TSTP Solution File: KRS119+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : KRS119+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 : 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 : Sun May  5 07:19:35 EDT 2024

% Result   : Unsatisfiable 0.15s 0.38s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   67 (   6 unt;   0 def)
%            Number of atoms       :  230 (   0 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  268 ( 105   ~;  86   |;  54   &)
%                                         (  14 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    9 (   8 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   1 con; 0-1 aty)
%            Number of variables   :  125 ( 100   !;  25   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f214,plain,
    $false,
    inference(resolution,[],[f211,f112]) ).

fof(f112,plain,
    cUnsatisfiable(i2003_11_14_17_21_44786),
    inference(cnf_transformation,[],[f31]) ).

fof(f31,axiom,
    cUnsatisfiable(i2003_11_14_17_21_44786),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_11) ).

fof(f211,plain,
    ~ cUnsatisfiable(i2003_11_14_17_21_44786),
    inference(resolution,[],[f209,f129]) ).

fof(f129,plain,
    ! [X0] :
      ( rr(X0,sK4(X0))
      | ~ cUnsatisfiable(X0) ),
    inference(cnf_transformation,[],[f109]) ).

fof(f109,plain,
    ! [X0] :
      ( ( cUnsatisfiable(X0)
        | ~ cp1(X0)
        | ! [X1] :
            ( ~ ca_Vx3(X1)
            | ~ rr(X0,X1) ) )
      & ( ( cp1(X0)
          & ca_Vx3(sK4(X0))
          & rr(X0,sK4(X0)) )
        | ~ cUnsatisfiable(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f107,f108]) ).

fof(f108,plain,
    ! [X0] :
      ( ? [X2] :
          ( ca_Vx3(X2)
          & rr(X0,X2) )
     => ( ca_Vx3(sK4(X0))
        & rr(X0,sK4(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f107,plain,
    ! [X0] :
      ( ( cUnsatisfiable(X0)
        | ~ cp1(X0)
        | ! [X1] :
            ( ~ ca_Vx3(X1)
            | ~ rr(X0,X1) ) )
      & ( ( cp1(X0)
          & ? [X2] :
              ( ca_Vx3(X2)
              & rr(X0,X2) ) )
        | ~ cUnsatisfiable(X0) ) ),
    inference(rectify,[],[f106]) ).

fof(f106,plain,
    ! [X0] :
      ( ( cUnsatisfiable(X0)
        | ~ cp1(X0)
        | ! [X1] :
            ( ~ ca_Vx3(X1)
            | ~ rr(X0,X1) ) )
      & ( ( cp1(X0)
          & ? [X1] :
              ( ca_Vx3(X1)
              & rr(X0,X1) ) )
        | ~ cUnsatisfiable(X0) ) ),
    inference(flattening,[],[f105]) ).

fof(f105,plain,
    ! [X0] :
      ( ( cUnsatisfiable(X0)
        | ~ cp1(X0)
        | ! [X1] :
            ( ~ ca_Vx3(X1)
            | ~ rr(X0,X1) ) )
      & ( ( cp1(X0)
          & ? [X1] :
              ( ca_Vx3(X1)
              & rr(X0,X1) ) )
        | ~ cUnsatisfiable(X0) ) ),
    inference(nnf_transformation,[],[f39]) ).

fof(f39,plain,
    ! [X0] :
      ( cUnsatisfiable(X0)
    <=> ( cp1(X0)
        & ? [X1] :
            ( ca_Vx3(X1)
            & rr(X0,X1) ) ) ),
    inference(rectify,[],[f22]) ).

fof(f22,axiom,
    ! [X3] :
      ( cUnsatisfiable(X3)
    <=> ( cp1(X3)
        & ? [X4] :
            ( ca_Vx3(X4)
            & rr(X3,X4) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).

fof(f209,plain,
    ~ rr(i2003_11_14_17_21_44786,sK4(i2003_11_14_17_21_44786)),
    inference(resolution,[],[f207,f112]) ).

