%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP002-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:32:13 PM UTC 2026
% Result : Unsatisfiable 0.13s 10.54s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 8
% Syntax : Number of formulae : 150 ( 150 unt; 0 def)
% Number of atoms : 150 ( 149 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 8 ( 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 : 294 ( 294 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : multiply(X,identity) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : multiply(X,inverse(X)) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] : commutator(X,Y) = multiply(X,multiply(Y,multiply(inverse(X),inverse(Y)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,hypothesis,
! [X] : multiply(X,multiply(X,X)) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
commutator(commutator(a,b),b) != identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f10,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f11,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f12,plain,
! [X0] : multiply(X0,identity) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f13,plain,
! [X0] : multiply(X0,inverse(X0)) = identity,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f14,plain,
! [X0,X1] : commutator(X0,X1) = multiply(X0,multiply(X1,multiply(inverse(X0),inverse(X1)))),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f15,plain,
! [X0] : multiply(X0,multiply(X0,X0)) = identity,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f16,plain,
commutator(commutator(a,b),b) != identity,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f42,plain,
inverse(identity) = identity,
inference(paramodulation,[status(thm)],[f12,f10]) ).
fof(f84,plain,
! [X0,X1] : identity = multiply(X0,multiply(X1,inverse(multiply(X0,X1)))),
inference(paramodulation,[status(thm)],[f13,f11]) ).
fof(f85,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(f89,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f10,f11]) ).
fof(f91,plain,
! [X0,X1] : multiply(identity,X0) = multiply(X1,multiply(inverse(X1),X0)),
inference(paramodulation,[status(thm)],[f13,f11]) ).
fof(f96,plain,
! [X0,X1,X2] : commutator(X0,multiply(X1,X2)) = multiply(X0,multiply(X1,multiply(X2,multiply(inverse(X0),inverse(multiply(X1,X2)))))),
inference(paramodulation,[status(thm)],[f11,f14]) ).
fof(f104,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f9,f89]) ).
fof(f105,plain,
! [X0,X1] : X0 = multiply(X1,multiply(inverse(X1),X0)),
inference(forward_demodulation,[status(thm)],[f9,f91]) ).
fof(f188,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f10,f104]) ).
fof(f193,plain,
! [X0] : multiply(X0,X0) = multiply(inverse(X0),identity),
inference(paramodulation,[status(thm)],[f15,f104]) ).
fof(f210,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f12,f188]) ).
fof(f213,plain,
! [X0] : multiply(X0,X0) = inverse(X0),
inference(forward_demodulation,[status(thm)],[f12,f193]) ).
fof(f246,plain,
! [X0,X1] : multiply(X0,multiply(X1,multiply(X0,X1))) = inverse(multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f11,f213]) ).
fof(f256,plain,
! [X0,X1] : multiply(inverse(X0),X1) = multiply(X0,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f213,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)],[f256,f85]) ).
fof(f406,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X1,X0))) = multiply(inverse(X1),identity),
inference(paramodulation,[status(thm)],[f84,f104]) ).
fof(f446,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X1,X0))) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f12,f406]) ).
fof(f463,plain,
! [X0,X1] : multiply(inverse(multiply(X0,X1)),inverse(inverse(X0))) = inverse(X1),
inference(paramodulation,[status(thm)],[f446,f446]) ).
fof(f473,plain,
! [X0,X1] : commutator(X0,multiply(X1,inverse(X0))) = multiply(X0,multiply(multiply(X1,inverse(X0)),inverse(X1))),
inference(paramodulation,[status(thm)],[f446,f14]) ).
fof(f474,plain,
! [X0,X1] : inverse(multiply(X0,inverse(X1))) = multiply(X1,inverse(X0)),
inference(paramodulation,[status(thm)],[f446,f105]) ).
fof(f477,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = multiply(inverse(X1),inverse(X0)),
inference(paramodulation,[status(thm)],[f446,f104]) ).
