TSTP Solution File: KRS101+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : KRS101+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 : n015.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 07:19:32 EDT 2024

% Result   : Unsatisfiable 0.21s 0.38s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   53 (  13 unt;   0 def)
%            Number of atoms       :  265 (  34 equ)
%            Maximal formula atoms :   12 (   5 avg)
%            Number of connectives :  330 ( 118   ~;  95   |;  95   &)
%                                         (   9 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   1 con; 0-1 aty)
%            Number of variables   :  135 (  90   !;  45   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f160,plain,
    $false,
    inference(unit_resulting_resolution,[],[f141,f131,f135,f137,f133,f116]) ).

fof(f116,plain,
    ! [X6,X4,X5] :
      ( ~ rs(X4,X6)
      | X5 = X6
      | cc(X4)
      | ~ rs(X4,X5)
      | ~ sP11(X4) ),
    inference(general_splitting,[],[f83,f115_D]) ).

fof(f115,plain,
    ! [X0,X4] :
      ( ~ rr(X0,X4)
      | ~ sP0(X0)
      | sP11(X4) ),
    inference(cnf_transformation,[],[f115_D]) ).

fof(f115_D,plain,
    ! [X4] :
      ( ! [X0] :
          ( ~ rr(X0,X4)
          | ~ sP0(X0) )
    <=> ~ sP11(X4) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP11])]) ).

fof(f83,plain,
    ! [X0,X6,X4,X5] :
      ( cc(X4)
      | X5 = X6
      | ~ rs(X4,X6)
      | ~ rs(X4,X5)
      | ~ rr(X0,X4)
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f65]) ).

fof(f65,plain,
    ! [X0] :
      ( ( sP0(X0)
        | ( ~ cc(sK7(X0))
          & sK8(X0) != sK9(X0)
          & rs(sK7(X0),sK9(X0))
          & rs(sK7(X0),sK8(X0))
          & rr(X0,sK7(X0)) ) )
      & ( ! [X4] :
            ( cc(X4)
            | ! [X5,X6] :
                ( X5 = X6
                | ~ rs(X4,X6)
                | ~ rs(X4,X5) )
            | ~ rr(X0,X4) )
        | ~ sP0(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f62,f64,f63]) ).

fof(f63,plain,
    ! [X0] :
      ( ? [X1] :
          ( ~ cc(X1)
          & ? [X2,X3] :
              ( X2 != X3
              & rs(X1,X3)
              & rs(X1,X2) )
          & rr(X0,X1) )
     => ( ~ cc(sK7(X0))
        & ? [X3,X2] :
            ( X2 != X3
            & rs(sK7(X0),X3)
            & rs(sK7(X0),X2) )
        & rr(X0,sK7(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f64,plain,
    ! [X0] :
      ( ? [X3,X2] :
          ( X2 != X3
          & rs(sK7(X0),X3)
          & rs(sK7(X0),X2) )
     => ( sK8(X0) != sK9(X0)
        & rs(sK7(X0),sK9(X0))
        & rs(sK7(X0),sK8(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f62,plain,
    ! [X0] :
      ( ( sP0(X0)
        | ? [X1] :
            ( ~ cc(X1)
            & ? [X2,X3] :
                ( X2 != X3
                & rs(X1,X3)
                & rs(X1,X2) )
            & rr(X0,X1) ) )
      & ( ! [X4] :
            ( cc(X4)
            | ! [X5,X6] :
                ( X5 = X6
                | ~ rs(X4,X6)
                | ~ rs(X4,X5) )
            | ~ rr(X0,X4) )
        | ~ sP0(X0) ) ),
    inference(rectify,[],[f61]) ).

fof(f61,plain,
    ! [X0] :
      ( ( sP0(X0)
        | ? [X4] :
            ( ~ cc(X4)
            & ? [X5,X6] :
                ( X5 != X6
                & rs(X4,X6)
                & rs(X4,X5) )
            & rr(X0,X4) ) )
      & ( ! [X4] :
            ( cc(X4)
            | ! [X5,X6] :
                ( X5 = X6
                | ~ rs(X4,X6)
                | ~ rs(X4,X5) )
            | ~ rr(X0,X4) )
        | ~ sP0(X0) ) ),
    inference(nnf_transformation,[],[f46]) ).

