TSTP Solution File: GRP002-4 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : GRP002-4 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n018.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 20:18:44 EDT 2024
% Result : Unsatisfiable 0.14s 0.56s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 8
% Syntax : Number of formulae : 80 ( 80 unt; 0 def)
% Number of atoms : 80 ( 79 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 148 ( 148 !; 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,axiom,
! [X,Y] : commutator(X,Y) = multiply(X,multiply(Y,multiply(inverse(X),inverse(Y)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,hypothesis,
! [X] : multiply(X,multiply(X,X)) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
commutator(commutator(a,b),b) != identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f10,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f11,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f12,plain,
! [X0] : multiply(X0,identity) = X0,
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f13,plain,
! [X0] : multiply(X0,inverse(X0)) = identity,
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f14,plain,
! [X0,X1] : commutator(X0,X1) = multiply(X0,multiply(X1,multiply(inverse(X0),inverse(X1)))),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f15,plain,
! [X0] : multiply(X0,multiply(X0,X0)) = identity,
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f16,plain,
commutator(commutator(a,b),b) != identity,
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f70,plain,
! [X0,X1] : identity = multiply(X0,multiply(X1,inverse(multiply(X0,X1)))),
inference(paramodulation,[status(thm)],[f13,f11]) ).
fof(f71,plain,
! [X0,X1,X2] : commutator(multiply(X0,X1),X2) = multiply(X0,multiply(X1,multiply(X2,multiply(inverse(multiply(X0,X1)),inverse(X2))))),
inference(paramodulation,[status(thm)],[f14,f11]) ).
fof(f78,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f10,f11]) ).
fof(f79,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f9,f78]) ).
fof(f81,plain,
! [X0,X1] : multiply(identity,X0) = multiply(X1,multiply(inverse(X1),X0)),
inference(paramodulation,[status(thm)],[f13,f11]) ).
fof(f82,plain,
! [X0,X1] : X0 = multiply(X1,multiply(inverse(X1),X0)),
inference(forward_demodulation,[status(thm)],[f9,f81]) ).
fof(f83,plain,
! [X0,X1,X2] : multiply(commutator(X0,X1),X2) = multiply(X0,multiply(multiply(X1,multiply(inverse(X0),inverse(X1))),X2)),
inference(paramodulation,[status(thm)],[f14,f11]) ).
fof(f84,plain,
! [X0,X1,X2] : multiply(commutator(X0,X1),X2) = multiply(X0,multiply(X1,multiply(multiply(inverse(X0),inverse(X1)),X2))),
inference(forward_demodulation,[status(thm)],[f11,f83]) ).
fof(f85,plain,
! [X0,X1,X2] : multiply(commutator(X0,X1),X2) = multiply(X0,multiply(X1,multiply(inverse(X0),multiply(inverse(X1),X2)))),
inference(forward_demodulation,[status(thm)],[f11,f84]) ).
fof(f181,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f10,f79]) ).
fof(f182,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f12,f181]) ).
fof(f188,plain,
! [X0] : multiply(X0,X0) = multiply(inverse(X0),identity),
inference(paramodulation,[status(thm)],[f15,f79]) ).
fof(f189,plain,
! [X0] : multiply(X0,X0) = inverse(X0),
inference(forward_demodulation,[status(thm)],[f12,f188]) ).
fof(f244,plain,
! [X0,X1] : multiply(inverse(X0),X1) = multiply(X0,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f189,f11]) ).
fof(f341,plain,
! [X0,X1] : commutator(multiply(X0,X1),X1) = multiply(X0,multiply(inverse(X1),multiply(inverse(multiply(X0,X1)),inverse(X1)))),
inference(paramodulation,[status(thm)],[f244,f71]) ).
fof(f417,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X1,X0))) = multiply(inverse(X1),identity),
inference(paramodulation,[status(thm)],[f70,f79]) ).
fof(f418,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X1,X0))) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f12,f417]) ).
fof(f446,plain,
! [X0,X1] : multiply(inverse(multiply(X0,X1)),inverse(inverse(X0))) = inverse(X1),
inference(paramodulation,[status(thm)],[f418,f418]) ).
fof(f447,plain,
! [X0,X1] : multiply(inverse(multiply(X0,X1)),X0) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f182,f446]) ).
fof(f472,plain,
! [X0,X1] : commutator(X0,multiply(X1,inverse(X0))) = multiply(X0,multiply(multiply(X1,inverse(X0)),inverse(X1))),
inference(paramodulation,[status(thm)],[f418,f14]) ).
fof(f473,plain,
! [X0,X1] : commutator(X0,multiply(X1,inverse(X0))) = multiply(X0,multiply(X1,multiply(inverse(X0),inverse(X1)))),
inference(forward_demodulation,[status(thm)],[f11,f472]) ).
fof(f474,plain,
! [X0,X1] : commutator(X0,multiply(X1,inverse(X0))) = commutator(X0,X1),
inference(forward_demodulation,[status(thm)],[f14,f473]) ).
