TSTP Solution File: BOO008-1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : BOO008-1 : 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 12:02:44 EDT 2023

% Result   : Unsatisfiable 67.11s 8.84s
% Output   : CNFRefutation 67.96s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :   19
% Syntax   : Number of formulae    :  164 (  97 unt;   0 def)
%            Number of atoms       :  305 (  61 equ)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :  284 ( 143   ~; 141   |;   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    :   12 (  12 usr;   9 con; 0-2 aty)
%            Number of variables   :  308 (; 308   !;   0   ?)

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

fof(f2,axiom,
    ! [X,Y] : product(X,Y,multiply(X,Y)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [X,Y,Z] :
      ( ~ sum(X,Y,Z)
      | sum(Y,X,Z) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [X,Y,Z] :
      ( ~ product(X,Y,Z)
      | product(Y,X,Z) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

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

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

fof(f7,axiom,
    ! [X] : product(multiplicative_identity,X,X),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).

fof(f12,axiom,
    ! [Y,X,V1,Z,V2,V3,V4] :
      ( ~ product(Y,X,V1)
      | ~ product(Z,X,V2)
      | ~ sum(Y,Z,V3)
      | ~ sum(V1,V2,V4)
      | product(V3,X,V4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f13,axiom,
    ! [X,Y,V1,Z,V2,V3,V4] :
      ( ~ sum(X,Y,V1)
      | ~ sum(X,Z,V2)
      | ~ product(Y,Z,V3)
      | ~ sum(X,V3,V4)
      | product(V1,V2,V4) ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).

fof(f20,axiom,
    ! [X] : product(X,inverse(X),additive_identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f21,axiom,
    ! [X,Y,U,V] :
      ( ~ sum(X,Y,U)
      | ~ sum(X,Y,V)
      | U = V ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f22,axiom,
    ! [X,Y,U,V] :
      ( ~ product(X,Y,U)
      | ~ product(X,Y,V)
      | U = V ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f23,hypothesis,
    sum(y,z,y_plus_z),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f24,hypothesis,
    sum(x,y_plus_z,x__plus_y_plus_z),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f25,hypothesis,
    sum(x,y,x_plus_y),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f26,hypothesis,
    sum(x_plus_y,z,x_plus_y__plus_z),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f27,negated_conjecture,
    x__plus_y_plus_z != x_plus_y__plus_z,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f28,plain,
    ! [X0,X1] : sum(X0,X1,add(X0,X1)),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f29,plain,
    ! [X0,X1] : product(X0,X1,multiply(X0,X1)),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f30,plain,
    ! [X0,X1,X2] :
      ( ~ sum(X0,X1,X2)
      | sum(X1,X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f31,plain,
    ! [X0,X1,X2] :
      ( ~ product(X0,X1,X2)
      | product(X1,X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f32,plain,
    ! [X0] : sum(additive_identity,X0,X0),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f33,plain,
    ! [X0] : sum(X0,additive_identity,X0),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f34,plain,
    ! [X0] : product(multiplicative_identity,X0,X0),
    inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f36,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(f37,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)],[f36]) ).

fof(f42,plain,
    ! [X,V3,V4] :
      ( ! [V1,V2] :
          ( ! [Y,Z] :
              ( ~ product(Y,X,V1)
              | ~ product(Z,X,V2)
              | ~ sum(Y,Z,V3) )
          | ~ sum(V1,V2,V4) )
      | product(V3,X,V4) ),
    inference(miniscoping,[status(esa)],[f12]) ).

fof(f43,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ~ product(X0,X1,X2)
      | ~ product(X3,X1,X4)
      | ~ sum(X0,X3,X5)
      | ~ sum(X2,X4,X6)
      | product(X5,X1,X6) ),
    inference(cnf_transformation,[status(esa)],[f42]) ).

fof(f44,plain,
    ! [V1,V2,V4] :
      ( ! [X,V3] :
          ( ! [Y,Z] :
              ( ~ sum(X,Y,V1)
              | ~ sum(X,Z,V2)
              | ~ product(Y,Z,V3) )
          | ~ sum(X,V3,V4) )
      | product(V1,V2,V4) ),
    inference(miniscoping,[status(esa)],[f13]) ).