fof(f46,plain,
    ! [X0] :
      ( sP0(X0)
    <=> ! [X4] :
          ( cc(X4)
          | ! [X5,X6] :
              ( X5 = X6
              | ~ rs(X4,X6)
              | ~ rs(X4,X5) )
          | ~ rr(X0,X4) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f133,plain,
    rs(sK4(i2003_11_14_17_20_36582),sK5(i2003_11_14_17_20_36582)),
    inference(unit_resulting_resolution,[],[f120,f79]) ).

fof(f79,plain,
    ! [X0] :
      ( ~ sP1(X0)
      | rs(sK4(X0),sK5(X0)) ),
    inference(cnf_transformation,[],[f60]) ).

fof(f60,plain,
    ! [X0] :
      ( ( sP1(X0)
        | ! [X1] :
            ( ! [X2,X3] :
                ( X2 = X3
                | ~ rs(X1,X3)
                | ~ rs(X1,X2) )
            | ~ rr(X0,X1) ) )
      & ( ( sK5(X0) != sK6(X0)
          & rs(sK4(X0),sK6(X0))
          & rs(sK4(X0),sK5(X0))
          & rr(X0,sK4(X0)) )
        | ~ sP1(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f57,f59,f58]) ).

fof(f58,plain,
    ! [X0] :
      ( ? [X4] :
          ( ? [X5,X6] :
              ( X5 != X6
              & rs(X4,X6)
              & rs(X4,X5) )
          & rr(X0,X4) )
     => ( ? [X6,X5] :
            ( X5 != X6
            & rs(sK4(X0),X6)
            & rs(sK4(X0),X5) )
        & rr(X0,sK4(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f59,plain,
    ! [X0] :
      ( ? [X6,X5] :
          ( X5 != X6
          & rs(sK4(X0),X6)
          & rs(sK4(X0),X5) )
     => ( sK5(X0) != sK6(X0)
        & rs(sK4(X0),sK6(X0))
        & rs(sK4(X0),sK5(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f57,plain,
    ! [X0] :
      ( ( sP1(X0)
        | ! [X1] :
            ( ! [X2,X3] :
                ( X2 = X3
                | ~ rs(X1,X3)
                | ~ rs(X1,X2) )
            | ~ rr(X0,X1) ) )
      & ( ? [X4] :
            ( ? [X5,X6] :
                ( X5 != X6
                & rs(X4,X6)
                & rs(X4,X5) )
            & rr(X0,X4) )
        | ~ sP1(X0) ) ),
    inference(rectify,[],[f56]) ).

fof(f56,plain,
    ! [X0] :
      ( ( sP1(X0)
        | ! [X1] :
            ( ! [X2,X3] :
                ( X2 = X3
                | ~ rs(X1,X3)
                | ~ rs(X1,X2) )
            | ~ rr(X0,X1) ) )
      & ( ? [X1] :
            ( ? [X2,X3] :
                ( X2 != X3
                & rs(X1,X3)
                & rs(X1,X2) )
            & rr(X0,X1) )
        | ~ sP1(X0) ) ),
    inference(nnf_transformation,[],[f47]) ).

fof(f47,plain,
    ! [X0] :
      ( sP1(X0)
    <=> ? [X1] :
          ( ? [X2,X3] :
              ( X2 != X3
              & rs(X1,X3)
              & rs(X1,X2) )
          & rr(X0,X1) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f120,plain,
    sP1(i2003_11_14_17_20_36582),
    inference(unit_resulting_resolution,[],[f118,f75]) ).

fof(f75,plain,
    ! [X0] :
      ( ~ sP2(X0)
      | sP1(X0) ),
    inference(cnf_transformation,[],[f55]) ).

fof(f55,plain,
    ! [X0] :
      ( ( sP2(X0)
        | ~ sP1(X0)
        | ~ sP0(X0)
        | ( ~ cd(sK3(X0))
          & rr(X0,sK3(X0)) ) )
      & ( ( sP1(X0)
          & sP0(X0)
          & ! [X2] :
              ( cd(X2)
              | ~ rr(X0,X2) ) )
        | ~ sP2(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f53,f54]) ).

fof(f54,plain,
    ! [X0] :
      ( ? [X1] :
          ( ~ cd(X1)
          & rr(X0,X1) )
     => ( ~ cd(sK3(X0))
        & rr(X0,sK3(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f53,plain,
    ! [X0] :
      ( ( sP2(X0)
        | ~ sP1(X0)
        | ~ sP0(X0)
        | ? [X1] :
            ( ~ cd(X1)
            & rr(X0,X1) ) )
      & ( ( sP1(X0)
          & sP0(X0)
          & ! [X2] :
              ( cd(X2)
              | ~ rr(X0,X2) ) )
        | ~ sP2(X0) ) ),
    inference(rectify,[],[f52]) ).

