TSTP Solution File: RNG083+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : RNG083+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%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 : Wed May 31 12:32:50 EDT 2023

% Result   : Theorem 3.39s 0.84s
% Output   : CNFRefutation 3.39s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   94 (  19 unt;   0 def)
%            Number of atoms       :  215 (  66 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  206 (  85   ~;  86   |;  18   &)
%                                         (   8 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   11 (   9 usr;   9 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   55 (;  55   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    aElement0(sz00),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

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(f8,axiom,
    ! [W0,W1,W2] :
      ( ( aElement0(W0)
        & aElement0(W1)
        & aElement0(W2) )
     => sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [W0] :
      ( aElement0(W0)
     => ( sdtpldt0(W0,sz00) = W0
        & W0 = sdtpldt0(sz00,W0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f10,axiom,
    ! [W0] :
      ( aElement0(W0)
     => ( sdtpldt0(W0,smndt0(W0)) = sz00
        & sz00 = sdtpldt0(smndt0(W0),W0) ) ),
    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(f13,axiom,
    ! [W0] :
      ( aElement0(W0)
     => ( sdtasdt0(W0,sz10) = W0
        & W0 = sdtasdt0(sz10,W0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f14,axiom,
    ! [W0,W1,W2] :
      ( ( aElement0(W0)
        & aElement0(W1)
        & aElement0(W2) )
     => ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
        & sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,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(f16,hypothesis,
    aElement0(xx),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f17,conjecture,
    ( sdtasdt0(xx,sz00) = sz00
    & sz00 = sdtasdt0(sz00,xx) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f18,negated_conjecture,
    ~ ( sdtasdt0(xx,sz00) = sz00
      & sz00 = sdtasdt0(sz00,xx) ),
    inference(negated_conjecture,[status(cth)],[f17]) ).

fof(f22,plain,
    aElement0(sz00),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f23,plain,
    aElement0(sz10),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f24,plain,
    ! [W0] :
      ( ~ aElement0(W0)
      | aElement0(smndt0(W0)) ),
    inference(pre_NNF_transformation,[status(esa)],[f4]) ).

fof(f25,plain,
    ! [X0] :
      ( ~ aElement0(X0)
      | aElement0(smndt0(X0)) ),
    inference(cnf_transformation,[status(esa)],[f24]) ).

fof(f28,plain,
    ! [W0,W1] :
      ( ~ aElement0(W0)
      | ~ aElement0(W1)
      | aElement0(sdtasdt0(W0,W1)) ),
    inference(pre_NNF_transformation,[status(esa)],[f6]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( ~ aElement0(X0)
      | ~ aElement0(X1)
      | aElement0(sdtasdt0(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f28]) ).

fof(f32,plain,
    ! [W0,W1,W2] :
      ( ~ aElement0(W0)
      | ~ aElement0(W1)
      | ~ aElement0(W2)
      | sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ),
    inference(pre_NNF_transformation,[status(esa)],[f8]) ).

fof(f33,plain,
    ! [X0,X1,X2] :
      ( ~ aElement0(X0)
      | ~ aElement0(X1)
      | ~ aElement0(X2)
      | sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ),
    inference(cnf_transformation,[status(esa)],[f32]) ).

fof(f34,plain,
    ! [W0] :
      ( ~ aElement0(W0)
      | ( sdtpldt0(W0,sz00) = W0
        & W0 = sdtpldt0(sz00,W0) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f9]) ).

fof(f35,plain,
    ! [X0] :
      ( ~ aElement0(X0)
      | sdtpldt0(X0,sz00) = X0 ),
    inference(cnf_transformation,[status(esa)],[f34]) ).

fof(f36,plain,
    ! [X0] :
      ( ~ aElement0(X0)
      | X0 = sdtpldt0(sz00,X0) ),
    inference(cnf_transformation,[status(esa)],[f34]) ).

fof(f37,plain,
    ! [W0] :
      ( ~ aElement0(W0)
      | ( sdtpldt0(W0,smndt0(W0)) = sz00
        & sz00 = sdtpldt0(smndt0(W0),W0) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f10]) ).

fof(f38,plain,
    ! [X0] :
      ( ~ aElement0(X0)
      | sdtpldt0(X0,smndt0(X0)) = sz00 ),
    inference(cnf_transformation,[status(esa)],[f37]) ).

fof(f40,plain,
    ! [W0,W1] :
      ( ~ aElement0(W0)
      | ~ aElement0(W1)
      | sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ),
    inference(pre_NNF_transformation,[status(esa)],[f11]) ).

