TSTP Solution File: LCL109-6 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : LCL109-6 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n009.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 12:18:17 EDT 2023

% Result   : Unsatisfiable 44.95s 6.06s
% Output   : CNFRefutation 45.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   31
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   93 (  93 unt;   0 def)
%            Number of atoms       :   93 (  92 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    7 (   7   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   3 avg)
%            Maximal term depth    :    6 (   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   :  146 (; 146   !;   0   ?)

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

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

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

fof(f5,axiom,
    ! [X] : and_star(X,falsehood) = falsehood,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [X] : and_star(xor(truth,X),X) = falsehood,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

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

fof(f10,axiom,
    ! [X,Y,Z] : and_star(and_star(X,Y),Z) = and_star(X,and_star(Y,Z)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

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

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

fof(f14,negated_conjecture,
    implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
    file('/export/starexec/sandbox/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(f19,plain,
    ! [X0] : and_star(X0,falsehood) = falsehood,
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f20,plain,
    ! [X0] : and_star(xor(truth,X0),X0) = falsehood,
    inference(cnf_transformation,[status(esa)],[f6]) ).

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(f24,plain,
    ! [X0,X1,X2] : and_star(and_star(X0,X1),X2) = and_star(X0,and_star(X1,X2)),
    inference(cnf_transformation,[status(esa)],[f10]) ).

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(implies(a,b),implies(b,a)),implies(b,a)) != truth,
    inference(cnf_transformation,[status(esa)],[f14]) ).

fof(f29,plain,
    ! [X0,X1] : xor(X0,xor(truth,X1)) = xor(not(X0),X1),
    inference(forward_demodulation,[status(thm)],[f15,f21]) ).

fof(f30,plain,
    ! [X0,X1] : and_star(not(and_star(xor(truth,X0),X1)),X1) = and_star(xor(and_star(xor(truth,X1),X0),truth),X0),
    inference(forward_demodulation,[status(thm)],[f15,f22]) ).

fof(f31,plain,
    ! [X0,X1] : and_star(not(and_star(xor(truth,X0),X1)),X1) = and_star(not(and_star(xor(truth,X1),X0)),X0),
    inference(forward_demodulation,[status(thm)],[f15,f30]) ).

fof(f34,plain,
    ! [X0] : not(X0) = xor(truth,X0),
    inference(paramodulation,[status(thm)],[f15,f23]) ).

fof(f35,plain,
    ! [X0] : X0 = xor(falsehood,X0),
    inference(paramodulation,[status(thm)],[f16,f23]) ).

fof(f42,plain,
    ! [X0,X1] : implies(X0,X1) = not(and_star(X0,xor(truth,X1))),
    inference(backward_demodulation,[status(thm)],[f34,f27]) ).

fof(f43,plain,
    ! [X0,X1] : implies(X0,X1) = not(and_star(X0,not(X1))),
    inference(forward_demodulation,[status(thm)],[f34,f42]) ).

fof(f44,plain,
    ! [X0,X1] : and_star(not(and_star(xor(truth,X0),X1)),X1) = and_star(not(and_star(not(X1),X0)),X0),
    inference(backward_demodulation,[status(thm)],[f34,f31]) ).

fof(f45,plain,
    ! [X0,X1] : and_star(X0,not(and_star(xor(truth,X1),X0))) = and_star(not(and_star(not(X0),X1)),X1),
    inference(forward_demodulation,[status(thm)],[f25,f44]) ).

fof(f46,plain,
    ! [X0,X1] : and_star(X0,not(and_star(not(X1),X0))) = and_star(not(and_star(not(X0),X1)),X1),
    inference(forward_demodulation,[status(thm)],[f34,f45]) ).

fof(f47,plain,
    ! [X0,X1] : and_star(X0,not(and_star(not(X1),X0))) = and_star(X1,not(and_star(not(X0),X1))),
    inference(forward_demodulation,[status(thm)],[f25,f46]) ).

