TSTP Solution File: FLD041-4 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : FLD041-4 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n002.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 20:16:28 EDT 2024

% Result   : Unsatisfiable 8.07s 1.49s
% Output   : CNFRefutation 8.07s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   30
% Syntax   : Number of formulae    :  103 (  34 unt;   0 def)
%            Number of atoms       :  223 (   0 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  223 ( 103   ~; 111   |;   0   &)
%                                         (   9 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   14 (  13 usr;  10 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-1 aty)
%            Number of variables   :  125 ( 125   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X,V,W,Y,U,Z] :
      ( sum(X,V,W)
      | ~ sum(X,Y,U)
      | ~ sum(Y,Z,V)
      | ~ sum(U,Z,W) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [U,Z,W,X,Y,V] :
      ( sum(U,Z,W)
      | ~ sum(X,Y,U)
      | ~ sum(Y,Z,V)
      | ~ sum(X,V,W) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [X] :
      ( sum(additive_identity,X,X)
      | ~ defined(X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [X] :
      ( sum(additive_inverse(X),X,additive_identity)
      | ~ defined(X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    ! [Y,X,Z] :
      ( sum(Y,X,Z)
      | ~ sum(X,Y,Z) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [X,V,W,Y,U,Z] :
      ( product(X,V,W)
      | ~ product(X,Y,U)
      | ~ product(Y,Z,V)
      | ~ product(U,Z,W) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [X] :
      ( product(multiplicative_identity,X,X)
      | ~ defined(X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [X] :
      ( product(multiplicative_inverse(X),X,multiplicative_identity)
      | sum(additive_identity,X,additive_identity)
      | ~ defined(X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f10,axiom,
    ! [Y,X,Z] :
      ( product(Y,X,Z)
      | ~ product(X,Y,Z) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f11,axiom,
    ! [C,D,B,X,Y,A,Z] :
      ( sum(C,D,B)
      | ~ sum(X,Y,A)
      | ~ product(A,Z,B)
      | ~ product(X,Z,C)
      | ~ product(Y,Z,D) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f14,axiom,
    defined(additive_identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f17,axiom,
    defined(multiplicative_identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f23,axiom,
    ! [X,Y] :
      ( less_or_equal(X,Y)
      | less_or_equal(Y,X)
      | ~ defined(X)
      | ~ defined(Y) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f26,axiom,
    ~ sum(additive_identity,additive_identity,multiplicative_identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f27,hypothesis,
    defined(a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f28,hypothesis,
    defined(b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f29,hypothesis,
    defined(c),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f30,negated_conjecture,
    ~ sum(additive_identity,a,additive_identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f31,negated_conjecture,
    ~ sum(additive_identity,b,additive_identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f32,negated_conjecture,
    product(a,b,c),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f33,negated_conjecture,
    sum(additive_identity,c,additive_identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f34,plain,
    ! [W,U,Z] :
      ( ! [V,Y] :
          ( ! [X] :
              ( sum(X,V,W)
              | ~ sum(X,Y,U) )
          | ~ sum(Y,Z,V) )
      | ~ sum(U,Z,W) ),
    inference(miniscoping,[status(esa)],[f1]) ).

fof(f35,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( sum(X0,X1,X2)
      | ~ sum(X0,X3,X4)
      | ~ sum(X3,X5,X1)
      | ~ sum(X4,X5,X2) ),
    inference(cnf_transformation,[status(esa)],[f34]) ).

fof(f36,plain,
    ! [W,X,V] :
      ( ! [Z,Y] :
          ( ! [U] :
              ( sum(U,Z,W)
              | ~ sum(X,Y,U) )
          | ~ sum(Y,Z,V) )
      | ~ sum(X,V,W) ),
    inference(miniscoping,[status(esa)],[f2]) ).

fof(f37,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( sum(X0,X1,X2)
      | ~ sum(X3,X4,X0)
      | ~ sum(X4,X1,X5)
      | ~ sum(X3,X5,X2) ),
    inference(cnf_transformation,[status(esa)],[f36]) ).

fof(f38,plain,
    ! [X0] :
      ( sum(additive_identity,X0,X0)
      | ~ defined(X0) ),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f39,plain,
    ! [X0] :
      ( sum(additive_inverse(X0),X0,additive_identity)
      | ~ defined(X0) ),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f40,plain,
    ! [X0,X1,X2] :
      ( sum(X0,X1,X2)
      | ~ sum(X1,X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f41,plain,
    ! [W,U,Z] :
      ( ! [V,Y] :
          ( ! [X] :
              ( product(X,V,W)
              | ~ product(X,Y,U) )
          | ~ product(Y,Z,V) )
      | ~ product(U,Z,W) ),
    inference(miniscoping,[status(esa)],[f6]) ).

