TSTP Solution File: RNG001-3 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : RNG001-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n023.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 12:32:32 EDT 2023

% Result   : Unsatisfiable 17.59s 2.58s
% Output   : CNFRefutation 17.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   46 (  12 unt;   0 def)
%            Number of atoms       :  138 (   0 equ)
%            Maximal formula atoms :    5 (   3 avg)
%            Number of connectives :  186 (  94   ~;  92   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   8 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :  189 (; 189   !;   0   ?)

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

fof(f2,axiom,
    ! [X] : sum(additive_inverse(X),X,additive_identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

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

fof(f5,axiom,
    ! [X,Y] : product(X,Y,multiply(X,Y)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f6,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(f7,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(f8,negated_conjecture,
    ~ product(a,additive_identity,additive_identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f9,plain,
    ! [X0] : sum(additive_identity,X0,X0),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f10,plain,
    ! [X0] : sum(additive_inverse(X0),X0,additive_identity),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f11,plain,
    ! [X,V,W] :
      ( ! [U,Z] :
          ( ! [Y] :
              ( ~ sum(X,Y,U)
              | ~ sum(Y,Z,V) )
          | ~ sum(U,Z,W) )
      | sum(X,V,W) ),
    inference(miniscoping,[status(esa)],[f3]) ).

fof(f12,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ~ sum(X0,X1,X2)
      | ~ sum(X1,X3,X4)
      | ~ sum(X2,X3,X5)
      | sum(X0,X4,X5) ),
    inference(cnf_transformation,[status(esa)],[f11]) ).

fof(f13,plain,
    ! [U,Z,W] :
      ( ! [X,V] :
          ( ! [Y] :
              ( ~ sum(X,Y,U)
              | ~ sum(Y,Z,V) )
          | ~ sum(X,V,W) )
      | sum(U,Z,W) ),
    inference(miniscoping,[status(esa)],[f4]) ).

fof(f14,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ~ sum(X0,X1,X2)
      | ~ sum(X1,X3,X4)
      | ~ sum(X0,X4,X5)
      | sum(X2,X3,X5) ),
    inference(cnf_transformation,[status(esa)],[f13]) ).

fof(f15,plain,
    ! [X0,X1] : product(X0,X1,multiply(X0,X1)),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f16,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)],[f6]) ).

fof(f17,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)],[f16]) ).

fof(f18,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)],[f7]) ).

fof(f19,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)],[f18]) ).

fof(f20,plain,
    ~ product(a,additive_identity,additive_identity),
    inference(cnf_transformation,[status(esa)],[f8]) ).

fof(f21,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ~ product(X0,X1,X2)
      | ~ sum(X1,X3,X4)
      | ~ sum(X2,multiply(X0,X3),X5)
      | product(X0,X4,X5) ),
    inference(resolution,[status(thm)],[f15,f19]) ).

fof(f25,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ~ product(X0,X1,X2)
      | ~ sum(X1,X3,X4)
      | ~ product(X0,X4,X5)
      | sum(X2,multiply(X0,X3),X5) ),
    inference(resolution,[status(thm)],[f15,f17]) ).

fof(f26,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ sum(X0,X1,X2)
      | ~ sum(multiply(X3,X0),multiply(X3,X1),X4)
      | product(X3,X2,X4) ),
    inference(resolution,[status(thm)],[f21,f15]) ).

fof(f30,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ~ product(X0,X1,multiply(X0,X2))
      | ~ sum(X1,X3,X4)
      | ~ product(X0,X4,X5)
      | ~ sum(X2,X3,X6)
      | product(X0,X6,X5) ),
    inference(resolution,[status(thm)],[f25,f26]) ).

fof(f40,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ~ sum(X0,X1,X2)
      | ~ product(X3,X2,X4)
      | ~ sum(X0,X1,X5)
      | product(X3,X5,X4) ),
    inference(resolution,[status(thm)],[f30,f15]) ).

fof(f47,plain,
    ! [X0,X1,X2,X3,X4,X5,X6,X7] :
      ( ~ sum(X0,X1,multiply(X2,X3))
      | ~ sum(X1,multiply(X2,X4),X5)
      | ~ sum(X0,X5,X6)
      | ~ sum(X3,X4,X7)
      | product(X2,X7,X6) ),
    inference(resolution,[status(thm)],[f14,f26]) ).

fof(f50,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ sum(X0,X1,X2)
      | ~ sum(X0,X1,X3)
      | product(X4,X3,multiply(X4,X2)) ),
    inference(resolution,[status(thm)],[f40,f15]) ).

fof(f52,plain,
    ! [X0,X1,X2] :
      ( ~ sum(additive_identity,X0,X1)
      | product(X2,X0,multiply(X2,X1)) ),
    inference(resolution,[status(thm)],[f50,f9]) ).

fof(f62,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( product(X0,X1,multiply(X0,X2))
      | ~ sum(X3,X4,additive_identity)
      | ~ sum(X4,X1,X5)
      | ~ sum(X3,X5,X2) ),
    inference(resolution,[status(thm)],[f52,f14]) ).

