TSTP Solution File: HEN009-2 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : HEN009-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n004.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 20:21:47 EDT 2024

% Result   : Unsatisfiable 0.16s 0.45s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   68 (  21 unt;   0 def)
%            Number of atoms       :  140 (   7 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  138 (  66   ~;  66   |;   0   &)
%                                         (   6 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   7 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :   85 (  85   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [X,Y,Z] :
      ( ~ quotient(X,Y,Z)
      | less_equal(Z,X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [X,Y] :
      ( ~ less_equal(X,Y)
      | ~ less_equal(Y,X)
      | X = Y ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [X] : less_equal(X,identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [X,Y] : quotient(X,Y,divide(X,Y)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f13,axiom,
    ! [X] : quotient(X,zero,X),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f14,axiom,
    ! [X,Y,Z] :
      ( ~ less_equal(X,Y)
      | ~ less_equal(Y,Z)
      | less_equal(X,Z) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f15,axiom,
    ! [X,Y,W1,Z,W2] :
      ( ~ quotient(X,Y,W1)
      | ~ less_equal(W1,Z)
      | ~ quotient(X,Z,W2)
      | less_equal(W2,Y) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f17,axiom,
    ! [X,Y,Z,W1,W2] :
      ( ~ less_equal(X,Y)
      | ~ quotient(X,Z,W1)
      | ~ quotient(Y,Z,W2)
      | less_equal(W1,W2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f18,hypothesis,
    quotient(identity,a,idQa),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f19,hypothesis,
    quotient(identity,idQa,idQ_idQa),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f20,hypothesis,
    quotient(identity,idQ_idQa,idQ__idQ_idQa),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f21,negated_conjecture,
    idQa != idQ__idQ_idQa,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f24,plain,
    ! [X,Z] :
      ( ! [Y] : ~ quotient(X,Y,Z)
      | less_equal(Z,X) ),
    inference(miniscoping,[status(esa)],[f3]) ).

fof(f25,plain,
    ! [X0,X1,X2] :
      ( ~ quotient(X0,X1,X2)
      | less_equal(X2,X0) ),
    inference(cnf_transformation,[status(esa)],[f24]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( ~ less_equal(X0,X1)
      | ~ less_equal(X1,X0)
      | X0 = X1 ),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f30,plain,
    ! [X0] : less_equal(X0,identity),
    inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f31,plain,
    ! [X0,X1] : quotient(X0,X1,divide(X0,X1)),
    inference(cnf_transformation,[status(esa)],[f8]) ).

fof(f37,plain,
    ! [X0] : quotient(X0,zero,X0),
    inference(cnf_transformation,[status(esa)],[f13]) ).

fof(f38,plain,
    ! [X,Z] :
      ( ! [Y] :
          ( ~ less_equal(X,Y)
          | ~ less_equal(Y,Z) )
      | less_equal(X,Z) ),
    inference(miniscoping,[status(esa)],[f14]) ).

fof(f39,plain,
    ! [X0,X1,X2] :
      ( ~ less_equal(X0,X1)
      | ~ less_equal(X1,X2)
      | less_equal(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f38]) ).

fof(f40,plain,
    ! [Y,W2] :
      ( ! [X,Z] :
          ( ! [W1] :
              ( ~ quotient(X,Y,W1)
              | ~ less_equal(W1,Z) )
          | ~ quotient(X,Z,W2) )
      | less_equal(W2,Y) ),
    inference(miniscoping,[status(esa)],[f15]) ).

fof(f41,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ quotient(X0,X1,X2)
      | ~ less_equal(X2,X3)
      | ~ quotient(X0,X3,X4)
      | less_equal(X4,X1) ),
    inference(cnf_transformation,[status(esa)],[f40]) ).

fof(f44,plain,
    ! [W1,W2] :
      ( ! [Y,Z] :
          ( ! [X] :
              ( ~ less_equal(X,Y)
              | ~ quotient(X,Z,W1) )
          | ~ quotient(Y,Z,W2) )
      | less_equal(W1,W2) ),
    inference(miniscoping,[status(esa)],[f17]) ).

fof(f45,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ less_equal(X0,X1)
      | ~ quotient(X0,X2,X3)
      | ~ quotient(X1,X2,X4)
      | less_equal(X3,X4) ),
    inference(cnf_transformation,[status(esa)],[f44]) ).

