TSTP Solution File: BOO017-1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : BOO017-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n003.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 20:12:57 EDT 2024

% Result   : Unsatisfiable 1.88s 0.60s
% Output   : CNFRefutation 1.88s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   57 (  27 unt;   0 def)
%            Number of atoms       :  129 (  10 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  146 (  74   ~;  72   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :  163 ( 163   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X,Y] : sum(X,Y,add(X,Y)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [X,Y] : product(X,Y,multiply(X,Y)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

fof(f4,axiom,
    ! [X,Y,Z] :
      ( ~ product(X,Y,Z)
      | product(Y,X,Z) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [X] : sum(X,additive_identity,X),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

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

fof(f11,axiom,
    ! [Y,X,V1,Z,V2,V3,V4] :
      ( ~ product(Y,X,V1)
      | ~ product(Z,X,V2)
      | ~ sum(Y,Z,V3)
      | ~ product(V3,X,V4)
      | sum(V1,V2,V4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f13,axiom,
    ! [X,Y,V1,Z,V2,V3,V4] :
      ( ~ sum(X,Y,V1)
      | ~ sum(X,Z,V2)
      | ~ product(Y,Z,V3)
      | ~ sum(X,V3,V4)
      | product(V1,V2,V4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f15,axiom,
    ! [Y,X,V1,Z,V2,V3,V4] :
      ( ~ sum(Y,X,V1)
      | ~ sum(Z,X,V2)
      | ~ product(Y,Z,V3)
      | ~ sum(V3,X,V4)
      | product(V1,V2,V4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f17,axiom,
    ! [X] : sum(inverse(X),X,multiplicative_identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f21,axiom,
    ! [X,Y,U,V] :
      ( ~ sum(X,Y,U)
      | ~ sum(X,Y,V)
      | U = V ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f22,axiom,
    ! [X,Y,U,V] :
      ( ~ product(X,Y,U)
      | ~ product(X,Y,V)
      | U = V ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f23,hypothesis,
    sum(x,y,z),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f24,negated_conjecture,
    ~ product(x,z,x),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f25,plain,
    ! [X0,X1] : sum(X0,X1,add(X0,X1)),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f26,plain,
    ! [X0,X1] : product(X0,X1,multiply(X0,X1)),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f27,plain,
    ! [X0,X1,X2] :
      ( ~ sum(X0,X1,X2)
      | sum(X1,X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f28,plain,
    ! [X0,X1,X2] :
      ( ~ product(X0,X1,X2)
      | product(X1,X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f30,plain,
    ! [X0] : sum(X0,additive_identity,X0),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f31,plain,
    ! [X0] : product(multiplicative_identity,X0,X0),
    inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f32,plain,
    ! [X0] : product(X0,multiplicative_identity,X0),
    inference(cnf_transformation,[status(esa)],[f8]) ).

fof(f37,plain,
    ! [V1,V2,V4] :
      ( ! [X,V3] :
          ( ! [Y,Z] :
              ( ~ product(Y,X,V1)
              | ~ product(Z,X,V2)
              | ~ sum(Y,Z,V3) )
          | ~ product(V3,X,V4) )
      | sum(V1,V2,V4) ),
    inference(miniscoping,[status(esa)],[f11]) ).

fof(f38,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ~ product(X0,X1,X2)
      | ~ product(X3,X1,X4)
      | ~ sum(X0,X3,X5)
      | ~ product(X5,X1,X6)
      | sum(X2,X4,X6) ),
    inference(cnf_transformation,[status(esa)],[f37]) ).

fof(f41,plain,
    ! [V1,V2,V4] :
      ( ! [X,V3] :
          ( ! [Y,Z] :
              ( ~ sum(X,Y,V1)
              | ~ sum(X,Z,V2)
              | ~ product(Y,Z,V3) )
          | ~ sum(X,V3,V4) )
      | product(V1,V2,V4) ),
    inference(miniscoping,[status(esa)],[f13]) ).

fof(f42,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ~ sum(X0,X1,X2)
      | ~ sum(X0,X3,X4)
      | ~ product(X1,X3,X5)
      | ~ sum(X0,X5,X6)
      | product(X2,X4,X6) ),
    inference(cnf_transformation,[status(esa)],[f41]) ).

fof(f45,plain,
    ! [V1,V2,V4] :
      ( ! [X,V3] :
          ( ! [Y,Z] :
              ( ~ sum(Y,X,V1)
              | ~ sum(Z,X,V2)
              | ~ product(Y,Z,V3) )
          | ~ sum(V3,X,V4) )
      | product(V1,V2,V4) ),
    inference(miniscoping,[status(esa)],[f15]) ).

fof(f46,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ~ sum(X0,X1,X2)
      | ~ sum(X3,X1,X4)
      | ~ product(X0,X3,X5)
      | ~ sum(X5,X1,X6)
      | product(X2,X4,X6) ),
    inference(cnf_transformation,[status(esa)],[f45]) ).

fof(f49,plain,
    ! [X0] : sum(inverse(X0),X0,multiplicative_identity),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f53,plain,
    ! [U,V] :
      ( ! [X,Y] :
          ( ~ sum(X,Y,U)
          | ~ sum(X,Y,V) )
      | U = V ),
    inference(miniscoping,[status(esa)],[f21]) ).

fof(f54,plain,
    ! [X0,X1,X2,X3] :
      ( ~ sum(X0,X1,X2)
      | ~ sum(X0,X1,X3)
      | X2 = X3 ),
    inference(cnf_transformation,[status(esa)],[f53]) ).

fof(f55,plain,
    ! [U,V] :
      ( ! [X,Y] :
          ( ~ product(X,Y,U)
          | ~ product(X,Y,V) )
      | U = V ),
    inference(miniscoping,[status(esa)],[f22]) ).

