TSTP Solution File: RNG005-1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : RNG005-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n025.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 12:32:33 EDT 2023

% Result   : Unsatisfiable 3.65s 0.84s
% Output   : CNFRefutation 3.86s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   72 (  44 unt;   0 def)
%            Number of atoms       :  125 (  20 equ)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :  108 (  55   ~;  53   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Maximal term depth    :    4 (   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   :  148 (; 148   !;   0   ?)

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

fof(f2,axiom,
    ! [X] : sum(X,additive_identity,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(f5,axiom,
    ! [X] : sum(additive_inverse(X),X,additive_identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

fof(f7,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(f9,axiom,
    ! [X,Y,Z] :
      ( ~ sum(X,Y,Z)
      | sum(Y,X,Z) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f14,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(f16,axiom,
    ! [X,Y,U,V] :
      ( ~ sum(X,Y,U)
      | ~ sum(X,Y,V)
      | U = V ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f18,hypothesis,
    product(a,b,d),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f19,hypothesis,
    product(additive_inverse(a),b,c),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f20,negated_conjecture,
    ~ sum(c,d,additive_identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f21,plain,
    ! [X0] : sum(additive_identity,X0,X0),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f22,plain,
    ! [X0] : sum(X0,additive_identity,X0),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f23,plain,
    ! [X0,X1] : product(X0,X1,multiply(X0,X1)),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f24,plain,
    ! [X0,X1] : sum(X0,X1,add(X0,X1)),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f25,plain,
    ! [X0] : sum(additive_inverse(X0),X0,additive_identity),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f26,plain,
    ! [X0] : sum(X0,additive_inverse(X0),additive_identity),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f27,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)],[f7]) ).

fof(f28,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)],[f27]) ).

fof(f31,plain,
    ! [X0,X1,X2] :
      ( ~ sum(X0,X1,X2)
      | sum(X1,X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f40,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)],[f14]) ).

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

fof(f44,plain,
    ! [U,V] :
      ( ! [X,Y] :
          ( ~ sum(X,Y,U)
          | ~ sum(X,Y,V) )
      | U = V ),
    inference(miniscoping,[status(esa)],[f16]) ).

fof(f45,plain,
    ! [X0,X1,X2,X3] :
      ( ~ sum(X0,X1,X2)
      | ~ sum(X0,X1,X3)
      | X2 = X3 ),
    inference(cnf_transformation,[status(esa)],[f44]) ).

fof(f48,plain,
    product(a,b,d),
    inference(cnf_transformation,[status(esa)],[f18]) ).

fof(f49,plain,
    product(additive_inverse(a),b,c),
    inference(cnf_transformation,[status(esa)],[f19]) ).

fof(f50,plain,
    ~ sum(c,d,additive_identity),
    inference(cnf_transformation,[status(esa)],[f20]) ).

fof(f56,plain,
    ! [X0,X1,X2,X3] :
      ( ~ sum(X0,X1,additive_identity)
      | ~ sum(X1,X2,X3)
      | sum(X0,X3,X2) ),
    inference(resolution,[status(thm)],[f28,f21]) ).

fof(f58,plain,
    ! [X0,X1,X2,X3] :
      ( ~ sum(X0,X1,X1)
      | ~ sum(X1,X2,X3)
      | sum(X0,X3,X3) ),
    inference(factoring,[status(esa)],[f28]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( ~ sum(X0,additive_identity,X1)
      | X1 = X0 ),
    inference(resolution,[status(thm)],[f45,f22]) ).

fof(f85,plain,
    ! [X0,X1,X2] :
      ( ~ sum(X0,X1,X2)
      | X2 = add(X0,X1) ),
    inference(resolution,[status(thm)],[f24,f45]) ).

fof(f90,plain,
    ! [X0,X1] : sum(X0,X1,add(X1,X0)),
    inference(resolution,[status(thm)],[f24,f31]) ).

