%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP002-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 0.62s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 8
% Syntax : Number of formulae : 112 ( 112 unt; 2 def)
% Number of atoms : 112 ( 111 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 : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 166 ( 166 !; 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,Y] : commutator(X,Y) = multiply(X,multiply(Y,multiply(inverse(X),inverse(Y)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,hypothesis,
! [X] : multiply(X,multiply(X,X)) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
commutator(commutator(a,b),b) != identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f8,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f9,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f10,plain,
! [X0,X1] : commutator(X0,X1) = multiply(X0,multiply(X1,multiply(inverse(X0),inverse(X1)))),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f11,plain,
! [X0] : multiply(X0,multiply(X0,X0)) = identity,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f12,plain,
commutator(commutator(a,b),b) != identity,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f13,definition,
sF1_fnc = commutator(a,b),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f14,definition,
sF0_fnc = commutator(sF1_fnc,b),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f15,plain,
sF0_fnc != identity,
inference(definition_folding,[],[f12,f14,f13]) ).
fof(f36,plain,
! [X0] : commutator(inverse(X0),X0) = multiply(inverse(X0),multiply(X0,identity)),
inference(paramodulation,[status(thm)],[f8,f10]) ).
fof(f44,plain,
! [X0,X1] : identity = multiply(X0,multiply(X1,multiply(multiply(X0,X1),multiply(X0,X1)))),
inference(paramodulation,[status(thm)],[f11,f9]) ).
fof(f49,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f8,f9]) ).
fof(f53,plain,
! [X0,X1,X2] : multiply(commutator(X0,X1),X2) = multiply(X0,multiply(multiply(X1,multiply(inverse(X0),inverse(X1))),X2)),
inference(paramodulation,[status(thm)],[f10,f9]) ).
fof(f54,plain,
! [X0,X1] : multiply(identity,X0) = multiply(X1,multiply(multiply(X1,X1),X0)),
inference(paramodulation,[status(thm)],[f11,f9]) ).
fof(f58,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)],[f9,f10]) ).
fof(f62,plain,
! [X0,X1] : identity = multiply(X0,multiply(X1,multiply(X0,multiply(X1,multiply(X0,X1))))),
inference(forward_demodulation,[status(thm)],[f9,f44]) ).
fof(f68,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f7,f49]) ).
fof(f71,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)],[f9,f53]) ).
fof(f72,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)],[f9,f71]) ).
fof(f73,plain,
! [X0,X1] : X0 = multiply(X1,multiply(multiply(X1,X1),X0)),
inference(forward_demodulation,[status(thm)],[f7,f54]) ).
fof(f74,plain,
! [X0,X1] : X0 = multiply(X1,multiply(X1,multiply(X1,X0))),
inference(forward_demodulation,[status(thm)],[f9,f73]) ).
fof(f77,plain,
! [X0] : commutator(inverse(X0),X0) = identity,
inference(backward_demodulation,[status(thm)],[f68,f36]) ).
fof(f84,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f8,f68]) ).
fof(f169,plain,
! [X0] : identity = multiply(X0,multiply(inverse(X0),multiply(X0,inverse(X0)))),
inference(paramodulation,[status(thm)],[f68,f62]) ).
fof(f203,plain,
! [X0] : identity = multiply(X0,inverse(X0)),
inference(forward_demodulation,[status(thm)],[f68,f169]) ).
fof(f334,plain,
! [X0,X1] : identity = multiply(X0,multiply(X1,inverse(multiply(X0,X1)))),
inference(paramodulation,[status(thm)],[f9,f203]) ).
fof(f343,plain,
! [X0] : inverse(X0) = multiply(inverse(X0),identity),
inference(paramodulation,[status(thm)],[f203,f68]) ).
fof(f344,plain,
! [X0,X1] : multiply(identity,X0) = multiply(X1,multiply(inverse(X1),X0)),
inference(paramodulation,[status(thm)],[f203,f9]) ).
fof(f350,plain,
! [X0,X1] : X0 = multiply(X1,multiply(inverse(X1),X0)),
inference(forward_demodulation,[status(thm)],[f7,f344]) ).
fof(f365,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(backward_demodulation,[status(thm)],[f343,f84]) ).