fof(f45,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ~ sum(X0,X1,X2)
      | ~ sum(X0,X3,X4)
      | ~ product(X1,X3,X5)
      | ~ sum(X0,X5,X6)
      | product(X2,X4,X6) ),
    inference(cnf_transformation,[status(esa)],[f44]) ).

fof(f48,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(f49,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)],[f48]) ).

fof(f55,plain,
    ! [X0] : product(X0,inverse(X0),additive_identity),
    inference(cnf_transformation,[status(esa)],[f20]) ).

fof(f56,plain,
    ! [U,V] :
      ( ! [X,Y] :
          ( ~ sum(X,Y,U)
          | ~ sum(X,Y,V) )
      | U = V ),
    inference(miniscoping,[status(esa)],[f21]) ).

fof(f57,plain,
    ! [X0,X1,X2,X3] :
      ( ~ sum(X0,X1,X2)
      | ~ sum(X0,X1,X3)
      | X2 = X3 ),
    inference(cnf_transformation,[status(esa)],[f56]) ).

fof(f58,plain,
    ! [U,V] :
      ( ! [X,Y] :
          ( ~ product(X,Y,U)
          | ~ product(X,Y,V) )
      | U = V ),
    inference(miniscoping,[status(esa)],[f22]) ).

fof(f59,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product(X0,X1,X2)
      | ~ product(X0,X1,X3)
      | X2 = X3 ),
    inference(cnf_transformation,[status(esa)],[f58]) ).

fof(f60,plain,
    sum(y,z,y_plus_z),
    inference(cnf_transformation,[status(esa)],[f23]) ).

fof(f61,plain,
    sum(x,y_plus_z,x__plus_y_plus_z),
    inference(cnf_transformation,[status(esa)],[f24]) ).

fof(f62,plain,
    sum(x,y,x_plus_y),
    inference(cnf_transformation,[status(esa)],[f25]) ).

fof(f63,plain,
    sum(x_plus_y,z,x_plus_y__plus_z),
    inference(cnf_transformation,[status(esa)],[f26]) ).

fof(f64,plain,
    x__plus_y_plus_z != x_plus_y__plus_z,
    inference(cnf_transformation,[status(esa)],[f27]) ).

fof(f65,plain,
    sum(z,y,y_plus_z),
    inference(resolution,[status(thm)],[f30,f60]) ).

fof(f68,plain,
    sum(z,x_plus_y,x_plus_y__plus_z),
    inference(resolution,[status(thm)],[f30,f63]) ).

fof(f69,plain,
    sum(y,x,x_plus_y),
    inference(resolution,[status(thm)],[f30,f62]) ).

fof(f70,plain,
    sum(y_plus_z,x,x__plus_y_plus_z),
    inference(resolution,[status(thm)],[f30,f61]) ).

fof(f73,plain,
    ! [X0,X1] : sum(X0,X1,add(X1,X0)),
    inference(resolution,[status(thm)],[f30,f28]) ).

fof(f83,plain,
    ! [X0,X1] : product(X0,X1,multiply(X1,X0)),
    inference(resolution,[status(thm)],[f31,f29]) ).

fof(f85,plain,
    ! [X0] :
      ( ~ sum(y_plus_z,x,X0)
      | x__plus_y_plus_z = X0 ),
    inference(resolution,[status(thm)],[f57,f70]) ).

fof(f86,plain,
    ! [X0] :
      ( ~ sum(z,y,X0)
      | y_plus_z = X0 ),
    inference(resolution,[status(thm)],[f57,f65]) ).

fof(f87,plain,
    ! [X0] :
      ( ~ sum(z,x_plus_y,X0)
      | x_plus_y__plus_z = X0 ),
    inference(resolution,[status(thm)],[f57,f68]) ).

fof(f88,plain,
    ! [X0] :
      ( ~ sum(y,x,X0)
      | x_plus_y = X0 ),
    inference(resolution,[status(thm)],[f57,f69]) ).

