TSTP Solution File: GRP715-10 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : GRP715-10 : TPTP v8.1.2. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n006.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 20:21:29 EDT 2024

% Result   : Unsatisfiable 38.14s 5.18s
% Output   : CNFRefutation 38.85s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   54 (  54 unt;   0 def)
%            Number of atoms       :   54 (  53 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    3 (   3   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   60 (  60   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f6,axiom,
    ! [A,B,C] : mult(mult(mult(A,B),C),B) = mult(A,mult(mult(B,C),B)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [A,B] : mult(A,mult(B,B)) = mult(mult(A,B),B),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [A] : mult(A,unit) = A,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [A] : mult(unit,A) = A,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f10,axiom,
    mult(op_a,op_b) = unit,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f11,axiom,
    mult(op_b,op_a) = unit,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f12,negated_conjecture,
    mult(mult(x0,op_a),op_b) != x0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f18,plain,
    ! [X0,X1,X2] : mult(mult(mult(X0,X1),X2),X1) = mult(X0,mult(mult(X1,X2),X1)),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f19,plain,
    ! [X0,X1] : mult(X0,mult(X1,X1)) = mult(mult(X0,X1),X1),
    inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f20,plain,
    ! [X0] : mult(X0,unit) = X0,
    inference(cnf_transformation,[status(esa)],[f8]) ).

fof(f21,plain,
    ! [X0] : mult(unit,X0) = X0,
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f22,plain,
    mult(op_a,op_b) = unit,
    inference(cnf_transformation,[status(esa)],[f10]) ).

fof(f23,plain,
    mult(op_b,op_a) = unit,
    inference(cnf_transformation,[status(esa)],[f11]) ).

fof(f24,plain,
    mult(mult(x0,op_a),op_b) != x0,
    inference(cnf_transformation,[status(esa)],[f12]) ).

fof(f26,plain,
    mult(op_b,mult(op_a,op_a)) = mult(unit,op_a),
    inference(paramodulation,[status(thm)],[f23,f19]) ).

fof(f27,plain,
    mult(op_b,mult(op_a,op_a)) = op_a,
    inference(forward_demodulation,[status(thm)],[f21,f26]) ).

fof(f31,plain,
    ! [X0,X1] : mult(mult(X0,X1),mult(X1,X1)) = mult(X0,mult(mult(X1,X1),X1)),
    inference(paramodulation,[status(thm)],[f19,f18]) ).

fof(f32,plain,
    ! [X0,X1] : mult(mult(X0,X1),mult(X1,X1)) = mult(X0,mult(X1,mult(X1,X1))),
    inference(forward_demodulation,[status(thm)],[f19,f31]) ).

fof(f33,plain,
    ! [X0,X1,X2] : mult(mult(X0,mult(mult(X1,X2),X1)),X2) = mult(mult(X0,X1),mult(mult(X2,X1),X2)),
    inference(paramodulation,[status(thm)],[f18,f18]) ).

fof(f37,plain,
    ! [X0,X1,X2,X3] : mult(mult(mult(X0,mult(mult(X1,X2),X1)),X3),X1) = mult(mult(mult(X0,X1),X2),mult(mult(X1,X3),X1)),
    inference(paramodulation,[status(thm)],[f18,f18]) ).

fof(f40,plain,
    ! [X0] : mult(mult(unit,X0),op_a) = mult(op_b,mult(mult(op_a,X0),op_a)),
    inference(paramodulation,[status(thm)],[f23,f18]) ).

fof(f41,plain,
    ! [X0] : mult(X0,op_a) = mult(op_b,mult(mult(op_a,X0),op_a)),
    inference(forward_demodulation,[status(thm)],[f21,f40]) ).

fof(f42,plain,
    ! [X0] : mult(mult(unit,X0),op_b) = mult(op_a,mult(mult(op_b,X0),op_b)),
    inference(paramodulation,[status(thm)],[f22,f18]) ).

fof(f43,plain,
    ! [X0] : mult(X0,op_b) = mult(op_a,mult(mult(op_b,X0),op_b)),
    inference(forward_demodulation,[status(thm)],[f21,f42]) ).

fof(f53,plain,
    mult(op_a,op_a) = mult(op_b,mult(op_a,mult(op_a,op_a))),
    inference(paramodulation,[status(thm)],[f19,f41]) ).

