TSTP Solution File: GRP063-1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : GRP063-1 : TPTP v8.1.2. Bugfixed v2.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n011.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 20:19:07 EDT 2024

% Result   : Unsatisfiable 0.17s 0.46s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   34
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   86 (  71 unt;   0 def)
%            Number of atoms       :  104 (  82 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   33 (  15   ~;  15   |;   0   &)
%                                         (   3 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of predicates  :    5 (   3 usr;   4 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   7 con; 0-2 aty)
%            Number of variables   :  174 ( 174   !;   0   ?)

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

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

fof(f3,axiom,
    ! [X,Z] : inverse(X) = divide(divide(Z,Z),X),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f4,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)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f5,plain,
    ! [X0,X1,X2] : divide(X0,divide(divide(divide(divide(X0,X0),X1),X2),divide(divide(divide(X0,X0),X0),X2))) = X1,
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f6,plain,
    ! [X0,X1,X2] : multiply(X0,X1) = divide(X0,divide(divide(X2,X2),X1)),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f7,plain,
    ! [X0,X1] : inverse(X0) = divide(divide(X1,X1),X0),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f8,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)) ),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f9,plain,
    ( spl0_0
  <=> multiply(inverse(a1),a1) = multiply(inverse(b1),b1) ),
    introduced(split_symbol_definition) ).

fof(f11,plain,
    ( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f9]) ).

fof(f12,plain,
    ( spl0_1
  <=> multiply(multiply(inverse(b2),b2),a2) = a2 ),
    introduced(split_symbol_definition) ).

fof(f14,plain,
    ( multiply(multiply(inverse(b2),b2),a2) != a2
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f12]) ).

fof(f15,plain,
    ( spl0_2
  <=> multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)) ),
    introduced(split_symbol_definition) ).

fof(f17,plain,
    ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
    | spl0_2 ),
    inference(component_clause,[status(thm)],[f15]) ).

fof(f18,plain,
    ( ~ spl0_0
    | ~ spl0_1
    | ~ spl0_2 ),
    inference(split_clause,[status(thm)],[f8,f9,f12,f15]) ).

fof(f19,plain,
    ! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
    inference(backward_demodulation,[status(thm)],[f7,f6]) ).

fof(f20,plain,
    ! [X0,X1,X2] : divide(X0,divide(divide(divide(divide(X0,X0),X1),X2),divide(inverse(X0),X2))) = X1,
    inference(backward_demodulation,[status(thm)],[f7,f5]) ).

fof(f21,plain,
    ! [X0,X1,X2] : divide(X0,divide(divide(inverse(X1),X2),divide(inverse(X0),X2))) = X1,
    inference(forward_demodulation,[status(thm)],[f7,f20]) ).

fof(f22,plain,
    ! [X0,X1] : inverse(X0) = divide(inverse(divide(X1,X1)),X0),
    inference(paramodulation,[status(thm)],[f7,f7]) ).

fof(f23,plain,
    ! [X0,X1] : multiply(divide(X0,X0),X1) = inverse(inverse(X1)),
    inference(paramodulation,[status(thm)],[f7,f19]) ).

fof(f25,plain,
    ! [X0,X1] : inverse(X0) = divide(multiply(inverse(X1),X1),X0),
    inference(paramodulation,[status(thm)],[f19,f7]) ).

fof(f26,plain,
    ! [X0,X1] : inverse(inverse(X0)) = multiply(inverse(divide(X1,X1)),X0),
    inference(paramodulation,[status(thm)],[f19,f22]) ).

fof(f29,plain,
    ! [X0,X1] : inverse(X0) = divide(inverse(multiply(inverse(X1),X1)),X0),
    inference(paramodulation,[status(thm)],[f19,f22]) ).

fof(f40,plain,
    ! [X0,X1,X2] : inverse(divide(divide(inverse(X0),X1),divide(inverse(multiply(inverse(X2),X2)),X1))) = X0,
    inference(paramodulation,[status(thm)],[f25,f21]) ).

fof(f41,plain,
    ! [X0,X1] : inverse(divide(divide(inverse(X0),X1),inverse(X1))) = X0,
    inference(forward_demodulation,[status(thm)],[f29,f40]) ).

fof(f42,plain,
    ! [X0,X1] : inverse(multiply(divide(inverse(X0),X1),X1)) = X0,
    inference(forward_demodulation,[status(thm)],[f19,f41]) ).

