TSTP Solution File: GRP617-1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : GRP617-1 : TPTP v8.1.2. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n014.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 12:12:13 EDT 2023

% Result   : Unsatisfiable 5.24s 1.04s
% Output   : CNFRefutation 5.50s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   94 (  54 unt;   0 def)
%            Number of atoms       :  167 (  31 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  148 (  75   ~;  73   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :  176 (; 176   !;   0   ?)

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

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

fof(f3,axiom,
    ! [X] : product(inverse(X),X,identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [X] : product(X,inverse(X),identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    ! [X,Y] : product(X,Y,multiply(X,Y)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

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

fof(f8,axiom,
    ! [X,Y,U,Z,V,W] :
      ( ~ product(X,Y,U)
      | ~ product(Y,Z,V)
      | ~ product(X,V,W)
      | product(U,Z,W) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [X] :
      ( ~ subgroup1_member(X)
      | subgroup1_member(inverse(X)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f10,axiom,
    ! [A,B,C] :
      ( ~ subgroup1_member(A)
      | ~ subgroup1_member(B)
      | ~ product(A,B,C)
      | subgroup1_member(C) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f11,axiom,
    ! [X] :
      ( ~ subgroup2_member(X)
      | subgroup2_member(inverse(X)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f12,axiom,
    ! [A,B,C] :
      ( ~ subgroup2_member(A)
      | ~ subgroup2_member(B)
      | ~ product(A,B,C)
      | subgroup2_member(C) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f13,hypothesis,
    ! [X,A] :
      ( ~ subgroup1_member(X)
      | subgroup1_member(multiply(A,multiply(X,inverse(A)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f14,hypothesis,
    ! [X,A] :
      ( ~ subgroup2_member(X)
      | subgroup2_member(multiply(A,multiply(X,inverse(A)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f15,hypothesis,
    ! [X] :
      ( ~ subgroup1_member(X)
      | ~ subgroup2_member(X)
      | X = identity ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f16,hypothesis,
    subgroup1_member(v),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f17,hypothesis,
    subgroup2_member(u),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f18,negated_conjecture,
    multiply(v,u) != multiply(u,v),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f19,plain,
    ! [X0] : product(identity,X0,X0),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f20,plain,
    ! [X0] : product(X0,identity,X0),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f21,plain,
    ! [X0] : product(inverse(X0),X0,identity),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f22,plain,
    ! [X0] : product(X0,inverse(X0),identity),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f23,plain,
    ! [X0,X1] : product(X0,X1,multiply(X0,X1)),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f24,plain,
    ! [Z,W] :
      ( ! [X,Y] :
          ( ~ product(X,Y,Z)
          | ~ product(X,Y,W) )
      | Z = W ),
    inference(miniscoping,[status(esa)],[f6]) ).

fof(f25,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product(X0,X1,X2)
      | ~ product(X0,X1,X3)
      | X2 = X3 ),
    inference(cnf_transformation,[status(esa)],[f24]) ).

fof(f26,plain,
    ! [X,V,W] :
      ( ! [U,Z] :
          ( ! [Y] :
              ( ~ product(X,Y,U)
              | ~ product(Y,Z,V) )
          | ~ product(U,Z,W) )
      | product(X,V,W) ),
    inference(miniscoping,[status(esa)],[f7]) ).

fof(f27,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ~ product(X0,X1,X2)
      | ~ product(X1,X3,X4)
      | ~ product(X2,X3,X5)
      | product(X0,X4,X5) ),
    inference(cnf_transformation,[status(esa)],[f26]) ).

fof(f28,plain,
    ! [U,Z,W] :
      ( ! [X,V] :
          ( ! [Y] :
              ( ~ product(X,Y,U)
              | ~ product(Y,Z,V) )
          | ~ product(X,V,W) )
      | product(U,Z,W) ),
    inference(miniscoping,[status(esa)],[f8]) ).

fof(f29,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ~ product(X0,X1,X2)
      | ~ product(X1,X3,X4)
      | ~ product(X0,X4,X5)
      | product(X2,X3,X5) ),
    inference(cnf_transformation,[status(esa)],[f28]) ).

fof(f30,plain,
    ! [X0] :
      ( ~ subgroup1_member(X0)
      | subgroup1_member(inverse(X0)) ),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f31,plain,
    ! [C] :
      ( ! [A,B] :
          ( ~ subgroup1_member(A)
          | ~ subgroup1_member(B)
          | ~ product(A,B,C) )
      | subgroup1_member(C) ),
    inference(miniscoping,[status(esa)],[f10]) ).

