TSTP Solution File: RNG008-5 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : RNG008-5 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n013.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 : Tue Apr 30 20:37:42 EDT 2024

% Result   : Unsatisfiable 55.20s 7.33s
% Output   : CNFRefutation 55.56s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   35
%            Number of leaves      :   18
% Syntax   : Number of formulae    :  138 (  86 unt;   0 def)
%            Number of atoms       :  228 (  48 equ)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :  182 (  92   ~;  90   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    5 (   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   :  355 ( 355   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X] : sum(additive_identity,X,X),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [X,Y] : product(X,Y,multiply(X,Y)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [X,Y] : sum(X,Y,add(X,Y)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    ! [X] : sum(additive_inverse(X),X,additive_identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [X] : sum(X,additive_inverse(X),additive_identity),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [X,Y,Z] :
      ( ~ sum(X,Y,Z)
      | sum(Y,X,Z) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f12,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/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).

fof(f16,axiom,
    ! [X,Y,U,V] :
      ( ~ sum(X,Y,U)
      | ~ sum(X,Y,V)
      | U = V ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f17,axiom,
    ! [X,Y,U,V] :
      ( ~ product(X,Y,U)
      | ~ product(X,Y,V)
      | U = V ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f19,axiom,
    ! [X] : sum(additive_inverse(additive_inverse(X)),additive_identity,X),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f21,axiom,
    ! [X] : product(additive_identity,X,additive_identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f22,axiom,
    ! [X,Y] : sum(additive_inverse(X),additive_inverse(Y),additive_inverse(add(X,Y))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f23,axiom,
    ! [X,Y] : product(X,additive_inverse(Y),additive_inverse(multiply(X,Y))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f24,hypothesis,
    ! [X] : product(X,X,X),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f25,hypothesis,
    product(a,b,c),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f26,negated_conjecture,
    ~ product(b,a,c),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f27,plain,
    ! [X0] : sum(additive_identity,X0,X0),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f29,plain,
    ! [X0,X1] : product(X0,X1,multiply(X0,X1)),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f30,plain,
    ! [X0,X1] : sum(X0,X1,add(X0,X1)),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f31,plain,
    ! [X0] : sum(additive_inverse(X0),X0,additive_identity),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f32,plain,
    ! [X0] : sum(X0,additive_inverse(X0),additive_identity),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f33,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(f34,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)],[f33]) ).

fof(f37,plain,
    ! [X0,X1,X2] :
      ( ~ sum(X0,X1,X2)
      | sum(X1,X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f42,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)],[f12]) ).

fof(f43,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)],[f42]) ).

fof(f46,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(f47,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)],[f46]) ).

fof(f50,plain,
    ! [U,V] :
      ( ! [X,Y] :
          ( ~ sum(X,Y,U)
          | ~ sum(X,Y,V) )
      | U = V ),
    inference(miniscoping,[status(esa)],[f16]) ).

fof(f51,plain,
    ! [X0,X1,X2,X3] :
      ( ~ sum(X0,X1,X2)
      | ~ sum(X0,X1,X3)
      | X2 = X3 ),
    inference(cnf_transformation,[status(esa)],[f50]) ).

fof(f52,plain,
    ! [U,V] :
      ( ! [X,Y] :
          ( ~ product(X,Y,U)
          | ~ product(X,Y,V) )
      | U = V ),
    inference(miniscoping,[status(esa)],[f17]) ).