fof(f475,plain,
! [X0,X1] : inverse(multiply(X0,inverse(X1))) = multiply(X1,inverse(X0)),
inference(paramodulation,[status(thm)],[f418,f82]) ).
fof(f478,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = multiply(inverse(X1),inverse(X0)),
inference(paramodulation,[status(thm)],[f418,f79]) ).
fof(f487,plain,
! [X0,X1] : commutator(X0,X1) = multiply(X0,multiply(X1,inverse(multiply(X1,X0)))),
inference(backward_demodulation,[status(thm)],[f478,f14]) ).
fof(f492,plain,
! [X0,X1] : commutator(multiply(X0,X1),X1) = multiply(X0,multiply(inverse(X1),inverse(multiply(X1,multiply(X0,X1))))),
inference(backward_demodulation,[status(thm)],[f478,f341]) ).
fof(f493,plain,
! [X0,X1] : commutator(multiply(X0,X1),X1) = multiply(X0,inverse(multiply(multiply(X1,multiply(X0,X1)),X1))),
inference(forward_demodulation,[status(thm)],[f478,f492]) ).
fof(f494,plain,
! [X0,X1] : commutator(multiply(X0,X1),X1) = multiply(X0,inverse(multiply(X1,multiply(multiply(X0,X1),X1)))),
inference(forward_demodulation,[status(thm)],[f11,f493]) ).
fof(f495,plain,
! [X0,X1] : commutator(multiply(X0,X1),X1) = multiply(X0,inverse(multiply(X1,multiply(X0,multiply(X1,X1))))),
inference(forward_demodulation,[status(thm)],[f11,f494]) ).
fof(f496,plain,
! [X0,X1] : commutator(multiply(X0,X1),X1) = multiply(X0,inverse(multiply(X1,multiply(X0,inverse(X1))))),
inference(forward_demodulation,[status(thm)],[f189,f495]) ).
fof(f540,plain,
! [X0,X1] : multiply(inverse(inverse(multiply(X0,X1))),X0) = multiply(inverse(multiply(X0,X1)),inverse(X1)),
inference(paramodulation,[status(thm)],[f447,f244]) ).
fof(f541,plain,
! [X0,X1] : multiply(multiply(X0,X1),X0) = multiply(inverse(multiply(X0,X1)),inverse(X1)),
inference(forward_demodulation,[status(thm)],[f182,f540]) ).
fof(f542,plain,
! [X0,X1] : multiply(X0,multiply(X1,X0)) = multiply(inverse(multiply(X0,X1)),inverse(X1)),
inference(forward_demodulation,[status(thm)],[f11,f541]) ).
fof(f543,plain,
! [X0,X1] : multiply(X0,multiply(X1,X0)) = inverse(multiply(X1,multiply(X0,X1))),
inference(forward_demodulation,[status(thm)],[f478,f542]) ).
fof(f561,plain,
! [X0,X1] : commutator(multiply(X0,X1),inverse(X0)) = commutator(multiply(X0,X1),X1),
inference(paramodulation,[status(thm)],[f418,f474]) ).
fof(f571,plain,
! [X0,X1,X2] : inverse(multiply(X0,multiply(X1,inverse(X2)))) = multiply(X2,inverse(multiply(X0,X1))),
inference(paramodulation,[status(thm)],[f11,f475]) ).
fof(f619,plain,
! [X0,X1] : commutator(multiply(X0,X1),X1) = multiply(X0,multiply(X1,inverse(multiply(X1,X0)))),
inference(backward_demodulation,[status(thm)],[f571,f496]) ).
fof(f620,plain,
! [X0,X1] : commutator(multiply(X0,X1),X1) = commutator(X0,X1),
inference(forward_demodulation,[status(thm)],[f487,f619]) ).
fof(f621,plain,
! [X0,X1] : commutator(multiply(X0,X1),inverse(X0)) = commutator(X0,X1),
inference(backward_demodulation,[status(thm)],[f620,f561]) ).
fof(f643,plain,
! [X0,X1] : commutator(X0,inverse(inverse(X1))) = commutator(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f79,f621]) ).
fof(f644,plain,
! [X0,X1] : commutator(X0,X1) = commutator(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f182,f643]) ).
fof(f890,plain,
! [X0,X1] : multiply(commutator(X0,X1),X1) = multiply(X0,multiply(X1,multiply(inverse(X0),identity))),
inference(paramodulation,[status(thm)],[f10,f85]) ).
fof(f891,plain,
! [X0,X1] : multiply(commutator(X0,X1),X1) = multiply(X0,multiply(X1,inverse(X0))),
inference(forward_demodulation,[status(thm)],[f12,f890]) ).
fof(f1563,plain,
! [X0,X1] : multiply(X0,multiply(multiply(X1,X0),X0)) = inverse(multiply(multiply(X1,X0),inverse(multiply(X1,multiply(X0,X1))))),
inference(paramodulation,[status(thm)],[f543,f543]) ).
