TSTP Solution File: LCL163-1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : LCL163-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n020.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 20:26:31 EDT 2024

% Result   : Unsatisfiable 0.16s 0.47s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   67 (  67 unt;   0 def)
%            Number of atoms       :   67 (  66 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    2 (   2   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   3 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :  110 ( 110   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X] : not(X) = xor(X,truth),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [X] : xor(X,falsehood) = X,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [X] : and_star(X,truth) = X,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [X,Y] : xor(X,xor(truth,Y)) = xor(xor(X,truth),Y),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [X,Y] : and_star(xor(and_star(xor(truth,X),Y),truth),Y) = and_star(xor(and_star(xor(truth,Y),X),truth),X),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [X,Y] : xor(X,Y) = xor(Y,X),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f11,axiom,
    ! [X,Y] : and_star(X,Y) = and_star(Y,X),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f12,axiom,
    not(truth) = falsehood,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f13,axiom,
    ! [X,Y] : implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f14,negated_conjecture,
    implies(implies(x,y),y) != implies(implies(y,x),x),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f15,plain,
    ! [X0] : not(X0) = xor(X0,truth),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f16,plain,
    ! [X0] : xor(X0,falsehood) = X0,
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f18,plain,
    ! [X0] : and_star(X0,truth) = X0,
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f21,plain,
    ! [X0,X1] : xor(X0,xor(truth,X1)) = xor(xor(X0,truth),X1),
    inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f22,plain,
    ! [X0,X1] : and_star(xor(and_star(xor(truth,X0),X1),truth),X1) = and_star(xor(and_star(xor(truth,X1),X0),truth),X0),
    inference(cnf_transformation,[status(esa)],[f8]) ).

fof(f23,plain,
    ! [X0,X1] : xor(X0,X1) = xor(X1,X0),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f25,plain,
    ! [X0,X1] : and_star(X0,X1) = and_star(X1,X0),
    inference(cnf_transformation,[status(esa)],[f11]) ).

fof(f26,plain,
    not(truth) = falsehood,
    inference(cnf_transformation,[status(esa)],[f12]) ).

fof(f27,plain,
    ! [X0,X1] : implies(X0,X1) = xor(truth,and_star(X0,xor(truth,X1))),
    inference(cnf_transformation,[status(esa)],[f13]) ).

fof(f28,plain,
    implies(implies(x,y),y) != implies(implies(y,x),x),
    inference(cnf_transformation,[status(esa)],[f14]) ).

fof(f29,plain,
    ! [X0,X1,X2] : implies(X0,and_star(X1,xor(truth,X2))) = xor(truth,and_star(X0,implies(X1,X2))),
    inference(paramodulation,[status(thm)],[f27,f27]) ).

fof(f69,plain,
    ! [X0] : not(X0) = xor(truth,X0),
    inference(paramodulation,[status(thm)],[f15,f23]) ).

fof(f70,plain,
    ! [X0] : X0 = xor(falsehood,X0),
    inference(paramodulation,[status(thm)],[f16,f23]) ).

fof(f75,plain,
    ! [X0,X1] : implies(X0,X1) = xor(truth,and_star(X0,xor(X1,truth))),
    inference(paramodulation,[status(thm)],[f23,f27]) ).

fof(f76,plain,
    ! [X0,X1] : implies(X0,X1) = xor(truth,and_star(X0,not(X1))),
    inference(forward_demodulation,[status(thm)],[f15,f75]) ).

fof(f92,plain,
    ! [X0] : X0 = and_star(truth,X0),
    inference(paramodulation,[status(thm)],[f18,f25]) ).

fof(f98,plain,
    ! [X0,X1] : implies(X0,X1) = xor(truth,and_star(xor(truth,X1),X0)),
    inference(paramodulation,[status(thm)],[f25,f27]) ).

fof(f106,plain,
    ! [X0] : implies(truth,X0) = xor(truth,xor(truth,X0)),
    inference(paramodulation,[status(thm)],[f92,f27]) ).

fof(f127,plain,
    ! [X0,X1] : xor(X0,xor(truth,X1)) = xor(not(X0),X1),
    inference(forward_demodulation,[status(thm)],[f15,f21]) ).

fof(f166,plain,
    ! [X0,X1] : and_star(X0,xor(and_star(xor(truth,X1),X0),truth)) = and_star(xor(and_star(xor(truth,X0),X1),truth),X1),
    inference(forward_demodulation,[status(thm)],[f25,f22]) ).