fof(f488,plain,
! [X0,X1] : multiply(inverse(multiply(X0,X1)),X0) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f210,f463]) ).
fof(f504,plain,
! [X0,X1] : commutator(X0,multiply(X1,inverse(X0))) = multiply(X0,multiply(X1,multiply(inverse(X0),inverse(X1)))),
inference(forward_demodulation,[status(thm)],[f11,f473]) ).
fof(f506,plain,
! [X0,X1] : commutator(X0,multiply(X1,inverse(X0))) = commutator(X0,X1),
inference(forward_demodulation,[status(thm)],[f14,f504]) ).
fof(f508,plain,
! [X0,X1] : commutator(X0,X1) = multiply(X0,multiply(X1,inverse(multiply(X1,X0)))),
inference(backward_demodulation,[status(thm)],[f477,f14]) ).
fof(f512,plain,
! [X0,X1] : commutator(multiply(X0,X1),X1) = multiply(X0,multiply(inverse(X1),inverse(multiply(X1,multiply(X0,X1))))),
inference(backward_demodulation,[status(thm)],[f477,f341]) ).
fof(f517,plain,
! [X0,X1,X2] : commutator(X0,multiply(X1,X2)) = multiply(X0,multiply(X1,multiply(X2,inverse(multiply(multiply(X1,X2),X0))))),
inference(backward_demodulation,[status(thm)],[f477,f96]) ).
fof(f526,plain,
! [X0,X1] : commutator(multiply(X0,X1),X1) = multiply(X0,inverse(multiply(multiply(X1,multiply(X0,X1)),X1))),
inference(forward_demodulation,[status(thm)],[f477,f512]) ).
fof(f527,plain,
! [X0,X1] : commutator(multiply(X0,X1),X1) = multiply(X0,inverse(multiply(X1,multiply(multiply(X0,X1),X1)))),
inference(forward_demodulation,[status(thm)],[f11,f526]) ).
fof(f528,plain,
! [X0,X1] : commutator(multiply(X0,X1),X1) = multiply(X0,inverse(multiply(X1,multiply(X0,multiply(X1,X1))))),
inference(forward_demodulation,[status(thm)],[f11,f527]) ).
fof(f529,plain,
! [X0,X1] : commutator(multiply(X0,X1),X1) = multiply(X0,inverse(multiply(X1,multiply(X0,inverse(X1))))),
inference(forward_demodulation,[status(thm)],[f213,f528]) ).
fof(f534,plain,
! [X0,X1,X2] : commutator(X0,multiply(X1,X2)) = multiply(X0,multiply(X1,multiply(X2,inverse(multiply(X1,multiply(X2,X0)))))),
inference(forward_demodulation,[status(thm)],[f11,f517]) ).
fof(f543,plain,
! [X0,X1] : multiply(inverse(X0),X1) = inverse(multiply(inverse(X1),X0)),
inference(paramodulation,[status(thm)],[f105,f488]) ).
fof(f550,plain,
! [X0,X1] : multiply(inverse(inverse(multiply(X0,X1))),X0) = multiply(inverse(multiply(X0,X1)),inverse(X1)),
inference(paramodulation,[status(thm)],[f488,f256]) ).
fof(f567,plain,
! [X0,X1] : multiply(multiply(X0,X1),X0) = multiply(inverse(multiply(X0,X1)),inverse(X1)),
inference(forward_demodulation,[status(thm)],[f210,f550]) ).
fof(f568,plain,
! [X0,X1] : multiply(X0,multiply(X1,X0)) = multiply(inverse(multiply(X0,X1)),inverse(X1)),
inference(forward_demodulation,[status(thm)],[f11,f567]) ).
fof(f569,plain,
! [X0,X1] : multiply(X0,multiply(X1,X0)) = inverse(multiply(X1,multiply(X0,X1))),
inference(forward_demodulation,[status(thm)],[f477,f568]) ).
