TSTP Solution File: GRP087-1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : GRP087-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n005.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 20:19:11 EDT 2024

% Result   : Unsatisfiable 0.21s 0.40s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   26
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   63 (  42 unt;   0 def)
%            Number of atoms       :   90 (  59 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   49 (  22   ~;  23   |;   0   &)
%                                         (   4 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    6 (   4 usr;   5 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   9 con; 0-2 aty)
%            Number of variables   :  100 ( 100   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X,Y,Z] : multiply(X,multiply(multiply(inverse(multiply(X,Y)),Z),Y)) = Z,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f2,negated_conjecture,
    ( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
    | multiply(multiply(inverse(b2),b2),a2) != a2
    | multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
    | multiply(a4,b4) != multiply(b4,a4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f3,plain,
    ! [X0,X1,X2] : multiply(X0,multiply(multiply(inverse(multiply(X0,X1)),X2),X1)) = X2,
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f4,plain,
    ( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
    | multiply(multiply(inverse(b2),b2),a2) != a2
    | multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
    | multiply(a4,b4) != multiply(b4,a4) ),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f5,plain,
    ( spl0_0
  <=> multiply(inverse(a1),a1) = multiply(inverse(b1),b1) ),
    introduced(split_symbol_definition) ).

fof(f7,plain,
    ( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f5]) ).

fof(f8,plain,
    ( spl0_1
  <=> multiply(multiply(inverse(b2),b2),a2) = a2 ),
    introduced(split_symbol_definition) ).

fof(f10,plain,
    ( multiply(multiply(inverse(b2),b2),a2) != a2
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f8]) ).

fof(f11,plain,
    ( spl0_2
  <=> multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)) ),
    introduced(split_symbol_definition) ).

fof(f13,plain,
    ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
    | spl0_2 ),
    inference(component_clause,[status(thm)],[f11]) ).

fof(f14,plain,
    ( spl0_3
  <=> multiply(a4,b4) = multiply(b4,a4) ),
    introduced(split_symbol_definition) ).

fof(f16,plain,
    ( multiply(a4,b4) != multiply(b4,a4)
    | spl0_3 ),
    inference(component_clause,[status(thm)],[f14]) ).

fof(f17,plain,
    ( ~ spl0_0
    | ~ spl0_1
    | ~ spl0_2
    | ~ spl0_3 ),
    inference(split_clause,[status(thm)],[f4,f5,f8,f11,f14]) ).

fof(f18,plain,
    ! [X0,X1,X2,X3] : multiply(X0,multiply(X1,X2)) = multiply(multiply(inverse(multiply(inverse(multiply(X0,X2)),X3)),X1),X3),
    inference(paramodulation,[status(thm)],[f3,f3]) ).

fof(f27,plain,
    ! [X0,X1,X2] : multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X2,X1))) = X2,
    inference(paramodulation,[status(thm)],[f18,f3]) ).

fof(f34,plain,
    ! [X0,X1,X2] : multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X2,X1))),X2) = X0,
    inference(paramodulation,[status(thm)],[f27,f27]) ).

fof(f45,plain,
    ! [X0,X1,X2,X3] : multiply(inverse(multiply(inverse(X0),multiply(X1,X2))),X1) = inverse(multiply(inverse(multiply(X0,X3)),multiply(X2,X3))),
    inference(paramodulation,[status(thm)],[f34,f34]) ).

fof(f46,plain,
    ! [X0,X1,X2,X3] : multiply(inverse(multiply(inverse(X0),multiply(X1,multiply(X2,multiply(X0,X3))))),X1) = inverse(multiply(X2,X3)),
    inference(paramodulation,[status(thm)],[f27,f34]) ).

fof(f53,plain,
    ! [X0,X1,X2,X3] : multiply(inverse(multiply(X0,X1)),multiply(X2,multiply(X3,X1))) = multiply(multiply(inverse(X0),X2),X3),
    inference(paramodulation,[status(thm)],[f34,f18]) ).

fof(f57,plain,
    ! [X0,X1,X2,X3] : multiply(inverse(X0),multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X2,X1))),multiply(X3,X2))) = X3,
    inference(paramodulation,[status(thm)],[f34,f27]) ).

fof(f58,plain,
    ! [X0,X1,X2,X3,X4] : multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X2,X1))),multiply(X3,X2)) = multiply(multiply(inverse(multiply(inverse(X0),X4)),X3),X4),
    inference(paramodulation,[status(thm)],[f34,f18]) ).