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

fof(f55,plain,
    ! [X0] : sum(additive_inverse(additive_inverse(X0)),additive_identity,X0),
    inference(cnf_transformation,[status(esa)],[f19]) ).

fof(f57,plain,
    ! [X0] : product(additive_identity,X0,additive_identity),
    inference(cnf_transformation,[status(esa)],[f21]) ).

fof(f58,plain,
    ! [X0,X1] : sum(additive_inverse(X0),additive_inverse(X1),additive_inverse(add(X0,X1))),
    inference(cnf_transformation,[status(esa)],[f22]) ).

fof(f59,plain,
    ! [X0,X1] : product(X0,additive_inverse(X1),additive_inverse(multiply(X0,X1))),
    inference(cnf_transformation,[status(esa)],[f23]) ).

fof(f60,plain,
    ! [X0] : product(X0,X0,X0),
    inference(cnf_transformation,[status(esa)],[f24]) ).

fof(f61,plain,
    product(a,b,c),
    inference(cnf_transformation,[status(esa)],[f25]) ).

fof(f62,plain,
    ~ product(b,a,c),
    inference(cnf_transformation,[status(esa)],[f26]) ).

fof(f64,plain,
    ! [X0,X1] :
      ( ~ product(X0,X0,X1)
      | X0 = X1 ),
    inference(resolution,[status(thm)],[f53,f60]) ).

fof(f102,plain,
    ! [X0] : X0 = multiply(X0,X0),
    inference(resolution,[status(thm)],[f29,f64]) ).

fof(f103,plain,
    ! [X0,X1,X2] :
      ( ~ product(X0,X1,X2)
      | multiply(X0,X1) = X2 ),
    inference(resolution,[status(thm)],[f29,f53]) ).

fof(f111,plain,
    ! [X0,X1,X2,X3] :
      ( ~ sum(X0,X1,X2)
      | ~ sum(additive_identity,X1,X3)
      | sum(additive_inverse(X0),X2,X3) ),
    inference(resolution,[status(thm)],[f34,f31]) ).

fof(f115,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ sum(X0,X1,X2)
      | ~ sum(add(X3,X0),X1,X4)
      | sum(X3,X2,X4) ),
    inference(resolution,[status(thm)],[f34,f30]) ).

fof(f125,plain,
    ! [X0,X1] : sum(X0,X1,add(X1,X0)),
    inference(resolution,[status(thm)],[f37,f30]) ).

fof(f239,plain,
    ! [X0] : sum(additive_identity,additive_inverse(additive_inverse(X0)),X0),
    inference(resolution,[status(thm)],[f55,f37]) ).

fof(f303,plain,
    ! [X0,X1] :
      ( ~ sum(additive_identity,X0,X1)
      | X0 = X1 ),
    inference(resolution,[status(thm)],[f51,f27]) ).

fof(f306,plain,
    ! [X0,X1,X2] :
      ( ~ sum(X0,X1,X2)
      | add(X1,X0) = X2 ),
    inference(resolution,[status(thm)],[f51,f125]) ).

fof(f307,plain,
    ! [X0,X1,X2] :
      ( ~ sum(X0,X1,X2)
      | add(X0,X1) = X2 ),
    inference(resolution,[status(thm)],[f51,f30]) ).

fof(f308,plain,
    ! [X0] : additive_inverse(additive_inverse(X0)) = X0,
    inference(resolution,[status(thm)],[f303,f239]) ).

fof(f310,plain,
    ! [X0] : X0 = add(X0,additive_identity),
    inference(resolution,[status(thm)],[f303,f125]) ).

fof(f344,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ product(X0,X1,X2)
      | ~ sum(X0,X1,X3)
      | ~ product(X0,X3,X4)
      | sum(X0,X2,X4) ),
    inference(resolution,[status(thm)],[f43,f60]) ).

fof(f360,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ product(X0,X1,X2)
      | ~ sum(X1,X0,X3)
      | ~ product(X3,X1,X4)
      | sum(X1,X2,X4) ),
    inference(resolution,[status(thm)],[f47,f60]) ).

fof(f449,plain,
    ! [X0,X1] : add(X0,X1) = add(X1,X0),
    inference(resolution,[status(thm)],[f306,f30]) ).

fof(f513,plain,
    ! [X0] : product(X0,additive_inverse(X0),additive_inverse(X0)),
    inference(paramodulation,[status(thm)],[f102,f59]) ).

