TSTP Solution File: BOO012-3 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : BOO012-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n011.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 20:12:54 EDT 2024
% Result : Unsatisfiable 54.68s 7.18s
% Output : CNFRefutation 55.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 20
% Syntax : Number of formulae : 101 ( 57 unt; 0 def)
% Number of atoms : 183 ( 33 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 167 ( 85 ~; 82 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 259 ( 259 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] : sum(X,Y,add(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,Z] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : sum(additive_identity,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] : product(multiplicative_identity,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y,V1,Z,V2,V3,V4] :
( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(X,V3,V4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [Y,X,V1,Z,V2,V3,V4] :
( ~ product(Y,X,V1)
| ~ product(Z,X,V2)
| ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X] : sum(inverse(X),X,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X] : sum(X,inverse(X),multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X] : product(inverse(X),X,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [X] : product(X,inverse(X),additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X,Y,U,V] :
( ~ sum(X,Y,U)
| ~ sum(X,Y,V)
| U = V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X,Y,U,V] :
( ~ product(X,Y,U)
| ~ product(X,Y,V)
| U = V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [X] : sum(X,multiplicative_identity,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [X,Y,Z] :
( ~ product(X,Y,Z)
| sum(X,Z,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [X,Y,Z] :
( ~ sum(X,Y,Z)
| product(X,Z,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [X,Y] : product(X,add(X,Y),X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [X,Y,X_plus_Y,Z,Y_plus_Z,X_plus_Y_plus_Z] :
( ~ sum(X,Y,X_plus_Y)
| ~ sum(Y,Z,Y_plus_Z)
| ~ sum(X,Y_plus_Z,X_plus_Y_plus_Z)
| sum(X_plus_Y,Z,X_plus_Y_plus_Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
inverse(inverse(x)) != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,plain,
! [X0,X1] : sum(X0,X1,add(X0,X1)),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f37,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| sum(X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ~ product(X0,X1,X2)
| product(X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f40,plain,
! [X0] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f42,plain,
! [X0] : product(multiplicative_identity,X0,X0),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f46,plain,
! [X,V3,V4] :
( ! [V1,V2] :
( ! [Y,Z] :
( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3) )
| ~ sum(V1,V2,V4) )
| product(X,V3,V4) ),
inference(miniscoping,[status(esa)],[f10]) ).
fof(f47,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X4)
| ~ sum(X1,X3,X5)
| ~ sum(X2,X4,X6)
| product(X0,X5,X6) ),
inference(cnf_transformation,[status(esa)],[f46]) ).
fof(f50,plain,
! [X,V3,V4] :
( ! [V1,V2] :
( ! [Y,Z] :
( ~ product(Y,X,V1)
| ~ product(Z,X,V2)
| ~ sum(Y,Z,V3) )
| ~ sum(V1,V2,V4) )
| product(V3,X,V4) ),
inference(miniscoping,[status(esa)],[f12]) ).
fof(f51,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ product(X0,X1,X2)
| ~ product(X3,X1,X4)
| ~ sum(X0,X3,X5)
| ~ sum(X2,X4,X6)
| product(X5,X1,X6) ),
inference(cnf_transformation,[status(esa)],[f50]) ).
fof(f60,plain,
! [X0] : sum(inverse(X0),X0,multiplicative_identity),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f61,plain,
! [X0] : sum(X0,inverse(X0),multiplicative_identity),
inference(cnf_transformation,[status(esa)],[f18]) ).
fof(f62,plain,
! [X0] : product(inverse(X0),X0,additive_identity),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f63,plain,
! [X0] : product(X0,inverse(X0),additive_identity),
inference(cnf_transformation,[status(esa)],[f20]) ).
fof(f64,plain,
! [U,V] :
( ! [X,Y] :
( ~ sum(X,Y,U)
| ~ sum(X,Y,V) )
| U = V ),
inference(miniscoping,[status(esa)],[f21]) ).
fof(f65,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,X1,X2)
| ~ sum(X0,X1,X3)
| X2 = X3 ),
inference(cnf_transformation,[status(esa)],[f64]) ).
fof(f66,plain,
! [U,V] :
( ! [X,Y] :
( ~ product(X,Y,U)
| ~ product(X,Y,V) )
| U = V ),
inference(miniscoping,[status(esa)],[f22]) ).
fof(f67,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X0,X1,X3)
| X2 = X3 ),
inference(cnf_transformation,[status(esa)],[f66]) ).
