TSTP Solution File: RNG120+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : RNG120+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n024.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 : Tue Apr 30 20:38:04 EDT 2024

% Result   : Theorem 211.69s 26.98s
% Output   : CNFRefutation 212.36s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   73 (  18 unt;   1 def)
%            Number of atoms       :  205 (  18 equ)
%            Maximal formula atoms :   14 (   2 avg)
%            Number of connectives :  213 (  81   ~;  78   |;  35   &)
%                                         (   9 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   14 (  12 usr;   8 prp; 0-2 aty)
%            Number of functors    :   17 (  17 usr;   8 con; 0-2 aty)
%            Number of variables   :   62 (  56   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    aElement0(sz10),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [W0] :
      ( aElement0(W0)
     => aElement0(smndt0(W0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [W0,W1] :
      ( ( aElement0(W0)
        & aElement0(W1) )
     => aElement0(sdtasdt0(W0,W1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f11,axiom,
    ! [W0,W1] :
      ( ( aElement0(W0)
        & aElement0(W1) )
     => sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f15,axiom,
    ! [W0] :
      ( aElement0(W0)
     => ( sdtasdt0(smndt0(sz10),W0) = smndt0(W0)
        & smndt0(W0) = sdtasdt0(W0,smndt0(sz10)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f20,axiom,
    ! [W0] :
      ( aSet0(W0)
     => ! [W1] :
          ( aElementOf0(W1,W0)
         => aElement0(W1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f24,definition,
    ! [W0] :
      ( aIdeal0(W0)
    <=> ( aSet0(W0)
        & ! [W1] :
            ( aElementOf0(W1,W0)
           => ( ! [W2] :
                  ( aElementOf0(W2,W0)
                 => aElementOf0(sdtpldt0(W1,W2),W0) )
              & ! [W2] :
                  ( aElement0(W2)
                 => aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f42,hypothesis,
    ( aIdeal0(xI)
    & xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f45,hypothesis,
    ( aElementOf0(xu,xI)
    & xu != sz00
    & ! [W0] :
        ( ( aElementOf0(W0,xI)
          & W0 != sz00 )
       => ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f50,hypothesis,
    ( aElement0(xq)
    & aElement0(xr)
    & xb = sdtpldt0(sdtasdt0(xq,xu),xr)
    & ( xr = sz00
      | iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f52,conjecture,
    aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f53,negated_conjecture,
    ~ aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
    inference(negated_conjecture,[status(cth)],[f52]) ).

fof(f58,plain,
    aElement0(sz10),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f59,plain,
    ! [W0] :
      ( ~ aElement0(W0)
      | aElement0(smndt0(W0)) ),
    inference(pre_NNF_transformation,[status(esa)],[f4]) ).

fof(f60,plain,
    ! [X0] :
      ( ~ aElement0(X0)
      | aElement0(smndt0(X0)) ),
    inference(cnf_transformation,[status(esa)],[f59]) ).

fof(f63,plain,
    ! [W0,W1] :
      ( ~ aElement0(W0)
      | ~ aElement0(W1)
      | aElement0(sdtasdt0(W0,W1)) ),
    inference(pre_NNF_transformation,[status(esa)],[f6]) ).

fof(f64,plain,
    ! [X0,X1] :
      ( ~ aElement0(X0)
      | ~ aElement0(X1)
      | aElement0(sdtasdt0(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f63]) ).

fof(f75,plain,
    ! [W0,W1] :
      ( ~ aElement0(W0)
      | ~ aElement0(W1)
      | sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ),
    inference(pre_NNF_transformation,[status(esa)],[f11]) ).

fof(f76,plain,
    ! [X0,X1] :
      ( ~ aElement0(X0)
      | ~ aElement0(X1)
      | sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f75]) ).

fof(f85,plain,
    ! [W0] :
      ( ~ aElement0(W0)
      | ( sdtasdt0(smndt0(sz10),W0) = smndt0(W0)
        & smndt0(W0) = sdtasdt0(W0,smndt0(sz10)) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f15]) ).