fof(f46,plain,
    quotient(identity,a,idQa),
    inference(cnf_transformation,[status(esa)],[f18]) ).

fof(f47,plain,
    quotient(identity,idQa,idQ_idQa),
    inference(cnf_transformation,[status(esa)],[f19]) ).

fof(f48,plain,
    quotient(identity,idQ_idQa,idQ__idQ_idQa),
    inference(cnf_transformation,[status(esa)],[f20]) ).

fof(f49,plain,
    idQa != idQ__idQ_idQa,
    inference(cnf_transformation,[status(esa)],[f21]) ).

fof(f57,plain,
    ! [X0] : less_equal(X0,X0),
    inference(resolution,[status(thm)],[f25,f37]) ).

fof(f115,plain,
    ! [X0,X1] :
      ( ~ less_equal(idQ_idQa,X0)
      | ~ quotient(identity,X0,X1)
      | less_equal(X1,idQa) ),
    inference(resolution,[status(thm)],[f41,f47]) ).

fof(f116,plain,
    ! [X0,X1] :
      ( ~ less_equal(idQa,X0)
      | ~ quotient(identity,X0,X1)
      | less_equal(X1,a) ),
    inference(resolution,[status(thm)],[f41,f46]) ).

fof(f120,plain,
    ! [X0,X1,X2,X3] :
      ( ~ less_equal(divide(X0,X1),X2)
      | ~ quotient(X0,X2,X3)
      | less_equal(X3,X1) ),
    inference(resolution,[status(thm)],[f41,f31]) ).

fof(f130,plain,
    ( spl0_0
  <=> less_equal(idQ__idQ_idQa,idQa) ),
    introduced(split_symbol_definition) ).

fof(f131,plain,
    ( less_equal(idQ__idQ_idQa,idQa)
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f130]) ).

fof(f133,plain,
    ( spl0_1
  <=> less_equal(idQ_idQa,idQ_idQa) ),
    introduced(split_symbol_definition) ).

fof(f135,plain,
    ( ~ less_equal(idQ_idQa,idQ_idQa)
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f133]) ).

fof(f380,plain,
    ! [X0,X1,X2,X3] :
      ( ~ quotient(X0,X1,X2)
      | ~ quotient(identity,X1,X3)
      | less_equal(X2,X3) ),
    inference(resolution,[status(thm)],[f45,f30]) ).

fof(f872,plain,
    ! [X0,X1,X2] :
      ( ~ quotient(identity,X0,X1)
      | less_equal(divide(X2,X0),X1) ),
    inference(resolution,[status(thm)],[f380,f31]) ).

fof(f980,plain,
    ! [X0] : less_equal(divide(X0,idQ_idQa),idQ__idQ_idQa),
    inference(resolution,[status(thm)],[f872,f48]) ).

fof(f1160,plain,
    ( ~ less_equal(idQ_idQa,idQ_idQa)
    | less_equal(idQ__idQ_idQa,idQa) ),
    inference(resolution,[status(thm)],[f115,f48]) ).

fof(f1161,plain,
    ( ~ spl0_1
    | spl0_0 ),
    inference(split_clause,[status(thm)],[f1160,f133,f130]) ).

fof(f1164,plain,
    ( spl0_33
  <=> less_equal(idQ_idQa,a) ),
    introduced(split_symbol_definition) ).

fof(f1165,plain,
    ( less_equal(idQ_idQa,a)
    | ~ spl0_33 ),
    inference(component_clause,[status(thm)],[f1164]) ).

fof(f1167,plain,
    ( spl0_34
  <=> less_equal(idQa,idQa) ),
    introduced(split_symbol_definition) ).

fof(f1169,plain,
    ( ~ less_equal(idQa,idQa)
    | spl0_34 ),
    inference(component_clause,[status(thm)],[f1167]) ).

fof(f1187,plain,
    ( $false
    | spl0_1 ),
    inference(forward_subsumption_resolution,[status(thm)],[f135,f57]) ).

fof(f1188,plain,
    spl0_1,
    inference(contradiction_clause,[status(thm)],[f1187]) ).

fof(f1195,plain,
    ( spl0_37
  <=> less_equal(idQa,idQ__idQ_idQa) ),
    introduced(split_symbol_definition) ).

fof(f1197,plain,
    ( ~ less_equal(idQa,idQ__idQ_idQa)
    | spl0_37 ),
    inference(component_clause,[status(thm)],[f1195]) ).