fof(f1564,plain,
! [X0,X1] : multiply(X0,multiply(X1,multiply(X0,X0))) = inverse(multiply(multiply(X1,X0),inverse(multiply(X1,multiply(X0,X1))))),
inference(forward_demodulation,[status(thm)],[f11,f1563]) ).
fof(f1565,plain,
! [X0,X1] : multiply(X0,multiply(X1,inverse(X0))) = inverse(multiply(multiply(X1,X0),inverse(multiply(X1,multiply(X0,X1))))),
inference(forward_demodulation,[status(thm)],[f189,f1564]) ).
fof(f1566,plain,
! [X0,X1] : multiply(X0,multiply(X1,inverse(X0))) = multiply(multiply(X1,multiply(X0,X1)),inverse(multiply(X1,X0))),
inference(forward_demodulation,[status(thm)],[f475,f1565]) ).
fof(f1567,plain,
! [X0,X1] : multiply(X0,multiply(X1,inverse(X0))) = multiply(X1,multiply(multiply(X0,X1),inverse(multiply(X1,X0)))),
inference(forward_demodulation,[status(thm)],[f11,f1566]) ).
fof(f1568,plain,
! [X0,X1] : multiply(X0,multiply(X1,inverse(X0))) = multiply(X1,multiply(X0,multiply(X1,inverse(multiply(X1,X0))))),
inference(forward_demodulation,[status(thm)],[f11,f1567]) ).
fof(f1569,plain,
! [X0,X1] : multiply(X0,multiply(X1,inverse(X0))) = multiply(X1,commutator(X0,X1)),
inference(forward_demodulation,[status(thm)],[f487,f1568]) ).
fof(f2223,plain,
! [X0,X1] : multiply(commutator(X0,X1),multiply(X1,X0)) = multiply(inverse(X1),multiply(multiply(X1,X0),inverse(inverse(X1)))),
inference(paramodulation,[status(thm)],[f644,f891]) ).
fof(f2224,plain,
! [X0,X1] : multiply(commutator(X0,X1),multiply(X1,X0)) = multiply(inverse(X1),multiply(X1,multiply(X0,inverse(inverse(X1))))),
inference(forward_demodulation,[status(thm)],[f11,f2223]) ).
fof(f2225,plain,
! [X0,X1] : multiply(commutator(X0,X1),multiply(X1,X0)) = multiply(X0,inverse(inverse(X1))),
inference(forward_demodulation,[status(thm)],[f79,f2224]) ).
fof(f2226,plain,
! [X0,X1] : multiply(commutator(X0,X1),multiply(X1,X0)) = multiply(X0,X1),
inference(forward_demodulation,[status(thm)],[f182,f2225]) ).
fof(f2556,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(commutator(X0,X1),multiply(multiply(X1,X0),X2)),
inference(paramodulation,[status(thm)],[f2226,f11]) ).
fof(f2557,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(commutator(X0,X1),multiply(multiply(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f11,f2556]) ).
fof(f2558,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(commutator(X0,X1),multiply(X1,multiply(X0,X2))),
inference(forward_demodulation,[status(thm)],[f11,f2557]) ).
fof(f2915,plain,
! [X0,X1] : commutator(commutator(X0,X1),X1) = multiply(commutator(X0,X1),multiply(X1,inverse(multiply(X0,multiply(X1,inverse(X0)))))),
inference(paramodulation,[status(thm)],[f1569,f487]) ).
fof(f2916,plain,
! [X0,X1] : commutator(commutator(X0,X1),X1) = multiply(commutator(X0,X1),multiply(X1,multiply(X0,inverse(multiply(X0,X1))))),
inference(forward_demodulation,[status(thm)],[f571,f2915]) ).
fof(f2917,plain,
! [X0,X1] : commutator(commutator(X0,X1),X1) = multiply(X0,multiply(X1,inverse(multiply(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f2558,f2916]) ).
fof(f2918,plain,
! [X0,X1] : commutator(commutator(X0,X1),X1) = multiply(X0,inverse(X0)),
inference(forward_demodulation,[status(thm)],[f418,f2917]) ).
fof(f2919,plain,
! [X0,X1] : commutator(commutator(X0,X1),X1) = identity,
inference(forward_demodulation,[status(thm)],[f13,f2918]) ).
fof(f3069,plain,
identity != identity,
inference(backward_demodulation,[status(thm)],[f2919,f16]) ).
fof(f3070,plain,
$false,
inference(trivial_equality_resolution,[status(esa)],[f3069]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : GRP002-4 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.31 % Computer : n018.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 Apr 30 00:35:58 EDT 2024
% 0.09/0.31 % CPUTime :
% 0.14/0.31 % Drodi V3.6.0
% 0.14/0.56 % Refutation found
% 0.14/0.56 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.04/0.59 % Elapsed time: 0.277976 seconds
% 2.04/0.59 % CPU time: 2.065449 seconds
% 2.04/0.59 % Total memory used: 56.174 MB
% 2.04/0.59 % Net memory used: 53.691 MB
%------------------------------------------------------------------------------