fof(f97,plain,
    ! [X0,X1,X2] :
      ( ~ sum(X0,X1,X2)
      | add(X1,X0) = X2 ),
    inference(resolution,[status(thm)],[f57,f73]) ).

fof(f98,plain,
    ! [X0,X1,X2] :
      ( ~ sum(X0,X1,X2)
      | add(X0,X1) = X2 ),
    inference(resolution,[status(thm)],[f57,f28]) ).

fof(f113,plain,
    x__plus_y_plus_z = add(x,y_plus_z),
    inference(resolution,[status(thm)],[f85,f73]) ).

fof(f120,plain,
    y_plus_z = add(z,y),
    inference(resolution,[status(thm)],[f86,f28]) ).

fof(f122,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ product(multiplicative_identity,X0,X1)
      | ~ sum(X2,X0,X3)
      | ~ product(multiplicative_identity,X3,X4)
      | sum(X2,X1,X4) ),
    inference(resolution,[status(thm)],[f37,f34]) ).

fof(f123,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ product(X0,X1,X2)
      | ~ sum(inverse(X0),X1,X3)
      | ~ product(X0,X3,X4)
      | sum(additive_identity,X2,X4) ),
    inference(resolution,[status(thm)],[f37,f55]) ).

fof(f126,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ~ product(X0,X1,X2)
      | ~ sum(X3,X1,X4)
      | ~ product(X0,X4,X5)
      | sum(multiply(X0,X3),X2,X5) ),
    inference(resolution,[status(thm)],[f37,f29]) ).

fof(f139,plain,
    x_plus_y__plus_z = add(x_plus_y,z),
    inference(resolution,[status(thm)],[f87,f73]) ).

fof(f154,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ~ product(X0,X1,X2)
      | ~ sum(X3,X0,X4)
      | ~ sum(multiply(X3,X1),X2,X5)
      | product(X4,X1,X5) ),
    inference(resolution,[status(thm)],[f43,f29]) ).

fof(f159,plain,
    x_plus_y = add(x,y),
    inference(resolution,[status(thm)],[f88,f73]) ).

fof(f187,plain,
    ! [X0,X1,X2,X3] :
      ( ~ sum(y,X0,X1)
      | ~ product(z,X0,X2)
      | ~ sum(y,X2,X3)
      | product(y_plus_z,X1,X3) ),
    inference(resolution,[status(thm)],[f45,f60]) ).

fof(f189,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ sum(additive_identity,X0,X1)
      | ~ product(X2,X0,X3)
      | ~ sum(additive_identity,X3,X4)
      | product(X2,X1,X4) ),
    inference(resolution,[status(thm)],[f45,f32]) ).

fof(f191,plain,
    ! [X0,X1,X2,X3] :
      ( ~ sum(x,X0,X1)
      | ~ product(y,X0,X2)
      | ~ sum(x,X2,X3)
      | product(x_plus_y,X1,X3) ),
    inference(resolution,[status(thm)],[f45,f62]) ).

fof(f192,plain,
    ! [X0,X1,X2,X3] :
      ( ~ sum(x,X0,X1)
      | ~ product(y_plus_z,X0,X2)
      | ~ sum(x,X2,X3)
      | product(x__plus_y_plus_z,X1,X3) ),
    inference(resolution,[status(thm)],[f45,f61]) ).

fof(f194,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ sum(X0,X1,X2)
      | ~ product(additive_identity,X1,X3)
      | ~ sum(X0,X3,X4)
      | product(X0,X2,X4) ),
    inference(resolution,[status(thm)],[f45,f33]) ).

fof(f218,plain,
    ! [X0,X1] : add(X0,X1) = add(X1,X0),
    inference(resolution,[status(thm)],[f97,f28]) ).

fof(f265,plain,
    ! [X0,X1] :
      ( ~ product(multiplicative_identity,X0,X1)
      | X0 = X1 ),
    inference(resolution,[status(thm)],[f59,f34]) ).

