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
%------------------------------------------------------------------------------