fof(f42,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( product(X0,X1,X2)
      | ~ product(X0,X3,X4)
      | ~ product(X3,X5,X1)
      | ~ product(X4,X5,X2) ),
    inference(cnf_transformation,[status(esa)],[f41]) ).

fof(f45,plain,
    ! [X0] :
      ( product(multiplicative_identity,X0,X0)
      | ~ defined(X0) ),
    inference(cnf_transformation,[status(esa)],[f8]) ).

fof(f46,plain,
    ! [X0] :
      ( product(multiplicative_inverse(X0),X0,multiplicative_identity)
      | sum(additive_identity,X0,additive_identity)
      | ~ defined(X0) ),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f47,plain,
    ! [X0,X1,X2] :
      ( product(X0,X1,X2)
      | ~ product(X1,X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f10]) ).

fof(f48,plain,
    ! [D,Y,Z] :
      ( ! [C,X] :
          ( ! [B,A] :
              ( sum(C,D,B)
              | ~ sum(X,Y,A)
              | ~ product(A,Z,B) )
          | ~ product(X,Z,C) )
      | ~ product(Y,Z,D) ),
    inference(miniscoping,[status(esa)],[f11]) ).

fof(f49,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( sum(X0,X1,X2)
      | ~ sum(X3,X4,X5)
      | ~ product(X5,X6,X2)
      | ~ product(X3,X6,X0)
      | ~ product(X4,X6,X1) ),
    inference(cnf_transformation,[status(esa)],[f48]) ).

fof(f54,plain,
    defined(additive_identity),
    inference(cnf_transformation,[status(esa)],[f14]) ).

fof(f58,plain,
    defined(multiplicative_identity),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f67,plain,
    ! [Y] :
      ( ! [X] :
          ( less_or_equal(X,Y)
          | less_or_equal(Y,X)
          | ~ defined(X) )
      | ~ defined(Y) ),
    inference(miniscoping,[status(esa)],[f23]) ).

fof(f68,plain,
    ! [X0,X1] :
      ( less_or_equal(X0,X1)
      | less_or_equal(X1,X0)
      | ~ defined(X0)
      | ~ defined(X1) ),
    inference(cnf_transformation,[status(esa)],[f67]) ).

fof(f72,plain,
    ~ sum(additive_identity,additive_identity,multiplicative_identity),
    inference(cnf_transformation,[status(esa)],[f26]) ).

fof(f73,plain,
    defined(a),
    inference(cnf_transformation,[status(esa)],[f27]) ).

fof(f74,plain,
    defined(b),
    inference(cnf_transformation,[status(esa)],[f28]) ).

fof(f75,plain,
    defined(c),
    inference(cnf_transformation,[status(esa)],[f29]) ).

fof(f76,plain,
    ~ sum(additive_identity,a,additive_identity),
    inference(cnf_transformation,[status(esa)],[f30]) ).

fof(f77,plain,
    ~ sum(additive_identity,b,additive_identity),
    inference(cnf_transformation,[status(esa)],[f31]) ).

fof(f78,plain,
    product(a,b,c),
    inference(cnf_transformation,[status(esa)],[f32]) ).

fof(f79,plain,
    sum(additive_identity,c,additive_identity),
    inference(cnf_transformation,[status(esa)],[f33]) ).

fof(f81,plain,
    sum(additive_identity,c,c),
    inference(resolution,[status(thm)],[f38,f75]) ).

fof(f85,plain,
    sum(c,additive_identity,additive_identity),
    inference(resolution,[status(thm)],[f40,f79]) ).

fof(f103,plain,
    product(multiplicative_identity,b,b),
    inference(resolution,[status(thm)],[f45,f74]) ).

fof(f108,plain,
    sum(additive_inverse(b),b,additive_identity),
    inference(resolution,[status(thm)],[f39,f74]) ).

fof(f181,plain,
    ( spl0_5
  <=> sum(additive_identity,b,additive_identity) ),
    introduced(split_symbol_definition) ).

fof(f182,plain,
    ( sum(additive_identity,b,additive_identity)
    | ~ spl0_5 ),
    inference(component_clause,[status(thm)],[f181]) ).

fof(f186,plain,
    ( spl0_6
  <=> product(multiplicative_inverse(a),a,multiplicative_identity) ),
    introduced(split_symbol_definition) ).

fof(f187,plain,
    ( product(multiplicative_inverse(a),a,multiplicative_identity)
    | ~ spl0_6 ),
    inference(component_clause,[status(thm)],[f186]) ).

fof(f189,plain,
    ( spl0_7
  <=> sum(additive_identity,a,additive_identity) ),
    introduced(split_symbol_definition) ).

fof(f190,plain,
    ( sum(additive_identity,a,additive_identity)
    | ~ spl0_7 ),
    inference(component_clause,[status(thm)],[f189]) ).