fof(f581,plain,
! [X0,X1] : commutator(multiply(X0,X1),inverse(X0)) = commutator(multiply(X0,X1),X1),
inference(paramodulation,[status(thm)],[f446,f506]) ).
fof(f584,plain,
! [X0,X1] : commutator(inverse(X0),multiply(X1,X0)) = commutator(inverse(X0),X1),
inference(paramodulation,[status(thm)],[f210,f506]) ).
fof(f595,plain,
! [X0,X1,X2] : inverse(multiply(X0,multiply(X1,inverse(X2)))) = multiply(X2,inverse(multiply(X0,X1))),
inference(paramodulation,[status(thm)],[f11,f474]) ).
fof(f615,plain,
! [X0,X1] : commutator(multiply(X0,X1),X1) = multiply(X0,multiply(X1,inverse(multiply(X1,X0)))),
inference(backward_demodulation,[status(thm)],[f595,f529]) ).
fof(f644,plain,
! [X0,X1] : commutator(multiply(X0,X1),inverse(X0)) = commutator(X0,X1),
inference(backward_demodulation,[status(thm)],[f645,f581]) ).
fof(f645,plain,
! [X0,X1] : commutator(multiply(X0,X1),X1) = commutator(X0,X1),
inference(forward_demodulation,[status(thm)],[f508,f615]) ).
fof(f648,plain,
! [X0,X1] : commutator(inverse(X0),X1) = commutator(inverse(multiply(X1,X0)),X1),
inference(paramodulation,[status(thm)],[f488,f645]) ).
fof(f649,plain,
! [X0,X1] : commutator(X0,multiply(X1,X0)) = commutator(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f104,f645]) ).
fof(f667,plain,
! [X0,X1] : commutator(X0,inverse(inverse(X1))) = commutator(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f104,f644]) ).
fof(f682,plain,
! [X0,X1] : commutator(X0,multiply(X1,X0)) = commutator(X0,X1),
inference(backward_demodulation,[status(thm)],[f683,f649]) ).
fof(f683,plain,
! [X0,X1] : commutator(X0,X1) = commutator(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f210,f667]) ).
fof(f696,plain,
! [X0,X1] : commutator(X0,inverse(X1)) = commutator(X0,inverse(multiply(X0,X1))),
inference(paramodulation,[status(thm)],[f488,f682]) ).
fof(f723,plain,
! [X0,X1] : commutator(inverse(multiply(X0,X1)),X1) = commutator(inverse(X1),inverse(X0)),
inference(paramodulation,[status(thm)],[f446,f683]) ).
fof(f726,plain,
! [X0,X1] : commutator(multiply(X0,X1),X0) = commutator(inverse(X0),multiply(inverse(X0),X1)),
inference(paramodulation,[status(thm)],[f256,f683]) ).
fof(f759,plain,
! [X0,X1] : commutator(X0,inverse(multiply(X0,X1))) = multiply(X0,multiply(inverse(multiply(X0,X1)),inverse(inverse(X1)))),
inference(paramodulation,[status(thm)],[f488,f508]) ).
fof(f763,plain,
! [X0,X1] : commutator(inverse(multiply(X0,X1)),X1) = multiply(inverse(multiply(X0,X1)),multiply(X1,inverse(inverse(X0)))),
inference(paramodulation,[status(thm)],[f446,f508]) ).
fof(f784,plain,
! [X0,X1,X2] : multiply(commutator(X0,X1),X2) = multiply(X0,multiply(multiply(X1,inverse(multiply(X1,X0))),X2)),
inference(paramodulation,[status(thm)],[f508,f11]) ).
fof(f801,plain,
! [X0,X1] : commutator(X0,inverse(X1)) = multiply(X0,multiply(inverse(multiply(X0,X1)),inverse(inverse(X1)))),
inference(forward_demodulation,[status(thm)],[f696,f759]) ).
fof(f802,plain,
! [X0,X1] : commutator(X0,inverse(X1)) = multiply(X0,inverse(multiply(inverse(X1),multiply(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f477,f801]) ).
