TSTP Solution File: BOO005-1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : BOO005-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n012.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 12:02:42 EDT 2023

% Result   : Unsatisfiable 5.57s 1.13s
% Output   : CNFRefutation 5.57s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   52 (  24 unt;   0 def)
%            Number of atoms       :  118 (  10 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  134 (  68   ~;  66   |;   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    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :  157 (; 157   !;   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(f5,axiom,
    ! [X] : sum(additive_identity,X,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(f9,axiom,
    ! [X,Y,V1,Z,V2,V3,V4] :
      ( ~ product(X,Y,V1)
      | ~ product(X,Z,V2)
      | ~ sum(Y,Z,V3)
      | ~ product(X,V3,V4)
      | sum(V1,V2,V4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f10,axiom,
    ! [X,Y,V1,Z,V2,V3,V4] :
      ( ~ product(X,Y,V1)
      | ~ product(X,Z,V2)
      | ~ sum(Y,Z,V3)
      | ~ sum(V1,V2,V4)
      | product(X,V3,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(f20,axiom,
    ! [X] : product(X,inverse(X),additive_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,negated_conjecture,
    ~ sum(x,multiplicative_identity,multiplicative_identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f24,plain,
    ! [X0,X1] : sum(X0,X1,add(X0,X1)),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f25,plain,
    ! [X0,X1] : product(X0,X1,multiply(X0,X1)),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f26,plain,
    ! [X0,X1,X2] :
      ( ~ sum(X0,X1,X2)
      | sum(X1,X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f27,plain,
    ! [X0,X1,X2] :
      ( ~ product(X0,X1,X2)
      | product(X1,X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f28,plain,
    ! [X0] : sum(additive_identity,X0,X0),
    inference(cnf_transformation,[status(esa)],[f5]) ).

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

fof(f32,plain,
    ! [V1,V2,V4] :
      ( ! [X,V3] :
          ( ! [Y,Z] :
              ( ~ product(X,Y,V1)
              | ~ product(X,Z,V2)
              | ~ sum(Y,Z,V3) )
          | ~ product(X,V3,V4) )
      | sum(V1,V2,V4) ),
    inference(miniscoping,[status(esa)],[f9]) ).

fof(f33,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ~ product(X0,X1,X2)
      | ~ product(X0,X3,X4)
      | ~ sum(X1,X3,X5)
      | ~ product(X0,X5,X6)
      | sum(X2,X4,X6) ),
    inference(cnf_transformation,[status(esa)],[f32]) ).

fof(f34,plain,
    ! [X,V3,V4] :
      ( ! [V1,V2] :
          ( ! [Y,Z] :
              ( ~ product(X,Y,V1)
              | ~ product(X,Z,V2)
              | ~ sum(Y,Z,V3) )
          | ~ sum(V1,V2,V4) )
      | product(X,V3,V4) ),
    inference(miniscoping,[status(esa)],[f10]) ).

fof(f35,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ~ product(X0,X1,X2)
      | ~ product(X0,X3,X4)
      | ~ sum(X1,X3,X5)
      | ~ sum(X2,X4,X6)
      | product(X0,X5,X6) ),
    inference(cnf_transformation,[status(esa)],[f34]) ).

fof(f40,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(f41,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)],[f40]) ).

fof(f51,plain,
    ! [X0] : product(X0,inverse(X0),additive_identity),
    inference(cnf_transformation,[status(esa)],[f20]) ).

fof(f52,plain,
    ! [U,V] :
      ( ! [X,Y] :
          ( ~ sum(X,Y,U)
          | ~ sum(X,Y,V) )
      | U = V ),
    inference(miniscoping,[status(esa)],[f21]) ).

fof(f53,plain,
    ! [X0,X1,X2,X3] :
      ( ~ sum(X0,X1,X2)
      | ~ sum(X0,X1,X3)
      | X2 = X3 ),
    inference(cnf_transformation,[status(esa)],[f52]) ).

fof(f54,plain,
    ! [U,V] :
      ( ! [X,Y] :
          ( ~ product(X,Y,U)
          | ~ product(X,Y,V) )
      | U = V ),
    inference(miniscoping,[status(esa)],[f22]) ).

fof(f55,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product(X0,X1,X2)
      | ~ product(X0,X1,X3)
      | X2 = X3 ),
    inference(cnf_transformation,[status(esa)],[f54]) ).

fof(f56,plain,
    ~ sum(x,multiplicative_identity,multiplicative_identity),
    inference(cnf_transformation,[status(esa)],[f23]) ).

