TSTP Solution File: RNG039-1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : RNG039-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n009.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 12:32:41 EDT 2023

% Result   : Unsatisfiable 0.14s 0.37s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   30
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   96 (  74 unt;   0 def)
%            Number of atoms       :  131 (  42 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   74 (  39   ~;  35   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :  116 (; 116   !;   0   ?)

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

fof(f3,axiom,
    ! [X,Y] : product(X,Y,multiply(X,Y)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [X,Y] : sum(X,Y,add(X,Y)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [X,Y,Z] :
      ( ~ sum(X,Y,Z)
      | sum(Y,X,Z) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f10,axiom,
    ! [X,Y,U,Z,V,W] :
      ( ~ product(X,Y,U)
      | ~ product(Y,Z,V)
      | ~ product(U,Z,W)
      | product(X,V,W) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f16,axiom,
    ! [X,Y,U,V] :
      ( ~ sum(X,Y,U)
      | ~ sum(X,Y,V)
      | U = V ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f17,axiom,
    ! [X,Y,U,V] :
      ( ~ product(X,Y,U)
      | ~ product(X,Y,V)
      | U = V ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f18,axiom,
    ! [A,B] : sum(A,add(A,B),B),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f22,axiom,
    ! [A] : add(A,A) = additive_identity,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f23,axiom,
    ! [A] : multiply(A,A) = A,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f25,axiom,
    multiply(b,a) = d,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f26,axiom,
    ! [A,B] : sum(A,B,add(B,A)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f27,axiom,
    product(a,c,c),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f28,axiom,
    product(b,d,d),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f30,axiom,
    product(d,a,d),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f31,axiom,
    ! [A,B] : product(A,multiply(A,B),multiply(A,B)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f32,axiom,
    ! [A,B] : product(a,multiply(b,A),multiply(B,A)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f41,axiom,
    ! [A] : product(multiply(A,a),b,multiply(A,c)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f47,axiom,
    product(multiply(d,b),a,d),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f53,axiom,
    product(add(a,b),b,add(c,b)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f56,axiom,
    product(add(a,b),a,add(a,d)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f59,negated_conjecture,
    product(b,a,d),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f60,negated_conjecture,
    c != d,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f61,plain,
    ! [X0] : sum(additive_identity,X0,X0),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f63,plain,
    ! [X0,X1] : product(X0,X1,multiply(X0,X1)),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f64,plain,
    ! [X0,X1] : sum(X0,X1,add(X0,X1)),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f71,plain,
    ! [X0,X1,X2] :
      ( ~ sum(X0,X1,X2)
      | sum(X1,X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f72,plain,
    ! [X,V,W] :
      ( ! [U,Z] :
          ( ! [Y] :
              ( ~ product(X,Y,U)
              | ~ product(Y,Z,V) )
          | ~ product(U,Z,W) )
      | product(X,V,W) ),
    inference(miniscoping,[status(esa)],[f10]) ).

fof(f73,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ~ product(X0,X1,X2)
      | ~ product(X1,X3,X4)
      | ~ product(X2,X3,X5)
      | product(X0,X4,X5) ),
    inference(cnf_transformation,[status(esa)],[f72]) ).

fof(f84,plain,
    ! [U,V] :
      ( ! [X,Y] :
          ( ~ sum(X,Y,U)
          | ~ sum(X,Y,V) )
      | U = V ),
    inference(miniscoping,[status(esa)],[f16]) ).

fof(f85,plain,
    ! [X0,X1,X2,X3] :
      ( ~ sum(X0,X1,X2)
      | ~ sum(X0,X1,X3)
      | X2 = X3 ),
    inference(cnf_transformation,[status(esa)],[f84]) ).

fof(f86,plain,
    ! [U,V] :
      ( ! [X,Y] :
          ( ~ product(X,Y,U)
          | ~ product(X,Y,V) )
      | U = V ),
    inference(miniscoping,[status(esa)],[f17]) ).

fof(f87,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product(X0,X1,X2)
      | ~ product(X0,X1,X3)
      | X2 = X3 ),
    inference(cnf_transformation,[status(esa)],[f86]) ).

fof(f88,plain,
    ! [X0,X1] : sum(X0,add(X0,X1),X1),
    inference(cnf_transformation,[status(esa)],[f18]) ).

fof(f92,plain,
    ! [X0] : add(X0,X0) = additive_identity,
    inference(cnf_transformation,[status(esa)],[f22]) ).

fof(f93,plain,
    ! [X0] : multiply(X0,X0) = X0,
    inference(cnf_transformation,[status(esa)],[f23]) ).

fof(f95,plain,
    multiply(b,a) = d,
    inference(cnf_transformation,[status(esa)],[f25]) ).

fof(f96,plain,
    ! [X0,X1] : sum(X0,X1,add(X1,X0)),
    inference(cnf_transformation,[status(esa)],[f26]) ).