fof(f803,plain,
! [X0,X1] : commutator(X0,inverse(X1)) = multiply(X0,multiply(inverse(multiply(X0,X1)),X1)),
inference(forward_demodulation,[status(thm)],[f543,f802]) ).
fof(f811,plain,
! [X0,X1] : commutator(inverse(X0),inverse(X1)) = multiply(inverse(multiply(X1,X0)),multiply(X0,inverse(inverse(X1)))),
inference(forward_demodulation,[status(thm)],[f723,f763]) ).
fof(f812,plain,
! [X0,X1] : commutator(inverse(X0),inverse(X1)) = multiply(inverse(multiply(X1,X0)),multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f210,f811]) ).
fof(f843,plain,
! [X0,X1,X2] : multiply(commutator(X0,X1),X2) = multiply(X0,multiply(X1,multiply(inverse(multiply(X1,X0)),X2))),
inference(forward_demodulation,[status(thm)],[f11,f784]) ).
fof(f1207,plain,
! [X0,X1,X2] : inverse(multiply(multiply(X0,inverse(X1)),X2)) = multiply(inverse(X2),multiply(X1,inverse(X0))),
inference(paramodulation,[status(thm)],[f474,f477]) ).
fof(f1231,plain,
! [X0,X1,X2] : multiply(inverse(multiply(X0,X1)),X2) = multiply(inverse(X1),multiply(inverse(X0),X2)),
inference(paramodulation,[status(thm)],[f477,f11]) ).
fof(f1241,plain,
! [X0,X1,X2] : inverse(multiply(X0,multiply(inverse(X1),X2))) = multiply(inverse(X2),multiply(X1,inverse(X0))),
inference(forward_demodulation,[status(thm)],[f11,f1207]) ).
fof(f1314,plain,
! [X0,X1] : multiply(inverse(multiply(X0,inverse(multiply(X0,inverse(X1))))),X1) = inverse(commutator(inverse(X1),X0)),
inference(paramodulation,[status(thm)],[f508,f543]) ).
fof(f1357,plain,
! [X0,X1] : multiply(multiply(multiply(X0,inverse(X1)),inverse(X0)),X1) = inverse(commutator(inverse(X1),X0)),
inference(forward_demodulation,[status(thm)],[f474,f1314]) ).
fof(f1358,plain,
! [X0,X1] : multiply(multiply(X0,inverse(X1)),multiply(inverse(X0),X1)) = inverse(commutator(inverse(X1),X0)),
inference(forward_demodulation,[status(thm)],[f11,f1357]) ).
fof(f1359,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X1),multiply(inverse(X0),X1))) = inverse(commutator(inverse(X1),X0)),
inference(forward_demodulation,[status(thm)],[f11,f1358]) ).
fof(f1360,plain,
! [X0,X1] : multiply(X0,multiply(inverse(multiply(X0,X1)),X1)) = inverse(commutator(inverse(X1),X0)),
inference(forward_demodulation,[status(thm)],[f1231,f1359]) ).
fof(f1361,plain,
! [X0,X1] : commutator(X0,inverse(X1)) = inverse(commutator(inverse(X1),X0)),
inference(forward_demodulation,[status(thm)],[f803,f1360]) ).
fof(f1398,plain,
! [X0,X1] : commutator(multiply(X0,X1),inverse(X0)) = inverse(commutator(X1,X0)),
inference(paramodulation,[status(thm)],[f683,f1361]) ).
fof(f1430,plain,
! [X0,X1] : commutator(X0,X1) = inverse(commutator(X1,X0)),
inference(forward_demodulation,[status(thm)],[f644,f1398]) ).
fof(f1458,plain,
! [X0,X1,X2] : inverse(multiply(X0,commutator(X1,X2))) = multiply(commutator(X2,X1),inverse(X0)),
inference(paramodulation,[status(thm)],[f1430,f477]) ).
fof(f1467,plain,
! [X0,X1] : multiply(commutator(X0,X1),commutator(X1,X0)) = identity,
inference(paramodulation,[status(thm)],[f1430,f13]) ).