fof(f78,plain,
    mult(mult(op_a,op_a),op_b) = mult(op_a,mult(op_a,op_b)),
    inference(paramodulation,[status(thm)],[f27,f43]) ).

fof(f79,plain,
    mult(mult(op_a,op_a),op_b) = mult(op_a,unit),
    inference(forward_demodulation,[status(thm)],[f22,f78]) ).

fof(f80,plain,
    mult(mult(op_a,op_a),op_b) = op_a,
    inference(forward_demodulation,[status(thm)],[f20,f79]) ).

fof(f177,plain,
    ! [X0,X1,X2] : mult(X0,mult(mult(X1,mult(mult(X2,X1),X2)),X1)) = mult(mult(mult(X0,X1),X2),mult(mult(X1,X2),X1)),
    inference(paramodulation,[status(thm)],[f18,f33]) ).

fof(f178,plain,
    ! [X0,X1,X2] : mult(X0,mult(mult(X1,X2),mult(mult(X1,X2),X1))) = mult(mult(mult(X0,X1),X2),mult(mult(X1,X2),X1)),
    inference(forward_demodulation,[status(thm)],[f33,f177]) ).

fof(f206,plain,
    ! [X0] : mult(mult(X0,mult(op_a,mult(op_a,op_a))),op_b) = mult(mult(X0,mult(op_a,op_a)),mult(mult(op_b,mult(op_a,op_a)),op_b)),
    inference(paramodulation,[status(thm)],[f80,f33]) ).

fof(f207,plain,
    ! [X0] : mult(mult(X0,mult(op_a,mult(op_a,op_a))),op_b) = mult(mult(X0,mult(op_a,op_a)),mult(op_a,op_b)),
    inference(forward_demodulation,[status(thm)],[f27,f206]) ).

fof(f208,plain,
    ! [X0] : mult(mult(X0,mult(op_a,mult(op_a,op_a))),op_b) = mult(mult(X0,mult(op_a,op_a)),unit),
    inference(forward_demodulation,[status(thm)],[f22,f207]) ).

fof(f209,plain,
    ! [X0] : mult(mult(X0,mult(op_a,mult(op_a,op_a))),op_b) = mult(X0,mult(op_a,op_a)),
    inference(forward_demodulation,[status(thm)],[f20,f208]) ).

fof(f228,plain,
    ! [X0] : mult(mult(X0,mult(op_a,op_b)),mult(op_a,op_a)) = mult(mult(X0,op_b),mult(mult(mult(op_a,op_a),op_b),mult(op_a,op_a))),
    inference(paramodulation,[status(thm)],[f27,f33]) ).

fof(f229,plain,
    ! [X0] : mult(mult(X0,unit),mult(op_a,op_a)) = mult(mult(X0,op_b),mult(mult(mult(op_a,op_a),op_b),mult(op_a,op_a))),
    inference(forward_demodulation,[status(thm)],[f22,f228]) ).

fof(f230,plain,
    ! [X0] : mult(X0,mult(op_a,op_a)) = mult(mult(X0,op_b),mult(mult(mult(op_a,op_a),op_b),mult(op_a,op_a))),
    inference(forward_demodulation,[status(thm)],[f20,f229]) ).

fof(f231,plain,
    ! [X0] : mult(X0,mult(op_a,op_a)) = mult(mult(X0,op_b),mult(op_a,mult(op_a,op_a))),
    inference(forward_demodulation,[status(thm)],[f80,f230]) ).

fof(f677,plain,
    ! [X0,X1] : mult(mult(mult(X0,mult(mult(op_a,op_a),op_b)),X1),op_b) = mult(mult(mult(X0,op_b),mult(op_a,mult(op_a,op_a))),mult(mult(op_b,X1),op_b)),
    inference(paramodulation,[status(thm)],[f53,f37]) ).

fof(f678,plain,
    ! [X0,X1] : mult(mult(mult(X0,op_a),X1),op_b) = mult(mult(mult(X0,op_b),mult(op_a,mult(op_a,op_a))),mult(mult(op_b,X1),op_b)),
    inference(forward_demodulation,[status(thm)],[f80,f677]) ).