fof(f268,plain,
    ! [X0,X1,X2] :
      ( ~ product(X0,X1,X2)
      | multiply(X1,X0) = X2 ),
    inference(resolution,[status(thm)],[f59,f83]) ).

fof(f269,plain,
    ! [X0,X1,X2] :
      ( ~ product(X0,X1,X2)
      | multiply(X0,X1) = X2 ),
    inference(resolution,[status(thm)],[f59,f29]) ).

fof(f314,plain,
    ! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
    inference(resolution,[status(thm)],[f268,f29]) ).

fof(f336,plain,
    ! [X0,X1,X2,X3] :
      ( ~ sum(X0,z,X1)
      | ~ product(x_plus_y,X0,X2)
      | ~ sum(X2,z,X3)
      | product(x_plus_y__plus_z,X1,X3) ),
    inference(resolution,[status(thm)],[f49,f63]) ).

fof(f372,plain,
    ! [X0,X1] :
      ( ~ product(y_plus_z,y,X0)
      | ~ sum(x,X0,X1)
      | product(x__plus_y_plus_z,x_plus_y,X1) ),
    inference(resolution,[status(thm)],[f192,f62]) ).

fof(f485,plain,
    ! [X0] :
      ( ~ sum(x,multiply(y,y_plus_z),X0)
      | product(x__plus_y_plus_z,x_plus_y,X0) ),
    inference(resolution,[status(thm)],[f372,f83]) ).

fof(f488,plain,
    product(x__plus_y_plus_z,x_plus_y,add(multiply(y,y_plus_z),x)),
    inference(resolution,[status(thm)],[f485,f73]) ).

fof(f489,plain,
    product(x__plus_y_plus_z,x_plus_y,add(x,multiply(y,y_plus_z))),
    inference(forward_demodulation,[status(thm)],[f218,f488]) ).

fof(f500,plain,
    ! [X0,X1,X2,X3] :
      ( ~ sum(X0,X1,X2)
      | ~ product(multiplicative_identity,X2,X3)
      | sum(X0,X1,X3) ),
    inference(resolution,[status(thm)],[f122,f34]) ).

fof(f513,plain,
    ! [X0,X1,X2,X3] :
      ( ~ sum(inverse(X0),X1,X2)
      | ~ product(X0,X2,X3)
      | sum(additive_identity,multiply(X1,X0),X3) ),
    inference(resolution,[status(thm)],[f123,f83]) ).

fof(f516,plain,
    multiply(x__plus_y_plus_z,x_plus_y) = add(x,multiply(y,y_plus_z)),
    inference(resolution,[status(thm)],[f489,f269]) ).

fof(f529,plain,
    ! [X0,X1] :
      ( ~ product(x_plus_y,y,X0)
      | ~ sum(X0,z,X1)
      | product(x_plus_y__plus_z,y_plus_z,X1) ),
    inference(resolution,[status(thm)],[f336,f60]) ).

fof(f607,plain,
    ! [X0,X1,X2] :
      ( ~ product(multiplicative_identity,add(X0,X1),X2)
      | sum(X0,X1,X2) ),
    inference(resolution,[status(thm)],[f500,f28]) ).

fof(f733,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ sum(X0,X1,X2)
      | ~ product(X3,X2,X4)
      | sum(multiply(X3,X0),multiply(X1,X3),X4) ),
    inference(resolution,[status(thm)],[f126,f83]) ).

fof(f1393,plain,
    ! [X0] :
      ( ~ sum(multiply(y,x_plus_y),z,X0)
      | product(x_plus_y__plus_z,y_plus_z,X0) ),
    inference(resolution,[status(thm)],[f529,f83]) ).

fof(f1396,plain,
    product(x_plus_y__plus_z,y_plus_z,add(z,multiply(y,x_plus_y))),
    inference(resolution,[status(thm)],[f1393,f73]) ).

fof(f1416,plain,
    multiply(x_plus_y__plus_z,y_plus_z) = add(z,multiply(y,x_plus_y)),
    inference(resolution,[status(thm)],[f1396,f269]) ).