fof(f86,plain,
    ! [X0] :
      ( ~ aElement0(X0)
      | sdtasdt0(smndt0(sz10),X0) = smndt0(X0) ),
    inference(cnf_transformation,[status(esa)],[f85]) ).

fof(f97,plain,
    ! [W0] :
      ( ~ aSet0(W0)
      | ! [W1] :
          ( ~ aElementOf0(W1,W0)
          | aElement0(W1) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f20]) ).

fof(f98,plain,
    ! [X0,X1] :
      ( ~ aSet0(X0)
      | ~ aElementOf0(X1,X0)
      | aElement0(X1) ),
    inference(cnf_transformation,[status(esa)],[f97]) ).

fof(f127,plain,
    ! [W0] :
      ( aIdeal0(W0)
    <=> ( aSet0(W0)
        & ! [W1] :
            ( ~ aElementOf0(W1,W0)
            | ( ! [W2] :
                  ( ~ aElementOf0(W2,W0)
                  | aElementOf0(sdtpldt0(W1,W2),W0) )
              & ! [W2] :
                  ( ~ aElement0(W2)
                  | aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f24]) ).

fof(f128,plain,
    ! [W0] :
      ( ( ~ aIdeal0(W0)
        | ( aSet0(W0)
          & ! [W1] :
              ( ~ aElementOf0(W1,W0)
              | ( ! [W2] :
                    ( ~ aElementOf0(W2,W0)
                    | aElementOf0(sdtpldt0(W1,W2),W0) )
                & ! [W2] :
                    ( ~ aElement0(W2)
                    | aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
      & ( aIdeal0(W0)
        | ~ aSet0(W0)
        | ? [W1] :
            ( aElementOf0(W1,W0)
            & ( ? [W2] :
                  ( aElementOf0(W2,W0)
                  & ~ aElementOf0(sdtpldt0(W1,W2),W0) )
              | ? [W2] :
                  ( aElement0(W2)
                  & ~ aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f127]) ).

fof(f129,plain,
    ( ! [W0] :
        ( ~ aIdeal0(W0)
        | ( aSet0(W0)
          & ! [W1] :
              ( ~ aElementOf0(W1,W0)
              | ( ! [W2] :
                    ( ~ aElementOf0(W2,W0)
                    | aElementOf0(sdtpldt0(W1,W2),W0) )
                & ! [W2] :
                    ( ~ aElement0(W2)
                    | aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
    & ! [W0] :
        ( aIdeal0(W0)
        | ~ aSet0(W0)
        | ? [W1] :
            ( aElementOf0(W1,W0)
            & ( ? [W2] :
                  ( aElementOf0(W2,W0)
                  & ~ aElementOf0(sdtpldt0(W1,W2),W0) )
              | ? [W2] :
                  ( aElement0(W2)
                  & ~ aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ),
    inference(miniscoping,[status(esa)],[f128]) ).

fof(f130,plain,
    ( ! [W0] :
        ( ~ aIdeal0(W0)
        | ( aSet0(W0)
          & ! [W1] :
              ( ~ aElementOf0(W1,W0)
              | ( ! [W2] :
                    ( ~ aElementOf0(W2,W0)
                    | aElementOf0(sdtpldt0(W1,W2),W0) )
                & ! [W2] :
                    ( ~ aElement0(W2)
                    | aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
    & ! [W0] :
        ( aIdeal0(W0)
        | ~ aSet0(W0)
        | ( aElementOf0(sk0_8(W0),W0)
          & ( ( aElementOf0(sk0_9(W0),W0)
              & ~ aElementOf0(sdtpldt0(sk0_8(W0),sk0_9(W0)),W0) )
            | ( aElement0(sk0_10(W0))
              & ~ aElementOf0(sdtasdt0(sk0_10(W0),sk0_8(W0)),W0) ) ) ) ) ),
    inference(skolemization,[status(esa)],[f129]) ).

fof(f131,plain,
    ! [X0] :
      ( ~ aIdeal0(X0)
      | aSet0(X0) ),
    inference(cnf_transformation,[status(esa)],[f130]) ).