fof(f380,plain,
! [X0] : inverse(inverse(X0)) = multiply(X0,identity),
inference(paramodulation,[status(thm)],[f365,f343]) ).
fof(f383,plain,
! [X0] : commutator(X0,inverse(X0)) = identity,
inference(paramodulation,[status(thm)],[f365,f77]) ).
fof(f388,plain,
! [X0] : X0 = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f365,f380]) ).
fof(f426,plain,
! [X0,X1] : multiply(commutator(X0,X1),X1) = multiply(X0,multiply(X1,multiply(inverse(X0),identity))),
inference(paramodulation,[status(thm)],[f8,f72]) ).
fof(f466,plain,
! [X0,X1] : multiply(commutator(X0,X1),X1) = multiply(X0,multiply(X1,inverse(X0))),
inference(forward_demodulation,[status(thm)],[f388,f426]) ).
fof(f514,plain,
! [X0] : inverse(X0) = multiply(X0,multiply(X0,identity)),
inference(paramodulation,[status(thm)],[f203,f74]) ).
fof(f544,plain,
! [X0] : inverse(X0) = multiply(X0,X0),
inference(forward_demodulation,[status(thm)],[f388,f514]) ).
fof(f701,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = multiply(X0,multiply(X1,multiply(X0,X1))),
inference(paramodulation,[status(thm)],[f9,f544]) ).
fof(f1011,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X1,X0))) = multiply(inverse(X1),identity),
inference(paramodulation,[status(thm)],[f334,f68]) ).
fof(f1082,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X1,X0))) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f388,f1011]) ).
fof(f1171,plain,
! [X0,X1] : multiply(inverse(multiply(X0,X1)),inverse(inverse(X0))) = inverse(X1),
inference(paramodulation,[status(thm)],[f1082,f1082]) ).
fof(f1183,plain,
! [X0,X1] : commutator(X0,multiply(X1,inverse(X0))) = multiply(X0,multiply(X1,multiply(inverse(X0),inverse(X1)))),
inference(paramodulation,[status(thm)],[f1082,f58]) ).
fof(f1185,plain,
! [X0,X1] : inverse(multiply(X0,inverse(X1))) = multiply(X1,inverse(X0)),
inference(paramodulation,[status(thm)],[f1082,f350]) ).
fof(f1192,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = multiply(inverse(X1),inverse(X0)),
inference(paramodulation,[status(thm)],[f1082,f68]) ).
fof(f1200,plain,
! [X0,X1] : multiply(inverse(multiply(X0,X1)),X0) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f365,f1171]) ).
fof(f1228,plain,
! [X0,X1] : commutator(X0,multiply(X1,inverse(X0))) = commutator(X0,X1),
inference(forward_demodulation,[status(thm)],[f10,f1183]) ).
fof(f1310,plain,
! [X0,X1] : commutator(inverse(X0),multiply(X1,X0)) = commutator(inverse(X0),X1),
inference(paramodulation,[status(thm)],[f365,f1228]) ).
fof(f1502,plain,
! [X0,X1] : commutator(multiply(X0,inverse(X1)),multiply(X1,inverse(X0))) = identity,
inference(paramodulation,[status(thm)],[f1185,f383]) ).
fof(f1554,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)],[f1192,f58]) ).
fof(f1555,plain,
! [X0,X1] : commutator(X0,X1) = multiply(X0,multiply(X1,inverse(multiply(X1,X0)))),
inference(backward_demodulation,[status(thm)],[f1192,f10]) ).
fof(f1585,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)],[f9,f1554]) ).
fof(f1650,plain,
! [X0,X1] : commutator(multiply(X0,X1),inverse(X0)) = multiply(multiply(X0,X1),multiply(inverse(X0),inverse(X1))),
inference(paramodulation,[status(thm)],[f68,f1555]) ).
fof(f1657,plain,
! [X0,X1] : commutator(multiply(X0,inverse(multiply(X0,X1))),X1) = multiply(multiply(X0,inverse(multiply(X0,X1))),multiply(X1,inverse(commutator(X1,X0)))),
inference(paramodulation,[status(thm)],[f1555,f1555]) ).