fof(f538,plain,
    ! [X0] : product(additive_inverse(X0),X0,additive_inverse(additive_inverse(X0))),
    inference(paramodulation,[status(thm)],[f308,f513]) ).

fof(f539,plain,
    ! [X0] : product(additive_inverse(X0),X0,X0),
    inference(forward_demodulation,[status(thm)],[f308,f538]) ).

fof(f551,plain,
    ! [X0] : multiply(additive_inverse(X0),X0) = X0,
    inference(resolution,[status(thm)],[f539,f103]) ).

fof(f606,plain,
    ! [X0,X1] : sum(additive_inverse(X0),additive_inverse(X1),additive_inverse(add(X1,X0))),
    inference(resolution,[status(thm)],[f58,f37]) ).

fof(f634,plain,
    ! [X0,X1,X2] :
      ( ~ sum(additive_identity,X0,X1)
      | sum(additive_inverse(X2),add(X0,X2),X1) ),
    inference(resolution,[status(thm)],[f111,f125]) ).

fof(f783,plain,
    ! [X0,X1,X2,X3] :
      ( ~ sum(X0,X1,X2)
      | ~ product(X0,X2,X3)
      | sum(X0,multiply(X0,X1),X3) ),
    inference(resolution,[status(thm)],[f344,f29]) ).

fof(f1239,plain,
    ! [X0,X1,X2,X3] :
      ( ~ sum(X0,X1,X2)
      | ~ product(X2,X0,X3)
      | sum(X0,multiply(X1,X0),X3) ),
    inference(resolution,[status(thm)],[f360,f29]) ).

fof(f1502,plain,
    ! [X0,X1,X2,X3] :
      ( ~ sum(add(X0,additive_inverse(X1)),additive_inverse(X2),X3)
      | sum(X0,additive_inverse(add(X2,X1)),X3) ),
    inference(resolution,[status(thm)],[f115,f606]) ).

fof(f1503,plain,
    ! [X0,X1,X2,X3] :
      ( ~ sum(add(X0,additive_inverse(X1)),additive_inverse(X2),X3)
      | sum(X0,additive_inverse(add(X1,X2)),X3) ),
    inference(resolution,[status(thm)],[f115,f58]) ).

fof(f7006,plain,
    ! [X0,X1,X2] :
      ( ~ product(additive_inverse(X0),additive_inverse(add(X1,X0)),X2)
      | sum(additive_inverse(X0),multiply(additive_inverse(X0),additive_inverse(X1)),X2) ),
    inference(resolution,[status(thm)],[f783,f606]) ).

fof(f7372,plain,
    ! [X0,X1] : sum(additive_inverse(X0),add(X1,X0),X1),
    inference(resolution,[status(thm)],[f634,f27]) ).

fof(f7652,plain,
    ! [X0,X1] : add(additive_inverse(X0),add(X1,X0)) = X1,
    inference(resolution,[status(thm)],[f7372,f307]) ).

fof(f7666,plain,
    ! [X0,X1] : sum(X0,add(X1,additive_inverse(X0)),X1),
    inference(paramodulation,[status(thm)],[f308,f7372]) ).

fof(f7689,plain,
    ! [X0,X1] : add(X0,add(X1,additive_inverse(X0))) = X1,
    inference(paramodulation,[status(thm)],[f308,f7652]) ).

fof(f7932,plain,
    ! [X0,X1] : add(X0,add(additive_inverse(X0),X1)) = X1,
    inference(paramodulation,[status(thm)],[f449,f7689]) ).

fof(f9613,plain,
    ! [X0,X1,X2] :
      ( ~ product(additive_inverse(add(X0,X1)),additive_inverse(X0),X2)
      | sum(additive_inverse(X0),multiply(additive_inverse(X1),additive_inverse(X0)),X2) ),
    inference(resolution,[status(thm)],[f1239,f58]) ).