fof(f97,plain,
    product(a,c,c),
    inference(cnf_transformation,[status(esa)],[f27]) ).

fof(f98,plain,
    product(b,d,d),
    inference(cnf_transformation,[status(esa)],[f28]) ).

fof(f100,plain,
    product(d,a,d),
    inference(cnf_transformation,[status(esa)],[f30]) ).

fof(f101,plain,
    ! [X0,X1] : product(X0,multiply(X0,X1),multiply(X0,X1)),
    inference(cnf_transformation,[status(esa)],[f31]) ).

fof(f102,plain,
    ! [X0,X1] : product(a,multiply(b,X0),multiply(X1,X0)),
    inference(cnf_transformation,[status(esa)],[f32]) ).

fof(f111,plain,
    ! [X0] : product(multiply(X0,a),b,multiply(X0,c)),
    inference(cnf_transformation,[status(esa)],[f41]) ).

fof(f117,plain,
    product(multiply(d,b),a,d),
    inference(cnf_transformation,[status(esa)],[f47]) ).

fof(f123,plain,
    product(add(a,b),b,add(c,b)),
    inference(cnf_transformation,[status(esa)],[f53]) ).

fof(f126,plain,
    product(add(a,b),a,add(a,d)),
    inference(cnf_transformation,[status(esa)],[f56]) ).

fof(f129,plain,
    product(b,a,d),
    inference(cnf_transformation,[status(esa)],[f59]) ).

fof(f130,plain,
    c != d,
    inference(cnf_transformation,[status(esa)],[f60]) ).

fof(f131,plain,
    ! [X0,X1,X2] :
      ( ~ product(a,X0,X1)
      | ~ product(d,X0,X2)
      | product(b,X1,X2) ),
    inference(resolution,[status(thm)],[f73,f129]) ).

fof(f138,plain,
    ! [X0] :
      ( ~ product(d,a,X0)
      | d = X0 ),
    inference(resolution,[status(thm)],[f87,f100]) ).

fof(f140,plain,
    ! [X0] :
      ( ~ product(b,d,X0)
      | d = X0 ),
    inference(resolution,[status(thm)],[f87,f98]) ).

fof(f155,plain,
    d = multiply(b,d),
    inference(resolution,[status(thm)],[f63,f140]) ).

fof(f157,plain,
    d = multiply(d,a),
    inference(resolution,[status(thm)],[f63,f138]) ).

fof(f160,plain,
    ! [X0,X1,X2] :
      ( ~ product(X0,X1,X2)
      | multiply(X0,X1) = X2 ),
    inference(resolution,[status(thm)],[f63,f87]) ).

fof(f197,plain,
    ! [X0,X1] : sum(add(X0,X1),X0,X1),
    inference(resolution,[status(thm)],[f71,f88]) ).

fof(f205,plain,
    ! [X0] :
      ( ~ product(d,c,X0)
      | product(b,c,X0) ),
    inference(resolution,[status(thm)],[f131,f97]) ).

fof(f209,plain,
    product(b,c,multiply(d,c)),
    inference(resolution,[status(thm)],[f205,f63]) ).

fof(f223,plain,
    multiply(b,c) = multiply(d,c),
    inference(resolution,[status(thm)],[f160,f209]) ).

fof(f392,plain,
    ! [X0,X1,X2] :
      ( ~ sum(add(X0,X1),X0,X2)
      | X1 = X2 ),
    inference(resolution,[status(thm)],[f85,f197]) ).

fof(f395,plain,
    ! [X0,X1] :
      ( ~ sum(additive_identity,X0,X1)
      | X0 = X1 ),
    inference(resolution,[status(thm)],[f85,f61]) ).

fof(f404,plain,
    ! [X0] : add(additive_identity,X0) = X0,
    inference(resolution,[status(thm)],[f395,f88]) ).

fof(f424,plain,
    ! [X0,X1] : X0 = add(X1,add(X1,X0)),
    inference(resolution,[status(thm)],[f392,f96]) ).

fof(f425,plain,
    ! [X0,X1] : X0 = add(add(X1,X0),X1),
    inference(resolution,[status(thm)],[f392,f64]) ).

fof(f495,plain,
    product(multiply(d,a),b,multiply(b,c)),
    inference(paramodulation,[status(thm)],[f223,f111]) ).

fof(f496,plain,
    product(d,b,multiply(b,c)),
    inference(forward_demodulation,[status(thm)],[f157,f495]) ).

fof(f513,plain,
    multiply(d,b) = multiply(b,c),
    inference(resolution,[status(thm)],[f496,f160]) ).

fof(f559,plain,
    product(multiply(b,c),a,d),
    inference(forward_demodulation,[status(thm)],[f513,f117]) ).

fof(f563,plain,
    multiply(multiply(b,c),a) = d,
    inference(resolution,[status(thm)],[f559,f160]) ).