fof(f58,plain,
    ! [X0,X1] : sum(X0,X1,add(X1,X0)),
    inference(resolution,[status(thm)],[f24,f26]) ).

fof(f70,plain,
    ! [X0] : sum(X0,additive_identity,X0),
    inference(resolution,[status(thm)],[f28,f26]) ).

fof(f85,plain,
    ! [X0,X1] :
      ( ~ sum(X0,additive_identity,X1)
      | X1 = X0 ),
    inference(resolution,[status(thm)],[f70,f53]) ).

fof(f117,plain,
    ! [X0,X1] : product(X0,X1,multiply(X1,X0)),
    inference(resolution,[status(thm)],[f27,f25]) ).

fof(f128,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ product(multiplicative_identity,X0,X1)
      | ~ sum(X0,X2,X3)
      | ~ sum(X1,X2,X4)
      | product(multiplicative_identity,X3,X4) ),
    inference(resolution,[status(thm)],[f35,f30]) ).

fof(f196,plain,
    ! [X0,X1,X2] :
      ( ~ product(X0,X1,X2)
      | ~ sum(X1,inverse(X0),inverse(X0))
      | sum(X2,additive_identity,additive_identity) ),
    inference(resolution,[status(thm)],[f51,f33]) ).

fof(f305,plain,
    ! [X0,X1,X2] :
      ( ~ sum(X0,X1,X2)
      | ~ product(X1,additive_identity,additive_identity)
      | product(X2,X0,X0) ),
    inference(resolution,[status(thm)],[f41,f70]) ).

fof(f447,plain,
    ! [X0,X1,X2,X3] :
      ( ~ sum(X0,X1,X2)
      | ~ sum(X0,X1,X3)
      | product(multiplicative_identity,X2,X3) ),
    inference(resolution,[status(thm)],[f128,f30]) ).

fof(f854,plain,
    ! [X0,X1,X2] :
      ( ~ sum(X0,X1,X2)
      | product(multiplicative_identity,X2,add(X1,X0)) ),
    inference(resolution,[status(thm)],[f447,f58]) ).

fof(f920,plain,
    ! [X0,X1] : product(multiplicative_identity,add(X0,X1),add(X1,X0)),
    inference(resolution,[status(thm)],[f854,f24]) ).

fof(f970,plain,
    ! [X0,X1] : product(add(X0,X1),multiplicative_identity,add(X1,X0)),
    inference(resolution,[status(thm)],[f920,f27]) ).

fof(f1055,plain,
    ! [X0,X1,X2] :
      ( ~ product(add(X0,X1),multiplicative_identity,X2)
      | X2 = add(X1,X0) ),
    inference(resolution,[status(thm)],[f970,f55]) ).

fof(f2457,plain,
    ! [X0,X1] :
      ( ~ product(X0,additive_identity,X1)
      | sum(X1,additive_identity,additive_identity) ),
    inference(resolution,[status(thm)],[f196,f28]) ).

fof(f2602,plain,
    ! [X0] : sum(multiply(additive_identity,X0),additive_identity,additive_identity),
    inference(resolution,[status(thm)],[f2457,f117]) ).

fof(f2608,plain,
    ! [X0] : additive_identity = multiply(additive_identity,X0),
    inference(resolution,[status(thm)],[f2602,f85]) ).

fof(f2657,plain,
    ! [X0] : product(X0,additive_identity,additive_identity),
    inference(paramodulation,[status(thm)],[f2608,f117]) ).

fof(f3139,plain,
    ! [X0,X1,X2] :
      ( ~ sum(X0,X1,X2)
      | product(X2,X0,X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[f305,f2657]) ).

fof(f3152,plain,
    ! [X0,X1] : product(add(X0,X1),X1,X1),
    inference(resolution,[status(thm)],[f3139,f58]) ).

fof(f3258,plain,
    ! [X0] : multiplicative_identity = add(multiplicative_identity,X0),
    inference(resolution,[status(thm)],[f3152,f1055]) ).

fof(f3380,plain,
    ! [X0] : sum(X0,multiplicative_identity,multiplicative_identity),
    inference(paramodulation,[status(thm)],[f3258,f58]) ).

fof(f3547,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[f56,f3380]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : BOO005-1 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n012.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Tue May 30 10:38:40 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  % Drodi V3.5.1
% 5.57/1.13  % Refutation found
% 5.57/1.13  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 5.57/1.13  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 5.57/1.16  % Elapsed time: 0.811261 seconds
% 5.57/1.16  % CPU time: 6.274843 seconds
% 5.57/1.16  % Memory used: 48.430 MB
%------------------------------------------------------------------------------