TSTP Solution File: GRP002-2 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : GRP002-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n008.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 20:18:43 EDT 2024
% Result : Unsatisfiable 0.15s 0.51s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 12
% Syntax : Number of formulae : 111 ( 111 unt; 0 def)
% Number of atoms : 111 ( 110 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 60 ( 60 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : multiply(X,identity) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : multiply(X,inverse(X)) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,hypothesis,
! [X] : multiply(X,multiply(X,X)) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
multiply(a,b) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
multiply(c,inverse(a)) = d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
multiply(d,inverse(b)) = h,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
multiply(h,b) = j,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
multiply(j,inverse(h)) = k,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
multiply(k,inverse(b)) != identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f14,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f15,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f16,plain,
! [X0] : multiply(X0,identity) = X0,
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f17,plain,
! [X0] : multiply(X0,inverse(X0)) = identity,
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f18,plain,
! [X0] : multiply(X0,multiply(X0,X0)) = identity,
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f19,plain,
multiply(a,b) = c,
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f20,plain,
multiply(c,inverse(a)) = d,
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f21,plain,
multiply(d,inverse(b)) = h,
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f22,plain,
multiply(h,b) = j,
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f23,plain,
multiply(j,inverse(h)) = k,
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f24,plain,
multiply(k,inverse(b)) != identity,
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f31,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f14,f15]) ).
fof(f32,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f13,f31]) ).
fof(f33,plain,
! [X0] : multiply(j,X0) = multiply(h,multiply(b,X0)),
inference(paramodulation,[status(thm)],[f22,f15]) ).
fof(f34,plain,
! [X0] : multiply(c,X0) = multiply(a,multiply(b,X0)),
inference(paramodulation,[status(thm)],[f19,f15]) ).
fof(f39,plain,
! [X0,X1] : multiply(X0,multiply(X1,inverse(multiply(X0,X1)))) = identity,
inference(paramodulation,[status(thm)],[f15,f17]) ).
fof(f44,plain,
! [X0,X1] : multiply(identity,X0) = multiply(X1,multiply(inverse(X1),X0)),
inference(paramodulation,[status(thm)],[f17,f15]) ).
fof(f45,plain,
! [X0,X1] : X0 = multiply(X1,multiply(inverse(X1),X0)),
inference(forward_demodulation,[status(thm)],[f13,f44]) ).
fof(f46,plain,
! [X0] : multiply(d,X0) = multiply(c,multiply(inverse(a),X0)),
inference(paramodulation,[status(thm)],[f20,f15]) ).
fof(f67,plain,
! [X0] : multiply(inverse(X0),inverse(X0)) = multiply(X0,identity),
inference(paramodulation,[status(thm)],[f18,f45]) ).
fof(f68,plain,
! [X0] : multiply(inverse(X0),inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f16,f67]) ).
fof(f69,plain,
! [X0] : inverse(inverse(X0)) = multiply(X0,identity),
inference(paramodulation,[status(thm)],[f17,f45]) ).
fof(f70,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f16,f69]) ).
fof(f83,plain,
! [X0] : multiply(X0,inverse(inverse(X0))) = inverse(X0),
inference(paramodulation,[status(thm)],[f70,f68]) ).
fof(f84,plain,
! [X0] : multiply(X0,X0) = inverse(X0),
inference(forward_demodulation,[status(thm)],[f70,f83]) ).
fof(f95,plain,
! [X0,X1] : multiply(X0,multiply(X1,multiply(X0,X1))) = inverse(multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f15,f84]) ).
fof(f103,plain,
! [X0,X1] : multiply(inverse(X0),X1) = multiply(X0,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f84,f15]) ).
fof(f110,plain,
inverse(h) = multiply(inverse(j),k),
inference(paramodulation,[status(thm)],[f23,f32]) ).
fof(f111,plain,
inverse(b) = multiply(inverse(d),h),
inference(paramodulation,[status(thm)],[f21,f32]) ).