fof(f650,plain,
    ! [X0,X1] : add(X0,X1) = add(X1,X0),
    inference(paramodulation,[status(thm)],[f424,f425]) ).

fof(f796,plain,
    ! [X0] : product(a,d,multiply(X0,d)),
    inference(paramodulation,[status(thm)],[f155,f102]) ).

fof(f797,plain,
    ! [X0] : product(a,d,multiply(X0,a)),
    inference(paramodulation,[status(thm)],[f95,f102]) ).

fof(f835,plain,
    product(a,multiply(b,a),d),
    inference(paramodulation,[status(thm)],[f563,f102]) ).

fof(f836,plain,
    product(a,d,d),
    inference(forward_demodulation,[status(thm)],[f95,f835]) ).

fof(f858,plain,
    ! [X0] :
      ( ~ product(a,d,X0)
      | d = X0 ),
    inference(resolution,[status(thm)],[f836,f87]) ).

fof(f945,plain,
    product(add(a,b),b,add(b,c)),
    inference(forward_demodulation,[status(thm)],[f650,f123]) ).

fof(f1072,plain,
    ! [X0] : d = multiply(X0,d),
    inference(resolution,[status(thm)],[f796,f858]) ).

fof(f1107,plain,
    ! [X0] : product(X0,multiply(X0,d),d),
    inference(paramodulation,[status(thm)],[f1072,f101]) ).

fof(f1108,plain,
    ! [X0] : product(X0,d,d),
    inference(forward_demodulation,[status(thm)],[f1072,f1107]) ).

fof(f1123,plain,
    ! [X0,X1] :
      ( ~ product(X0,d,X1)
      | d = X1 ),
    inference(resolution,[status(thm)],[f1108,f87]) ).

fof(f1129,plain,
    ! [X0] : d = multiply(X0,a),
    inference(resolution,[status(thm)],[f797,f1123]) ).

fof(f1147,plain,
    d = a,
    inference(paramodulation,[status(thm)],[f93,f1129]) ).

fof(f1187,plain,
    ! [X0,X1] :
      ( ~ product(X0,d,X1)
      | a = X1 ),
    inference(backward_demodulation,[status(thm)],[f1147,f1123]) ).

fof(f1188,plain,
    ! [X0,X1] :
      ( ~ product(X0,a,X1)
      | a = X1 ),
    inference(forward_demodulation,[status(thm)],[f1147,f1187]) ).

fof(f1217,plain,
    c != a,
    inference(backward_demodulation,[status(thm)],[f1147,f130]) ).

fof(f1250,plain,
    product(add(a,b),a,add(a,a)),
    inference(forward_demodulation,[status(thm)],[f1147,f126]) ).

fof(f1251,plain,
    product(add(a,b),a,additive_identity),
    inference(forward_demodulation,[status(thm)],[f92,f1250]) ).

fof(f1252,plain,
    a = additive_identity,
    inference(resolution,[status(thm)],[f1251,f1188]) ).

fof(f1287,plain,
    c != additive_identity,
    inference(backward_demodulation,[status(thm)],[f1252,f1217]) ).

fof(f1289,plain,
    product(add(additive_identity,b),b,add(b,c)),
    inference(backward_demodulation,[status(thm)],[f1252,f945]) ).

fof(f1290,plain,
    product(b,b,add(b,c)),
    inference(forward_demodulation,[status(thm)],[f404,f1289]) ).

fof(f1472,plain,
    multiply(b,b) = add(b,c),
    inference(resolution,[status(thm)],[f1290,f160]) ).

fof(f1473,plain,
    b = add(b,c),
    inference(forward_demodulation,[status(thm)],[f93,f1472]) ).

fof(f1509,plain,
    c = add(b,b),
    inference(paramodulation,[status(thm)],[f1473,f425]) ).

fof(f1510,plain,
    c = additive_identity,
    inference(forward_demodulation,[status(thm)],[f92,f1509]) ).

fof(f1511,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f1510,f1287]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09  % Problem  : RNG039-1 : TPTP v8.1.2. Released v1.0.0.
% 0.04/0.10  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30  % Computer : n009.cluster.edu
% 0.09/0.30  % Model    : x86_64 x86_64
% 0.09/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30  % Memory   : 8042.1875MB
% 0.09/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30  % CPULimit : 300
% 0.09/0.30  % WCLimit  : 300
% 0.09/0.30  % DateTime : Tue May 30 10:32:01 EDT 2023
% 0.09/0.30  % CPUTime  : 
% 0.09/0.31  % Drodi V3.5.1
% 0.14/0.37  % Refutation found
% 0.14/0.37  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.37  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.38  % Elapsed time: 0.076437 seconds
% 0.14/0.38  % CPU time: 0.206388 seconds
% 0.14/0.38  % Memory used: 21.777 MB
%------------------------------------------------------------------------------