fof(f32,plain,
    ! [X0,X1,X2] :
      ( ~ subgroup1_member(X0)
      | ~ subgroup1_member(X1)
      | ~ product(X0,X1,X2)
      | subgroup1_member(X2) ),
    inference(cnf_transformation,[status(esa)],[f31]) ).

fof(f33,plain,
    ! [X0] :
      ( ~ subgroup2_member(X0)
      | subgroup2_member(inverse(X0)) ),
    inference(cnf_transformation,[status(esa)],[f11]) ).

fof(f34,plain,
    ! [C] :
      ( ! [A,B] :
          ( ~ subgroup2_member(A)
          | ~ subgroup2_member(B)
          | ~ product(A,B,C) )
      | subgroup2_member(C) ),
    inference(miniscoping,[status(esa)],[f12]) ).

fof(f35,plain,
    ! [X0,X1,X2] :
      ( ~ subgroup2_member(X0)
      | ~ subgroup2_member(X1)
      | ~ product(X0,X1,X2)
      | subgroup2_member(X2) ),
    inference(cnf_transformation,[status(esa)],[f34]) ).

fof(f36,plain,
    ! [X] :
      ( ~ subgroup1_member(X)
      | ! [A] : subgroup1_member(multiply(A,multiply(X,inverse(A)))) ),
    inference(miniscoping,[status(esa)],[f13]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( ~ subgroup1_member(X0)
      | subgroup1_member(multiply(X1,multiply(X0,inverse(X1)))) ),
    inference(cnf_transformation,[status(esa)],[f36]) ).

fof(f38,plain,
    ! [X] :
      ( ~ subgroup2_member(X)
      | ! [A] : subgroup2_member(multiply(A,multiply(X,inverse(A)))) ),
    inference(miniscoping,[status(esa)],[f14]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( ~ subgroup2_member(X0)
      | subgroup2_member(multiply(X1,multiply(X0,inverse(X1)))) ),
    inference(cnf_transformation,[status(esa)],[f38]) ).

fof(f40,plain,
    ! [X0] :
      ( ~ subgroup1_member(X0)
      | ~ subgroup2_member(X0)
      | X0 = identity ),
    inference(cnf_transformation,[status(esa)],[f15]) ).

fof(f41,plain,
    subgroup1_member(v),
    inference(cnf_transformation,[status(esa)],[f16]) ).

fof(f42,plain,
    subgroup2_member(u),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f43,plain,
    multiply(v,u) != multiply(u,v),
    inference(cnf_transformation,[status(esa)],[f18]) ).

fof(f44,plain,
    subgroup1_member(inverse(v)),
    inference(resolution,[status(thm)],[f30,f41]) ).

fof(f54,plain,
    subgroup2_member(inverse(u)),
    inference(resolution,[status(thm)],[f33,f42]) ).

fof(f90,plain,
    ! [X0,X1] :
      ( ~ product(inverse(X0),X0,X1)
      | identity = X1 ),
    inference(resolution,[status(thm)],[f25,f21]) ).

fof(f91,plain,
    ! [X0,X1] :
      ( ~ product(identity,X0,X1)
      | X0 = X1 ),
    inference(resolution,[status(thm)],[f25,f19]) ).

fof(f94,plain,
    ! [X0,X1,X2] :
      ( ~ product(X0,X1,X2)
      | multiply(X0,X1) = X2 ),
    inference(resolution,[status(thm)],[f25,f23]) ).

fof(f95,plain,
    inverse(identity) = identity,
    inference(resolution,[status(thm)],[f91,f22]) ).

fof(f96,plain,
    ! [X0] : X0 = multiply(identity,X0),
    inference(resolution,[status(thm)],[f91,f23]) ).

fof(f104,plain,
    ! [X0] : identity = multiply(inverse(X0),X0),
    inference(resolution,[status(thm)],[f90,f23]) ).

fof(f121,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ product(X0,X1,X2)
      | ~ product(multiply(X3,X0),X1,X4)
      | product(X3,X2,X4) ),
    inference(resolution,[status(thm)],[f27,f23]) ).