fof(f1701,plain,
! [X0,X1] : commutator(multiply(X0,X1),inverse(X0)) = multiply(X0,multiply(X1,multiply(inverse(X0),inverse(X1)))),
inference(forward_demodulation,[status(thm)],[f9,f1650]) ).
fof(f1702,plain,
! [X0,X1] : commutator(multiply(X0,X1),inverse(X0)) = multiply(X0,multiply(X1,inverse(multiply(X1,X0)))),
inference(forward_demodulation,[status(thm)],[f1192,f1701]) ).
fof(f1703,plain,
! [X0,X1] : commutator(multiply(X0,X1),inverse(X0)) = commutator(X0,X1),
inference(forward_demodulation,[status(thm)],[f1555,f1702]) ).
fof(f1714,plain,
! [X0,X1] : commutator(multiply(X0,inverse(multiply(X0,X1))),X1) = multiply(X0,multiply(inverse(multiply(X0,X1)),multiply(X1,inverse(commutator(X1,X0))))),
inference(forward_demodulation,[status(thm)],[f9,f1657]) ).
fof(f1959,plain,
! [X0,X1] : commutator(X0,inverse(inverse(X1))) = commutator(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f68,f1703]) ).
fof(f1978,plain,
! [X0,X1] : commutator(X0,X1) = commutator(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f365,f1959]) ).
fof(f2051,plain,
! [X0,X1] : commutator(inverse(inverse(multiply(X0,X1))),inverse(X0)) = commutator(inverse(inverse(multiply(X0,X1))),X1),
inference(paramodulation,[status(thm)],[f1082,f1310]) ).
fof(f2071,plain,
! [X0,X1] : commutator(multiply(X0,X1),inverse(X0)) = commutator(inverse(inverse(multiply(X0,X1))),X1),
inference(forward_demodulation,[status(thm)],[f365,f2051]) ).
fof(f2072,plain,
! [X0,X1] : commutator(X0,X1) = commutator(inverse(inverse(multiply(X0,X1))),X1),
inference(forward_demodulation,[status(thm)],[f1703,f2071]) ).
fof(f2073,plain,
! [X0,X1] : commutator(X0,X1) = commutator(multiply(X0,X1),X1),
inference(forward_demodulation,[status(thm)],[f365,f2072]) ).
fof(f2088,plain,
! [X0,X1] : commutator(inverse(multiply(X0,X1)),X0) = commutator(inverse(X1),X0),
inference(paramodulation,[status(thm)],[f1200,f2073]) ).
fof(f2489,plain,
! [X0,X1] : commutator(multiply(X0,inverse(X1)),X1) = commutator(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f1185,f2088]) ).
fof(f2508,plain,
! [X0,X1] : commutator(multiply(X0,inverse(X1)),X1) = commutator(X0,X1),
inference(forward_demodulation,[status(thm)],[f365,f2489]) ).
fof(f3155,plain,
! [X0,X1] : multiply(commutator(X0,X1),multiply(X1,X0)) = multiply(inverse(X1),multiply(multiply(X1,X0),inverse(inverse(X1)))),
inference(paramodulation,[status(thm)],[f1978,f466]) ).
fof(f3212,plain,
! [X0,X1] : commutator(inverse(X0),multiply(X0,X1)) = multiply(inverse(X0),multiply(X0,multiply(X1,inverse(multiply(commutator(X0,X1),X1))))),
inference(paramodulation,[status(thm)],[f466,f1585]) ).
fof(f3225,plain,
! [X0,X1] : commutator(multiply(X0,inverse(X1)),X1) = commutator(inverse(X1),multiply(commutator(X1,X0),X0)),
inference(paramodulation,[status(thm)],[f466,f1978]) ).
fof(f3241,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)],[f9,f3155]) ).
fof(f3242,plain,
! [X0,X1] : multiply(commutator(X0,X1),multiply(X1,X0)) = multiply(X0,inverse(inverse(X1))),
inference(forward_demodulation,[status(thm)],[f68,f3241]) ).
fof(f3243,plain,
! [X0,X1] : multiply(commutator(X0,X1),multiply(X1,X0)) = multiply(X0,X1),
inference(forward_demodulation,[status(thm)],[f365,f3242]) ).