fof(f1580,plain,
! [X0,X1] : commutator(X0,multiply(X0,X1)) = multiply(inverse(X0),multiply(X1,inverse(multiply(X0,multiply(X1,X0))))),
inference(paramodulation,[status(thm)],[f256,f534]) ).
fof(f1647,plain,
! [X0,X1] : commutator(X0,multiply(X0,X1)) = inverse(multiply(multiply(X0,multiply(X1,X0)),multiply(inverse(X1),X0))),
inference(forward_demodulation,[status(thm)],[f1241,f1580]) ).
fof(f1648,plain,
! [X0,X1] : commutator(X0,multiply(X0,X1)) = inverse(multiply(X0,multiply(multiply(X1,X0),multiply(inverse(X1),X0)))),
inference(forward_demodulation,[status(thm)],[f11,f1647]) ).
fof(f1649,plain,
! [X0,X1] : commutator(X0,multiply(X0,X1)) = inverse(multiply(X0,multiply(X1,multiply(X0,multiply(inverse(X1),X0))))),
inference(forward_demodulation,[status(thm)],[f11,f1648]) ).
fof(f1873,plain,
! [X0,X1,X2] : commutator(inverse(X0),multiply(X1,X2)) = commutator(inverse(multiply(X1,multiply(X2,X0))),multiply(X1,X2)),
inference(paramodulation,[status(thm)],[f11,f648]) ).
fof(f2042,plain,
! [X0,X1] : commutator(inverse(multiply(X0,multiply(X1,X0))),X1) = commutator(inverse(inverse(multiply(X1,X0))),X1),
inference(paramodulation,[status(thm)],[f246,f648]) ).
fof(f2162,plain,
! [X0,X1] : commutator(inverse(multiply(X0,multiply(X1,X0))),X1) = commutator(multiply(X1,X0),X1),
inference(forward_demodulation,[status(thm)],[f210,f2042]) ).
fof(f2211,plain,
! [X0,X1] : multiply(multiply(X0,X1),multiply(inverse(X0),X1)) = inverse(multiply(X0,multiply(multiply(X0,X1),X0))),
inference(paramodulation,[status(thm)],[f256,f569]) ).
fof(f2240,plain,
! [X0,X1] : commutator(X0,multiply(X0,X1)) = multiply(X0,multiply(X0,multiply(X1,inverse(inverse(multiply(X1,multiply(X0,X1))))))),
inference(paramodulation,[status(thm)],[f569,f534]) ).
fof(f2245,plain,
! [X0,X1] : commutator(inverse(multiply(X0,X1)),inverse(multiply(X0,multiply(X1,X0)))) = commutator(inverse(multiply(X0,X1)),X1),
inference(paramodulation,[status(thm)],[f569,f584]) ).
fof(f2249,plain,
! [X0,X1] : commutator(multiply(X0,X1),X1) = commutator(inverse(X1),inverse(multiply(X0,multiply(X1,X0)))),
inference(paramodulation,[status(thm)],[f569,f683]) ).
fof(f2336,plain,
! [X0,X1] : multiply(X0,multiply(X1,multiply(inverse(X0),X1))) = inverse(multiply(X0,multiply(multiply(X0,X1),X0))),
inference(forward_demodulation,[status(thm)],[f11,f2211]) ).
fof(f2337,plain,
! [X0,X1] : multiply(X0,multiply(X1,multiply(inverse(X0),X1))) = inverse(multiply(X0,multiply(X0,multiply(X1,X0)))),
inference(forward_demodulation,[status(thm)],[f11,f2336]) ).
fof(f2338,plain,
! [X0,X1] : multiply(X0,multiply(X1,multiply(inverse(X0),X1))) = inverse(multiply(inverse(X0),multiply(X1,X0))),
inference(forward_demodulation,[status(thm)],[f256,f2337]) ).