fof(f112,plain,
inverse(a) = multiply(inverse(c),d),
inference(paramodulation,[status(thm)],[f20,f32]) ).
fof(f117,plain,
b = multiply(inverse(h),j),
inference(paramodulation,[status(thm)],[f22,f32]) ).
fof(f118,plain,
b = multiply(inverse(a),c),
inference(paramodulation,[status(thm)],[f19,f32]) ).
fof(f134,plain,
! [X0] : multiply(b,X0) = multiply(inverse(a),multiply(c,X0)),
inference(paramodulation,[status(thm)],[f118,f15]) ).
fof(f148,plain,
multiply(j,inverse(b)) = multiply(h,identity),
inference(paramodulation,[status(thm)],[f17,f33]) ).
fof(f149,plain,
multiply(j,inverse(b)) = h,
inference(forward_demodulation,[status(thm)],[f16,f148]) ).
fof(f168,plain,
multiply(c,inverse(b)) = multiply(a,identity),
inference(paramodulation,[status(thm)],[f17,f34]) ).
fof(f169,plain,
multiply(c,inverse(b)) = a,
inference(forward_demodulation,[status(thm)],[f16,f168]) ).
fof(f177,plain,
inverse(b) = multiply(inverse(c),a),
inference(paramodulation,[status(thm)],[f169,f32]) ).
fof(f267,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X1,X0))) = multiply(inverse(X1),identity),
inference(paramodulation,[status(thm)],[f39,f32]) ).
fof(f268,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X1,X0))) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f16,f267]) ).
fof(f286,plain,
multiply(inverse(b),inverse(h)) = inverse(j),
inference(paramodulation,[status(thm)],[f149,f268]) ).
fof(f288,plain,
multiply(inverse(b),inverse(h)) = inverse(d),
inference(paramodulation,[status(thm)],[f21,f268]) ).
fof(f289,plain,
inverse(j) = inverse(d),
inference(forward_demodulation,[status(thm)],[f286,f288]) ).
fof(f292,plain,
! [X0,X1,X2] : multiply(X0,inverse(multiply(X1,multiply(X2,X0)))) = inverse(multiply(X1,X2)),
inference(paramodulation,[status(thm)],[f15,f268]) ).
fof(f296,plain,
multiply(d,inverse(inverse(a))) = inverse(inverse(c)),
inference(paramodulation,[status(thm)],[f112,f268]) ).
fof(f297,plain,
multiply(d,a) = inverse(inverse(c)),
inference(forward_demodulation,[status(thm)],[f70,f296]) ).
fof(f298,plain,
multiply(d,a) = c,
inference(forward_demodulation,[status(thm)],[f70,f297]) ).
fof(f299,plain,
multiply(h,inverse(inverse(b))) = inverse(inverse(d)),
inference(paramodulation,[status(thm)],[f111,f268]) ).
fof(f300,plain,
multiply(h,b) = inverse(inverse(d)),
inference(forward_demodulation,[status(thm)],[f70,f299]) ).
fof(f301,plain,
j = inverse(inverse(d)),
inference(forward_demodulation,[status(thm)],[f22,f300]) ).
fof(f302,plain,
j = d,
inference(forward_demodulation,[status(thm)],[f70,f301]) ).
fof(f308,plain,
multiply(k,inverse(inverse(h))) = inverse(inverse(j)),
inference(paramodulation,[status(thm)],[f110,f268]) ).
fof(f309,plain,
multiply(k,h) = inverse(inverse(j)),
inference(forward_demodulation,[status(thm)],[f70,f308]) ).
fof(f310,plain,
multiply(k,h) = j,
inference(forward_demodulation,[status(thm)],[f70,f309]) ).
fof(f311,plain,
multiply(k,h) = d,
inference(forward_demodulation,[status(thm)],[f302,f310]) ).