fof(f1417,plain,
    multiply(y_plus_z,x_plus_y__plus_z) = add(z,multiply(y,x_plus_y)),
    inference(forward_demodulation,[status(thm)],[f314,f1416]) ).

fof(f2575,plain,
    ! [X0,X1,X2,X3] :
      ( ~ sum(X0,multiplicative_identity,X1)
      | ~ sum(multiply(X0,X2),X2,X3)
      | product(X1,X2,X3) ),
    inference(resolution,[status(thm)],[f154,f34]) ).

fof(f2585,plain,
    ! [X0,X1] :
      ( ~ product(z,additive_identity,X0)
      | ~ sum(y,X0,X1)
      | product(y_plus_z,y,X1) ),
    inference(resolution,[status(thm)],[f187,f33]) ).

fof(f2849,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product(X0,X1,X2)
      | ~ sum(additive_identity,X2,X3)
      | product(X0,X1,X3) ),
    inference(resolution,[status(thm)],[f189,f32]) ).

fof(f2868,plain,
    ! [X0,X1] :
      ( ~ product(y,additive_identity,X0)
      | ~ sum(x,X0,X1)
      | product(x_plus_y,x,X1) ),
    inference(resolution,[status(thm)],[f191,f33]) ).

fof(f3208,plain,
    ! [X0,X1,X2] :
      ( ~ sum(additive_identity,multiply(X0,X1),X2)
      | product(X1,X0,X2) ),
    inference(resolution,[status(thm)],[f2849,f83]) ).

fof(f3209,plain,
    ! [X0,X1,X2] :
      ( ~ sum(additive_identity,multiply(X0,X1),X2)
      | product(X0,X1,X2) ),
    inference(resolution,[status(thm)],[f2849,f29]) ).

fof(f3313,plain,
    ! [X0,X1] :
      ( ~ product(additive_identity,y,X0)
      | ~ sum(z,X0,X1)
      | product(z,y_plus_z,X1) ),
    inference(resolution,[status(thm)],[f194,f65]) ).

fof(f3315,plain,
    ! [X0,X1] :
      ( ~ product(additive_identity,x,X0)
      | ~ sum(y,X0,X1)
      | product(y,x_plus_y,X1) ),
    inference(resolution,[status(thm)],[f194,f69]) ).

fof(f3332,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product(additive_identity,X0,X1)
      | ~ sum(X2,X1,X3)
      | product(X2,add(X0,X2),X3) ),
    inference(resolution,[status(thm)],[f194,f73]) ).

fof(f11095,plain,
    ! [X0,X1] :
      ( ~ product(X0,inverse(X0),X1)
      | sum(additive_identity,multiply(additive_identity,X0),X1) ),
    inference(resolution,[status(thm)],[f513,f33]) ).

fof(f11994,plain,
    ! [X0,X1] :
      ( ~ product(X0,x__plus_y_plus_z,X1)
      | sum(multiply(X0,y_plus_z),multiply(x,X0),X1) ),
    inference(resolution,[status(thm)],[f733,f70]) ).

fof(f11998,plain,
    ! [X0,X1] :
      ( ~ product(X0,x_plus_y__plus_z,X1)
      | sum(multiply(X0,z),multiply(x_plus_y,X0),X1) ),
    inference(resolution,[status(thm)],[f733,f68]) ).

fof(f13874,plain,
    ! [X0] : sum(multiply(X0,y_plus_z),multiply(x,X0),multiply(x__plus_y_plus_z,X0)),
    inference(resolution,[status(thm)],[f11994,f83]) ).

fof(f14412,plain,
    ! [X0] : add(multiply(X0,y_plus_z),multiply(x,X0)) = multiply(x__plus_y_plus_z,X0),
    inference(resolution,[status(thm)],[f13874,f98]) ).

fof(f14427,plain,
    ! [X0] : sum(multiply(y_plus_z,X0),multiply(x,X0),multiply(x__plus_y_plus_z,X0)),
    inference(paramodulation,[status(thm)],[f314,f13874]) ).

fof(f14939,plain,
    ! [X0] : add(multiply(y_plus_z,X0),multiply(x,X0)) = multiply(x__plus_y_plus_z,X0),
    inference(paramodulation,[status(thm)],[f314,f14412]) ).