fof(f2339,plain,
! [X0,X1] : commutator(X0,multiply(X0,X1)) = inverse(multiply(X0,multiply(inverse(multiply(X0,X1)),X1))),
inference(backward_demodulation,[status(thm)],[f2340,f1649]) ).
fof(f2340,plain,
! [X0,X1] : multiply(X0,multiply(X1,multiply(inverse(X0),X1))) = multiply(inverse(multiply(X1,X0)),X0),
inference(forward_demodulation,[status(thm)],[f543,f2338]) ).
fof(f2430,plain,
! [X0,X1] : commutator(X0,multiply(X0,X1)) = multiply(inverse(X0),multiply(X1,inverse(inverse(multiply(X1,multiply(X0,X1)))))),
inference(forward_demodulation,[status(thm)],[f256,f2240]) ).
fof(f2431,plain,
! [X0,X1] : commutator(X0,multiply(X0,X1)) = inverse(multiply(inverse(multiply(X1,multiply(X0,X1))),multiply(inverse(X1),X0))),
inference(forward_demodulation,[status(thm)],[f1241,f2430]) ).
fof(f2432,plain,
! [X0,X1] : commutator(X0,multiply(X0,X1)) = multiply(inverse(multiply(inverse(X1),X0)),multiply(X1,multiply(X0,X1))),
inference(forward_demodulation,[status(thm)],[f543,f2431]) ).
fof(f2433,plain,
! [X0,X1] : commutator(X0,multiply(X0,X1)) = multiply(multiply(inverse(X0),X1),multiply(X1,multiply(X0,X1))),
inference(forward_demodulation,[status(thm)],[f543,f2432]) ).
fof(f2434,plain,
! [X0,X1] : commutator(X0,multiply(X0,X1)) = multiply(inverse(X0),multiply(X1,multiply(X1,multiply(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f11,f2433]) ).
fof(f2435,plain,
! [X0,X1] : commutator(X0,multiply(X0,X1)) = multiply(inverse(X0),multiply(inverse(X1),multiply(X0,X1))),
inference(forward_demodulation,[status(thm)],[f256,f2434]) ).
fof(f2436,plain,
! [X0,X1] : commutator(X0,multiply(X0,X1)) = multiply(inverse(multiply(X1,X0)),multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f1231,f2435]) ).
fof(f2437,plain,
! [X0,X1] : commutator(multiply(X0,X1),X0) = commutator(inverse(inverse(X0)),inverse(X1)),
inference(backward_demodulation,[status(thm)],[f2438,f726]) ).
fof(f2438,plain,
! [X0,X1] : commutator(X0,multiply(X0,X1)) = commutator(inverse(X0),inverse(X1)),
inference(forward_demodulation,[status(thm)],[f812,f2436]) ).
fof(f2449,plain,
! [X0,X1] : commutator(inverse(multiply(X0,X1)),inverse(multiply(X0,multiply(X1,X0)))) = commutator(inverse(X1),inverse(X0)),
inference(forward_demodulation,[status(thm)],[f723,f2245]) ).
fof(f2467,plain,
! [X0,X1] : commutator(X0,X1) = commutator(inverse(X1),inverse(multiply(X0,multiply(X1,X0)))),
inference(forward_demodulation,[status(thm)],[f645,f2249]) ).
fof(f2528,plain,
! [X0,X1] : commutator(X0,multiply(X0,X1)) = inverse(commutator(X0,inverse(X1))),
inference(forward_demodulation,[status(thm)],[f803,f2339]) ).
fof(f2529,plain,
! [X0,X1] : commutator(inverse(X0),X1) = commutator(inverse(X1),inverse(X0)),
inference(backward_demodulation,[status(thm)],[f2532,f2438]) ).
fof(f2532,plain,
! [X0,X1] : commutator(X0,multiply(X0,X1)) = commutator(inverse(X1),X0),
inference(forward_demodulation,[status(thm)],[f1430,f2528]) ).