fof(f41,plain,
    ! [X0,X1] :
      ( ~ aElement0(X0)
      | ~ aElement0(X1)
      | sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f40]) ).

fof(f44,plain,
    ! [W0] :
      ( ~ aElement0(W0)
      | ( sdtasdt0(W0,sz10) = W0
        & W0 = sdtasdt0(sz10,W0) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f13]) ).

fof(f45,plain,
    ! [X0] :
      ( ~ aElement0(X0)
      | sdtasdt0(X0,sz10) = X0 ),
    inference(cnf_transformation,[status(esa)],[f44]) ).

fof(f47,plain,
    ! [W0,W1,W2] :
      ( ~ aElement0(W0)
      | ~ aElement0(W1)
      | ~ aElement0(W2)
      | ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
        & sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f14]) ).

fof(f48,plain,
    ! [X0,X1,X2] :
      ( ~ aElement0(X0)
      | ~ aElement0(X1)
      | ~ aElement0(X2)
      | sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ),
    inference(cnf_transformation,[status(esa)],[f47]) ).

fof(f50,plain,
    ! [W0] :
      ( ~ aElement0(W0)
      | ( sdtasdt0(smndt0(sz10),W0) = smndt0(W0)
        & smndt0(W0) = sdtasdt0(W0,smndt0(sz10)) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f15]) ).

fof(f51,plain,
    ! [X0] :
      ( ~ aElement0(X0)
      | sdtasdt0(smndt0(sz10),X0) = smndt0(X0) ),
    inference(cnf_transformation,[status(esa)],[f50]) ).

fof(f53,plain,
    aElement0(xx),
    inference(cnf_transformation,[status(esa)],[f16]) ).

fof(f54,plain,
    ( sdtasdt0(xx,sz00) != sz00
    | sz00 != sdtasdt0(sz00,xx) ),
    inference(pre_NNF_transformation,[status(esa)],[f18]) ).

fof(f55,plain,
    ( sdtasdt0(xx,sz00) != sz00
    | sz00 != sdtasdt0(sz00,xx) ),
    inference(cnf_transformation,[status(esa)],[f54]) ).

fof(f56,plain,
    ( spl0_0
  <=> sdtasdt0(xx,sz00) = sz00 ),
    introduced(split_symbol_definition) ).

fof(f58,plain,
    ( sdtasdt0(xx,sz00) != sz00
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f56]) ).

fof(f59,plain,
    ( spl0_1
  <=> sz00 = sdtasdt0(sz00,xx) ),
    introduced(split_symbol_definition) ).

fof(f61,plain,
    ( sz00 != sdtasdt0(sz00,xx)
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f59]) ).

fof(f62,plain,
    ( ~ spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f55,f56,f59]) ).

fof(f70,plain,
    ! [X0] :
      ( ~ aElement0(X0)
      | sdtasdt0(X0,xx) = sdtasdt0(xx,X0) ),
    inference(resolution,[status(thm)],[f41,f53]) ).

fof(f73,plain,
    sdtasdt0(sz00,xx) = sdtasdt0(xx,sz00),
    inference(resolution,[status(thm)],[f70,f22]) ).

fof(f74,plain,
    ( sdtasdt0(sz00,xx) != sz00
    | spl0_0 ),
    inference(backward_demodulation,[status(thm)],[f73,f58]) ).

fof(f75,plain,
    ( spl0_2
  <=> aElement0(xx) ),
    introduced(split_symbol_definition) ).

fof(f77,plain,
    ( ~ aElement0(xx)
    | spl0_2 ),
    inference(component_clause,[status(thm)],[f75]) ).

fof(f78,plain,
    ( spl0_3
  <=> aElement0(sz00) ),
    introduced(split_symbol_definition) ).

fof(f80,plain,
    ( ~ aElement0(sz00)
    | spl0_3 ),
    inference(component_clause,[status(thm)],[f78]) ).

fof(f81,plain,
    ( spl0_4
  <=> aElement0(sdtasdt0(sz00,xx)) ),
    introduced(split_symbol_definition) ).

fof(f82,plain,
    ( aElement0(sdtasdt0(sz00,xx))
    | ~ spl0_4 ),
    inference(component_clause,[status(thm)],[f81]) ).

fof(f84,plain,
    ( ~ aElement0(xx)
    | ~ aElement0(sz00)
    | aElement0(sdtasdt0(sz00,xx)) ),
    inference(paramodulation,[status(thm)],[f73,f29]) ).