fof(f192,plain,
    ( product(multiplicative_inverse(a),a,multiplicative_identity)
    | sum(additive_identity,a,additive_identity) ),
    inference(resolution,[status(thm)],[f46,f73]) ).

fof(f193,plain,
    ( spl0_6
    | spl0_7 ),
    inference(split_clause,[status(thm)],[f192,f186,f189]) ).

fof(f209,plain,
    ! [X0,X1,X2] :
      ( product(multiplicative_inverse(a),X0,X1)
      | ~ product(a,X2,X0)
      | ~ product(multiplicative_identity,X2,X1)
      | ~ spl0_6 ),
    inference(resolution,[status(thm)],[f187,f42]) ).

fof(f212,plain,
    ! [X0] :
      ( product(multiplicative_inverse(a),c,X0)
      | ~ product(multiplicative_identity,b,X0)
      | ~ spl0_6 ),
    inference(resolution,[status(thm)],[f209,f78]) ).

fof(f259,plain,
    ! [X0,X1,X2] :
      ( sum(c,X0,X1)
      | ~ sum(additive_identity,X2,X0)
      | ~ sum(additive_identity,X2,X1) ),
    inference(resolution,[status(thm)],[f85,f35]) ).

fof(f286,plain,
    ! [X0] :
      ( sum(c,c,X0)
      | ~ sum(additive_identity,c,X0) ),
    inference(resolution,[status(thm)],[f259,f81]) ).

fof(f289,plain,
    sum(c,c,c),
    inference(resolution,[status(thm)],[f286,f81]) ).

fof(f378,plain,
    ( $false
    | ~ spl0_7 ),
    inference(forward_subsumption_resolution,[status(thm)],[f190,f76]) ).

fof(f379,plain,
    ~ spl0_7,
    inference(contradiction_clause,[status(thm)],[f378]) ).

fof(f380,plain,
    ( $false
    | ~ spl0_5 ),
    inference(forward_subsumption_resolution,[status(thm)],[f182,f77]) ).

fof(f381,plain,
    ~ spl0_5,
    inference(contradiction_clause,[status(thm)],[f380]) ).

fof(f384,plain,
    ! [X0] :
      ( less_or_equal(multiplicative_identity,X0)
      | less_or_equal(X0,multiplicative_identity)
      | ~ defined(X0) ),
    inference(resolution,[status(thm)],[f68,f58]) ).

fof(f385,plain,
    ! [X0] :
      ( less_or_equal(c,X0)
      | less_or_equal(X0,c)
      | ~ defined(X0) ),
    inference(resolution,[status(thm)],[f68,f75]) ).

fof(f386,plain,
    ! [X0] :
      ( less_or_equal(b,X0)
      | less_or_equal(X0,b)
      | ~ defined(X0) ),
    inference(resolution,[status(thm)],[f68,f74]) ).

fof(f387,plain,
    ! [X0] :
      ( less_or_equal(a,X0)
      | less_or_equal(X0,a)
      | ~ defined(X0) ),
    inference(resolution,[status(thm)],[f68,f73]) ).

fof(f388,plain,
    ! [X0] :
      ( less_or_equal(additive_identity,X0)
      | less_or_equal(X0,additive_identity)
      | ~ defined(X0) ),
    inference(resolution,[status(thm)],[f68,f54]) ).

fof(f561,plain,
    ! [X0,X1,X2,X3] :
      ( sum(X0,X1,X2)
      | ~ product(c,X3,X2)
      | ~ product(c,X3,X0)
      | ~ product(c,X3,X1) ),
    inference(resolution,[status(thm)],[f289,f49]) ).

fof(f747,plain,
    ( spl0_37
  <=> less_or_equal(additive_identity,additive_identity) ),
    introduced(split_symbol_definition) ).

fof(f1275,plain,
    ( product(multiplicative_inverse(a),c,b)
    | ~ spl0_6 ),
    inference(resolution,[status(thm)],[f103,f212]) ).

fof(f1656,plain,
    ! [X0,X1,X2] :
      ( sum(additive_identity,X0,X1)
      | ~ sum(b,X0,X2)
      | ~ sum(additive_inverse(b),X2,X1) ),
    inference(resolution,[status(thm)],[f108,f37]) ).

fof(f1705,plain,
    ( product(c,multiplicative_inverse(a),b)
    | ~ spl0_6 ),
    inference(resolution,[status(thm)],[f1275,f47]) ).

fof(f2522,plain,
    ( spl0_188
  <=> less_or_equal(c,c) ),
    introduced(split_symbol_definition) ).

fof(f2525,plain,
    ( less_or_equal(c,c)
    | less_or_equal(c,c) ),
    inference(resolution,[status(thm)],[f385,f75]) ).