fof(f49,plain,
    ! [X0,X1] : divide(X0,inverse(divide(inverse(X0),inverse(X1)))) = X1,
    inference(paramodulation,[status(thm)],[f7,f21]) ).

fof(f50,plain,
    ! [X0,X1] : multiply(X0,divide(inverse(X0),inverse(X1))) = X1,
    inference(forward_demodulation,[status(thm)],[f19,f49]) ).

fof(f51,plain,
    ! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
    inference(forward_demodulation,[status(thm)],[f19,f50]) ).

fof(f53,plain,
    ! [X0,X1,X2,X3] : divide(X0,divide(X1,divide(inverse(X0),divide(divide(inverse(X1),X2),divide(inverse(inverse(X3)),X2))))) = X3,
    inference(paramodulation,[status(thm)],[f21,f21]) ).

fof(f59,plain,
    ! [X0,X1,X2,X3] : divide(X0,divide(divide(inverse(X1),divide(divide(inverse(X2),X3),divide(inverse(inverse(X0)),X3))),X2)) = X1,
    inference(paramodulation,[status(thm)],[f21,f21]) ).

fof(f71,plain,
    ! [X0,X1] : inverse(inverse(multiply(inverse(divide(X0,X0)),X1))) = X1,
    inference(paramodulation,[status(thm)],[f23,f51]) ).

fof(f72,plain,
    ! [X0] : inverse(inverse(inverse(inverse(X0)))) = X0,
    inference(forward_demodulation,[status(thm)],[f26,f71]) ).

fof(f73,plain,
    ! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
    inference(paramodulation,[status(thm)],[f51,f51]) ).

fof(f77,plain,
    ! [X0,X1] : multiply(inverse(inverse(inverse(X0))),multiply(X0,X1)) = X1,
    inference(paramodulation,[status(thm)],[f72,f51]) ).

fof(f78,plain,
    ! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
    inference(forward_demodulation,[status(thm)],[f73,f77]) ).

fof(f92,plain,
    ! [X0,X1] : inverse(multiply(multiply(inverse(X0),X1),inverse(X1))) = X0,
    inference(paramodulation,[status(thm)],[f19,f42]) ).

fof(f151,plain,
    ! [X0,X1] : inverse(multiply(multiply(X0,X1),inverse(X1))) = inverse(X0),
    inference(paramodulation,[status(thm)],[f73,f92]) ).

fof(f152,plain,
    ! [X0,X1] : inverse(multiply(X0,inverse(multiply(X1,X0)))) = X1,
    inference(paramodulation,[status(thm)],[f78,f92]) ).

fof(f153,plain,
    ! [X0,X1] : inverse(multiply(X0,inverse(multiply(inverse(inverse(X1)),X0)))) = X1,
    inference(paramodulation,[status(thm)],[f51,f92]) ).

fof(f154,plain,
    ! [X0] : inverse(inverse(X0)) = X0,
    inference(forward_demodulation,[status(thm)],[f152,f153]) ).

fof(f155,plain,
    ! [X0,X1,X2] : inverse(multiply(multiply(X0,X1),inverse(X1))) = multiply(multiply(inverse(X0),X2),inverse(X2)),
    inference(paramodulation,[status(thm)],[f92,f92]) ).

fof(f156,plain,
    ! [X0,X1] : inverse(X0) = multiply(multiply(inverse(X0),X1),inverse(X1)),
    inference(forward_demodulation,[status(thm)],[f151,f155]) ).

fof(f179,plain,
    ! [X0,X1,X2] : multiply(X0,multiply(multiply(inverse(X1),X2),inverse(X2))) = divide(X0,X1),
    inference(paramodulation,[status(thm)],[f92,f19]) ).

fof(f180,plain,
    ! [X0,X1] : multiply(X0,inverse(X1)) = divide(X0,X1),
    inference(forward_demodulation,[status(thm)],[f156,f179]) ).

fof(f204,plain,
    ! [X0,X1,X2,X3] : divide(X0,divide(divide(inverse(X1),divide(divide(inverse(X2),X3),divide(X0,X3))),X2)) = X1,
    inference(backward_demodulation,[status(thm)],[f154,f59]) ).

fof(f205,plain,
    ! [X0,X1,X2,X3] : divide(X0,divide(X1,divide(inverse(X0),divide(divide(inverse(X1),X2),divide(X3,X2))))) = X3,
    inference(backward_demodulation,[status(thm)],[f154,f53]) ).