fof(f133,plain,
    ! [X0,X1,X2] :
      ( ~ aIdeal0(X0)
      | ~ aElementOf0(X1,X0)
      | ~ aElement0(X2)
      | aElementOf0(sdtasdt0(X2,X1),X0) ),
    inference(cnf_transformation,[status(esa)],[f130]) ).

fof(f210,plain,
    aIdeal0(xI),
    inference(cnf_transformation,[status(esa)],[f42]) ).

fof(f219,plain,
    ( aElementOf0(xu,xI)
    & xu != sz00
    & ! [W0] :
        ( ~ aElementOf0(W0,xI)
        | W0 = sz00
        | ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu)) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f45]) ).

fof(f220,plain,
    aElementOf0(xu,xI),
    inference(cnf_transformation,[status(esa)],[f219]) ).

fof(f231,plain,
    aElement0(xq),
    inference(cnf_transformation,[status(esa)],[f50]) ).

fof(f236,plain,
    ~ aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
    inference(cnf_transformation,[status(esa)],[f53]) ).

fof(f296,plain,
    ! [X0] :
      ( ~ aElement0(X0)
      | sdtasdt0(X0,xq) = sdtasdt0(xq,X0) ),
    inference(resolution,[status(thm)],[f76,f231]) ).

fof(f429,plain,
    aSet0(xI),
    inference(resolution,[status(thm)],[f131,f210]) ).

fof(f493,plain,
    ( spl0_7
  <=> aElement0(xq) ),
    introduced(split_symbol_definition) ).

fof(f495,plain,
    ( ~ aElement0(xq)
    | spl0_7 ),
    inference(component_clause,[status(thm)],[f493]) ).

fof(f501,plain,
    ( $false
    | spl0_7 ),
    inference(forward_subsumption_resolution,[status(thm)],[f495,f231]) ).

fof(f502,plain,
    spl0_7,
    inference(contradiction_clause,[status(thm)],[f501]) ).

fof(f961,plain,
    ( spl0_37
  <=> aElement0(smndt0(sz10)) ),
    introduced(split_symbol_definition) ).

fof(f963,plain,
    ( ~ aElement0(smndt0(sz10))
    | spl0_37 ),
    inference(component_clause,[status(thm)],[f961]) ).

fof(f1118,plain,
    ! [X0] :
      ( ~ aElementOf0(X0,xI)
      | aElement0(X0) ),
    inference(resolution,[status(thm)],[f98,f429]) ).

fof(f1120,plain,
    aElement0(xu),
    inference(resolution,[status(thm)],[f1118,f220]) ).

fof(f1200,plain,
    sdtasdt0(xu,xq) = sdtasdt0(xq,xu),
    inference(resolution,[status(thm)],[f1120,f296]) ).

fof(f1205,plain,
    ~ aElementOf0(smndt0(sdtasdt0(xu,xq)),xI),
    inference(backward_demodulation,[status(thm)],[f1200,f236]) ).

fof(f1364,plain,
    ( ~ aElement0(sz10)
    | spl0_37 ),
    inference(resolution,[status(thm)],[f963,f60]) ).

fof(f1365,plain,
    ( $false
    | spl0_37 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1364,f58]) ).

fof(f1366,plain,
    spl0_37,
    inference(contradiction_clause,[status(thm)],[f1365]) ).

fof(f1776,plain,
    ( spl0_64
  <=> aElement0(sdtasdt0(xu,xq)) ),
    introduced(split_symbol_definition) ).

fof(f1777,plain,
    ( aElement0(sdtasdt0(xu,xq))
    | ~ spl0_64 ),
    inference(component_clause,[status(thm)],[f1776]) ).

fof(f1791,plain,
    ( spl0_67
  <=> aElement0(xu) ),
    introduced(split_symbol_definition) ).

fof(f1793,plain,
    ( ~ aElement0(xu)
    | spl0_67 ),
    inference(component_clause,[status(thm)],[f1791]) ).

fof(f1799,plain,
    ( $false
    | spl0_67 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1793,f1120]) ).

fof(f1800,plain,
    spl0_67,
    inference(contradiction_clause,[status(thm)],[f1799]) ).

fof(f1806,plain,
    ( ~ aElement0(xq)
    | ~ aElement0(xu)
    | aElement0(sdtasdt0(xu,xq)) ),
    inference(paramodulation,[status(thm)],[f1200,f64]) ).