fof(f85,plain,
    ( ~ spl0_2
    | ~ spl0_3
    | spl0_4 ),
    inference(split_clause,[status(thm)],[f84,f75,f78,f81]) ).

fof(f86,plain,
    ( $false
    | spl0_3 ),
    inference(forward_subsumption_resolution,[status(thm)],[f80,f22]) ).

fof(f87,plain,
    spl0_3,
    inference(contradiction_clause,[status(thm)],[f86]) ).

fof(f88,plain,
    ( $false
    | spl0_2 ),
    inference(forward_subsumption_resolution,[status(thm)],[f77,f53]) ).

fof(f89,plain,
    spl0_2,
    inference(contradiction_clause,[status(thm)],[f88]) ).

fof(f93,plain,
    ( sdtpldt0(sdtasdt0(sz00,xx),sz00) = sdtasdt0(sz00,xx)
    | ~ spl0_4 ),
    inference(resolution,[status(thm)],[f82,f35]) ).

fof(f135,plain,
    sdtasdt0(xx,sz10) = xx,
    inference(resolution,[status(thm)],[f45,f53]) ).

fof(f137,plain,
    ( spl0_5
  <=> aElement0(sz10) ),
    introduced(split_symbol_definition) ).

fof(f139,plain,
    ( ~ aElement0(sz10)
    | spl0_5 ),
    inference(component_clause,[status(thm)],[f137]) ).

fof(f147,plain,
    sdtpldt0(xx,smndt0(xx)) = sz00,
    inference(resolution,[status(thm)],[f38,f53]) ).

fof(f163,plain,
    ! [X0,X1] :
      ( ~ aElement0(X0)
      | ~ aElement0(X1)
      | sdtpldt0(sdtpldt0(X0,xx),X1) = sdtpldt0(X0,sdtpldt0(xx,X1)) ),
    inference(resolution,[status(thm)],[f33,f53]) ).

fof(f191,plain,
    ! [X0,X1] :
      ( ~ aElement0(X0)
      | ~ aElement0(X1)
      | sdtasdt0(X0,sdtpldt0(sz00,X1)) = sdtpldt0(sdtasdt0(X0,sz00),sdtasdt0(X0,X1)) ),
    inference(resolution,[status(thm)],[f48,f22]) ).

fof(f229,plain,
    sz10 = sdtpldt0(sz00,sz10),
    inference(resolution,[status(thm)],[f23,f36]) ).

fof(f262,plain,
    ( spl0_7
  <=> aElement0(smndt0(xx)) ),
    introduced(split_symbol_definition) ).

fof(f263,plain,
    ( aElement0(smndt0(xx))
    | ~ spl0_7 ),
    inference(component_clause,[status(thm)],[f262]) ).

fof(f321,plain,
    ! [X0] :
      ( ~ aElement0(X0)
      | sdtasdt0(X0,sdtpldt0(sz00,sz10)) = sdtpldt0(sdtasdt0(X0,sz00),sdtasdt0(X0,sz10)) ),
    inference(resolution,[status(thm)],[f191,f23]) ).

fof(f322,plain,
    ! [X0] :
      ( ~ aElement0(X0)
      | sdtasdt0(X0,sz10) = sdtpldt0(sdtasdt0(X0,sz00),sdtasdt0(X0,sz10)) ),
    inference(forward_demodulation,[status(thm)],[f229,f321]) ).

fof(f335,plain,
    sdtasdt0(xx,sz10) = sdtpldt0(sdtasdt0(xx,sz00),sdtasdt0(xx,sz10)),
    inference(resolution,[status(thm)],[f322,f53]) ).

fof(f336,plain,
    xx = sdtpldt0(sdtasdt0(xx,sz00),sdtasdt0(xx,sz10)),
    inference(forward_demodulation,[status(thm)],[f135,f335]) ).

fof(f337,plain,
    xx = sdtpldt0(sdtasdt0(sz00,xx),sdtasdt0(xx,sz10)),
    inference(forward_demodulation,[status(thm)],[f73,f336]) ).

fof(f338,plain,
    xx = sdtpldt0(sdtasdt0(sz00,xx),xx),
    inference(forward_demodulation,[status(thm)],[f135,f337]) ).

fof(f689,plain,
    ( spl0_10
  <=> aElement0(smndt0(sz10)) ),
    introduced(split_symbol_definition) ).

fof(f691,plain,
    ( ~ aElement0(smndt0(sz10))
    | spl0_10 ),
    inference(component_clause,[status(thm)],[f689]) ).