fof(f215,plain,
    ! [X0,X1] : inverse(divide(X0,multiply(X1,X0))) = X1,
    inference(backward_demodulation,[status(thm)],[f180,f152]) ).

fof(f267,plain,
    ! [X0,X1,X2,X3,X4] : divide(divide(inverse(X0),divide(divide(inverse(X1),X2),divide(divide(inverse(X3),X1),X2))),divide(divide(inverse(X4),X0),X3)) = X4,
    inference(paramodulation,[status(thm)],[f204,f204]) ).

fof(f310,plain,
    ! [X0,X1] : inverse(inverse(multiply(X0,multiply(inverse(X1),X1)))) = X0,
    inference(paramodulation,[status(thm)],[f25,f215]) ).

fof(f311,plain,
    ! [X0,X1] : multiply(X0,multiply(inverse(X1),X1)) = X0,
    inference(forward_demodulation,[status(thm)],[f154,f310]) ).

fof(f325,plain,
    ! [X0,X1] : inverse(X0) = divide(X1,multiply(X0,X1)),
    inference(paramodulation,[status(thm)],[f215,f154]) ).

fof(f441,plain,
    ! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
    inference(paramodulation,[status(thm)],[f311,f78]) ).

fof(f473,plain,
    ! [X0,X1] : inverse(inverse(X0)) = divide(multiply(X0,X1),X1),
    inference(paramodulation,[status(thm)],[f78,f325]) ).

fof(f474,plain,
    ! [X0,X1] : X0 = divide(multiply(X0,X1),X1),
    inference(forward_demodulation,[status(thm)],[f154,f473]) ).

fof(f476,plain,
    ! [X0,X1] : inverse(X0) = divide(inverse(X1),divide(X0,X1)),
    inference(paramodulation,[status(thm)],[f180,f325]) ).

fof(f495,plain,
    ! [X0,X1] : X0 = multiply(multiply(X0,inverse(X1)),X1),
    inference(paramodulation,[status(thm)],[f19,f474]) ).

fof(f496,plain,
    ! [X0,X1] : X0 = multiply(divide(X0,X1),X1),
    inference(forward_demodulation,[status(thm)],[f180,f495]) ).

fof(f530,plain,
    ! [X0,X1] : inverse(divide(X0,X1)) = divide(X1,X0),
    inference(paramodulation,[status(thm)],[f496,f325]) ).

fof(f641,plain,
    ! [X0,X1] : inverse(multiply(X0,X1)) = divide(inverse(X1),X0),
    inference(paramodulation,[status(thm)],[f19,f530]) ).

fof(f652,plain,
    ! [X0,X1,X2] : multiply(X0,divide(X1,X2)) = divide(X0,divide(X2,X1)),
    inference(paramodulation,[status(thm)],[f530,f180]) ).

fof(f834,plain,
    ! [X0,X1,X2,X3] : divide(X0,divide(X1,divide(inverse(X0),divide(divide(inverse(X1),X2),X3)))) = multiply(X3,X2),
    inference(paramodulation,[status(thm)],[f474,f205]) ).

fof(f1001,plain,
    ! [X0,X1,X2,X3] : divide(divide(inverse(X0),inverse(divide(divide(inverse(X1),X2),inverse(X2)))),divide(divide(inverse(X3),X0),X1)) = X3,
    inference(paramodulation,[status(thm)],[f7,f267]) ).

fof(f1002,plain,
    ! [X0,X1,X2,X3] : divide(multiply(inverse(X0),divide(divide(inverse(X1),X2),inverse(X2))),divide(divide(inverse(X3),X0),X1)) = X3,
    inference(forward_demodulation,[status(thm)],[f19,f1001]) ).

fof(f1003,plain,
    ! [X0,X1,X2,X3] : divide(divide(inverse(X0),divide(inverse(X1),divide(inverse(X2),X1))),divide(divide(inverse(X3),X0),X2)) = X3,
    inference(forward_demodulation,[status(thm)],[f652,f1002]) ).

fof(f1004,plain,
    ! [X0,X1,X2] : divide(divide(inverse(X0),inverse(inverse(X1))),divide(divide(inverse(X2),X0),X1)) = X2,
    inference(forward_demodulation,[status(thm)],[f476,f1003]) ).

fof(f1005,plain,
    ! [X0,X1,X2] : divide(multiply(inverse(X0),inverse(X1)),divide(divide(inverse(X2),X0),X1)) = X2,
    inference(forward_demodulation,[status(thm)],[f19,f1004]) ).