fof(f167,plain,
    ! [X0,X1] : and_star(X0,not(and_star(xor(truth,X1),X0))) = and_star(xor(and_star(xor(truth,X0),X1),truth),X1),
    inference(forward_demodulation,[status(thm)],[f15,f166]) ).

fof(f168,plain,
    ! [X0,X1] : and_star(X0,not(and_star(xor(truth,X1),X0))) = and_star(X1,xor(and_star(xor(truth,X0),X1),truth)),
    inference(forward_demodulation,[status(thm)],[f25,f167]) ).

fof(f169,plain,
    ! [X0,X1] : and_star(X0,not(and_star(xor(truth,X1),X0))) = and_star(X1,not(and_star(xor(truth,X0),X1))),
    inference(forward_demodulation,[status(thm)],[f15,f168]) ).

fof(f307,plain,
    ! [X0,X1] : implies(X0,X1) = xor(truth,and_star(not(X1),X0)),
    inference(paramodulation,[status(thm)],[f25,f76]) ).

fof(f332,plain,
    ! [X0] : implies(truth,X0) = xor(not(truth),X0),
    inference(forward_demodulation,[status(thm)],[f127,f106]) ).

fof(f333,plain,
    ! [X0] : implies(truth,X0) = xor(falsehood,X0),
    inference(forward_demodulation,[status(thm)],[f26,f332]) ).

fof(f334,plain,
    ! [X0] : implies(truth,X0) = X0,
    inference(forward_demodulation,[status(thm)],[f70,f333]) ).

fof(f344,plain,
    ! [X0,X1] : implies(not(X0),X1) = implies(not(X1),X0),
    inference(paramodulation,[status(thm)],[f76,f307]) ).

fof(f345,plain,
    ! [X0,X1] : implies(xor(truth,X0),X1) = implies(not(X1),X0),
    inference(paramodulation,[status(thm)],[f27,f307]) ).

fof(f504,plain,
    ! [X0,X1] : implies(not(and_star(xor(truth,X0),xor(truth,X1))),X1) = xor(truth,and_star(X0,not(and_star(xor(truth,xor(truth,X1)),X0)))),
    inference(paramodulation,[status(thm)],[f169,f98]) ).

fof(f505,plain,
    ! [X0,X1] : implies(not(X0),and_star(xor(truth,X1),xor(truth,X0))) = xor(truth,and_star(X1,not(and_star(xor(truth,xor(truth,X0)),X1)))),
    inference(forward_demodulation,[status(thm)],[f344,f504]) ).

fof(f506,plain,
    ! [X0,X1] : xor(truth,and_star(not(X0),implies(xor(truth,X1),X0))) = xor(truth,and_star(X1,not(and_star(xor(truth,xor(truth,X0)),X1)))),
    inference(forward_demodulation,[status(thm)],[f29,f505]) ).

fof(f507,plain,
    ! [X0,X1] : implies(implies(xor(truth,X0),X1),X1) = xor(truth,and_star(X0,not(and_star(xor(truth,xor(truth,X1)),X0)))),
    inference(forward_demodulation,[status(thm)],[f307,f506]) ).

fof(f508,plain,
    ! [X0,X1] : implies(implies(not(X0),X1),X0) = xor(truth,and_star(X1,not(and_star(xor(truth,xor(truth,X0)),X1)))),
    inference(forward_demodulation,[status(thm)],[f345,f507]) ).

fof(f509,plain,
    ! [X0,X1] : implies(implies(not(X0),X1),X0) = implies(X1,and_star(xor(truth,xor(truth,X0)),X1)),
    inference(forward_demodulation,[status(thm)],[f76,f508]) ).

fof(f510,plain,
    ! [X0,X1] : implies(implies(not(X0),X1),X0) = implies(X1,and_star(xor(not(truth),X0),X1)),
    inference(forward_demodulation,[status(thm)],[f127,f509]) ).

fof(f511,plain,
    ! [X0,X1] : implies(implies(not(X0),X1),X0) = implies(X1,and_star(xor(falsehood,X0),X1)),
    inference(forward_demodulation,[status(thm)],[f26,f510]) ).

fof(f512,plain,
    ! [X0,X1] : implies(implies(not(X0),X1),X0) = implies(X1,and_star(X0,X1)),
    inference(forward_demodulation,[status(thm)],[f70,f511]) ).

fof(f589,plain,
    ! [X0,X1] : implies(X0,X1) = not(and_star(xor(truth,X1),X0)),
    inference(backward_demodulation,[status(thm)],[f69,f98]) ).

