TSTP Solution File: BOO010-1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : BOO010-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n027.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 12:02:45 EDT 2023

% Result   : Unsatisfiable 0.18s 0.44s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   61 (  36 unt;   0 def)
%            Number of atoms       :  112 (  22 equ)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :  104 (  53   ~;  51   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :  152 (; 152   !;   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(f8,axiom,
    ! [X] : product(X,multiplicative_identity,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(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(f19,axiom,
    ! [X] : product(inverse(X),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,multiply(x,y),x),
    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(f31,plain,
    ! [X0] : product(X0,multiplicative_identity,X0),
    inference(cnf_transformation,[status(esa)],[f8]) ).

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(f44,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(f45,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)],[f44]) ).

fof(f50,plain,
    ! [X0] : product(inverse(X0),X0,additive_identity),
    inference(cnf_transformation,[status(esa)],[f19]) ).

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,multiply(x,y),x),
    inference(cnf_transformation,[status(esa)],[f23]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( ~ sum(additive_identity,X0,X1)
      | X1 = X0 ),
    inference(resolution,[status(thm)],[f28,f53]) ).

fof(f61,plain,
    ! [X0] : add(additive_identity,X0) = X0,
    inference(resolution,[status(thm)],[f24,f57]) ).

fof(f64,plain,
    ! [X0,X1] : sum(X0,X1,add(X1,X0)),
    inference(resolution,[status(thm)],[f24,f26]) ).

fof(f69,plain,
    ! [X0,X1,X2] :
      ( ~ sum(X0,X1,X2)
      | X2 = add(X1,X0) ),
    inference(resolution,[status(thm)],[f64,f53]) ).

fof(f126,plain,
    ! [X0,X1] : product(X0,X1,multiply(X1,X0)),
    inference(resolution,[status(thm)],[f27,f25]) ).

fof(f135,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product(X0,X1,X2)
      | ~ sum(X1,X3,X3)
      | sum(X2,multiply(X0,X3),multiply(X0,X3)) ),
    inference(resolution,[status(thm)],[f33,f25]) ).

fof(f158,plain,
    ! [X0,X1,X2] :
      ( ~ sum(X0,X1,X1)
      | sum(multiply(X0,X2),multiply(X2,X1),multiply(X2,X1)) ),
    inference(resolution,[status(thm)],[f135,f126]) ).

fof(f184,plain,
    ! [X0,X1] : sum(multiply(additive_identity,X0),multiply(X0,X1),multiply(X0,X1)),
    inference(resolution,[status(thm)],[f158,f28]) ).

fof(f188,plain,
    ! [X0,X1] : multiply(X0,X1) = add(multiply(X0,X1),multiply(additive_identity,X0)),
    inference(resolution,[status(thm)],[f184,f69]) ).

fof(f210,plain,
    ! [X0,X1] :
      ( ~ product(inverse(X0),X0,X1)
      | X1 = additive_identity ),
    inference(resolution,[status(thm)],[f55,f50]) ).

fof(f213,plain,
    ! [X0,X1] :
      ( ~ product(X0,multiplicative_identity,X1)
      | X1 = X0 ),
    inference(resolution,[status(thm)],[f55,f31]) ).

fof(f214,plain,
    ! [X0,X1,X2] :
      ( ~ product(X0,X1,X2)
      | X2 = multiply(X1,X0) ),
    inference(resolution,[status(thm)],[f55,f126]) ).

fof(f217,plain,
    ! [X0] : multiply(X0,inverse(X0)) = additive_identity,
    inference(resolution,[status(thm)],[f210,f126]) ).

fof(f225,plain,
    ! [X0] : X0 = multiply(X0,multiplicative_identity),
    inference(resolution,[status(thm)],[f214,f30]) ).

fof(f228,plain,
    ! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
    inference(resolution,[status(thm)],[f214,f25]) ).

fof(f367,plain,
    ! [X0] : multiply(X0,inverse(X0)) = add(additive_identity,multiply(additive_identity,X0)),
    inference(paramodulation,[status(thm)],[f217,f188]) ).

fof(f368,plain,
    ! [X0] : additive_identity = add(additive_identity,multiply(additive_identity,X0)),
    inference(forward_demodulation,[status(thm)],[f217,f367]) ).

fof(f369,plain,
    ! [X0] : additive_identity = multiply(additive_identity,X0),
    inference(forward_demodulation,[status(thm)],[f61,f368]) ).

fof(f393,plain,
    ! [X0] : product(X0,additive_identity,additive_identity),
    inference(paramodulation,[status(thm)],[f369,f126]) ).

fof(f509,plain,
    ! [X0,X1,X2] :
      ( ~ sum(X0,X1,X2)
      | ~ product(X0,additive_identity,additive_identity)
      | product(X2,X1,X1) ),
    inference(resolution,[status(thm)],[f45,f28]) ).

fof(f510,plain,
    ! [X0,X1,X2] :
      ( ~ sum(X0,X1,X2)
      | product(X2,X1,X1) ),
    inference(forward_subsumption_resolution,[status(thm)],[f509,f393]) ).

fof(f566,plain,
    ! [X0,X1] : product(add(X0,X1),X0,X0),
    inference(resolution,[status(thm)],[f510,f64]) ).

fof(f611,plain,
    ! [X0] : multiplicative_identity = add(multiplicative_identity,X0),
    inference(resolution,[status(thm)],[f566,f213]) ).

fof(f703,plain,
    ! [X0] : sum(X0,multiplicative_identity,multiplicative_identity),
    inference(paramodulation,[status(thm)],[f611,f64]) ).

fof(f915,plain,
    ! [X0,X1] : sum(multiply(X0,X1),multiply(X1,multiplicative_identity),multiply(X1,multiplicative_identity)),
    inference(resolution,[status(thm)],[f703,f158]) ).

fof(f916,plain,
    ! [X0,X1] : sum(multiply(X0,X1),X1,multiply(X1,multiplicative_identity)),
    inference(forward_demodulation,[status(thm)],[f225,f915]) ).

fof(f917,plain,
    ! [X0,X1] : sum(multiply(X0,X1),X1,X1),
    inference(forward_demodulation,[status(thm)],[f225,f916]) ).

fof(f1072,plain,
    ! [X0,X1] : X0 = add(X0,multiply(X1,X0)),
    inference(resolution,[status(thm)],[f917,f69]) ).

fof(f1098,plain,
    ! [X0,X1] : X0 = add(X0,multiply(X0,X1)),
    inference(paramodulation,[status(thm)],[f228,f1072]) ).

fof(f1138,plain,
    ! [X0,X1] : sum(X0,multiply(X0,X1),X0),
    inference(paramodulation,[status(thm)],[f1098,f24]) ).

fof(f1684,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[f56,f1138]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : BOO010-1 : TPTP v8.1.2. Released v1.0.0.
% 0.10/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.32  % Computer : n027.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Tue May 30 11:01:33 EDT 2023
% 0.11/0.32  % CPUTime  : 
% 0.11/0.33  % Drodi V3.5.1
% 0.18/0.44  % Refutation found
% 0.18/0.44  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.18/0.44  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.45  % Elapsed time: 0.122677 seconds
% 0.18/0.45  % CPU time: 0.875171 seconds
% 0.18/0.45  % Memory used: 21.474 MB
%------------------------------------------------------------------------------