fof(f325,plain,
! [X0] : multiply(multiply(b,X0),inverse(multiply(j,X0))) = inverse(h),
inference(paramodulation,[status(thm)],[f33,f268]) ).
fof(f326,plain,
! [X0] : multiply(b,multiply(X0,inverse(multiply(j,X0)))) = inverse(h),
inference(forward_demodulation,[status(thm)],[f15,f325]) ).
fof(f327,plain,
multiply(b,inverse(j)) = inverse(h),
inference(forward_demodulation,[status(thm)],[f268,f326]) ).
fof(f328,plain,
multiply(b,inverse(d)) = inverse(h),
inference(forward_demodulation,[status(thm)],[f289,f327]) ).
fof(f332,plain,
! [X0] : multiply(multiply(b,X0),inverse(multiply(c,X0))) = inverse(a),
inference(paramodulation,[status(thm)],[f34,f268]) ).
fof(f333,plain,
! [X0] : multiply(b,multiply(X0,inverse(multiply(c,X0)))) = inverse(a),
inference(forward_demodulation,[status(thm)],[f15,f332]) ).
fof(f334,plain,
multiply(b,inverse(c)) = inverse(a),
inference(forward_demodulation,[status(thm)],[f268,f333]) ).
fof(f352,plain,
! [X0,X1] : inverse(multiply(X0,inverse(X1))) = multiply(X1,inverse(X0)),
inference(paramodulation,[status(thm)],[f268,f45]) ).
fof(f354,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = multiply(inverse(X1),inverse(X0)),
inference(paramodulation,[status(thm)],[f268,f32]) ).
fof(f371,plain,
b = multiply(inverse(h),d),
inference(backward_demodulation,[status(thm)],[f302,f117]) ).
fof(f393,plain,
! [X0] : multiply(c,X0) = multiply(d,multiply(a,X0)),
inference(paramodulation,[status(thm)],[f298,f15]) ).
fof(f400,plain,
! [X0] : multiply(d,X0) = multiply(k,multiply(h,X0)),
inference(paramodulation,[status(thm)],[f311,f15]) ).
fof(f401,plain,
d = multiply(h,b),
inference(paramodulation,[status(thm)],[f371,f45]) ).
fof(f409,plain,
! [X0] : multiply(d,X0) = multiply(h,multiply(b,X0)),
inference(paramodulation,[status(thm)],[f401,f15]) ).
fof(f422,plain,
multiply(d,c) = multiply(c,b),
inference(paramodulation,[status(thm)],[f118,f46]) ).
fof(f435,plain,
multiply(d,inverse(a)) = multiply(c,inverse(inverse(a))),
inference(paramodulation,[status(thm)],[f84,f46]) ).
fof(f436,plain,
multiply(d,inverse(a)) = multiply(c,a),
inference(forward_demodulation,[status(thm)],[f70,f435]) ).
fof(f455,plain,
multiply(c,inverse(d)) = multiply(a,inverse(h)),
inference(paramodulation,[status(thm)],[f328,f34]) ).
fof(f502,plain,
! [X0] : multiply(c,multiply(b,X0)) = multiply(d,multiply(c,X0)),
inference(paramodulation,[status(thm)],[f34,f393]) ).
fof(f537,plain,
multiply(d,inverse(c)) = multiply(h,inverse(a)),
inference(paramodulation,[status(thm)],[f334,f409]) ).
fof(f547,plain,
! [X0] : multiply(d,multiply(b,X0)) = multiply(k,multiply(d,X0)),
inference(paramodulation,[status(thm)],[f409,f400]) ).
fof(f892,plain,
inverse(multiply(c,a)) = multiply(a,inverse(d)),
inference(paramodulation,[status(thm)],[f436,f352]) ).
fof(f1086,plain,
multiply(b,c) = multiply(inverse(a),inverse(c)),
inference(paramodulation,[status(thm)],[f84,f134]) ).