fof(f2540,plain,
! [X0,X1] : commutator(multiply(X0,X1),X0) = commutator(X0,inverse(X1)),
inference(forward_demodulation,[status(thm)],[f210,f2437]) ).
fof(f2543,plain,
! [X0,X1] : commutator(inverse(multiply(X0,multiply(X1,X0))),multiply(X0,X1)) = commutator(inverse(X1),inverse(X0)),
inference(backward_demodulation,[status(thm)],[f2529,f2449]) ).
fof(f2546,plain,
! [X0,X1] : commutator(X0,X1) = commutator(inverse(multiply(X0,multiply(X1,X0))),X1),
inference(backward_demodulation,[status(thm)],[f2529,f2467]) ).
fof(f2561,plain,
! [X0,X1] : commutator(inverse(X0),multiply(X0,X1)) = commutator(inverse(X1),inverse(X0)),
inference(forward_demodulation,[status(thm)],[f1873,f2543]) ).
fof(f2562,plain,
! [X0,X1] : commutator(X0,X1) = commutator(inverse(X0),inverse(X1)),
inference(forward_demodulation,[status(thm)],[f683,f2561]) ).
fof(f2600,plain,
! [X0,X1] : commutator(X0,X1) = commutator(inverse(X1),X0),
inference(forward_demodulation,[status(thm)],[f2529,f2562]) ).
fof(f2607,plain,
! [X0,X1] : commutator(X0,X1) = commutator(multiply(X1,X0),X1),
inference(forward_demodulation,[status(thm)],[f2162,f2546]) ).
fof(f2637,plain,
! [X0,X1] : commutator(X0,X1) = commutator(X1,inverse(X0)),
inference(forward_demodulation,[status(thm)],[f2540,f2607]) ).
fof(f2721,plain,
! [X0,X1,X2] : commutator(X0,commutator(X1,X2)) = commutator(commutator(X2,X1),X0),
inference(paramodulation,[status(thm)],[f1430,f2600]) ).
fof(f2724,plain,
! [X0,X1,X2] : commutator(X0,multiply(X1,inverse(X2))) = commutator(multiply(X2,inverse(X1)),X0),
inference(paramodulation,[status(thm)],[f474,f2600]) ).
fof(f2728,plain,
! [X0,X1] : commutator(multiply(X0,inverse(X1)),X1) = commutator(inverse(X1),X0),
inference(paramodulation,[status(thm)],[f2600,f682]) ).
fof(f2740,plain,
commutator(b,commutator(b,a)) != identity,
inference(backward_demodulation,[status(thm)],[f2721,f16]) ).
fof(f2755,plain,
! [X0,X1] : commutator(X0,multiply(X0,inverse(X1))) = commutator(inverse(X0),X1),
inference(forward_demodulation,[status(thm)],[f2724,f2728]) ).
fof(f2756,plain,
! [X0,X1] : commutator(X0,multiply(X0,inverse(X1))) = commutator(X1,X0),
inference(forward_demodulation,[status(thm)],[f2600,f2755]) ).
fof(f2815,plain,
! [X0,X1] : commutator(X0,multiply(X0,X1)) = commutator(inverse(X1),X0),
inference(paramodulation,[status(thm)],[f210,f2756]) ).
fof(f2857,plain,
! [X0,X1] : commutator(X0,multiply(X0,X1)) = commutator(X0,X1),
inference(forward_demodulation,[status(thm)],[f2600,f2815]) ).
fof(f2891,plain,
! [X0,X1] : commutator(X0,commutator(X0,X1)) = commutator(X0,multiply(X1,inverse(multiply(X1,X0)))),
inference(paramodulation,[status(thm)],[f508,f2857]) ).
fof(f2942,plain,
! [X0,X1] : multiply(commutator(X0,X1),inverse(multiply(X1,multiply(inverse(multiply(X1,X0)),X0)))) = commutator(X0,multiply(X1,inverse(multiply(X1,X0)))),
inference(paramodulation,[status(thm)],[f534,f843]) ).