fof(f1807,plain,
    ( ~ spl0_7
    | ~ spl0_67
    | spl0_64 ),
    inference(split_clause,[status(thm)],[f1806,f493,f1791,f1776]) ).

fof(f2474,plain,
    ( sdtasdt0(smndt0(sz10),sdtasdt0(xu,xq)) = smndt0(sdtasdt0(xu,xq))
    | ~ spl0_64 ),
    inference(resolution,[status(thm)],[f1777,f86]) ).

fof(f35211,plain,
    ! [X0,X1] :
      ( ~ aElementOf0(X0,xI)
      | ~ aElement0(X1)
      | aElementOf0(sdtasdt0(X1,X0),xI) ),
    inference(resolution,[status(thm)],[f133,f210]) ).

fof(f35230,plain,
    ( spl0_293
  <=> aElementOf0(xu,xI) ),
    introduced(split_symbol_definition) ).

fof(f35232,plain,
    ( ~ aElementOf0(xu,xI)
    | spl0_293 ),
    inference(component_clause,[status(thm)],[f35230]) ).

fof(f35257,plain,
    ( $false
    | spl0_293 ),
    inference(forward_subsumption_resolution,[status(thm)],[f35232,f220]) ).

fof(f35258,plain,
    spl0_293,
    inference(contradiction_clause,[status(thm)],[f35257]) ).

fof(f50627,plain,
    ( spl0_298
  <=> aElementOf0(smndt0(sdtasdt0(xu,xq)),xI) ),
    introduced(split_symbol_definition) ).

fof(f50628,plain,
    ( aElementOf0(smndt0(sdtasdt0(xu,xq)),xI)
    | ~ spl0_298 ),
    inference(component_clause,[status(thm)],[f50627]) ).

fof(f50647,plain,
    ( spl0_302
  <=> aElementOf0(sdtasdt0(xu,xq),xI) ),
    introduced(split_symbol_definition) ).

fof(f50650,plain,
    ( ~ aElementOf0(sdtasdt0(xu,xq),xI)
    | ~ aElement0(smndt0(sz10))
    | aElementOf0(smndt0(sdtasdt0(xu,xq)),xI)
    | ~ spl0_64 ),
    inference(paramodulation,[status(thm)],[f2474,f35211]) ).

fof(f50651,plain,
    ( ~ spl0_302
    | ~ spl0_37
    | spl0_298
    | ~ spl0_64 ),
    inference(split_clause,[status(thm)],[f50650,f50647,f961,f50627,f1776]) ).

fof(f50682,plain,
    ( ~ aElementOf0(xu,xI)
    | ~ aElement0(xq)
    | aElementOf0(sdtasdt0(xu,xq),xI) ),
    inference(paramodulation,[status(thm)],[f1200,f35211]) ).

fof(f50683,plain,
    ( ~ spl0_293
    | ~ spl0_7
    | spl0_302 ),
    inference(split_clause,[status(thm)],[f50682,f35230,f493,f50647]) ).

fof(f50693,plain,
    ( $false
    | ~ spl0_298 ),
    inference(forward_subsumption_resolution,[status(thm)],[f50628,f1205]) ).

fof(f50694,plain,
    ~ spl0_298,
    inference(contradiction_clause,[status(thm)],[f50693]) ).

fof(f50695,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f502,f1366,f1800,f1807,f35258,f50651,f50683,f50694]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : RNG120+1 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.33  % Computer : n024.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Mon Apr 29 22:17:51 EDT 2024
% 0.11/0.33  % CPUTime  : 
% 0.11/0.35  % Drodi V3.6.0
% 211.69/26.98  % Refutation found
% 211.69/26.98  % SZS status Theorem for theBenchmark: Theorem is valid
% 211.69/26.98  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 212.78/27.14  % Elapsed time: 26.789165 seconds
% 212.78/27.14  % CPU time: 212.572680 seconds
% 212.78/27.14  % Total memory used: 877.300 MB
% 212.78/27.14  % Net memory used: 821.719 MB
%------------------------------------------------------------------------------