fof(f16528,plain,
    ! [X0] : sum(multiply(y_plus_z,X0),multiply(X0,x),multiply(x__plus_y_plus_z,X0)),
    inference(paramodulation,[status(thm)],[f314,f14427]) ).

fof(f17909,plain,
    ! [X0] : add(multiply(X0,x),multiply(y_plus_z,X0)) = multiply(x__plus_y_plus_z,X0),
    inference(resolution,[status(thm)],[f16528,f97]) ).

fof(f27482,plain,
    ! [X0] : sum(multiply(X0,z),multiply(x_plus_y,X0),multiply(x_plus_y__plus_z,X0)),
    inference(resolution,[status(thm)],[f11998,f83]) ).

fof(f27483,plain,
    ! [X0] : sum(multiply(X0,z),multiply(x_plus_y,X0),multiply(X0,x_plus_y__plus_z)),
    inference(resolution,[status(thm)],[f11998,f29]) ).

fof(f27999,plain,
    ! [X0] : sum(multiply(z,X0),multiply(x_plus_y,X0),multiply(x_plus_y__plus_z,X0)),
    inference(paramodulation,[status(thm)],[f314,f27482]) ).

fof(f28996,plain,
    ! [X0] : sum(multiply(z,X0),multiply(x_plus_y,X0),multiply(X0,x_plus_y__plus_z)),
    inference(paramodulation,[status(thm)],[f314,f27483]) ).

fof(f30682,plain,
    ! [X0] : sum(multiply(z,X0),multiply(X0,x_plus_y),multiply(x_plus_y__plus_z,X0)),
    inference(paramodulation,[status(thm)],[f314,f27999]) ).

fof(f31154,plain,
    ! [X0] : sum(multiply(z,X0),multiply(X0,x_plus_y),multiply(X0,x_plus_y__plus_z)),
    inference(paramodulation,[status(thm)],[f314,f28996]) ).

fof(f32711,plain,
    ! [X0] : add(multiply(X0,x_plus_y),multiply(z,X0)) = multiply(x_plus_y__plus_z,X0),
    inference(resolution,[status(thm)],[f30682,f97]) ).

fof(f35614,plain,
    ! [X0] : sum(additive_identity,multiply(additive_identity,X0),additive_identity),
    inference(resolution,[status(thm)],[f11095,f55]) ).

fof(f35624,plain,
    ! [X0] : product(additive_identity,X0,additive_identity),
    inference(resolution,[status(thm)],[f35614,f3209]) ).

fof(f35625,plain,
    ! [X0] : product(X0,additive_identity,additive_identity),
    inference(resolution,[status(thm)],[f35614,f3208]) ).

fof(f36180,plain,
    ! [X0] :
      ( ~ sum(x,additive_identity,X0)
      | product(x_plus_y,x,X0) ),
    inference(resolution,[status(thm)],[f35625,f2868]) ).

fof(f36253,plain,
    ! [X0] :
      ( ~ sum(y,additive_identity,X0)
      | product(y_plus_z,y,X0) ),
    inference(resolution,[status(thm)],[f35625,f2585]) ).

fof(f37946,plain,
    ! [X0] :
      ( ~ sum(z,additive_identity,X0)
      | product(z,y_plus_z,X0) ),
    inference(resolution,[status(thm)],[f3313,f35624]) ).

fof(f38239,plain,
    ! [X0] :
      ( ~ sum(y,additive_identity,X0)
      | product(y,x_plus_y,X0) ),
    inference(resolution,[status(thm)],[f3315,f35624]) ).

fof(f38321,plain,
    ! [X0,X1,X2] :
      ( ~ sum(X0,additive_identity,X1)
      | product(X0,add(X2,X0),X1) ),
    inference(resolution,[status(thm)],[f3332,f35624]) ).

fof(f42043,plain,
    product(x_plus_y,x,x),
    inference(resolution,[status(thm)],[f36180,f33]) ).