fof(f207,plain,
    ( ~ cUnsatisfiable(i2003_11_14_17_21_44786)
    | ~ rr(i2003_11_14_17_21_44786,sK4(i2003_11_14_17_21_44786)) ),
    inference(resolution,[],[f204,f130]) ).

fof(f130,plain,
    ! [X0] :
      ( ca_Vx3(sK4(X0))
      | ~ cUnsatisfiable(X0) ),
    inference(cnf_transformation,[],[f109]) ).

fof(f204,plain,
    ( ~ ca_Vx3(sK4(i2003_11_14_17_21_44786))
    | ~ rr(i2003_11_14_17_21_44786,sK4(i2003_11_14_17_21_44786)) ),
    inference(resolution,[],[f197,f124]) ).

fof(f124,plain,
    ! [X0] :
      ( rr(X0,sK2(X0))
      | ~ ca_Vx3(X0) ),
    inference(cnf_transformation,[],[f100]) ).

fof(f100,plain,
    ! [X0] :
      ( ( ca_Vx3(X0)
        | ! [X1] :
            ( ~ ca_Ax2(X1)
            | ~ rr(X0,X1) ) )
      & ( ( ca_Ax2(sK2(X0))
          & rr(X0,sK2(X0)) )
        | ~ ca_Vx3(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f98,f99]) ).

fof(f99,plain,
    ! [X0] :
      ( ? [X2] :
          ( ca_Ax2(X2)
          & rr(X0,X2) )
     => ( ca_Ax2(sK2(X0))
        & rr(X0,sK2(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f98,plain,
    ! [X0] :
      ( ( ca_Vx3(X0)
        | ! [X1] :
            ( ~ ca_Ax2(X1)
            | ~ rr(X0,X1) ) )
      & ( ? [X2] :
            ( ca_Ax2(X2)
            & rr(X0,X2) )
        | ~ ca_Vx3(X0) ) ),
    inference(rectify,[],[f97]) ).

fof(f97,plain,
    ! [X0] :
      ( ( ca_Vx3(X0)
        | ! [X1] :
            ( ~ ca_Ax2(X1)
            | ~ rr(X0,X1) ) )
      & ( ? [X1] :
            ( ca_Ax2(X1)
            & rr(X0,X1) )
        | ~ ca_Vx3(X0) ) ),
    inference(nnf_transformation,[],[f37]) ).

fof(f37,plain,
    ! [X0] :
      ( ca_Vx3(X0)
    <=> ? [X1] :
          ( ca_Ax2(X1)
          & rr(X0,X1) ) ),
    inference(rectify,[],[f26]) ).

fof(f26,axiom,
    ! [X3] :
      ( ca_Vx3(X3)
    <=> ? [X4] :
          ( ca_Ax2(X4)
          & rr(X3,X4) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).

fof(f197,plain,
    ! [X0] :
      ( ~ rr(X0,sK2(sK4(i2003_11_14_17_21_44786)))
      | ~ rr(i2003_11_14_17_21_44786,X0) ),
    inference(resolution,[],[f195,f156]) ).

fof(f156,plain,
    ! [X2,X0,X1] :
      ( rr(X0,X2)
      | ~ rr(X1,X2)
      | ~ rr(X0,X1) ),
    inference(cnf_transformation,[],[f86]) ).

fof(f86,plain,
    ! [X0,X1,X2] :
      ( rr(X0,X2)
      | ~ rr(X1,X2)
      | ~ rr(X0,X1) ),
    inference(flattening,[],[f85]) ).

fof(f85,plain,
    ! [X0,X1,X2] :
      ( rr(X0,X2)
      | ~ rr(X1,X2)
      | ~ rr(X0,X1) ),
    inference(ennf_transformation,[],[f42]) ).

fof(f42,plain,
    ! [X0,X1,X2] :
      ( ( rr(X1,X2)
        & rr(X0,X1) )
     => rr(X0,X2) ),
    inference(rectify,[],[f30]) ).