fof(f70,plain,
    ! [X0,X1,X2,X3,X4] :
      ( product(X0,X1,multiply(X0,X2))
      | ~ sum(X3,X1,X4)
      | ~ sum(additive_inverse(X3),X4,X2) ),
    inference(resolution,[status(thm)],[f62,f10]) ).

fof(f75,plain,
    ! [X0,X1,X2] :
      ( product(X0,X1,multiply(X0,additive_identity))
      | ~ sum(X2,X1,X2) ),
    inference(resolution,[status(thm)],[f70,f10]) ).

fof(f86,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( product(X0,X1,multiply(X0,additive_identity))
      | ~ sum(X2,X3,X4)
      | ~ sum(X3,X5,X1)
      | ~ sum(X4,X5,X2) ),
    inference(resolution,[status(thm)],[f75,f12]) ).

fof(f146,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ~ sum(multiply(X0,X1),multiply(X0,X2),X3)
      | ~ sum(additive_identity,X3,X4)
      | ~ sum(X1,X2,X5)
      | product(X0,X5,X4) ),
    inference(resolution,[status(thm)],[f47,f9]) ).

fof(f296,plain,
    ! [X0,X1] :
      ( product(X0,X1,multiply(X0,additive_identity))
      | ~ sum(X1,additive_identity,additive_identity) ),
    inference(resolution,[status(thm)],[f86,f9]) ).

fof(f316,plain,
    ! [X0] : product(X0,additive_inverse(additive_identity),multiply(X0,additive_identity)),
    inference(resolution,[status(thm)],[f296,f10]) ).

fof(f330,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ product(X0,X1,X2)
      | ~ product(X0,X3,X4)
      | ~ sum(X1,X3,additive_inverse(additive_identity))
      | sum(X2,X4,multiply(X0,additive_identity)) ),
    inference(resolution,[status(thm)],[f316,f17]) ).

fof(f3041,plain,
    ! [X0,X1,X2] :
      ( ~ product(X0,additive_identity,X1)
      | ~ product(X0,additive_inverse(additive_identity),X2)
      | sum(X1,X2,multiply(X0,additive_identity)) ),
    inference(resolution,[status(thm)],[f330,f9]) ).

fof(f3057,plain,
    ! [X0,X1] :
      ( ~ product(X0,additive_identity,X1)
      | sum(X1,multiply(X0,additive_identity),multiply(X0,additive_identity)) ),
    inference(resolution,[status(thm)],[f3041,f316]) ).

fof(f3084,plain,
    ! [X0] : sum(multiply(X0,additive_identity),multiply(X0,additive_identity),multiply(X0,additive_identity)),
    inference(resolution,[status(thm)],[f3057,f15]) ).

fof(f3093,plain,
    ! [X0,X1,X2] :
      ( ~ sum(additive_identity,multiply(X0,additive_identity),X1)
      | ~ sum(additive_identity,additive_identity,X2)
      | product(X0,X2,X1) ),
    inference(resolution,[status(thm)],[f3084,f146]) ).

fof(f3317,plain,
    ! [X0,X1] :
      ( ~ sum(additive_identity,multiply(X0,additive_identity),X1)
      | product(X0,additive_identity,X1) ),
    inference(resolution,[status(thm)],[f3093,f9]) ).

fof(f3325,plain,
    ! [X0,X1,X2,X3,X4] :
      ( product(X0,additive_identity,X1)
      | ~ sum(X2,X3,additive_identity)
      | ~ sum(X3,multiply(X0,additive_identity),X4)
      | ~ sum(X2,X4,X1) ),
    inference(resolution,[status(thm)],[f3317,f14]) ).

fof(f4439,plain,
    ! [X0,X1,X2,X3] :
      ( product(X0,additive_identity,X1)
      | ~ sum(X2,multiply(X0,additive_identity),X3)
      | ~ sum(additive_inverse(X2),X3,X1) ),
    inference(resolution,[status(thm)],[f3325,f10]) ).

fof(f4446,plain,
    ! [X0,X1] :
      ( product(X0,additive_identity,additive_identity)
      | ~ sum(X1,multiply(X0,additive_identity),X1) ),
    inference(resolution,[status(thm)],[f4439,f10]) ).

fof(f4465,plain,
    ! [X0] : product(X0,additive_identity,additive_identity),
    inference(resolution,[status(thm)],[f4446,f3084]) ).

fof(f4472,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[f20,f4465]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : RNG001-3 : TPTP v8.1.2. Released v1.0.0.
% 0.03/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34  % Computer : n023.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Tue May 30 10:54:08 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.12/0.35  % Drodi V3.5.1
% 17.59/2.58  % Refutation found
% 17.59/2.58  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 17.59/2.58  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 17.59/2.61  % Elapsed time: 2.252738 seconds
% 17.59/2.61  % CPU time: 17.810871 seconds
% 17.59/2.61  % Memory used: 125.411 MB
%------------------------------------------------------------------------------