fof(f70,plain,
! [X0] : sum(X0,multiplicative_identity,multiplicative_identity),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f72,plain,
! [X,Z] :
( ! [Y] : ~ product(X,Y,Z)
| sum(X,Z,X) ),
inference(miniscoping,[status(esa)],[f27]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ~ product(X0,X1,X2)
| sum(X0,X2,X0) ),
inference(cnf_transformation,[status(esa)],[f72]) ).
fof(f74,plain,
! [X,Z] :
( ! [Y] : ~ sum(X,Y,Z)
| product(X,Z,X) ),
inference(miniscoping,[status(esa)],[f28]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| product(X0,X2,X0) ),
inference(cnf_transformation,[status(esa)],[f74]) ).
fof(f77,plain,
! [X0,X1] : product(X0,add(X0,X1),X0),
inference(cnf_transformation,[status(esa)],[f30]) ).
fof(f78,plain,
! [X_plus_Y,Z,X_plus_Y_plus_Z] :
( ! [X,Y_plus_Z] :
( ! [Y] :
( ~ sum(X,Y,X_plus_Y)
| ~ sum(Y,Z,Y_plus_Z) )
| ~ sum(X,Y_plus_Z,X_plus_Y_plus_Z) )
| sum(X_plus_Y,Z,X_plus_Y_plus_Z) ),
inference(miniscoping,[status(esa)],[f31]) ).
fof(f79,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sum(X0,X1,X2)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X4,X5)
| sum(X2,X3,X5) ),
inference(cnf_transformation,[status(esa)],[f78]) ).
fof(f86,plain,
inverse(inverse(x)) != x,
inference(cnf_transformation,[status(esa)],[f35]) ).
fof(f90,plain,
! [X0] : sum(multiplicative_identity,X0,multiplicative_identity),
inference(resolution,[status(thm)],[f38,f70]) ).
fof(f93,plain,
! [X0,X1] : sum(X0,X1,add(X1,X0)),
inference(resolution,[status(thm)],[f38,f36]) ).
fof(f100,plain,
! [X0,X1] : product(X0,X1,multiply(X1,X0)),
inference(resolution,[status(thm)],[f39,f37]) ).
fof(f102,plain,
! [X0,X1] : product(add(X0,X1),X0,X0),
inference(resolution,[status(thm)],[f77,f39]) ).
fof(f117,plain,
! [X0,X1] : sum(X0,multiply(X1,X0),X0),
inference(resolution,[status(thm)],[f73,f100]) ).
fof(f120,plain,
! [X0,X1] : sum(multiply(X0,X1),X1,X1),
inference(resolution,[status(thm)],[f117,f38]) ).
fof(f123,plain,
! [X0,X1] : product(multiply(X0,X1),X1,multiply(X0,X1)),
inference(resolution,[status(thm)],[f75,f120]) ).
fof(f139,plain,
! [X0,X1] :
( ~ sum(multiplicative_identity,X0,X1)
| multiplicative_identity = X1 ),
inference(resolution,[status(thm)],[f65,f90]) ).
fof(f140,plain,
! [X0,X1,X2] :
( ~ sum(multiply(X0,X1),X1,X2)
| X1 = X2 ),
inference(resolution,[status(thm)],[f65,f120]) ).
fof(f150,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| add(X0,X1) = X2 ),
inference(resolution,[status(thm)],[f65,f36]) ).
fof(f176,plain,
! [X0,X1,X2,X3,X4] :
( ~ product(X0,X1,X2)
| ~ sum(inverse(X0),X1,X3)
| ~ sum(additive_identity,X2,X4)
| product(X0,X3,X4) ),
inference(resolution,[status(thm)],[f47,f63]) ).
fof(f292,plain,
! [X0,X1] : X0 = add(multiply(X1,X0),X0),
inference(resolution,[status(thm)],[f140,f36]) ).
fof(f393,plain,
! [X0,X1,X2,X3,X4] :
( ~ product(X0,X1,X2)
| ~ sum(inverse(X1),X0,X3)
| ~ sum(additive_identity,X2,X4)
| product(X3,X1,X4) ),
inference(resolution,[status(thm)],[f51,f62]) ).
fof(f446,plain,
! [X0,X1,X2,X3] :
( ~ sum(inverse(X0),X1,X2)
| ~ sum(additive_identity,multiply(X1,X0),X3)
| product(X0,X2,X3) ),
inference(resolution,[status(thm)],[f176,f100]) ).