fof(f679,plain,
    ! [X0,X1] : mult(mult(mult(X0,op_a),X1),op_b) = mult(mult(X0,mult(op_a,op_a)),mult(mult(op_b,X1),op_b)),
    inference(forward_demodulation,[status(thm)],[f231,f678]) ).

fof(f31799,plain,
    ! [X0] : mult(X0,mult(mult(op_b,mult(op_a,op_a)),mult(mult(op_b,mult(op_a,op_a)),op_b))) = mult(mult(mult(X0,op_b),mult(op_a,op_a)),mult(op_a,op_b)),
    inference(paramodulation,[status(thm)],[f27,f178]) ).

fof(f31800,plain,
    ! [X0] : mult(X0,mult(mult(mult(op_b,op_a),mult(op_a,op_a)),op_b)) = mult(mult(mult(X0,op_b),mult(op_a,op_a)),mult(op_a,op_b)),
    inference(forward_demodulation,[status(thm)],[f679,f31799]) ).

fof(f31801,plain,
    ! [X0] : mult(X0,mult(mult(op_b,mult(op_a,mult(op_a,op_a))),op_b)) = mult(mult(mult(X0,op_b),mult(op_a,op_a)),mult(op_a,op_b)),
    inference(forward_demodulation,[status(thm)],[f32,f31800]) ).

fof(f31802,plain,
    ! [X0] : mult(X0,mult(op_b,mult(op_a,op_a))) = mult(mult(mult(X0,op_b),mult(op_a,op_a)),mult(op_a,op_b)),
    inference(forward_demodulation,[status(thm)],[f209,f31801]) ).

fof(f31803,plain,
    ! [X0] : mult(X0,op_a) = mult(mult(mult(X0,op_b),mult(op_a,op_a)),mult(op_a,op_b)),
    inference(forward_demodulation,[status(thm)],[f27,f31802]) ).

fof(f31804,plain,
    ! [X0] : mult(X0,op_a) = mult(mult(mult(X0,op_b),mult(op_a,op_a)),unit),
    inference(forward_demodulation,[status(thm)],[f22,f31803]) ).

fof(f31805,plain,
    ! [X0] : mult(X0,op_a) = mult(mult(X0,op_b),mult(op_a,op_a)),
    inference(forward_demodulation,[status(thm)],[f20,f31804]) ).

fof(f32385,plain,
    ! [X0] : mult(mult(X0,op_a),op_b) = mult(X0,mult(mult(op_b,mult(op_a,op_a)),op_b)),
    inference(paramodulation,[status(thm)],[f31805,f18]) ).

fof(f32386,plain,
    ! [X0] : mult(mult(X0,op_a),op_b) = mult(X0,mult(op_a,op_b)),
    inference(forward_demodulation,[status(thm)],[f27,f32385]) ).

fof(f32387,plain,
    ! [X0] : mult(mult(X0,op_a),op_b) = mult(X0,unit),
    inference(forward_demodulation,[status(thm)],[f22,f32386]) ).

fof(f32388,plain,
    ! [X0] : mult(mult(X0,op_a),op_b) = X0,
    inference(forward_demodulation,[status(thm)],[f20,f32387]) ).

fof(f32475,plain,
    x0 != x0,
    inference(backward_demodulation,[status(thm)],[f32388,f24]) ).

fof(f32476,plain,
    $false,
    inference(trivial_equality_resolution,[status(esa)],[f32475]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : GRP715-10 : TPTP v8.1.2. Released v8.1.0.
% 0.10/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.34  % Computer : n006.cluster.edu
% 0.10/0.34  % Model    : x86_64 x86_64
% 0.10/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34  % Memory   : 8042.1875MB
% 0.10/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.34  % CPULimit : 300
% 0.10/0.34  % WCLimit  : 300
% 0.10/0.34  % DateTime : Tue Apr 30 00:26:35 EDT 2024
% 0.10/0.34  % CPUTime  : 
% 0.16/0.35  % Drodi V3.6.0
% 38.14/5.18  % Refutation found
% 38.14/5.18  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 38.14/5.18  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 38.85/5.35  % Elapsed time: 4.984276 seconds
% 38.85/5.35  % CPU time: 38.991160 seconds
% 38.85/5.35  % Total memory used: 450.378 MB
% 38.85/5.35  % Net memory used: 444.995 MB
%------------------------------------------------------------------------------