fof(f2526,plain,
    spl0_188,
    inference(split_clause,[status(thm)],[f2525,f2522]) ).

fof(f2720,plain,
    ( spl0_236
  <=> less_or_equal(b,b) ),
    introduced(split_symbol_definition) ).

fof(f2723,plain,
    ( less_or_equal(b,b)
    | less_or_equal(b,b) ),
    inference(resolution,[status(thm)],[f386,f74]) ).

fof(f2724,plain,
    spl0_236,
    inference(split_clause,[status(thm)],[f2723,f2720]) ).

fof(f2975,plain,
    ( spl0_280
  <=> less_or_equal(multiplicative_identity,multiplicative_identity) ),
    introduced(split_symbol_definition) ).

fof(f2978,plain,
    ( less_or_equal(multiplicative_identity,multiplicative_identity)
    | less_or_equal(multiplicative_identity,multiplicative_identity) ),
    inference(resolution,[status(thm)],[f384,f58]) ).

fof(f2979,plain,
    spl0_280,
    inference(split_clause,[status(thm)],[f2978,f2975]) ).

fof(f3460,plain,
    ( spl0_369
  <=> less_or_equal(a,a) ),
    introduced(split_symbol_definition) ).

fof(f3463,plain,
    ( less_or_equal(a,a)
    | less_or_equal(a,a) ),
    inference(resolution,[status(thm)],[f387,f73]) ).

fof(f3464,plain,
    spl0_369,
    inference(split_clause,[status(thm)],[f3463,f3460]) ).

fof(f3619,plain,
    ( less_or_equal(additive_identity,additive_identity)
    | less_or_equal(additive_identity,additive_identity) ),
    inference(resolution,[status(thm)],[f388,f54]) ).

fof(f3620,plain,
    spl0_37,
    inference(split_clause,[status(thm)],[f3619,f747]) ).

fof(f4723,plain,
    ! [X0,X1] :
      ( sum(X0,X1,b)
      | ~ product(c,multiplicative_inverse(a),X0)
      | ~ product(c,multiplicative_inverse(a),X1)
      | ~ spl0_6 ),
    inference(resolution,[status(thm)],[f1705,f561]) ).

fof(f4794,plain,
    ! [X0] :
      ( sum(b,X0,b)
      | ~ product(c,multiplicative_inverse(a),X0)
      | ~ spl0_6 ),
    inference(resolution,[status(thm)],[f4723,f1705]) ).

fof(f4796,plain,
    ( sum(b,b,b)
    | ~ spl0_6 ),
    inference(resolution,[status(thm)],[f4794,f1705]) ).

fof(f6612,plain,
    ( spl0_716
  <=> sum(additive_identity,additive_identity,multiplicative_identity) ),
    introduced(split_symbol_definition) ).

fof(f6613,plain,
    ( sum(additive_identity,additive_identity,multiplicative_identity)
    | ~ spl0_716 ),
    inference(component_clause,[status(thm)],[f6612]) ).

fof(f6617,plain,
    ( $false
    | ~ spl0_716 ),
    inference(forward_subsumption_resolution,[status(thm)],[f6613,f72]) ).

fof(f6618,plain,
    ~ spl0_716,
    inference(contradiction_clause,[status(thm)],[f6617]) ).

fof(f8147,plain,
    ! [X0] :
      ( sum(additive_identity,b,X0)
      | ~ sum(additive_inverse(b),b,X0)
      | ~ spl0_6 ),
    inference(resolution,[status(thm)],[f4796,f1656]) ).

fof(f8161,plain,
    ( sum(additive_identity,b,additive_identity)
    | ~ spl0_6 ),
    inference(resolution,[status(thm)],[f8147,f108]) ).

fof(f8162,plain,
    ( spl0_5
    | ~ spl0_6 ),
    inference(split_clause,[status(thm)],[f8161,f181,f186]) ).

fof(f8163,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f193,f379,f381,f2526,f2724,f2979,f3464,f3620,f6618,f8162]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : FLD041-4 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.32  % Computer : n002.cluster.edu
% 0.10/0.32  % Model    : x86_64 x86_64
% 0.10/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32  % Memory   : 8042.1875MB
% 0.10/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32  % CPULimit : 300
% 0.10/0.32  % WCLimit  : 300
% 0.10/0.32  % DateTime : Mon Apr 29 23:38:54 EDT 2024
% 0.10/0.32  % CPUTime  : 
% 0.10/0.32  % Drodi V3.6.0
% 8.07/1.49  % Refutation found
% 8.07/1.49  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 8.07/1.49  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 8.07/1.53  % Elapsed time: 1.199447 seconds
% 8.07/1.53  % CPU time: 8.197033 seconds
% 8.07/1.53  % Total memory used: 72.517 MB
% 8.07/1.53  % Net memory used: 67.320 MB
%------------------------------------------------------------------------------