fof(f52,plain,
    ! [X0] :
      ( ( sP2(X0)
        | ~ sP1(X0)
        | ~ sP0(X0)
        | ? [X7] :
            ( ~ cd(X7)
            & rr(X0,X7) ) )
      & ( ( sP1(X0)
          & sP0(X0)
          & ! [X7] :
              ( cd(X7)
              | ~ rr(X0,X7) ) )
        | ~ sP2(X0) ) ),
    inference(flattening,[],[f51]) ).

fof(f51,plain,
    ! [X0] :
      ( ( sP2(X0)
        | ~ sP1(X0)
        | ~ sP0(X0)
        | ? [X7] :
            ( ~ cd(X7)
            & rr(X0,X7) ) )
      & ( ( sP1(X0)
          & sP0(X0)
          & ! [X7] :
              ( cd(X7)
              | ~ rr(X0,X7) ) )
        | ~ sP2(X0) ) ),
    inference(nnf_transformation,[],[f48]) ).

fof(f48,plain,
    ! [X0] :
      ( sP2(X0)
    <=> ( sP1(X0)
        & sP0(X0)
        & ! [X7] :
            ( cd(X7)
            | ~ rr(X0,X7) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

fof(f118,plain,
    sP2(i2003_11_14_17_20_36582),
    inference(unit_resulting_resolution,[],[f67,f89]) ).

fof(f89,plain,
    ! [X0] :
      ( ~ cUnsatisfiable(X0)
      | sP2(X0) ),
    inference(cnf_transformation,[],[f66]) ).

fof(f66,plain,
    ! [X0] :
      ( ( cUnsatisfiable(X0)
        | ~ sP2(X0) )
      & ( sP2(X0)
        | ~ cUnsatisfiable(X0) ) ),
    inference(nnf_transformation,[],[f49]) ).

fof(f49,plain,
    ! [X0] :
      ( cUnsatisfiable(X0)
    <=> sP2(X0) ),
    inference(definition_folding,[],[f23,f48,f47,f46]) ).

fof(f23,plain,
    ! [X0] :
      ( cUnsatisfiable(X0)
    <=> ( ? [X1] :
            ( ? [X2,X3] :
                ( X2 != X3
                & rs(X1,X3)
                & rs(X1,X2) )
            & rr(X0,X1) )
        & ! [X4] :
            ( cc(X4)
            | ! [X5,X6] :
                ( X5 = X6
                | ~ rs(X4,X6)
                | ~ rs(X4,X5) )
            | ~ rr(X0,X4) )
        & ! [X7] :
            ( cd(X7)
            | ~ rr(X0,X7) ) ) ),
    inference(flattening,[],[f22]) ).

fof(f22,plain,
    ! [X0] :
      ( cUnsatisfiable(X0)
    <=> ( ? [X1] :
            ( ? [X2,X3] :
                ( X2 != X3
                & rs(X1,X3)
                & rs(X1,X2) )
            & rr(X0,X1) )
        & ! [X4] :
            ( cc(X4)
            | ! [X5,X6] :
                ( X5 = X6
                | ~ rs(X4,X6)
                | ~ rs(X4,X5) )
            | ~ rr(X0,X4) )
        & ! [X7] :
            ( cd(X7)
            | ~ rr(X0,X7) ) ) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f20,plain,
    ! [X0] :
      ( cUnsatisfiable(X0)
    <=> ( ? [X1] :
            ( ~ ! [X2,X3] :
                  ( ( rs(X1,X3)
                    & rs(X1,X2) )
                 => X2 = X3 )
            & rr(X0,X1) )
        & ! [X4] :
            ( rr(X0,X4)
           => ( cc(X4)
              | ~ ? [X5,X6] :
                    ( X5 != X6
                    & rs(X4,X6)
                    & rs(X4,X5) ) ) )
        & ! [X7] :
            ( rr(X0,X7)
           => cd(X7) ) ) ),
    inference(rectify,[],[f14]) ).