fof(f3300,plain,
! [X0,X1] : commutator(X0,X1) = multiply(inverse(X1),multiply(X1,multiply(X0,inverse(multiply(commutator(X1,X0),X0))))),
inference(forward_demodulation,[status(thm)],[f1978,f3212]) ).
fof(f3301,plain,
! [X0,X1] : commutator(X0,X1) = multiply(X0,inverse(multiply(commutator(X1,X0),X0))),
inference(forward_demodulation,[status(thm)],[f68,f3300]) ).
fof(f3302,plain,
! [X0,X1] : commutator(X0,X1) = inverse(commutator(X1,X0)),
inference(forward_demodulation,[status(thm)],[f1082,f3301]) ).
fof(f3325,plain,
! [X0,X1] : commutator(X0,X1) = commutator(inverse(X1),multiply(commutator(X1,X0),X0)),
inference(forward_demodulation,[status(thm)],[f2508,f3225]) ).
fof(f3353,plain,
commutator(b,a) = inverse(sF1_fnc),
inference(paramodulation,[status(thm)],[f13,f3302]) ).
fof(f3406,plain,
! [X0,X1] : commutator(multiply(X0,inverse(multiply(X0,X1))),X1) = multiply(X0,multiply(inverse(multiply(X0,X1)),multiply(X1,commutator(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f3302,f1714]) ).
fof(f4089,plain,
multiply(sF1_fnc,multiply(b,a)) = multiply(a,b),
inference(paramodulation,[status(thm)],[f13,f3243]) ).
fof(f4552,plain,
! [X0,X1] : multiply(inverse(inverse(multiply(X0,X1))),X0) = inverse(multiply(X1,multiply(X0,X1))),
inference(paramodulation,[status(thm)],[f701,f1200]) ).
fof(f4736,plain,
! [X0,X1] : multiply(multiply(X0,X1),X0) = inverse(multiply(X1,multiply(X0,X1))),
inference(forward_demodulation,[status(thm)],[f365,f4552]) ).
fof(f4737,plain,
! [X0,X1] : multiply(X0,multiply(X1,X0)) = inverse(multiply(X1,multiply(X0,X1))),
inference(forward_demodulation,[status(thm)],[f9,f4736]) ).
fof(f6713,plain,
commutator(b,a) = commutator(inverse(a),multiply(sF1_fnc,b)),
inference(paramodulation,[status(thm)],[f13,f3325]) ).
fof(f6780,plain,
inverse(sF1_fnc) = commutator(inverse(a),multiply(sF1_fnc,b)),
inference(forward_demodulation,[status(thm)],[f3353,f6713]) ).
fof(f7872,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)],[f4737,f4737]) ).
fof(f8241,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)],[f9,f7872]) ).
fof(f8242,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)],[f544,f8241]) ).
fof(f8243,plain,
! [X0,X1] : multiply(X0,multiply(X1,inverse(X0))) = multiply(multiply(X1,multiply(X0,X1)),inverse(multiply(X1,X0))),
inference(forward_demodulation,[status(thm)],[f1185,f8242]) ).
fof(f8244,plain,
! [X0,X1] : multiply(X0,multiply(X1,inverse(X0))) = multiply(X1,multiply(multiply(X0,X1),inverse(multiply(X1,X0)))),
inference(forward_demodulation,[status(thm)],[f9,f8243]) ).
fof(f8245,plain,
! [X0,X1] : multiply(X0,multiply(X1,inverse(X0))) = multiply(X1,multiply(X0,multiply(X1,inverse(multiply(X1,X0))))),
inference(forward_demodulation,[status(thm)],[f9,f8244]) ).
fof(f8246,plain,
! [X0,X1] : multiply(X0,multiply(X1,inverse(X0))) = multiply(X1,commutator(X0,X1)),
inference(forward_demodulation,[status(thm)],[f1555,f8245]) ).
fof(f8476,plain,
multiply(inverse(a),multiply(multiply(sF1_fnc,b),inverse(inverse(a)))) = multiply(multiply(sF1_fnc,b),inverse(sF1_fnc)),
inference(paramodulation,[status(thm)],[f6780,f8246]) ).