fof(f30,axiom,
    ! [X3,X4,X7] :
      ( ( rr(X4,X7)
        & rr(X3,X4) )
     => rr(X3,X7) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_10) ).

fof(f195,plain,
    ~ rr(i2003_11_14_17_21_44786,sK2(sK4(i2003_11_14_17_21_44786))),
    inference(resolution,[],[f192,f112]) ).

fof(f192,plain,
    ! [X0] :
      ( ~ cUnsatisfiable(X0)
      | ~ rr(X0,sK2(sK4(i2003_11_14_17_21_44786))) ),
    inference(resolution,[],[f190,f131]) ).

fof(f131,plain,
    ! [X0] :
      ( cp1(X0)
      | ~ cUnsatisfiable(X0) ),
    inference(cnf_transformation,[],[f109]) ).

fof(f190,plain,
    ! [X0] :
      ( ~ cp1(X0)
      | ~ rr(X0,sK2(sK4(i2003_11_14_17_21_44786))) ),
    inference(resolution,[],[f188,f112]) ).

fof(f188,plain,
    ! [X0,X1] :
      ( ~ cUnsatisfiable(X1)
      | ~ cp1(X0)
      | ~ rr(X0,sK2(sK4(X1))) ),
    inference(resolution,[],[f184,f130]) ).

fof(f184,plain,
    ! [X0,X1] :
      ( ~ ca_Vx3(X1)
      | ~ rr(X0,sK2(X1))
      | ~ cp1(X0) ),
    inference(resolution,[],[f183,f125]) ).

fof(f125,plain,
    ! [X0] :
      ( ca_Ax2(sK2(X0))
      | ~ ca_Vx3(X0) ),
    inference(cnf_transformation,[],[f100]) ).

fof(f183,plain,
    ! [X0,X1] :
      ( ~ ca_Ax2(X0)
      | ~ cp1(X1)
      | ~ rr(X1,X0) ),
    inference(resolution,[],[f180,f145]) ).

fof(f145,plain,
    ! [X0,X1] :
      ( rinvR(X0,X1)
      | ~ rr(X1,X0) ),
    inference(cnf_transformation,[],[f111]) ).

fof(f111,plain,
    ! [X0,X1] :
      ( ( rinvR(X0,X1)
        | ~ rr(X1,X0) )
      & ( rr(X1,X0)
        | ~ rinvR(X0,X1) ) ),
    inference(nnf_transformation,[],[f41]) ).

fof(f41,plain,
    ! [X0,X1] :
      ( rinvR(X0,X1)
    <=> rr(X1,X0) ),
    inference(rectify,[],[f29]) ).

fof(f29,axiom,
    ! [X3,X4] :
      ( rinvR(X3,X4)
    <=> rr(X4,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_9) ).

fof(f180,plain,
    ! [X0,X1] :
      ( ~ rinvR(X0,X1)
      | ~ ca_Ax2(X0)
      | ~ cp1(X1) ),
    inference(resolution,[],[f119,f177]) ).

fof(f177,plain,
    ! [X0] :
      ( ~ cp1xcomp(X0)
      | ~ cp1(X0) ),
    inference(resolution,[],[f122,f127]) ).

fof(f127,plain,
    ! [X2,X0] :
      ( ~ ra_Px1(X0,X2)
      | ~ cp1(X0) ),
    inference(cnf_transformation,[],[f104]) ).

fof(f104,plain,
    ! [X0] :
      ( ( cp1(X0)
        | ra_Px1(X0,sK3(X0)) )
      & ( ! [X2] : ~ ra_Px1(X0,X2)
        | ~ cp1(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f102,f103]) ).

fof(f103,plain,
    ! [X0] :
      ( ? [X1] : ra_Px1(X0,X1)
     => ra_Px1(X0,sK3(X0)) ),
    introduced(choice_axiom,[]) ).

