TSTP Solution File: RNG004-1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : RNG004-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n008.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 20:37:39 EDT 2024

% Result   : Unsatisfiable 3.57s 0.83s
% Output   : CNFRefutation 3.57s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   79 (  47 unt;   0 def)
%            Number of atoms       :  147 (  20 equ)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :  138 (  70   ~;  68   |;   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   :  153 ( 153   !;   0   ?)

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

fof(f2,axiom,
    ! [X] : sum(X,additive_identity,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(f18,hypothesis,
    product(a,b,c),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f19,hypothesis,
    product(additive_inverse(a),additive_inverse(b),d),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f20,negated_conjecture,
    c != d,
    file('/export/starexec/sandbox2/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(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)],[f12]) ).

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(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,c),
    inference(cnf_transformation,[status(esa)],[f18]) ).

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

fof(f50,plain,
    c != d,
    inference(cnf_transformation,[status(esa)],[f20]) ).

fof(f55,plain,
    ! [X0,X1] : sum(X0,X1,add(X1,X0)),
    inference(resolution,[status(thm)],[f31,f24]) ).

fof(f58,plain,
    ! [X0,X1] :
      ( ~ sum(additive_identity,X0,X1)
      | X1 = X0 ),
    inference(resolution,[status(thm)],[f45,f21]) ).

fof(f60,plain,
    ! [X0,X1] :
      ( ~ sum(X0,additive_identity,X1)
      | X1 = X0 ),
    inference(resolution,[status(thm)],[f45,f22]) ).

fof(f61,plain,
    ! [X0,X1,X2] :
      ( ~ sum(X0,X1,X2)
      | X2 = add(X1,X0) ),
    inference(resolution,[status(thm)],[f45,f55]) ).

fof(f62,plain,
    ! [X0,X1,X2] :
      ( ~ sum(X0,X1,X2)
      | X2 = add(X0,X1) ),
    inference(resolution,[status(thm)],[f45,f24]) ).

fof(f64,plain,
    ! [X0] : add(X0,additive_identity) = X0,
    inference(resolution,[status(thm)],[f58,f55]) ).

fof(f76,plain,
    ! [X0,X1] :
      ( ~ sum(X0,X1,X1)
      | sum(X0,additive_identity,additive_identity) ),
    inference(resolution,[status(thm)],[f28,f26]) ).

fof(f84,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(f133,plain,
    ! [X0,X1] : add(X0,X1) = add(X1,X0),
    inference(resolution,[status(thm)],[f61,f24]) ).

fof(f195,plain,
    ! [X0,X1] :
      ( ~ product(a,X0,X1)
      | ~ sum(X0,b,b)
      | sum(X1,c,c) ),
    inference(resolution,[status(thm)],[f37,f48]) ).

fof(f196,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product(a,X0,X1)
      | ~ sum(X0,b,X2)
      | ~ product(a,X2,X3)
      | sum(X1,c,X3) ),
    inference(resolution,[status(thm)],[f37,f48]) ).

fof(f257,plain,
    ! [X0] :
      ( ~ sum(X0,b,b)
      | sum(multiply(a,X0),c,c) ),
    inference(resolution,[status(thm)],[f195,f23]) ).

fof(f258,plain,
    sum(multiply(a,additive_identity),c,c),
    inference(resolution,[status(thm)],[f257,f21]) ).

fof(f259,plain,
    sum(multiply(a,additive_identity),additive_identity,additive_identity),
    inference(resolution,[status(thm)],[f258,f76]) ).

fof(f274,plain,
    additive_identity = multiply(a,additive_identity),
    inference(resolution,[status(thm)],[f259,f60]) ).

fof(f292,plain,
    product(a,additive_identity,additive_identity),
    inference(paramodulation,[status(thm)],[f274,f23]) ).

fof(f331,plain,
    ! [X0,X1] :
      ( ~ product(a,X0,X1)
      | ~ sum(X0,b,additive_identity)
      | sum(X1,c,additive_identity) ),
    inference(resolution,[status(thm)],[f196,f292]) ).

fof(f438,plain,
    ! [X0,X1] :
      ( ~ product(X0,additive_inverse(b),X1)
      | ~ sum(X0,additive_inverse(a),additive_inverse(a))
      | sum(X1,d,d) ),
    inference(resolution,[status(thm)],[f41,f49]) ).

fof(f439,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product(X0,additive_inverse(b),X1)
      | ~ sum(X0,additive_inverse(a),X2)
      | ~ product(X2,additive_inverse(b),X3)
      | sum(X1,d,X3) ),
    inference(resolution,[status(thm)],[f41,f49]) ).

fof(f573,plain,
    ! [X0] :
      ( ~ product(additive_identity,additive_inverse(b),X0)
      | sum(X0,d,d) ),
    inference(resolution,[status(thm)],[f438,f21]) ).

fof(f612,plain,
    sum(multiply(additive_identity,additive_inverse(b)),d,d),
    inference(resolution,[status(thm)],[f573,f23]) ).

fof(f615,plain,
    sum(multiply(additive_identity,additive_inverse(b)),additive_identity,additive_identity),
    inference(resolution,[status(thm)],[f612,f76]) ).

fof(f630,plain,
    additive_identity = multiply(additive_identity,additive_inverse(b)),
    inference(resolution,[status(thm)],[f615,f60]) ).