fof(f126,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ product(X0,X1,X2)
      | ~ product(X3,X2,X4)
      | product(multiply(X3,X0),X1,X4) ),
    inference(resolution,[status(thm)],[f29,f23]) ).

fof(f144,plain,
    ! [X0,X1] :
      ( ~ subgroup1_member(X0)
      | ~ subgroup1_member(X1)
      | subgroup1_member(multiply(X0,X1)) ),
    inference(resolution,[status(thm)],[f32,f23]) ).

fof(f157,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product(multiply(X0,X1),X2,X3)
      | product(X0,multiply(X1,X2),X3) ),
    inference(resolution,[status(thm)],[f121,f23]) ).

fof(f158,plain,
    ! [X0,X1,X2] :
      ( ~ product(X0,identity,X1)
      | product(multiply(X0,inverse(X2)),X2,X1) ),
    inference(resolution,[status(thm)],[f126,f21]) ).

fof(f162,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product(X0,multiply(X1,X2),X3)
      | product(multiply(X0,X1),X2,X3) ),
    inference(resolution,[status(thm)],[f126,f23]) ).

fof(f253,plain,
    ! [X0,X1,X2] : product(X0,multiply(X1,X2),multiply(multiply(X0,X1),X2)),
    inference(resolution,[status(thm)],[f157,f23]) ).

fof(f297,plain,
    ! [X0,X1] : product(multiply(X0,inverse(X1)),X1,X0),
    inference(resolution,[status(thm)],[f158,f20]) ).

fof(f316,plain,
    ! [X0,X1] : multiply(multiply(X0,inverse(X1)),X1) = X0,
    inference(resolution,[status(thm)],[f297,f94]) ).

fof(f328,plain,
    ! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
    inference(paramodulation,[status(thm)],[f104,f316]) ).

fof(f329,plain,
    ! [X0] : X0 = inverse(inverse(X0)),
    inference(forward_demodulation,[status(thm)],[f96,f328]) ).

fof(f359,plain,
    ! [X0,X1] : multiply(multiply(X0,X1),inverse(X1)) = X0,
    inference(paramodulation,[status(thm)],[f329,f316]) ).

fof(f438,plain,
    ! [X0,X1,X2] : product(multiply(X0,X1),X2,multiply(X0,multiply(X1,X2))),
    inference(resolution,[status(thm)],[f162,f23]) ).

fof(f498,plain,
    ! [X0,X1] :
      ( ~ subgroup2_member(X0)
      | ~ subgroup2_member(X1)
      | subgroup2_member(multiply(X0,X1)) ),
    inference(resolution,[status(thm)],[f35,f23]) ).

fof(f501,plain,
    ! [X0] :
      ( ~ subgroup2_member(X0)
      | subgroup2_member(multiply(u,X0)) ),
    inference(resolution,[status(thm)],[f498,f42]) ).

fof(f576,plain,
    ! [X0] : subgroup1_member(multiply(X0,multiply(v,inverse(X0)))),
    inference(resolution,[status(thm)],[f37,f41]) ).

fof(f587,plain,
    ! [X0] : subgroup2_member(multiply(X0,multiply(inverse(u),inverse(X0)))),
    inference(resolution,[status(thm)],[f39,f54]) ).

fof(f613,plain,
    ! [X0,X1] :
      ( ~ subgroup1_member(X0)
      | subgroup1_member(multiply(multiply(X1,multiply(v,inverse(X1))),X0)) ),
    inference(resolution,[status(thm)],[f576,f144]) ).

fof(f663,plain,
    ! [X0] : subgroup2_member(multiply(u,multiply(X0,multiply(inverse(u),inverse(X0))))),
    inference(resolution,[status(thm)],[f587,f501]) ).

fof(f776,plain,
    ! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,X1),X2),
    inference(resolution,[status(thm)],[f253,f94]) ).

fof(f799,plain,
    ! [X0,X1] : product(inverse(X0),multiply(X0,X1),multiply(identity,X1)),
    inference(paramodulation,[status(thm)],[f104,f253]) ).

fof(f800,plain,
    ! [X0,X1] : product(inverse(X0),multiply(X0,X1),X1),
    inference(forward_demodulation,[status(thm)],[f96,f799]) ).

fof(f858,plain,
    ! [X0] : subgroup1_member(multiply(multiply(X0,multiply(v,inverse(X0))),inverse(v))),
    inference(resolution,[status(thm)],[f613,f44]) ).

