    ! [X0] :
      ( cUnsatisfiable(X0)
    <=> ( ? [X1] :
            ( sP0(X1)
            & rr(X0,X1) )
        & cp1(X0) ) ),
    inference(definition_folding,[],[f30,f63]) ).

fof(f30,plain,
    ! [X0] :
      ( cUnsatisfiable(X0)
    <=> ( ? [X1] :
            ( ? [X2] :
                ( cp1(X2)
                & ! [X3] :
                    ( ~ cp1(X3)
                    | ~ rinvR(X2,X3) )
                & rr(X1,X2) )
            & rr(X0,X1) )
        & cp1(X0) ) ),
    inference(ennf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X0] :
      ( cUnsatisfiable(X0)
    <=> ( ? [X1] :
            ( ? [X2] :
                ( cp1(X2)
                & ! [X3] :
                    ( rinvR(X2,X3)
                   => ~ cp1(X3) )
                & rr(X1,X2) )
            & rr(X0,X1) )
        & cp1(X0) ) ),
    inference(rectify,[],[f17]) ).

fof(f17,axiom,
    ! [X3] :
      ( cUnsatisfiable(X3)
    <=> ( ? [X4] :
            ( ? [X5] :
                ( cp1(X5)
                & ! [X6] :
                    ( rinvR(X5,X6)
                   => ~ cp1(X6) )
                & rr(X4,X5) )
            & rr(X3,X4) )
        & cp1(X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).

fof(f78,plain,
    cUnsatisfiable(i2003_11_14_17_19_46763),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,axiom,
    cUnsatisfiable(i2003_11_14_17_19_46763),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).

fof(f150,plain,
    ~ rr(i2003_11_14_17_19_46763,sK2(sK3(i2003_11_14_17_19_46763))),
    inference(unit_resulting_resolution,[],[f145,f101]) ).

fof(f101,plain,
    ! [X0,X1] :
      ( ~ rr(X1,X0)
      | rinvR(X0,X1) ),
    inference(cnf_transformation,[],[f77]) ).

fof(f77,plain,
    ! [X0,X1] :
      ( ( rinvR(X0,X1)
        | ~ rr(X1,X0) )
      & ( rr(X1,X0)
        | ~ rinvR(X0,X1) ) ),
    inference(nnf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( rinvR(X0,X1)
    <=> rr(X1,X0) ),
    inference(rectify,[],[f20]) ).

fof(f20,axiom,
    ! [X3,X4] :
      ( rinvR(X3,X4)
    <=> rr(X4,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).

fof(f145,plain,
    ~ rinvR(sK2(sK3(i2003_11_14_17_19_46763)),i2003_11_14_17_19_46763),
    inference(unit_resulting_resolution,[],[f129,f127,f84]) ).

fof(f84,plain,
    ! [X0,X4] :
      ( ~ rinvR(sK2(X0),X4)
      | ~ cp1(X4)
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f70]) ).

fof(f127,plain,
    cp1(i2003_11_14_17_19_46763),
    inference(unit_resulting_resolution,[],[f78,f88]) ).

fof(f88,plain,
    ! [X0] :
      ( ~ cUnsatisfiable(X0)
      | cp1(X0) ),
    inference(cnf_transformation,[],[f75]) ).

fof(f135,plain,
    rr(i2003_11_14_17_19_46763,sK3(i2003_11_14_17_19_46763)),
    inference(unit_resulting_resolution,[],[f78,f89]) ).

fof(f89,plain,
    ! [X0] :
      ( ~ cUnsatisfiable(X0)
      | rr(X0,sK3(X0)) ),
    inference(cnf_transformation,[],[f75]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : KRS087+1 : TPTP v8.1.2. Released v3.1.0.
% 0.03/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n025.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Fri May  3 19:50:23 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  % (3141)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.38  % (3144)WARNING: value z3 for option sas not known
% 0.21/0.38  % (3143)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  % (3145)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.38  % (3146)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  % (3144)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  % (3148)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  % (3142)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.38  % (3147)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  TRYING [1]
% 0.21/0.38  TRYING [1]
% 0.21/0.38  TRYING [2]
% 0.21/0.38  TRYING [2]
% 0.21/0.38  TRYING [3]
% 0.21/0.38  TRYING [3]
% 0.21/0.38  % (3148)First to succeed.
% 0.21/0.38  % (3147)Also succeeded, but the first one will report.
% 0.21/0.38  TRYING [4]
% 0.21/0.38  % (3148)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3141"
% 0.21/0.38  TRYING [4]
% 0.21/0.38  % (3148)Refutation found. Thanks to Tanya!
% 0.21/0.38  % SZS status Unsatisfiable for theBenchmark
% 0.21/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.38  % (3148)------------------------------
% 0.21/0.38  % (3148)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.38  % (3148)Termination reason: Refutation
% 0.21/0.38  
% 0.21/0.38  % (3148)Memory used [KB]: 838
% 0.21/0.38  % (3148)Time elapsed: 0.005 s
% 0.21/0.38  % (3148)Instructions burned: 5 (million)
% 0.21/0.38  % (3141)Success in time 0.021 s
%------------------------------------------------------------------------------