fof(f102,plain,
    ! [X0] :
      ( ( cp1(X0)
        | ? [X1] : ra_Px1(X0,X1) )
      & ( ! [X2] : ~ ra_Px1(X0,X2)
        | ~ cp1(X0) ) ),
    inference(rectify,[],[f101]) ).

fof(f101,plain,
    ! [X0] :
      ( ( cp1(X0)
        | ? [X1] : ra_Px1(X0,X1) )
      & ( ! [X1] : ~ ra_Px1(X0,X1)
        | ~ cp1(X0) ) ),
    inference(nnf_transformation,[],[f46]) ).

fof(f46,plain,
    ! [X0] :
      ( cp1(X0)
    <=> ! [X1] : ~ ra_Px1(X0,X1) ),
    inference(ennf_transformation,[],[f38]) ).

fof(f38,plain,
    ! [X0] :
      ( cp1(X0)
    <=> ~ ? [X1] : ra_Px1(X0,X1) ),
    inference(rectify,[],[f23]) ).

fof(f23,axiom,
    ! [X3] :
      ( cp1(X3)
    <=> ~ ? [X4] : ra_Px1(X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).

fof(f122,plain,
    ! [X0] :
      ( ra_Px1(X0,sK1(X0))
      | ~ cp1xcomp(X0) ),
    inference(cnf_transformation,[],[f96]) ).

fof(f96,plain,
    ! [X0] :
      ( ( cp1xcomp(X0)
        | ! [X1] : ~ ra_Px1(X0,X1) )
      & ( ra_Px1(X0,sK1(X0))
        | ~ cp1xcomp(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f94,f95]) ).

fof(f95,plain,
    ! [X0] :
      ( ? [X2] : ra_Px1(X0,X2)
     => ra_Px1(X0,sK1(X0)) ),
    introduced(choice_axiom,[]) ).

fof(f94,plain,
    ! [X0] :
      ( ( cp1xcomp(X0)
        | ! [X1] : ~ ra_Px1(X0,X1) )
      & ( ? [X2] : ra_Px1(X0,X2)
        | ~ cp1xcomp(X0) ) ),
    inference(rectify,[],[f93]) ).

fof(f93,plain,
    ! [X0] :
      ( ( cp1xcomp(X0)
        | ! [X1] : ~ ra_Px1(X0,X1) )
      & ( ? [X1] : ra_Px1(X0,X1)
        | ~ cp1xcomp(X0) ) ),
    inference(nnf_transformation,[],[f36]) ).

fof(f36,plain,
    ! [X0] :
      ( cp1xcomp(X0)
    <=> ? [X1] : ra_Px1(X0,X1) ),
    inference(rectify,[],[f24]) ).

fof(f24,axiom,
    ! [X3] :
      ( cp1xcomp(X3)
    <=> ? [X5] : ra_Px1(X3,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).

fof(f119,plain,
    ! [X2,X0] :
      ( cp1xcomp(X2)
      | ~ rinvR(X0,X2)
      | ~ ca_Ax2(X0) ),
    inference(cnf_transformation,[],[f92]) ).

fof(f92,plain,
    ! [X0] :
      ( ( ca_Ax2(X0)
        | ( ~ cp1xcomp(sK0(X0))
          & rinvR(X0,sK0(X0)) )
        | ~ cp1(X0) )
      & ( ( ! [X2] :
              ( cp1xcomp(X2)
              | ~ rinvR(X0,X2) )
          & cp1(X0) )
        | ~ ca_Ax2(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f90,f91]) ).