fof(f1198,plain,
    ( spl0_38
  <=> idQ__idQ_idQa = idQa ),
    introduced(split_symbol_definition) ).

fof(f1199,plain,
    ( idQ__idQ_idQa = idQa
    | ~ spl0_38 ),
    inference(component_clause,[status(thm)],[f1198]) ).

fof(f1201,plain,
    ( ~ less_equal(idQa,idQ__idQ_idQa)
    | idQ__idQ_idQa = idQa
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f131,f29]) ).

fof(f1202,plain,
    ( ~ spl0_37
    | spl0_38
    | ~ spl0_0 ),
    inference(split_clause,[status(thm)],[f1201,f1195,f1198,f130]) ).

fof(f1374,plain,
    ( ~ less_equal(idQa,idQa)
    | less_equal(idQ_idQa,a) ),
    inference(resolution,[status(thm)],[f116,f47]) ).

fof(f1375,plain,
    ( ~ spl0_34
    | spl0_33 ),
    inference(split_clause,[status(thm)],[f1374,f1167,f1164]) ).

fof(f1396,plain,
    ( $false
    | spl0_34 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1169,f57]) ).

fof(f1397,plain,
    spl0_34,
    inference(contradiction_clause,[status(thm)],[f1396]) ).

fof(f1401,plain,
    ! [X0,X1] :
      ( ~ quotient(X0,idQ__idQ_idQa,X1)
      | less_equal(X1,idQ_idQa) ),
    inference(resolution,[status(thm)],[f120,f980]) ).

fof(f1671,plain,
    ! [X0] : less_equal(divide(X0,idQ__idQ_idQa),idQ_idQa),
    inference(resolution,[status(thm)],[f1401,f31]) ).

fof(f1679,plain,
    ! [X0,X1] :
      ( ~ less_equal(idQ_idQa,X0)
      | less_equal(divide(X1,idQ__idQ_idQa),X0) ),
    inference(resolution,[status(thm)],[f1671,f39]) ).

fof(f2604,plain,
    ! [X0] :
      ( less_equal(divide(X0,idQ__idQ_idQa),a)
      | ~ spl0_33 ),
    inference(resolution,[status(thm)],[f1679,f1165]) ).

fof(f2611,plain,
    ! [X0,X1] :
      ( ~ quotient(X0,a,X1)
      | less_equal(X1,idQ__idQ_idQa)
      | ~ spl0_33 ),
    inference(resolution,[status(thm)],[f2604,f120]) ).

fof(f2631,plain,
    ( less_equal(idQa,idQ__idQ_idQa)
    | ~ spl0_33 ),
    inference(resolution,[status(thm)],[f2611,f46]) ).

fof(f2632,plain,
    ( $false
    | spl0_37
    | ~ spl0_33 ),
    inference(forward_subsumption_resolution,[status(thm)],[f2631,f1197]) ).

fof(f2633,plain,
    ( spl0_37
    | ~ spl0_33 ),
    inference(contradiction_clause,[status(thm)],[f2632]) ).

fof(f2636,plain,
    ( $false
    | ~ spl0_38 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1199,f49]) ).

fof(f2637,plain,
    ~ spl0_38,
    inference(contradiction_clause,[status(thm)],[f2636]) ).

fof(f2638,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f1161,f1188,f1202,f1375,f1397,f2633,f2637]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : HEN009-2 : TPTP v8.1.2. Released v1.0.0.
% 0.10/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.32  % Computer : n004.cluster.edu
% 0.10/0.32  % Model    : x86_64 x86_64
% 0.10/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32  % Memory   : 8042.1875MB
% 0.10/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32  % CPULimit : 300
% 0.10/0.32  % WCLimit  : 300
% 0.10/0.32  % DateTime : Mon Apr 29 20:02:48 EDT 2024
% 0.10/0.32  % CPUTime  : 
% 0.10/0.33  % Drodi V3.6.0
% 0.16/0.45  % Refutation found
% 0.16/0.45  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.16/0.45  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.47  % Elapsed time: 0.137874 seconds
% 0.16/0.47  % CPU time: 0.974252 seconds
% 0.16/0.47  % Total memory used: 33.954 MB
% 0.16/0.47  % Net memory used: 31.397 MB
%------------------------------------------------------------------------------