fof(f614,plain,
! [X0,X1,X2] :
( ~ product(add(X0,X1),X0,X2)
| X0 = X2 ),
inference(resolution,[status(thm)],[f67,f102]) ).
fof(f616,plain,
! [X0,X1] :
( ~ product(multiplicative_identity,X0,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[f67,f42]) ).
fof(f623,plain,
! [X0,X1,X2] :
( ~ product(X0,X1,X2)
| multiply(X1,X0) = X2 ),
inference(resolution,[status(thm)],[f67,f100]) ).
fof(f653,plain,
! [X0,X1,X2,X3] :
( ~ sum(inverse(X0),X1,X2)
| ~ sum(additive_identity,multiply(X1,X0),X3)
| product(X2,X0,X3) ),
inference(resolution,[status(thm)],[f393,f37]) ).
fof(f710,plain,
! [X0,X1] : X0 = multiply(X0,add(X0,X1)),
inference(resolution,[status(thm)],[f614,f100]) ).
fof(f782,plain,
! [X0] : X0 = multiply(X0,multiplicative_identity),
inference(resolution,[status(thm)],[f616,f100]) ).
fof(f783,plain,
! [X0] : X0 = multiply(multiplicative_identity,X0),
inference(resolution,[status(thm)],[f616,f37]) ).
fof(f852,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,X1,X2)
| ~ sum(inverse(X0),X2,X3)
| sum(multiplicative_identity,X1,X3) ),
inference(resolution,[status(thm)],[f79,f60]) ).
fof(f857,plain,
! [X0,X1,X2,X3] :
( ~ sum(inverse(X0),X1,X2)
| ~ sum(X0,X2,X3)
| sum(multiplicative_identity,X1,X3) ),
inference(resolution,[status(thm)],[f79,f61]) ).
fof(f1036,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(resolution,[status(thm)],[f150,f93]) ).
fof(f1265,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(resolution,[status(thm)],[f623,f37]) ).
fof(f1465,plain,
! [X0,X1] : product(multiply(X0,X1),X1,multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f1265,f123]) ).
fof(f1530,plain,
! [X0,X1,X2] :
( ~ sum(inverse(multiply(X0,X1)),X1,X2)
| sum(multiplicative_identity,X1,X2) ),
inference(resolution,[status(thm)],[f852,f120]) ).
fof(f1584,plain,
! [X0,X1] : sum(multiplicative_identity,X0,add(X0,inverse(multiply(X1,X0)))),
inference(resolution,[status(thm)],[f1530,f93]) ).
fof(f1600,plain,
! [X0,X1] : multiplicative_identity = add(X0,inverse(multiply(X1,X0))),
inference(resolution,[status(thm)],[f1584,f139]) ).
fof(f1693,plain,
! [X0,X1] : multiplicative_identity = add(X0,inverse(multiply(X0,X1))),
inference(paramodulation,[status(thm)],[f1265,f1600]) ).
fof(f1722,plain,
! [X0,X1,X2] :
( ~ sum(X0,add(X1,inverse(X0)),X2)
| sum(multiplicative_identity,X1,X2) ),
inference(resolution,[status(thm)],[f857,f93]) ).
fof(f2503,plain,
! [X0,X1] : sum(X0,inverse(multiply(X0,X1)),multiplicative_identity),
inference(paramodulation,[status(thm)],[f1693,f36]) ).
fof(f3966,plain,
! [X0,X1,X2] :
( ~ product(multiply(X0,X1),X1,X2)
| multiply(X1,X0) = X2 ),
inference(resolution,[status(thm)],[f1465,f67]) ).
fof(f5196,plain,
! [X0,X1] : sum(multiplicative_identity,X0,add(add(X0,inverse(X1)),X1)),
inference(resolution,[status(thm)],[f1722,f93]) ).
fof(f5197,plain,
! [X0,X1] : sum(multiplicative_identity,X0,add(X1,add(X0,inverse(X1)))),
inference(forward_demodulation,[status(thm)],[f1036,f5196]) ).
fof(f5214,plain,
! [X0,X1] : multiplicative_identity = add(X0,add(X1,inverse(X0))),
inference(resolution,[status(thm)],[f5197,f139]) ).
fof(f5342,plain,
! [X0,X1] : multiplicative_identity = add(X0,add(inverse(X0),X1)),
inference(paramodulation,[status(thm)],[f1036,f5214]) ).