fof(f9623,plain,
    ! [X0,X1] :
      ( ~ product(additive_identity,X0,X1)
      | sum(X0,multiply(additive_inverse(X0),X0),X1) ),
    inference(resolution,[status(thm)],[f1239,f32]) ).

fof(f9624,plain,
    ! [X0,X1] :
      ( ~ product(additive_identity,X0,X1)
      | sum(X0,X0,X1) ),
    inference(forward_demodulation,[status(thm)],[f551,f9623]) ).

fof(f9627,plain,
    ! [X0,X1,X2] :
      ( ~ product(add(X0,X1),X1,X2)
      | sum(X1,multiply(X0,X1),X2) ),
    inference(resolution,[status(thm)],[f1239,f125]) ).

fof(f9629,plain,
    ! [X0] : sum(X0,X0,additive_identity),
    inference(resolution,[status(thm)],[f9624,f57]) ).

fof(f9705,plain,
    ! [X0] : add(X0,X0) = additive_identity,
    inference(resolution,[status(thm)],[f9629,f307]) ).

fof(f9741,plain,
    ! [X0] : add(X0,additive_identity) = additive_inverse(X0),
    inference(paramodulation,[status(thm)],[f9705,f7932]) ).

fof(f9742,plain,
    ! [X0] : X0 = additive_inverse(X0),
    inference(forward_demodulation,[status(thm)],[f310,f9741]) ).

fof(f9932,plain,
    ! [X0,X1] : add(X0,add(X0,X1)) = X1,
    inference(backward_demodulation,[status(thm)],[f9742,f7932]) ).

fof(f9938,plain,
    ! [X0,X1] : add(X0,add(X1,X0)) = X1,
    inference(backward_demodulation,[status(thm)],[f9742,f7689]) ).

fof(f9940,plain,
    ! [X0,X1] : sum(X0,add(X1,X0),X1),
    inference(backward_demodulation,[status(thm)],[f9742,f7666]) ).

fof(f10578,plain,
    ! [X0,X1,X2,X3] :
      ( ~ sum(add(X0,X1),additive_inverse(X2),X3)
      | sum(X0,additive_inverse(add(X2,X1)),X3) ),
    inference(forward_demodulation,[status(thm)],[f9742,f1502]) ).

fof(f10579,plain,
    ! [X0,X1,X2,X3] :
      ( ~ sum(add(X0,X1),X2,X3)
      | sum(X0,additive_inverse(add(X2,X1)),X3) ),
    inference(forward_demodulation,[status(thm)],[f9742,f10578]) ).

fof(f10580,plain,
    ! [X0,X1,X2,X3] :
      ( ~ sum(add(X0,X1),X2,X3)
      | sum(X0,add(X2,X1),X3) ),
    inference(forward_demodulation,[status(thm)],[f9742,f10579]) ).

fof(f10586,plain,
    ! [X0,X1,X2] : sum(X0,add(add(X1,add(X0,X2)),X2),X1),
    inference(resolution,[status(thm)],[f10580,f9940]) ).

fof(f10587,plain,
    ! [X0,X1,X2] : sum(X0,add(X1,add(X2,add(X0,X1))),X2),
    inference(forward_demodulation,[status(thm)],[f449,f10586]) ).

fof(f10595,plain,
    ! [X0,X1,X2] : sum(X0,add(X1,X2),add(X1,add(X0,X2))),
    inference(resolution,[status(thm)],[f10580,f125]) ).

fof(f10604,plain,
    ! [X0,X1,X2,X3] :
      ( ~ sum(add(X0,X1),additive_inverse(X2),X3)
      | sum(X0,additive_inverse(add(X1,X2)),X3) ),
    inference(forward_demodulation,[status(thm)],[f9742,f1503]) ).