fof(f730,plain,
    ( $false
    | spl0_5 ),
    inference(forward_subsumption_resolution,[status(thm)],[f139,f23]) ).

fof(f731,plain,
    spl0_5,
    inference(contradiction_clause,[status(thm)],[f730]) ).

fof(f913,plain,
    sdtasdt0(smndt0(sz10),xx) = smndt0(xx),
    inference(resolution,[status(thm)],[f51,f53]) ).

fof(f920,plain,
    ( ~ aElement0(smndt0(sz10))
    | ~ aElement0(xx)
    | aElement0(smndt0(xx)) ),
    inference(paramodulation,[status(thm)],[f913,f29]) ).

fof(f921,plain,
    ( ~ spl0_10
    | ~ spl0_2
    | spl0_7 ),
    inference(split_clause,[status(thm)],[f920,f689,f75,f262]) ).

fof(f922,plain,
    ( ~ aElement0(sz10)
    | spl0_10 ),
    inference(resolution,[status(thm)],[f691,f25]) ).

fof(f923,plain,
    ( ~ spl0_5
    | spl0_10 ),
    inference(split_clause,[status(thm)],[f922,f137,f689]) ).

fof(f1012,plain,
    ! [X0] :
      ( ~ aElement0(X0)
      | sdtpldt0(sdtpldt0(X0,xx),smndt0(xx)) = sdtpldt0(X0,sdtpldt0(xx,smndt0(xx)))
      | ~ spl0_7 ),
    inference(resolution,[status(thm)],[f263,f163]) ).

fof(f1013,plain,
    ! [X0] :
      ( ~ aElement0(X0)
      | sdtpldt0(sdtpldt0(X0,xx),smndt0(xx)) = sdtpldt0(X0,sz00)
      | ~ spl0_7 ),
    inference(forward_demodulation,[status(thm)],[f147,f1012]) ).

fof(f1041,plain,
    ( sdtpldt0(sdtpldt0(sdtasdt0(sz00,xx),xx),smndt0(xx)) = sdtpldt0(sdtasdt0(sz00,xx),sz00)
    | ~ spl0_7
    | ~ spl0_4 ),
    inference(resolution,[status(thm)],[f1013,f82]) ).

fof(f1042,plain,
    ( sdtpldt0(xx,smndt0(xx)) = sdtpldt0(sdtasdt0(sz00,xx),sz00)
    | ~ spl0_7
    | ~ spl0_4 ),
    inference(forward_demodulation,[status(thm)],[f338,f1041]) ).

fof(f1043,plain,
    ( sz00 = sdtpldt0(sdtasdt0(sz00,xx),sz00)
    | ~ spl0_7
    | ~ spl0_4 ),
    inference(forward_demodulation,[status(thm)],[f147,f1042]) ).

fof(f1050,plain,
    ( sz00 = sdtasdt0(sz00,xx)
    | ~ spl0_7
    | ~ spl0_4 ),
    inference(backward_demodulation,[status(thm)],[f1043,f93]) ).

fof(f1051,plain,
    ( $false
    | spl0_0
    | ~ spl0_7
    | ~ spl0_4 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1050,f74]) ).

fof(f1052,plain,
    ( spl0_0
    | ~ spl0_7
    | ~ spl0_4 ),
    inference(contradiction_clause,[status(thm)],[f1051]) ).

fof(f1055,plain,
    ( $false
    | spl0_1
    | ~ spl0_7
    | ~ spl0_4 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1050,f61]) ).

fof(f1056,plain,
    ( spl0_1
    | ~ spl0_7
    | ~ spl0_4 ),
    inference(contradiction_clause,[status(thm)],[f1055]) ).

fof(f1057,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f62,f85,f87,f89,f731,f921,f923,f1052,f1056]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09  % Problem  : RNG083+1 : TPTP v8.1.2. Released v4.0.0.
% 0.04/0.10  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.30  % Computer : n015.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit : 300
% 0.10/0.30  % WCLimit  : 300
% 0.10/0.30  % DateTime : Tue May 30 10:51:49 EDT 2023
% 0.10/0.30  % CPUTime  : 
% 0.10/0.30  % Drodi V3.5.1
% 3.39/0.84  % Refutation found
% 3.39/0.84  % SZS status Theorem for theBenchmark: Theorem is valid
% 3.39/0.84  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.39/0.86  % Elapsed time: 0.553823 seconds
% 3.39/0.86  % CPU time: 3.725141 seconds
% 3.39/0.86  % Memory used: 76.718 MB
%------------------------------------------------------------------------------