fof(f98,plain,
    ! [X0,X1,X2] :
      ( ~ sum(X0,X1,X2)
      | sum(additive_inverse(X0),X2,X1) ),
    inference(resolution,[status(thm)],[f25,f56]) ).

fof(f119,plain,
    ! [X0,X1] :
      ( ~ sum(X0,additive_inverse(X0),X1)
      | X1 = additive_identity ),
    inference(resolution,[status(thm)],[f26,f45]) ).

fof(f127,plain,
    ! [X0] : add(X0,additive_inverse(X0)) = additive_identity,
    inference(resolution,[status(thm)],[f119,f24]) ).

fof(f142,plain,
    ! [X0,X1,X2] :
      ( ~ sum(X0,X1,X2)
      | X2 = add(X1,X0) ),
    inference(resolution,[status(thm)],[f90,f45]) ).

fof(f199,plain,
    ! [X0,X1] : add(X0,X1) = add(X1,X0),
    inference(resolution,[status(thm)],[f85,f90]) ).

fof(f221,plain,
    ! [X0] : sum(additive_inverse(additive_inverse(X0)),additive_identity,X0),
    inference(resolution,[status(thm)],[f98,f25]) ).

fof(f226,plain,
    ! [X0,X1] : sum(additive_inverse(X0),add(X1,X0),X1),
    inference(resolution,[status(thm)],[f98,f90]) ).

fof(f227,plain,
    ! [X0,X1] : sum(additive_inverse(X0),add(X0,X1),X1),
    inference(resolution,[status(thm)],[f98,f24]) ).

fof(f234,plain,
    ! [X0] : X0 = additive_inverse(additive_inverse(X0)),
    inference(resolution,[status(thm)],[f221,f62]) ).

fof(f310,plain,
    ! [X0,X1] : X0 = add(add(X0,X1),additive_inverse(X1)),
    inference(resolution,[status(thm)],[f226,f142]) ).

fof(f311,plain,
    ! [X0,X1] : X0 = add(additive_inverse(X1),add(X0,X1)),
    inference(forward_demodulation,[status(thm)],[f199,f310]) ).

fof(f322,plain,
    ! [X0,X1] : sum(X0,add(X1,additive_inverse(X0)),X1),
    inference(paramodulation,[status(thm)],[f234,f226]) ).

fof(f338,plain,
    ! [X0,X1] : X0 = add(add(X1,X0),additive_inverse(X1)),
    inference(resolution,[status(thm)],[f227,f142]) ).

fof(f339,plain,
    ! [X0,X1] : X0 = add(additive_inverse(X1),add(X1,X0)),
    inference(forward_demodulation,[status(thm)],[f199,f338]) ).

fof(f349,plain,
    ! [X0,X1] : sum(add(X0,X1),additive_inverse(X0),X1),
    inference(resolution,[status(thm)],[f227,f31]) ).

fof(f365,plain,
    ! [X0,X1] : additive_inverse(X0) = add(additive_inverse(add(X1,X0)),X1),
    inference(paramodulation,[status(thm)],[f311,f311]) ).

fof(f366,plain,
    ! [X0,X1] : additive_inverse(X0) = add(X1,additive_inverse(add(X1,X0))),
    inference(forward_demodulation,[status(thm)],[f199,f365]) ).

fof(f429,plain,
    ! [X0,X1,X2] :
      ( ~ sum(X0,X1,X1)
      | sum(X0,X2,X2) ),
    inference(resolution,[status(thm)],[f322,f58]) ).

fof(f447,plain,
    ! [X0,X1] : X0 = add(X1,add(additive_inverse(X1),X0)),
    inference(paramodulation,[status(thm)],[f234,f339]) ).

fof(f472,plain,
    ! [X0,X1] :
      ( ~ product(X0,b,X1)
      | ~ sum(X0,additive_inverse(a),additive_inverse(a))
      | sum(X1,c,c) ),
    inference(resolution,[status(thm)],[f41,f49]) ).