fof(f590,plain,
    ! [X0,X1] : implies(X0,X1) = not(and_star(not(X1),X0)),
    inference(forward_demodulation,[status(thm)],[f69,f589]) ).

fof(f592,plain,
    ! [X0,X1] : implies(X0,X1) = not(and_star(X0,not(X1))),
    inference(backward_demodulation,[status(thm)],[f69,f76]) ).

fof(f634,plain,
    ! [X0] : implies(truth,X0) = not(not(X0)),
    inference(paramodulation,[status(thm)],[f18,f590]) ).

fof(f635,plain,
    ! [X0] : X0 = not(not(X0)),
    inference(forward_demodulation,[status(thm)],[f334,f634]) ).

fof(f818,plain,
    ! [X0,X1] : and_star(not(X0),X1) = not(implies(X1,X0)),
    inference(paramodulation,[status(thm)],[f590,f635]) ).

fof(f819,plain,
    ! [X0,X1] : and_star(X0,not(X1)) = not(implies(X0,X1)),
    inference(paramodulation,[status(thm)],[f592,f635]) ).

fof(f828,plain,
    ! [X0,X1] : implies(X0,not(X1)) = not(and_star(X0,X1)),
    inference(paramodulation,[status(thm)],[f635,f592]) ).

fof(f1828,plain,
    ! [X0,X1] : implies(not(and_star(not(X0),X1)),X0) = implies(not(X1),and_star(X0,not(X1))),
    inference(paramodulation,[status(thm)],[f828,f512]) ).

fof(f1829,plain,
    ! [X0,X1] : implies(not(X0),and_star(not(X0),X1)) = implies(not(X1),and_star(X0,not(X1))),
    inference(forward_demodulation,[status(thm)],[f344,f1828]) ).

fof(f1830,plain,
    ! [X0,X1] : implies(not(X0),not(implies(X1,X0))) = implies(not(X1),and_star(X0,not(X1))),
    inference(forward_demodulation,[status(thm)],[f818,f1829]) ).

fof(f1831,plain,
    ! [X0,X1] : not(and_star(not(X0),implies(X1,X0))) = implies(not(X1),and_star(X0,not(X1))),
    inference(forward_demodulation,[status(thm)],[f828,f1830]) ).

fof(f1832,plain,
    ! [X0,X1] : not(not(implies(implies(X0,X1),X1))) = implies(not(X0),and_star(X1,not(X0))),
    inference(forward_demodulation,[status(thm)],[f818,f1831]) ).

fof(f1833,plain,
    ! [X0,X1] : implies(implies(X0,X1),X1) = implies(not(X0),and_star(X1,not(X0))),
    inference(forward_demodulation,[status(thm)],[f635,f1832]) ).

fof(f1834,plain,
    ! [X0,X1] : implies(implies(X0,X1),X1) = implies(not(X0),not(implies(X1,X0))),
    inference(forward_demodulation,[status(thm)],[f819,f1833]) ).

fof(f1835,plain,
    ! [X0,X1] : implies(implies(X0,X1),X1) = not(and_star(not(X0),implies(X1,X0))),
    inference(forward_demodulation,[status(thm)],[f828,f1834]) ).

fof(f1836,plain,
    ! [X0,X1] : implies(implies(X0,X1),X1) = not(not(implies(implies(X1,X0),X0))),
    inference(forward_demodulation,[status(thm)],[f818,f1835]) ).

fof(f1837,plain,
    ! [X0,X1] : implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0),
    inference(forward_demodulation,[status(thm)],[f635,f1836]) ).

fof(f1910,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[f28,f1837]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.12  % Problem  : LCL163-1 : TPTP v8.1.2. Released v1.0.0.
% 0.05/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.33  % Computer : n020.cluster.edu
% 0.10/0.33  % Model    : x86_64 x86_64
% 0.10/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.33  % Memory   : 8042.1875MB
% 0.10/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.33  % CPULimit : 300
% 0.10/0.33  % WCLimit  : 300
% 0.10/0.33  % DateTime : Mon Apr 29 20:30:02 EDT 2024
% 0.10/0.33  % CPUTime  : 
% 0.10/0.34  % Drodi V3.6.0
% 0.16/0.47  % Refutation found
% 0.16/0.47  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.16/0.47  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.49  % Elapsed time: 0.149579 seconds
% 0.16/0.49  % CPU time: 1.098296 seconds
% 0.16/0.49  % Total memory used: 32.344 MB
% 0.16/0.49  % Net memory used: 31.659 MB
%------------------------------------------------------------------------------