fof(f868,plain,
    ! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
    inference(resolution,[status(thm)],[f800,f94]) ).

fof(f909,plain,
    ! [X0,X1] : multiply(inverse(multiply(X0,inverse(X1))),X0) = X1,
    inference(paramodulation,[status(thm)],[f316,f868]) ).

fof(f910,plain,
    ! [X0,X1] : multiply(inverse(multiply(X0,X1)),X0) = inverse(X1),
    inference(paramodulation,[status(thm)],[f359,f868]) ).

fof(f1132,plain,
    ! [X0,X1] : multiply(X0,inverse(X1)) = inverse(multiply(X1,inverse(X0))),
    inference(paramodulation,[status(thm)],[f909,f359]) ).

fof(f1144,plain,
    ! [X0,X1] : multiply(inverse(X0),inverse(X1)) = inverse(multiply(X1,X0)),
    inference(paramodulation,[status(thm)],[f868,f910]) ).

fof(f1588,plain,
    ! [X0,X1,X2] : product(multiply(X0,multiply(X1,inverse(X2))),X2,multiply(X0,X1)),
    inference(paramodulation,[status(thm)],[f316,f438]) ).

fof(f4594,plain,
    ! [X0] : subgroup2_member(multiply(u,multiply(X0,inverse(multiply(X0,u))))),
    inference(forward_demodulation,[status(thm)],[f1144,f663]) ).

fof(f4614,plain,
    ! [X0] :
      ( ~ subgroup1_member(multiply(u,multiply(X0,inverse(multiply(X0,u)))))
      | multiply(u,multiply(X0,inverse(multiply(X0,u)))) = identity ),
    inference(resolution,[status(thm)],[f4594,f40]) ).

fof(f7001,plain,
    ! [X0] : subgroup1_member(multiply(X0,multiply(multiply(v,inverse(X0)),inverse(v)))),
    inference(forward_demodulation,[status(thm)],[f776,f858]) ).

fof(f7002,plain,
    ! [X0] : subgroup1_member(multiply(X0,multiply(v,multiply(inverse(X0),inverse(v))))),
    inference(forward_demodulation,[status(thm)],[f776,f7001]) ).

fof(f7003,plain,
    ! [X0] : subgroup1_member(multiply(X0,multiply(v,inverse(multiply(v,X0))))),
    inference(forward_demodulation,[status(thm)],[f1144,f7002]) ).

fof(f36854,plain,
    multiply(u,multiply(v,inverse(multiply(v,u)))) = identity,
    inference(resolution,[status(thm)],[f4614,f7003]) ).

fof(f51887,plain,
    multiply(inverse(identity),u) = inverse(multiply(v,inverse(multiply(v,u)))),
    inference(paramodulation,[status(thm)],[f36854,f910]) ).

fof(f51888,plain,
    multiply(identity,u) = inverse(multiply(v,inverse(multiply(v,u)))),
    inference(forward_demodulation,[status(thm)],[f95,f51887]) ).

fof(f51889,plain,
    u = inverse(multiply(v,inverse(multiply(v,u)))),
    inference(forward_demodulation,[status(thm)],[f96,f51888]) ).

fof(f51890,plain,
    u = multiply(multiply(v,u),inverse(v)),
    inference(forward_demodulation,[status(thm)],[f1132,f51889]) ).

fof(f51891,plain,
    u = multiply(v,multiply(u,inverse(v))),
    inference(forward_demodulation,[status(thm)],[f776,f51890]) ).

fof(f52149,plain,
    product(u,v,multiply(v,u)),
    inference(paramodulation,[status(thm)],[f51891,f1588]) ).

fof(f52640,plain,
    multiply(u,v) = multiply(v,u),
    inference(resolution,[status(thm)],[f52149,f94]) ).

fof(f52641,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f52640,f43]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : GRP617-1 : TPTP v8.1.2. Released v3.1.0.
% 0.04/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n014.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % 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 : Tue May 30 11:23:34 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  % Drodi V3.5.1
% 5.24/1.04  % Refutation found
% 5.24/1.04  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 5.24/1.04  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 5.50/1.10  % Elapsed time: 0.735054 seconds
% 5.50/1.10  % CPU time: 5.565068 seconds
% 5.50/1.10  % Memory used: 79.159 MB
%------------------------------------------------------------------------------