fof(f42124,plain,
    multiply(x_plus_y,x) = x,
    inference(resolution,[status(thm)],[f42043,f269]) ).

fof(f42125,plain,
    multiply(x,x_plus_y) = x,
    inference(forward_demodulation,[status(thm)],[f314,f42124]) ).

fof(f42239,plain,
    sum(multiply(z,x),x,multiply(x,x_plus_y__plus_z)),
    inference(paramodulation,[status(thm)],[f42125,f31154]) ).

fof(f42507,plain,
    product(y_plus_z,y,y),
    inference(resolution,[status(thm)],[f36253,f33]) ).

fof(f42594,plain,
    multiply(y_plus_z,y) = y,
    inference(resolution,[status(thm)],[f42507,f269]) ).

fof(f42595,plain,
    multiply(y,y_plus_z) = y,
    inference(forward_demodulation,[status(thm)],[f314,f42594]) ).

fof(f42612,plain,
    multiply(x__plus_y_plus_z,x_plus_y) = add(x,y),
    inference(backward_demodulation,[status(thm)],[f42595,f516]) ).

fof(f42613,plain,
    multiply(x__plus_y_plus_z,x_plus_y) = x_plus_y,
    inference(forward_demodulation,[status(thm)],[f159,f42612]) ).

fof(f42921,plain,
    add(x_plus_y,multiply(z,x__plus_y_plus_z)) = multiply(x_plus_y__plus_z,x__plus_y_plus_z),
    inference(paramodulation,[status(thm)],[f42613,f32711]) ).

fof(f42922,plain,
    add(x_plus_y,multiply(z,x__plus_y_plus_z)) = multiply(x__plus_y_plus_z,x_plus_y__plus_z),
    inference(forward_demodulation,[status(thm)],[f314,f42921]) ).

fof(f44230,plain,
    product(z,y_plus_z,z),
    inference(resolution,[status(thm)],[f37946,f33]) ).

fof(f44318,plain,
    multiply(z,y_plus_z) = z,
    inference(resolution,[status(thm)],[f44230,f269]) ).

fof(f45068,plain,
    product(y,x_plus_y,y),
    inference(resolution,[status(thm)],[f38239,f33]) ).

fof(f45154,plain,
    multiply(y,x_plus_y) = y,
    inference(resolution,[status(thm)],[f45068,f269]) ).

fof(f45172,plain,
    multiply(y_plus_z,x_plus_y__plus_z) = add(z,y),
    inference(backward_demodulation,[status(thm)],[f45154,f1417]) ).

fof(f45173,plain,
    multiply(y_plus_z,x_plus_y__plus_z) = y_plus_z,
    inference(forward_demodulation,[status(thm)],[f120,f45172]) ).

fof(f46872,plain,
    ! [X0,X1] : product(X0,add(X1,X0),X0),
    inference(resolution,[status(thm)],[f38321,f33]) ).

fof(f46991,plain,
    ! [X0] : sum(X0,multiplicative_identity,multiplicative_identity),
    inference(resolution,[status(thm)],[f46872,f607]) ).

fof(f47048,plain,
    ! [X0,X1] : multiply(X0,add(X1,X0)) = X0,
    inference(resolution,[status(thm)],[f46872,f269]) ).

fof(f48063,plain,
    ! [X0,X1,X2] :
      ( ~ sum(multiply(X0,X1),X1,X2)
      | product(multiplicative_identity,X1,X2) ),
    inference(resolution,[status(thm)],[f46991,f2575]) ).

fof(f57209,plain,
    product(multiplicative_identity,x,multiply(x,x_plus_y__plus_z)),
    inference(resolution,[status(thm)],[f48063,f42239]) ).

fof(f57219,plain,
    ! [X0,X1] : product(multiplicative_identity,X0,add(X0,multiply(X1,X0))),
    inference(resolution,[status(thm)],[f48063,f73]) ).

fof(f57307,plain,
    x = multiply(x,x_plus_y__plus_z),
    inference(resolution,[status(thm)],[f57209,f265]) ).