fof(f48,plain,
    ! [X0,X1] : xor(X0,not(X1)) = xor(not(X0),X1),
    inference(backward_demodulation,[status(thm)],[f34,f29]) ).

fof(f49,plain,
    ! [X0] : and_star(not(X0),X0) = falsehood,
    inference(backward_demodulation,[status(thm)],[f34,f20]) ).

fof(f50,plain,
    ! [X0] : and_star(X0,not(X0)) = falsehood,
    inference(forward_demodulation,[status(thm)],[f25,f49]) ).

fof(f51,plain,
    truth = not(falsehood),
    inference(paramodulation,[status(thm)],[f15,f35]) ).

fof(f58,plain,
    ! [X0] : X0 = and_star(truth,X0),
    inference(paramodulation,[status(thm)],[f18,f25]) ).

fof(f107,plain,
    ! [X0,X1,X2] : implies(and_star(X0,X1),X2) = not(and_star(X0,and_star(X1,not(X2)))),
    inference(paramodulation,[status(thm)],[f24,f43]) ).

fof(f109,plain,
    ! [X0,X1] : implies(X0,X1) = not(and_star(not(X1),X0)),
    inference(paramodulation,[status(thm)],[f25,f43]) ).

fof(f114,plain,
    ! [X0] : implies(X0,truth) = not(and_star(X0,falsehood)),
    inference(paramodulation,[status(thm)],[f26,f43]) ).

fof(f115,plain,
    ! [X0] : implies(X0,truth) = not(falsehood),
    inference(forward_demodulation,[status(thm)],[f19,f114]) ).

fof(f116,plain,
    ! [X0] : implies(X0,truth) = truth,
    inference(forward_demodulation,[status(thm)],[f51,f115]) ).

fof(f117,plain,
    ! [X0,X1] : and_star(X0,not(and_star(not(X1),X0))) = and_star(X1,implies(X1,X0)),
    inference(backward_demodulation,[status(thm)],[f109,f47]) ).

fof(f118,plain,
    ! [X0,X1] : and_star(X0,implies(X0,X1)) = and_star(X1,implies(X1,X0)),
    inference(forward_demodulation,[status(thm)],[f109,f117]) ).

fof(f129,plain,
    ! [X0] : xor(X0,not(truth)) = not(not(X0)),
    inference(paramodulation,[status(thm)],[f15,f48]) ).

fof(f130,plain,
    ! [X0] : xor(X0,falsehood) = not(not(X0)),
    inference(forward_demodulation,[status(thm)],[f26,f129]) ).

fof(f131,plain,
    ! [X0] : X0 = not(not(X0)),
    inference(forward_demodulation,[status(thm)],[f16,f130]) ).

fof(f155,plain,
    ! [X0,X1] : and_star(X0,not(X1)) = not(implies(X0,X1)),
    inference(paramodulation,[status(thm)],[f43,f131]) ).

fof(f160,plain,
    ! [X0,X1] : implies(X0,not(X1)) = not(and_star(X0,X1)),
    inference(paramodulation,[status(thm)],[f131,f43]) ).

fof(f165,plain,
    ! [X0,X1,X2] : implies(and_star(X0,X1),X2) = not(and_star(X0,not(implies(X1,X2)))),
    inference(backward_demodulation,[status(thm)],[f155,f107]) ).

fof(f166,plain,
    ! [X0,X1,X2] : implies(and_star(X0,X1),X2) = implies(X0,implies(X1,X2)),
    inference(forward_demodulation,[status(thm)],[f43,f165]) ).

fof(f167,plain,
    ! [X0] : not(implies(X0,X0)) = falsehood,
    inference(backward_demodulation,[status(thm)],[f155,f50]) ).

fof(f171,plain,
    ! [X0] : implies(X0,X0) = not(falsehood),
    inference(paramodulation,[status(thm)],[f167,f131]) ).

fof(f172,plain,
    ! [X0] : implies(X0,X0) = truth,
    inference(forward_demodulation,[status(thm)],[f51,f171]) ).