fof(f8607,plain,
multiply(inverse(a),multiply(sF1_fnc,multiply(b,inverse(inverse(a))))) = multiply(multiply(sF1_fnc,b),inverse(sF1_fnc)),
inference(forward_demodulation,[status(thm)],[f9,f8476]) ).
fof(f8608,plain,
multiply(inverse(a),multiply(sF1_fnc,multiply(b,a))) = multiply(multiply(sF1_fnc,b),inverse(sF1_fnc)),
inference(forward_demodulation,[status(thm)],[f365,f8607]) ).
fof(f8609,plain,
multiply(inverse(a),multiply(a,b)) = multiply(multiply(sF1_fnc,b),inverse(sF1_fnc)),
inference(forward_demodulation,[status(thm)],[f4089,f8608]) ).
fof(f8610,plain,
b = multiply(multiply(sF1_fnc,b),inverse(sF1_fnc)),
inference(forward_demodulation,[status(thm)],[f68,f8609]) ).
fof(f8611,plain,
b = multiply(sF1_fnc,multiply(b,inverse(sF1_fnc))),
inference(forward_demodulation,[status(thm)],[f9,f8610]) ).
fof(f10479,plain,
commutator(multiply(sF1_fnc,inverse(multiply(sF1_fnc,multiply(b,inverse(sF1_fnc))))),multiply(b,inverse(sF1_fnc))) = multiply(sF1_fnc,multiply(inverse(b),multiply(multiply(b,inverse(sF1_fnc)),commutator(sF1_fnc,multiply(b,inverse(sF1_fnc)))))),
inference(paramodulation,[status(thm)],[f8611,f3406]) ).
fof(f10540,plain,
commutator(multiply(sF1_fnc,inverse(b)),multiply(b,inverse(sF1_fnc))) = multiply(sF1_fnc,multiply(inverse(b),multiply(multiply(b,inverse(sF1_fnc)),commutator(sF1_fnc,multiply(b,inverse(sF1_fnc)))))),
inference(forward_demodulation,[status(thm)],[f8611,f10479]) ).
fof(f10541,plain,
identity = multiply(sF1_fnc,multiply(inverse(b),multiply(multiply(b,inverse(sF1_fnc)),commutator(sF1_fnc,multiply(b,inverse(sF1_fnc)))))),
inference(forward_demodulation,[status(thm)],[f1502,f10540]) ).
fof(f10542,plain,
identity = multiply(sF1_fnc,multiply(inverse(b),multiply(b,multiply(inverse(sF1_fnc),commutator(sF1_fnc,multiply(b,inverse(sF1_fnc))))))),
inference(forward_demodulation,[status(thm)],[f9,f10541]) ).
fof(f10543,plain,
identity = multiply(sF1_fnc,multiply(inverse(sF1_fnc),commutator(sF1_fnc,multiply(b,inverse(sF1_fnc))))),
inference(forward_demodulation,[status(thm)],[f68,f10542]) ).
fof(f10544,plain,
identity = commutator(sF1_fnc,multiply(b,inverse(sF1_fnc))),
inference(forward_demodulation,[status(thm)],[f350,f10543]) ).
fof(f10545,plain,
identity = commutator(sF1_fnc,b),
inference(forward_demodulation,[status(thm)],[f1228,f10544]) ).
fof(f10546,plain,
identity = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f14,f10545]) ).
fof(f10547,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f10546,f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP002-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.55 % Computer : n002.cluster.edu
% 0.09/0.55 % Model : x86_64 x86_64
% 0.09/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.55 % Memory : 8046.5625MB
% 0.09/0.55 % OS : Linux 6.8.0-71-generic
% 0.09/0.55 % CPULimit : 300
% 0.09/0.55 % WCLimit : 300
% 0.09/0.55 % DateTime : Sun Sep 20 19:55:47 UTC 2026
% 0.09/0.55 % CPUTime :
% 0.09/0.56 % Drodi V4.1.1
% 0.13/0.62 % Refutation found
% 0.13/0.62 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.92/1.84 % Elapsed time: 1.070752 seconds
% 3.92/1.84 % CPU time: 0.487414 seconds
% 3.92/1.84 % Total memory used: 18.718 MB
% 3.92/1.84 % Net memory used: 18.085 MB
%------------------------------------------------------------------------------