fof(f2968,plain,
! [X0,X1,X2] : multiply(commutator(X0,inverse(X1)),X2) = multiply(X0,multiply(inverse(X1),multiply(multiply(inverse(X0),X1),X2))),
inference(paramodulation,[status(thm)],[f543,f843]) ).
fof(f3028,plain,
! [X0,X1] : inverse(multiply(multiply(X0,multiply(inverse(multiply(X0,X1)),X1)),commutator(X0,X1))) = commutator(X1,multiply(X0,inverse(multiply(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f1458,f2942]) ).
fof(f3029,plain,
! [X0,X1] : inverse(multiply(X0,multiply(multiply(inverse(multiply(X0,X1)),X1),commutator(X0,X1)))) = commutator(X1,multiply(X0,inverse(multiply(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f11,f3028]) ).
fof(f3030,plain,
! [X0,X1] : inverse(multiply(X0,multiply(inverse(multiply(X0,X1)),multiply(X1,commutator(X0,X1))))) = commutator(X1,multiply(X0,inverse(multiply(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f11,f3029]) ).
fof(f3031,plain,
! [X0,X1] : inverse(multiply(X0,multiply(inverse(multiply(X0,X1)),multiply(X1,commutator(X0,X1))))) = commutator(X1,commutator(X1,X0)),
inference(forward_demodulation,[status(thm)],[f2891,f3030]) ).
fof(f3101,plain,
! [X0,X1,X2] : multiply(commutator(X0,X1),X2) = multiply(X1,multiply(inverse(X0),multiply(multiply(inverse(X1),X0),X2))),
inference(forward_demodulation,[status(thm)],[f2637,f2968]) ).
fof(f3102,plain,
! [X0,X1,X2] : multiply(commutator(X0,X1),X2) = multiply(X1,multiply(inverse(X0),multiply(inverse(X1),multiply(X0,X2)))),
inference(forward_demodulation,[status(thm)],[f11,f3101]) ).
fof(f3103,plain,
! [X0,X1] : inverse(multiply(commutator(X0,X1),commutator(X1,X0))) = commutator(X0,commutator(X0,X1)),
inference(backward_demodulation,[status(thm)],[f3105,f3031]) ).
fof(f3105,plain,
! [X0,X1,X2] : multiply(commutator(X0,X1),X2) = multiply(X1,multiply(inverse(multiply(X1,X0)),multiply(X0,X2))),
inference(forward_demodulation,[status(thm)],[f1231,f3102]) ).
fof(f3265,plain,
! [X0,X1] : inverse(identity) = commutator(X0,commutator(X0,X1)),
inference(forward_demodulation,[status(thm)],[f1467,f3103]) ).
fof(f3266,plain,
identity != identity,
inference(backward_demodulation,[status(thm)],[f3269,f2740]) ).
fof(f3269,plain,
! [X0,X1] : identity = commutator(X0,commutator(X0,X1)),
inference(forward_demodulation,[status(thm)],[f42,f3265]) ).
fof(f3270,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f3266]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP002-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/10.37 % Computer : n008.cluster.edu
% 0.11/10.37 % Model : x86_64 x86_64
% 0.11/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.37 % Memory : 8046.5625MB
% 0.11/10.37 % OS : Linux 6.8.0-71-generic
% 0.11/10.37 % CPULimit : 300
% 0.11/10.37 % WCLimit : 300
% 0.11/10.37 % DateTime : Sun Sep 20 19:54:20 UTC 2026
% 0.11/10.37 % CPUTime :
% 0.11/10.38 % Drodi V4.1.1
% 0.13/10.54 % Refutation found
% 0.13/10.54 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/10.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.57/11.78 % Elapsed time: 1.186895 seconds
% 7.57/11.78 % CPU time: 1.150253 seconds
% 7.57/11.78 % Total memory used: 36.788 MB
% 7.57/11.78 % Net memory used: 35.740 MB
%------------------------------------------------------------------------------