fof(f184,plain,
    ! [X0] : implies(truth,X0) = and_star(X0,implies(X0,truth)),
    inference(paramodulation,[status(thm)],[f58,f118]) ).

fof(f185,plain,
    ! [X0] : implies(truth,X0) = and_star(X0,truth),
    inference(forward_demodulation,[status(thm)],[f116,f184]) ).

fof(f186,plain,
    ! [X0] : implies(truth,X0) = X0,
    inference(forward_demodulation,[status(thm)],[f18,f185]) ).

fof(f252,plain,
    ! [X0,X1] : implies(implies(not(X0),X1),X0) = not(and_star(X1,implies(X1,not(X0)))),
    inference(paramodulation,[status(thm)],[f118,f109]) ).

fof(f253,plain,
    ! [X0,X1] : implies(implies(not(X0),X1),X0) = not(and_star(X1,not(and_star(X1,X0)))),
    inference(forward_demodulation,[status(thm)],[f160,f252]) ).

fof(f254,plain,
    ! [X0,X1] : implies(implies(not(X0),X1),X0) = not(not(implies(X1,and_star(X1,X0)))),
    inference(forward_demodulation,[status(thm)],[f155,f253]) ).

fof(f255,plain,
    ! [X0,X1] : implies(implies(not(X0),X1),X0) = implies(X1,and_star(X1,X0)),
    inference(forward_demodulation,[status(thm)],[f131,f254]) ).

fof(f276,plain,
    ! [X0,X1] : and_star(not(X0),X1) = not(implies(X1,X0)),
    inference(paramodulation,[status(thm)],[f109,f131]) ).

fof(f763,plain,
    ! [X0,X1,X2] : implies(and_star(X0,implies(X0,X1)),X2) = implies(X1,implies(implies(X1,X0),X2)),
    inference(paramodulation,[status(thm)],[f118,f166]) ).

fof(f764,plain,
    ! [X0,X1,X2] : implies(X0,implies(implies(X0,X1),X2)) = implies(X1,implies(implies(X1,X0),X2)),
    inference(forward_demodulation,[status(thm)],[f166,f763]) ).

fof(f771,plain,
    ! [X0,X1,X2] : implies(and_star(X0,X1),X2) = implies(X1,implies(X0,X2)),
    inference(paramodulation,[status(thm)],[f25,f166]) ).

fof(f772,plain,
    ! [X0,X1,X2] : implies(X0,implies(X1,X2)) = implies(X1,implies(X0,X2)),
    inference(forward_demodulation,[status(thm)],[f166,f771]) ).

fof(f1016,plain,
    ! [X0,X1] : implies(X0,truth) = implies(X1,implies(X0,X1)),
    inference(paramodulation,[status(thm)],[f172,f772]) ).

fof(f1017,plain,
    ! [X0,X1] : truth = implies(X0,implies(X1,X0)),
    inference(forward_demodulation,[status(thm)],[f116,f1016]) ).

fof(f1047,plain,
    implies(implies(b,implies(implies(a,b),a)),implies(b,a)) != truth,
    inference(paramodulation,[status(thm)],[f772,f28]) ).

fof(f1048,plain,
    implies(b,implies(implies(b,implies(implies(a,b),a)),a)) != truth,
    inference(forward_demodulation,[status(thm)],[f772,f1047]) ).

fof(f2288,plain,
    ! [X0,X1] : implies(not(and_star(not(X0),X1)),X0) = implies(not(X1),and_star(not(X1),X0)),
    inference(paramodulation,[status(thm)],[f160,f255]) ).

fof(f2289,plain,
    ! [X0,X1] : implies(not(not(implies(X0,X1))),X1) = implies(not(X0),and_star(not(X0),X1)),
    inference(forward_demodulation,[status(thm)],[f276,f2288]) ).

fof(f2290,plain,
    ! [X0,X1] : implies(implies(X0,X1),X1) = implies(not(X0),and_star(not(X0),X1)),
    inference(forward_demodulation,[status(thm)],[f131,f2289]) ).