fof(f60,plain,
    ! [X0,X1] : multiply(multiply(inverse(X0),X0),X1) = X1,
    inference(backward_demodulation,[status(thm)],[f53,f27]) ).

fof(f110,plain,
    ! [X0,X1,X2] : multiply(inverse(multiply(inverse(X0),multiply(X1,X0))),X1) = multiply(inverse(X2),X2),
    inference(paramodulation,[status(thm)],[f60,f34]) ).

fof(f111,plain,
    ! [X0,X1,X2,X3] : multiply(multiply(inverse(X0),X0),multiply(X1,X2)) = multiply(multiply(inverse(multiply(inverse(X2),X3)),X1),X3),
    inference(paramodulation,[status(thm)],[f60,f18]) ).

fof(f112,plain,
    ! [X0,X1,X2] : multiply(X0,X1) = multiply(multiply(inverse(multiply(inverse(X1),X2)),X0),X2),
    inference(forward_demodulation,[status(thm)],[f60,f111]) ).

fof(f115,plain,
    ! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(X1,multiply(X0,X2)),
    inference(backward_demodulation,[status(thm)],[f112,f18]) ).

fof(f119,plain,
    ! [X0,X1,X2,X3] : multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X2,X1))),multiply(X3,X2)) = multiply(X3,X0),
    inference(backward_demodulation,[status(thm)],[f112,f58]) ).

fof(f124,plain,
    ! [X0,X1] : multiply(inverse(X0),multiply(X1,X0)) = X1,
    inference(backward_demodulation,[status(thm)],[f119,f57]) ).

fof(f131,plain,
    ! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
    inference(backward_demodulation,[status(thm)],[f124,f110]) ).

fof(f134,plain,
    ! [X0,X1,X2] : multiply(inverse(X0),X1) = inverse(multiply(inverse(multiply(X1,X2)),multiply(X0,X2))),
    inference(paramodulation,[status(thm)],[f34,f124]) ).

fof(f135,plain,
    ! [X0,X1] : multiply(inverse(multiply(X0,X1)),X0) = inverse(X1),
    inference(paramodulation,[status(thm)],[f124,f124]) ).

fof(f153,plain,
    ! [X0,X1,X2] : multiply(inverse(multiply(inverse(X0),multiply(X1,X2))),X1) = multiply(inverse(X2),X0),
    inference(backward_demodulation,[status(thm)],[f134,f45]) ).

fof(f158,plain,
    ! [X0,X1,X2] : multiply(inverse(multiply(X0,multiply(X1,X2))),X1) = inverse(multiply(X0,X2)),
    inference(backward_demodulation,[status(thm)],[f153,f46]) ).

fof(f179,plain,
    ! [X0,X1] : inverse(multiply(inverse(X0),X1)) = multiply(inverse(X1),X0),
    inference(backward_demodulation,[status(thm)],[f158,f153]) ).

fof(f201,plain,
    ! [X0,X1] : multiply(inverse(inverse(X0)),inverse(multiply(X1,X0))) = inverse(X1),
    inference(paramodulation,[status(thm)],[f135,f135]) ).

fof(f202,plain,
    ! [X0,X1] : multiply(inverse(X0),inverse(X1)) = inverse(multiply(X0,X1)),
    inference(paramodulation,[status(thm)],[f124,f135]) ).

fof(f212,plain,
    ! [X0,X1] : inverse(multiply(inverse(X0),multiply(X1,X0))) = inverse(X1),
    inference(backward_demodulation,[status(thm)],[f202,f201]) ).

fof(f213,plain,
    ! [X0,X1] : multiply(inverse(multiply(X0,X1)),X1) = inverse(X0),
    inference(forward_demodulation,[status(thm)],[f179,f212]) ).

fof(f215,plain,
    ! [X0,X1] : multiply(inverse(inverse(X0)),X1) = inverse(inverse(multiply(X0,X1))),
    inference(paramodulation,[status(thm)],[f213,f213]) ).

fof(f216,plain,
    ! [X0,X1] : multiply(inverse(inverse(X0)),X1) = inverse(inverse(multiply(X1,X0))),
    inference(paramodulation,[status(thm)],[f135,f213]) ).