fof(f14,axiom,
    ! [X3] :
      ( cUnsatisfiable(X3)
    <=> ( ? [X4] :
            ( ~ ! [X5,X6] :
                  ( ( rs(X4,X6)
                    & rs(X4,X5) )
                 => X5 = X6 )
            & rr(X3,X4) )
        & ! [X4] :
            ( rr(X3,X4)
           => ( cc(X4)
              | ~ ? [X5,X6] :
                    ( X5 != X6
                    & rs(X4,X6)
                    & rs(X4,X5) ) ) )
        & ! [X4] :
            ( rr(X3,X4)
           => cd(X4) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).

fof(f67,plain,
    cUnsatisfiable(i2003_11_14_17_20_36582),
    inference(cnf_transformation,[],[f16]) ).

fof(f16,axiom,
    cUnsatisfiable(i2003_11_14_17_20_36582),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).

fof(f137,plain,
    sK5(i2003_11_14_17_20_36582) != sK6(i2003_11_14_17_20_36582),
    inference(unit_resulting_resolution,[],[f120,f81]) ).

fof(f81,plain,
    ! [X0] :
      ( ~ sP1(X0)
      | sK5(X0) != sK6(X0) ),
    inference(cnf_transformation,[],[f60]) ).

fof(f135,plain,
    rs(sK4(i2003_11_14_17_20_36582),sK6(i2003_11_14_17_20_36582)),
    inference(unit_resulting_resolution,[],[f120,f80]) ).

fof(f80,plain,
    ! [X0] :
      ( ~ sP1(X0)
      | rs(sK4(X0),sK6(X0)) ),
    inference(cnf_transformation,[],[f60]) ).

fof(f131,plain,
    ~ cc(sK4(i2003_11_14_17_20_36582)),
    inference(unit_resulting_resolution,[],[f128,f70]) ).

fof(f70,plain,
    ! [X0] :
      ( ~ cd(X0)
      | ~ cc(X0) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,plain,
    ! [X0] :
      ( ~ cd(X0)
      | ~ cc(X0) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f18,plain,
    ! [X0] :
      ( cc(X0)
     => ~ cd(X0) ),
    inference(rectify,[],[f15]) ).

fof(f15,axiom,
    ! [X3] :
      ( cc(X3)
     => ~ cd(X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).

fof(f128,plain,
    cd(sK4(i2003_11_14_17_20_36582)),
    inference(unit_resulting_resolution,[],[f118,f126,f73]) ).

fof(f73,plain,
    ! [X2,X0] :
      ( ~ rr(X0,X2)
      | cd(X2)
      | ~ sP2(X0) ),
    inference(cnf_transformation,[],[f55]) ).

fof(f126,plain,
    rr(i2003_11_14_17_20_36582,sK4(i2003_11_14_17_20_36582)),
    inference(unit_resulting_resolution,[],[f120,f78]) ).

fof(f78,plain,
    ! [X0] :
      ( ~ sP1(X0)
      | rr(X0,sK4(X0)) ),
    inference(cnf_transformation,[],[f60]) ).

fof(f141,plain,
    sP11(sK4(i2003_11_14_17_20_36582)),
    inference(unit_resulting_resolution,[],[f121,f126,f115]) ).

fof(f121,plain,
    sP0(i2003_11_14_17_20_36582),
    inference(unit_resulting_resolution,[],[f118,f74]) ).

fof(f74,plain,
    ! [X0] :
      ( ~ sP2(X0)
      | sP0(X0) ),
    inference(cnf_transformation,[],[f55]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : KRS101+1 : TPTP v8.1.2. Released v3.1.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n015.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 19:54:23 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  % (32623)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38  % (32626)WARNING: value z3 for option sas not known
% 0.14/0.38  % (32625)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38  % (32624)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38  % (32627)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38  % (32626)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)
% 0.14/0.38  % (32628)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)
% 0.14/0.38  % (32629)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)
% 0.14/0.38  % (32630)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  % (32630)First to succeed.
% 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  % (32630)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-32623"
% 0.21/0.38  % (32629)Also succeeded, but the first one will report.
% 0.21/0.38  % (32626)Also succeeded, but the first one will report.
% 0.21/0.38  TRYING [4]
% 0.21/0.38  TRYING [4]
% 0.21/0.38  % (32630)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  % (32630)------------------------------
% 0.21/0.38  % (32630)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.38  % (32630)Termination reason: Refutation
% 0.21/0.38  
% 0.21/0.38  % (32630)Memory used [KB]: 839
% 0.21/0.38  % (32630)Time elapsed: 0.006 s
% 0.21/0.38  % (32630)Instructions burned: 7 (million)
% 0.21/0.38  % (32623)Success in time 0.022 s
%------------------------------------------------------------------------------