fof(f57454,plain,
    add(multiply(y_plus_z,x_plus_y__plus_z),x) = multiply(x__plus_y_plus_z,x_plus_y__plus_z),
    inference(paramodulation,[status(thm)],[f57307,f14939]) ).

fof(f57455,plain,
    add(x,multiply(y_plus_z,x_plus_y__plus_z)) = multiply(x__plus_y_plus_z,x_plus_y__plus_z),
    inference(forward_demodulation,[status(thm)],[f218,f57454]) ).

fof(f57456,plain,
    add(x,y_plus_z) = multiply(x__plus_y_plus_z,x_plus_y__plus_z),
    inference(forward_demodulation,[status(thm)],[f45173,f57455]) ).

fof(f57457,plain,
    x__plus_y_plus_z = multiply(x__plus_y_plus_z,x_plus_y__plus_z),
    inference(forward_demodulation,[status(thm)],[f113,f57456]) ).

fof(f57652,plain,
    add(x_plus_y,multiply(z,x__plus_y_plus_z)) = x__plus_y_plus_z,
    inference(backward_demodulation,[status(thm)],[f57457,f42922]) ).

fof(f58335,plain,
    ! [X0,X1] : X0 = add(X0,multiply(X1,X0)),
    inference(resolution,[status(thm)],[f57219,f265]) ).

fof(f58760,plain,
    ! [X0,X1] : X0 = add(X0,multiply(X0,X1)),
    inference(paramodulation,[status(thm)],[f314,f58335]) ).

fof(f58861,plain,
    ! [X0,X1] : multiply(multiply(X0,X1),X1) = multiply(X0,X1),
    inference(paramodulation,[status(thm)],[f58335,f47048]) ).

fof(f58862,plain,
    ! [X0,X1] : multiply(X0,multiply(X1,X0)) = multiply(X1,X0),
    inference(forward_demodulation,[status(thm)],[f314,f58861]) ).

fof(f66345,plain,
    ! [X0] : add(multiply(multiply(X0,y_plus_z),x),multiply(X0,y_plus_z)) = multiply(x__plus_y_plus_z,multiply(X0,y_plus_z)),
    inference(paramodulation,[status(thm)],[f58862,f17909]) ).

fof(f66346,plain,
    ! [X0] : add(multiply(X0,y_plus_z),multiply(multiply(X0,y_plus_z),x)) = multiply(x__plus_y_plus_z,multiply(X0,y_plus_z)),
    inference(forward_demodulation,[status(thm)],[f218,f66345]) ).

fof(f66347,plain,
    ! [X0] : multiply(X0,y_plus_z) = multiply(x__plus_y_plus_z,multiply(X0,y_plus_z)),
    inference(forward_demodulation,[status(thm)],[f58760,f66346]) ).

fof(f88070,plain,
    multiply(z,y_plus_z) = multiply(x__plus_y_plus_z,z),
    inference(paramodulation,[status(thm)],[f44318,f66347]) ).

fof(f88071,plain,
    z = multiply(x__plus_y_plus_z,z),
    inference(forward_demodulation,[status(thm)],[f44318,f88070]) ).

fof(f88072,plain,
    z = multiply(z,x__plus_y_plus_z),
    inference(forward_demodulation,[status(thm)],[f314,f88071]) ).

fof(f88334,plain,
    add(x_plus_y,z) = x__plus_y_plus_z,
    inference(backward_demodulation,[status(thm)],[f88072,f57652]) ).

fof(f88335,plain,
    x_plus_y__plus_z = x__plus_y_plus_z,
    inference(forward_demodulation,[status(thm)],[f139,f88334]) ).

fof(f88336,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f88335,f64]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : BOO008-1 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33  % Computer : n027.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Tue May 30 11:01:48 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  % Drodi V3.5.1
% 67.11/8.84  % Refutation found
% 67.11/8.84  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 67.11/8.84  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 68.36/8.93  % Elapsed time: 8.575099 seconds
% 68.36/8.93  % CPU time: 68.011506 seconds
% 68.36/8.93  % Memory used: 371.772 MB
%------------------------------------------------------------------------------