fof(f2291,plain,
    ! [X0,X1] : implies(implies(X0,X1),X1) = implies(not(X0),not(implies(X1,X0))),
    inference(forward_demodulation,[status(thm)],[f276,f2290]) ).

fof(f2292,plain,
    ! [X0,X1] : implies(implies(X0,X1),X1) = not(and_star(not(X0),implies(X1,X0))),
    inference(forward_demodulation,[status(thm)],[f160,f2291]) ).

fof(f2293,plain,
    ! [X0,X1] : implies(implies(X0,X1),X1) = not(not(implies(implies(X1,X0),X0))),
    inference(forward_demodulation,[status(thm)],[f276,f2292]) ).

fof(f2294,plain,
    ! [X0,X1] : implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0),
    inference(forward_demodulation,[status(thm)],[f131,f2293]) ).

fof(f2436,plain,
    ! [X0,X1] : implies(truth,implies(X0,X1)) = implies(implies(implies(X0,X1),X1),X1),
    inference(paramodulation,[status(thm)],[f1017,f2294]) ).

fof(f2437,plain,
    ! [X0,X1] : implies(X0,X1) = implies(implies(implies(X0,X1),X1),X1),
    inference(forward_demodulation,[status(thm)],[f186,f2436]) ).

fof(f2713,plain,
    ! [X0,X1] : implies(X0,X1) = implies(implies(implies(X1,X0),X0),X1),
    inference(paramodulation,[status(thm)],[f2294,f2437]) ).

fof(f34264,plain,
    ! [X0,X1] : implies(implies(X0,X1),implies(X1,X0)) = implies(X1,implies(implies(X1,implies(X0,X1)),X0)),
    inference(paramodulation,[status(thm)],[f2713,f764]) ).

fof(f34265,plain,
    ! [X0,X1] : implies(X0,implies(implies(X1,X0),X1)) = implies(X0,implies(implies(X0,implies(X1,X0)),X1)),
    inference(forward_demodulation,[status(thm)],[f772,f34264]) ).

fof(f34266,plain,
    ! [X0,X1] : implies(X0,implies(implies(X1,X0),X1)) = implies(X0,implies(truth,X1)),
    inference(forward_demodulation,[status(thm)],[f1017,f34265]) ).

fof(f34267,plain,
    ! [X0,X1] : implies(X0,implies(implies(X1,X0),X1)) = implies(X0,X1),
    inference(forward_demodulation,[status(thm)],[f186,f34266]) ).

fof(f35254,plain,
    implies(b,implies(implies(b,a),a)) != truth,
    inference(backward_demodulation,[status(thm)],[f34267,f1048]) ).

fof(f35255,plain,
    implies(a,implies(implies(a,b),a)) != truth,
    inference(forward_demodulation,[status(thm)],[f764,f35254]) ).

fof(f35256,plain,
    truth != truth,
    inference(forward_demodulation,[status(thm)],[f1017,f35255]) ).

fof(f35257,plain,
    $false,
    inference(trivial_equality_resolution,[status(esa)],[f35256]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10  % Problem  : LCL109-6 : TPTP v8.1.2. Released v1.0.0.
% 0.02/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.31  % Computer : n009.cluster.edu
% 0.09/0.31  % Model    : x86_64 x86_64
% 0.09/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.31  % Memory   : 8042.1875MB
% 0.09/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.31  % CPULimit : 300
% 0.09/0.31  % WCLimit  : 300
% 0.09/0.31  % DateTime : Tue May 30 09:42:01 EDT 2023
% 0.09/0.31  % CPUTime  : 
% 0.15/0.31  % Drodi V3.5.1
% 44.95/6.06  % Refutation found
% 44.95/6.06  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 44.95/6.06  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 46.21/6.21  % Elapsed time: 5.880523 seconds
% 46.21/6.21  % CPU time: 46.089197 seconds
% 46.21/6.21  % Memory used: 373.508 MB
%------------------------------------------------------------------------------