fof(f10605,plain,
    ! [X0,X1,X2,X3] :
      ( ~ sum(add(X0,X1),X2,X3)
      | sum(X0,additive_inverse(add(X1,X2)),X3) ),
    inference(forward_demodulation,[status(thm)],[f9742,f10604]) ).

fof(f10606,plain,
    ! [X0,X1,X2,X3] :
      ( ~ sum(add(X0,X1),X2,X3)
      | sum(X0,add(X1,X2),X3) ),
    inference(forward_demodulation,[status(thm)],[f9742,f10605]) ).

fof(f10619,plain,
    ! [X0,X1,X2] : sum(X0,add(X1,X2),add(add(X0,X1),X2)),
    inference(resolution,[status(thm)],[f10606,f30]) ).

fof(f11599,plain,
    ! [X0,X1,X2] : add(X0,add(X1,add(X2,add(X0,X1)))) = X2,
    inference(resolution,[status(thm)],[f10587,f307]) ).

fof(f11828,plain,
    ! [X0,X1,X2] : add(add(X0,X1),X2) = add(X0,add(X2,X1)),
    inference(resolution,[status(thm)],[f10595,f306]) ).

fof(f12277,plain,
    ! [X0,X1,X2] : add(X0,add(X1,X2)) = add(add(X0,X1),X2),
    inference(resolution,[status(thm)],[f10619,f307]) ).

fof(f13003,plain,
    ! [X0,X1,X2] : add(X0,X1) = add(X2,add(X1,add(X0,X2))),
    inference(paramodulation,[status(thm)],[f11599,f9932]) ).

fof(f18726,plain,
    multiply(a,b) = c,
    inference(resolution,[status(thm)],[f61,f103]) ).

fof(f21307,plain,
    ! [X0,X1,X2] : add(X0,add(X1,X2)) = add(X0,add(X2,X1)),
    inference(forward_demodulation,[status(thm)],[f11828,f12277]) ).

fof(f30679,plain,
    ! [X0,X1,X2] :
      ( ~ product(X0,additive_inverse(add(X1,X0)),X2)
      | sum(additive_inverse(X0),multiply(additive_inverse(X0),additive_inverse(X1)),X2) ),
    inference(forward_demodulation,[status(thm)],[f9742,f7006]) ).

fof(f30680,plain,
    ! [X0,X1,X2] :
      ( ~ product(X0,add(X1,X0),X2)
      | sum(additive_inverse(X0),multiply(additive_inverse(X0),additive_inverse(X1)),X2) ),
    inference(forward_demodulation,[status(thm)],[f9742,f30679]) ).

fof(f30681,plain,
    ! [X0,X1,X2] :
      ( ~ product(X0,add(X1,X0),X2)
      | sum(X0,multiply(additive_inverse(X0),additive_inverse(X1)),X2) ),
    inference(forward_demodulation,[status(thm)],[f9742,f30680]) ).

fof(f30682,plain,
    ! [X0,X1,X2] :
      ( ~ product(X0,add(X1,X0),X2)
      | sum(X0,multiply(X0,additive_inverse(X1)),X2) ),
    inference(forward_demodulation,[status(thm)],[f9742,f30681]) ).

fof(f30683,plain,
    ! [X0,X1,X2] :
      ( ~ product(X0,add(X1,X0),X2)
      | sum(X0,multiply(X0,X1),X2) ),
    inference(forward_demodulation,[status(thm)],[f9742,f30682]) ).

fof(f30688,plain,
    ! [X0,X1] : sum(X0,multiply(X0,X1),multiply(X0,add(X1,X0))),
    inference(resolution,[status(thm)],[f30683,f29]) ).

fof(f30817,plain,
    ! [X0,X1] : add(X0,multiply(X0,X1)) = multiply(X0,add(X1,X0)),
    inference(resolution,[status(thm)],[f30688,f307]) ).

fof(f30885,plain,
    ! [X0,X1] : sum(X0,multiply(X0,X1),multiply(X0,add(X0,X1))),
    inference(paramodulation,[status(thm)],[f449,f30688]) ).