fof(f676,plain,
    ! [X0,X1,X2] :
      ( ~ product(X0,additive_inverse(b),X1)
      | ~ sum(X0,additive_inverse(a),X2)
      | sum(X1,d,multiply(X2,additive_inverse(b))) ),
    inference(resolution,[status(thm)],[f439,f23]) ).

fof(f757,plain,
    ! [X0,X1,X2] :
      ( ~ sum(X0,X1,X2)
      | sum(additive_inverse(X0),X2,X1) ),
    inference(resolution,[status(thm)],[f84,f25]) ).

fof(f759,plain,
    ! [X0,X1,X2] :
      ( ~ sum(additive_inverse(X0),X1,X2)
      | sum(X0,X2,X1) ),
    inference(resolution,[status(thm)],[f84,f26]) ).

fof(f761,plain,
    ! [X0] : sum(additive_inverse(additive_inverse(X0)),additive_identity,X0),
    inference(resolution,[status(thm)],[f757,f25]) ).

fof(f767,plain,
    ! [X0,X1] : sum(additive_inverse(X0),add(X0,X1),X1),
    inference(resolution,[status(thm)],[f757,f24]) ).

fof(f773,plain,
    ! [X0] : X0 = additive_inverse(additive_inverse(X0)),
    inference(resolution,[status(thm)],[f761,f60]) ).

fof(f861,plain,
    ! [X0,X1] : X0 = add(additive_inverse(X1),add(X1,X0)),
    inference(resolution,[status(thm)],[f767,f62]) ).

fof(f871,plain,
    ! [X0,X1] : sum(add(X0,X1),additive_inverse(X0),X1),
    inference(resolution,[status(thm)],[f767,f31]) ).

fof(f1378,plain,
    ! [X0,X1] : sum(add(additive_inverse(X0),X1),X0,X1),
    inference(paramodulation,[status(thm)],[f773,f871]) ).

fof(f1826,plain,
    ! [X0,X1] :
      ( ~ sum(X0,additive_inverse(a),X1)
      | sum(multiply(X0,additive_inverse(b)),d,multiply(X1,additive_inverse(b))) ),
    inference(resolution,[status(thm)],[f676,f23]) ).

fof(f2318,plain,
    ! [X0] :
      ( ~ sum(X0,b,additive_identity)
      | sum(multiply(a,X0),c,additive_identity) ),
    inference(resolution,[status(thm)],[f331,f23]) ).

fof(f2319,plain,
    sum(multiply(a,add(additive_inverse(b),additive_identity)),c,additive_identity),
    inference(resolution,[status(thm)],[f2318,f1378]) ).

fof(f2320,plain,
    sum(multiply(a,additive_inverse(b)),c,additive_identity),
    inference(forward_demodulation,[status(thm)],[f64,f2319]) ).

fof(f2329,plain,
    additive_identity = add(multiply(a,additive_inverse(b)),c),
    inference(resolution,[status(thm)],[f2320,f62]) ).

fof(f2330,plain,
    additive_identity = add(c,multiply(a,additive_inverse(b))),
    inference(forward_demodulation,[status(thm)],[f133,f2329]) ).

fof(f2341,plain,
    multiply(a,additive_inverse(b)) = add(additive_inverse(c),additive_identity),
    inference(paramodulation,[status(thm)],[f2330,f861]) ).

fof(f2342,plain,
    multiply(a,additive_inverse(b)) = additive_inverse(c),
    inference(forward_demodulation,[status(thm)],[f64,f2341]) ).

fof(f3588,plain,
    sum(multiply(additive_inverse(additive_inverse(a)),additive_inverse(b)),d,multiply(additive_identity,additive_inverse(b))),
    inference(resolution,[status(thm)],[f1826,f25]) ).

fof(f3589,plain,
    sum(multiply(a,additive_inverse(b)),d,multiply(additive_identity,additive_inverse(b))),
    inference(forward_demodulation,[status(thm)],[f773,f3588]) ).

fof(f3590,plain,
    sum(additive_inverse(c),d,multiply(additive_identity,additive_inverse(b))),
    inference(forward_demodulation,[status(thm)],[f2342,f3589]) ).

fof(f3591,plain,
    sum(additive_inverse(c),d,additive_identity),
    inference(forward_demodulation,[status(thm)],[f630,f3590]) ).

fof(f3601,plain,
    sum(c,additive_identity,d),
    inference(resolution,[status(thm)],[f3591,f759]) ).

fof(f3624,plain,
    d = c,
    inference(resolution,[status(thm)],[f3601,f60]) ).

fof(f3625,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f3624,f50]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : RNG004-1 : TPTP v8.1.2. Released v1.0.0.
% 0.08/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.34  % Computer : n008.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.35  % DateTime : Mon Apr 29 22:21:13 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.14/0.36  % Drodi V3.6.0
% 3.57/0.83  % Refutation found
% 3.57/0.83  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 3.57/0.83  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.57/0.86  % Elapsed time: 0.503152 seconds
% 3.57/0.86  % CPU time: 3.845637 seconds
% 3.57/0.86  % Total memory used: 57.059 MB
% 3.57/0.86  % Net memory used: 52.586 MB
%------------------------------------------------------------------------------