fof(f473,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product(X0,b,X1)
      | ~ sum(X0,additive_inverse(a),X2)
      | ~ product(X2,b,X3)
      | sum(X1,c,X3) ),
    inference(resolution,[status(thm)],[f41,f49]) ).

fof(f519,plain,
    ! [X0,X1] : sum(add(additive_inverse(X0),X1),X0,X1),
    inference(paramodulation,[status(thm)],[f234,f349]) ).

fof(f861,plain,
    ! [X0,X1] : additive_inverse(add(X0,X1)) = add(additive_inverse(X0),additive_inverse(X1)),
    inference(paramodulation,[status(thm)],[f339,f366]) ).

fof(f866,plain,
    ! [X0,X1] : additive_inverse(add(additive_inverse(X0),X1)) = add(X0,additive_inverse(X1)),
    inference(paramodulation,[status(thm)],[f447,f366]) ).

fof(f3752,plain,
    ! [X0] :
      ( ~ product(add(additive_inverse(additive_inverse(a)),additive_inverse(a)),b,X0)
      | sum(X0,c,c) ),
    inference(resolution,[status(thm)],[f472,f519]) ).

fof(f3753,plain,
    ! [X0] :
      ( ~ product(additive_inverse(add(additive_inverse(a),a)),b,X0)
      | sum(X0,c,c) ),
    inference(forward_demodulation,[status(thm)],[f861,f3752]) ).

fof(f3754,plain,
    ! [X0] :
      ( ~ product(add(a,additive_inverse(a)),b,X0)
      | sum(X0,c,c) ),
    inference(forward_demodulation,[status(thm)],[f866,f3753]) ).

fof(f3755,plain,
    ! [X0] :
      ( ~ product(additive_identity,b,X0)
      | sum(X0,c,c) ),
    inference(forward_demodulation,[status(thm)],[f127,f3754]) ).

fof(f4250,plain,
    ! [X0,X1] :
      ( ~ product(additive_inverse(additive_inverse(a)),b,X0)
      | ~ product(additive_identity,b,X1)
      | sum(X0,c,X1) ),
    inference(resolution,[status(thm)],[f473,f25]) ).

fof(f4251,plain,
    ! [X0,X1] :
      ( ~ product(a,b,X0)
      | ~ product(additive_identity,b,X1)
      | sum(X0,c,X1) ),
    inference(forward_demodulation,[status(thm)],[f234,f4250]) ).

fof(f4675,plain,
    sum(multiply(additive_identity,b),c,c),
    inference(resolution,[status(thm)],[f3755,f23]) ).

fof(f4689,plain,
    ! [X0] : sum(multiply(additive_identity,b),X0,X0),
    inference(resolution,[status(thm)],[f4675,f429]) ).

fof(f4768,plain,
    additive_identity = multiply(additive_identity,b),
    inference(resolution,[status(thm)],[f4689,f62]) ).

fof(f4810,plain,
    product(additive_identity,b,additive_identity),
    inference(paramodulation,[status(thm)],[f4768,f23]) ).

fof(f12753,plain,
    ! [X0] :
      ( ~ product(additive_identity,b,X0)
      | sum(d,c,X0) ),
    inference(resolution,[status(thm)],[f4251,f48]) ).

fof(f12756,plain,
    sum(d,c,additive_identity),
    inference(resolution,[status(thm)],[f12753,f4810]) ).

fof(f12818,plain,
    sum(c,d,additive_identity),
    inference(resolution,[status(thm)],[f12756,f31]) ).

fof(f12819,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f12818,f50]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09  % Problem  : RNG005-1 : 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 : n025.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 10:46:12 EDT 2023
% 0.09/0.30  % CPUTime  : 
% 0.09/0.31  % Drodi V3.5.1
% 3.65/0.84  % Refutation found
% 3.65/0.84  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 3.65/0.84  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.86/0.87  % Elapsed time: 0.557677 seconds
% 3.86/0.87  % CPU time: 3.934201 seconds
% 3.86/0.87  % Memory used: 45.276 MB
%------------------------------------------------------------------------------