fof(f217,plain,
    ! [X0,X1] : inverse(inverse(multiply(X0,X1))) = inverse(inverse(multiply(X1,X0))),
    inference(forward_demodulation,[status(thm)],[f215,f216]) ).

fof(f220,plain,
    ! [X0,X1] : multiply(inverse(multiply(inverse(X0),X0)),X1) = inverse(inverse(X1)),
    inference(paramodulation,[status(thm)],[f131,f213]) ).

fof(f221,plain,
    ! [X0,X1] : multiply(multiply(inverse(X0),X0),X1) = inverse(inverse(X1)),
    inference(forward_demodulation,[status(thm)],[f179,f220]) ).

fof(f222,plain,
    ! [X0] : X0 = inverse(inverse(X0)),
    inference(forward_demodulation,[status(thm)],[f60,f221]) ).

fof(f242,plain,
    ! [X0,X1] : inverse(inverse(multiply(X0,X1))) = multiply(X1,X0),
    inference(backward_demodulation,[status(thm)],[f222,f217]) ).

fof(f243,plain,
    ! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
    inference(forward_demodulation,[status(thm)],[f222,f242]) ).

fof(f248,plain,
    ( $false
    | spl0_3 ),
    inference(backward_subsumption_resolution,[status(thm)],[f16,f243]) ).

fof(f249,plain,
    spl0_3,
    inference(contradiction_clause,[status(thm)],[f248]) ).

fof(f250,plain,
    ( multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3))
    | spl0_2 ),
    inference(forward_demodulation,[status(thm)],[f243,f13]) ).

fof(f251,plain,
    ( multiply(a3,multiply(c3,b3)) != multiply(a3,multiply(b3,c3))
    | spl0_2 ),
    inference(forward_demodulation,[status(thm)],[f115,f250]) ).

fof(f252,plain,
    ( multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
    | spl0_2 ),
    inference(forward_demodulation,[status(thm)],[f243,f251]) ).

fof(f253,plain,
    ( $false
    | spl0_2 ),
    inference(trivial_equality_resolution,[status(esa)],[f252]) ).

fof(f254,plain,
    spl0_2,
    inference(contradiction_clause,[status(thm)],[f253]) ).

fof(f255,plain,
    ( multiply(a1,inverse(a1)) != multiply(inverse(b1),b1)
    | spl0_0 ),
    inference(forward_demodulation,[status(thm)],[f243,f7]) ).

fof(f256,plain,
    ( multiply(a1,inverse(a1)) != multiply(b1,inverse(b1))
    | spl0_0 ),
    inference(forward_demodulation,[status(thm)],[f243,f255]) ).

fof(f259,plain,
    ! [X0,X1] : multiply(inverse(X0),X0) = multiply(X1,inverse(X1)),
    inference(paramodulation,[status(thm)],[f222,f131]) ).

fof(f260,plain,
    ! [X0,X1] : multiply(X0,inverse(X0)) = multiply(X1,inverse(X1)),
    inference(forward_demodulation,[status(thm)],[f243,f259]) ).

fof(f265,plain,
    ( $false
    | spl0_0 ),
    inference(backward_subsumption_resolution,[status(thm)],[f256,f260]) ).

fof(f266,plain,
    spl0_0,
    inference(contradiction_clause,[status(thm)],[f265]) ).

fof(f267,plain,
    ( a2 != a2
    | spl0_1 ),
    inference(forward_demodulation,[status(thm)],[f60,f10]) ).

fof(f268,plain,
    ( $false
    | spl0_1 ),
    inference(trivial_equality_resolution,[status(esa)],[f267]) ).

fof(f269,plain,
    spl0_1,
    inference(contradiction_clause,[status(thm)],[f268]) ).

fof(f270,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f17,f249,f254,f266,f269]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : GRP087-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.07/0.14  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.15/0.35  % Computer : n005.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Tue Apr 30 00:14:56 EDT 2024
% 0.15/0.35  % CPUTime  : 
% 0.15/0.36  % Drodi V3.6.0
% 0.21/0.40  % Refutation found
% 0.21/0.40  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.21/0.40  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.41  % Elapsed time: 0.056112 seconds
% 0.21/0.41  % CPU time: 0.343434 seconds
% 0.21/0.41  % Total memory used: 44.748 MB
% 0.21/0.41  % Net memory used: 44.280 MB
%------------------------------------------------------------------------------