fof(f56,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product(X0,X1,X2)
      | ~ product(X0,X1,X3)
      | X2 = X3 ),
    inference(cnf_transformation,[status(esa)],[f55]) ).

fof(f57,plain,
    sum(x,y,z),
    inference(cnf_transformation,[status(esa)],[f23]) ).

fof(f58,plain,
    ~ product(x,z,x),
    inference(cnf_transformation,[status(esa)],[f24]) ).

fof(f60,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ product(X0,X1,X2)
      | ~ product(X3,X1,X4)
      | ~ sum(X0,X3,X3)
      | sum(X2,X4,X4) ),
    inference(factoring,[status(esa)],[f38]) ).

fof(f61,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ sum(X0,X1,X2)
      | ~ sum(X0,X3,X4)
      | ~ product(X1,X3,X3)
      | product(X2,X4,X4) ),
    inference(factoring,[status(esa)],[f42]) ).

fof(f63,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ sum(X0,X1,X2)
      | ~ sum(X3,X1,X4)
      | ~ product(X0,X3,X3)
      | product(X2,X4,X4) ),
    inference(factoring,[status(esa)],[f46]) ).

fof(f100,plain,
    ! [X0,X1,X2] :
      ( ~ sum(X0,X1,X2)
      | ~ product(X1,additive_identity,additive_identity)
      | product(X2,X0,X0) ),
    inference(resolution,[status(thm)],[f30,f61]) ).

fof(f107,plain,
    ! [X0,X1,X2,X3] :
      ( ~ sum(multiplicative_identity,X0,X1)
      | ~ sum(X2,X0,X3)
      | product(X1,X3,X3) ),
    inference(resolution,[status(thm)],[f31,f63]) ).

fof(f114,plain,
    ! [X0,X1,X2] :
      ( ~ product(X0,X1,X2)
      | ~ sum(X0,multiplicative_identity,multiplicative_identity)
      | sum(X2,X1,X1) ),
    inference(resolution,[status(thm)],[f31,f60]) ).

fof(f147,plain,
    ! [X0,X1] :
      ( ~ product(X0,multiplicative_identity,X1)
      | X1 = X0 ),
    inference(resolution,[status(thm)],[f32,f56]) ).

fof(f174,plain,
    ! [X0,X1] : product(X0,X1,multiply(X1,X0)),
    inference(resolution,[status(thm)],[f26,f28]) ).

fof(f286,plain,
    ! [X0,X1] :
      ( ~ sum(X0,additive_identity,X1)
      | X1 = X0 ),
    inference(resolution,[status(thm)],[f54,f30]) ).

fof(f492,plain,
    ! [X0,X1,X2] :
      ( ~ sum(X0,X1,X2)
      | product(add(multiplicative_identity,X1),X2,X2) ),
    inference(resolution,[status(thm)],[f107,f25]) ).

fof(f506,plain,
    ! [X0] : product(add(multiplicative_identity,X0),multiplicative_identity,multiplicative_identity),
    inference(resolution,[status(thm)],[f492,f49]) ).

fof(f612,plain,
    ! [X0] : multiplicative_identity = add(multiplicative_identity,X0),
    inference(resolution,[status(thm)],[f506,f147]) ).

fof(f671,plain,
    ! [X0] : sum(multiplicative_identity,X0,multiplicative_identity),
    inference(paramodulation,[status(thm)],[f612,f25]) ).

fof(f681,plain,
    ! [X0] : sum(X0,multiplicative_identity,multiplicative_identity),
    inference(resolution,[status(thm)],[f671,f27]) ).

fof(f1280,plain,
    ! [X0,X1,X2] :
      ( ~ product(X0,X1,X2)
      | sum(X2,X1,X1) ),
    inference(forward_subsumption_resolution,[status(thm)],[f114,f681]) ).

fof(f1285,plain,
    ! [X0,X1] : sum(multiply(X0,X1),X0,X0),
    inference(resolution,[status(thm)],[f1280,f174]) ).

fof(f1363,plain,
    ! [X0] : additive_identity = multiply(additive_identity,X0),
    inference(resolution,[status(thm)],[f1285,f286]) ).

fof(f1401,plain,
    ! [X0] : product(X0,additive_identity,additive_identity),
    inference(paramodulation,[status(thm)],[f1363,f174]) ).

fof(f1410,plain,
    ! [X0,X1,X2] :
      ( ~ sum(X0,X1,X2)
      | product(X2,X0,X0) ),
    inference(backward_subsumption_resolution,[status(thm)],[f100,f1401]) ).

fof(f1829,plain,
    product(z,x,x),
    inference(resolution,[status(thm)],[f1410,f57]) ).

fof(f2035,plain,
    product(x,z,x),
    inference(resolution,[status(thm)],[f1829,f28]) ).

fof(f2036,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f2035,f58]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : BOO017-1 : TPTP v8.1.2. Released v1.0.0.
% 0.03/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.34  % Computer : n003.cluster.edu
% 0.11/0.34  % Model    : x86_64 x86_64
% 0.11/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34  % Memory   : 8042.1875MB
% 0.11/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34  % CPULimit : 300
% 0.11/0.34  % WCLimit  : 300
% 0.11/0.34  % DateTime : Mon Apr 29 22:40:48 EDT 2024
% 0.11/0.35  % CPUTime  : 
% 0.11/0.35  % Drodi V3.6.0
% 1.88/0.60  % Refutation found
% 1.88/0.60  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.88/0.60  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.88/0.62  % Elapsed time: 0.265205 seconds
% 1.88/0.62  % CPU time: 1.970349 seconds
% 1.88/0.62  % Total memory used: 37.177 MB
% 1.88/0.62  % Net memory used: 34.180 MB
%------------------------------------------------------------------------------