fof(f31630,plain,
    ! [X0,X1] : add(X0,multiply(X0,X1)) = multiply(X0,add(X0,X1)),
    inference(resolution,[status(thm)],[f30885,f307]) ).

fof(f31631,plain,
    ! [X0,X1] : multiply(X0,add(X1,X0)) = multiply(X0,add(X0,X1)),
    inference(forward_demodulation,[status(thm)],[f30817,f31630]) ).

fof(f33079,plain,
    ! [X0,X1] : product(X0,add(X1,X0),multiply(X0,add(X0,X1))),
    inference(paramodulation,[status(thm)],[f31631,f29]) ).

fof(f34632,plain,
    ! [X0,X1,X2] : product(X0,add(add(X1,add(X2,X0)),X0),multiply(X0,add(X2,X1))),
    inference(paramodulation,[status(thm)],[f13003,f33079]) ).

fof(f34633,plain,
    ! [X0,X1,X2] : product(X0,add(X1,add(X0,add(X2,X0))),multiply(X0,add(X2,X1))),
    inference(forward_demodulation,[status(thm)],[f11828,f34632]) ).

fof(f34634,plain,
    ! [X0,X1,X2] : product(X0,add(X1,X2),multiply(X0,add(X2,X1))),
    inference(forward_demodulation,[status(thm)],[f9938,f34633]) ).

fof(f34952,plain,
    ! [X0,X1,X2] : multiply(X0,add(X1,X2)) = multiply(X0,add(X2,X1)),
    inference(resolution,[status(thm)],[f34634,f103]) ).

fof(f45536,plain,
    ! [X0,X1] : sum(X0,multiply(X1,X0),multiply(add(X1,X0),X0)),
    inference(resolution,[status(thm)],[f9627,f29]) ).

fof(f46184,plain,
    ! [X0,X1,X2] :
      ( ~ product(add(X0,X1),additive_inverse(X0),X2)
      | sum(additive_inverse(X0),multiply(additive_inverse(X1),additive_inverse(X0)),X2) ),
    inference(forward_demodulation,[status(thm)],[f9742,f9613]) ).

fof(f46185,plain,
    ! [X0,X1,X2] :
      ( ~ product(add(X0,X1),X0,X2)
      | sum(additive_inverse(X0),multiply(additive_inverse(X1),additive_inverse(X0)),X2) ),
    inference(forward_demodulation,[status(thm)],[f9742,f46184]) ).

fof(f46186,plain,
    ! [X0,X1,X2] :
      ( ~ product(add(X0,X1),X0,X2)
      | sum(X0,multiply(additive_inverse(X1),additive_inverse(X0)),X2) ),
    inference(forward_demodulation,[status(thm)],[f9742,f46185]) ).

fof(f46187,plain,
    ! [X0,X1,X2] :
      ( ~ product(add(X0,X1),X0,X2)
      | sum(X0,multiply(X1,additive_inverse(X0)),X2) ),
    inference(forward_demodulation,[status(thm)],[f9742,f46186]) ).

fof(f46188,plain,
    ! [X0,X1,X2] :
      ( ~ product(add(X0,X1),X0,X2)
      | sum(X0,multiply(X1,X0),X2) ),
    inference(forward_demodulation,[status(thm)],[f9742,f46187]) ).

fof(f46193,plain,
    ! [X0,X1] : sum(X0,multiply(X1,X0),multiply(add(X0,X1),X0)),
    inference(resolution,[status(thm)],[f46188,f29]) ).

fof(f49482,plain,
    ! [X0,X1] : add(X0,multiply(X1,X0)) = multiply(add(X1,X0),X0),
    inference(resolution,[status(thm)],[f45536,f307]) ).

fof(f50178,plain,
    ! [X0,X1] : add(X0,multiply(X1,X0)) = multiply(add(X0,X1),X0),
    inference(resolution,[status(thm)],[f46193,f307]) ).