fof(f1087,plain,
multiply(b,c) = inverse(multiply(c,a)),
inference(forward_demodulation,[status(thm)],[f354,f1086]) ).
fof(f1088,plain,
multiply(b,c) = multiply(a,inverse(d)),
inference(forward_demodulation,[status(thm)],[f892,f1087]) ).
fof(f1106,plain,
multiply(c,inverse(d)) = multiply(d,multiply(b,c)),
inference(paramodulation,[status(thm)],[f1088,f393]) ).
fof(f1107,plain,
multiply(a,inverse(h)) = multiply(d,multiply(b,c)),
inference(forward_demodulation,[status(thm)],[f455,f1106]) ).
fof(f1108,plain,
inverse(multiply(b,c)) = multiply(d,inverse(a)),
inference(paramodulation,[status(thm)],[f1088,f352]) ).
fof(f1109,plain,
inverse(multiply(b,c)) = multiply(c,a),
inference(forward_demodulation,[status(thm)],[f436,f1108]) ).
fof(f2519,plain,
multiply(c,multiply(b,c)) = multiply(d,inverse(c)),
inference(paramodulation,[status(thm)],[f84,f502]) ).
fof(f3624,plain,
multiply(d,multiply(b,c)) = multiply(k,multiply(c,b)),
inference(paramodulation,[status(thm)],[f422,f547]) ).
fof(f3625,plain,
multiply(a,inverse(h)) = multiply(k,multiply(c,b)),
inference(forward_demodulation,[status(thm)],[f1107,f3624]) ).
fof(f3696,plain,
multiply(b,inverse(multiply(a,inverse(h)))) = inverse(multiply(k,c)),
inference(paramodulation,[status(thm)],[f3625,f292]) ).
fof(f3697,plain,
multiply(b,multiply(h,inverse(a))) = inverse(multiply(k,c)),
inference(forward_demodulation,[status(thm)],[f352,f3696]) ).
fof(f3698,plain,
multiply(b,multiply(d,inverse(c))) = inverse(multiply(k,c)),
inference(forward_demodulation,[status(thm)],[f537,f3697]) ).
fof(f3972,plain,
multiply(b,multiply(d,inverse(c))) = inverse(multiply(b,c)),
inference(paramodulation,[status(thm)],[f2519,f95]) ).
fof(f3973,plain,
inverse(multiply(k,c)) = inverse(multiply(b,c)),
inference(forward_demodulation,[status(thm)],[f3698,f3972]) ).
fof(f3974,plain,
inverse(multiply(k,c)) = multiply(c,a),
inference(forward_demodulation,[status(thm)],[f1109,f3973]) ).
fof(f4723,plain,
multiply(multiply(k,c),multiply(c,a)) = identity,
inference(paramodulation,[status(thm)],[f3974,f17]) ).
fof(f4724,plain,
multiply(k,multiply(c,multiply(c,a))) = identity,
inference(forward_demodulation,[status(thm)],[f15,f4723]) ).
fof(f4725,plain,
multiply(k,multiply(inverse(c),a)) = identity,
inference(forward_demodulation,[status(thm)],[f103,f4724]) ).
fof(f4726,plain,
multiply(k,inverse(b)) = identity,
inference(forward_demodulation,[status(thm)],[f177,f4725]) ).
fof(f4727,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f4726,f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : GRP002-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.02/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30 % Computer : n008.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Tue Apr 30 00:18:42 EDT 2024
% 0.09/0.30 % CPUTime :
% 0.09/0.31 % Drodi V3.6.0
% 0.15/0.51 % Refutation found
% 0.15/0.51 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.54 % Elapsed time: 0.229271 seconds
% 0.15/0.54 % CPU time: 1.737476 seconds
% 0.15/0.54 % Total memory used: 49.387 MB
% 0.15/0.54 % Net memory used: 47.398 MB
%------------------------------------------------------------------------------