fof(f1006,plain,
    ! [X0,X1,X2] : divide(divide(inverse(X0),X1),divide(divide(inverse(X2),X0),X1)) = X2,
    inference(forward_demodulation,[status(thm)],[f180,f1005]) ).

fof(f1196,plain,
    ! [X0,X1,X2,X3,X4] : divide(inverse(X0),divide(divide(inverse(X1),X2),divide(divide(inverse(X3),X1),X2))) = multiply(X4,divide(divide(inverse(X4),X0),X3)),
    inference(paramodulation,[status(thm)],[f267,f496]) ).

fof(f1197,plain,
    ! [X0,X1,X2] : divide(inverse(X0),X1) = multiply(X2,divide(divide(inverse(X2),X0),X1)),
    inference(forward_demodulation,[status(thm)],[f1006,f1196]) ).

fof(f1198,plain,
    ! [X0,X1,X2] : divide(inverse(X0),X1) = divide(X2,divide(X1,divide(inverse(X2),X0))),
    inference(forward_demodulation,[status(thm)],[f652,f1197]) ).

fof(f1227,plain,
    ! [X0,X1,X2] : divide(inverse(divide(divide(inverse(X0),X1),X2)),X0) = multiply(X2,X1),
    inference(backward_demodulation,[status(thm)],[f1198,f834]) ).

fof(f1228,plain,
    ! [X0,X1,X2] : divide(divide(X0,divide(inverse(X1),X2)),X1) = multiply(X0,X2),
    inference(forward_demodulation,[status(thm)],[f530,f1227]) ).

fof(f1279,plain,
    ! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = divide(X0,divide(inverse(X2),X1)),
    inference(paramodulation,[status(thm)],[f641,f19]) ).

fof(f1283,plain,
    ! [X0,X1,X2] : divide(multiply(X0,multiply(X1,X2)),X2) = multiply(X0,X1),
    inference(backward_demodulation,[status(thm)],[f1279,f1228]) ).

fof(f1491,plain,
    ! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,X1),X2),
    inference(paramodulation,[status(thm)],[f1283,f496]) ).

fof(f1535,plain,
    ( multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
    | spl0_2 ),
    inference(backward_demodulation,[status(thm)],[f1491,f17]) ).

fof(f1536,plain,
    ( $false
    | spl0_2 ),
    inference(trivial_equality_resolution,[status(esa)],[f1535]) ).

fof(f1537,plain,
    spl0_2,
    inference(contradiction_clause,[status(thm)],[f1536]) ).

fof(f1543,plain,
    ( $false
    | spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f11,f441]) ).

fof(f1544,plain,
    spl0_0,
    inference(contradiction_clause,[status(thm)],[f1543]) ).

fof(f1545,plain,
    ( multiply(inverse(b2),multiply(b2,a2)) != a2
    | spl0_1 ),
    inference(forward_demodulation,[status(thm)],[f1491,f14]) ).

fof(f1546,plain,
    ( a2 != a2
    | spl0_1 ),
    inference(forward_demodulation,[status(thm)],[f78,f1545]) ).

fof(f1547,plain,
    ( $false
    | spl0_1 ),
    inference(trivial_equality_resolution,[status(esa)],[f1546]) ).

fof(f1548,plain,
    spl0_1,
    inference(contradiction_clause,[status(thm)],[f1547]) ).

fof(f1549,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f18,f1537,f1544,f1548]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.14  % Problem  : GRP063-1 : TPTP v8.1.2. Bugfixed v2.3.0.
% 0.10/0.14  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.35  % Computer : n011.cluster.edu
% 0.11/0.35  % Model    : x86_64 x86_64
% 0.11/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35  % Memory   : 8042.1875MB
% 0.11/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35  % CPULimit : 300
% 0.17/0.35  % WCLimit  : 300
% 0.17/0.35  % DateTime : Tue Apr 30 00:20:46 EDT 2024
% 0.17/0.35  % CPUTime  : 
% 0.17/0.36  % Drodi V3.6.0
% 0.17/0.46  % Refutation found
% 0.17/0.46  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.17/0.46  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.48  % Elapsed time: 0.112447 seconds
% 0.17/0.48  % CPU time: 0.778628 seconds
% 0.17/0.48  % Total memory used: 55.473 MB
% 0.17/0.48  % Net memory used: 54.250 MB
%------------------------------------------------------------------------------