fof(f91,plain,
    ! [X0] :
      ( ? [X1] :
          ( ~ cp1xcomp(X1)
          & rinvR(X0,X1) )
     => ( ~ cp1xcomp(sK0(X0))
        & rinvR(X0,sK0(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f90,plain,
    ! [X0] :
      ( ( ca_Ax2(X0)
        | ? [X1] :
            ( ~ cp1xcomp(X1)
            & rinvR(X0,X1) )
        | ~ cp1(X0) )
      & ( ( ! [X2] :
              ( cp1xcomp(X2)
              | ~ rinvR(X0,X2) )
          & cp1(X0) )
        | ~ ca_Ax2(X0) ) ),
    inference(rectify,[],[f89]) ).

fof(f89,plain,
    ! [X0] :
      ( ( ca_Ax2(X0)
        | ? [X1] :
            ( ~ cp1xcomp(X1)
            & rinvR(X0,X1) )
        | ~ cp1(X0) )
      & ( ( ! [X1] :
              ( cp1xcomp(X1)
              | ~ rinvR(X0,X1) )
          & cp1(X0) )
        | ~ ca_Ax2(X0) ) ),
    inference(flattening,[],[f88]) ).

fof(f88,plain,
    ! [X0] :
      ( ( ca_Ax2(X0)
        | ? [X1] :
            ( ~ cp1xcomp(X1)
            & rinvR(X0,X1) )
        | ~ cp1(X0) )
      & ( ( ! [X1] :
              ( cp1xcomp(X1)
              | ~ rinvR(X0,X1) )
          & cp1(X0) )
        | ~ ca_Ax2(X0) ) ),
    inference(nnf_transformation,[],[f45]) ).

fof(f45,plain,
    ! [X0] :
      ( ca_Ax2(X0)
    <=> ( ! [X1] :
            ( cp1xcomp(X1)
            | ~ rinvR(X0,X1) )
        & cp1(X0) ) ),
    inference(ennf_transformation,[],[f35]) ).

fof(f35,plain,
    ! [X0] :
      ( ca_Ax2(X0)
    <=> ( ! [X1] :
            ( rinvR(X0,X1)
           => cp1xcomp(X1) )
        & cp1(X0) ) ),
    inference(rectify,[],[f25]) ).

fof(f25,axiom,
    ! [X3] :
      ( ca_Ax2(X3)
    <=> ( ! [X4] :
            ( rinvR(X3,X4)
           => cp1xcomp(X4) )
        & cp1(X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : KRS119+1 : TPTP v8.1.2. Released v3.1.0.
% 0.12/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35  % Computer : n028.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Fri May  3 19:51:23 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  % (16140)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38  % (16143)WARNING: value z3 for option sas not known
% 0.15/0.38  % (16144)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38  % (16141)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38  % (16142)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38  % (16143)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)
% 0.15/0.38  % (16145)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)
% 0.15/0.38  % (16146)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)
% 0.15/0.38  % (16147)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)
% 0.15/0.38  TRYING [1]
% 0.15/0.38  TRYING [1]
% 0.15/0.38  TRYING [2]
% 0.15/0.38  TRYING [2]
% 0.15/0.38  TRYING [3]
% 0.15/0.38  TRYING [3]
% 0.15/0.38  % (16146)First to succeed.
% 0.15/0.38  % (16147)Also succeeded, but the first one will report.
% 0.15/0.38  TRYING [4]
% 0.15/0.38  TRYING [4]
% 0.15/0.38  % (16146)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-16140"
% 0.15/0.38  % (16143)Also succeeded, but the first one will report.
% 0.15/0.38  TRYING [1]
% 0.15/0.38  % (16146)Refutation found. Thanks to Tanya!
% 0.15/0.38  % SZS status Unsatisfiable for theBenchmark
% 0.15/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.38  % (16146)------------------------------
% 0.15/0.38  % (16146)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.38  % (16146)Termination reason: Refutation
% 0.15/0.38  
% 0.15/0.38  % (16146)Memory used [KB]: 901
% 0.15/0.38  % (16146)Time elapsed: 0.006 s
% 0.15/0.38  % (16146)Instructions burned: 7 (million)
% 0.15/0.38  % (16140)Success in time 0.022 s
%------------------------------------------------------------------------------