fof(f5605,plain,
! [X0,X1] : sum(add(inverse(X0),X1),X0,multiplicative_identity),
inference(paramodulation,[status(thm)],[f5342,f93]) ).
fof(f10719,plain,
! [X0,X1,X2] :
( ~ sum(additive_identity,multiply(inverse(multiply(inverse(X0),X1)),X0),X2)
| product(X0,multiplicative_identity,X2) ),
inference(resolution,[status(thm)],[f446,f2503]) ).
fof(f10720,plain,
! [X0,X1,X2] :
( ~ sum(additive_identity,multiply(X0,inverse(multiply(inverse(X0),X1))),X2)
| product(X0,multiplicative_identity,X2) ),
inference(forward_demodulation,[status(thm)],[f1265,f10719]) ).
fof(f10770,plain,
! [X0,X1] : product(X0,multiplicative_identity,multiply(X0,inverse(multiply(inverse(X0),X1)))),
inference(resolution,[status(thm)],[f10720,f40]) ).
fof(f23769,plain,
! [X0,X1] : multiply(multiplicative_identity,X0) = multiply(multiply(X0,multiplicative_identity),inverse(multiply(inverse(multiply(X0,multiplicative_identity)),X1))),
inference(resolution,[status(thm)],[f10770,f3966]) ).
fof(f23770,plain,
! [X0,X1] : X0 = multiply(multiply(X0,multiplicative_identity),inverse(multiply(inverse(multiply(X0,multiplicative_identity)),X1))),
inference(forward_demodulation,[status(thm)],[f783,f23769]) ).
fof(f23771,plain,
! [X0,X1] : X0 = multiply(X0,inverse(multiply(inverse(multiply(X0,multiplicative_identity)),X1))),
inference(forward_demodulation,[status(thm)],[f782,f23770]) ).
fof(f23772,plain,
! [X0,X1] : X0 = multiply(X0,inverse(multiply(inverse(X0),X1))),
inference(forward_demodulation,[status(thm)],[f782,f23771]) ).
fof(f24438,plain,
! [X0] : X0 = multiply(X0,inverse(inverse(X0))),
inference(paramodulation,[status(thm)],[f710,f23772]) ).
fof(f26050,plain,
! [X0] : inverse(inverse(X0)) = add(X0,inverse(inverse(X0))),
inference(paramodulation,[status(thm)],[f24438,f292]) ).
fof(f29119,plain,
! [X0] : sum(inverse(inverse(inverse(X0))),X0,multiplicative_identity),
inference(paramodulation,[status(thm)],[f26050,f5605]) ).
fof(f29706,plain,
! [X0,X1] :
( ~ sum(additive_identity,multiply(X0,inverse(inverse(X0))),X1)
| product(multiplicative_identity,inverse(inverse(X0)),X1) ),
inference(resolution,[status(thm)],[f29119,f653]) ).
fof(f29707,plain,
! [X0,X1] :
( ~ sum(additive_identity,X0,X1)
| product(multiplicative_identity,inverse(inverse(X0)),X1) ),
inference(forward_demodulation,[status(thm)],[f24438,f29706]) ).
fof(f58224,plain,
! [X0] : product(multiplicative_identity,inverse(inverse(X0)),X0),
inference(resolution,[status(thm)],[f29707,f40]) ).
fof(f58316,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(resolution,[status(thm)],[f58224,f616]) ).
fof(f58616,plain,
x != x,
inference(backward_demodulation,[status(thm)],[f58316,f86]) ).
fof(f58617,plain,
$false,
inference(trivial_equality_resolution,[status(esa)],[f58616]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : BOO012-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.08 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.07/0.27 % Computer : n011.cluster.edu
% 0.07/0.27 % Model : x86_64 x86_64
% 0.07/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27 % Memory : 8042.1875MB
% 0.07/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27 % CPULimit : 300
% 0.07/0.27 % WCLimit : 300
% 0.07/0.27 % DateTime : Mon Apr 29 22:38:31 EDT 2024
% 0.07/0.27 % CPUTime :
% 0.12/0.28 % Drodi V3.6.0
% 54.68/7.18 % Refutation found
% 54.68/7.18 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 54.68/7.18 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 55.24/7.28 % Elapsed time: 6.995220 seconds
% 55.24/7.28 % CPU time: 55.357212 seconds
% 55.24/7.28 % Total memory used: 444.895 MB
% 55.24/7.28 % Net memory used: 421.618 MB
%------------------------------------------------------------------------------