fof(f52755,plain,
    ! [X0,X1] : multiply(add(X0,X1),X1) = multiply(add(X1,X0),X1),
    inference(forward_demodulation,[status(thm)],[f49482,f50178]) ).

fof(f52890,plain,
    ! [X0,X1] : add(add(X0,X1),multiply(add(X1,X0),X1)) = multiply(add(X0,X1),add(X1,add(X0,X1))),
    inference(paramodulation,[status(thm)],[f52755,f30817]) ).

fof(f52891,plain,
    ! [X0,X1] : add(X0,add(multiply(add(X1,X0),X1),X1)) = multiply(add(X0,X1),add(X1,add(X0,X1))),
    inference(forward_demodulation,[status(thm)],[f11828,f52890]) ).

fof(f52892,plain,
    ! [X0,X1] : add(X0,add(X1,multiply(add(X1,X0),X1))) = multiply(add(X0,X1),add(X1,add(X0,X1))),
    inference(forward_demodulation,[status(thm)],[f21307,f52891]) ).

fof(f52893,plain,
    ! [X0,X1] : add(X0,multiply(add(add(X1,X0),X1),X1)) = multiply(add(X0,X1),add(X1,add(X0,X1))),
    inference(forward_demodulation,[status(thm)],[f49482,f52892]) ).

fof(f52894,plain,
    ! [X0,X1] : add(X0,multiply(add(X1,add(X1,X0)),X1)) = multiply(add(X0,X1),add(X1,add(X0,X1))),
    inference(forward_demodulation,[status(thm)],[f52755,f52893]) ).

fof(f52895,plain,
    ! [X0,X1] : add(X0,multiply(X0,X1)) = multiply(add(X0,X1),add(X1,add(X0,X1))),
    inference(forward_demodulation,[status(thm)],[f9932,f52894]) ).

fof(f52896,plain,
    ! [X0,X1] : multiply(X0,add(X1,X0)) = multiply(add(X0,X1),add(X1,add(X0,X1))),
    inference(forward_demodulation,[status(thm)],[f30817,f52895]) ).

fof(f52897,plain,
    ! [X0,X1] : multiply(X0,add(X1,X0)) = multiply(add(X0,X1),X0),
    inference(forward_demodulation,[status(thm)],[f9938,f52896]) ).

fof(f55922,plain,
    ! [X0,X1] : multiply(X0,add(add(X1,X0),X0)) = multiply(X1,X0),
    inference(paramodulation,[status(thm)],[f9938,f52897]) ).

fof(f55923,plain,
    ! [X0,X1] : multiply(X0,add(X0,add(X1,X0))) = multiply(X1,X0),
    inference(forward_demodulation,[status(thm)],[f34952,f55922]) ).

fof(f55924,plain,
    ! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
    inference(forward_demodulation,[status(thm)],[f9938,f55923]) ).

fof(f56306,plain,
    ! [X0,X1] : product(X0,X1,multiply(X1,X0)),
    inference(paramodulation,[status(thm)],[f55924,f29]) ).

fof(f56730,plain,
    product(b,a,c),
    inference(paramodulation,[status(thm)],[f18726,f56306]) ).

fof(f56731,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f56730,f62]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : RNG008-5 : TPTP v8.1.2. Released v1.0.0.
% 0.04/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35  % Computer : n013.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Mon Apr 29 22:13:49 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.13/0.36  % Drodi V3.6.0
% 55.20/7.33  % Refutation found
% 55.20/7.33  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 55.20/7.33  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 55.56/7.44  % Elapsed time: 7.073301 seconds
% 55.56/7.44  % CPU time: 55.732033 seconds
% 55.56/7.44  % Total memory used: 342.603 MB
% 55.56/7.44  % Net memory used: 316.217 MB
%------------------------------------------------------------------------------